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Cathodic Reduction of Acetophenone in Acidic Methanol Electrode Kinetic Study of a Novel Vicinal Diether Synthesis BY MARAJ UD DIN BHATTI AND OLIVER R. BROWN * Electrochemistry Research Laboratories, Department of Physical Chemistry, The University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU Received 10th April, 1974 The polarisation curve for the reduction of acetophenone in acidic methanol shows a prewave and a mainwave; the total wave height is diffusion controlled, corresponding to a reaction involving one electron per molecule. The prewave is kinetically controlled, except of course when it contributes a large fraction of the total wave. The products formed at potentials on the shoulder of the prewave are the acetophenone pinacol dimethyl diethers. The mechanism is analogous to that which operates in acetophenone pinacol formation, the reaction which predominates in aqueous media.In the presence of acid, methanol and acetophenone are shown to form the dimethyl ketal ; a value for the equilibrium constant is determined. An earlier paper presented an electrode kinetic study of the cathodic hydro- dimerisation of acetophenone, carried out in acidic aqueous-methanol solution. The rate-determining step in pinacol formation was shown to be an irreversible dimerisation of free ketyl radicals following a reversible electron and proton transfer. However, a previous study conducted in " anhydrous " methanol containing H2S04 reported for acetophenone reduction a Tafel slope of approximately 4.6 RT/F, a value which is usually taken to indicate rate control by the first charge transfer step.A somewhat perfunctory repetition of that work lent support to that result. The present study was undertaken to examine more closely the " anhydrous " methanolic system. HCl has been employed as an alternative to H2S04 as the electrolyte. The water content of the solvent is described in the experimental section and that of the solutions in the discussion section; in general it was less than 0.2 % by volume. EXPERIMENTAL All kinetic work was performed in B.D.H. AristaR methanol, solutions being made up in a dry-bag filled with a nitrogen atmosphere. B.D.H. claim a maximum water content of 0.1 % for this solvent. Solutions of HCI in methanol were prepared simply by the uptake of gas generated by the action of B.D.H. AnalaR HzSO4 upon sodium chloride.AnalaR H2S04 was also used to make up the sulphuric acid solutions. Acetophenone (B.D.H.) was purified by distillation through a Vigreux condenser ; the first and final quarters of the distillate were discarded. Anhydrous lithium chloride was a B.D.H. product. All cells were divided by glass sinters. Counter electrodes in preliminary work were of platinum but this resulted in eventual deposition of the noble metal on the cathode when anhydrous methanolic HCI was the electrolyte ; subsequently carbon counter electrodes were adopted. Reference electrodes were separated from the Luggin capillary by a glass frit inserted between two closed taps, all in series; the tap nearer to the reference electrode contained the liquid junction.The high electrical resistance of the taps was by-passed by a.c. signals through a 1 pF capacitance connected between the reference electrode lead and a platinum wire sealed into the Luggin capillary. The Hg/Hg2C12/satd. KCI aq. reference electrode (s.c.e.) was used with HCI catholytes and Hg/Hg2S04/H2S04 aq. (1 mol dm-3) was used with H2S04 catholytes. All potentials are quoted relative to these electrodes. Solid rotating disc electrodes (r.d.e.) of lead, amalgamated gold and pyrolytic graphite 106M. D. BHATTI AND 0. R. BROWN 107 were prepared as previously described.l Most of the kinetic work, however, employed liquid mercury cathodes. Lifetimes of these dropping mercury electrodes (d.m.e.) were imposed by means of a striker operating on the capillary.Currents with values far below the mass transfer limited currents for acetophenone were obtained as the instantaneous currents at the end of the drop life (3.0 s or 5.0 s). These were recorded at 1 mV s-' on a fast-response X- Y plotter (Bryans 26000). Higher currents corresponding to more severe cathodic polarisations were obtained in the absence of mass transfer control by means of the potential step relaxation method. The drop striker initiated the potential programme which consisted of a 3.0s delay at the base potential, where no reaction occurred, followed by 32 ms at the cathodic polarisation potential before the return to the base potential. During the polarisation period, currents were recorded in a digital store (Hitek Instruments signal averager AA1) and subsequently plotted on the X- Y recorder.Acetophenone concentrations were varied by means of additions from precision microsyringes. The resistance within the capillary was directly measured whereas the total ohmic resistance (at 3.0 s) was obtained from the limiting slope of the i against Vrelation at extreme cathodic potentials. Experimental points were corrected by an appropriate voltage shift in a positive direction. The ohmic error at 5.0 s was easily derived, assuming the drop to be spherical. The Luggin capillary was placed approximately 0.4 cm from the drop. Electrode areas were easily evaluated from a measurement of the mercury flow rate. Results presented are those after correction. Mercury pool cathodes and AnalaR methanol were employed in preparative electrolyses.All kinetic experiments were performed at 22f 1°C and preparative electrolyses were carried out at 30+ 5°C. A Hewlett-Packard 185 Analyser was used for elemental analysis. N.m.r. spectra were run in deutrochloroform with tetramethylsilane internal standard on a Bruker- Spectrospin instrument at ambient temperature. Mass spectra were taken on a high resolution MS 9 instrument. Ultra-violet absorption measurements were carried out using 1 .O cm cells and a Hitachi- Perkin Elmer 124 instrument. RESULTS On lead, pyrolytic graphite or mercury-coated r.d.e. or at the d.m.e., aceto- phenone in 1 mol dm-3 HCl solution in methanol gave two waves. The total wave height varied linearly with the acetophenone concentration and with m* (cu is the r.d.e.rotation velocity) or h* (when a d.m.e. was used without the striker, h being the mercury column height). The first wave height was sensitive to traces of water in the electrolyte, especially when dilute solutions of acetophenone were used ; addition of traces of water caused a fall in the first wave. This wave height was independent of (I) or h (when no striker was used) except when the solutions were dilute and almost completely anhydrous ; then the prewave almost reached the total wave height, particularly at low (I) values. Polarisation data were essentially independent of the electrode material with the exception that the prewave on lead was distorted by the anodic oxidation of the metal. Fig. 1 shows results obtained at the d.m.e. in nominally anhydrous methanol.There is no indication of the high values of the Tafel slopes previously reported. It can be seen that the currents at the foot of the prewave give linear Tafel plots with slopes 40f 1 mV and a reaction order of approximately 1.5 with respect to aceto- phenone. Although the prewave does not give a perfect plateau on account of the commencement of the main wave, it is clear that currents in the region of the point of inflexion have an order unity. Accurate kinetic analysis of the main wave was precluded by the large value of the ohmic overpotential at the relatively high current densities involved. However, the limiting currents of the total wave essentially were the same as those obtained in aqueous-methanol solutions and can be considered to indicate a 1 F per mole process.108 CATHODIC REDUCTION OF ACETOPHENONE FIG.1 dm-3) - EJV .-Cathodic polarisation data in nominally anhydrous methanol containing HCI (1 .O mol and acetophenone (concentrations shown on the figure in mol dm-3). 0, instantaneous polarographic currents ; x , diffusion-relaxed data. N b 6 -c + 0.6 0.7 0.8 0.9 - E/V FIG 2.-The effect of progressive additions of water (amounts shown as parts per thousand by volume) on the polarisation data for the prewave given by a 0.03 mol dm-3 solution of acetophenone in an- hydrous methanol (1.0 mol dm-3 in HCl) at a mercury cathode.M. D . BHATTI AND 0. R. BROWN 109 The effect on the prewave of adding water to a 0.03 mol dm-3 acetophenone solution in nominally anhydrous methanol (1.0 mol dm-3 in HCl) is illustrated in fig.2. The addition of 1 % (by volume) water decreased prewave currents by an order of magnitude. The same phenomenon was observed at all acetophenone concentrations ; currents over the entire prewave fell markedly whereas the main wave was relatively unaffected. The net result was that the prewave fell in height and simultaneously moved towards more negative potentials until both waves merged into one distorted wave. I. I 1.2 1.3 I :L - E/V FIG. 3.-Cathodic polarisation data in 80 mole % methanol/20 % water containing H2S04 (1 .O mol dm-3) and acetophenone (concentrations shown in mol dm-3). 0, instantaneous polarographic currents ; 0, diffusion-relaxed data. Whereas the polarisation data obtained during any one experimental run were highly reproducible, differences in the intrinsic water contents of the solutions made reproducibility of the prewave polarisation data poor from one run to another.Thus measurements of the reaction order with respect to HC1 were subject to con- siderable error. Currents obtained using a nominally anhydrous methanol solution (0.1 mol dm-3 HCl and 0.9 mol dm-3 LiCl) were always considerably lower, at a given potential and acetophenone concentration, than those obtained with 1 .O mol dm-3 HCl in the nominally similar solvent but the difference factor varied widely. Polarisation experiments using the d.m.e. were repeated with 1.0 mol dm-3 methanolic sulphuric acid, and similar results were obtained. In fig. 3 are presented polarisation curves of acetophenone in 1.0 rnol dm-3 H2S04 solution prepared in the mixed solvent 80 mole % methanol 20 % water.In order to examine the nature of acidified methanol solutions of acetophenone, the main ultraviolet absorption peak of acetophenone (7c - z* transition, A = 242 nm, c - lo3 mol-' m2) was measured for mol dm-3 acetophenone solutions in110 CATHODIC REDUCTION OF ACETOPHENONE methanol, with and without HCl and water. The acidified nominally anhydrous solutions gave considerably smaller absorptions ( A ) than corresponding solutions without acid (Ao). The concentration of HCl in the range investigated (0.01 to 1.0 mol dm-3) appeared to be unimportant. In some cases the presence of HCl more than halved the acetophenone absorption but, as with the electrochemical kinetic behaviour of the prewave, traces of water had a considerable effect and merely 2 % (by volume) water caused the peak to return essentially to the height observed in unacidified “anhydrous” methanol.Fig. 4 shows a plot of relative decrease in absorbance A/(& - A ) against the volume fraction of added water. Finally, preparative electrolyses have been carried out on a solution of aceto- phenone (1.0 mol drn-,) in “ anhydrous ” methanol containing HCl (1.0 mol dm-3) at an electrode potential -0.66 V (against s.c.e.) corresponding to the shoulder of the pre-wave. Within an hour of the commencement of electrolysis white crystals X began to separate out on the cathode. After electrolysis the crystals were collected and recrystallised from methanol. The remaining catholyte was neutralised by addition of solid sodium carbonate and the solution filtered.The residue was dissolved in water and extracted with diethyl ether. The ether layer was added to the filtrate and the total volume reduced using a rotary evaporator at 100°C to obtain a further crop of crystals. The crystalline product X was examined by proton resonance spectroscopy, mass spectrometry and CH analysis. The n.m.r. spectrum consisted of a singlet at 1.46 p.p.m., another at 3.05 and an aromatic peak at 7.27 p.p.m. ; these peak areas were in the approximate ratio 1 : 1 :2. The mass spectrum at 80°C showed a small peak at 270 mass number, with progressively larger contributions at 255 and 249. However, by far the largest peak was at 135. The elemental analysis was C 79.5 %, H 8.14 %, 0 (by difference) 12.36 %.A cryoscopic determination of molecular weight was also carried out using benzene as solvent. A value of 250+ 10 % was obtained. The melting point (ca. 160°C) of the product was not sharp indicating a mixture of materials. DISCUSSION The crystalline product formed at potentials corresponding to the prewave is almost certainly a mixture of the stereoisomeric diethers, each with the formula CH3 CH3 I I I I OCH, OCH, C6Hj-C-- C C6H5. The n.m.r. spectrum can be interpreted as due to six methyl protons at 6 = 1.46, six methoxy protons at 3.05 and two phenyl groups at 7.27. The C, H, 0 figures (79.5, 8.14, 12.36 %) compare with those calculated (80.0, 8.15, 11.85 % respectively). The mass spectrum was clearly dominated by fragments resulting from a symmetrical dissociation although the parent ion (270) and fragments due to loss of methyl or methoxy groups were in evidence.The n.m.r. result and the cryoscopic measurement indicate the dimers in preference to the monomeric ethers C6H5CH(OCH3)CH3. Since the main wave was relatively unaffected by the presence of water it is reasonable to suppose that it corresponds to the formation of acetophenone pinacols.’ The prewave observed for acetophenone in acidified anhydrous methanol possesses all of the characteristics of a kinetic wave, i.e. the limiting current is determined by the rate of a homogeneous chemical reaction preceding the charge transfer step.M. D. BHATTI AND 0. R. BROWN 1 1 1 The electrochemical kinetic data obtained for the foot of the prewave indicate that the reaction mechanism is of the type already reported for the hydromerisation of acetophenone.A Tafel slope of 1.5 RT/Fand a reaction order of 1.5 are characteristic of a mechanism in which rate control is by an irreversible homogeneous bimolecular step involving species produced in an initial reversible one electron electrochemical event. However, in the present system the reaction product is not the pinacol but instead the corresponding diether. Arguing by analogy with the pinacolisation reaction it is reasonable to consider that the present reaction is a reduction of the x 2 Phc(0Me)Me + e- + Phc(0Me)Me -+ \ Me OMe / It is necessary therefore to explain the occurrence of the phenyl methoxy methyl carbonium ion in this system.It is well known that acetals can be prepared by the reaction between aldehydes and alcohols in the presence of dry HCl. Ketals too, although not usually isolated from such reactions, have been shown to form in equilibria involving the ketone and alcohol under anhydrous conditions. As acetal formations are acid-catalysed one can propose the usual type of mechanism : OH Me + H+ + R1R2C(OMe)OH MeOH / R1R2CO+H+ + (R1R2COH)+ + R1R2C - MeOH Hf + R'R2C(OMe)OH + R1R2C(OMe)OH2 - H+ \ / hemi ke t a1 0' H + (R1R2COMe)+ + \ - H20 MeOH - MeOH H2O OMe / R ~ R ~ C - H + H+ + R1R2C(OMe)2. \+/ ketal 0 Me \ SCHEME 1 The ketal of acetophenone is known; it has been prepared from acetophenone in methanol by the action of either formimido methyl ether or methyl orthoformate.6 There do not appear to have been any studies of the equilibrium between aceto- phenone and methanol although U.V.absorption has been used often to study ketone/ ketal equilibria.'112 CATHODIC REDUCTION OF ACETOPHENONE The linear plot of fig, 4 is consistent with the assumptions that (a) the equilibrium is set up rapidly in acid solution, (b) the amounts of hemiketal and other intermediates in scheme 1 are negligible, and (c) the ketal has an insignificant extinction coefficient at 242 nm. From the slope we deduce that the equilibrium constant at 22°C is PhCOCH3 + 2CH3OH + PhC(OCH3)2CH3 + H20 K = c ~ ~ ~ ~ ~ c ~ ~ ~ / c ~ = 3 x mol dm-3 and that the initial water content of the solution was slightly in excess of 0.1 volume % (the methanol manufacturer’s specified limit).-I 0 I 2 3 1, 5 6 7 6 lo3 x vol H20/vol solution FIG. 4.-Variation of the relative decrease in absorbance of acetophenone in the presence of acid with the concentration of added water. From the electrode kinetic results it is not possible to conclude whether the chemical process which limits the currents on the first wave is the formation of phenyl methoxy methyl carbonium ion from the ketal, or from the acetophenone or by a mixture of both routes (scheme 1). The effect of added water on the kinetics of reductions in the Tafel region is readily understood in terms of the pre-equilibrium + PhCOCH3 + CH30H +HI- + PhC(OCH3)CH3 + H20. It might be expected that the reaction order with respect to added water should be - 1.5 according to the theory How- ever, the solvent contains an unknown residual trace of water.Thus if the data of fig. 2 are plotted as log c~~~ against E at constant current i a linear relation is not obtained. However, if we guess values of the total residual water c,,, and plot log ( C ~ ~ ~ + C ~ , , ) against E until a linear relation is obtained then the slope of the plot should equal 2.303 RT/F. This is found to apply in fig. 5 where the potentials corresponding to a current density of 17.7 pA cm-2 are plotted against log cHz0 and against log ( c ~ ~ ~ + c,) with cres corresponding to 0.2 vol % water. This value is almost double that obtained from the U.V. measurements (fig. 4) but the methanol had less opportunity to pick up extraneous water in those experiments. Deviations from of reactions of the type described by eqn (1).\ \ OCH341430H CH3 CH3 / PhC-CH3 0.6 0.65 0.7 0.75 - E/V FIG.5.-Analysis of the potential shift with water concentration for current density = 17.7pA ciir2 from the data in fig. 2. 0, zero initial water ; 0, 2 parts per thousand water by volume. \ / OCH3 CH3 Conway and Rudd unfortunately made their measurements at lower current densities where, as fig. 3 shows, the polarisation data are distorted by the prewave so that in the region of - 1180 mV the reaction order with respect to acetophenone is unity and the Tafel plots are in fact gentle curves with a mean slope of some 52 mV. Those workers believed the pinacol formation was quantitative in that system but in fact their kinetic measurements were made under conditions where it is now evident that one reaction gradually gave way to another.Each electrode reaction separately follows the kinetic scheme first discussed by Koutecky and Hanus but in the region of mixed kinetics such behaviour is not observed owing to the influence of the preceding chemical reaction which limits the first wave.114 CATHODIC REDUCTION OF ACETOPHENONE The current yield of 2,3-dimethoxy-2,3-diphenylbutane obtained from methanolic acetophenone (0.3 mol dm-3) containing HCl (1 .O mol dm-3) at - 0.68 V was 23 %. This unexpectedly low value is undoubtedly due to the fall in the current for this reaction owing to the water it produces, and the consequent relative increase in the pinacol formation current. Other products were found to include the pinacols and there were also other gas chromatographic peaks which were probably due to the mixed dimers (mono ethers).Further work is in progress to investigate the synthetic scope of this type of reaction. M. D. B. thanks the British Council for a studentship. M. P. J. Brennan and 0. R. Brown, J.C.S. Faruday I, 1973, 69, 132. E. J. Rudd and B. E. Conway, Trans. Faraday Soc., 1971,67,440. 0. R. Brown, Disc. Faraday Sac., 1968, 45, 126. 1964), p. 296. L. Claisen, Ber., 1898, 31, 1010. M. T. Bogart and P.P. Herrera, J. Amer. Chem. SOC., 1923,45, 238. ' 0. H. Wheeler, J. Amer. Chem. SOC., 1957, 79, 4191. a J. Koutecky and V. Hanus, Coll. Czech. Chem. Comm., 1955, 20, 124. 4B. J. Cram and J. S. Hammond, Organic Chemistry (McGraw-Hill, New York, 2nd edn., Cathodic Reduction of Acetophenone in Acidic Methanol Electrode Kinetic Study of a Novel Vicinal Diether Synthesis BY MARAJ UD DIN BHATTI AND OLIVER R.BROWN * Electrochemistry Research Laboratories, Department of Physical Chemistry, The University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU Received 10th April, 1974 The polarisation curve for the reduction of acetophenone in acidic methanol shows a prewave and a mainwave; the total wave height is diffusion controlled, corresponding to a reaction involving one electron per molecule. The prewave is kinetically controlled, except of course when it contributes a large fraction of the total wave. The products formed at potentials on the shoulder of the prewave are the acetophenone pinacol dimethyl diethers. The mechanism is analogous to that which operates in acetophenone pinacol formation, the reaction which predominates in aqueous media.In the presence of acid, methanol and acetophenone are shown to form the dimethyl ketal ; a value for the equilibrium constant is determined. An earlier paper presented an electrode kinetic study of the cathodic hydro- dimerisation of acetophenone, carried out in acidic aqueous-methanol solution. The rate-determining step in pinacol formation was shown to be an irreversible dimerisation of free ketyl radicals following a reversible electron and proton transfer. However, a previous study conducted in " anhydrous " methanol containing H2S04 reported for acetophenone reduction a Tafel slope of approximately 4.6 RT/F, a value which is usually taken to indicate rate control by the first charge transfer step.A somewhat perfunctory repetition of that work lent support to that result. The present study was undertaken to examine more closely the " anhydrous " methanolic system. HCl has been employed as an alternative to H2S04 as the electrolyte. The water content of the solvent is described in the experimental section and that of the solutions in the discussion section; in general it was less than 0.2 % by volume. EXPERIMENTAL All kinetic work was performed in B.D.H. AristaR methanol, solutions being made up in a dry-bag filled with a nitrogen atmosphere. B.D.H. claim a maximum water content of 0.1 % for this solvent. Solutions of HCI in methanol were prepared simply by the uptake of gas generated by the action of B.D.H.AnalaR HzSO4 upon sodium chloride. AnalaR H2S04 was also used to make up the sulphuric acid solutions. Acetophenone (B.D.H.) was purified by distillation through a Vigreux condenser ; the first and final quarters of the distillate were discarded. Anhydrous lithium chloride was a B.D.H. product. All cells were divided by glass sinters. Counter electrodes in preliminary work were of platinum but this resulted in eventual deposition of the noble metal on the cathode when anhydrous methanolic HCI was the electrolyte ; subsequently carbon counter electrodes were adopted. Reference electrodes were separated from the Luggin capillary by a glass frit inserted between two closed taps, all in series; the tap nearer to the reference electrode contained the liquid junction.The high electrical resistance of the taps was by-passed by a.c. signals through a 1 pF capacitance connected between the reference electrode lead and a platinum wire sealed into the Luggin capillary. The Hg/Hg2C12/satd. KCI aq. reference electrode (s.c.e.) was used with HCI catholytes and Hg/Hg2S04/H2S04 aq. (1 mol dm-3) was used with H2S04 catholytes. All potentials are quoted relative to these electrodes. Solid rotating disc electrodes (r.d.e.) of lead, amalgamated gold and pyrolytic graphite 106M. D. BHATTI AND 0. R. BROWN 107 were prepared as previously described.l Most of the kinetic work, however, employed liquid mercury cathodes. Lifetimes of these dropping mercury electrodes (d.m.e.) were imposed by means of a striker operating on the capillary.Currents with values far below the mass transfer limited currents for acetophenone were obtained as the instantaneous currents at the end of the drop life (3.0 s or 5.0 s). These were recorded at 1 mV s-' on a fast-response X- Y plotter (Bryans 26000). Higher currents corresponding to more severe cathodic polarisations were obtained in the absence of mass transfer control by means of the potential step relaxation method. The drop striker initiated the potential programme which consisted of a 3.0s delay at the base potential, where no reaction occurred, followed by 32 ms at the cathodic polarisation potential before the return to the base potential. During the polarisation period, currents were recorded in a digital store (Hitek Instruments signal averager AA1) and subsequently plotted on the X- Y recorder. Acetophenone concentrations were varied by means of additions from precision microsyringes.The resistance within the capillary was directly measured whereas the total ohmic resistance (at 3.0 s) was obtained from the limiting slope of the i against Vrelation at extreme cathodic potentials. Experimental points were corrected by an appropriate voltage shift in a positive direction. The ohmic error at 5.0 s was easily derived, assuming the drop to be spherical. The Luggin capillary was placed approximately 0.4 cm from the drop. Electrode areas were easily evaluated from a measurement of the mercury flow rate. Results presented are those after correction. Mercury pool cathodes and AnalaR methanol were employed in preparative electrolyses.All kinetic experiments were performed at 22f 1°C and preparative electrolyses were carried out at 30+ 5°C. A Hewlett-Packard 185 Analyser was used for elemental analysis. N.m.r. spectra were run in deutrochloroform with tetramethylsilane internal standard on a Bruker- Spectrospin instrument at ambient temperature. Mass spectra were taken on a high resolution MS 9 instrument. Ultra-violet absorption measurements were carried out using 1 .O cm cells and a Hitachi- Perkin Elmer 124 instrument. RESULTS On lead, pyrolytic graphite or mercury-coated r.d.e. or at the d.m.e., aceto- phenone in 1 mol dm-3 HCl solution in methanol gave two waves. The total wave height varied linearly with the acetophenone concentration and with m* (cu is the r.d.e.rotation velocity) or h* (when a d.m.e. was used without the striker, h being the mercury column height). The first wave height was sensitive to traces of water in the electrolyte, especially when dilute solutions of acetophenone were used ; addition of traces of water caused a fall in the first wave. This wave height was independent of (I) or h (when no striker was used) except when the solutions were dilute and almost completely anhydrous ; then the prewave almost reached the total wave height, particularly at low (I) values. Polarisation data were essentially independent of the electrode material with the exception that the prewave on lead was distorted by the anodic oxidation of the metal. Fig. 1 shows results obtained at the d.m.e. in nominally anhydrous methanol.There is no indication of the high values of the Tafel slopes previously reported. It can be seen that the currents at the foot of the prewave give linear Tafel plots with slopes 40f 1 mV and a reaction order of approximately 1.5 with respect to aceto- phenone. Although the prewave does not give a perfect plateau on account of the commencement of the main wave, it is clear that currents in the region of the point of inflexion have an order unity. Accurate kinetic analysis of the main wave was precluded by the large value of the ohmic overpotential at the relatively high current densities involved. However, the limiting currents of the total wave essentially were the same as those obtained in aqueous-methanol solutions and can be considered to indicate a 1 F per mole process.108 CATHODIC REDUCTION OF ACETOPHENONE FIG.1 dm-3) - EJV .-Cathodic polarisation data in nominally anhydrous methanol containing HCI (1 .O mol and acetophenone (concentrations shown on the figure in mol dm-3). 0, instantaneous polarographic currents ; x , diffusion-relaxed data. N b 6 -c + 0.6 0.7 0.8 0.9 - E/V FIG 2.-The effect of progressive additions of water (amounts shown as parts per thousand by volume) on the polarisation data for the prewave given by a 0.03 mol dm-3 solution of acetophenone in an- hydrous methanol (1.0 mol dm-3 in HCl) at a mercury cathode.M. D . BHATTI AND 0. R. BROWN 109 The effect on the prewave of adding water to a 0.03 mol dm-3 acetophenone solution in nominally anhydrous methanol (1.0 mol dm-3 in HCl) is illustrated in fig.2. The addition of 1 % (by volume) water decreased prewave currents by an order of magnitude. The same phenomenon was observed at all acetophenone concentrations ; currents over the entire prewave fell markedly whereas the main wave was relatively unaffected. The net result was that the prewave fell in height and simultaneously moved towards more negative potentials until both waves merged into one distorted wave. I. I 1.2 1.3 I :L - E/V FIG. 3.-Cathodic polarisation data in 80 mole % methanol/20 % water containing H2S04 (1 .O mol dm-3) and acetophenone (concentrations shown in mol dm-3). 0, instantaneous polarographic currents ; 0, diffusion-relaxed data. Whereas the polarisation data obtained during any one experimental run were highly reproducible, differences in the intrinsic water contents of the solutions made reproducibility of the prewave polarisation data poor from one run to another.Thus measurements of the reaction order with respect to HC1 were subject to con- siderable error. Currents obtained using a nominally anhydrous methanol solution (0.1 mol dm-3 HCl and 0.9 mol dm-3 LiCl) were always considerably lower, at a given potential and acetophenone concentration, than those obtained with 1 .O mol dm-3 HCl in the nominally similar solvent but the difference factor varied widely. Polarisation experiments using the d.m.e. were repeated with 1.0 mol dm-3 methanolic sulphuric acid, and similar results were obtained. In fig. 3 are presented polarisation curves of acetophenone in 1.0 rnol dm-3 H2S04 solution prepared in the mixed solvent 80 mole % methanol 20 % water.In order to examine the nature of acidified methanol solutions of acetophenone, the main ultraviolet absorption peak of acetophenone (7c - z* transition, A = 242 nm, c - lo3 mol-' m2) was measured for mol dm-3 acetophenone solutions in110 CATHODIC REDUCTION OF ACETOPHENONE methanol, with and without HCl and water. The acidified nominally anhydrous solutions gave considerably smaller absorptions ( A ) than corresponding solutions without acid (Ao). The concentration of HCl in the range investigated (0.01 to 1.0 mol dm-3) appeared to be unimportant. In some cases the presence of HCl more than halved the acetophenone absorption but, as with the electrochemical kinetic behaviour of the prewave, traces of water had a considerable effect and merely 2 % (by volume) water caused the peak to return essentially to the height observed in unacidified “anhydrous” methanol. Fig.4 shows a plot of relative decrease in absorbance A/(& - A ) against the volume fraction of added water. Finally, preparative electrolyses have been carried out on a solution of aceto- phenone (1.0 mol drn-,) in “ anhydrous ” methanol containing HCl (1.0 mol dm-3) at an electrode potential -0.66 V (against s.c.e.) corresponding to the shoulder of the pre-wave. Within an hour of the commencement of electrolysis white crystals X began to separate out on the cathode. After electrolysis the crystals were collected and recrystallised from methanol. The remaining catholyte was neutralised by addition of solid sodium carbonate and the solution filtered.The residue was dissolved in water and extracted with diethyl ether. The ether layer was added to the filtrate and the total volume reduced using a rotary evaporator at 100°C to obtain a further crop of crystals. The crystalline product X was examined by proton resonance spectroscopy, mass spectrometry and CH analysis. The n.m.r. spectrum consisted of a singlet at 1.46 p.p.m., another at 3.05 and an aromatic peak at 7.27 p.p.m. ; these peak areas were in the approximate ratio 1 : 1 :2. The mass spectrum at 80°C showed a small peak at 270 mass number, with progressively larger contributions at 255 and 249. However, by far the largest peak was at 135. The elemental analysis was C 79.5 %, H 8.14 %, 0 (by difference) 12.36 %.A cryoscopic determination of molecular weight was also carried out using benzene as solvent. A value of 250+ 10 % was obtained. The melting point (ca. 160°C) of the product was not sharp indicating a mixture of materials. DISCUSSION The crystalline product formed at potentials corresponding to the prewave is almost certainly a mixture of the stereoisomeric diethers, each with the formula CH3 CH3 I I I I OCH, OCH, C6Hj-C-- C C6H5. The n.m.r. spectrum can be interpreted as due to six methyl protons at 6 = 1.46, six methoxy protons at 3.05 and two phenyl groups at 7.27. The C, H, 0 figures (79.5, 8.14, 12.36 %) compare with those calculated (80.0, 8.15, 11.85 % respectively). The mass spectrum was clearly dominated by fragments resulting from a symmetrical dissociation although the parent ion (270) and fragments due to loss of methyl or methoxy groups were in evidence.The n.m.r. result and the cryoscopic measurement indicate the dimers in preference to the monomeric ethers C6H5CH(OCH3)CH3. Since the main wave was relatively unaffected by the presence of water it is reasonable to suppose that it corresponds to the formation of acetophenone pinacols.’ The prewave observed for acetophenone in acidified anhydrous methanol possesses all of the characteristics of a kinetic wave, i.e. the limiting current is determined by the rate of a homogeneous chemical reaction preceding the charge transfer step.M. D. BHATTI AND 0. R. BROWN 1 1 1 The electrochemical kinetic data obtained for the foot of the prewave indicate that the reaction mechanism is of the type already reported for the hydromerisation of acetophenone.A Tafel slope of 1.5 RT/Fand a reaction order of 1.5 are characteristic of a mechanism in which rate control is by an irreversible homogeneous bimolecular step involving species produced in an initial reversible one electron electrochemical event. However, in the present system the reaction product is not the pinacol but instead the corresponding diether. Arguing by analogy with the pinacolisation reaction it is reasonable to consider that the present reaction is a reduction of the x 2 Phc(0Me)Me + e- + Phc(0Me)Me -+ \ Me OMe / It is necessary therefore to explain the occurrence of the phenyl methoxy methyl carbonium ion in this system.It is well known that acetals can be prepared by the reaction between aldehydes and alcohols in the presence of dry HCl. Ketals too, although not usually isolated from such reactions, have been shown to form in equilibria involving the ketone and alcohol under anhydrous conditions. As acetal formations are acid-catalysed one can propose the usual type of mechanism : OH Me + H+ + R1R2C(OMe)OH MeOH / R1R2CO+H+ + (R1R2COH)+ + R1R2C - MeOH Hf + R'R2C(OMe)OH + R1R2C(OMe)OH2 - H+ \ / hemi ke t a1 0' H + (R1R2COMe)+ + \ - H20 MeOH - MeOH H2O OMe / R ~ R ~ C - H + H+ + R1R2C(OMe)2. \+/ ketal 0 Me \ SCHEME 1 The ketal of acetophenone is known; it has been prepared from acetophenone in methanol by the action of either formimido methyl ether or methyl orthoformate.6 There do not appear to have been any studies of the equilibrium between aceto- phenone and methanol although U.V.absorption has been used often to study ketone/ ketal equilibria.'112 CATHODIC REDUCTION OF ACETOPHENONE The linear plot of fig, 4 is consistent with the assumptions that (a) the equilibrium is set up rapidly in acid solution, (b) the amounts of hemiketal and other intermediates in scheme 1 are negligible, and (c) the ketal has an insignificant extinction coefficient at 242 nm. From the slope we deduce that the equilibrium constant at 22°C is PhCOCH3 + 2CH3OH + PhC(OCH3)2CH3 + H20 K = c ~ ~ ~ ~ ~ c ~ ~ ~ / c ~ = 3 x mol dm-3 and that the initial water content of the solution was slightly in excess of 0.1 volume % (the methanol manufacturer’s specified limit).-I 0 I 2 3 1, 5 6 7 6 lo3 x vol H20/vol solution FIG. 4.-Variation of the relative decrease in absorbance of acetophenone in the presence of acid with the concentration of added water. From the electrode kinetic results it is not possible to conclude whether the chemical process which limits the currents on the first wave is the formation of phenyl methoxy methyl carbonium ion from the ketal, or from the acetophenone or by a mixture of both routes (scheme 1). The effect of added water on the kinetics of reductions in the Tafel region is readily understood in terms of the pre-equilibrium + PhCOCH3 + CH30H +HI- + PhC(OCH3)CH3 + H20. It might be expected that the reaction order with respect to added water should be - 1.5 according to the theory How- ever, the solvent contains an unknown residual trace of water.Thus if the data of fig. 2 are plotted as log c~~~ against E at constant current i a linear relation is not obtained. However, if we guess values of the total residual water c,,, and plot log ( C ~ ~ ~ + C ~ , , ) against E until a linear relation is obtained then the slope of the plot should equal 2.303 RT/F. This is found to apply in fig. 5 where the potentials corresponding to a current density of 17.7 pA cm-2 are plotted against log cHz0 and against log ( c ~ ~ ~ + c,) with cres corresponding to 0.2 vol % water. This value is almost double that obtained from the U.V. measurements (fig. 4) but the methanol had less opportunity to pick up extraneous water in those experiments. Deviations from of reactions of the type described by eqn (1).\ \ OCH341430H CH3 CH3 / PhC-CH3 0.6 0.65 0.7 0.75 - E/V FIG.5.-Analysis of the potential shift with water concentration for current density = 17.7pA ciir2 from the data in fig. 2. 0, zero initial water ; 0, 2 parts per thousand water by volume. \ / OCH3 CH3 Conway and Rudd unfortunately made their measurements at lower current densities where, as fig. 3 shows, the polarisation data are distorted by the prewave so that in the region of - 1180 mV the reaction order with respect to acetophenone is unity and the Tafel plots are in fact gentle curves with a mean slope of some 52 mV. Those workers believed the pinacol formation was quantitative in that system but in fact their kinetic measurements were made under conditions where it is now evident that one reaction gradually gave way to another. Each electrode reaction separately follows the kinetic scheme first discussed by Koutecky and Hanus but in the region of mixed kinetics such behaviour is not observed owing to the influence of the preceding chemical reaction which limits the first wave.114 CATHODIC REDUCTION OF ACETOPHENONE The current yield of 2,3-dimethoxy-2,3-diphenylbutane obtained from methanolic acetophenone (0.3 mol dm-3) containing HCl (1 .O mol dm-3) at - 0.68 V was 23 %. This unexpectedly low value is undoubtedly due to the fall in the current for this reaction owing to the water it produces, and the consequent relative increase in the pinacol formation current. Other products were found to include the pinacols and there were also other gas chromatographic peaks which were probably due to the mixed dimers (mono ethers). Further work is in progress to investigate the synthetic scope of this type of reaction. M. D. B. thanks the British Council for a studentship. M. P. J. Brennan and 0. R. Brown, J.C.S. Faruday I, 1973, 69, 132. E. J. Rudd and B. E. Conway, Trans. Faraday Soc., 1971,67,440. 0. R. Brown, Disc. Faraday Sac., 1968, 45, 126. 1964), p. 296. L. Claisen, Ber., 1898, 31, 1010. M. T. Bogart and P.P. Herrera, J. Amer. Chem. SOC., 1923,45, 238. ' 0. H. Wheeler, J. Amer. Chem. SOC., 1957, 79, 4191. a J. Koutecky and V. Hanus, Coll. Czech. Chem. Comm., 1955, 20, 124. 4B. J. Cram and J. S. Hammond, Organic Chemistry (McGraw-Hill, New York, 2nd edn.,

ISSN:0300-9599    

DOI:10.1039/F19757100106

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Application of Time-dependent Rate Constant Theory to Reactions of Solvated Electrons Reaction Distances, Rate Constants and Diffusion Coefficients in Concentrated Aqueous Solutions BY GEORGE V. BUXTON," FRANK C. R. CATTELL? AND FREDERICK S. DAINTON~ Cookridge Hospital, Leeds LS16 6QB University of Leeds, Cookridge Radiation Research Centre, Received 20th May, 1974 The rates of reaction of e; with a number of solutes have been measured in the temperature range 190 - 260 K in concentrated aqueous solutions of LiCl and NaOH + KOH. The rate coefficients are observed to be time-dependent and fit the equations developed by Noyes. Using these equations we have obtained estimates of diffusion controlled rate constants, reaction distances and diffusion coefficients for each reaction. These suggest that e; reacts, and may also diffuse, by a tunnelling mechanism. The temperature dependences of the rate constants and diffusion coefficients are similar to those of other transport processes in glass forming solutions. For rapid bimolecular reactions in solution diffusive transport can be so slow that the average distance between potentially reactive molecules soon exceeds that pre- dicted for a random equilibrium distribution.The measured rate coefficient will decrease, therefore, from an initial value k , characteristic of the random distribution, to a steady state value k' given by eqn (1),l 47cnaD' 1 + 4naD'/k k' = where a is the reaction distance and D' is the sum of the diffusion coefficients of the two molecules. This eqn reduces to the familiar Smoluchowski eqn (2)2 k' = 47cuD' (2) when k 9 47caD'.Noyes efficient from its initial value k to its final value k' is given by eqn (3) has shown that the change with time of the rate co- 1 k k, = k' 1 +-, ex' erfc x [ 4xaD where k, is the rate coefficient at time t, and x = k( JD't)/k'a. For very short times when t 4 (a2/D')(k'/k)2 the observed rate coefficient approaches k. Typically, for diffusion controlled reactions of the hydrated electron at room temperature, Q - 0.5 nm and D' - 7 x lo-' cm2 s-l, implying that a time resolution better than 10-l' s is needed to explore this region. When t 9 (a2/D')(k'/k)2 eqn (3) reduces to (4) t present address : C.S.I.R.O., Division of Cloud Physics, P.O. Box 134, Epping, New South Wales $ present address : University Grants Committee, 14 Park Crescent, London W1N 4DH.Australia. 115116 TIME-DEPENDENT RATE CONSTANTS For typical diffusion controlled reactions of the hydrated electron * with values of CT and D’ given above and k + 4naD’, the observed rate coefficient is expected to be greater than k‘ by 1 % at s, 3 % at lo-’ s, 11 % at s and 34 % at 10-l’~. Through the pulse radiolysis technique it is possible to form essentially instan- taneously, a strongly absorbing reactive species (e;) in a solution containing randomly distributed solute molecules, and to measure its rate of reaction. For time-dependent changes in the rate coefficient to be conveniently observed on a timescale of tens of nanoseconds or longer, D’ must be reduced by several orders of magnitude.This is most satisfactorily achieved by the use of liquids which on cooling progressively become more viscous and eventually vitrefy, and several aqueous solutions fall into this category. Rate coefficients which have already been reported over a very wide temperature range for one such aqueous system are consistent with a variation of D’ with temperature, over at least eight orders of magnitude, given by where To = 135 K and B w 800 K. D’ = Dd exp[ - B/(T- To)] (5) The disappearance of solvated electrons, e;, by reaction with a solute, S, is given by eqn (6) and if k, is given by eqn (4) and [S] % [e;], the decrease in optical density, OD, with time due to e; is given by eqn (7) where ODo is the optical destity at t = 0. The variation of OD with time allows the evaluation of k’ and D’, and provided k % 4noD’, a can be calculated from In this paper we have applied the time dependent rate constant theory of Noyes to the reactions of e; with a number of solutes in 9.5 mol dm-3 LiCl and in 10 mol dm-3 OH- (5 mol dm-3 NaOH + 5 mol dm-3 KOH) over a wide temperature range and have obtained estimates of o and D‘.eqn (2). EXPERIMENTAL APPARATUS The irradiation cell and assembly has been de~cribed.~ Solutions were irradiated with pulses of 2.9 MeV electrons from a Van de Graaff accelerator. Pulse durations of 5 ns, 0.2 p s and 0.6 ps were used, and the dose per pulse (1 to 2 krad) was monitored by a secondary emission chamber which was calibrated with the iodide and ferrocyanide dosimeters6 Corrections were made for the different electron densities of the solutions. Details of the pulse radiolysis apparatus have been reported el~ewhere.~ MATERIALS All solutions were prepared from triply distilled H20 and were purged with argon or LiCl was Eastman certified reagent grade or Merck analytical grade.All other reagents 10 mol dm-3 OH- solutions con- With this composition the solutions exp [U(r)/kT]r-’dr)-’ nitrogen. were AnalaR grade (B.D.H. or Hopkin and Williams). sisted of 5 mol dm-3 NaOH+ 5 rnol dm-3 KOH. could be cooled slowly without crystallisation occurring. * When eiq reacts with an ion, B in eqn (1) -(3) is replaced by3 of= 1 where U(Y) is the potential energy of the reacting ions at separation Y.G . V. BUXTON, F. C . R . CATTELL AND F . S . DAINTON 117 RESULTS Conditions were chosen such that (i) the pulse length was very short compared with the lifetime of e;, and (ii) the decay of e; in the absence of reactive solutes was negligible on the timescale of its decay in the presence of such solutes.This latter condition was generally satisfied for solute concentrations 3 Kinetic measurements were generally made in the temperature range 190 to 260 K. The decay of e; was independent of wavelength in this temperature range, although the spectrum of e; does change with time at lower temperature^.^^ Fig. 1 illustrates typical decays of e; in the presence and absence of reactive solutes. Because of possible distortion of the oscilloscope trace depicting these decays, due to the risetime of the detection system (-4 ns) and to the possible contribution of spur reactions to the decay of e; at very short times, eqn (7) was modified to (8) to permit kinetic analysis to be made a finite time after the pulse.In eqn (8) ODi is the optical density at time ti after the end of the pulse, which is taken as time zero, and t2 > t l . mol dm-3. k''[S] (t$-tb>-' In ___ OD1 = k'[S](tf+t$)+--- OD2 2(nD)+' In fig. 2 we show typical data plotted according to eqn (8). From the slopes and intercepts of such plots values of k' and D' have been obtained between 190 and 260 K. Also shown in fig. 2 is a first order plot of the same data. At first sight such plots may appear to be acceptably linear, but close inspection reveals a systematic decrease in slope with time and the mean slope is appreciably larger than that predicted by eqn (8)..I .I CI) 4 5 ps per division mol dm-3 Cr02,. FIG. 1.-Decay of e; in 10 mol dm-3 OH- solution at 200 K containing (a) no solute, (b) 2 x The temperature dependences of k' and D' are illustrated in fig. 3 for the LiCl system, and in fig. 4 for the OH- system. Also shown in fig. 3 is the temperature dependence of T/r, where y is the shear viscosity derived from data in ref. (8). For both solutions the temperature dependence of D' is given by eqn (3, and of k' by eqn (9) k' = A exp[ - B/(T- To)]. (9) In these equations A. B, D6 and T are constants and are listed in table 1.( t t + 4 4 5 . 5 3 x 10-~~3) FIG. 2.-Kinetics of e, decay in 9.5 mol dm-3 LiCl solution at 211 K containing mol dm-3 Cr02,. ( 0 ) Plot of kinetic data according to eqn (S), (0) first order plot, (- - -) first order line having the same slope as plot (0) i.e.k' [S]. I I I I - *. - ...- FIG. 3.-Temperature dependence of k'(0) and D'(0) for the reaction of e; with acetone (1.09 x lo-' mol dm-3) in 9.5 mol dm-3 LiCl solution. Also shown is the self diffusion coefficient of H20 (H) from ref. (9), and log,, [8RT/3m)/dm3 mol-' s-'1 (..--) taking values of from ref. (8).G . V. BUXTON, F . C. R . CATTELL AND F . S . DAINTON 119 1 0 3 ~ / ( ~ - 135 K) FIG. 4.-Temperature dependence of k' (open points) and D' (solid points) for the reaction of e, with NO; in 10 mol dm-3 OH- solution, [NO;] = 4.7 x mol dm-3 (0) and lo-' rnol dm-3 (0). Also shown are values of loglo [(8RT/30007)/dm3 mol-' s-'1 w) taking values of 7 measured in this laboratory.rnol dm-3 (A), 5 x TABLE VA VALUES OF THE PARAMETERS IN EQN (2), (5) AND (9) FOR THE REACTIONS OF e ; WITH SOLUTES IN 9.5 mol dm3 LiCl AND 10 mol d ~ n - ~ OH- SOLUTIONS eqn (9) eqn (5) eqn (2) log 10 system solute (A/cim3 mol-1 s-1) B/K p$Z:s-1) B/ K of Inm 9.5 mol dm-3 LiCl (CH&CO 10.68 f 0.05 613 f 7 - 3.65 f 0.15 656k 20 0.60+ 0.27 (f = 1) To = 129K Hf 10.50+0.12 557+16 -4-02f0.29 578f39 0.6850.17 NO; 11.03+0.18 666&41 -3.61 f0.54 688k106 0.4220.07 NO; 11.35t0.44 716f88 -3.77f0.19 631 A37 0.81 k0.22 CrO2- 11.30f0.22 655f49 -3.91kO.30 633f71 1.73k0.33 10mol dm-3 OH- NO; 11430f0.12 905f21 -2.2050.42 1020k74 0.77f0.24 CrOi- 11.93f0.10 824f17 -2.78k0.18 902f31 2.01f0.54 To = 135K NO, 12.15k0.12 956f21 -2.5720.31 986f51 1.05f0.37 Quoted errors are standard deviations from least squares fits.Values of To are best values common to all the data. DISCUSSION Since the kinetic data fit eqn (8) (see fig. 2) it follows that eqn (4) is a good repre- sentation of the time-dependence of the rate coefficient kt on the timescale of our experiments. Thus the data are consistent with the time-dependence theory developed by Noyes for diffusion controlled reactions, implying that the reactions we have studied are diffusion controlled. This might have been anticipated from the fact that the majority of the reactions of solvated electrons in dilute aqueous solution are accepted as being diffusion controlled, but the following points provide firm evidence that this is the case in the present work. (i) Eqn (5) and (9) are examples of the general phenomenon that mass transport processes, P, in glass forming liquids are accurately described by equations of the form P = AP exp[ - B/(T- To)] (10)120 TIME-DEPENDENT RATE CONSTANTS where the parameters B and To are scarcely dependent on the particular transport process, e.g.fluidity, conductance, diffusion, mobility, dielectric relaxation time etc. (ii) Within the limits of our measurements B and To have the same values in eqn ( 5 ) and (9) for a given reaction (see table) and similar values for all the reactions studied in each system. has a similar temperature dependence (fig. 3) as does the self diffusion of H20 (fig. 3), although this was measured in a higher temperature range (280-370 K), where slightly different parameters may be expected.O Eqn (1) may be rewritten as For the LiCl system the shear viscosity 1 1 1 - = -+- k’ k 4naD” and the fact that k’ and D’ have the same temperature dependence indicates that k % 4noD’, unless k also has the same temperature dependence, in which case no conclusion can be drawn about the relative magnitude of k and 4noD’. However, there is evidence from other work l 1 on the effect of solutes on the yield of solvated electrons that e; reacts effectively instantaneously with the solute when formed at the encounter distance, i.e. when no diffusion is necessary for reaction to occur. We conclude, therefore, that eqn (2) is appropriate. Combining eqn (2) and (5) gives eqn ( 1 3 , and comparison with eqn (9) shows that A = 4ncrfDb. Values of afare listed in the table, and because of (ii) above are independent of temperature in the range 190- 260 K.The value o f f depends on the magnitude of U(r)/kT which is equal to Zie$j/kT, the ratio of the electrical and thermal energy of an ion i of charge Z i e in the field $ j of an ionj. Unfortunately one cannot calculate 1+9~ with any confidence except in dilute solutions l2 so we are unable to compute the magnitude off. How- ever, it is likely that there will be a large degree of association of cations and anions in 10 mol dm-3 salt solutions so that ionic solutes may behave as neutral species, in which casefwill be close to unity. The similar values of of for the reactions of e; with H+, acetone and NO: provide some support for this conclusion and we tenta- tively equate of with the actual reaction distance.The striking feature of the reaction distances listed in the table is the very large value for the reaction of e; with CrOi- in both systems. Such distances are only compatible with a mechanism in which the electron transfers from its solvent trap to the solute by tunnelling. Hart and Anbar l 3 have discussed possible mechanisms of the transfer of hydrated electrons to solutes and favour a tunnelling mechanism. It is interesting that o = 0.98 nm l 3 for the reaction of e; with CrOi- in dilute aqueous solution. This is also an abnormally large value which was estimated from a comparison of the measured rate constant with that predicted by the Debye- Smoluchowski equation. The similar values of Db for all the reactant pairs in the LiCl system imply that the mechanism of the diffusion of H+ is predominantly the hydrodynamic type rather than the proton transfer type in these concentrated solutions.This is not unexpected since a similar conclusion has been drawn by Lown and Thirsk l4 from the effect of pressure and concentration on the electrical conductivity of solutions of alkali metal hydroxides and orthophosphoric acid. They suggest that the proton transfer mechanism is suppressed at high solute concentrations because of the very small fraction of water molecules which are free to rotate in a manner which allows this mechanism to operate. k’ = 4nofDb exp[ - B/(T- To)]. (12)G . V. BUXTON, F. C. R. CATTELL AND F . S . DAINTON 121 It is interesting that the values of Db (see table) for the hydroxide solutions are about an order of magnitude larger than those for the LiCl solutions.This is most likely to be due to a difference in the values of Do for e, rather than Do for the solutes in the two systems. If the solvated electron diffuses in these media by tunnelling from trap to trap, as has been suggested for e; in H,0,13 then Do for e; will reflect the density of trapping sites in the medium, There is evidence from the depression of the yield of solvated electrons in these systems by reactive solutes that the OH- system is more efficient than the LiCl system at trapping electrons, particularly as the temperature is lowered, implying that there is indeed a higher density of electron trapping configurations in the OH- system. In this respect it is known that LiCl and KOH have profoundly different effects on the water structure.15 Thus Li+ breaks down the tetrahedral structure whereas Kf, being of similar size to HzO, can substitute into the water lattice.In addition C1-, because of its large size, contributes more to structure breakdown that does OH- which is also close in size to H20. If all these effects are causally related then they point to the importance of the tetrahedral water structure to the trapping of electrons in aqueous media. Several theoretical models have been proposed to account for the properties of glass forming liquids and to interpret the physical significance of the parameters in eqn (10). Among these are the free volume theory of Cohen and Turnbull," the configurational entropy theory of Adam and Gibbs,'7 and more recently the bond- lattice model of Angel1 and Rao l8 which can be grouped with the entropy theory.In each case To represents the temperature at which mass transport ceases. In the free volume model this is associated with the free volume falling to zero,I6 in the entropy case it is the temperature at which the configurational entropy falls to zero,17 corresponding to no broken bonds in the bond-lattice model. The parameter B in the free volume model is proportional to v*/av,, where v* is the minimum volume of the hole required to permit molecular displacement, and a and v, are the mean values of the coefficient of thermal expansion and molecular volume respectively. In the configurational entropy model lo* l8 B relates inversely the number of broken lattice bonds, or configurational excitations, to the temperature T when T > To and is shown to be proportional to To for a given system in agreement with experimental findings. lo In our experiments B for LiCl solutions is about 30 % lower than the hydroxide value, although a is larger for the hydroxide solution,* which seems contradictory to the requirements of the free volume theory.This theory has also been criticised for other reasons.19 In terms of the entropy theory a smaller value of B indicates a larger configurational entropy change with temperature, and more configurational entropy at a given temperature. This is in keeping with less disruption of the solvent network in the hydroxide solutions. We are grateful to the S.R.C.and General Electric Research for financial assistance. R. M. Noyes, Progr. Reaction Kinetics, 1961, 1, 129. M. von Smoluchowski, 2. ghys. Chem., 1917, 92,129. P. Debye, Trans. Electrochem. Soc., 1942, 82,265. G. V. Buxton, F. C. R. Cattell and F. S. Dainton, Truns. Furuduy Soc., 1971, 67, 687. G. V. Buxton, Proc. Roy. SOC. A , 1972, 328, 9. G. E. Adams, J. W. Boag and B. D. Michael, Trans. Furaday SOC., 1965, 61,492. ' G. V. Buxton, F. C. R. Cattell and F. S. Dainton, to be published. * C. T. Moynihan, N. Balitactac, L. Boone and T. A. Litovitz, J. Chem. Phys., 1971, 55, 3013. A. Weiss and K. H. Nothnagel, Ber. Bunsenges. phys. Chem., 1971, 75, 216. * On cooling from room temperature to 190 K 10 mol dm-3 OH- contracts by 3.3% and 9.5 mol dm-3 LiCl by 1.5 %.122 TIME-DEPENDENT RATE CONSTANTS lo C.A. Angell and R. D. Bressell, J. Phys. Chem., 1972, 76,3244. G. V. Buxton and K. G. Kemsley, J.C.S. FaraCiay I, in press. l2 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn., 1959). l3 E. J. Hart and M. Anbar, The Hydrated Efectron (Wiley-Interscience, New York, 1970). l4 D. A. Lown and H. R. Thirsk, Trans. Furaday SOC., 1971,67, 132, 149. l5 G. W. Brady, J. Chem. Phys., 1958,28,464. l6 M. H. Cohen and D. Turnbull, J. Chem. Phys., 1959,31,1164. l7 G. Adam and J. H. Gibbs, J. Chem. Phys., 1965,43, 139. l8 C. A. Angell and K. J. Rao, J. Chem. Phys., 1972,57,470. l9 M. Goldstein, J. Chem. Phys., 1969, 51, 3728. Application of Time-dependent Rate Constant Theory to Reactions of Solvated Electrons Reaction Distances, Rate Constants and Diffusion Coefficients in Concentrated Aqueous Solutions BY GEORGE V.BUXTON," FRANK C. R. CATTELL? AND FREDERICK S. DAINTON~ Cookridge Hospital, Leeds LS16 6QB University of Leeds, Cookridge Radiation Research Centre, Received 20th May, 1974 The rates of reaction of e; with a number of solutes have been measured in the temperature range 190 - 260 K in concentrated aqueous solutions of LiCl and NaOH + KOH. The rate coefficients are observed to be time-dependent and fit the equations developed by Noyes. Using these equations we have obtained estimates of diffusion controlled rate constants, reaction distances and diffusion coefficients for each reaction. These suggest that e; reacts, and may also diffuse, by a tunnelling mechanism.The temperature dependences of the rate constants and diffusion coefficients are similar to those of other transport processes in glass forming solutions. For rapid bimolecular reactions in solution diffusive transport can be so slow that the average distance between potentially reactive molecules soon exceeds that pre- dicted for a random equilibrium distribution. The measured rate coefficient will decrease, therefore, from an initial value k , characteristic of the random distribution, to a steady state value k' given by eqn (1),l 47cnaD' 1 + 4naD'/k k' = where a is the reaction distance and D' is the sum of the diffusion coefficients of the two molecules. This eqn reduces to the familiar Smoluchowski eqn (2)2 k' = 47cuD' (2) when k 9 47caD'. Noyes efficient from its initial value k to its final value k' is given by eqn (3) has shown that the change with time of the rate co- 1 k k, = k' 1 +-, ex' erfc x [ 4xaD where k, is the rate coefficient at time t, and x = k( JD't)/k'a. For very short times when t 4 (a2/D')(k'/k)2 the observed rate coefficient approaches k.Typically, for diffusion controlled reactions of the hydrated electron at room temperature, Q - 0.5 nm and D' - 7 x lo-' cm2 s-l, implying that a time resolution better than 10-l' s is needed to explore this region. When t 9 (a2/D')(k'/k)2 eqn (3) reduces to (4) t present address : C.S.I.R.O., Division of Cloud Physics, P.O. Box 134, Epping, New South Wales $ present address : University Grants Committee, 14 Park Crescent, London W1N 4DH.Australia. 115116 TIME-DEPENDENT RATE CONSTANTS For typical diffusion controlled reactions of the hydrated electron * with values of CT and D’ given above and k + 4naD’, the observed rate coefficient is expected to be greater than k‘ by 1 % at s, 3 % at lo-’ s, 11 % at s and 34 % at 10-l’~. Through the pulse radiolysis technique it is possible to form essentially instan- taneously, a strongly absorbing reactive species (e;) in a solution containing randomly distributed solute molecules, and to measure its rate of reaction. For time-dependent changes in the rate coefficient to be conveniently observed on a timescale of tens of nanoseconds or longer, D’ must be reduced by several orders of magnitude. This is most satisfactorily achieved by the use of liquids which on cooling progressively become more viscous and eventually vitrefy, and several aqueous solutions fall into this category.Rate coefficients which have already been reported over a very wide temperature range for one such aqueous system are consistent with a variation of D’ with temperature, over at least eight orders of magnitude, given by where To = 135 K and B w 800 K. D’ = Dd exp[ - B/(T- To)] (5) The disappearance of solvated electrons, e;, by reaction with a solute, S, is given by eqn (6) and if k, is given by eqn (4) and [S] % [e;], the decrease in optical density, OD, with time due to e; is given by eqn (7) where ODo is the optical destity at t = 0. The variation of OD with time allows the evaluation of k’ and D’, and provided k % 4noD’, a can be calculated from In this paper we have applied the time dependent rate constant theory of Noyes to the reactions of e; with a number of solutes in 9.5 mol dm-3 LiCl and in 10 mol dm-3 OH- (5 mol dm-3 NaOH + 5 mol dm-3 KOH) over a wide temperature range and have obtained estimates of o and D‘.eqn (2). EXPERIMENTAL APPARATUS The irradiation cell and assembly has been de~cribed.~ Solutions were irradiated with pulses of 2.9 MeV electrons from a Van de Graaff accelerator. Pulse durations of 5 ns, 0.2 p s and 0.6 ps were used, and the dose per pulse (1 to 2 krad) was monitored by a secondary emission chamber which was calibrated with the iodide and ferrocyanide dosimeters6 Corrections were made for the different electron densities of the solutions. Details of the pulse radiolysis apparatus have been reported el~ewhere.~ MATERIALS All solutions were prepared from triply distilled H20 and were purged with argon or LiCl was Eastman certified reagent grade or Merck analytical grade.All other reagents 10 mol dm-3 OH- solutions con- With this composition the solutions exp [U(r)/kT]r-’dr)-’ nitrogen. were AnalaR grade (B.D.H. or Hopkin and Williams). sisted of 5 mol dm-3 NaOH+ 5 rnol dm-3 KOH. could be cooled slowly without crystallisation occurring. * When eiq reacts with an ion, B in eqn (1) -(3) is replaced by3 of= 1 where U(Y) is the potential energy of the reacting ions at separation Y.G . V. BUXTON, F. C . R . CATTELL AND F . S . DAINTON 117 RESULTS Conditions were chosen such that (i) the pulse length was very short compared with the lifetime of e;, and (ii) the decay of e; in the absence of reactive solutes was negligible on the timescale of its decay in the presence of such solutes.This latter condition was generally satisfied for solute concentrations 3 Kinetic measurements were generally made in the temperature range 190 to 260 K. The decay of e; was independent of wavelength in this temperature range, although the spectrum of e; does change with time at lower temperature^.^^ Fig. 1 illustrates typical decays of e; in the presence and absence of reactive solutes. Because of possible distortion of the oscilloscope trace depicting these decays, due to the risetime of the detection system (-4 ns) and to the possible contribution of spur reactions to the decay of e; at very short times, eqn (7) was modified to (8) to permit kinetic analysis to be made a finite time after the pulse.In eqn (8) ODi is the optical density at time ti after the end of the pulse, which is taken as time zero, and t2 > t l . mol dm-3. k''[S] (t$-tb>-' In ___ OD1 = k'[S](tf+t$)+--- OD2 2(nD)+' In fig. 2 we show typical data plotted according to eqn (8). From the slopes and intercepts of such plots values of k' and D' have been obtained between 190 and 260 K. Also shown in fig. 2 is a first order plot of the same data. At first sight such plots may appear to be acceptably linear, but close inspection reveals a systematic decrease in slope with time and the mean slope is appreciably larger than that predicted by eqn (8). .I .I CI) 4 5 ps per division mol dm-3 Cr02,.FIG. 1.-Decay of e; in 10 mol dm-3 OH- solution at 200 K containing (a) no solute, (b) 2 x The temperature dependences of k' and D' are illustrated in fig. 3 for the LiCl system, and in fig. 4 for the OH- system. Also shown in fig. 3 is the temperature dependence of T/r, where y is the shear viscosity derived from data in ref. (8). For both solutions the temperature dependence of D' is given by eqn (3, and of k' by eqn (9) k' = A exp[ - B/(T- To)]. (9) In these equations A. B, D6 and T are constants and are listed in table 1.( t t + 4 4 5 . 5 3 x 10-~~3) FIG. 2.-Kinetics of e, decay in 9.5 mol dm-3 LiCl solution at 211 K containing mol dm-3 Cr02,. ( 0 ) Plot of kinetic data according to eqn (S), (0) first order plot, (- - -) first order line having the same slope as plot (0) i.e.k' [S]. I I I I - *. - ...- FIG. 3.-Temperature dependence of k'(0) and D'(0) for the reaction of e; with acetone (1.09 x lo-' mol dm-3) in 9.5 mol dm-3 LiCl solution. Also shown is the self diffusion coefficient of H20 (H) from ref. (9), and log,, [8RT/3m)/dm3 mol-' s-'1 (..--) taking values of from ref. (8).G . V. BUXTON, F . C. R . CATTELL AND F . S . DAINTON 119 1 0 3 ~ / ( ~ - 135 K) FIG. 4.-Temperature dependence of k' (open points) and D' (solid points) for the reaction of e, with NO; in 10 mol dm-3 OH- solution, [NO;] = 4.7 x mol dm-3 (0) and lo-' rnol dm-3 (0). Also shown are values of loglo [(8RT/30007)/dm3 mol-' s-'1 w) taking values of 7 measured in this laboratory. rnol dm-3 (A), 5 x TABLE VA VALUES OF THE PARAMETERS IN EQN (2), (5) AND (9) FOR THE REACTIONS OF e ; WITH SOLUTES IN 9.5 mol dm3 LiCl AND 10 mol d ~ n - ~ OH- SOLUTIONS eqn (9) eqn (5) eqn (2) log 10 system solute (A/cim3 mol-1 s-1) B/K p$Z:s-1) B/ K of Inm 9.5 mol dm-3 LiCl (CH&CO 10.68 f 0.05 613 f 7 - 3.65 f 0.15 656k 20 0.60+ 0.27 (f = 1) To = 129K Hf 10.50+0.12 557+16 -4-02f0.29 578f39 0.6850.17 NO; 11.03+0.18 666&41 -3.61 f0.54 688k106 0.4220.07 NO; 11.35t0.44 716f88 -3.77f0.19 631 A37 0.81 k0.22 CrO2- 11.30f0.22 655f49 -3.91kO.30 633f71 1.73k0.33 10mol dm-3 OH- NO; 11430f0.12 905f21 -2.2050.42 1020k74 0.77f0.24 CrOi- 11.93f0.10 824f17 -2.78k0.18 902f31 2.01f0.54 To = 135K NO, 12.15k0.12 956f21 -2.5720.31 986f51 1.05f0.37 Quoted errors are standard deviations from least squares fits. Values of To are best values common to all the data.DISCUSSION Since the kinetic data fit eqn (8) (see fig. 2) it follows that eqn (4) is a good repre- sentation of the time-dependence of the rate coefficient kt on the timescale of our experiments. Thus the data are consistent with the time-dependence theory developed by Noyes for diffusion controlled reactions, implying that the reactions we have studied are diffusion controlled. This might have been anticipated from the fact that the majority of the reactions of solvated electrons in dilute aqueous solution are accepted as being diffusion controlled, but the following points provide firm evidence that this is the case in the present work. (i) Eqn (5) and (9) are examples of the general phenomenon that mass transport processes, P, in glass forming liquids are accurately described by equations of the form P = AP exp[ - B/(T- To)] (10)120 TIME-DEPENDENT RATE CONSTANTS where the parameters B and To are scarcely dependent on the particular transport process, e.g.fluidity, conductance, diffusion, mobility, dielectric relaxation time etc. (ii) Within the limits of our measurements B and To have the same values in eqn ( 5 ) and (9) for a given reaction (see table) and similar values for all the reactions studied in each system. has a similar temperature dependence (fig. 3) as does the self diffusion of H20 (fig. 3), although this was measured in a higher temperature range (280-370 K), where slightly different parameters may be expected. O Eqn (1) may be rewritten as For the LiCl system the shear viscosity 1 1 1 - = -+- k’ k 4naD” and the fact that k’ and D’ have the same temperature dependence indicates that k % 4noD’, unless k also has the same temperature dependence, in which case no conclusion can be drawn about the relative magnitude of k and 4noD’.However, there is evidence from other work l 1 on the effect of solutes on the yield of solvated electrons that e; reacts effectively instantaneously with the solute when formed at the encounter distance, i.e. when no diffusion is necessary for reaction to occur. We conclude, therefore, that eqn (2) is appropriate. Combining eqn (2) and (5) gives eqn ( 1 3 , and comparison with eqn (9) shows that A = 4ncrfDb. Values of afare listed in the table, and because of (ii) above are independent of temperature in the range 190- 260 K.The value o f f depends on the magnitude of U(r)/kT which is equal to Zie$j/kT, the ratio of the electrical and thermal energy of an ion i of charge Z i e in the field $ j of an ionj. Unfortunately one cannot calculate 1+9~ with any confidence except in dilute solutions l2 so we are unable to compute the magnitude off. How- ever, it is likely that there will be a large degree of association of cations and anions in 10 mol dm-3 salt solutions so that ionic solutes may behave as neutral species, in which casefwill be close to unity. The similar values of of for the reactions of e; with H+, acetone and NO: provide some support for this conclusion and we tenta- tively equate of with the actual reaction distance.The striking feature of the reaction distances listed in the table is the very large value for the reaction of e; with CrOi- in both systems. Such distances are only compatible with a mechanism in which the electron transfers from its solvent trap to the solute by tunnelling. Hart and Anbar l 3 have discussed possible mechanisms of the transfer of hydrated electrons to solutes and favour a tunnelling mechanism. It is interesting that o = 0.98 nm l 3 for the reaction of e; with CrOi- in dilute aqueous solution. This is also an abnormally large value which was estimated from a comparison of the measured rate constant with that predicted by the Debye- Smoluchowski equation. The similar values of Db for all the reactant pairs in the LiCl system imply that the mechanism of the diffusion of H+ is predominantly the hydrodynamic type rather than the proton transfer type in these concentrated solutions.This is not unexpected since a similar conclusion has been drawn by Lown and Thirsk l4 from the effect of pressure and concentration on the electrical conductivity of solutions of alkali metal hydroxides and orthophosphoric acid. They suggest that the proton transfer mechanism is suppressed at high solute concentrations because of the very small fraction of water molecules which are free to rotate in a manner which allows this mechanism to operate. k’ = 4nofDb exp[ - B/(T- To)]. (12)G . V. BUXTON, F. C. R. CATTELL AND F . S . DAINTON 121 It is interesting that the values of Db (see table) for the hydroxide solutions are about an order of magnitude larger than those for the LiCl solutions.This is most likely to be due to a difference in the values of Do for e, rather than Do for the solutes in the two systems. If the solvated electron diffuses in these media by tunnelling from trap to trap, as has been suggested for e; in H,0,13 then Do for e; will reflect the density of trapping sites in the medium, There is evidence from the depression of the yield of solvated electrons in these systems by reactive solutes that the OH- system is more efficient than the LiCl system at trapping electrons, particularly as the temperature is lowered, implying that there is indeed a higher density of electron trapping configurations in the OH- system. In this respect it is known that LiCl and KOH have profoundly different effects on the water structure.15 Thus Li+ breaks down the tetrahedral structure whereas Kf, being of similar size to HzO, can substitute into the water lattice.In addition C1-, because of its large size, contributes more to structure breakdown that does OH- which is also close in size to H20. If all these effects are causally related then they point to the importance of the tetrahedral water structure to the trapping of electrons in aqueous media. Several theoretical models have been proposed to account for the properties of glass forming liquids and to interpret the physical significance of the parameters in eqn (10). Among these are the free volume theory of Cohen and Turnbull," the configurational entropy theory of Adam and Gibbs,'7 and more recently the bond- lattice model of Angel1 and Rao l8 which can be grouped with the entropy theory.In each case To represents the temperature at which mass transport ceases. In the free volume model this is associated with the free volume falling to zero,I6 in the entropy case it is the temperature at which the configurational entropy falls to zero,17 corresponding to no broken bonds in the bond-lattice model. The parameter B in the free volume model is proportional to v*/av,, where v* is the minimum volume of the hole required to permit molecular displacement, and a and v, are the mean values of the coefficient of thermal expansion and molecular volume respectively. In the configurational entropy model lo* l8 B relates inversely the number of broken lattice bonds, or configurational excitations, to the temperature T when T > To and is shown to be proportional to To for a given system in agreement with experimental findings.lo In our experiments B for LiCl solutions is about 30 % lower than the hydroxide value, although a is larger for the hydroxide solution,* which seems contradictory to the requirements of the free volume theory. This theory has also been criticised for other reasons.19 In terms of the entropy theory a smaller value of B indicates a larger configurational entropy change with temperature, and more configurational entropy at a given temperature. This is in keeping with less disruption of the solvent network in the hydroxide solutions. We are grateful to the S.R.C. and General Electric Research for financial assistance. R. M. Noyes, Progr. Reaction Kinetics, 1961, 1, 129. M. von Smoluchowski, 2. ghys. Chem., 1917, 92,129. P. Debye, Trans. Electrochem. Soc., 1942, 82,265. G. V. Buxton, F. C. R. Cattell and F. S. Dainton, Truns. Furuduy Soc., 1971, 67, 687. G. V. Buxton, Proc. Roy. SOC. A , 1972, 328, 9. G. E. Adams, J. W. Boag and B. D. Michael, Trans. Furaday SOC., 1965, 61,492. ' G. V. Buxton, F. C. R. Cattell and F. S. Dainton, to be published. * C. T. Moynihan, N. Balitactac, L. Boone and T. A. Litovitz, J. Chem. Phys., 1971, 55, 3013. A. Weiss and K. H. Nothnagel, Ber. Bunsenges. phys. Chem., 1971, 75, 216. * On cooling from room temperature to 190 K 10 mol dm-3 OH- contracts by 3.3% and 9.5 mol dm-3 LiCl by 1.5 %.122 TIME-DEPENDENT RATE CONSTANTS lo C. A. Angell and R. D. Bressell, J. Phys. Chem., 1972, 76,3244. G. V. Buxton and K. G. Kemsley, J.C.S. FaraCiay I, in press. l2 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn., 1959). l3 E. J. Hart and M. Anbar, The Hydrated Efectron (Wiley-Interscience, New York, 1970). l4 D. A. Lown and H. R. Thirsk, Trans. Furaday SOC., 1971,67, 132, 149. l5 G. W. Brady, J. Chem. Phys., 1958,28,464. l6 M. H. Cohen and D. Turnbull, J. Chem. Phys., 1959,31,1164. l7 G. Adam and J. H. Gibbs, J. Chem. Phys., 1965,43, 139. l8 C. A. Angell and K. J. Rao, J. Chem. Phys., 1972,57,470. l9 M. Goldstein, J. Chem. Phys., 1969, 51, 3728.

ISSN:0300-9599    

DOI:10.1039/F19757100115

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Thermodynamics of Adsorption from Solution Adsorption by Graphon from Binary Mixtures of Benzene, Cyclohexane and n-Heptane BY STUART G. ASH,^ RICHARD BOWN; AND DOUGLAS H. EVERETT* Department of Physical Chemistry, School of Chemistry, The University, Bristol BS8 1TS Received 6th May, 1974 Experimental data for adsorption at the solution/Graphon interface from the systems benzene + cyclohexane, benzene + heptane and cyclohexane + heptane are presented and analysed in terms of the Gibbs adsorption isotherm. The data for the three systems are shown to be thermodynamically mutually consistent. The surface excess isotherms may be described with reasonable accuracy in terms of simple statistical thermodynamic monolayer models. Evidence is found that the molecular interactions which lead to non-ideality in the bulk phase are much less pronounced in the adsorption region.In a previous paper attention was drawn to the paucity of precise experimental data suitable for comparison with recently developed theories of adsorption from solution, and an apparatus was described which is capable of yielding such data. The present paper analyses in terms of some current theories, the results obtained with this apparatus for three relatively simple systems. Theories of adsorption from solution have been developed in several forms.*" The simplest treats ideal adsorption from a perfect binary mixture of molecules of equal size in contact with a plane homogeneous surface. Successive developments describe adsorption from regular mixtures of equal sized molecules (1 : 1 regular solutions) ; from athermal mixtures of molecules of different sizes (1 : r athermal solution) (r is the ratio of molecular sizes); and from non-athermal mixtures of molecules of different sizes (1 : r non-athermal solutions).In their simpler forms the theories employ a monolayer model of the adsorbed phase ; multilayer theories have also been developed,2* 6* but these are generally less readily compared with experi- mental data. It would be logical to initiate comparison between experiment and theory using a near-perfect binary mixture. However, because of the close similarity between the physical and chemical properties of the components of near-perfect solutions, the difference in their adsorption at a solid interface is likely to be small and difficult to measure accurately.We have therefore studied first a near-regular 1 : 1 solution, the system benzene + cyclohexane. Although this does not follow exactly regular behaviour in the bulk phase, it has been extensively studied and its properties are well-established. * The cyclohexane + n-heptane and benzene + n-heptane systems are representative of the class of (1 : r ) systems with values of r not far from unity ; the former is nearly athermal [HM(x = 0.5) w 260 J mol-l at 293 K] while the latter is distinctly non-athermal [HM(x = 0.5) w 950 J mol-' at 298 K]. Again these have been selected because reliable thermodynamic data are available for the bulk j- present address : Shell Research Limited, Thornton, Cheshire. $ present address : Central Research Laboratories, English Clays, Lovering Pochin Ltd., St.Austell, Cornwall. 123124 ADSORPTION FROM SOLUTION mixtures 9 9 lo Furthermore, by choosing this set of three systems it is possible to test the mutual thermodynamic consistency of the experimental data, and so to confirm the reliability of the experimental method. Examples of systems in which the values of r are larger will be discussed later. Graphon was chosen as the adsorbent since it has a well characterised, nearly homogeneous, graphitic surface whose vapour adsorption properties for the three components used in this work are known.ll* l2 EXPERIMENTAL The experimental methods, including the procedures used for the purification of the liquids and pretreatment of the adsorbent, have been described.' The same sample of Graphon was used for all the experiments reported here.The surface excess isotherms for benzene (l)+cyclohexane (2) in the temperature range 298-328 K, and of benzene (1)+ n-heptane (3) between 283 and 343 K have been reported.' Those for cyclohexane (2)+ n-heptane (3) between 283 and 343 K are shown in fig. 1. 0 . 6 0.5 .+ 0.4 I M .-. \ 8 n E 0.3 9 F 2 0.2 \ Wrn Y W 0. I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 x i FIG. 1.-Experimental surface excess isotherms for the system [cyclohexane (2) + heptane (3111 Graphon as a function of xk : 0 , 2 8 3 K ; A, 298 K ; 0, 323 K ; A, 328 K ; a, 343 K. THERMODYNAMIC CONSISTENCY Each system is treated as a mixture of liquid components, i and j, in equilibrium with a solid interface which provides a force field leading to differential adsorption of i orj, but is otherwise inert.The surface excess concentration of component i, T? is defined as the excess amount of i in the real system, per unit area of solid, over the amount of i in a reference system which contains the same total amount n of material, and in which the mole fraction, xf, of i is equal to that in the bulk phase of the real system :S . G . ASH, R. BOWN AND D. H. EVERETT 125 Here A is the surface area of the solid and xp is the mole fraction of component i in the real system before the adsorbent is introduced.13* l4 This definition implies that The surface excess concentration is related to the interfacial tension, o, at the solid/ solution interface, and to the chemical potentials of the liquid components pi and p j at equilibrium by the Gibbs adsorption equation p'+q' -i 0.(2) - do = ry' dpi + Ty) dpj. (3) Eqn (2) and (3) may be combined with the Gibbs-Duhem equation for the bulk phase to give r(9 do = J dpi. (4) dpi = RT d In xiyf, (5) X j Writing where r f is the activity coefficient of i in the bulk liquid phase, and integrating (4) leads to 4* l4 a; and oj are the interfacial tensions of pure i and j respectively at the liquid/solid interface. Eqn (6) is of general validity and does not imply any model of the interfacial layer. Thus if the activity coefficients of i in the bulk solution are known, the ad- sorption isotherm of F y ) as a function of xi, can be used to calculate (ap-o;). If data are available for the three binary pairs (1 +2), (2+ 3) and (3 + l), then if the experimental results are mutually consistent, the sum of (0; - 002) + (a; - a:) + (05 -a?) should be zero.5.c - 4.0 - 3.0 - rq 2.0- I E 1 xjyf FIG. 2.--Zntegrand of eqn (6) [r:"'/xfxfyf] as function of x:yE for the three systems at 298 K : 0, 1 + 3 ; 0,l + 2;n, 3 + 1.126 ADSORPTION FROM SOLUTION Fig. 2 shows [rs.",/x~x~y~ at 298 K plotted as a function of x:y: for the three systems studied ; the integrals of these curves at various temperatures are given in table 1. The activity coefficients of the bulk solutions required for these calculations were derived from the sources indicated in the table. At the three temperatures, 298, 313 and 328 K, for which data for all three systems are available, the condition for thermo- dynamic consistency is satisfied to within the experimental uncertainty.This test of thermodynamic consistency has also been successfully applied to three systems formed from the same three components as those used here, adsorbed on silica gel.15 TABLE 1 .-THERMODYNAMIC FUNCTIONS FOR THE ADSORPTION BY GRAPHON FROM THE SYSTEMS BENZENE (I)+ CYCLOHEXANE (2) ; BENZENE (I)+ n-HEPTANE (3) ; AND CYCLOHEXANE (2)+ n-HEPTANE (3) system T/K 283.15 - 6.30k0.1 1.98 + 0.1 - 298.15 -7.85k0.2 5.50k0.1 2.74k 0.1 0.4f 0.4 313.15 -7.74k0.2 4.6020.1 3.56k0.1 0.42 0.4 328.15 -7.66k0.2 3.75kO.l 4.25k0.1 0.3 k 0.4 343.15 - 3.232 0.1 4.85+ 0.1 - (A,HP-A,H;)/mJ m-2 - 9.9+ 0.4 21k0.2 - 10.5k0.2 X-0.620.8 (A,Sp-A,Sg)/mJ m-2 K-l -0.008+0.005 0.055+0.005 -0.044+0.005 Z0.003+0.015 (A,HiQ-A,H;)/mJ m-2 I -6+2 16+2 -1022 Z0+4 * denotes preferentially adsorbed component (over majority of concentration range).t from calorimetric measurements of the individual values of A,H i. l 6 The activity coefficients of the bulk solutions were taken from the following sources : 1 + 2, ref. (8); 2 + 3, ref. (9); 3 + 1, ref. (10). In principle the differences (0; - 0;) can also be calculated from the vapour adsorp- tion isotherms of i and j over the whole range of relative pressures; the presently available data are not, however, of adequate precision to make a comparison worth- while between the values obtained from vapour adsorption and liquid adsorption. The interfacial tensions 0; are excess free energy functions and may be written in terms of enthalpy and entropy terms as follows : (7) where AwHis;.are the enthalpies of immersion of unit area of solid into the pure liquids i, j and A w S z j are the corresponding entropy changes. Consequently the enthalpy difference should be calculable from the gradient of a graph of (a; - o;)/Tas a function of 1/T. For the present set of systems these graphs are linear [see, e.g., fig. 5 of ref. (l)] and the values of (A,Hf-A,Hj") are given in table 1. The thermodynamic consistency of these enthalpy differences is shown by the fact that their sum is also zero to within experimental error. A reliable calorimetric technique for the determin- ation of enthalpies of immersion using a Calvet calorimeter has been developed by Thorne. l 6 Values of (A,HiQ - A,Hj") derived from direct measurements of the enthal- pies of immersion are also included in table 1 ; the agreement between the values calculated from adsorption isotherms and those measured calorimetrically provides further confirmation of the self-consistency of the data and the applicability of the above methods of analysis. (0; - u;) = (A,H: - A,HY) - T(A,S,O - AwS;),S.G. ASH, R . BOWN AND D. H . EVERETT 127 COMPARISON WITH STATISTICAL MODELS Theoretical models of adsorption from regular, athermal and non-athermal 1 : r type solutions involve the use of the parameters ai, r, a and K, where ai is the area occupied by one mole of component i on the surface, r is the ratio of molecular sizes j to i, a is the parameter of regular solution theory related to the interaction energy (w) of molecules i and j , and K is an equilibrium constant describing the adsorption equilibrium.The most convincing comparison between theory and experiment will result if all these parameters can be obtained from measurements other than adsorption isotherms. In the present work values of ai were obtained from the adsorption isotherms of vapour i by Graphon, taking the surface area of the Graphon as 86 m2 g-l. For convenience of calculation, r was taken as the ratio aj/al ; strictly this applies only to the surface layer and the ratio of molar volumes should be used in the bulk liquid. However, the two estimates of r did not differ greatly, and the theoretical results are not so critically dependent on the choice of r as to make this approximation un- reasonable.The values of a were obtained by analysing the vapour pressure data for the bulk solutions on the basis of conventional regular solution theory. The assump- tions of this theory are consistent with those used in the adsorption models to be tested. It was assumed initially that the same parameter CI is appropriately used for the inter- facial region. Formally the equilibrium constant K is related to the interfacial free energies of the two pure liquid/solid interfaces by (04 - 0;). In Kij = -ai- RT ' and refers to the equilibrium process (component i)' + ai/aj (component j)" + (component i>" + ai/aj (component j ) ' . For comparing experimental data with statistical models the components are arranged so that r is greater than unity. Thus although K is derived from the adsorption isotherms, it is independent of the assumption implied by the statistical models as to the character of the interfacial region.The values of the parameters selected for the analysis of the present work, and their sources, are summarised in table 2. TABLE 2.-PARAMETERS EMPLOYED IN THE ANALYSIS OF THE EXPERIMENTAL RESULTS IN TERMS OF STATISTICAL MECHANICAL THEORIES substance benzene (1) cyclohexane (2) n-heptane ( 3 ) (a)* aJm2 mo1-I 2.41 x 105 2.41 x 105 3.43 x 105 system 1+2 2+ 3 1+3 r 1 .o 1.4 1.5 mi- TIK ~12.303 RT X i 2 ~12.303 RT K23 ~12.303 RT K13 283.15 - - 0.03 0.519 0.289 1.22 298.15 0.232 2.15 0.03 0.581 0.248 1.31 313.15 0.206 2.05 0.02 0.653 0.214 1.39 328.15 0.185 1.97 0.02 0.718 0.188 1.46 343.15 - - 0.01 0.764 0.166 1.51 Source of data: * ref.(11) and (12); 7 ref. (8), (9) and (10). Values of K calculated using eqn. (6) and (8).128 ADSORPTION FROM SOLUTION [BENZENE (1) + CYCLOHEXANE (2)]/GRAPHON For this system r - 1 and the bulk solution follows the equations for regular solution behaviour with reasonable accuracy as shown in fig. 3. The adsorption data were therefore compared with theoretical treatments of adsorption from regular solutions. 9 Consideration of the theoretical results for the multilayer theory indicates that for the low values of K and a exhibited by this system it should be possible to analyse the data adequately in terms of the monolayer theory. We therefore calculate the activity coefficients of the components in the adsorbed moao- layer from the following equation 4 9 l4 x f = l rp, log y; = log - +- dxf yt, x; 2.3 s xi - xf&f (9) where 7: is the activity coefficient and x: is the mole fraction of i in the adsorbed layer ; x; is obtained from the surface excess isotherm by assuming monolayer adsorption : X; = x:+airln).(10) In fig. 3, log y; calculated from the experimental data at 298, 313 and 328 K is shown as a function of x;. According to the theoretical treatment logy: should be related to the surface and bulk mole fraction by the equation where I is the fraction of nearest neighbours within each molecular layer parallel to the surface, and rn is the fraction of nearest neighbours in each adjacent layer, 1+2m = 1. The theoretical curve at 313 K, taking I = 3 and m = *, is shown in the figure: it lies well above the experimental points.This discrepancy may indicate either that the monolayer model is inadequate, or that the assumed equality of a in the bulk solution and in the adsorbed monolayer is unjustified. Evidence that the interaction between benzene molecules adsorbed from the vapour phase on a graphite surface is very much smaller than that between benzene molecules in the gas phase (as evidenced from its second virial coefficient) comes from the work of Pierce and Ewing l1 and Kiselev and his co-workers.12 This has been interpreted in terms of the " flat " orientation of adsorbed benzene molecules which results in the elimination of" face to face " interaction between the n-electrons of the molecules. In the same way, it may be expected that the interaction between an adsorbed benzene molecule and an adsorbed cyclohexane molecule will be smaller than in the liquid state. These effects, which tend to equalise benzene-benzene, benzene-cyclohexane and cyclo- hexane-cyclohexane interactions in the adsorbed monolayer will reduce the value of a in the adsorbed phase.Eqn (1 1) may be written as ma' la" logyp = ~ (1 - xf)2 + 2TT( 1 - xp)2, 2.3 RT where a" is related to the interaction energy in the adsorbed monolayer;" if a" is now set as zero, then eqn (12) reduces to ma 2.3 RT log yp = -(l - X f ) 2 . * Strictly this equation should also include a third parameter to take account of interactions between adsorbed molecules and those in the liquid : it is assumed here that aUl1 = d.S. G . ASH, R. BOWN AND D. H.EVERETT 129 0.1 0 . 2 0.3 0.4 0.5 0 . 6 0.7 0 . 8 0 . 9 1.0 Xl;U FIG. 3.-Logarithm of the activity coefficients of benzene ( 1 ) in the bulk and surface phases for the system [benzene ( 1 ) + cyclohexane (2)]/Graphon. Curves (a), (b), (c), log 7; at 298, 313 and 328 K respectively ; dotted line (d), log yi at 313 K calculated for regular solution behaviour with a/2.303 RT = 0.206. Experimental points for log yy : A, 298 K ; 0, 313 K ; A, 328 K. Curve (e) log fl for adsorption from regular solution with al/2.303 RT = au/2.303 RT = 0.206 ; curve (f) as (e) but with a' = 0. 0.2 FIG. 4.-Comparison of observed and calculated surface excess isotherms at 313 K for the system [benzene ( 1 ) + cyclohexane (2)]/Graphon : 0, experimental data ; curves calculated for, . .., ideal adsorption from ideal solution ; - . - ., monolayer adsorption from regular solution with a Q= al; - , monolayer adsorption from regular solution with a' = 0 ; - - - - , multilayer adsorption from regular solution with a' = 0. 1-5130 ADSORPTION FROM SOLUTION The curve corresponding to this equation at 313 K is also shown in fig. 3 : it agrees with the experimental points to within their scatter.* In fig. 4 the experimental excess isotherm at 313 K is compared with various theoretical predictions using the value of K calculated through eqn (8). The ideal adsorption model is clearly inadequate, while the monolayer regular solution model deviates systematically from experiment. The modification of setting a' = 0 is seen to fit the data satisfactorily. Also shown in fig.4 is the curve obtained using the multilayer theory (which does not, of course, lead to the concept of surface activity coefficients) subject to the same modification. The small deviation between the predictions of the monolayer and multilayer theories for this system justifies the use of the former in this analysis. [BENZENE ( 1 ) n-HEPTANE (3)]/GRAPHON This system may be analysed in a similar manner to the benzene+cyclohexane system, except that r is no longer unity, so that, on the basis of a monolayer model, x: is now given by 5 * l4 and the activity coefficients based on the non-athermal monomer + r-mer adsorption model are la ma 2.3 RT 2.3 RT logy? = - (l-&)2+-(l-+;)2, where &' and 6: are the volume fractions of component i in the adsorbed monolayer and bulk liquid respectively : Fig.5 shows the bulk activity coefficients as a function of x i , the surface activity coefficients calculated from (9) and (14) at 283 and 343 K, together with the curves corresponding to eqn (15). In, this case also the observed activity coefficients are substantially lower than those predicted by the theory. The discrepancy is brought out even more strikingly by comparison of the observed and calculated isotherms (fig. 6) : although the simple theory represents the isotherm reasonably well at 343 K it fails to predict the inversion in the preferential adsorption which is observed at 283 K. This probably arises in part from the failure of the statistical theory to describe the properties of the bulk solution very precisely (see fig.5), and in part from the effect postulated in the above analysis of the benzene + cyclohexane system, of a reduction in the effective lateral interaction parameter in the adsorbed monolayer. Attempts to improve the fit for the present system by taking a' in the adsorbed phase as either zero or 0.5 az lead to activity coefficients close to those observed, and calcu- lated isotherms which, although they fit the observed data somewhat less well at 343 K, are a better fit at 283 K. The failure of the theory to account for this system as satisfactorily as it does the benzene + cyclohexane system is probably also related to the different shapes of the benzene and n-heptane molecules, and the flexibility of the latter : the data may even indicate that the relative orientation of the molecules in the adsorbed state may be temperature dependent, so that the value of a' appro- priate to 283 K may be lower than that at 343 K.This system is also interesting in * These data were the first to be obtained with the apparatus, using a Rayleigh interferometer, and are somewhat less precise than those for the other two systems.S. G. ASH, R. BOWN AND D. H. EVERETT 131 that whereas on the basis of a comparison of enthalpies of immersion of Graphon in the pure liquids one would expect n-heptane to be the more strongly adsorbed, the entropies of immersion are such that benzene is preferentially adsorbed except at high benzene concentrations and at lower temperatures. 4Y FIG. 5.-Logarithm of the activity coefficients of benzene (1) in the bulk and surface phases for the system [benzene (1) + n-heptane (3)]/Graphon. Curves (a), (b), logy: at 283 and 343 K respectively ; dotted line, curve (c), log y: at 283 K calculated for regular solution behaviour with a/2.303 RT = 0.289.Experimental points for log yy : 0, 283 K ; 0, 343 K. Curve (d) log fl for adsorption from regular solution with a@/2.303 RT = a1/2.303 RT = 0.289 ; curve (e) as (d) but with an = 0. [CYCLOHEXANE (2) -I- HEPTANE (3)]/GRAPHON The system shows relatively small deviations from ideality in the bulk phase which can be attributed to the discrepancy between the sizes of the molecules. The adsorption data have therefore been compared with the predictions of the simple athermal mixtures model according to which the equilibrium constant is related to the volume fractions in the bulk and surface phases by (g)($$)'* = Kz3.Fig. 7 shows the experimental and calculated isotherms at 283 and 343 K using values of K obtained from (6) and (8). The fit, although not quite perfect, must be regarded as satisfactory, bearing in mind the differing molecular shapes of the two components, which must in some measure limit the applicability of the theoretical model.132 ADSORPTION FROM SOLUTION 4: FIG. 6.-Comparison of observed and calculated surface excess isotherms in terms of (4: - 4;) against 4; for the system [benzene (1) + n-heptane (3)]/Graphon. Experimental data : 0, 283 K ; 0, 343 K. Curves calculated for, - - -, monolayer adsorption from (1 : r) non-athermal solution with a' = az at 283 and 343 K ; . .., monolayer adsorption from (1 : u) non-athermal solution with a' = 0 at 283 and 343 K ; -, monolayer adsorption from (1 : r) non-athermal solution with a' = 0.5a at 283 and 343 K. 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 4; FIG. 7.--cOmparison of observed and calculated surface excess isotherms, in terms of (4; - 4;) against 4; for the system [cyclohexane (2) + n-heptane (3)]/Graphon. Experimental data : 0,293 K : 0, 343 K. Curves calculated for monolayer adsorption from (1 : r ) athermal solution at 283 and 343 K.S . G . ASH, R . BOWN AND D . H . EVERETT 133 CONCLUSION The three systems studied here, although showing somewhat different adsorption characteristics, are shown to behave in a thermodynamically mutually consistent fashion.Their individual behaviour may be accounted for reasonably satisfactorily in terms of simple monolayer theories of adsorption. The benzene + cyclohexane system is an example of a near-regular solution of molecules of approximately equal size ; its adsorption characteristics on a Graphon surface can, however, be explained quantitatively only on the assumption that in the adsorbed phase the intermolecular energies are modified so that the parameter a of the regular theory (or the interchange energy w) is reduced to near zero. The cyclohexane+n-heptane system is a nearly athermal system of molecules differing in size by a factor Y M 1.5 ; adsorption from this solution by Graphon is satisfactorily accounted for on the basis of a monolayer model for the adsorption of molecules of different size from an athermal solution.On the other hand, the benzene+n-heptane system exhibits, at low temperatures, a surface excess isotherm showing a reversal of sign at an azeotropic point. The data at higher temperatures can be fitted reasonably well by equations corresponding to adsorption from a non-athermal mixture of molecules of different size, using the same parameter a for the bulk and adsorbed phases. At lower temperatures, no close fit was obtained, although improved agreement with experiment was obtained by choos- ing a for the surface phase either as zero or about one half of that in the bulk phase. The present work thus provides evidence that in the liquid/solid interface region intermolecular forces between adsorbed molecules are influenced considerably by the presence of the adsorbent surface.That this is also true in vapour/solid systems has been known for some tim3.l’ These conclusions are in agreement with earlier observations * that adsorption from solution can often be discussed reasonably satisfactorily by assuming the adsorbed phase to behave as an ideal monolayer in equilibrium with a non-ideal bulk phase. It is suggested that the data for the system benzene + n-heptane may indicate that the relative orientations of the adsorbed molecules are temperature dependent. S. G. Ash, R. Bown and D. H. Everett, J. Chem. Thermodynamics, 1973, 5,239. ’ S. Ono and S. Kondo in Handbuch der Physik, ed. S . Flugge (Springer, Berlin 1960), vol. 10, p. 134. A. V. Kiselev and L. F. Pavlova, Bull. Acad. Sci. U.S.S.R. Chem. Ser., 1965, 15 ; A. V. Kiselev and I. V. Shikalova, Doklady Phys, Chem., 1966, 171,808 ; A. V. Kiselev and V. V. Khopina, Trans. Faraday Soc., 1969, 65, 1936. L. G. Nagy and G. Schay, Actu Chim. Acad. Sci. Hungary, 1963, 39, 365 ; L. G. Nagy, G. Schay and T. Szekvenyesy, Periodica Polytechnica, 1962, 6, 91. D. H. Everett, Trans. Faraday Soc., 1964, 60, 1803 ; 1965, 61, 2478 ; S. G. Ash, D. H. Everett and G. H. Findenegg, Trans. Faraday Soc., 1968, 64,2639. J. E. Lane, Austral. J. Chem., 1967, 20, 827. G. Scatchard, S. E. Wood and J. M. Mochel, J. Phys. Chem., 1939, 43, 119. J. L. Crutzen, R. Haase and L. Sieg, 2. Naturforsch., 1950, 5a, 600. ’ A. R. Altenberger and J. Stecki, Chem. Phys. Letters, 1970, 5, 29. lo I. Brown and A. H. Ewald, Austral. J. Chem., 1951, A4, 198. l 1 C. Pierce and B. Ewing, J. Phys. Chem., 1967, 71, 3408. l2 A. V. Kiselev and A. A. Isirikyan, J. Phys, Chem.. 1961, 65, 601. l3 see e.g., De$nitions, Terminology and Symbols in Colloid and Surface Chemistry, Pure Appl. l4 D. H. Everett in Specialist Periodical Report, ColloidScience (Chem. SOC., London, 1973), vol 1, l5 A. L. Myers and S. Sircar, A. Ch. E. J., 1971, 17, 186. l6 P. E. Thorne, Ph.D. Thesis (Bristol, 1974). l’ 0. Sinanoglu and K. S. Pitzer, J. Chem. Phys,. 1960,32, 1279 ; A. D. McLachlan, Mol. Phys., l8 see ref. (3), (4) and (15). Chem., 1972, 31, 579, section 1.1.10. p. 58. 1964, 7, 381; D. H. Everett, Disc. Faraday Soc., 1965, 40, 177.

ISSN:0300-9599    

DOI:10.1039/F19757100123

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Catalysis by Group lk Metals Part 1 ,-Reaction of Buta-1,3-diene with Hydrogen and with Deuterium catalysed by Alumina-supported Gold BY DOUGLAS A. BUCHANAN AND GEOFFREY WEBB* Chemistry Department, The University, Glasgow G12 SQQ, Scotland Received 23rd May, 1974 The reaction of buta-l,3-diene with hydrogen and deuterium has been studied using gold supported on y-alumina and a mixed boehmite+y-alumina in the temperature range 443-533 K. The reaction is completely selective for butene formation and, although both catalysts are active for the hydro- isomerisation of but-l-ene at 473 K, they do not catalyse the hydrogenation of n-butenes to n-butane. The kinetics and activation energy have been determined together with the variation in product distributions with hydrogen uptake, initial reactant pressures and temperature.The distribution of deuterium in each of the products has been determined and in the reaction with deuterium the prod- ducts contain an excess of hydrogen over that expected from hydrogen-deuterium mass balance. Buta-1,3-diene is adsorbed on the surface of the gold and subsequently reacts with hydrogen which migrates from the support to the metal. Type A hydrogen equilibrates with gas phase deuterium, whereas type B hydrogen does not react with gas phase deuterium but interacts with adsorbed hydrocarbon. Values for the sizes of the type A and B hydrogen pools are quoted. Two types of hydrogen exist on the alumina support. The low activity of gold for many catalysed reactions has been attributed to its lack of a partially filled d-band at the usual temperatures, and its consequent inability to chemisorb simple molecules.Gold will not adsorb or activate molecular hydrogen at temperatures below 473 K,I although ethylene can be chemisorbed in a weakly held form on gold surfaces.2 This chemisorption of olefins is consistent with the observa- tion that gold, when dispersed on alumina or magnesium oxide, possesses apprec- iable activity for the equilibration of benzene + cyclohexane mixtures. Gold powder will catalyse the skeletal isomerisation of ne~pentane,~ although, compared with Group VIII metal catalysts, the temperature required for this reaction is rather high being around 800 K, where thermal promotion of electrons from the 5d to the 6s level may occur.'* 4-6 Gold, when electroplated on to the surface of a palladium-silver alloy, will catalyse the hydrogenation of but-1-ene and cy~lohexene,~* but only when hydrogen atoms are provided to the gold surface by diffusion through the palladium-silver alloy.This pre-requisite, for hydrogenation activity, of the provision of atomic hydrogen at the gold surface has also been demonstrated in a study of the hydrogenation of ethylene on evaporated gold films, using the gold-catalysed dehydrogenation of formic acid as the source of hydrogen atom^.^ that in the reactions of unsaturated hydrocarbons using supported Group VIII metal catalysts, the support plays a significant role in deter- mining the catalytic behaviour. In particular the migration of adsorbed species between metal and support, and the role of hydrogen associated with the support have been discussed.In view of the apparent inability of gold to activate molecular hydrogen, the present studies were undertaken in an attempt to separate the catalytic effects of the metal and the support in hydrogenation reactions, particularly with reference to the availability of hydrogen and the migration of adsorbed species be- tween metal and support. It has been shown 134D. A. BUCHANAN AND G. WEBB 135 EXPERIMENTAL CATALYSTS Two catalyst supports were used; y-alumina (Degussa Ltd.), and y-alumina, from the same source, which had been pretreated by refluxing with a 1 mol dm-3 aqueous sodium acetate solution for 24 h, followed by washing with distilled water, until all traces of acetate ion had been removed, and finally drying in an air oven at 393-423 K.This latter support is designated alumina-A. X-ray analysis of alumina-A showed that it consisted of a mixture of y-alumina and the alumina hydrate, boehmite, although the relative proportions of each component could not be satisfactorily determined. The catalysts, containing 1 % w/w gold, were prepared by adding an aqueous solution of chloroauric acid (HAuCI,), containing the required weight of gold, to an aqueous suspension of the support. The excess water was removed by evaporation and the catalyst fmally dried in an air oven at a temperature between 393 and 423 K. During the preparation the supported salt was observed to undergo thermal decomposition resulting in the formation of a mauve coloured product containing metallic gold. In addition to the above catalysts, 1 % wlw gold supported on a-alumina (I.C.I. Ltd.) and Aerosil silica (Degussa Ltd.) were prepared.However, under the reaction conditions used in this study, neither of these catalysts was observed to possess any catalytic activity. MATERIALS Buta-l,3-diene (Matheson Co.) contained no impurities detectable by gas chromato- graphy and was merely degassed before use. Cylinder hydrogen was purifi5d by diffusion through a palladium-silver alloy thimble. Deuterium (Norsk Hydro) was of purity 99.8 atom % D and contained less than 10 p.p.m. oxygen impurity. It was used as supplied. APPARATUS A N D PROCEDURE Reactions were carried out with the catalyst, usually 0.5 g, resting on the bottom of a cylindrical Pyrex reaction vessel (capacity ca. 100 cm3).The reaction vessel was connected to a conventional high vacuum system maintained at Nm-2 or better by means of an oil diffusion pump backed by an oil rotary-pump. The catalyst was activated by treatment with three successive volumes of hydrogen, at a pressure of 2.66 x lo4 N m-2, for a total of 12 h at 523 K. The catalyst was then evacuated for 30 min and cooled to the reaction temperature. The reaction mixture was admitted to the reaction vessel and the reaction followed by the pressure fall observed on a mercury manometer. At the required pressure fall the reaction products were extracted for analysis. In those reactions where deuterium wasused, following the activation in hydrogen, the catalyst was treated with three successive volumes of deuterium (pressure 3.33 x lo4 N m-2) at 673 K, each sample of deuterium being left in contact with the catalyst for 12 h.Mass spectro- metric analysis of the deuterium after the pretreatment showed that this treatment was effect- ive in exchanging all of the exchangeabk hydrogen in the catalyst. ANALYSIS OF REACTION PRODUCTS The analysis of reaction products was effected by gas-liquid chromatography using an 8 m column packed with a 40 % w/w dispersion of hexa-2,5-dione supported on 30-60 mesh Silocel firebrick. In the experiments using deuterium each reaction product was, on elution from the gas chromatograph, condensed out of the helium carrier gas stream in a trap cooled in liquid nitrogen. The products were then analysed for deuterium content using an A.E.I.MS20 mass spectrometer. For the hydrocarbon analyses an ionizing beam voltage of 15 V was used, while for the analysis of residual deuterium a beam voltage of 70 V was used.136 B u TAD I E N E H Y D R o GEN A T I ON OVE R Au/AI,O, RESULTS THE REACTION OF BUTA-I,3-DIENE WITH HYDROGEN The variation in the distribution of reaction products with pressure fall was studied using both Au/y-alumina and Au/alumina-A at 473 K and a pressure of 6.7 x lo3 N rn-, of buta-1,3-diene and 1.33 x lo4 N rn-, of hydrogen. Under these conditions the reaction was completely selective for the formation of n-butene; no butane was ever observed as a reaction product and the reaction ceased at a pressure fall corresponding to the uptake of 1 mole of hydrogen per mole of buta-1,3-diene.The variation in the butene distribution with hydrogen uptake per mole of buta- 1,3- diene (AH) is shown in fig. l(a) and (b) for Au/y-alumina and Aulalumina-A res- pectively. X I I I I 1 I I 0 0.2 0.4 0.6 0.8 1.0 1 I I I I 0 0.2 0.4 0.6 0.8 1.0 hydrogen consumed (AH)/mol (mol diene)-l FIG. 1.-Variation of butene distribution with hydrogen uptake over Au/y-alumina (a), and Au/ alumina-A (6) at 473 K. (&4&)0 = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.33 x 104N m-2. (0, but-1-ene ; 0, cis-but-Zene ; 0, trans-but-Zene). (a) (6) time/h FIG. 2.-Variation in butene distribution with time of contact of but-1-ene+ hydrogen mixture with Au/alumina-A at 473 K. ( P ~ 4 ~ s ) o = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.33 x 104N m-2. Broken lines indicate the thermodynamic equilibrium values.(0, but-1-ene ; 0, cis-but-Zene ; (>, tvans-but-2- ene).D . A. BUCHANAN AND G . WEBB 137 These results show that the butene distribution was independent of hydrogen uptake up to AH = 0.6 for Au/y-alumina or AH = 0.90 with Au/alumina-A. The initial but- 1 -ene/but-2-ene ratio was greater with Au/y-alumina. In the latter stages of the reaction the butenes effectively competed with the buta-1,3-diene for the catalyst surface and underwent isomerisation, although no n-butane was detected. This effect was more marked with Au/y-alumina than with Aulalumina-A. If the reaction products were left in contact with the catalyst for a further 18 h, the butenes underwent extensive isomerisation, eventually attaining their thermodynamic equi- librium proportions, as indicated by the points shown at AH = 1.0 in fig.l(a) and (6) although again no n-butane was detectable. Under comparable conditions, Au/ alumina-A will effect the hydroisomerisation of but-1-ene (see fig. 2), although but-l- ene hydrogenation does not occur. It was noticeable throughout this work that the catalytic activity progressively decreased from reaction to reaction until, after about twenty reactions, a low limiting value was attained. By adopting a standard run technique, in which alternate reac- tions were carried out using a standard butene/hydrogen mixture, it was possible to correct for changes in catalytic activity and hence, using catalysts which had already been subjected to a number (usually 8-10) of reactions, to determine initial rate orders with respect to both hydrogen and buta-1,3-diene over the pressure range 6.7 x lo3 to 3.33 x 104N m-2 using each catalyst at 473 K.The results for the two catalysts were similar, the reaction following the rate expression ; This rate expression is also consistent with the observed pressure fall against time curves, which were first order with respect to the total pressure. The product distributions were independent of initial reactant pressures ; again the reaction was completely selective, no n-butane being observed under the condition used. The effect of temperature in the range 473 to 533 K (Au/y-alumina) and 443 to 533 K (Au/alumina-A) was studied using 6.7 x 103N m-2 buta-1,3-diene and 1.33 x 104Nm-2 hydrogen. Using a standard run technique to correct for variations in catalyst activity, an apparent activation energy of 36.5 4.0 kJ mol-1 was obtained for each catalyst.The reaction products were extracted at a pressure fall of (2 & 0.1) x 103N m-2 and analysed. With both catalysts the but-1 -ene/but-2-ene ratio appeared to be independent of temperature, although the trans/& ratio in the but-2-ene yield increased with increasing temperature (see table 1) THE REACTION BETWEEN BUTA-I ,3-DIENE AND DEUTERIUM The variation in the distribution of deuterium in the reaction products with pres- sure fall was determined using both Au/y-alumina and Au/alumina-A. The varia- tions of deuterated product distributions with pressure fall are shown in table 2, in which D.N. represents the deuterium number, defined as the average number of deuterium atoms per hydrocarbon molecule. With both catalysts the three n-butenes exhibit very similar deuterium distributions, although the extent of deuteration is surprisingly low.The extent of deuteration of both the butenes and the buta-l,3-diene is substantially less using Au/alumina-A than using Au/y-alumina, although the amounts of hydrogen exchange are comparable for the two catalysts. At first sight it would appear that, as expected in view of the increasing amount of hydro- gen exchange, the degree of deuteration of the butenes decreased with increasing conversion of buta-I ,3-diene. However, consideration of the sequence in which the Several interesting features emerge from these results.138 BUTADIENE HYDROGENATION OVER Au/A1,0, reactions were performed shows that any effects of pressure fall are completely masked by the variation of the extent of deuteration with reaction number.The variation is such that the deuterium number of each butene increased from one reaction to the next. These observations are further substantiated by studying the variation of the extent of deuteration with reaction number in a series of reactions, carried out under TABLE 1 .-VARIATION OF THE DISTRIBUTION OF BUTENES WITH TEMPERATURE butene distribution (%) temperature/K 1 -B t-2-B C-2-B (t-2-B/c-2-B) Au /alumina- A 473 50.5 17.6 31.9 0.55 493 51.3 16.8 31.9 0.53 518 50.9 19.7 29.4 0.66 533 51.9 20.6 27.5 0.75 Au/y -alumina 443 58.4 12.8 27.8 0.46 473 58.1 14.3 27.6 0.52 488 58.7 14.5 26.8 0.54 503 59.2 14.7 26.1 0.56 533 59.7 15.4 24.9 0.62 (Pc.,H& = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.3 x 1 0 4 ~ m-2.Pressure fall at analysis = (25 0.1) x 103N m-2. TABLE 2.-vARIATION OF DEUTERATED PRODUCT DISTRIBUTIONS WITH PRESSURE FALL catalyst Au/y-alumina reaction no. pressure fall/ lO2N m-2 product 1 -B DO 25.6 D1 44.2 D2 25.7 D3 3.9 D4 0.6 D5 0.1 D.N. 1.10 x in HxD2-x catalyst reaction no. pressure fall/ 102N m-2 product DO D1 D2 D3 D4 D5 D.N. x in HxD2-x A3 16.0 t-2-B C-2-B 25.2 24.8 46.6 44.3 26.4 24.6 4.2 4.7 1.2 1.3 0.4 0.4 1.15 1.14 0.23 1.3-B 1 -B 82.9 42.0 14.7 39.6 1.8 15.6 0.6 2.4 0.0 0.4 0.0 0.0 0.20 0.79 Aulalumina-A A1 41.6 t-2-B C-2-B 39.6 42.9 38.5 38.7 18.5 15.1 3.0 2.8 0.5 0.5 0.0 0.0 0.86 0.79 0.27 AS 20.8 - - 1,3-B 1 -B 77.1 19.5 17.4 42.0 3.9 31.7 1 .l 5.9 0.5 0.9 0.0 0.0 0.30 1.27 0.22 1-B t-2-B 48.3 45.9 40.4 39.5 10.4 12.8 0.7 1.2 0.2 0.6 0.0 0.0 0.64 0.71 C-2-B 45.8 42.2 11.3 0.5 0.2 0.0 0.67 0.24 F6 18.0 1,3-B 1-B 97.3 52.6 2.1 37.7 0.6 9.1 0.0 0.5 0.0 0.0 0.0 0.0 0.03 0.65 F3 42.0 t-2-B C-2-B 51.0 53.7 36.5 37.6 11.2 8.2 1.2 0.6 0.0 0.0 0.0 0.0 0.69 0.63 0.30 1,3-B 95.1 4.0 0.7 0.2 0.0 0.0 0.06 Initial buta-1,3-diene pressure = 6.7 x 103N m-2 ; initial deuterium pressure = 1.33 x 104N m-2 ; temperature = 473 K.No species above Ds were observed.D. A . BUCHANAN AND G. WEBB 139 identical conditions to those used above, and analysed at a constant pressure fall of (2 +_ 0.1) x 103N m-2. The results show that, for each catalyst, although the butene distribution remained constant, the deuterium number of each n-butene increased with increasing reaction number as shown in fig.3. It is also of interest to compare the extent of deuteration, as indicated by the deuterium number, with the initial rate of deuteration. The results for but-1-ene are shown, using each catalyst, in fig. 4. Similar trends were observed for cis- and trans-but-2-ene. I L2- 1.0- 5 8 0.8- .- 8 - El ?-I Q) c) 3 0.6- 0.4 - - I I I t i 1 2 3 4 5 reaction number FIG. 3.-Variation in deuterium number of but-l-ene (filled symbols), trans-but-Zene (open symbols) and cis-but-2-ene (half-filled symbols) with reaction number over Au/y-alumina (circles) and Au/ alumina-A (squares). [(PC.,HJ~ = 6.7 x 103N m-2 ( P D ~ ) ~ = 1.33 x 104N m-2 ; temperature = 473 KI] 1 I I 1 I I 0 5.0 10.0 initial rate/N m-2 min-l FIG. 4.-Variation of deuterium number of but-1-ene with initial rate of deuteration over AuJp alumina (0) and Aulalumina-A (a) (conditions as in fig.3).140 BUTDAIENE HYDROGENATION OVER Au/A1,03 Although the “ reaction number ” effect tended to mask the effect of temperature upon the deuterobutene distribution and the extent of buta-l,3-diene exchange, it was possible to detect a temperature effect with both catalysts. From the results, shown in table 3, it is possible to see that, with both Au/y-alumina and Au/alumina-A, increasing temperature caused a decrease in the deuterium content of each butene, whereas the extent of hydrogen exchange tended to increase with increasing temper- ature. TABLE 3 .-THE VARIATION OF THE DEUTERATED PRODUCT DISTRIBUTIONS WITH TEMPERATURE catalyst Au /alumina-A temperature/K reaction no.product D.N. x in H,D2-x catalyst temperature/K reaction no. product 443 W 3 1-B t-2-B C-2-B 48.0 43.4 49.8 39.3 37.4 39.5 11.4 15.0 9.5 0.6 2.0 0.6 0.0 1.2 0.4 0.0 0.0 0.2 533 H/5 1.3-B 1-B t-2-B ~-24B 1,3-B 98.0 64.3 63.0 63.4 97.8 1.5 31.0 31.2 30.9 1.6 0.4 4.4 5.2 4.9 0.6 0.0 0.3 0.3 0.5 0.0 0.0 0.0 0.3 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.67 0.83 0.63 0.03 0.41 . 0.33 0.43 0.03 0.22 0.54 Au /y-alumina 473 D /2 533 D/3 1-B t-2-B C-2-B 1,3-B 28.7 27.7 28.4 80.4 45.1 44.1 45.7 17.1 22.5 23.8 22.2 2.2 3.2 4.0 3.5 0.3 0.6 0.5 0.2 0.0 0.0 0.0 0.0 0.0 1-B t-2-B C-2-B 33.8 33.1 31.3 43.3 43.2 44.2 19.1 19.7 19.6 3.2 3.3 3.8 0.5 0.7 0.8 0.1 0.0 0.3 1,3-B 79.7 17.6 2.5 0.1 0.0 0.0 D.N.1.02 1.05 1.02 0.22 0.94 0.95 0.99 0.23 0.18 0.28 Initial buta-1,3-diene pressure = 6.7 x 103N m-2 ; initial deuterium pressure = 1.3 x 104N m-’ ; pressure fall at analysis = 2.0 x 103N m-2. It was found that in all the buta-l,3-diene + deuterium reactions it was not possible to obtain a satisfactory mass balance for hydrogen and deuterium in the reactants and products. In all cases the products were considerably hydrogen rich. It was also noticeable that with Au/y-alumina the effect was less than with Au/alumina-A. Furthermore, with both catalysts, the mass imbalance became less from reaction to reaction, as the catalyst activity decreased. THE CATALYST-DEUTERIUM EXCHANGE REACTION The apparent lack of a good hydrogen-deuterium mass balance, together with the low deuterium content of the n-butenes suggest that the catalyst contains a source of hydrogen atoms capable of taking part in the ‘‘ hydrogenation ” reaction.In order to investigate this possibility, the interaction of deuterium with the catalyst was examined to determine the extent of hydrogen-deuterium exchange at 473 K following catalyst activation at 523 or 673 K. The catalyst (0.75 g) was first activated in hydrogenD. A. BUCHANAN AND G. WEBB 141 (2.66 x 104N m-2) for 12 h. The vessel containing the catalyst was then evacuated for 30 min at the activation temperature and the sample allowed to cool in vacuo to 473 K. The catalyst was then allowed to equilibrate with 2.66 x 104N m-2 of deuterium for varying times. Following each equilibration the deuterium was analysed for hydrogen content, the catalyst evacuated for 30 min and a further 2.66 x 104N m-2 of deuterium allowed to equilibrate with the catalyst for the same time as was used in the first reaction.For each catalyst this procedure was repeated twice and the results are shown in table 4. TABLE 4.-cATALY ST-DEUTERIUM EXCHANGE REACTION hydrogen number reduction temp./ exchange time/ K m n reaction 1 reaction 2 reaction 3 Au/ y-alumina 523 720 1.30 0.98 0.68 523 230 0.65 0.47 0.35 673 720 0.35 0.29 0.22 Au/alumina-A 523 720 0.82 0.65 0.60 523 30 0.24 0 . 1 7 0.10 673 720 0 . 1 4 0.10 0.08 Wt. of catalyst = 0.75 g; temperature of exchange = 473 K ; initial deuterium pressure = 1.33 x 104N m-2. CATALYST STRUCTURE Using an ultramicrotoming technique in which catalyst samples were embedded in Araldite, six to eight thin sections of each catalyst were examined by electron micro- scopy to determine the size distribution of the gold particles.Approximately 200 particles were counted from each section; the results for both Au/y-alumina and Au/alumina-A are shown 3 3 2 .- 4 4 a cd - c, c, x FIG. 5.-Distribution of metal particle size/A lines). particle sizes in Au/y-alumina (broken line) and Au/aulmina-A (full Some catalyst samples were also examined after use and it was found that, although these used catalysts had lost most of their activity, there was no detectable change in the particle size distributions relative to the unused catalysts.142 BUTADIENE HYDROGENATION OVER Au/A1203 DISCUSSION The results presented above show that gold, when supported in a finely divided state on alumina will effectively catalyse the reaction between buta-l,3-diene and hydrogen without, as reported previously,'* * the necessity of continuously providing hydrogen in atomic form to the gold surface.The activity of these gold catalysts is, not surprisingly, somewhat lower than that of the more conventional supported Group VIII metals such as palladium or platinum. Furthermore, the gold catalysts tend to progressively lose activity in use, the activity after around twenty reactions being approximately two orders of magnitude below the initial activity. The gold-catalysed reactions show some similarities to those observed with supported Group VIII metals and copper.13 Thus all three n-butenes are formed as initial products and the butene distribution and trans/cis ratio in but-2-ene are similar to those observed with ~1atinum.l~ However, unlike copper or the Group VIII metals, alumina-supported gold will not, under the conditions used in this study, catalyse the hydrogenation of n-butenes to butane, although it will catalyse the slow isomerisation of but-1-ene to cis- and trans-but-2-ene as shown in fig.2. This apparent lack of hydrogenation activity may be kinetic in its origin since studies of the hydrogenation of pent- 1 -ene over these catalysts, using hydrogen/hydrocarbon ratios of ca. 700, show that at 373 K both pentene hydrogenation and isomerisation occur. One of the most significant features to arise from the studies of the interaction of buta-l,3-diene with deuterium is the close relationship between the extent of deuter- ation of the products and the catalyst activity as determined from the initial rates of reaction, together with the considerable hydrogen-deuterium mass imbalance between reactants and products.Clearly, even after the extensive pretreatment in deuterium, the freshly prepared catalysts still contain a source of hydrogen which can partake in the hydrogenation reaction. Examination of the results in table 4 reveals that, with both the Au/y-alumina and the Au/alumina-A, extensive exchange occurs between catalyst hydrogen and gas- phase deuterium. Furthermore, the amounts of catalyst hydrogen are dependent upon the catalyst pretreatment temperature. Thus for Au/y-alumina the total numbers of exchangeable H-atoms per gram of catalyst following pretreatment at 523 and 673 K are 1.93 x 1021 and 5.59 x 1020 respectively.The corresponding values for Au/ alumina-A are 1.45 x 1021 and 2.08 x 1020 atoms per gram of catalyst. This effect of high temperature pretreatment suggests that the surface undergoes an irreversible change with loss of hydrogen, probably due to either dehydration or progressive dehydroxylation of the alumina surface. The results in table 3 show that the extent of deuterium incorporation in the pro- ducts was less with Au/alumina-A than with Au/y-alumina, although the initial rate of " hydrogenation " was higher with the former catalyst. In view of the prolonged catalyst pretreatment in deuterium during activation, and the lower total amount of exchangeable hydrogen on the Au/alumina-A catalyst, the results indicate that, on both catalysts, at least two types of surface hydrogen exist : type A, which undergoes equilibration with deuterium, and type B, which does not undergo ready exchange with deuterium, but which can readily partake in the hydrocarbon hydrogenation reaction.The relative amounts of type A and type B hydrogen must be different on the two catalysts such that the ratio (type A/type B) is greater on Au/y-alumina than on Au/alumina-A. Since with both catalysts the extent of deuterium incorporation in the products increases as the activity decreases, the pool of type B hydrogen must gradually become depleted and not replaced by " hydrogen " from the gas-phase.D.A. BUCHANAN AND G . WEBB 143 The magnitude of the type B pool can be estimated for each catalyst from the amounts of excess hydrogen in the products as determined from the hydrogen-deuterium mass balance between reactants and products. Using this method the respective values for Au/y-alumina and Au/alumina-A are 7.36 x 1020 atoms per gram and 2.62 x 1021 atoms per gram. With regard to the identity of the types A and B hydrogen, comparison of the results presented in table 4 with results obtained for tritium exchange of y-alumina and alumina-A at 523 K l6 suggests that the type A hydrogen may be identified with the surface hydroxyl groups on the alumina. The identity of the type B hydrogen is less clear. The occlusion of hydrogen in Group VIII metal powders,13 platinum black l7 and palladium black l8 and the reaction of occluded hydrogen with olefins is well established.However, comparison of the magnitude of the type B hydrogen pool with the gold concentration [-3 x 1019 atom (g catalyst)-l] rules out any possi- bility of the type B hydrogen being occluded in the metal. Clearly type B hydrogen is associated with the support, although its precise chemical identity is yet to be estab- lished. In view of the complete absence of activity of either the y-alumina or alumina-A for buta-l,3-diene hydrogenation, under the conditions used in the present study, the results presented above are explicable in terms of a mechanism in which buta-1,3- diene is adsorbed at the gold surface, and subsequently undergoes reaction with hydrogen atoms which migrate from the support to the metal. From the particle size distributions of the gold particles, it seems unlikely that the gold itself will contain special sites capable of activating molecular hydrogen, unless the activity resides in extremely small particles not sensed by electron microscopy.Thus the support plays a significant role in that it provides a source of atomic " hydrogen " for reaction. Such a conclusion is in agreement with the suggestions of previous workers regarding the catalytic activity of gold for hydrocarbon hydrogenation.'. The kinetics, high selectivity and the butene isomerisation activity of these catalysts is also consistent with the above conclusion, since it is envisaged that the steady state surface concentra- tion of hydrogen atoms on the metal will be very small under these conditions.The butene distributions show that, over both catalysts, the but- l-ene/but-2-ene ratio is slightly greater than unity and the cisltrans ratio in but-2-ene is around 1.5. Furthermore, the butene distribution is invariant with conversion until most of the buta- 1,3-diene has reacted. These observations together with the close similarities in the deuterium content of all three n-butenes suggest that the butenes are all formed directly from adsorbed buta-l,3-diene by a mechanism similar to that proposed by Phillipson et al. In conclusion, the results presented above show that gold when supported on y-alumina, or a mixed y-alumina-boehmite support, will catalyse the hydrogenation of buta-1,3-diene to butene, although the support plays a significant role by providing a source of atomic hydrogen to the gold surface.Further, at least two types of reactive hydrogen exist on the support, although the precise chemical identity of the various forms of support hydrogen is not established. Further investigations of the hydrogen associated with the support are at present being carried out. for the copper-catalysed reaction. The authors thank the S.R.C. for the award of a maintenance grant to one of us (D. A. B.), and for a grant to purchase the A.E.I. MS20 mass spectrometer. R. J. Mikovsky, M. Boudart and H. S. Taylor, J. Arner. Chem. Soc., 1954, 76, 3814. G. Parravano, J. Catalysis, 1970, 18, 320. * N. W. Cant and W. K. Hall, J. Phys. Chem., 1971,75,2914.144 BUTADIENE HYDROGENATION OVER Au/A1203 M.Boudart and L. D. Ptak, J. Catalysis, 1970, 16,90. D. D. Eley and D. R. Rossington, Chemisorption, ed. W. E. Garner (Butterworth, London, 1957), p. 137. R. P. Chambers and M. Boudart, J. Catalysis, 1966, 5, 517. B. J. Wood and H. Wise, J. Catalysis, 1966, 5, 135. W. M. H. Sachtler and N. H. De Boer, J. Phys. Chem., 1960,64,1579. * R. S. Yolles, B. J. Wood and H. Wise, J. Catalysis, 1971, 21, 66. lo G. Webb and J. I. Macnab, J. Catalysis, 1972, 26,226. l1 G. Webb and J. A. Altham, J. Catalysis, 1970, 18, 133. l2 J. U. Reid, S. J. Thomson and G. Webb, J. Catalysis, 1973, 29, 421 ; 1973, 30, 372. l3 P. B. Wells, Surface and Defect Properties of Solids (The Chemical Society, London, 1971), l4 G. C. Bond, G. Webb, P.B. Wells and J. M. Winterbottom, J. Chem. SOC., 1965, 3218. l5 G. C. Bond, P. A. Sermon, D. A. Buchanan, G. Webb and P. B. Wells, Chem. Comm., 1973 l 6 P. A. Sermon, G. C. Bond and G. Webb, Chem. Comm., 1974,417. vol. 1, p. 236. 444. Z. Paal and S. J. Thomson, J. CataZysis, 1973, 30,96. L. V. Babenkova, N. M. Popova, D. V. Sokol’skii and V. K. Solynserkova, Doklady Akad. Nauk S.S.S.R., 1973, 210, 888. l9 J. J. Phillipson, P. B. Wells and G. R. Wilson, J. Chem. SOC. A, 1969, 1351. Catalysis by Group lk Metals Part 1 ,-Reaction of Buta-1,3-diene with Hydrogen and with Deuterium catalysed by Alumina-supported Gold BY DOUGLAS A. BUCHANAN AND GEOFFREY WEBB* Chemistry Department, The University, Glasgow G12 SQQ, Scotland Received 23rd May, 1974 The reaction of buta-l,3-diene with hydrogen and deuterium has been studied using gold supported on y-alumina and a mixed boehmite+y-alumina in the temperature range 443-533 K.The reaction is completely selective for butene formation and, although both catalysts are active for the hydro- isomerisation of but-l-ene at 473 K, they do not catalyse the hydrogenation of n-butenes to n-butane. The kinetics and activation energy have been determined together with the variation in product distributions with hydrogen uptake, initial reactant pressures and temperature. The distribution of deuterium in each of the products has been determined and in the reaction with deuterium the prod- ducts contain an excess of hydrogen over that expected from hydrogen-deuterium mass balance. Buta-1,3-diene is adsorbed on the surface of the gold and subsequently reacts with hydrogen which migrates from the support to the metal.Type A hydrogen equilibrates with gas phase deuterium, whereas type B hydrogen does not react with gas phase deuterium but interacts with adsorbed hydrocarbon. Values for the sizes of the type A and B hydrogen pools are quoted. Two types of hydrogen exist on the alumina support. The low activity of gold for many catalysed reactions has been attributed to its lack of a partially filled d-band at the usual temperatures, and its consequent inability to chemisorb simple molecules. Gold will not adsorb or activate molecular hydrogen at temperatures below 473 K,I although ethylene can be chemisorbed in a weakly held form on gold surfaces.2 This chemisorption of olefins is consistent with the observa- tion that gold, when dispersed on alumina or magnesium oxide, possesses apprec- iable activity for the equilibration of benzene + cyclohexane mixtures.Gold powder will catalyse the skeletal isomerisation of ne~pentane,~ although, compared with Group VIII metal catalysts, the temperature required for this reaction is rather high being around 800 K, where thermal promotion of electrons from the 5d to the 6s level may occur.'* 4-6 Gold, when electroplated on to the surface of a palladium-silver alloy, will catalyse the hydrogenation of but-1-ene and cy~lohexene,~* but only when hydrogen atoms are provided to the gold surface by diffusion through the palladium-silver alloy. This pre-requisite, for hydrogenation activity, of the provision of atomic hydrogen at the gold surface has also been demonstrated in a study of the hydrogenation of ethylene on evaporated gold films, using the gold-catalysed dehydrogenation of formic acid as the source of hydrogen atom^.^ that in the reactions of unsaturated hydrocarbons using supported Group VIII metal catalysts, the support plays a significant role in deter- mining the catalytic behaviour. In particular the migration of adsorbed species between metal and support, and the role of hydrogen associated with the support have been discussed.In view of the apparent inability of gold to activate molecular hydrogen, the present studies were undertaken in an attempt to separate the catalytic effects of the metal and the support in hydrogenation reactions, particularly with reference to the availability of hydrogen and the migration of adsorbed species be- tween metal and support.It has been shown 134D. A. BUCHANAN AND G. WEBB 135 EXPERIMENTAL CATALYSTS Two catalyst supports were used; y-alumina (Degussa Ltd.), and y-alumina, from the same source, which had been pretreated by refluxing with a 1 mol dm-3 aqueous sodium acetate solution for 24 h, followed by washing with distilled water, until all traces of acetate ion had been removed, and finally drying in an air oven at 393-423 K. This latter support is designated alumina-A. X-ray analysis of alumina-A showed that it consisted of a mixture of y-alumina and the alumina hydrate, boehmite, although the relative proportions of each component could not be satisfactorily determined.The catalysts, containing 1 % w/w gold, were prepared by adding an aqueous solution of chloroauric acid (HAuCI,), containing the required weight of gold, to an aqueous suspension of the support. The excess water was removed by evaporation and the catalyst fmally dried in an air oven at a temperature between 393 and 423 K. During the preparation the supported salt was observed to undergo thermal decomposition resulting in the formation of a mauve coloured product containing metallic gold. In addition to the above catalysts, 1 % wlw gold supported on a-alumina (I.C.I. Ltd.) and Aerosil silica (Degussa Ltd.) were prepared. However, under the reaction conditions used in this study, neither of these catalysts was observed to possess any catalytic activity.MATERIALS Buta-l,3-diene (Matheson Co.) contained no impurities detectable by gas chromato- graphy and was merely degassed before use. Cylinder hydrogen was purifi5d by diffusion through a palladium-silver alloy thimble. Deuterium (Norsk Hydro) was of purity 99.8 atom % D and contained less than 10 p.p.m. oxygen impurity. It was used as supplied. APPARATUS A N D PROCEDURE Reactions were carried out with the catalyst, usually 0.5 g, resting on the bottom of a cylindrical Pyrex reaction vessel (capacity ca. 100 cm3). The reaction vessel was connected to a conventional high vacuum system maintained at Nm-2 or better by means of an oil diffusion pump backed by an oil rotary-pump. The catalyst was activated by treatment with three successive volumes of hydrogen, at a pressure of 2.66 x lo4 N m-2, for a total of 12 h at 523 K.The catalyst was then evacuated for 30 min and cooled to the reaction temperature. The reaction mixture was admitted to the reaction vessel and the reaction followed by the pressure fall observed on a mercury manometer. At the required pressure fall the reaction products were extracted for analysis. In those reactions where deuterium wasused, following the activation in hydrogen, the catalyst was treated with three successive volumes of deuterium (pressure 3.33 x lo4 N m-2) at 673 K, each sample of deuterium being left in contact with the catalyst for 12 h. Mass spectro- metric analysis of the deuterium after the pretreatment showed that this treatment was effect- ive in exchanging all of the exchangeabk hydrogen in the catalyst.ANALYSIS OF REACTION PRODUCTS The analysis of reaction products was effected by gas-liquid chromatography using an 8 m column packed with a 40 % w/w dispersion of hexa-2,5-dione supported on 30-60 mesh Silocel firebrick. In the experiments using deuterium each reaction product was, on elution from the gas chromatograph, condensed out of the helium carrier gas stream in a trap cooled in liquid nitrogen. The products were then analysed for deuterium content using an A.E.I. MS20 mass spectrometer. For the hydrocarbon analyses an ionizing beam voltage of 15 V was used, while for the analysis of residual deuterium a beam voltage of 70 V was used.136 B u TAD I E N E H Y D R o GEN A T I ON OVE R Au/AI,O, RESULTS THE REACTION OF BUTA-I,3-DIENE WITH HYDROGEN The variation in the distribution of reaction products with pressure fall was studied using both Au/y-alumina and Au/alumina-A at 473 K and a pressure of 6.7 x lo3 N rn-, of buta-1,3-diene and 1.33 x lo4 N rn-, of hydrogen.Under these conditions the reaction was completely selective for the formation of n-butene; no butane was ever observed as a reaction product and the reaction ceased at a pressure fall corresponding to the uptake of 1 mole of hydrogen per mole of buta-1,3-diene. The variation in the butene distribution with hydrogen uptake per mole of buta- 1,3- diene (AH) is shown in fig. l(a) and (b) for Au/y-alumina and Aulalumina-A res- pectively. X I I I I 1 I I 0 0.2 0.4 0.6 0.8 1.0 1 I I I I 0 0.2 0.4 0.6 0.8 1.0 hydrogen consumed (AH)/mol (mol diene)-l FIG.1.-Variation of butene distribution with hydrogen uptake over Au/y-alumina (a), and Au/ alumina-A (6) at 473 K. (&4&)0 = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.33 x 104N m-2. (0, but-1-ene ; 0, cis-but-Zene ; 0, trans-but-Zene). (a) (6) time/h FIG. 2.-Variation in butene distribution with time of contact of but-1-ene+ hydrogen mixture with Au/alumina-A at 473 K. ( P ~ 4 ~ s ) o = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.33 x 104N m-2. Broken lines indicate the thermodynamic equilibrium values. (0, but-1-ene ; 0, cis-but-Zene ; (>, tvans-but-2- ene).D . A. BUCHANAN AND G . WEBB 137 These results show that the butene distribution was independent of hydrogen uptake up to AH = 0.6 for Au/y-alumina or AH = 0.90 with Au/alumina-A. The initial but- 1 -ene/but-2-ene ratio was greater with Au/y-alumina. In the latter stages of the reaction the butenes effectively competed with the buta-1,3-diene for the catalyst surface and underwent isomerisation, although no n-butane was detected.This effect was more marked with Au/y-alumina than with Aulalumina-A. If the reaction products were left in contact with the catalyst for a further 18 h, the butenes underwent extensive isomerisation, eventually attaining their thermodynamic equi- librium proportions, as indicated by the points shown at AH = 1.0 in fig. l(a) and (6) although again no n-butane was detectable. Under comparable conditions, Au/ alumina-A will effect the hydroisomerisation of but-1-ene (see fig. 2), although but-l- ene hydrogenation does not occur.It was noticeable throughout this work that the catalytic activity progressively decreased from reaction to reaction until, after about twenty reactions, a low limiting value was attained. By adopting a standard run technique, in which alternate reac- tions were carried out using a standard butene/hydrogen mixture, it was possible to correct for changes in catalytic activity and hence, using catalysts which had already been subjected to a number (usually 8-10) of reactions, to determine initial rate orders with respect to both hydrogen and buta-1,3-diene over the pressure range 6.7 x lo3 to 3.33 x 104N m-2 using each catalyst at 473 K. The results for the two catalysts were similar, the reaction following the rate expression ; This rate expression is also consistent with the observed pressure fall against time curves, which were first order with respect to the total pressure.The product distributions were independent of initial reactant pressures ; again the reaction was completely selective, no n-butane being observed under the condition used. The effect of temperature in the range 473 to 533 K (Au/y-alumina) and 443 to 533 K (Au/alumina-A) was studied using 6.7 x 103N m-2 buta-1,3-diene and 1.33 x 104Nm-2 hydrogen. Using a standard run technique to correct for variations in catalyst activity, an apparent activation energy of 36.5 4.0 kJ mol-1 was obtained for each catalyst. The reaction products were extracted at a pressure fall of (2 & 0.1) x 103N m-2 and analysed. With both catalysts the but-1 -ene/but-2-ene ratio appeared to be independent of temperature, although the trans/& ratio in the but-2-ene yield increased with increasing temperature (see table 1) THE REACTION BETWEEN BUTA-I ,3-DIENE AND DEUTERIUM The variation in the distribution of deuterium in the reaction products with pres- sure fall was determined using both Au/y-alumina and Au/alumina-A.The varia- tions of deuterated product distributions with pressure fall are shown in table 2, in which D.N. represents the deuterium number, defined as the average number of deuterium atoms per hydrocarbon molecule. With both catalysts the three n-butenes exhibit very similar deuterium distributions, although the extent of deuteration is surprisingly low. The extent of deuteration of both the butenes and the buta-l,3-diene is substantially less using Au/alumina-A than using Au/y-alumina, although the amounts of hydrogen exchange are comparable for the two catalysts.At first sight it would appear that, as expected in view of the increasing amount of hydro- gen exchange, the degree of deuteration of the butenes decreased with increasing conversion of buta-I ,3-diene. However, consideration of the sequence in which the Several interesting features emerge from these results.138 BUTADIENE HYDROGENATION OVER Au/A1,0, reactions were performed shows that any effects of pressure fall are completely masked by the variation of the extent of deuteration with reaction number. The variation is such that the deuterium number of each butene increased from one reaction to the next.These observations are further substantiated by studying the variation of the extent of deuteration with reaction number in a series of reactions, carried out under TABLE 1 .-VARIATION OF THE DISTRIBUTION OF BUTENES WITH TEMPERATURE butene distribution (%) temperature/K 1 -B t-2-B C-2-B (t-2-B/c-2-B) Au /alumina- A 473 50.5 17.6 31.9 0.55 493 51.3 16.8 31.9 0.53 518 50.9 19.7 29.4 0.66 533 51.9 20.6 27.5 0.75 Au/y -alumina 443 58.4 12.8 27.8 0.46 473 58.1 14.3 27.6 0.52 488 58.7 14.5 26.8 0.54 503 59.2 14.7 26.1 0.56 533 59.7 15.4 24.9 0.62 (Pc.,H& = 6.7 x 103N m-2 ; ( P H ~ ) ~ = 1.3 x 1 0 4 ~ m-2. Pressure fall at analysis = (25 0.1) x 103N m-2. TABLE 2.-vARIATION OF DEUTERATED PRODUCT DISTRIBUTIONS WITH PRESSURE FALL catalyst Au/y-alumina reaction no.pressure fall/ lO2N m-2 product 1 -B DO 25.6 D1 44.2 D2 25.7 D3 3.9 D4 0.6 D5 0.1 D.N. 1.10 x in HxD2-x catalyst reaction no. pressure fall/ 102N m-2 product DO D1 D2 D3 D4 D5 D.N. x in HxD2-x A3 16.0 t-2-B C-2-B 25.2 24.8 46.6 44.3 26.4 24.6 4.2 4.7 1.2 1.3 0.4 0.4 1.15 1.14 0.23 1.3-B 1 -B 82.9 42.0 14.7 39.6 1.8 15.6 0.6 2.4 0.0 0.4 0.0 0.0 0.20 0.79 Aulalumina-A A1 41.6 t-2-B C-2-B 39.6 42.9 38.5 38.7 18.5 15.1 3.0 2.8 0.5 0.5 0.0 0.0 0.86 0.79 0.27 AS 20.8 - - 1,3-B 1 -B 77.1 19.5 17.4 42.0 3.9 31.7 1 .l 5.9 0.5 0.9 0.0 0.0 0.30 1.27 0.22 1-B t-2-B 48.3 45.9 40.4 39.5 10.4 12.8 0.7 1.2 0.2 0.6 0.0 0.0 0.64 0.71 C-2-B 45.8 42.2 11.3 0.5 0.2 0.0 0.67 0.24 F6 18.0 1,3-B 1-B 97.3 52.6 2.1 37.7 0.6 9.1 0.0 0.5 0.0 0.0 0.0 0.0 0.03 0.65 F3 42.0 t-2-B C-2-B 51.0 53.7 36.5 37.6 11.2 8.2 1.2 0.6 0.0 0.0 0.0 0.0 0.69 0.63 0.30 1,3-B 95.1 4.0 0.7 0.2 0.0 0.0 0.06 Initial buta-1,3-diene pressure = 6.7 x 103N m-2 ; initial deuterium pressure = 1.33 x 104N m-2 ; temperature = 473 K.No species above Ds were observed.D. A . BUCHANAN AND G. WEBB 139 identical conditions to those used above, and analysed at a constant pressure fall of (2 +_ 0.1) x 103N m-2. The results show that, for each catalyst, although the butene distribution remained constant, the deuterium number of each n-butene increased with increasing reaction number as shown in fig. 3. It is also of interest to compare the extent of deuteration, as indicated by the deuterium number, with the initial rate of deuteration. The results for but-1-ene are shown, using each catalyst, in fig.4. Similar trends were observed for cis- and trans-but-2-ene. I L2- 1.0- 5 8 0.8- .- 8 - El ?-I Q) c) 3 0.6- 0.4 - - I I I t i 1 2 3 4 5 reaction number FIG. 3.-Variation in deuterium number of but-l-ene (filled symbols), trans-but-Zene (open symbols) and cis-but-2-ene (half-filled symbols) with reaction number over Au/y-alumina (circles) and Au/ alumina-A (squares). [(PC.,HJ~ = 6.7 x 103N m-2 ( P D ~ ) ~ = 1.33 x 104N m-2 ; temperature = 473 KI] 1 I I 1 I I 0 5.0 10.0 initial rate/N m-2 min-l FIG. 4.-Variation of deuterium number of but-1-ene with initial rate of deuteration over AuJp alumina (0) and Aulalumina-A (a) (conditions as in fig. 3).140 BUTDAIENE HYDROGENATION OVER Au/A1,03 Although the “ reaction number ” effect tended to mask the effect of temperature upon the deuterobutene distribution and the extent of buta-l,3-diene exchange, it was possible to detect a temperature effect with both catalysts.From the results, shown in table 3, it is possible to see that, with both Au/y-alumina and Au/alumina-A, increasing temperature caused a decrease in the deuterium content of each butene, whereas the extent of hydrogen exchange tended to increase with increasing temper- ature. TABLE 3 .-THE VARIATION OF THE DEUTERATED PRODUCT DISTRIBUTIONS WITH TEMPERATURE catalyst Au /alumina-A temperature/K reaction no. product D.N. x in H,D2-x catalyst temperature/K reaction no. product 443 W 3 1-B t-2-B C-2-B 48.0 43.4 49.8 39.3 37.4 39.5 11.4 15.0 9.5 0.6 2.0 0.6 0.0 1.2 0.4 0.0 0.0 0.2 533 H/5 1.3-B 1-B t-2-B ~-24B 1,3-B 98.0 64.3 63.0 63.4 97.8 1.5 31.0 31.2 30.9 1.6 0.4 4.4 5.2 4.9 0.6 0.0 0.3 0.3 0.5 0.0 0.0 0.0 0.3 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.67 0.83 0.63 0.03 0.41 .0.33 0.43 0.03 0.22 0.54 Au /y-alumina 473 D /2 533 D/3 1-B t-2-B C-2-B 1,3-B 28.7 27.7 28.4 80.4 45.1 44.1 45.7 17.1 22.5 23.8 22.2 2.2 3.2 4.0 3.5 0.3 0.6 0.5 0.2 0.0 0.0 0.0 0.0 0.0 1-B t-2-B C-2-B 33.8 33.1 31.3 43.3 43.2 44.2 19.1 19.7 19.6 3.2 3.3 3.8 0.5 0.7 0.8 0.1 0.0 0.3 1,3-B 79.7 17.6 2.5 0.1 0.0 0.0 D.N. 1.02 1.05 1.02 0.22 0.94 0.95 0.99 0.23 0.18 0.28 Initial buta-1,3-diene pressure = 6.7 x 103N m-2 ; initial deuterium pressure = 1.3 x 104N m-’ ; pressure fall at analysis = 2.0 x 103N m-2. It was found that in all the buta-l,3-diene + deuterium reactions it was not possible to obtain a satisfactory mass balance for hydrogen and deuterium in the reactants and products.In all cases the products were considerably hydrogen rich. It was also noticeable that with Au/y-alumina the effect was less than with Au/alumina-A. Furthermore, with both catalysts, the mass imbalance became less from reaction to reaction, as the catalyst activity decreased. THE CATALYST-DEUTERIUM EXCHANGE REACTION The apparent lack of a good hydrogen-deuterium mass balance, together with the low deuterium content of the n-butenes suggest that the catalyst contains a source of hydrogen atoms capable of taking part in the ‘‘ hydrogenation ” reaction. In order to investigate this possibility, the interaction of deuterium with the catalyst was examined to determine the extent of hydrogen-deuterium exchange at 473 K following catalyst activation at 523 or 673 K.The catalyst (0.75 g) was first activated in hydrogenD. A. BUCHANAN AND G. WEBB 141 (2.66 x 104N m-2) for 12 h. The vessel containing the catalyst was then evacuated for 30 min at the activation temperature and the sample allowed to cool in vacuo to 473 K. The catalyst was then allowed to equilibrate with 2.66 x 104N m-2 of deuterium for varying times. Following each equilibration the deuterium was analysed for hydrogen content, the catalyst evacuated for 30 min and a further 2.66 x 104N m-2 of deuterium allowed to equilibrate with the catalyst for the same time as was used in the first reaction. For each catalyst this procedure was repeated twice and the results are shown in table 4.TABLE 4.-cATALY ST-DEUTERIUM EXCHANGE REACTION hydrogen number reduction temp./ exchange time/ K m n reaction 1 reaction 2 reaction 3 Au/ y-alumina 523 720 1.30 0.98 0.68 523 230 0.65 0.47 0.35 673 720 0.35 0.29 0.22 Au/alumina-A 523 720 0.82 0.65 0.60 523 30 0.24 0 . 1 7 0.10 673 720 0 . 1 4 0.10 0.08 Wt. of catalyst = 0.75 g; temperature of exchange = 473 K ; initial deuterium pressure = 1.33 x 104N m-2. CATALYST STRUCTURE Using an ultramicrotoming technique in which catalyst samples were embedded in Araldite, six to eight thin sections of each catalyst were examined by electron micro- scopy to determine the size distribution of the gold particles. Approximately 200 particles were counted from each section; the results for both Au/y-alumina and Au/alumina-A are shown 3 3 2 .- 4 4 a cd - c, c, x FIG.5.-Distribution of metal particle size/A lines). particle sizes in Au/y-alumina (broken line) and Au/aulmina-A (full Some catalyst samples were also examined after use and it was found that, although these used catalysts had lost most of their activity, there was no detectable change in the particle size distributions relative to the unused catalysts.142 BUTADIENE HYDROGENATION OVER Au/A1203 DISCUSSION The results presented above show that gold, when supported in a finely divided state on alumina will effectively catalyse the reaction between buta-l,3-diene and hydrogen without, as reported previously,'* * the necessity of continuously providing hydrogen in atomic form to the gold surface.The activity of these gold catalysts is, not surprisingly, somewhat lower than that of the more conventional supported Group VIII metals such as palladium or platinum. Furthermore, the gold catalysts tend to progressively lose activity in use, the activity after around twenty reactions being approximately two orders of magnitude below the initial activity. The gold-catalysed reactions show some similarities to those observed with supported Group VIII metals and copper.13 Thus all three n-butenes are formed as initial products and the butene distribution and trans/cis ratio in but-2-ene are similar to those observed with ~1atinum.l~ However, unlike copper or the Group VIII metals, alumina-supported gold will not, under the conditions used in this study, catalyse the hydrogenation of n-butenes to butane, although it will catalyse the slow isomerisation of but-1-ene to cis- and trans-but-2-ene as shown in fig.2. This apparent lack of hydrogenation activity may be kinetic in its origin since studies of the hydrogenation of pent- 1 -ene over these catalysts, using hydrogen/hydrocarbon ratios of ca. 700, show that at 373 K both pentene hydrogenation and isomerisation occur. One of the most significant features to arise from the studies of the interaction of buta-l,3-diene with deuterium is the close relationship between the extent of deuter- ation of the products and the catalyst activity as determined from the initial rates of reaction, together with the considerable hydrogen-deuterium mass imbalance between reactants and products.Clearly, even after the extensive pretreatment in deuterium, the freshly prepared catalysts still contain a source of hydrogen which can partake in the hydrogenation reaction. Examination of the results in table 4 reveals that, with both the Au/y-alumina and the Au/alumina-A, extensive exchange occurs between catalyst hydrogen and gas- phase deuterium. Furthermore, the amounts of catalyst hydrogen are dependent upon the catalyst pretreatment temperature. Thus for Au/y-alumina the total numbers of exchangeable H-atoms per gram of catalyst following pretreatment at 523 and 673 K are 1.93 x 1021 and 5.59 x 1020 respectively. The corresponding values for Au/ alumina-A are 1.45 x 1021 and 2.08 x 1020 atoms per gram of catalyst. This effect of high temperature pretreatment suggests that the surface undergoes an irreversible change with loss of hydrogen, probably due to either dehydration or progressive dehydroxylation of the alumina surface.The results in table 3 show that the extent of deuterium incorporation in the pro- ducts was less with Au/alumina-A than with Au/y-alumina, although the initial rate of " hydrogenation " was higher with the former catalyst. In view of the prolonged catalyst pretreatment in deuterium during activation, and the lower total amount of exchangeable hydrogen on the Au/alumina-A catalyst, the results indicate that, on both catalysts, at least two types of surface hydrogen exist : type A, which undergoes equilibration with deuterium, and type B, which does not undergo ready exchange with deuterium, but which can readily partake in the hydrocarbon hydrogenation reaction.The relative amounts of type A and type B hydrogen must be different on the two catalysts such that the ratio (type A/type B) is greater on Au/y-alumina than on Au/alumina-A. Since with both catalysts the extent of deuterium incorporation in the products increases as the activity decreases, the pool of type B hydrogen must gradually become depleted and not replaced by " hydrogen " from the gas-phase.D. A. BUCHANAN AND G . WEBB 143 The magnitude of the type B pool can be estimated for each catalyst from the amounts of excess hydrogen in the products as determined from the hydrogen-deuterium mass balance between reactants and products. Using this method the respective values for Au/y-alumina and Au/alumina-A are 7.36 x 1020 atoms per gram and 2.62 x 1021 atoms per gram.With regard to the identity of the types A and B hydrogen, comparison of the results presented in table 4 with results obtained for tritium exchange of y-alumina and alumina-A at 523 K l6 suggests that the type A hydrogen may be identified with the surface hydroxyl groups on the alumina. The identity of the type B hydrogen is less clear. The occlusion of hydrogen in Group VIII metal powders,13 platinum black l7 and palladium black l8 and the reaction of occluded hydrogen with olefins is well established. However, comparison of the magnitude of the type B hydrogen pool with the gold concentration [-3 x 1019 atom (g catalyst)-l] rules out any possi- bility of the type B hydrogen being occluded in the metal.Clearly type B hydrogen is associated with the support, although its precise chemical identity is yet to be estab- lished. In view of the complete absence of activity of either the y-alumina or alumina-A for buta-l,3-diene hydrogenation, under the conditions used in the present study, the results presented above are explicable in terms of a mechanism in which buta-1,3- diene is adsorbed at the gold surface, and subsequently undergoes reaction with hydrogen atoms which migrate from the support to the metal. From the particle size distributions of the gold particles, it seems unlikely that the gold itself will contain special sites capable of activating molecular hydrogen, unless the activity resides in extremely small particles not sensed by electron microscopy.Thus the support plays a significant role in that it provides a source of atomic " hydrogen " for reaction. Such a conclusion is in agreement with the suggestions of previous workers regarding the catalytic activity of gold for hydrocarbon hydrogenation.'. The kinetics, high selectivity and the butene isomerisation activity of these catalysts is also consistent with the above conclusion, since it is envisaged that the steady state surface concentra- tion of hydrogen atoms on the metal will be very small under these conditions. The butene distributions show that, over both catalysts, the but- l-ene/but-2-ene ratio is slightly greater than unity and the cisltrans ratio in but-2-ene is around 1.5. Furthermore, the butene distribution is invariant with conversion until most of the buta- 1,3-diene has reacted. These observations together with the close similarities in the deuterium content of all three n-butenes suggest that the butenes are all formed directly from adsorbed buta-l,3-diene by a mechanism similar to that proposed by Phillipson et al. In conclusion, the results presented above show that gold when supported on y-alumina, or a mixed y-alumina-boehmite support, will catalyse the hydrogenation of buta-1,3-diene to butene, although the support plays a significant role by providing a source of atomic hydrogen to the gold surface. Further, at least two types of reactive hydrogen exist on the support, although the precise chemical identity of the various forms of support hydrogen is not established. Further investigations of the hydrogen associated with the support are at present being carried out. for the copper-catalysed reaction. The authors thank the S.R.C. for the award of a maintenance grant to one of us (D. A. B.), and for a grant to purchase the A.E.I. MS20 mass spectrometer. R. J. Mikovsky, M. Boudart and H. S. Taylor, J. Arner. Chem. Soc., 1954, 76, 3814. G. Parravano, J. Catalysis, 1970, 18, 320. * N. W. Cant and W. K. Hall, J. Phys. Chem., 1971,75,2914.144 BUTADIENE HYDROGENATION OVER Au/A1203 M. Boudart and L. D. Ptak, J. Catalysis, 1970, 16,90. D. D. Eley and D. R. Rossington, Chemisorption, ed. W. E. Garner (Butterworth, London, 1957), p. 137. R. P. Chambers and M. Boudart, J. Catalysis, 1966, 5, 517. B. J. Wood and H. Wise, J. Catalysis, 1966, 5, 135. W. M. H. Sachtler and N. H. De Boer, J. Phys. Chem., 1960,64,1579. * R. S. Yolles, B. J. Wood and H. Wise, J. Catalysis, 1971, 21, 66. lo G. Webb and J. I. Macnab, J. Catalysis, 1972, 26,226. l1 G. Webb and J. A. Altham, J. Catalysis, 1970, 18, 133. l2 J. U. Reid, S. J. Thomson and G. Webb, J. Catalysis, 1973, 29, 421 ; 1973, 30, 372. l3 P. B. Wells, Surface and Defect Properties of Solids (The Chemical Society, London, 1971), l4 G. C. Bond, G. Webb, P. B. Wells and J. M. Winterbottom, J. Chem. SOC., 1965, 3218. l5 G. C. Bond, P. A. Sermon, D. A. Buchanan, G. Webb and P. B. Wells, Chem. Comm., 1973 l 6 P. A. Sermon, G. C. Bond and G. Webb, Chem. Comm., 1974,417. vol. 1, p. 236. 444. Z. Paal and S. J. Thomson, J. CataZysis, 1973, 30,96. L. V. Babenkova, N. M. Popova, D. V. Sokol’skii and V. K. Solynserkova, Doklady Akad. Nauk S.S.S.R., 1973, 210, 888. l9 J. J. Phillipson, P. B. Wells and G. R. Wilson, J. Chem. SOC. A, 1969, 1351.

ISSN:0300-9599    

DOI:10.1039/F19757100134

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Kinetics of Reaction of Low-spin Iron@) Complexes in Aqueous Gels BY MICHAEL J. BLANDAMER," JOHN BURGESS AND JILL R. MEMBREY Department of Chemistry, The University, Leicester LEI 7RH Received 22nd May, 1974 The kinetics of the aquation of tris(5-nitro-l,lO-phenanthroline)iron(n) and of the reaction of tris(5-methyl-1 ,lo-phenanthroline)iron(n) with cyanide ion have been studied in aqueous gels and sols. Determined rate constants for these reactions in agar and gelatine-containing systems are remarkably close to those in water, indicating that much of the water in the gels is in a very similar state to that in ordinary water. Recently the role of water in biochemical systems has received a great deal of attention [see for example ref. (l)], and in this connection aqueous gels have been used as model systems in conjunction with studies of the structure and function of water in, for example, living cells [e.g.ref. (2)]. Indeed, Freundlich indicated that enzyme reactions in vivo should be discussed in the light of the chemistry of gels.3 However, before considering the very complex question of enzyme kinetics in gels, it seemed important to examine the kinetics of simpler reactions in these systems and to probe the effects of changing the reaction medium from water to sol to gel. The choice of the reaction is limited by a number of factors. First the substrate(s) must form a homogeneous system both in sol and gel states. Second, the reaction must be sufficiently fast so that the kinetic data can be obtained before appreciable syneresis occurs.Finally, the reaction must be sufficiently slow that kinetic data can be obtained after the gel has formed. Two closely related reactions were eventually found to satisfy these conditions ; (1) the aquation of tris(5-nitro-1,lO-phenanthroline) iron@) and (2) the reaction between cyanide ion and tris(5-methyl-l , 10-phenanthro- line)iron(II). EXPERIMENTAL Two gel systems were used. Agar, impure agarose, is a polysaccharide gel whereas gelatine is a protein gel. Although the detailed structures of these aqueous gels are not precisely known a clearer picture is de~eloping.~ Information concerning the state of water in aqueous gels is also a~ailable,~ particularly from n.m.r. experiment^.^ SOLUTIONS Solutions containing known concentrations of potassium sulphate, nickel sulphate, zinc sulphate and potassium cyanide (all AnalaR grade) were prepared using freshly distilled water.Stock solutions of both 5-N02 and 5-Me complexes were prepared from iron@) ammonium sulphate and a slight excess of the appropriate ligand. The solutions were prepared by adding a known weight of either gelatin or agar (B.D.H. purified grade) to a solution containing known quantities of salts and complex. The gels were prepared by dissolving the agar or gelatin in the heated salt solution, cooling this solution in ice water and then adding a known amount of solution containing the complex. Gelation occurred when the solutions contained in 10 mm spectrophotometer cells were stood in an ice/water mixture. The cells were than transferred to the thermostatted cell block of either a Unicam SPSOOA or 145146 KINETICS OF REACTION I N GELS SP1800A spectrophotometer.The time required to come to thermal equilibrium depended on the system and the temperature. The contents of the reference cell comprised a system prepared in the same way but which did not contain an iron complex. KINETICS The rate constants were calculated from the change in optical density at 510 nm, recorded at preselected time intervals. Difficulties associated with thermal equilibration of the gel systems meant that it was more convenient to monitor the reaction in one cell at a time. Consequently it proved difficult to reproduce precisely the same temperature for every system. In the summary of the data given in the tables, the stated temperature is an average over many experimental runs, the deviation being < kO.4 K.Within a given run the temperature was controlled to better than 0.1 K. Kinetic data were recorded for at least three half lives in the aquation reaction but in the substitution reaction, CN-+ 5-Me complex, the data could only be recorded for approximately two half-lives. However, in both cases, the reactions eventually went to completion. RESULTS Aquation of the tris(5-nitro- 1 , 10-phenanthroline)iron(II) cation, as of other iron@) complexes of (substituted) 1 , 10-phenanthrolines, occurs through the stepwise equi- libria (LL = 5-nitro-1,lO-phenanthroline) Fe(LL)i++Fe(LL)i+ + LL (1) Fe(LL)i+fFe(LL)2+ + LL (2) Fe(LL)2++Fe2+aq + LL. (3) The three reversible reactions (1) to (3) are forced to proceed from left to right by the addition of a reagent which reacts either with the released ligand molecules or with the aquoiron(I1) cation; the rate determining step is the loss of the first ligand molecule [eqn (1)].6 The usual reagent for promoting this type of aquation is acid, as proton- ation of the liberated phenanthroline molecules prevents their recombination with the iron, It is well established that the rate-determining ligand loss is essentially independ- ent of acid concentration.Unfortunately it is impossible to use acids in the present work as they inhibit gel formation. We therefore followed a suggestion that the presence of cations such as zinc(@ or nickel(@ in sufficient concentration led to com- plete aquation. Aquation in the presence of a large excess of one of these cations follows first-order kinetics.Table 1 shows that the rate constant of aquation of the complex in the presence of either of these cations is independent both of the nature and of the concentration of the added cation. The rate constants are close to that reported for aquation of the complex in acid solution.6 These cations can thus be used as scavengers for the released ligand molecules in the same way as acids; they do not inhibit gel formation in the concentrations used here. The kinetic results for aquation of the Fe(S-NO,-phen);+ cation in aqueous solution and gel systems are recorded in table 2. When either agar or gelatin is added to form a sol or gel system, the rate constant for aquation remains unchanged and, for the agar system at least, this behaviour has been observed over the range 298-314 K.The reaction of the 5-nitro-complex with cyanide ion is too rapid for its kinetics to be monitored under the conditions and restrictions of the present systems (cf. Experimental section). We therefore studied the kinetics of the much slower reaction of the analogous 5-methyl-complex, Fe(S-Me-phen)i+, with cyanide ion, in aqueous sol and gels. The observed first order rate constants (cyanide ion is in large excess) are reported in table 3.M. J . BLANDAMBR, J . BURGESS AND J . R . MEMBREY 147 TABLE 1.-FIRST ORDER RATE CONSTANTS, k FOR THE AQUATION OF TRIS(S-NITRO-l,lO-PHEN- ANTHROLINE)IRON(II) AT 289.0+0.3 K IN THE PRESENCE OF EITHER Ni2+ OR Zn2+ cation Ni2+ Zn2+ salt concentration/ mol dm-3 1 04kls- 1 0.2 1.90+ O.O4(3) 1.87(2) 0.1 1.97(2) 1.92+0.03(3) 0.05 C 1.93(1) 1.91(2) a number of independent measurements; b +0.133 mol dm-3 &SO4; C +0.2 mol dm-3 &So.+ TABLE 2.-FIRST ORDER RATE CONSTANTS FOR THE AQUATION OF TRIS(5-NITRO-1 ,lO-PHENAN- THROLINE)IRON(II) COMPLEX IN AQUEOUS SOL AND GEL SYSTEMS CONTAINING 0.2 mol d ~ n - ~ NiS04 OR ZnS04 temperature /K 289.1 f 0.2 300f 0.4 307.5k0.1 314.6k0.4 system rate constant, i03k/s-' aqueous solution 0.188~0.005(8) 1.12+0.2(8) 2.4+0.2(4) 4.8+0.1(6) 0.1 % agar sol 0.147+ O.OOl(4) 0.95+ 0.04(8) 2.2f 0.1(4) 4.9+ 043) 0.2 % agar gel 0.167+0.009(8) 1.0+0.2(7) 1.9*0.2(4) 4.5f0.2(4) 1.0 % gelatin sol 0.166+0.004(4) 3 % gelatin gel 0.17+0.01(8) TABLE 3 .-PSEUDO FIRST ORDER RATE CONSTANTS FOR THE REACTION BETWEEN CN- AND TRIS( 5- METHYL-1 ,lo-PHENANTHROLINE)IRON(II) IN AQUEOUS AGAR SOL AND AGAR GEL systems, CONTAINING 0.5 mol dm-3 KCN temperature/K system 308 313 rate constant, 102k/s-1 aqueous solution 0.62+ 0.04(8) 1.2+ 0.2(11) 0.1 % agar sol 0.54f 0.06(6) 1.1 -I 0.05(7) 0.2 % agar gel 0.59-I 0.05(5) 1 .O+ 0.1(8) DISCUSSION The mechanism of aquation of iron(@-phenanthroline complexes has not been unequivocally established? though all the results to date can be satisfactorily accounted for on the basis of the dissociative mechanism intuitively expected for low-spin d6 complexes of the first-row transition series.Indeed a recent determination of the activation volume (AV* = + 18 cm3 mol-l) for the aquation of Fe(5-N02-phen)i+ strongly supports a dissociative mode of activation for this reactiom8 On the other hand the rate law and activation parameters for the reactions of many low-spin iron(I1) complexes, including the Fe(S-CH,-phen)$f cation, with cyanide ion indicate that these reactions [eqn (4)] proceed predominantly by an associative? bimolecular pathway.g* lo For the specific case of the Fe(S-CH,-phen)g+ cation and the cyanide concentration we have used, the alternative dissociative reaction path makes a negligible contribution to the overall observed rate of disappearance of the tris-complex.Previous studies have shown that rates of aquation of iron@)-phenanthroline complexes usually vary significantly with solvent composition in mixed aqueous Fe(LL),2++2CN--+Fe(LL),(CN), +LL. (4)148 KINETICS OF REACTION I N GELS solvents.ll They are also sensitive to the effects of added salts, for example tetra- alkylammonium bromides,12 on the structure of solvent water.In all cases the 5- nitro-complex is the most sensitive of this class of complexes to solvent variation. Rate constants for the reaction of this type of low-spin iron@) complex with cyanide ion are also noticeably sensitive to solvent composition.lO* l3 In view of this known sensitivity of kinetic behaviour to added co-solvents and solutes, the relative insens- itivity of the rate constants to the transition soljgel is at first sight surprising. The results show that there are sufficiently large volumes of water to contain the large iron@) complex cation and the M2+aq cation or CN-aq anion in a " free solution " state, and that in these regions the structure of the water closely resembles that in the aqueous solution.To this extent, therefore, the kinetic data support the conclusion concerning the structure of these gels drawn from other experiments. In the poly- saccharide gel, the water is trapped in the interstices of a network, the strands of which are formed by aggregates of double helices.14* Derbyshire and Duff show that while part of the water is bound to the macromolecule, the remainder can be con- sidered as bulk water although the self-diffusion of water in the gel is affected by the gel network. The gelation of a protein gel appears to involve a quite different arrange- ment. 6 s l7 Gelation is a limited aggregation process, involving the contact of gelatin spheres, but only a small proportion of the water is specifically associated with the gelatin framework.We thank the S.R.C. for their support. Ann. N.Y. Acad. Sci., 1973, 204. B. D. Allan and R. L. Norman, ref. (l), p. 150. H. Freundlich, Colloid and Capillary Chemistry, trans. H. H. Hatfield (Methuen, London, 1926), p. 761. Disc. Furaday SOC., 1974, 57, in press. W. Derbyshire and I. D. Duff, ref. (4). W. W. Brandt andD. K. Gullstrom, J. Amer. Chem. SOC., 1952,74,3532; J. Burgess and R. H. Prince, J. Chem. Soc., 1963, 5752, and references therein. L. Seiden, F. Basolo and H. M. Neumann, J. Amer. Chem. SOC., 1959,81,3809. D. W. Margerum and L. P. Morgenthaler, J. Amer. Chem. SOC., 1962, 84,706. * J. Burgess, J. M. Lucie and D. R. Stranks, unpublished observations.lo J. Burgess, Inorg. Chim. Acta, 1971, 5, 133. l1 see, e.g., J. Burgess, J. Chem. SOC. A, 1968, 1085; 1969, 1899; 1970 2351; J. Burgess, F. M. l2 M. J. Blandamer, J. Burgess and S. H. Morris, J. C. S. Dalton, 1974, 1717. l3 J. Burgess, G. E. Ellis, D. J. Evans, A. Porter, R. Wane and R. D. Wyvill, J. Chem. SOC. A, l4 D. A. Rees, Ado. Carbohydrate Chem. Biochem., 1969,24,267. l5 D. S. Reid, T. A. Bryce, A. H. Clark and D. A. Rees, ref. (4). l6 M. P. Tombs, ref. (4). I'D. Eagland, G. Pilling, A. Suggett and R. G. Wheeler, ref. (4). Mekhail and E. R. Gardner, J. C. S. Dalton, 1973, 1335. 1971,44. Kinetics of Reaction of Low-spin Iron@) Complexes in Aqueous Gels BY MICHAEL J. BLANDAMER," JOHN BURGESS AND JILL R. MEMBREY Department of Chemistry, The University, Leicester LEI 7RH Received 22nd May, 1974 The kinetics of the aquation of tris(5-nitro-l,lO-phenanthroline)iron(n) and of the reaction of tris(5-methyl-1 ,lo-phenanthroline)iron(n) with cyanide ion have been studied in aqueous gels and sols.Determined rate constants for these reactions in agar and gelatine-containing systems are remarkably close to those in water, indicating that much of the water in the gels is in a very similar state to that in ordinary water. Recently the role of water in biochemical systems has received a great deal of attention [see for example ref. (l)], and in this connection aqueous gels have been used as model systems in conjunction with studies of the structure and function of water in, for example, living cells [e.g.ref. (2)]. Indeed, Freundlich indicated that enzyme reactions in vivo should be discussed in the light of the chemistry of gels.3 However, before considering the very complex question of enzyme kinetics in gels, it seemed important to examine the kinetics of simpler reactions in these systems and to probe the effects of changing the reaction medium from water to sol to gel. The choice of the reaction is limited by a number of factors. First the substrate(s) must form a homogeneous system both in sol and gel states. Second, the reaction must be sufficiently fast so that the kinetic data can be obtained before appreciable syneresis occurs. Finally, the reaction must be sufficiently slow that kinetic data can be obtained after the gel has formed. Two closely related reactions were eventually found to satisfy these conditions ; (1) the aquation of tris(5-nitro-1,lO-phenanthroline) iron@) and (2) the reaction between cyanide ion and tris(5-methyl-l , 10-phenanthro- line)iron(II).EXPERIMENTAL Two gel systems were used. Agar, impure agarose, is a polysaccharide gel whereas gelatine is a protein gel. Although the detailed structures of these aqueous gels are not precisely known a clearer picture is de~eloping.~ Information concerning the state of water in aqueous gels is also a~ailable,~ particularly from n.m.r. experiment^.^ SOLUTIONS Solutions containing known concentrations of potassium sulphate, nickel sulphate, zinc sulphate and potassium cyanide (all AnalaR grade) were prepared using freshly distilled water.Stock solutions of both 5-N02 and 5-Me complexes were prepared from iron@) ammonium sulphate and a slight excess of the appropriate ligand. The solutions were prepared by adding a known weight of either gelatin or agar (B.D.H. purified grade) to a solution containing known quantities of salts and complex. The gels were prepared by dissolving the agar or gelatin in the heated salt solution, cooling this solution in ice water and then adding a known amount of solution containing the complex. Gelation occurred when the solutions contained in 10 mm spectrophotometer cells were stood in an ice/water mixture. The cells were than transferred to the thermostatted cell block of either a Unicam SPSOOA or 145146 KINETICS OF REACTION I N GELS SP1800A spectrophotometer.The time required to come to thermal equilibrium depended on the system and the temperature. The contents of the reference cell comprised a system prepared in the same way but which did not contain an iron complex. KINETICS The rate constants were calculated from the change in optical density at 510 nm, recorded at preselected time intervals. Difficulties associated with thermal equilibration of the gel systems meant that it was more convenient to monitor the reaction in one cell at a time. Consequently it proved difficult to reproduce precisely the same temperature for every system. In the summary of the data given in the tables, the stated temperature is an average over many experimental runs, the deviation being < kO.4 K. Within a given run the temperature was controlled to better than 0.1 K.Kinetic data were recorded for at least three half lives in the aquation reaction but in the substitution reaction, CN-+ 5-Me complex, the data could only be recorded for approximately two half-lives. However, in both cases, the reactions eventually went to completion. RESULTS Aquation of the tris(5-nitro- 1 , 10-phenanthroline)iron(II) cation, as of other iron@) complexes of (substituted) 1 , 10-phenanthrolines, occurs through the stepwise equi- libria (LL = 5-nitro-1,lO-phenanthroline) Fe(LL)i++Fe(LL)i+ + LL (1) Fe(LL)i+fFe(LL)2+ + LL (2) Fe(LL)2++Fe2+aq + LL. (3) The three reversible reactions (1) to (3) are forced to proceed from left to right by the addition of a reagent which reacts either with the released ligand molecules or with the aquoiron(I1) cation; the rate determining step is the loss of the first ligand molecule [eqn (1)].6 The usual reagent for promoting this type of aquation is acid, as proton- ation of the liberated phenanthroline molecules prevents their recombination with the iron, It is well established that the rate-determining ligand loss is essentially independ- ent of acid concentration.Unfortunately it is impossible to use acids in the present work as they inhibit gel formation. We therefore followed a suggestion that the presence of cations such as zinc(@ or nickel(@ in sufficient concentration led to com- plete aquation. Aquation in the presence of a large excess of one of these cations follows first-order kinetics. Table 1 shows that the rate constant of aquation of the complex in the presence of either of these cations is independent both of the nature and of the concentration of the added cation. The rate constants are close to that reported for aquation of the complex in acid solution.6 These cations can thus be used as scavengers for the released ligand molecules in the same way as acids; they do not inhibit gel formation in the concentrations used here.The kinetic results for aquation of the Fe(S-NO,-phen);+ cation in aqueous solution and gel systems are recorded in table 2. When either agar or gelatin is added to form a sol or gel system, the rate constant for aquation remains unchanged and, for the agar system at least, this behaviour has been observed over the range 298-314 K. The reaction of the 5-nitro-complex with cyanide ion is too rapid for its kinetics to be monitored under the conditions and restrictions of the present systems (cf.Experimental section). We therefore studied the kinetics of the much slower reaction of the analogous 5-methyl-complex, Fe(S-Me-phen)i+, with cyanide ion, in aqueous sol and gels. The observed first order rate constants (cyanide ion is in large excess) are reported in table 3.M. J . BLANDAMBR, J . BURGESS AND J . R . MEMBREY 147 TABLE 1.-FIRST ORDER RATE CONSTANTS, k FOR THE AQUATION OF TRIS(S-NITRO-l,lO-PHEN- ANTHROLINE)IRON(II) AT 289.0+0.3 K IN THE PRESENCE OF EITHER Ni2+ OR Zn2+ cation Ni2+ Zn2+ salt concentration/ mol dm-3 1 04kls- 1 0.2 1.90+ O.O4(3) 1.87(2) 0.1 1.97(2) 1.92+0.03(3) 0.05 C 1.93(1) 1.91(2) a number of independent measurements; b +0.133 mol dm-3 &SO4; C +0.2 mol dm-3 &So.+ TABLE 2.-FIRST ORDER RATE CONSTANTS FOR THE AQUATION OF TRIS(5-NITRO-1 ,lO-PHENAN- THROLINE)IRON(II) COMPLEX IN AQUEOUS SOL AND GEL SYSTEMS CONTAINING 0.2 mol d ~ n - ~ NiS04 OR ZnS04 temperature /K 289.1 f 0.2 300f 0.4 307.5k0.1 314.6k0.4 system rate constant, i03k/s-' aqueous solution 0.188~0.005(8) 1.12+0.2(8) 2.4+0.2(4) 4.8+0.1(6) 0.1 % agar sol 0.147+ O.OOl(4) 0.95+ 0.04(8) 2.2f 0.1(4) 4.9+ 043) 0.2 % agar gel 0.167+0.009(8) 1.0+0.2(7) 1.9*0.2(4) 4.5f0.2(4) 1.0 % gelatin sol 0.166+0.004(4) 3 % gelatin gel 0.17+0.01(8) TABLE 3 .-PSEUDO FIRST ORDER RATE CONSTANTS FOR THE REACTION BETWEEN CN- AND TRIS( 5- METHYL-1 ,lo-PHENANTHROLINE)IRON(II) IN AQUEOUS AGAR SOL AND AGAR GEL systems, CONTAINING 0.5 mol dm-3 KCN temperature/K system 308 313 rate constant, 102k/s-1 aqueous solution 0.62+ 0.04(8) 1.2+ 0.2(11) 0.1 % agar sol 0.54f 0.06(6) 1.1 -I 0.05(7) 0.2 % agar gel 0.59-I 0.05(5) 1 .O+ 0.1(8) DISCUSSION The mechanism of aquation of iron(@-phenanthroline complexes has not been unequivocally established? though all the results to date can be satisfactorily accounted for on the basis of the dissociative mechanism intuitively expected for low-spin d6 complexes of the first-row transition series.Indeed a recent determination of the activation volume (AV* = + 18 cm3 mol-l) for the aquation of Fe(5-N02-phen)i+ strongly supports a dissociative mode of activation for this reactiom8 On the other hand the rate law and activation parameters for the reactions of many low-spin iron(I1) complexes, including the Fe(S-CH,-phen)$f cation, with cyanide ion indicate that these reactions [eqn (4)] proceed predominantly by an associative? bimolecular pathway.g* lo For the specific case of the Fe(S-CH,-phen)g+ cation and the cyanide concentration we have used, the alternative dissociative reaction path makes a negligible contribution to the overall observed rate of disappearance of the tris-complex.Previous studies have shown that rates of aquation of iron@)-phenanthroline complexes usually vary significantly with solvent composition in mixed aqueous Fe(LL),2++2CN--+Fe(LL),(CN), +LL. (4)148 KINETICS OF REACTION I N GELS solvents.ll They are also sensitive to the effects of added salts, for example tetra- alkylammonium bromides,12 on the structure of solvent water.In all cases the 5- nitro-complex is the most sensitive of this class of complexes to solvent variation. Rate constants for the reaction of this type of low-spin iron@) complex with cyanide ion are also noticeably sensitive to solvent composition.lO* l3 In view of this known sensitivity of kinetic behaviour to added co-solvents and solutes, the relative insens- itivity of the rate constants to the transition soljgel is at first sight surprising. The results show that there are sufficiently large volumes of water to contain the large iron@) complex cation and the M2+aq cation or CN-aq anion in a " free solution " state, and that in these regions the structure of the water closely resembles that in the aqueous solution.To this extent, therefore, the kinetic data support the conclusion concerning the structure of these gels drawn from other experiments. In the poly- saccharide gel, the water is trapped in the interstices of a network, the strands of which are formed by aggregates of double helices.14* Derbyshire and Duff show that while part of the water is bound to the macromolecule, the remainder can be con- sidered as bulk water although the self-diffusion of water in the gel is affected by the gel network. The gelation of a protein gel appears to involve a quite different arrange- ment. 6 s l7 Gelation is a limited aggregation process, involving the contact of gelatin spheres, but only a small proportion of the water is specifically associated with the gelatin framework. We thank the S.R.C. for their support. Ann. N.Y. Acad. Sci., 1973, 204. B. D. Allan and R. L. Norman, ref. (l), p. 150. H. Freundlich, Colloid and Capillary Chemistry, trans. H. H. Hatfield (Methuen, London, 1926), p. 761. Disc. Furaday SOC., 1974, 57, in press. W. Derbyshire and I. D. Duff, ref. (4). W. W. Brandt andD. K. Gullstrom, J. Amer. Chem. SOC., 1952,74,3532; J. Burgess and R. H. Prince, J. Chem. Soc., 1963, 5752, and references therein. L. Seiden, F. Basolo and H. M. Neumann, J. Amer. Chem. SOC., 1959,81,3809. D. W. Margerum and L. P. Morgenthaler, J. Amer. Chem. SOC., 1962, 84,706. * J. Burgess, J. M. Lucie and D. R. Stranks, unpublished observations. lo J. Burgess, Inorg. Chim. Acta, 1971, 5, 133. l1 see, e.g., J. Burgess, J. Chem. SOC. A, 1968, 1085; 1969, 1899; 1970 2351; J. Burgess, F. M. l2 M. J. Blandamer, J. Burgess and S. H. Morris, J. C. S. Dalton, 1974, 1717. l3 J. Burgess, G. E. Ellis, D. J. Evans, A. Porter, R. Wane and R. D. Wyvill, J. Chem. SOC. A, l4 D. A. Rees, Ado. Carbohydrate Chem. Biochem., 1969,24,267. l5 D. S. Reid, T. A. Bryce, A. H. Clark and D. A. Rees, ref. (4). l6 M. P. Tombs, ref. (4). I'D. Eagland, G. Pilling, A. Suggett and R. G. Wheeler, ref. (4). Mekhail and E. R. Gardner, J. C. S. Dalton, 1973, 1335. 1971,44.

ISSN:0300-9599    

DOI:10.1039/F19757100145

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Mass-spectrometric Tracer and Photometric Studies of Catalysed Radical Recombination in Flames BY DAVID E. JENSEN" AND GEORGE A. JONES Rocket Propulsion Establishment, Westcott, Aylesbury, Buckinghamshire Received 31st May, 1974 Measurements of hydrogen atom concentrations in H2 + O2 + N2 flames with and without additives have been made by a mass-spectrometric tracer method dependent upon the reaction being balanced and by a well established photometric method dependent upon balance of the analogous reaction Results from the two methods agree well. Catalysis of flame radical recombination caused by addition of tin, molybdenum and tungsten is described. Mass-spectrometric results for tin are in good agreement with previous photometric measurements. Results for molybdenum and tungsten from both methods are quantitatively interpreted in terms of a cyclic homogeneous gas phase mechanism, with associated thermochemistry and reaction rate coefficients.Sr+ + H20 + SrOH+ + H, K = 47 exp( - 7 700 KIT), Li+ H20 + LiOH+H, K = 16 exp(- 10 O00 K/T). Recent work has shown that small quantities of various metal-containing additives can cause significant catalysis of recombination of the H, OH and 0 radicals generally present in above-equilibrium concentrations in H2 + 0, + N, flames. This work involved measurement of [HI by the well established Li/Na photometric m e t h ~ d . ~ In this method, known trace quantities (too small to perturb the flame properties significantly themselves) of lithium and sodium are added in turn to a flame and [Li] is measured via comparison of the Li first resonance doublet emission intensities or absorptions with those of the corresponding Na doublet.[HI is then calculated on the basis of the reasonable assumptions that the reaction is balanced,6* that lithium forms significant concentrations of Li and LiOH alone and that sodium exists largely as free atoms in the flame. (A reaction A+B + C + D is said to be " balanced " or " in equilibrium " when ([C][D])/([A][B]) is equal to the equilibrium constant for the reaction.) Under certain conditions, however (e.g. in fuel-lean flames where peroxide formation may occur,* in practical flames with interfering optical frequency radiation, or where additives form stable compounds with lithium and/or sodium) an alternative method is needed.Hayhurst and Kittel- son have suggested that a reaction analogous to (l), Sr+ + H20 + SrOH+ + H, Li + H 2 0 + LiOH + H (equilibrium constant K l ) (1) (2) balanced in a flame to which trace quantities of strontium are supplied, affords such an alternative if [SrOH+]/[Sr+] can be measured via mass-spectrometric sampling and K2 is known. The present paper describes application of both these methods to investigation of radical recombination catalysis in H2 + O2 + N2 flames caused by addition of tin, molybdenum and tungsten-containing compounds. The good agreement between results from the two methods supports the suggestion that the mass-spectrometric tracer method provides a useful means of studying radical 149150 RADICALS I N FLAMES recombination in flames and strengthens confidence in the quantitative data for the observed catalytic effects. The two methods of measuring [HI require knowledge of the equilibrium constants Kl and K2 as functions of temperature.On the basis of data from several sources, Kelly and Padley lo recommend a value for the standard zero-point enthalpy change AH; for Li(g)+OH(g) + LiOH(g) of 433 +8 kJ mol-l, in good agreement with another recommendation by Zeegers and A1kemade.l Vibration frequencies for the (assumed linear) LiOH molecule have been estimated lo as 66.5 (Li-0 stretch), 35.0 (bending mode) and 360.0 (0-H stretch) mm-l respectively, and the molecular moment of inertia ILioH estimated l2 to be 2 . 2 ~ kgm2. Together with other data, taken from the JANAF TabZes,13 this gives a recommended value Kl = 16 exp { - (10 OW_+ 1000 K ) / T ) for 1500 < T < 3000 K.K2 is less accurately known. If SrOH+ is assumed, by analogy with the iso- electronic RbOH,12 to be linear, having vibration frequencies v1 at 35.5 mm-’, v2 (doubly degenerate mode) at 31.0 mm-l and v3 at 360.0 mm-l and ISrOH+ = 1.35 x kg m2, the photometric measurements of Schofield and Sugden l4 may be interpreted to give AH;,2 = +74+40 kJ mol-l. The microwave measurements of Jensen,15 combined with Cotton and Jenkins’ value l6 for the bond energy of Sr-OH, lead to = + 52 35 kJ mol-I. After corrections for departures from equilibrium in the reaction 15* l7 Kelly and Padley’s electrostatic probe measurements l8 yield = + 38 f 35 kJ mol-l. Hayhurst and K i t t e l ~ o n , ~ ~ from mass-spectrometric experiments, find what is probably the most reliablevalue of = +40+ 10 kJ mol-l, although uncertainties caused by lack of knowledge concerning the chemical reactions occurring in the viscous flow field inside their sampling nozzle remain. A realistic best estimate of AH& would be +40+ 15 kJ mol-l, which, in combination withJANAFtabulations lS and the above data for SrOH+, yields K, = 47 exp(( - 7 700 5-2 000 K)/T).Sr + OH + SrOH+ + e-, (3) EXPERIMENTAL The burner, additive system and optical technique used were similar to those described previou~ly.~~~ 2o The flames were atmospheric-pressure, laminar, cylindrical, shielded, fuel-rich H2 + O2 + N2 flames in which distance downstream of the primary reaction zones was a measure of the reaction time available for recombination of the radicals produced in above-equilibrium amounts in these zones.Principal composition features, flow rates and temperatures are given in table 1. Tin was added to the flames as Sn(CH& and molybdenum and tungsten as hexacarbonyls, all in the form of vapours from an exponential decay reser- voir 21 at concentrations given by 5x 10l2 < [Melt < 5x 1014 molecule CM-~, where [Melt = ~i[Si] ; [Sj] is the concentration of the ith metal-containing species in the flame, which itself contains si atoms of metal per molecule. Lithium, sodium and strontium were added in known trace amounts (- 1 part in lo7) as salt solutions from a calibrated atomiser.lg Tests analogous to those described in ref. (19) confirmed the absence of significant quantities of condensed particles in the flames for all the additives.Hydroxyl radical concentrations were calculated from measured [HI on the assumption that the reaction is balanced. The mass spectrometer and sampling system used were similar to those described by Hayhurst, Mitchell and Telford.22 The ratio of mass spectrometer ion currents iSrOH+ /isr+ was measured with an ion multiplier, both currents being corrected for small proportions of ion h y d r a t i ~ n . ~ ~ 23 If the flame chemistry were unperturbed by the sampling process, one 1 1 H+H2O + OH+H2 (4)TABLE 1 .-FLAME TEMPERATURES AND COMPOSITIONS [HzOl/ [HzII LHlesl [HI3 om/ om/ reaction time flame unburned molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 T/K (3 cm)/ms H2/N2/02 3.3/4.0/1 .O 5.0/3.0/1.0 4.5/3.5/1.0 4.0/4.0/1 .O 3.5/4.5 /I .O 3.2/4.8/1.0 3.0/5.0/1.0 4.0/5.0/1.0 3.5/6.0/1.0 9.3 x 1017 8 .9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 6 ~ 1017 8 . 6 ~ 1017 6.1 x 1017 9 . o ~ 1017 5 . 4 ~ 1017 4 . 5 ~ 1017 6 . 4 ~ 1017 1 . 4 ~ 10l8 1.1 x l0l8 6 . 8 ~ 1017 8 . 6 ~ 1017 6.1 x 1015 4 . 6 ~ 1015 4.1 x 1015 3.7 x 1015 3 . 2 ~ 1015 2 . 9 ~ 1015 2 . 6 ~ 1015 1 . 4 ~ 1015 5.8 x 1014 1.ox 10l6 1 . 6 ~ 10l6 1 . 4 ~ 10l6 1.2 x 10l6 1.ox 10l6 8 . 5 ~ 1015 7 . 4 ~ 1015 1.1 x 1OI6 1.ox 10l6 2 . 0 ~ 1015 1.1 x 1015 1.2 x 1015 1.3 x 1015 1 . 4 ~ 1015 1 . 5 ~ 1015 1 . 6 ~ 1015 9.1 x 1014 8 . 9 ~ 1014 2150 2035 2035 203 5 2035 2035 2035 1900 1800 1.09 1.05 1.05 1.05 1.05 1.05 1.05 1 .oo 1 .oo [H]es and [HI3 cm are hydrogen atom concentrations at equilibrium and at 3 cm downstream of the reaction zone, respectively.Na D-line reversal temperature of the burned gases. [HJ, [H,O] and [Nz] are essentially independent of distance downstream. T/K is the measured152 RADICALS IN FLAMES could calculate [HI from the relationship iSrOH+/iSr+ = 47 exp(-7 700 K / T ) [H,O]/[H], where T is the flame temperature. Because chemical reactions do occur in the sampling cone,23 however, a careful analysis of the viscous (Reynolds number R! 100) flow in this nozzle would be required to make the mass-spectrometric tracer method of measuring [HI accurate and independent of all calibrations. In the present work, where the main require- ment is accurate knowledge of relative [HI, is^^ + /isr + was simply used as a measure of this quantity for flames with and without additives.Results like those shown in fig. 1, where the current ratio is shown to vary linearly with [HI-' as measured by the photometric method in the absence of a catalysing additive, confirm the validity of this approach. I I I I I 2 4 6 8 10 I2 14 1017[H]-1/cm3 molecule-1 [[Sr], = 3 x 10l1 molecule ~ m - ~ . No catalyst present. [HI-' from photometricImeasurements. FIG. 1.-Variation of mass spectrometer ion current ratio (iSflH+/iSr+) with [Hl-l for flame 4. Overall, either the photometric or the mass-spectrometric tracer method yields relative [HI for a set of flames like that employed in this work accurate to within &lo %. The uncertainty in absolute [HI from the photometric method stems chiefly from uncertainties in Kl and is probably about +50 %, smaller than would be suggested by the stated error bounds on AH& because the latter take account of possible errors in statistical data used to derive AH$,l from the experimentally-measured K I .The uncertainty in absolute [HI from the mass-spectrometric method is probably about a factor of 2, smaller again than might be expected from the uncertainty bounds assigned to AH&2 because errors incurred when i S r O ~ + / i s r + for any flame are converted to absolute [HI are likely to compensate, at east in part, for those in K2. RESULTS AND DISCUSSION TIN Fig. 2 shows typical plots of [HI-', measured by the mass-spectrometric method, against time for flame 8 (1900 IS) with and without added tin.In the absence of additive, recombination of radicals proceeds via the relatively slow three-body reactions H+H+M + Hz+M ( 5 )D. E . JENSEN AND G . A. JONES 153 and where the collision partner M is usually H20, H2 or N2. The rate of decay of [HI when [HI is well above equilibrium is then given by where a = K4[H20]/[H2] and k5 and k6 are rate coefficients for composite M. The uncatalysed recombination rates in the flames of this work are nicely described by k5 = 2 x K/T and k6 = 1.6 x K/T cm6 s-', with K4 = 4.4 exp( - 7 530 K/T).I3 In the presence of tin, the decay of [HI with time in different flames for the range of values of [Sn], tried was found to fit the expression in agreement with the photometric observations of Bulewicz and Padley.2* Values of k , were obtained from plots like those of fig.2. The agreement between these and OH+H+M H,O+M, (6) - d[H]/dt = 2(k5 + ak6)( 1 + a)-'[M][HI2, (7) -d[H]/dt = 2(k,[M]+ak6[M] +k,[Sn],)(l +a)-'[HI2, (8) I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 2.-Catalysis of hydrogen atom decay by tin. [HI measured by the mass-spectrometric method. the photometric values,2* although the trend with temperature is opposite in the two cases, as illustrated in table 2, is reasonably encouraging in the light of the fact that the results become less reliable as the flame temperature increases and radical concentrations approach equilibrium levels. suggest the following reaction scheme to explain the essential features of the catalytic effect : Temperature = 1900 K.(A) no tin added ; (B) [Sn], = 2 x 1014 molecule ~ r n - ~ . Bulewicz and Padley 2* SnO( l2) + H(2S)( + M) + SnOH*(A)( + M) (9) SnOH*(A) -+ SnOH*(B) (10 ( 1 1) SnOH*(B) + H(2S) --+ SnO( 'Z) + H2(12).154 RADICALS I N FLAMES TABLE 2.-RATE COEFFICIENTS FOR THE EMPIRICAL REACTION H+ H+ SnO + H2 + SnO temperature/K 1800 1860 1900 2010 2035 21 50 21 80 2330 1028 x rate coefficient/cms molecule-2 s-1 ref. (2) present work They do not, however, attempt to assign thermochemical properties to SnOH*(A) and SnOH*(B) and to fit such a scheme quantitatively to the results. Their interpretation thus remains tentative, especially in view of the absence of quantitative thermo- chemical data for Sn(OH), (the dihydroxides of Ca, Sr, Ba and Fe appear to play important parts in catalysis effects for these metals l* 4, and the dangers attached to assuming that certain reactions in a cyclic mechanism are balanced whilst others remain ~nbalanced.~ Until further work, probably on fuel-lean flames, clarifies the picture, effects of tin on free radical concentrations in fuel-rich flames may be adequately described in terms of the empirical reaction with k12 w 4 x H+H+SnO -P H2+Sn0, (12) cm6 molecule-2 s-l, where [SnO] w [Sn], for these flames., MOLYBDENUM The catalytic effect of molybdenum on free radical recombination is illustrated in fig.3, where [H]-l measured by both the mass-spectrometric tracer and the photo- metric method is shown as a function of time for flames 1 and 8. Lines 1 and 3 in this figure correspond to a total mole fraction of added molybdenum of approxi- mately whilst lines 2 and 4 represent results obtained in the absence of molybdenum.Agreement between results from the two methods is again good. In all the flames of table 1, the rate of catalysed recombination was found to be directly proportional to [Mo],, a feature consistent with homogeneous catalysis. Because the observed decreases in [HI and [OH] caused by addition of molybdenum are generally much greater than [Mo],, any interpretation of the effects of molybdenum on radical recombination must be based on a cyclic reaction sequence involving the regeneration of participating Mo-containing species. Calculations based on thermo- chemical data given in ref. (13) suggest that [MOO,] and [H2Mo04] contribute significantly to [Mo], but that other molybdenum-containing species for which data are available are present in concentrations too low for them to play significant parts in a catalytic cycle. It is therefore necessary to invoke the participation in the cycle of a molecule for which thermochemical data are currently unavailable.By analogy with the species involved in catalytic cycles based on such other metals as calcium [CaO, CaOH, Ca(OH),] and iron [FeO, FeOH and Fe(OH),], it is reasonable to suggest as a working hypothesis that HMoO, should participate, together with MOO, and H,Mo04, in a cycle for molybdenum. A likely catalytic cycle would then consist of the reactions HMoO, + H + MOO, + H2, (1 3) MOO, +H20 4 H2Mo0, (14)D. E . JENSEN AND G. A . JONES 155 and H2Mo0, + H + HMoO, + HzO.(1 5 ) To test this hypothesis, estimated data for HMoO, are required. By analogy with JANAF data,' the following set of vibration frequencies (as wavenumbers) seems reasonable: 80.0, 100.0, 95.0, 30.0, 35.0, 25.0, 150.0, 60.0 and 10.0mm-l. So also does a value of 7.5 x kg3 m6 for the product of the three principal molecular moments of inertia. With a symmetry number for HMoO, of 3, an electronic partition function for this molecule taken to be the same as that for MOO, and an energy for the HO-Mo0,H bond of 456 kJ rnol-l, these give a value for KI3 of 0.04 exp(l9 600 K/T) and a corresponding value for K15 of 0.24 exp(83 50 K/T). These values are consistent with the recent data of Farber and S r i v a s t a ~ a , ~ ~ obtained from mass-spectrometer studies on oxygen-rich flames containing molybdenum, inasmuch as they imply that HMoO, would be present in such flames in quantities too low to be detected.I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 3.-Catalysis of hydrogen atom decay by molybdenum. Points represent experimental measurements made between 7.5 and 40 min above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) Temperature = 2150 K, [Molt = 4.2 x 1013 molecule ~ m - ~ ; (2) T = 2150 K, [Molt = 0 ; (3) T = 1900 K, [Molt = 4.0 x loi3 molecule ~ r n - ~ ; (4) T = 1900 K, [MO]~ = 0 ; lines drawn are computed plots. With the method of ref. (4) and the computer program of ref. (25), it was found that the cycle consisting of reactions (13)-(15) provides computed lines giving an excellent fit to the experimental observations of temperature (fig.3) and composition (fig. 4) dependences when kI3 = 1.1 x exp(- 1 400 KIT), k14 = 1 x lo-', and k , , = 1.4 x lo-" exp( -300 K/T) cm3 molecule-1 s-l. All these rate coefficients appear reasonable. A number of alternative cycles involving HMoO, and HMoO,156 RADICALS IN FLAMES (observations of HMoO;; in flames similar to those of the present work 26 suggest that the radical HMoO, might be present in significant concentrations) was developed along the lines described in ref. (4), and attempts were made to fit these to the experi- mental measurements. No alternative cycle could be fitted to the data without an unreasonably high rate coefficient being assigned to at least one of the reactions involved.It is reasonable to rule out cycles including reactions of 0 and O2 on the basis that such reactions are likely to be too slow to contribute significantly at the low concentrations of these species in the fuel-rich flames. The interpretation based on reactions (13)-(15) is thus the only one found to account adequately for the experimental results. h I I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 4.-Composition dependence (flames 2-7) for molybdenum catalysis. [MO]~ = 4.1 x 1013 molecule ~ m - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above reaction zones. Lines drawn are computed plots. Typical rates of reactions (1 3)-( 15) under experimental conditions are given in table 3.Reaction (13) is seen to be the reaction furthest from equilibrium in the sense that ([Mo03][H,])/([HMo03][H]K13) is far from unity, but neither reaction (14) nor reaction (15) is quite balanced. It is difficult to assign probable uncertainty bounds to the rate coefficients given, partly because of the uncertainties in absolute [HI of about +50 % mentioned above and partly as a result of the uncertainties in the estimated thermochemical data for HMoO,. A series of calculations in which individual rate coefficients for reactions in the cycle were varied, separately and together, showed that changing k I 3 by a factor of 2 from the values of table 3 causedTABLE 3 .-MOLYBDENUM REACTION MECHANISM, RATE COEFFICIENTS AND RATES reaction rate coefficient rate difference reverse forward reverse forward 5.H+H+M + H2+M 2 x 10-30 K/T 2.8 x exp( - 52 650 K/T) 5.07 x 1017 8.75 x 1015 4.98 x 1017 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( - 60 180 K/T) 3.39 x 1OI8 5.63 x 10l6 3.34 x 10" 4. H20+H + H2+0H 1 . 6 ~ 10-'oexp(-10 130K/T) 3 . 6 ~ 10-l' exp(-2600K/T) 7.38 x lo2' 7.38 x 1021 2.31 x loi8 13. HMoO,+H + MOO,+H, 1.1 x 10-10exp(-1400K/T) 3 x 10-9exp(-21 000K/T) 3 . 9 0 ~ 10I8 1 . 0 2 ~ 1 0 ~ ~ 3 . 8 0 ~ 1 0 ~ ~ 14. MOO3+H20 + H2M004 1 x 10-l1 2.3 x 1011 exp(-24 700 K/T) 1 . 9 2 ~ lOI9 1 . 5 4 ~ loi9 3 . 7 9 ~ 10l8 15. H2Mo04+H + HMo0,+H20 1 . 4 ~ 10-lo exp(-300 K/T) 6 x 10-lo exp( - 8650 K/T) 4.02 x 1019 3.64 x 1019 3.75 x 1018 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2M004, 4.7 x 10l2 ; Moo3, 3.1 x 1013 ; HMo03, 3.8 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10l6 ; OH, 2.3 x 1015 ; H2, 8.6 x 1017 ; M, 3.9 x lo1*.The results are insensitive to the precise values of initial concentrations for the Mo-containing species. react ion TABLE 4.-TUNGSTEN REACTION MECHANISM, RATE COEFFICIENTS AND RATES rate coefficient rate forward reverse reverse difference forward 5. H+H+M +H2+M 2 x 10-30 KIT 2.8 x lo-' exp( - 52 650 K/T) 7.48 x 1017 8.74 x lo1' 7.40 x l O I 7 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( -60 180 K/T) 5.02 x 10I8 5.62 x 10l6 4.96 x 10l8 4. H20+H + OHfH2 1.6 x lo-'' exp(- 10 130 K/T) 3.6 x lo-" exp( -2600 K/T) 8.97 x lo2' 8.97 x 10'' 3.92 x 10I8 16. HW03 + H + W03 I- H2 1.1 x lO-'O exp(-lOOO K/T) 3 x lo-' exp( - 10 040 K/T) 2.25 x 10l8 3.54 x 1017 1.90 x 10l8 17.WOJ+H~O + H2W04 1 x 10-'O 5 x 10l2 exp(-38 600 K / T ) 2.08 x 10l8 1.83 x lo1' 1 . 9 0 ~ 10l8 18. HzW04+H + HW03+HzO 5.82 x lo1' 5.63 x lo1' 1.88 x 10l8 3 x 10-Io exp( - lo00 K/T) 6 x 10-lo exp( - 6010 K/T) 0 5 v1 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2W04, W03, HWO3, 9 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10I6 ; OH, 2.3 x 1015 ; H2, 8 . 6 ~ 1017 ; M, 3.9 x 10l8. The results are insensitive to the precise values of initial concentretions for the W-containing species.158 RADICALS IN FLAMES significant discrepancy between computations and experiment, whatever efforts were made to compensate by changing other rate coefficients.Similarly, changing kI4 and k15 by a factor of 5 resulted in significant discrepancies. Overall, it is reasonable to assign to k13, k14 and k15 rough uncertainty factors of 5, 10 and 10 respectively. TUNGSTEN Mass-spectrometric tracer and photometric values of [Hl-l are shown as functions of time for flames 1 and 8 with and without added tungsten in fig. 5. The significant catalytic effect of tungsten on radical recombination is apparent in this figure, even for a mole fraction of added metal as low as In a manner entirely analogous to that described above for molybdenum, the computer program 2 5 was used to show that the experimental results could be fitted to the catalytic cycle consisting of the reactions HW03 +H -+ W03 +H2, (16) W03 +H20 -+ H2W04 (17) and H2W04+H + HWO,+H,O (18) when k16 = 1.1 x 10-lo exp(- 1000 K/T), kl, = 1 x 10-lo and k18 = 3 x 10-lo exp( - 1000 K/T) cm3 molecule-I s-l.All these values appear reasonable. They rest again upon estimates of thermochemical data for the intermediate radical HW03, which in conjunction with JANAF data l 3 for H, H2, H20, W03 and H2W04 give rise to K16 = 0.04 exp(9 000 K / T ) and K18 = 0.5 exp(5 000 K/T). No other cycle (for HW03 or HWO,) was found that fitted the experimental temperature and 16 14 12 I0 8 6 I I I I I 1 I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 5.-Catalysis of hydrogen atom decay by tungsten. Points represent experimental measure- ments made between 7.5 and 40 mm above reaction zones.Open points, photometric method ; filled points, mass-spectrometric method. (1) T = 2150 K, [WIG = 2.9 x l O I 3 molecule ~ r n - ~ ; (2) T = 2150K, [WJc = 0; (3) T = 1900K, [WJc = 2 . 7 ~ 1013 molecule ~ m - ~ ; (4) T = 1900K, Iw], = 0. Lines drawn are computed plots.D. E. JENSEN AND G. A. JONES 159 composition dependences of the catalytic effect with reasonable rate coefficients for reactions included. Examples of how well the cycle consisting of reactions (1 6)-( 18) fits the experimental data are shown in fig. 5 (temperature dependence) and fig. 6 (composition dependence). 2 0 "i 2i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 6.-Composition dependence (flames 2-7) for tungsten catalysis. [W], = 2.8 x loi3 molecule ~ r n - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above the reaction zones.Lines drawn are computed plots. Typical rates of the reactions (1 6)-( 18) under experimental conditions are given in table 4. Reaction (17), as well as reaction (16), is well away from equilibrium, although reaction (18) is not far from balance. There is thus a significant kinetic difference between tungsten and molybdenum mechanisms which manifests itself in different composition dependences of catalytic effect for the two metals. An analysis of the effects of varying kI6, kI7 and kI8 upon computed [H]/time profiles, similar to that described for molybdenum above, suggests that rough uncertainty factors of 5 , 5 and 10 respectively may reasonably be assigned to these rate coefficients.CONCLUSIONS The good agreement between sets of results obtained by the two methods of determining [HI supports the suggestion that the mass-spectrometric tracer method provides a valuable quantitative means of studying radical reactions in flames. The results show that no significant compound formation between e.g. lithium and160 RADICALS IN FLAMES molybdenum or tungsten occurs for the values of [Mo], and [w, of this work. By analogy with corresponding potassium + molybdenum and potassium + tungsten 26* 27 such compound formation would be expected to occur at higher [MO]~ and [W],, under which circumstances the mass-spectrometric method could still be used straightforwardly but the photometric method could not. The catalytic mechanisms for tin, molybdenum and tungsten account quantita- tively for the effects of these metals on radical recombination.In the absence of reliable thermochemical data for such species as SnOH*(A), SnOH*(B), Sn(OH),, HMoO,, HW03, HMoO, and HW04, however, these mechanisms remain somewhat speculative. The mechanisms for molybdenum and tungsten are formally similar to those proposed for the alkaline earth metals and iron,4 although inspection of the rates of individual reactions in the catalytic cycles involved reveals differences in degree of departure from equilibrium for corresponding reactions which give rise to different composition-dependences of the catalytic effects. D. H. Cotton and D. R. Jenkins, Truns. Furuduy SOC., 1971,67,730, E. M. Bulewicz and P. J. Padley, 13th Int.Symp. Combustion (Combustion Institute, Pitts- burgh, 1971), p. 73. E. M. Bulewicz and P. J. Padley, Trans. Furuduy SOC., 1971, 67, 2337. D. E. Jensen and G. A. Jones, J. Chem. Phys., 1974, 60, 3421. ' E. M. Bulewicz, C. G. James and T. M. Sugden, Proc. Roy. SOC. A, 1956,235,89. T. M. Sugden, Truns. Furuduy SOC., 1956,52,1465. ' D. E. Jensen, Combustion and Flume, 1972, 18, 217. M. J. McEwan and L. F. Phillips, Combustion and Flume, 1967, 11, 63. A. N. Hayhurst and D. B. Kittelson, Nature Phys. Sci., 1972, 235, 136. P. J. Th. Zeegers and C. Th. J. Alkemade, Combustion and Flame, 1970, 15, 193. JANAF ThermochemicuE Tables (National Standard Reference Data System, National Bureau of Standards, Washington D.C., 1971), No. 37. 14K. Schofield and T. M. Sugden, 10th Int.Symp. Combustion. (The Combustion Institute, Pittsburgh, 1965), p. 589. D. E. Jensen, Combustion and Flume, 1968, 12,261. lo R. Kelly and P. J. Padley, Truns. Furuday SOC., 1971, 67, 740. I2 D. E. Jensen, J. Phys. Chem., 1970, 74, 207. l6 D. H. Cotton and D. R. Jenkins, Trans. Furuday SOC., 1968,64,2988. l7 A. N. Hayhurst and D. B. Kittelson, Combustion and Flume, 1972, 19, 306. l 8 R. Kelly and P. J. Padley, Trans. Faraduy SOC., 1971, 67, 1384. l 9 D. E. Jensen and G. A. Jones, J.C.S. Furuduy I, 1972,68,259. 2o D. E. Jensen and G. A. Jones, J.C.S. Faraduy I, 1973, 69, 1448. 21 D. E. Jensen, Trans. Furuduy SOC., 1969, 65,2123. " A. N. Hayhurst, F. R. G. Mitchell and N. R. Telford, Int. J. Mass Spectr. Ion Phys., 1971, 7, 177. 23 A. N. Hayhurst and N. R.Telford, Proc. Roy. SOC. A , 1971,322,483. 24 M. Farber and R. D. Srivastava, Combustion and Flame, 1973,20,33. 25 K. Allen and D. E. Jensen, Rocket Propulsion Establishment Tech. Rep. 73/1 (1973). 26 D. E. Jensen and W. J. Miller, 13th Int. Symp. Combustion (Combustion Institute, Pittsburgh, 27 D. E. Jensen and W. J. Miller, J. Chem. Phys., 1970,53, 3287. 1971), p. 363. Mass-spectrometric Tracer and Photometric Studies of Catalysed Radical Recombination in Flames BY DAVID E. JENSEN" AND GEORGE A. JONES Rocket Propulsion Establishment, Westcott, Aylesbury, Buckinghamshire Received 31st May, 1974 Measurements of hydrogen atom concentrations in H2 + O2 + N2 flames with and without additives have been made by a mass-spectrometric tracer method dependent upon the reaction being balanced and by a well established photometric method dependent upon balance of the analogous reaction Results from the two methods agree well.Catalysis of flame radical recombination caused by addition of tin, molybdenum and tungsten is described. Mass-spectrometric results for tin are in good agreement with previous photometric measurements. Results for molybdenum and tungsten from both methods are quantitatively interpreted in terms of a cyclic homogeneous gas phase mechanism, with associated thermochemistry and reaction rate coefficients. Sr+ + H20 + SrOH+ + H, K = 47 exp( - 7 700 KIT), Li+ H20 + LiOH+H, K = 16 exp(- 10 O00 K/T). Recent work has shown that small quantities of various metal-containing additives can cause significant catalysis of recombination of the H, OH and 0 radicals generally present in above-equilibrium concentrations in H2 + 0, + N, flames.This work involved measurement of [HI by the well established Li/Na photometric m e t h ~ d . ~ In this method, known trace quantities (too small to perturb the flame properties significantly themselves) of lithium and sodium are added in turn to a flame and [Li] is measured via comparison of the Li first resonance doublet emission intensities or absorptions with those of the corresponding Na doublet. [HI is then calculated on the basis of the reasonable assumptions that the reaction is balanced,6* that lithium forms significant concentrations of Li and LiOH alone and that sodium exists largely as free atoms in the flame. (A reaction A+B + C + D is said to be " balanced " or " in equilibrium " when ([C][D])/([A][B]) is equal to the equilibrium constant for the reaction.) Under certain conditions, however (e.g. in fuel-lean flames where peroxide formation may occur,* in practical flames with interfering optical frequency radiation, or where additives form stable compounds with lithium and/or sodium) an alternative method is needed.Hayhurst and Kittel- son have suggested that a reaction analogous to (l), Sr+ + H20 + SrOH+ + H, Li + H 2 0 + LiOH + H (equilibrium constant K l ) (1) (2) balanced in a flame to which trace quantities of strontium are supplied, affords such an alternative if [SrOH+]/[Sr+] can be measured via mass-spectrometric sampling and K2 is known. The present paper describes application of both these methods to investigation of radical recombination catalysis in H2 + O2 + N2 flames caused by addition of tin, molybdenum and tungsten-containing compounds.The good agreement between results from the two methods supports the suggestion that the mass-spectrometric tracer method provides a useful means of studying radical 149150 RADICALS I N FLAMES recombination in flames and strengthens confidence in the quantitative data for the observed catalytic effects. The two methods of measuring [HI require knowledge of the equilibrium constants Kl and K2 as functions of temperature. On the basis of data from several sources, Kelly and Padley lo recommend a value for the standard zero-point enthalpy change AH; for Li(g)+OH(g) + LiOH(g) of 433 +8 kJ mol-l, in good agreement with another recommendation by Zeegers and A1kemade.l Vibration frequencies for the (assumed linear) LiOH molecule have been estimated lo as 66.5 (Li-0 stretch), 35.0 (bending mode) and 360.0 (0-H stretch) mm-l respectively, and the molecular moment of inertia ILioH estimated l2 to be 2 .2 ~ kgm2. Together with other data, taken from the JANAF TabZes,13 this gives a recommended value Kl = 16 exp { - (10 OW_+ 1000 K ) / T ) for 1500 < T < 3000 K. K2 is less accurately known. If SrOH+ is assumed, by analogy with the iso- electronic RbOH,12 to be linear, having vibration frequencies v1 at 35.5 mm-’, v2 (doubly degenerate mode) at 31.0 mm-l and v3 at 360.0 mm-l and ISrOH+ = 1.35 x kg m2, the photometric measurements of Schofield and Sugden l4 may be interpreted to give AH;,2 = +74+40 kJ mol-l.The microwave measurements of Jensen,15 combined with Cotton and Jenkins’ value l6 for the bond energy of Sr-OH, lead to = + 52 35 kJ mol-I. After corrections for departures from equilibrium in the reaction 15* l7 Kelly and Padley’s electrostatic probe measurements l8 yield = + 38 f 35 kJ mol-l. Hayhurst and K i t t e l ~ o n , ~ ~ from mass-spectrometric experiments, find what is probably the most reliablevalue of = +40+ 10 kJ mol-l, although uncertainties caused by lack of knowledge concerning the chemical reactions occurring in the viscous flow field inside their sampling nozzle remain. A realistic best estimate of AH& would be +40+ 15 kJ mol-l, which, in combination withJANAFtabulations lS and the above data for SrOH+, yields K, = 47 exp(( - 7 700 5-2 000 K)/T).Sr + OH + SrOH+ + e-, (3) EXPERIMENTAL The burner, additive system and optical technique used were similar to those described previou~ly.~~~ 2o The flames were atmospheric-pressure, laminar, cylindrical, shielded, fuel-rich H2 + O2 + N2 flames in which distance downstream of the primary reaction zones was a measure of the reaction time available for recombination of the radicals produced in above-equilibrium amounts in these zones. Principal composition features, flow rates and temperatures are given in table 1. Tin was added to the flames as Sn(CH& and molybdenum and tungsten as hexacarbonyls, all in the form of vapours from an exponential decay reser- voir 21 at concentrations given by 5x 10l2 < [Melt < 5x 1014 molecule CM-~, where [Melt = ~i[Si] ; [Sj] is the concentration of the ith metal-containing species in the flame, which itself contains si atoms of metal per molecule.Lithium, sodium and strontium were added in known trace amounts (- 1 part in lo7) as salt solutions from a calibrated atomiser.lg Tests analogous to those described in ref. (19) confirmed the absence of significant quantities of condensed particles in the flames for all the additives. Hydroxyl radical concentrations were calculated from measured [HI on the assumption that the reaction is balanced. The mass spectrometer and sampling system used were similar to those described by Hayhurst, Mitchell and Telford.22 The ratio of mass spectrometer ion currents iSrOH+ /isr+ was measured with an ion multiplier, both currents being corrected for small proportions of ion h y d r a t i ~ n .~ ~ 23 If the flame chemistry were unperturbed by the sampling process, one 1 1 H+H2O + OH+H2 (4)TABLE 1 .-FLAME TEMPERATURES AND COMPOSITIONS [HzOl/ [HzII LHlesl [HI3 om/ om/ reaction time flame unburned molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 T/K (3 cm)/ms H2/N2/02 3.3/4.0/1 .O 5.0/3.0/1.0 4.5/3.5/1.0 4.0/4.0/1 .O 3.5/4.5 /I .O 3.2/4.8/1.0 3.0/5.0/1.0 4.0/5.0/1.0 3.5/6.0/1.0 9.3 x 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 6 ~ 1017 8 . 6 ~ 1017 6.1 x 1017 9 . o ~ 1017 5 . 4 ~ 1017 4 . 5 ~ 1017 6 . 4 ~ 1017 1 . 4 ~ 10l8 1.1 x l0l8 6 . 8 ~ 1017 8 . 6 ~ 1017 6.1 x 1015 4 .6 ~ 1015 4.1 x 1015 3.7 x 1015 3 . 2 ~ 1015 2 . 9 ~ 1015 2 . 6 ~ 1015 1 . 4 ~ 1015 5.8 x 1014 1.ox 10l6 1 . 6 ~ 10l6 1 . 4 ~ 10l6 1.2 x 10l6 1.ox 10l6 8 . 5 ~ 1015 7 . 4 ~ 1015 1.1 x 1OI6 1.ox 10l6 2 . 0 ~ 1015 1.1 x 1015 1.2 x 1015 1.3 x 1015 1 . 4 ~ 1015 1 . 5 ~ 1015 1 . 6 ~ 1015 9.1 x 1014 8 . 9 ~ 1014 2150 2035 2035 203 5 2035 2035 2035 1900 1800 1.09 1.05 1.05 1.05 1.05 1.05 1.05 1 .oo 1 .oo [H]es and [HI3 cm are hydrogen atom concentrations at equilibrium and at 3 cm downstream of the reaction zone, respectively. Na D-line reversal temperature of the burned gases. [HJ, [H,O] and [Nz] are essentially independent of distance downstream. T/K is the measured152 RADICALS IN FLAMES could calculate [HI from the relationship iSrOH+/iSr+ = 47 exp(-7 700 K / T ) [H,O]/[H], where T is the flame temperature.Because chemical reactions do occur in the sampling cone,23 however, a careful analysis of the viscous (Reynolds number R! 100) flow in this nozzle would be required to make the mass-spectrometric tracer method of measuring [HI accurate and independent of all calibrations. In the present work, where the main require- ment is accurate knowledge of relative [HI, is^^ + /isr + was simply used as a measure of this quantity for flames with and without additives. Results like those shown in fig. 1, where the current ratio is shown to vary linearly with [HI-' as measured by the photometric method in the absence of a catalysing additive, confirm the validity of this approach. I I I I I 2 4 6 8 10 I2 14 1017[H]-1/cm3 molecule-1 [[Sr], = 3 x 10l1 molecule ~ m - ~ .No catalyst present. [HI-' from photometricImeasurements. FIG. 1.-Variation of mass spectrometer ion current ratio (iSflH+/iSr+) with [Hl-l for flame 4. Overall, either the photometric or the mass-spectrometric tracer method yields relative [HI for a set of flames like that employed in this work accurate to within &lo %. The uncertainty in absolute [HI from the photometric method stems chiefly from uncertainties in Kl and is probably about +50 %, smaller than would be suggested by the stated error bounds on AH& because the latter take account of possible errors in statistical data used to derive AH$,l from the experimentally-measured K I . The uncertainty in absolute [HI from the mass-spectrometric method is probably about a factor of 2, smaller again than might be expected from the uncertainty bounds assigned to AH&2 because errors incurred when i S r O ~ + / i s r + for any flame are converted to absolute [HI are likely to compensate, at east in part, for those in K2.RESULTS AND DISCUSSION TIN Fig. 2 shows typical plots of [HI-', measured by the mass-spectrometric method, against time for flame 8 (1900 IS) with and without added tin. In the absence of additive, recombination of radicals proceeds via the relatively slow three-body reactions H+H+M + Hz+M ( 5 )D. E . JENSEN AND G . A. JONES 153 and where the collision partner M is usually H20, H2 or N2. The rate of decay of [HI when [HI is well above equilibrium is then given by where a = K4[H20]/[H2] and k5 and k6 are rate coefficients for composite M.The uncatalysed recombination rates in the flames of this work are nicely described by k5 = 2 x K/T and k6 = 1.6 x K/T cm6 s-', with K4 = 4.4 exp( - 7 530 K/T).I3 In the presence of tin, the decay of [HI with time in different flames for the range of values of [Sn], tried was found to fit the expression in agreement with the photometric observations of Bulewicz and Padley.2* Values of k , were obtained from plots like those of fig. 2. The agreement between these and OH+H+M H,O+M, (6) - d[H]/dt = 2(k5 + ak6)( 1 + a)-'[M][HI2, (7) -d[H]/dt = 2(k,[M]+ak6[M] +k,[Sn],)(l +a)-'[HI2, (8) I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 2.-Catalysis of hydrogen atom decay by tin. [HI measured by the mass-spectrometric method. the photometric values,2* although the trend with temperature is opposite in the two cases, as illustrated in table 2, is reasonably encouraging in the light of the fact that the results become less reliable as the flame temperature increases and radical concentrations approach equilibrium levels.suggest the following reaction scheme to explain the essential features of the catalytic effect : Temperature = 1900 K. (A) no tin added ; (B) [Sn], = 2 x 1014 molecule ~ r n - ~ . Bulewicz and Padley 2* SnO( l2) + H(2S)( + M) + SnOH*(A)( + M) (9) SnOH*(A) -+ SnOH*(B) (10 ( 1 1) SnOH*(B) + H(2S) --+ SnO( 'Z) + H2(12).154 RADICALS I N FLAMES TABLE 2.-RATE COEFFICIENTS FOR THE EMPIRICAL REACTION H+ H+ SnO + H2 + SnO temperature/K 1800 1860 1900 2010 2035 21 50 21 80 2330 1028 x rate coefficient/cms molecule-2 s-1 ref.(2) present work They do not, however, attempt to assign thermochemical properties to SnOH*(A) and SnOH*(B) and to fit such a scheme quantitatively to the results. Their interpretation thus remains tentative, especially in view of the absence of quantitative thermo- chemical data for Sn(OH), (the dihydroxides of Ca, Sr, Ba and Fe appear to play important parts in catalysis effects for these metals l* 4, and the dangers attached to assuming that certain reactions in a cyclic mechanism are balanced whilst others remain ~nbalanced.~ Until further work, probably on fuel-lean flames, clarifies the picture, effects of tin on free radical concentrations in fuel-rich flames may be adequately described in terms of the empirical reaction with k12 w 4 x H+H+SnO -P H2+Sn0, (12) cm6 molecule-2 s-l, where [SnO] w [Sn], for these flames., MOLYBDENUM The catalytic effect of molybdenum on free radical recombination is illustrated in fig.3, where [H]-l measured by both the mass-spectrometric tracer and the photo- metric method is shown as a function of time for flames 1 and 8. Lines 1 and 3 in this figure correspond to a total mole fraction of added molybdenum of approxi- mately whilst lines 2 and 4 represent results obtained in the absence of molybdenum. Agreement between results from the two methods is again good. In all the flames of table 1, the rate of catalysed recombination was found to be directly proportional to [Mo],, a feature consistent with homogeneous catalysis. Because the observed decreases in [HI and [OH] caused by addition of molybdenum are generally much greater than [Mo],, any interpretation of the effects of molybdenum on radical recombination must be based on a cyclic reaction sequence involving the regeneration of participating Mo-containing species.Calculations based on thermo- chemical data given in ref. (13) suggest that [MOO,] and [H2Mo04] contribute significantly to [Mo], but that other molybdenum-containing species for which data are available are present in concentrations too low for them to play significant parts in a catalytic cycle. It is therefore necessary to invoke the participation in the cycle of a molecule for which thermochemical data are currently unavailable. By analogy with the species involved in catalytic cycles based on such other metals as calcium [CaO, CaOH, Ca(OH),] and iron [FeO, FeOH and Fe(OH),], it is reasonable to suggest as a working hypothesis that HMoO, should participate, together with MOO, and H,Mo04, in a cycle for molybdenum.A likely catalytic cycle would then consist of the reactions HMoO, + H + MOO, + H2, (1 3) MOO, +H20 4 H2Mo0, (14)D. E . JENSEN AND G. A . JONES 155 and H2Mo0, + H + HMoO, + HzO. (1 5 ) To test this hypothesis, estimated data for HMoO, are required. By analogy with JANAF data,' the following set of vibration frequencies (as wavenumbers) seems reasonable: 80.0, 100.0, 95.0, 30.0, 35.0, 25.0, 150.0, 60.0 and 10.0mm-l. So also does a value of 7.5 x kg3 m6 for the product of the three principal molecular moments of inertia.With a symmetry number for HMoO, of 3, an electronic partition function for this molecule taken to be the same as that for MOO, and an energy for the HO-Mo0,H bond of 456 kJ rnol-l, these give a value for KI3 of 0.04 exp(l9 600 K/T) and a corresponding value for K15 of 0.24 exp(83 50 K/T). These values are consistent with the recent data of Farber and S r i v a s t a ~ a , ~ ~ obtained from mass-spectrometer studies on oxygen-rich flames containing molybdenum, inasmuch as they imply that HMoO, would be present in such flames in quantities too low to be detected. I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 3.-Catalysis of hydrogen atom decay by molybdenum. Points represent experimental measurements made between 7.5 and 40 min above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) Temperature = 2150 K, [Molt = 4.2 x 1013 molecule ~ m - ~ ; (2) T = 2150 K, [Molt = 0 ; (3) T = 1900 K, [Molt = 4.0 x loi3 molecule ~ r n - ~ ; (4) T = 1900 K, [MO]~ = 0 ; lines drawn are computed plots.With the method of ref. (4) and the computer program of ref. (25), it was found that the cycle consisting of reactions (13)-(15) provides computed lines giving an excellent fit to the experimental observations of temperature (fig. 3) and composition (fig. 4) dependences when kI3 = 1.1 x exp(- 1 400 KIT), k14 = 1 x lo-', and k , , = 1.4 x lo-" exp( -300 K/T) cm3 molecule-1 s-l. All these rate coefficients appear reasonable. A number of alternative cycles involving HMoO, and HMoO,156 RADICALS IN FLAMES (observations of HMoO;; in flames similar to those of the present work 26 suggest that the radical HMoO, might be present in significant concentrations) was developed along the lines described in ref.(4), and attempts were made to fit these to the experi- mental measurements. No alternative cycle could be fitted to the data without an unreasonably high rate coefficient being assigned to at least one of the reactions involved. It is reasonable to rule out cycles including reactions of 0 and O2 on the basis that such reactions are likely to be too slow to contribute significantly at the low concentrations of these species in the fuel-rich flames. The interpretation based on reactions (13)-(15) is thus the only one found to account adequately for the experimental results.h I I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 4.-Composition dependence (flames 2-7) for molybdenum catalysis. [MO]~ = 4.1 x 1013 molecule ~ m - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above reaction zones. Lines drawn are computed plots. Typical rates of reactions (1 3)-( 15) under experimental conditions are given in table 3. Reaction (13) is seen to be the reaction furthest from equilibrium in the sense that ([Mo03][H,])/([HMo03][H]K13) is far from unity, but neither reaction (14) nor reaction (15) is quite balanced. It is difficult to assign probable uncertainty bounds to the rate coefficients given, partly because of the uncertainties in absolute [HI of about +50 % mentioned above and partly as a result of the uncertainties in the estimated thermochemical data for HMoO,.A series of calculations in which individual rate coefficients for reactions in the cycle were varied, separately and together, showed that changing k I 3 by a factor of 2 from the values of table 3 causedTABLE 3 .-MOLYBDENUM REACTION MECHANISM, RATE COEFFICIENTS AND RATES reaction rate coefficient rate difference reverse forward reverse forward 5. H+H+M + H2+M 2 x 10-30 K/T 2.8 x exp( - 52 650 K/T) 5.07 x 1017 8.75 x 1015 4.98 x 1017 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( - 60 180 K/T) 3.39 x 1OI8 5.63 x 10l6 3.34 x 10" 4. H20+H + H2+0H 1 . 6 ~ 10-'oexp(-10 130K/T) 3 . 6 ~ 10-l' exp(-2600K/T) 7.38 x lo2' 7.38 x 1021 2.31 x loi8 13. HMoO,+H + MOO,+H, 1.1 x 10-10exp(-1400K/T) 3 x 10-9exp(-21 000K/T) 3 .9 0 ~ 10I8 1 . 0 2 ~ 1 0 ~ ~ 3 . 8 0 ~ 1 0 ~ ~ 14. MOO3+H20 + H2M004 1 x 10-l1 2.3 x 1011 exp(-24 700 K/T) 1 . 9 2 ~ lOI9 1 . 5 4 ~ loi9 3 . 7 9 ~ 10l8 15. H2Mo04+H + HMo0,+H20 1 . 4 ~ 10-lo exp(-300 K/T) 6 x 10-lo exp( - 8650 K/T) 4.02 x 1019 3.64 x 1019 3.75 x 1018 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2M004, 4.7 x 10l2 ; Moo3, 3.1 x 1013 ; HMo03, 3.8 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10l6 ; OH, 2.3 x 1015 ; H2, 8.6 x 1017 ; M, 3.9 x lo1*. The results are insensitive to the precise values of initial concentrations for the Mo-containing species. react ion TABLE 4.-TUNGSTEN REACTION MECHANISM, RATE COEFFICIENTS AND RATES rate coefficient rate forward reverse reverse difference forward 5.H+H+M +H2+M 2 x 10-30 KIT 2.8 x lo-' exp( - 52 650 K/T) 7.48 x 1017 8.74 x lo1' 7.40 x l O I 7 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( -60 180 K/T) 5.02 x 10I8 5.62 x 10l6 4.96 x 10l8 4. H20+H + OHfH2 1.6 x lo-'' exp(- 10 130 K/T) 3.6 x lo-" exp( -2600 K/T) 8.97 x lo2' 8.97 x 10'' 3.92 x 10I8 16. HW03 + H + W03 I- H2 1.1 x lO-'O exp(-lOOO K/T) 3 x lo-' exp( - 10 040 K/T) 2.25 x 10l8 3.54 x 1017 1.90 x 10l8 17. WOJ+H~O + H2W04 1 x 10-'O 5 x 10l2 exp(-38 600 K / T ) 2.08 x 10l8 1.83 x lo1' 1 . 9 0 ~ 10l8 18. HzW04+H + HW03+HzO 5.82 x lo1' 5.63 x lo1' 1.88 x 10l8 3 x 10-Io exp( - lo00 K/T) 6 x 10-lo exp( - 6010 K/T) 0 5 v1 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2W04, W03, HWO3, 9 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10I6 ; OH, 2.3 x 1015 ; H2, 8 .6 ~ 1017 ; M, 3.9 x 10l8. The results are insensitive to the precise values of initial concentretions for the W-containing species.158 RADICALS IN FLAMES significant discrepancy between computations and experiment, whatever efforts were made to compensate by changing other rate coefficients. Similarly, changing kI4 and k15 by a factor of 5 resulted in significant discrepancies. Overall, it is reasonable to assign to k13, k14 and k15 rough uncertainty factors of 5, 10 and 10 respectively. TUNGSTEN Mass-spectrometric tracer and photometric values of [Hl-l are shown as functions of time for flames 1 and 8 with and without added tungsten in fig.5. The significant catalytic effect of tungsten on radical recombination is apparent in this figure, even for a mole fraction of added metal as low as In a manner entirely analogous to that described above for molybdenum, the computer program 2 5 was used to show that the experimental results could be fitted to the catalytic cycle consisting of the reactions HW03 +H -+ W03 +H2, (16) W03 +H20 -+ H2W04 (17) and H2W04+H + HWO,+H,O (18) when k16 = 1.1 x 10-lo exp(- 1000 K/T), kl, = 1 x 10-lo and k18 = 3 x 10-lo exp( - 1000 K/T) cm3 molecule-I s-l. All these values appear reasonable. They rest again upon estimates of thermochemical data for the intermediate radical HW03, which in conjunction with JANAF data l 3 for H, H2, H20, W03 and H2W04 give rise to K16 = 0.04 exp(9 000 K / T ) and K18 = 0.5 exp(5 000 K/T).No other cycle (for HW03 or HWO,) was found that fitted the experimental temperature and 16 14 12 I0 8 6 I I I I I 1 I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 5.-Catalysis of hydrogen atom decay by tungsten. Points represent experimental measure- ments made between 7.5 and 40 mm above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) T = 2150 K, [WIG = 2.9 x l O I 3 molecule ~ r n - ~ ; (2) T = 2150K, [WJc = 0; (3) T = 1900K, [WJc = 2 . 7 ~ 1013 molecule ~ m - ~ ; (4) T = 1900K, Iw], = 0. Lines drawn are computed plots.D. E. JENSEN AND G. A. JONES 159 composition dependences of the catalytic effect with reasonable rate coefficients for reactions included.Examples of how well the cycle consisting of reactions (1 6)-( 18) fits the experimental data are shown in fig. 5 (temperature dependence) and fig. 6 (composition dependence). 2 0 "i 2i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 6.-Composition dependence (flames 2-7) for tungsten catalysis. [W], = 2.8 x loi3 molecule ~ r n - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above the reaction zones. Lines drawn are computed plots. Typical rates of the reactions (1 6)-( 18) under experimental conditions are given in table 4. Reaction (17), as well as reaction (16), is well away from equilibrium, although reaction (18) is not far from balance. There is thus a significant kinetic difference between tungsten and molybdenum mechanisms which manifests itself in different composition dependences of catalytic effect for the two metals.An analysis of the effects of varying kI6, kI7 and kI8 upon computed [H]/time profiles, similar to that described for molybdenum above, suggests that rough uncertainty factors of 5 , 5 and 10 respectively may reasonably be assigned to these rate coefficients. CONCLUSIONS The good agreement between sets of results obtained by the two methods of determining [HI supports the suggestion that the mass-spectrometric tracer method provides a valuable quantitative means of studying radical reactions in flames. The results show that no significant compound formation between e.g. lithium and160 RADICALS IN FLAMES molybdenum or tungsten occurs for the values of [Mo], and [w, of this work.By analogy with corresponding potassium + molybdenum and potassium + tungsten 26* 27 such compound formation would be expected to occur at higher [MO]~ and [W],, under which circumstances the mass-spectrometric method could still be used straightforwardly but the photometric method could not. The catalytic mechanisms for tin, molybdenum and tungsten account quantita- tively for the effects of these metals on radical recombination. In the absence of reliable thermochemical data for such species as SnOH*(A), SnOH*(B), Sn(OH),, HMoO,, HW03, HMoO, and HW04, however, these mechanisms remain somewhat speculative. The mechanisms for molybdenum and tungsten are formally similar to those proposed for the alkaline earth metals and iron,4 although inspection of the rates of individual reactions in the catalytic cycles involved reveals differences in degree of departure from equilibrium for corresponding reactions which give rise to different composition-dependences of the catalytic effects. D. H. Cotton and D. R. Jenkins, Truns. Furuduy SOC., 1971,67,730, E. M. Bulewicz and P. J. Padley, 13th Int. Symp. Combustion (Combustion Institute, Pitts- burgh, 1971), p. 73. E. M. Bulewicz and P. J. Padley, Trans. Furuduy SOC., 1971, 67, 2337. D. E. Jensen and G. A. Jones, J. Chem. Phys., 1974, 60, 3421. ' E. M. Bulewicz, C. G. James and T. M. Sugden, Proc. Roy. SOC. A, 1956,235,89. T. M. Sugden, Truns. Furuduy SOC., 1956,52,1465. ' D. E. Jensen, Combustion and Flume, 1972, 18, 217. M. J. McEwan and L. F. Phillips, Combustion and Flume, 1967, 11, 63. A. N. Hayhurst and D. B. Kittelson, Nature Phys. Sci., 1972, 235, 136. P. J. Th. Zeegers and C. Th. J. Alkemade, Combustion and Flame, 1970, 15, 193. JANAF ThermochemicuE Tables (National Standard Reference Data System, National Bureau of Standards, Washington D.C., 1971), No. 37. 14K. Schofield and T. M. Sugden, 10th Int. Symp. Combustion. (The Combustion Institute, Pittsburgh, 1965), p. 589. D. E. Jensen, Combustion and Flume, 1968, 12,261. lo R. Kelly and P. J. Padley, Truns. Furuday SOC., 1971, 67, 740. I2 D. E. Jensen, J. Phys. Chem., 1970, 74, 207. l6 D. H. Cotton and D. R. Jenkins, Trans. Furuday SOC., 1968,64,2988. l7 A. N. Hayhurst and D. B. Kittelson, Combustion and Flume, 1972, 19, 306. l 8 R. Kelly and P. J. Padley, Trans. Faraduy SOC., 1971, 67, 1384. l 9 D. E. Jensen and G. A. Jones, J.C.S. Furuduy I, 1972,68,259. 2o D. E. Jensen and G. A. Jones, J.C.S. Faraduy I, 1973, 69, 1448. 21 D. E. Jensen, Trans. Furuduy SOC., 1969, 65,2123. " A. N. Hayhurst, F. R. G. Mitchell and N. R. Telford, Int. J. Mass Spectr. Ion Phys., 1971, 7, 177. 23 A. N. Hayhurst and N. R. Telford, Proc. Roy. SOC. A , 1971,322,483. 24 M. Farber and R. D. Srivastava, Combustion and Flame, 1973,20,33. 25 K. Allen and D. E. Jensen, Rocket Propulsion Establishment Tech. Rep. 73/1 (1973). 26 D. E. Jensen and W. J. Miller, 13th Int. Symp. Combustion (Combustion Institute, Pittsburgh, 27 D. E. Jensen and W. J. Miller, J. Chem. Phys., 1970,53, 3287. 1971), p. 363.

ISSN:0300-9599    

DOI:10.1039/F19757100149

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Lauric Acid/Pentaerythrityl Monolaurate : A Model Melt Esterification Part 1 .-Kinetics BY MANFRED GORDON AND CONSTANTINE G. LEONIS Department of Chemistry, University of Essex, Wivenhoe Park, Colchester C04 3SQ Received 1 1 th February, 1974 The study of polyfunctional polycondensates and of the structure of gels is dependent on the availability of link-forming mechanisms which are simple and well understood. Esterification in the melt is a favoured method. Although some melt esterification reactions have been found to be repre- sented by third order kinetics and a mechanism free from measurable complicating effects, the study of esterification of dibasic acids with pentaerythritol (PE) has suggested a substitution effect, whereby each esterified OH accelerates the esterification of the remaining OH in the same PE unit by a factor of about N = 1.5.This effect is here confirmed by kinetic analysis of the (non-polymerisable) model system lauric acid/PE and, in more detail, lauric acid/pentaerythrityl monolaurate. Accurate and automated readings of about 300 conversion/time data per run, based on the pressure of evolved steam, were fitted to rival kinetic models, over a range of compositions and temperatures. Computer analysis in terms of standard deviations strongly supports the validity of the substitution effect (N- 1.4). The results are discussed in the context of previous work on esterification in bulk and in dilute solutions. In this work the kinetics and statistics of esterification of a monofunctional compound (lauric acid, LA) with polyols is studied in order to throw light on related polyfunctional condensations. For these, Flory and Stockmayer recognised from the start two sources of deviations from the ideal .or random intermolecular polycondensation theory, to be expected in principle for all real systems : substitution efects (of reacted functionalities on neighbouring unreacted ones) and cyclisation, i.e. the competition of intramolecular reactions.The theory did not furnish error limits for the effects of such deviations on struct- ural parameters (e.g. the gel point) or on physical properties, e.g. the elastic modulus, calculated from the ideal theory. This is serious because even small deviations of either kind can have profound physical effects, e.g. a modest amount of ring formation occurring before gelation is expected to reduce markedly diffusion rates through the gel subsequently formed.Equally seriously, it is difficult to measure the extent of substitution and cyclisation effects ; for instance, no direct measurements such as spectroscopic analysis give information on the presence of large rings. The serious- ness of this situation is underlined by the observation that the structure of weak gels is of great importance in the life sciences. The preferred method of attack on the prob- lem is a combination of chemical kinetics and statistics, e.g. gel points and various other parameters of molecular distributions. Such a combined study was made on polyesterification in the melt of adipic acid and pentaerythritol (AA/PE) or 1 , 1 , 1 - tri(hydroxymethy1) ethane(AA/TME).The results showed that, there was a substan- tial cyclisation effect with a critical conversion or gel point pc = 0.623 compared with 3-3 (= 0.577) predicted from the ring-free theory for (AA/PE). The full strength of 1-6 161162 A MODEL MELT ESTERIFICATION the effect was partly masked by a moderately strong substitution effect of the positive kind, i.e. an increase of rate of esterification of an OH due to each ester group in the same repeat unit. This effect was deduced quantitatively in terms of two parameters N1 and N2, which measure the factors by which the esterification rate constant in- creases in AA or PE, in respect of each previously reacted carboxyl or hydroxyl group carried on the same repeat unit respectively.Results of rate measurements, gel points, dilution with solvent, and statistical calculation of the ring-chain competition effect using known bond lengths and angles, combined to produce the results N1 = 0.9 & 0.1 and N2 = 1.5 &- 0.1. Of these two parameters, only N2 differs significantly from unity. The reasons for the sensitivity of hydroxyl groups to the prior substitution of neigh- bouring hydroxyl groups by ester groups were largely a matter for speculation. In terms of the activation energy of esterification, N2 corresponds to an effect given by so that N2 = 1.5 gives the very modest AE*z3 kJ mol-1 at a temperature of 170°C. The question of the reality and origin of this effect is still topical, even though other esterification systems have since been found, especially decane- 1 ,lo-diol/benzene- 1,3,5-triacetic acid (DMG/BTA), for which no substitution effect is rneas~rable.~ Results for the kinetics of esterification and gel points of PE with sebacic and tri- decanoic acid fully supported the existence of the substitution effect in PE.5 The effect in PE should be equally present in esterification in the melt with monofunctional carboxylic acids. Although such systems are in many ways simpler, gelation does not occur, and until recently it was not possible to make reliable measurements of sub- stitution effects.The present work was undertaken in an effort to establish the substitution effect in esterification of PE with a monocarboxylic acid, using g.p.c. (see Part 2 6, to study the distribution statistics of the products (in place of gelation which is not applicable) in conjunction with precise kinetic measurements. N2 = exp( - AE*/2RT) (1) KINETIC SCHEME FOR LA/PE AND LA/PEML In accordance with previous work on related irreversible self-catalysed esterifica- tion reactions, an overall third order reaction scheme is postulated, i.e. first order in hydroxyl groups and second order in carboxyl groups, perturbed by a linear first shell substitution effect (FSSE) among the hydroxyl group^.^ The basic third order esterification reaction introduces a third order rate constant k* (taken in units g2 mo1-2 min-I for convenience), and the substitution effect introduces a single dimensionless parameter N, where N i represents the factor multiplying k* when i previously esterified hydroxyl groups are borne by the reactant PE unit.Accordingly, the following rate equation applies : -dp,jdt = k*[Ni(4-i)pi-Ni-1(5-i)pi-1]p2C~2. (2) The following notation is employed : p i denotes the fraction ni/Cini of pentaerythritol residues in the system bearing i ester groups ; and p the fraction nL/nz of lauric acid residues, which are unsterified. Here ni is the number of moles of the i-ester of PE and nL the current number of moles of free LA, while n i is the initial number of moles. Ci is the initial concentration of LA of stsichiometric ratio E in units of moles per gram of system. Similarly C j j represents the original concentration of the polyol residues used as starting reactant, each possessing initially j ester groups.The stoichiometric ratio E is defined as : E = (4-j)(c;/c;j). (3)M. GORDON AND C . G . LEONIS 163 The rate of change of LA is governed by - dp/dt = k" (4 - i)Nipip2C;jCL. 1 (4) The initial conditions for these rate equations for the reaction between PE ( j = 0) and LA are given as : (where d i is the Kronecker delta), and between pentaerythritol monolaurate (PEML, j = 1) and LA: p-l = 0; p(0) = 1 ; pi(0) = &,i ; i = 0, 1 , 2, 3, 4 ( 5 ) p o = 0; p(0) = 1 ; pi(0) = 6 1 , i ; i = 1, 2, 3, 4. (6) For fitting kinetic data, i.e. the evolution in time of the system, computer solutions of eqn (2)-(6) were used. The programme, utilising an improved version written in Algol,7 is based on Gear's method for solving systems of simultaneous differential equations.For fitting statistical measurements, not involving time directly, explicit solutions are given in Part 2.6 EXPERIMENTAL FACTORS DETERMINING THE CHOICE OF REACTANTS Because of its high symmetry and H-bonding in the crystal, PE has a high melting point (262"C), and its solubility in lauric acid is insufficient to give a homogeneous equimolar solution in LA below about 195°C. At this temperature the reaction velocity is already so high, as to restrict severely the available temperature range for kinetic studies. A similar situation exists with benzene-l,3,5-triacetic acid/decametliylene glycol condensates BTA/ DMG, though it is less severe there (m.p. of BTA 209°C). In that case, the problem was solved by carrying out the esterification reaction in two stages, an initial four minutes at 170°C to achieve dissolution and about 10 % of the esterification, followed by a second stage at some lower temperature for kinetic study.This method was also tried for the system LA/PE but failed, because too much reaction had to be carried out before a homogeneous reaction was obtained, thus invalidating the use of the initial conditions and the proposed rate equations. A second method tried was based on the use of solvents of low vapour pressure for PE and LA, viz. the tribenzhydryl ester of BTA and pentaerythrityl tetralaurate (PETEL), but these were found inadequate solvents for PE. In addition, the presence of PE in reaction products causes trouble in subsequent g.p.c. analysis, because of its insolubility in tetrahydrofuran (THF). The only solution found to these problems was to abandon the first reaction step in the esterification sequence, by using as the starting material PEML [eqn (2), (3), (4), (6)], which has a melting point of 73°C and is miscible with LA above its melting point.The mixture LA/PEML has a convenient temperature range for kinetic study between 150 and 195°C. In addition, a few runs between pentaerythritol and lauric acid were also carried out for comparison at 195°C only. MATERIALS Pentaerythritol (PE) was obtained from British Drug Houses Ltd and recrystallized several times from 0.005 equiv. dm-3 HCl until big crystals (several mm in size) were formed. The melting point was 261.5"C (lit. 262°C). The percentage of hydroxyl groups was found lo to be 49.9 % (theoretical 50.0 %).Lauric acid (LA) was Koch-Light Laboratories Ltd pzrriss grade. It was recrystallized several times from alcohol (m.p. found 45"C, lit. 43-46°C). Pentaerythrityl monolaurate (PEML) was not available commercially and was prepared and purified in the way described below. PE powder containing a small amount of LA (to depress the melting point) was placed in the lower part of a glass reactor with a glass-lined magnetic stirrer, while LA was placed in the upper part above a break-seal. The molar ratio of PE : LA was approximately 9 : 1.164 A MODEL MELT ESTERIFICATION Both parts of the apparatus were evacuated to Torr (to avoid oxidation) and sealed under high vacuum. The apparatus was immersed in a silicone oil bath thermostated at 260°C equipped with a rotating magnetic plate.PE slowly decomposes at 260"C, but this did not materially affect the yield of monoester, as most of the LA is esterified in ca. 30 min. The break-seal was broken with the stirrer and the LA started to drip into the PE melt. A large excess of PE was always present and the formation of the monoester was favoured. After about 30 min no further bubbles were formed and the system was quenched. n elution volume/arbitrary units FIG. 1 .-Gel permeation chromatograms in THF : (a) reaction mixture, (6) purified PEML. The unreacted PE was separated by filtration using THF in which PE is insoluble. The remaining compounds in the mixture except the PEML were LA and higher esters, as shown by the g.p.c. chromatograph in fig. l(a). The monoester was separated from the other compounds by petroleum ether b.p.60-80°C extraction. After four to five purifications, glass-clear needles were produced, which gave a single-peak and an adequately smooth chromatogram [fig. l(b)]. The melting point was found to be 69"C, though the melt re- mained turbid to a temperature above 73°C (lit. m.p. = 75°C). The yield of the synthesis was only about 40 %. PREPARATION OF REACTION MIXTURES Each reactant was well dried and accurately weighed. The components of the mixture were quantitatively transferred to an agate mortar and were finely ground and thoroughly mixed with the pestle. To assure good mixing the whole mixture was heated gently on a hotplate to 55°C and the resultant paste was again well mixed and ground after cooling. The composition of these mixtures were checked quantitatively by means of 8.p.c.Pellets containing ca. 100 mg of mixture were made and stored in a silica gel desiccator. Three mixtures of different stoichiometries, i.e. E = 1, E = 3, E = 2 were used [eqn (3)]. For the system LA/PE only E = 1 was used. DENSITY DETERMINATIONS OF THE MELTS The densities of the reactants were measured in a simple dilatometer consisting of a bulb and a precision capillary tube. The volumes of the dilatometers (ca. 0.5 cm3 for the PEML, ca. 2.5 cm3 for the others) were determined with mercury. The samples were put into the dilatometer by means of a syringe taking care to keep everything at a temperature higher than the melting point of the injected compound. The best straight line between the data pairs of temperature and density furnished the densities of the compounds as a function of temperature. The density coefficients of expan- sion of the materials used are recorded in table 1.M.GORDON AND C. G . LEONIS 165 TABLE DENSITIES OF THE MELTS density at 170°C coefficient of thermal expansion compound PIS 6112-3 I04(dp/dT)/g cm-3 K-1 LA 0.779 -7.2 +0.2 PETEL 0.832 -7.3 20.2 PEML 0.909 -7.3 -12.0 PE 1.145" -7.5 f0.5 * extrapolated from ref. (5). APPARATUS FOR THE KINETICS OF THE ESTERIFICATION Esterification was followed by the pressure of the steam evolved as a function of time at fixed temperatures in the range 150-195°C. The cylindrical aluminium block thermostat is described first, followed by the pressure transducer measuring system and its calibrations.The A1 block (fig. 2), an improved version of that used e a ~ l i e r , ~ - ~ was encased in asbestos wool and composition insulation, and had central viewing ports A for observation of the glass apparatus, heating wires B, C and a contact thermometer for crude thermostating to & 0.05"C. The axial tunnel containing the glass apparatus was placed horizontally, which gave much better spatial temperature uniformity than the earlier vertical arrangement .3 The fine temperature control system (& O.O02"C), superposed upon the crude control just mentioned, employed a movable silicone oil cup (fig. 3) which could be positioned around the bottom of the reaction vessel containing the pellet (causing it to melt). The oil cup temperature was controlled at 1 or 2°C above that of the A1 block. The oil-cup (fig.3) together with the rigidly attached button magnet is rotated around the stationary frame holding the insulated heating wire (Thermocoax) and thermistor (Stantel type GT 15) regulating head, causing the oil to be stirred. A magnetic follower inside the reaction vessel at the same time stirs the reaction melt. FIG. 2-Sectioned front view of thermostat aluminium block. A, tunnel for glass reactor (not shown, see fig. 4), and viewing window (dotted line) ; B, C, heating wires ; D, contact thermometer ; E, asbestos composition insulator ; F, entry port for glass reactor and final position of transducer; FIG. 3.-Oil cup for fine temperature control. A, thermistor head; B, glass cup; C , threaded screw securing glass cup to supporting rod with leak-proof silicone rubber insulation ; D, Teflon washer; E, magnet fixed solidly to oil cup; F, frame for heating wire; G, reaction melt; H, insulated heating wire (Thermocoax). G, motor for driving oil cup (fig.3) ; H, supporting rod for oil cup.166 A MODEL MELT ESTERIFICATION 0.04 a 0 . 0 2 - 0 It is essential to delay the start '3f the reaction until thermal equilibrium is attained around the transducer measuring head (on the right of fig. 4), because of the sensitivity of this device to temperature changes. To implement such delay, the apparatus is designed so as to allow temperature control of the reaction mass independently of that of the transducer, which is deliberately placed as far as 25 cm away. A sharp start to the reaction can be achieved A n - .. . . b .' . .** .*- , FIG. 4.-Reaction vessel and transducer assembly (schematic) : A, break-seal ; B, pellet of reactants and magnetic stirrer ; C, capillary side-arm ; D, transducer diaphragm ; E, glass-metal seal ; F, air-space ; G, asbestos composition plug ; H, glass-metal seal to reaction vessel. The reactor volume is ca. 30 cm3. FIG. 5.-Pellet cooling device. A, pellet and magnetic stirrer ; By static oil ; C, inlet for circulating water; D, outlet. time/min data from transfer unit (see text). FIG, 6.-Initial part of rate plot for typical reaction. Conversion cc is plotted against time usingM. GORDON AND C . G . LEONIS 167 when desired, by exchanging the cooling cup (fig. 5 ) for the oil heating cup which takes about 10 s.The pellet is seen to melt almost at once. Judged by the smoothness of the rate curve (fig. 6), the melt reaches substantially the temperature of the oil cup within one or two minutes. THE PRESSURE TRANSDUCER MEASURING SYSTEM A N D ITS CALIBRATIONS The kinetics were followed in terms of the pressure of steam in the sealed reaction vessel, using type 4-3 16 transducer from Consolidated Electrodynamics, Bell and Howell, U.S.A. The reference side of the transducer contained a small pressure of argon. The glass reaction vessel and the argon reference cell were connected to the transducer by glass-metal seals. When connected to its ripple-free power supply (Solartron strain gauge power supply type A S 974.2), the transducer gave an output linear in the diaphragm pressure.This output was amplified by a Fylde type FE-164-BD/C amplifier, temperature controlled to k 1°C. The amplified signal was passed to a Solartron multi-channel data transfer unit, connected to a Solartron auto-ranging digital volt-meter. A Facit high-speed papertape punch recorded times and voltages automatically. Calibration measurements of transducer voltage V in mV against air pressure (P in Torr) using a Hg manometer at the two extreme temperatures used for the kinetic runs fit a linear relation : P = 727.i(ko.3)-4.889 v (e = 1 5 0 ~ ) ( 7 4 P = 652.4(+0.3)-4.681 v (e = 195°C). (76) The calibration constant (slope) was reproducible to within 0.15 % for several calibrations. It was thought desirable to check the calibration against steam pressure, in case there was any interference by sorption or interaction of steam with the measuring device.A thin-walled pear-shaped glass microampoule was weighed, filled almost completely with water (ca. 20 mg), sealed and re-weighed. It was placed in the reaction vessel and kept cool by the cooling cup (fig. 5) until the A1 block had reached thermal equilibrium at 160°C. When the cooling cup was exchanged for the oil cup, the thermal expansion of the water cracked the micro-ampoule. There was some time delay due to super-heating of residual water in the microampoule, but after about 12 min a steady pressure (ca. 1.5 atm) was reached. This pressure accounted for the weighed water to within 2 %, which was considered satisfactory. DESCRIPTION OF KINETIC R U N U S I N G STEAM PRESSURE MEASUREMENTS A pellet (ca.90 mg) of reactants, weighed to +O.l mg, and a glass covered magnetic follower were introduced (fig. 4) into the reaction vessel, which was then sealed under vac- uum, taking precautions to keep the pellet cool to avoid premature reaction. The reaction vessel was glassblown onto the transducer assembly, leading via the capillary side arm C to a vacuum line and pumped down to After the pressure had fallen to the required level (which took several hours), the transducer and the adjacent part of the reaction vessel were baked out at 200°C with an electric heating tape to remove volatile species. Then the seal A was broken by a steel weight and an external magnet exposing the pellet to vacuum. Pelletising the monomers prevents any fines being sucked down the vacuum line.The breakable seal acts as a precaution against loss of monomer (especially lauric acid) during the initial prolonged exposure to high vacuum. The bottom of the reaction vessel was immersed in hot water until the pellet began to melt and immediately recooled. This freed any trapped vapours or air in the pellet, which otherwise later interfered with determining the base line and the starting point by causing a sudden jump in pressure when the pellet melted. When the pressure had again fallen to its previous level the whole line was flushed several times with dry argon and again evacuated to remove any residual oxygen. The reaction vessel was then sealed at the point C (fig. 4) under a pressure of 20-30 Torr of dry argon (to suppress distillation of lauric acid at the early stages of the reaction, when the part of the reaction vessel just above the treating cup is still below the block temperature.) The trans- ducer reaction vessel assembly was then introduced into the A1 block.After thermal equilibrium was reached in the transducer head (constant voltage reading), the data transfer Torr.168 A MODEL MELT ESTERIFICATION unit was set to punch out values of time and voltage [at intervals A(conversion) = Act- 0.002-0.0031, the cooling cup was removed and the oil cup was raised to submerge the tip of the reaction vessel and the rotation of the oil cup started. VAPOUR PRESSURE OF THE REACTANTS Despite the relatively high pressure of pure liquid LA (-11 Torr at 170"C), the liquid mixtures of LA with PE and PEML had no measurable vapour pressure.This is seen by extrapolation to zero time of the rate curves, i.e. there was no measurable jump in pressure immediately after heating the melt to 195°C. The implication is that the vapour pressure of LA above the mixture falls far short of that predicted from Raoult's law. It is not surprising that such deviations from ideal solution behaviour in LA/PE and LA/PEML should occur (e.g. due to differences in H-bonding when compared to pure liquid LA). MEASUREMENT OF THE VOLUME OF THE REACTION VESSEL After the completion of a kinetic run, the volume of the vessel was determined by con- necting it to a gas burette, and evacuating both. The pressure in the reaction vessel was increased in increments, by opening alternately taps connecting the burette to the atmosphere and to the reaction vessel.A plot of log(P,-Pi) against i is found to be linear in accordance with Boyle's law, where Pa is atmospheric pressure, and Pi the pressure after the ith increment. The volume of the vessel is calculated from the slope, and found to be reproducible to 0.1 % by least-squares analysis. RESULTS DATA PROCESSING OF PRESSURE MEASUREMENT OF EXTENT OF REACTION Altogether 23 kinetic runs are reported here as set out in table 2, out of a total of 36 runs. Those discarded were suspected of errors due to accidents from various sources during the prolonged time of execution of a run. Each run comprised about 300 voltage (pressure) measurements collected by the data transfer unit and fig.7 shows the smoothness of the reaction as attested by a typical trace of pressure against time. The pressure of water vapour for each point was calculated from the calibration (see Experimental section). Each pressure reading was then converted to the cor- rected l1 specific volume of steam Vsp,corr at that temperature and this together with the reaction vessel volume VR, was used to calculate the mass of water m(t) given off and hence the conversion : where m(m) denotes the mass of the products at full conversion. The mean of each set of runs at fixed E and T was used to construct a mean kinetic curve. Chebychev polynomials of the order 14 or 15 were then fitted to a number ( N 100) of data pairs from each of these mean kinetic curves and the polynomials were used to regenerate the curve for all further analyses as described below.A typical plot (fig. 8) of the difference between the averaged experimental extents of reaction and those reproduced by the polynomial shows these differences to be negligible, since c~~~~~ z 0.0005 (table 4, column 5) and the absence of any systematic trend. FITTING OF RATE LAWS TO THE DATA Two separate one-parameter theories will be compared. The first formally adjusts the apparent reaction order n as a parameter, the second adjusts the linear first-shell substitution effect (FSSE), parameter N [cf. eqn (2), (4))E [eqn(3)1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1* 1* 2 2 1 /2 1 /2 a 0.25 0 M. GORDON AND C. G . LEONIS 169 TABLE 2.-oPTIMISED FIT TO APPARENT REACTION ORDER SCHEME i' - /.!' I I J' I I I apparent reaction correlation temp./"(= ordcr, n coefficientx 10-1 150 2.70 9.9965 150 2.70 9.9963 1 60 2.80 9.9987 1 60 2.80 9.9988 160 2.70 9.9886 1 60 2.70 9.9974 160 2.80 9.9986 160 2.70 9.9996 160 2.80 9.9996 170 2.80 9.9998 170 2.80 9.9998 170 2.80 9.9998 180 2.80 9.9998 180 2.80 9.9998 180 2.80 9.9998 195 2.70 9.9998 195 2.80 9.9998 195 2.70 9.9995 195 2.70 9.9995 160 2.50 9.8775 3 .OO 9.971 5 1 60 2.50 9.8883 3 .OO 9.9756 1 60 2.50 9.9820 3 .OO 9.9965 160 2.50 9.9832 3 .OO 9.9958 stand. dev.of k k/gn-l moll-" over points/ 103 x init. slope/ mu-' gn-1 moll-" min-1 min-1 97 96 252 250 134 135 268 138 256 518 486 477 567 577 58 1 567 1111 434 442 937 927 870 900 40.8 39.9 32.5 33.4 2.82 1.69 5.75 8.37 5.42 6.33 7.82 2.84 10.14 20.41 16.23 14.90 21.14 21.45 22.32 9.65 34.7 16.43 17.62 4.02 99.26 4.05 99.9 2.18 49.7 2.09 57.69 * starred entries refer to LA/PE non-starred to LA/PEML.4.90 5.10 7.92 6.51 8.35 5.75 7.43 7.1 1 6.71 12.76 14.25 13.28 15.81 14.94 14.94 30.03 28.75 29.2 3 1.24 11.90 10.07 4.47 4.06 FIG. 7.-Typical kinetic run : conversion a [eqn (S)] against time (at final a = 0.7 the pressure i s 202 Torr).170 A MODEL MELT ESTERIFICATION 0 . . . . .-. *. . 0 . 0 1 5 0 3 0 0 4 5 0 time/min FIG. 8.-A typical plot showing the difference between an original kinetic run and its smoothed reproduction. LA/PEML = 1, 0 = 170°C. APPARENT REACTION ORDER The absence of a substitution effect (N = 1) reduces eqn (2) to the special case of where the concentrations are expressed as equivalents of the functional groups per unit mass : d[COOH]/dt = k[COOH]2[0H] (9) [COOH] = (4-j)p2CL (10) ( j = 0 for PE/LA and j = 1 for PEML/LA), while the hydroxyl concentration is given by (11) d[COOH]/dt = k[COOH]"-l[OH].(12) 3 [OH] = (l-E(l-p))Cij = (1/(4-j)] i = C j (4-i)piC;j. The special case (n = 3) can formally be generalised : Let the initial concentration of carboxyl and hydroxyl groups be Co and Co/E (in equivalents of functional groups per unit volume) respectively, and C the carboxyl concentration at time t. If then Approximating, by neglect of change in volume during the course of the reaction [cf. eqn (18)] solutions of eqn (14) in terms of the conversion cc, of the carboxyl groups (see fig. 9) : were used by treating the apparent reaction order n as a parameter in the range 2 < n < 3.The best least-squares fit was computed for each run, as was the product moment correlation coefficient r, defined as A = (1 -E)/E, (13) (14) -dC/dt = k(AC0 + C)C"-l. a1 = (Co-C)/Co (15) where L is the number of data pairs used, and a, is the standard deviation of x values about the mean.M . GORDON AND C . G . LEONIS 171 The best fit was verified by noting the value of r, which maximises the correlation (table 2). The least squares fit equation was next utilised to calculate the overall rate constant for the n values used [eqn (14)]. Table 2 shows that the best fit is always for reaction orders between 2.7 and 2.8. For the reaction systems with initial stoichiometric ratio other than 1, the fittings for reaction order 2.50 and 3.00 are given instead of the best fit.Even for those cases the best fit lies between 2.7 and 2.8 as is obvious from fig. 9, where plots for different reaction orders are presented. The fit of the fractional-order scheme is not impressive The apparent rate constant is seen systematically to vary by several percent during the course of a run even for the best n-value as is demonstrated by the typical fig. 10. The percentage error in reaction time is equal to that in the apparent rate constant. The error induced in a is, on average, substantially larger than when fitting the FSSE scheme, discussed in the next section. I f a I 0 I50 3 0 0 4 5 0 6 00 (I) c.. .I I ?? P e r( (b) 5 8 I I 7 t time/min FIG. 9.-Degree of fit (linearity) to experimental data using the apparent reaction order as parameter (a) LA/PEML = 1, 8 = 160°C; (b) LA/PEML = 3, 8 = 160°C.I, n = 2.0; 11, n = 2.5; 111, n = 2.8; IV n = 3.0.172 A MODEL MELT ESTERIFICATION 9- 8 - 7, 3 - 2 - 5- FI I X -Y 2 a a m C - a ‘w.... s a N 2 X * w I 2 a a a a a a a a a a a a 0 a a a a time/min FIG. 10.-Typical plot demonstrating the variation of rate constant with time: I, n = 2.0; 11, It = 2.5; 111, n = 2.8; IV, n = 3.0. LINEAR FIRST SHELL SUBSTITUTION EFFECT If the reaction order n is not to be treated as adjustable, a value has to be fixed for it. The true order in the absence of all disturbing effects is thought to be three as shown in solution studies for different esterification systems. Flory confirmed this for bulk esterifications. Gordon and Scantlebury attributed the downward deviation they observed in esterification of PE and TME with adipic acid to cyclisation and substitution effects.Cyclisation is, of course, impossible with monofunctional acids like LA. Estimates of the two parameters k and N are, therefore, calculated using n = 3. The q h values calculated by computer from eqn (2)-(6) at different times were then compared with the corresponding aexp values. Each aexp point was taken from the Chebychev polynomial smoothed mean kinetic curve of the runs for the same reaction conditions. The standard deviation ofit is then calculated for various trial values of N and of k& using L ( N 50-60) data pairs, Table 3 shows the results of these calculations. The best fit was equated with the minimum of afit for given reaction conditions.The quality of the fittings will be discussed from two points of view. First it is seen in table 4 that for the eight rate curves, each of which is the mean of several such curves (23 in all), the standard deviation of the mean measured conversion a from theory was in the range 7 x < ofit < 4.7 x This is an excellent fit of experiment to theory, not significantly affected by the convenient Chebychev polynomial smoothing procedure, since the experimental data are reproduced by the polynomials to a standard deviation of 0.0005.M. GORDON AND C. G . LEONIS 173 The second mode of comparison shows more clearly that the fitting of the measure- ments within experimental error to the particular 1 -parameter theory of the linear first-shell substitution effect is highly significant (i.e.in comparison with possible alternative one-parameter fittings). TABLE 3.-PARAMETERS FROM OPTIMISED FIT TO LINEAR FSSE kinit.1 k&tNil kztl g2 mol-2 gz. mol-2 g: mol-2 kf,t I stoichiometric E g2 mol-2 [eqn (3)] temp./% polyol min-1 N i min-1 mm-1 min-1 1 1 1 1 1 2 1 112 150 160 170 180 195 160 160 195 PEML PEML PEML PEML PEML PEML PEML PE 331 1.45 1 470 480 326 491 1.40 1 668 687 477 915 1.43 1 1261 1309 911 1010 1.47 1 1430 1485 1001 1977 1.45 1 2760 2867 1958 501 1.39 1 705 696 490 483 1.53 1 727 739 488 1754 1.42 0 1660 1754 1612 N' 1.38 1.34 1.35 1.39 1.37 1.36 1.44 1.35 In fig. 11 which is typical for runs at all eight reaction conditions, the difference AN between the conversions taken (a) from the Chebychev-smoothed mean reaction curve for the runs at 160°C and of stoichiometric ratio 1 : 1, and (b) from four cal- culated rate curves, are plotted.These curves refer to the substitution effect para- meter N adjusted to 1.0 (absence of effect), 1.2, 1.4 and 1.5. It is apparent that an excellent fit is obtained using N = 1.4, when the maximum deviation over the range included (up to a = 0.75 of total conversion) is AN = 0.002. The transformation of plot I to a plot resembling I11 is clearly a severe test for any one-parameter theory, and the success lends support to the assumption of a substitution effect. ......... e-. 1. -21 I 0 I50 3 0 0 4 5 0 6 0 0 timelmin FIG. 11 .-Differences between experimental and calculated conversions for different values of the FSSE parameter are plotted against time. LA/PEML = 1, 8 = 160°C, I, N = 1.00, k* = 887; 11, N =? 1.20, k* = 640; 111, N = 1-40, k* = 491 ; IVY N = 1.50, k* = 436.k* in g2 min-l. COMPARISON WITH INITIAL SLOPES It is inherent in the substitution effect theory, and the fittings just discussed, that the initial part of each rate curve is asymptotic to the case N = 1 for PE (i.e. the first few ester links cannot be affected by the substitution effect). This means that in the case of LA/PE the rate constant kFi, from the optimal fitting (table 3) should equal the174 A MODEL MELT ESTERIFICATION third order constant kinit. calculated from the initial slope. In the case LA/PEML, krit should equal N times kinit., because the starting material PEML is subject to a rate increase by a factor N when fitting eqn (2), (4), (6), since it already contains one ester group.Table 3 shows good agreement between kinit. and kzt. EFFECT OF VOLUME CONTRACTION ON MASS LAW KINETICS The effect of volume change on the chemical kinetics is now examined. The appropriate theory has been derived l4 on the basis of the equation : d(N,/V) - 1 dNi Ni dV dt V dt V2 dt - ----- where Ni is the number of molecules of compound i in volume V, which has an initial value (t = 0) V,. Applying the above equation to the present situation of esterification in the melt, the law of mass action for a reaction of overall order 3 reads : dn, n,dV = k,*ntn,/V2 ~ - _ - dt V dt where n1 is the number of moles of PEML in the mixture, and k: is the rate constant expressed in dm6 equiv.-2 min-I.If the volume contraction parameter is represented by p (I( > 0) then at any time t : (20) V = Vo[1-p(l-nL/n~)] = Vo(l-p.la). The value of p is calculated from the stoichiometry and the densities assuming ideal volume mixing where Vm,i is the molar volume of compound i at temperature T. eqn (20) into eqn (19), we obtain By substituting or in more familiar terms dpidt = k*p2[3Np1 +2N2p2 + N3p3]CiC,0,/(l -p)[1 -p(l - p ) ] . (23) Eqn (23) shows that the correction factor for k* due to volume change is (1 -p) [l -p(l -p)]. In earlier work a correction was made to the kinetic data of this kind to allow for the effect of volume contraction during reaction. The effect was found to be fairly small in its effect on Nand moreover the formula then used overestimated the effect by a factor of 2.The shrinkage at full conversion for AA/PE was estimated to be 35 %. In the present case the shrinkage for full conversion was calculated from the measured densities to be 7.2 % for a stoichiometric mixture of LA/PEML at 170°C and 9.4 % for LA/PE at 195°C. To estimate the effect of the volume contraction on the parameter N the factor 1 /( 1 - p)[ 1 - ,u( 1 -p)] was incorporated into the differ- ential eqn (2)-(6) and the optimal values for kfit and N’ were obtained (table 3). The average of optimum values for N is thus lowered from 1.42 to 1.37. ASSESSMENT OF ACCURACY Table 4 summarises the accuracies of measurements and fittings in terms of the four standard deviations introduced. The reproducibility of steam pressure at fixedM .GORDON A N D C . G . LEONIS 175 times in different runs is measured by ore*, the averaged standard deviation from the mean curve for each set of experimental curves at fixed E and T. The error in a introduced by smoothing with Chebychev polynomials is given by opoly, which was found to lie in the range 1 x This may be taken to represent also the standard deviation in some measurement of AaxO.O1, say, in a given run (cf. fig. 11). The accuracy of absolute measurements of a is around 0.005. The accuracy of fitting the rate curves (averaged over a set of replicate runs) to the kinetic scheme is measured by ofit. Incorporation of the small volume correction described in the previous section changes ofit to oht, without conclusive improvement. < opOly 6 7 x TABLE 4.-sTANDARD DEVIATIONS FOR THE VARIOUS FITTINGS stoichiometry E [eqn ( 3 1 1 1 1 1 1 2 112 1 temp./"C polyol orepr x 1 0 3 150 1 60 170 180 195 1 60 1 60 195 PEML PEML PEML PEML PEML PEML PEML PE 1.462 4.357 4.909 1.458 1 .lo8 1.778 1.652 1.301 opOly x 1 0 3 0.49 0.68 0.10 0.17 0.13 0.61 0.10 0.14 oPit x 1 0 3 1.95 0.664 0.08 1 0.100 0.094 4.68 0.073 0.180 x 103 1.87 1.79 0.227 0.218 0.200 4.59 0.092 0.392 n M 0 s CI 21 22 23 24 lo4 KIT FIG.12.-Arrhenius plot for all sets of reaction conditions. TABLE 5.-ACTIVATION ENERGIES FOR ESTERIFICATION REACTIONS temperat!re (range)/ activation energy/ system and source C kJ mol-1 bulk { fiiEML} this work 150-195 64.8+ 2.9 bulk DMG/BTA-9 80-90 55.2 palmitic acid/cycIohexanol,l dilute solution 100-154 64.4 palmitic acid/ethyl alcoho1,18 dilute solution 75-154 63.2 THE ACTIVATION ENERGY Figure 12 presents an Arrhenius plot of the 23 runs on LA/PEML and LA/PE, in which the values of the rate constant were optimised over each set of reaction condi- tions.The activation energy is found from the slope to be 64.8k2.9 kJ mol-l. This is compared in table 5 with results relating to other mono- and poly-functional esterifications, which are seen to be very similar. Rate constants have been measured176 A MODEL MELT ESTERIPICATION in the past for a number of polyfunctional esterifications in the melt, and some typical ones are included in table 6. Their magnitudes do not differ greatly, supporting the conclusion that the general esterification mechanism is the same.TABLE 6.-COMPARISON OF ESTERIFICATION RATE CONSTANTS 10-2 x rate constant/ system and source temperaturel'c g2 mol-2 min-1 LA/PEML (this work) 175 9.50 adipic acid/PE 39 175 4.54 DMG/BTA 170 5.5 sebacic acid/PE 175 4.83 tridecanoic acid/PE 180 7.27 DISCUSSION The kinetics of self-catalysed esterification reactions of monocarboxylic acids have been extensively studied in solution, using monofunctional alcohols. Several studies have also been published on the kinetics of esterification of polyfunctional acids with polyfunctional alcohols in bulk,16 or in concentrated and in the present work as a bridging exercise, a monofunctional acid was esterified with poly- functional alcohols. A comparison of all these studies shows a remarkable degree of uniformity of the reaction kinetics. The reaction order with respect to COOH is generally found to be two ; when (OH) is not buffered by excess, as in dilute alcoholic solutions l8 of carboxylic acid, the order with respect to OH is generally found to be close to unity. Although the early work of Flory l 3 led to the postulate of an overall third order reaction scheme for the non-catalysed esterification, in more recent work it was claimed that the reaction rate is directly proportional to the hydrogen ion concentration and assigned a 2.5 order to polyesterifications with weak polyfunctional acids, but this is clearly not borne out by the present much more exact and detailed measurements.The activation energy (see final section of the Results) is generally close to 63 kJ mol-l (table 5).It seems reasonable to assume that the mechanism is essentially identical throughout these reactions. As shown especially accurately in the present work, the deviations in bulk ester- ification from overall third order kinetics are so small, that they would normally not be noticed. In this work, the optimal fitting always gave apparent reaction orders between 2.7 and 2.8 (cf. fig. lo), but strong evidence has been presented (fig. 11) that the deviations from third order kinetics are linked specifically to the degree of substi- tution of the alcohol moiety of the reacting complex. More exactly still they can be covered by a single linear first-shell substitution effect parameter N, there being quite sufficient information content in the measurements to lend conviction to the fitting in Implicitly, however, such data fittings, and the underlying rate eqn (2)-(6), assume the absence of various disturbing effects, which need justification. The most import- ant such effects are due to changes in medium and (on the basis of the collision theory of chemical kinetics) l8 in the size of reaction partners during the course of reaction.In the work of Fairclough and Hinshelwosd l8 with dilute solutions of monofunc- tional carboxylic acids in monofunctional alcohols, effects of medium and of size are discernible, nut in the course of any one reaction, but in passing from one reaction system to another. When studying polyfunctional systems in bulk, both effects might, therefore, be expected even in the course of a single reaction, since then both the size of the reagents and the medium change appreciably during the course of the reaction. fig.11.M . GORDON AND C. G . LEONIS 177 Unfortunately one cannot hope to study tree-like (ring-free) gels, or therefore, make significant deductions from model systems, without involving polyfunctional materials in bulk. To illustrate the magnitude of the effects found in dilute solution, the pseudo- second order rate constant increases by over 30 % when changing from butyric to palmitic acid in ethyl alcohol l 8 (an effect due to reagent size), and by 100 % when passing from cyclohexanol to ethyl alcohol as solvents for butyric or palmitic acids (an effect of the medium). These effects are clearly comparable in magnitude to our finding a change of -35 % in rate constant when passing from PEML to penta erythritol dilaurate (PEDL).We shall nevertheless contend (cf. Part 2) that the empirical evidence strongly indicates the absence of size effects in melt esterifications. Indeed we also deduce that a medium effect is absent in the course of a single reaction run in the melt, but here a single fortuitous cancellation is quite possible. All that is required is that the replacement of one OW and one COOH by one ester group happens to leave the " solvent " effectively unchanged in quality as regards its functioning as medium for subsequent esterification during the course of a run. P. J. Flory, J. Amer. Chem. SOC., 1941, 63, 3083. W. H. Stockmayer, Advancing Fronts in Chemistry (Reinhold, New York, 1945), vol. 1. M. Gordon and G. R. Scantlebury, J. Chem. SOC. B, 1967, 1. J. A. Love, Ph.D. Thesis (University of Strathclyde, 1968). T. G. Parker, Ph. D. Thesis (University of Strathclyde, 1969). M. Gordon and C. G . Leonis, J.C.S. Furaduy I, 1975, 71, 178. ' J. Oliver, Computing Centre, University of Essex, personal communication. ' (a) C. W. Gear, Comm. A.C.M., 1971,14,185; (b) C. W. Gear, Comm. A.C.M., 1971,14, 176. C . A. E. Peniche-Covas, Bh.D. Thesis (University of Essex, 1973). National Engineering Laboratory Steam Tables (H.M.S.O., Edinburgh, 1964). lo C . L. Ogg, W. L. Porter and C . 0. Willits, Ind. Eng. Chem. Anal., 1945, 17, 394. l 2 A. C. Rolfe and C. N. Hinshelwood, Trans. Faraday SOC., 1934, 30, 937. l3 (a) P. J. Flory, J . Amer. Chem. SOC., 1937, 59, 466; (6) P. J. Flory, Principles of Polymer Chemistry (Cornell U.P., Ithaca, 1953). l4 (a) P. D. Barlett and J. Altschul, J. Amer. Chem. SOC., 1945,67, 816 ; (b) B. Delmon, A. Giraud and P. Leprince, Compt. rend., 1957,244, 1920 ; (c) J. Hutchinson, R. S. Lehrle, J. C. Robb and J. R. Suggate, J.C.S. Faraday I, 1973, 69, 426. l 5 (a) C. N. Hinshelwood and A. R. Legard, J. Chem. SOC., 1935,587 ; (6) H. Goldschmi d., Ber., 1896, 29, 2208 ; (c) A. T. Williamson and C . N. Hinshelwood, Trans. Faruduy SOC., 19t34,30, 1145. l 6 (a) P. J. Flory, J. Amer. Chem. SOC., 1939, 61, 3334; (b) R. H. Kienle and A. G. Hovey, J. Amer. Chem Soc , 1929, 51, 509 ; (c) R. H. Kienle, P. A. van der Meulen and F. E. Petke J . Amer. Chem. Soc., 1939,61,2258, 2268 ; (d) R. H Kienle and F. E. Petke, J. Amer. Chem. SOC., 1940, 62, 1053 ; (e) R. H. Kienle and F. E. Petke, J. Amer Chem. Soc., 1941, 63, 481. R. A. Fairclough and C. N. Hinshelwood, J . Chem. Soc., 1939, 593. Tang and K. S. Yao, J. Polymer Sci., 1959, 35, 219. l7 G. R. Scantlebury, Ph.D. Thesis (University of London, 1964). l9 (a) I. Vansco-Szmercsanyi and E. Makay-Bodi, J. Polymer Sci. C, 1968, 16, 3709 ; (b) A. C.

ISSN:0300-9599    

DOI:10.1039/F19757100161

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Lauric AcidiPentaerythrityl Monolaurate : A Model Melt Esterification Part 2.-Statistical Distribution of Products BY MANFRED GORDON AND CONSTANTINE G. LEONIS Department of Chemistry, University of Essex, Wivenhoe Park, Colchester C04 3SQ Received 31st May, 1974 The esterification of lauric acid, LA, with pentaerythrityl monolaurate (PEML) has previously been shown to exhibit a positive kinetic substitution effect in the PEML moiety : each OH previously esterified in PEML (or in pentaerythritol, PE, itself) accelerates the esterification of any remaining OH in the same PEML unit (first-shell substitution effect, FSSE) by a factor of about 1.3-1.4. This corresponds to a small difference in activation free energy (2-3 kJmol-I), but a similar effect in polycondensations of PE with dibasic acids causes substantial changes in gel points, network structure and physical properties, so that the thorough investigation of the simple model system LA/PEML is of value.The substitution effect is here confirmed by comparing gel permeation chromatographic measurements of the composition as a function of conversion with the statistical theory of the FSSE. The mechanism of esterification in undiluted melts is briefly reviewed. In ungelled systems, no evidence for diffusion control, for effects due to the size of reagent species, or due to the change in medium with increasing conversion, is generally found. The occurrence of a positive substitution effect of an ester link on the rate of formation on another such link on the same pentaerythrityl repeat unit was confirmed in Part 1 by precise kinetic measurements on the esterification in melts of lauric acid (LA) with pentaerythritol (PE) and its monolaurate (PEML).A similar effect had been found earlier in polycondensations of PE or tri(hydroxymethy1)ethane with adipic acid. The motivation behind the careful measurement of even rather small substitution effects of this kind lies in the unexpectedly large changes they can cause in the physical properties of polycondensates, and especially in model gel systems. Such changes were illustrated in a recent theoretical calculation by Dugek on the swelling behaviour of gels formed under a regime of a linear first shell substitution effect The general importance of the FSSE model in physical chemistry is underlined by its history. The first formal treatment we have found was that of Pauling for the binding of oxygen by haemoglobin; and Bjerrum formulated the thermodynamic FSSE theory of ligand binding as the central theme of his book on metal ammines.The result of kinetic measurements in Part 1 was felt to be in need of confirmation by an independent method based on the analysis of the statistical distribution of the ester products. Since the FSSE found was relatively small, amounting to a difference in activation free energy of about 2.3 kJ mol-1 at 170°C, there remained some doubt in case the rate acceleration attributed to the FSSE was simulated by contributions from several experimental sources, even though individually these had been proved to be negligible, e.g.the solubility in the reaction mixture of the steam produced, the escape of a little LA into the vapour phase (followed by its redissolution as the (FSSE). 178M. GORDON AND C. G . LEONIS 179 reaction proceeds), the sorption of water on the glass surfaces, etc. These doubts are resolved by analysis of reaction mixtures using gel permeation chromatography (g.p.c.1. THE PRODUCT DISTRIBUTION I N ABSENCE AND PRESENCE OF SUBSTITUTION EFFECT The mde fractions pi of products carrying i ester groups in the random reaction, free from FSSE, between PEML and a monocarboxylic acid, are given by the Bernouilli distribution : where a is the fractional conversion of the functionalities. Eqn (1) is generalised and usefully expressed in terms of p 1 by eliminating the time from eqn (2)-(6) of the previous paper,l and integrating them, so that (in the same notation) 6NPl 6p2"3 6pY2I3 p 3 = ( 3 - 2N)(3 - N 2 ) - ( 3 - 2;)(2 - N ) (3 - N2)(2 - N ) ~ N ~ P ~ 3 Np: N13 6pY2I3 p4 = - ( 3 - 2N)( 3 - N 2 ) ( 3 - 2N)(2 - N ) - ( 3 - 1V2)(2 - N ) ( 3 ) (4) and the fractional conversion of lauric acid becomes : ( 5 ) 2( 1 - N)p:N13 2p72'3 (2N3-N2-4N+3)pl = ( 3 - 2 N ) ( 2 - N ) + ( 3 - N 2 ) ( 2 - N ) + ( 3 - N 2 ) ( 3 - 2 N ) ' Eqn (2)-(5) revert to (1) for the random case ( N = l), since then This work is concerned with experimental testing of these equations.Two comple- mentary methods were used : one to measure the overall conversion a as a function of time, and the other to measure the distribution pi as a function of time. 1 -G! = p = p1 +$p, + i p s .(6) EXPERIMENTAL MATERIALS Pentaerythrityl tetralaurate (PETEL) was obtained from Eastman Organic Chemicals and Naphthalene (NL) was obtained from British Drug Houses Lid. (microanalytical grade). Tetrahydrofuran (THF) was supplied by the East Anglia Chemical Company sufficiently pure as g.p.c. solvent (refractive index at 20°C : 1.4076). The preparation and purification of pentaerythrityl monolaurate (PEML) has been described in the previous paper,l as has the source and purification of lauric acid LA. Mixtures of esters of pentaerythritol and LA were produced by carrying out a reaction between LA and PEML of stoichiometric ratio 1 : 1 in the block thermostat as described.l The reaction was stopped at the desired time and the reaction vessel-pressure transducer assembly was taken out of the oven and the reaction vessel end immediately quenched in a Dewar vessel containing liquid nitrogen.This part of the vessel, containing the reaction mixture was cut off and put in a silica gel desiccator, evacuated and kept in a deep freeze until analysed. recrystallized from petroleum ether (m.p. found 50"C, lit. 49°C).180 MODEL MELT ESTERIFICATION APPARATUS Apart from its use for measuring molecular weight distributions of polymers, g.p.c. is an excellent tool for studying oligomer and low molecular weight mixtures6 The prospect of analysing reaction mixtures quantitatively by g.p.c. was one of the main factors for starting this work. The technique was used not merely to analyse compositions of reaction mixtures as a function of reaction progress, but to supplement titration procedures for assessing purity of the reactants, and for checking their initial concentrations in pellets made up by weighing.In the latter case, agreement was generally of the order of accuracy of the g.p.c. calibration ( N 4 %). A Waters Associates model 200 instrument equipped with differential refractometer, Leeds and Northrup Speedomax W recorder, and the usual accessories was used. Six columns, each 4 ft long with inner diameter of 3 inch with nominal permeability limits of 6, 10, 17, 10, 10 and 20x loF7 cm were used in that order. The last of these six columns was packed with Poragel WA200 using a method developed in this laboratory,' found to improve resolution R by about 25 %, as assessed from the formula : (7) R1,2 = (K- V d / ( K + W2) 1 I * 45 ' 4 0 35 30 elution volume (as 5 cm3 counts) I I .45 '4a 35 30 elution volume (as 5 cm3 counts) elution volume (as 5 cm3 counts) FIG. 1.-Gel permeation chromatogram of reactants and products, (a) at reaction time 77 min : I, naphthalene ; 11, LA ; 111, PEML ; IV, PEDL ; V, PETRL ; VI, PETEL. Length of original recorder trace: 75 cm. (b) As (a) at time 133.33 min. (c) As (a) at 944.33 min.M. GORDON AND C. G. LEONIS 181 where Vi is the elution volume and Wi the width of the peak of substance i. The gel was dispersed in acetone (or methanol), a non-solvent (to restrict swelling), of density less than that of the gel. The suspension was introduced into a column and the settling was accelerated by a simple vertical rocking machine, which tapped the column from below and slowly rotated it.Finally a good solvent was pumped in slowly to displace the non-solvent and to allow the complete swelling of the gel. This procedure gives close packing, good performance and reproducible results. All solutions for g.p.c. were made up at room temperature to ca. 1 % (w/v) in THF as solvent, taken directly from the g.p.c. output end. Each sample was inserted with a hypo- dermic needle, via a fdter over a period of ca. 1 min which still gives adequate resolution, but broadens the peaks a little to assist in the measurements of peak areas (see below). The maximum flow rate used was 2 cm3 m i d . Typical chromatograms obtained at 20°C are shown in fig. 1. To reduce errors from a variety of sources, a known weight fraction of a reference compound was added to all mixtures analysed.Naphthalene was chosen, because it is easily available in high purity, it is inert, soluble in THF and of refractive index substantially higher than the sample, thus giving relatively large peaks. It was also well resolved from all compounds to be analysed. MEASUREMENTS OF PEAK AREAS A Dupont 310 curve resolver (essentially an analogue computer) was used to measure peak areas. First the naphthalene reference peak was measured in the usual way by fitting to it a nearly Gaussian curve.8 The result was then used to set the integrator meter to 100 units so as to scale the measurements for the remaining 5 compounds. The peak of lauric acid was always completely resolved, and was determined next, and finally the partly overlapping peaks of the four esters were fitted and resolved together.The peak skewing facility was used to a minor extent, if necessary. The procedure was repeated 4-5 times for each chromatogram and the mean of these measurements for each component was used as the final result. The reproducibility of these measurements was found to be within 4 %. Average characteristics of the measured peaks are shown in table 1 ; the calibration procedure is outlined in the next section. TABLE 1 .-AVERAGE CHARACTERISTICS OF THE MEASURED PEAKS compound i Ve,i/5 NL 45.5 LA 36.6 PEML 33.5 PEDL 31 PETRL 29.3 PETEL 28 cm3 Ni 7959 4.8 (LA) 5937 1.8 (PEML) 4974 1.3 (PEDL) 4259 0.85 (PETRL) 3805 0.65 (PETEL) 3475 Ni = 16(vqi/Wi)2, theoretical plate number for the compound i with elution volume Ve,i.CALIBRATION OF G.P.C. Of the five compounds, only LA, PEML and PETEL were available in pure form. Accordingly the diester (PEDL) and the triester (PETRL) had their calibration constant determined by interpolation. The calibration constant ki,r of the ith compound available in pure form, relative to the reference compound Y (naphthalene) is defined by AJA, = ki,,wi/w, where A denotes peak area and w weight. According to theory, ki,, should be proportional to the difference An; between the refractive indices of the ith compound and the solvent THF in their pure liquid states, provided effects due to non-ideality of mixing may be neglected. Accordingly, the refractive182 MODEL MELT ESTERIFICATION indices of PEML and PETEL were measured at 74°C (above their melting points), and that of THF at the same temperature was found by extrapolation.The results are given in table 2. The calibration g.p.c. spectrum shown in fig. 2 is one of several taken with different weights of naphthalene, LA, PEML and PETEL, in the range to be expected when analysing the products of kinetic runs. Using two different methods for assessing the effective areas under the peaks of these calibration spectra, fig. 3 and 4 were produced to determine the ki,r [eqn (S)]. Fig. 3 was produced by use of the curve analyser following each peak with the optimal Gaussian curve closely all the way to its well-defined baseline. Fig. 4 was obtained by calculating the areas under the trace by numerical integration between data pairs which were read from the chromatogram without any restriction to obey a specified distribution.TABLE 2.-REFRACTIVE INDICES, AND SPECIFIC REFRACTIVE INCREMENTS FROM G.P.C. DATA kr.rx 102 k;.,x 102 III$& x 102 method 1 method 2 compound nl4'C PEML 1 . 4 5 3 1 7.46 2 6 . 3 5 27.30 PETEL 1 , 4 4 0 3 6 . 1 8 26.04 24.15 LA 1 . 4 2 0 8 4 . 2 3 16.80 1 5 . 9 6 THF 1 . 3 7 8 5 (extr) 0.0 0.0 0.0 , I 45 40 35 30 elution time (as 5 cm3 counts) FIG. 2.-Typical calibration chromatogram : I, NL ; 11, LA ; 111, PEML ; IV, PETEL. ' O t wi/mg FIG. 3.-Linearity of the specific refractive increment for the peaks as estimated by the curve resolver as function of concentration (mg/5 cm3) used. 0, LA ; A, PETEL ; 0, PEML. The second procedure leads to values of kj,r, which are more nearly proportional to Ani (table 2).Nevertheless, we adopt the ki.r obtained from fig. 3 for the following reasons. The differences between the two procedures lead to only small effects on kinetic parameters, especially since the same procedure is applied both to the calibration spectra and to those of reaction products to be analysed. The small error, if any, will be in the direction of decreas- ing the apparent substitution effect, so that the main aim, that of testing for the existence of aM . GORDON AND C . G . LEONIS 183 substitution effect, cannot be prejudiced. Finally, of course, the second method is incon- venient, especially in reaction products where neighbouring peaks may partly overlap (fig. 1).The ki,, values of the pantaerythritol dilaurate (PEDL) and trilaurate (PETRL) were taken by linear interpolation between those of PEML and PETEL (which lie very close to each other, column 2, table 3). The analysis of unknown mixtures (products of kinetic runs) was based on eqn (8), using the ki,? thus determined. 0 10 20 30 wilmg FIG. 4.-Linearity of the specific refractive increment for the same peaks as in fig. 3, as estimated by numerical integration using Simpson's method. 0, LA; A, PETEL; 0, PEML. For testing the integrated rate equations (2)-(5), the number of moles ni are required rather than the weights wj. We have : Ai/A, = ki,,wilw, = ki,rMini/w, = k&ni/w,. (9) The new calibration constants kzr thus defined are tabulated in column 3, table 3. The areas Ai and A , are measured by the curve resolver, and wr is the weight of naphthalene added to the reaction product; hence ni is calculated.Finally the ni are converted to the pi by normalisation. The pi (and the original ni) are subject to a further stoichiornetric constraint, viz. the second equality in eqn (6). This condition was used as a very minor constraint in adapting the pattern of the original g.p.c. trace to the output of the curve analyser, which was always easily satisfied without doing violence to the data. This is direct evidence that the linear interpolation used for calibrating g.p.c. peaks of PEDL and PETRL is satisfactory. TABLE 3 .-CALIBRATION CONSTANTS compound ki.t kp*.+ PEML 26.35 83.9 PEDL 26.257 131.57 PETRL 26.14t 178.6T PETEL 26.04 225.3 LA 16.80 36.65 4 interpolated TRANSESTERIFICATION All our results and those on analogous systems with polyfunctional acids can be explained on the assumption that, at least in the absence of strong acid catalysts, any transesterification component superimposed on the irreversible esterification reaction can be neglected.In this work, transesterification would lead to formation of some free PE when starting with PEML. PE is insoluble in THF, but no residue or turbidity was observed when preparing samples for g.p.c. analysis. In addition, the normalization condition of the solutes was always very closely obeyed, confirming the absence of loss of material by way of PE.184 MODEL MELT ESTERIFICATION R E S U L T S Seven samples of an equifunctional mixture of LA and PEML at 160°C were The results of prepared as described by stopping at various stages of esterification.the analyses are given in table 4. TABLE 4.-MEASURED DISTRIBUTION OF REACTANTS AND REACTION PRODUCTS timelmin compound AiIAr PEML 12.3 PEDL 24.8 PETRL 18.5 LA 31.0 N(aver age) PETEL 7.65 wrlmg, eqn (8) 77 n i x 1 0 3 Pi N 16.13 0.310 20.75 0.3g9 1.25 11.39 0.219 1.10 3.73 0.072 1.35 101.33 0.649 1.30 11 .oo 1 .Z5 timelmin compound PEML PEDL PETRL PETEL LA N(average) wrhg time/min compound PEML PEDL PETRL PETEL LA N(average) wr Img 195.66 Ai/Ar n i x 1 0 3 Pi N 5.3 2.84 o.140 19.0 6.50 0.319 1.30 26.75 6.74 0.331 1.41 21.4 4.27 0.210 1.32 21.2 28.35 0.464 1-30 1.33 4.50 400.33 Ai/Ar nix103 Pi N 2.75 3.31 0.062 17.45 13.41 0.253 1.11 29.1 16.46 0.310 1.47 44.3 19.86 0.374 1.32 17.75 53.27 0.335 1.25 1 .24 10.10 133.33 Ai/Ar ni X 103 Pi N 8.95 9.87 0.210 22.9 16.11 0.343 1.39 26.85 13.91 0.296 1.45 17.3 7.10 0.151 1.43 25.55 75.73 0.537 1.42 1.42 9.25 324.66 Pi N Ai/Ar ni X lo3 5.55 3.5, 0.0S3 28.3 ll.62 0.270 1.19 52.35 12.55 0.291 1.29 50.7 15.33 0.356 1.35 30.8 49.42 0.382 l.z3 1.26 5.40 645.33 timelmin compound AiIAr PEML 2.05 PEDL 9.8 PETRL 32.9 LA 13.7 N( average) wrlmg PETEL 73.75 944.33 n i x 103 Pi N 2.22 0.040 6.77 0.122 1.30 16.73 0.302 1.21 29.72 0.536 1.22 36.96 0.222 1.25 1-24 9.08 Next eqn (2)-(5) are utilised to determine the value of the parameter N.For the seven different times, the measured values of the four couples ( p , pl), ( p 2 , pl), ( p 3 , pl), (p4,p1) are substituted in these equations.Through a computer program the calculated values of N for each of these couples were obtained and the results are shown in table 4. The average value for the parameter N is 1.3 0.07. We now compare the g.p.c. results with the kinetic results. The comparison is based on the following tests : (i) the individual p i normalized as mentioned as function of time ;M. GORDON AND C. G . LEONIS 185 (ii) the recalculation of the conversion from the measured p , using the identity a = 1 - p [eqn (6)] and the comparison with the a measured from the steam pressure, where a denotes the extent of the reaction. Fig. 5 shows that a(t) compares favourably with that obtained from the steam pressure. In particular, there is no systematic deviation between the two sets of a values, as would result from faults introduced by the approximations mentioned in connection with the calibration procedure.The steam pressure measurements averaged over seven runs are more accurate, and as expected, they define a smoother curve. The triangles are sample points from the single runs which led to g.p.c. samples, where a(t) values are indicated as circles. od 250 500 750 time /min FIG. 5.-Comparison of the extent of reaction a between steam pressure results and g.p.c. [eqn (6)]. Solid line represents the mean kinetic curve for the same run conditions.' A, from p.t.d. ; 0, from g.p.c. ; -, mean experimental curve. In this way the calibration procedure adapted for g.p.c. is again validated. Fig. 6 shows all the p 1 , p 2 , p 3 , p 4 values obtained for the seven different runs at different times.For comparison the changes of these fractions with time are represented by smooth curves obtained by a computer program, using the differential equations (2)-(6) with parameters k* = 477 g2 mo1-2 min-l, and N = 1.34 which give the best fit for the same system for the kinetic study.l The g.p.c. results strongly support the existence of a positive substitution effect of about N = 1.3, by comparing the fit in fig. 6 with the attempted fit of the measurements to the curves for N = 1. This conclusion is unaffected even by attempts to readjust the rate constant k* as a free parameter, i.e. by a rescaling of the time axis in fig. 6, since the degree of fit of the measured p1 and p4 respond in opposite manner to such readjustment of the time scale.DISCUSSION The kinetic analysis supports the substitution effect strongly, and the statistical analysis of the g.p.c. data conclusively. The statistical data on the molecular distribution of ester species obtained by g.p.c., show that the distribution differs significantly from a Bernouilli distribution [eqn (l)]. The only conclusion to be drawn is that the chance of reaction of the hydroxyl groups within any one PE unit are not independent; a conclusion quite independent of the form of the rate law (e.g. the order of the reaction, whether it was steady or periodic, etc.). Thus the data on the distribution show that the definition of a substitution effect is fulfilled. Of course the data go much further, to show that the effect is positive ( N = 1.30,P1 0.5 0 - 8 J I 250 500 750 1000 timelmin 0 250 500 750 1000 P4 time /min 0.5 - 0 250 500 750 1000 time/min FIG.6.--See caption opposite.M. GORDON AND C. G. LEONIS 187 increase of chance of reaction with increasing substitution) and nearly of the same magnitude as deduced completely independently from the kinetics alone ( N = 1.37). Moreover, this effect is comparable in sign and magnitude to that deduced earlier 2 - for polyfunctional analogues of LA from kinetic and statistical data. The statistical data there represented gel points rather than g.p.c. analysis. On the basis of the rigorous statistical analysis, we are in a position to discuss the assumed absence of any disturbance of the random reaction scheme other than the substitution effect during the course of a single reaction run.THE ABSENCE OF REAGENT SIZE EFFECTS I N MELTS In polyfunctional melts, e.g. adipic acid (AA) + pentaerythritol (PE)2* or decane-1,lO-diol (DMB) + benzene-1,3,5-triacetic acid (BTA),1° it has been shown that polyesterification kinetics are described accurately by the same basically third- order scheme supported by the present analysis of a system using a monofunctional acid. Allowance had to be made for a positive substitution effect, of similar order to that observed here, in the case of AA+PE, and some small allowance for intra- molecular esterification in AA + PE and DMG + BTA. These reactions lead to gelation at points very close to those predicted by the classical theory of Flory." The operative size of a reagent molecule in such systems is the weight average, i.e.the mean size of molecule to which a randomly chosen free functionality is attached. This weight average and the viscosity diverge to infinity at the gel point. The esterification kinetics is not measurably changed from the simple third-order scheme up to and some way beyond l 2 the gel point before diffusion control is found to set in (as expected), and, therefore, there can be no measurable effect of reagent size on reaction velocity. Of course, the modern view of the process l 3 includes segmental motions inside a macromolecule as a mechanics whereby a functionality finds a partner for reaction; within the gel molecule, this must be the only cause, since wholesale translation of the molecule does not occur.In the present study, only small molecules are involved, there being a modest increase in reagent size when passing from mainly PEML at the beginning of a run to mainly PETEL near the end of a run. In view of the discussion of polyfunctional analogues, we may exclude the possibility of any effect of the size of the reagent on the kinetics of esterification in LA + PE systems, and of effects of viscosity of the medium, or diffusion of reagent molecules. THE ABSENCE OF MEDIUM EFFECT I N THE COURSE OF A KINETIC RUN There are systematic differences in esterification rate constants when passing from one melt system to another, even when changes in chemical structure of the reagents occur only at considerable distance from the reacting functionalities, e.g.in the series AA, sebacic acid, tridecanoic acid, k increases by ca. 30 %. If k is recalculated in units of dm6 mol-2 min-', which are more appropriate for a detailed comparison, the systematic difference is increased further. Thus a change in the medium brought about by additional CH, groups increases the reaction velocity, by amounts com- parable to the substitution effect deduced for PE and PEML. It is thus tempting to FIG. 6.-Plot I : calculated rate curve for PEML for random model [eqn (2)-(6) of ref. (1) ; k* = 799 g2 mok2 min-', N = 11. Plot I1 : calculated rate curve for FSSE model (same equations, k* = 477 gz mok2 min-', N = 1.34), i.e., the optimal parameter values from kinetic measurements.' Points : (a) experimental p 1 values from g.p.c., using the calibration eqn (9), and normalization 4 1 pi = ni/Ci ni ; (b) ~2 ; (c) ~3 ; (4 ~ 4 -188 MODEL MELT ESTERIFICATION attribute the observed acceleration of the rate during a run, relative to a pure third order scheme, to a medium effect caused by the removal of COOH and OH in favour of ester links (rendering the surroundings perhaps less polar), rather than to a substitu- tion effect within the PE molecular unit.However, in the kinetic analysis,' a medium effect would result in a progressive change in rate during a run, represented to a first approximation by an apparent drop in overall reaction order. The best fit of a single overall order was found for an order of 2.8 instead of 3 ; however, the initial part of the rate curve deviates markedly from 2.8 order (plot 3, fig.10 of Part l).' The fit of the kinetic data by the alternative single-parameter substitution effect scheme was noticeably better (fig. 11 of Part 1).l The crude collision theory has been largely superseded by the transition state theory [cf. ref. (13), (14)] of chemical kinetics. The observed third order kinetics perturbed by the linear first shell substitution effect is compatible with modern theory. No substitution effect is measurable in the esterification of decamethylene glycol,1o so that some specific cause inherent in the structure of PE is indicated. Only a specula- tive explanation has been given,2 which is still the most likely. The OH groups in PE and its derivatives may be partly intramolecularly H-bonded (6-membered rings) rendering them less accessible to esterification in proportion to the number of partners available for intramolecular H-bonding of a given OH.M. Gordon and C. G. Leonis, J.C.S. Faraday I, 1975, 71, 161. M. Gordon and G. R. Scantlebury, J. Chem. SOC. B, 1967, 1. K. DuSek, J. Polymer Sci. A, 1974, 2, in press ; Faraday Disc. Chem. SOC., 1974, 57, in press. L. Pauling, Proc. Nat. Acad. Sci. U.S.A., 1935, 21, 186. J. Bjerrum, Metalammine Formation in Aqueous Solution (Haase, Copenhagen, 1957). (a) J. Kalal, M. Gordon and C. Devoy, Makrornol. Chem., 1972, 152, 233 ; (b) W. Heitz, B. Bomer and H. Ullner, Makromol. Chem., 1969, 121, 102 ; (c) J. G. Hendrickson and J. C. Moore, J. Polymer Sci. A-1, 1966,4, 167 ; (d) G. D. Edwards and Q. Y . Ng, J. Polymer Sci. C, 1968, 21, 105. ' M.Iguchi and R. J. Ranson, personal communication. * (a) L. H. Tung, J. Appl. Polymer Sci., 1966, 10, 375. (b) L. H. Tung, J. C. Moore and G. W. Knight, J. Appl. Polymer Sci., 1966,10,1261 ; (c) E. Gleuckauf, Ion Exchange and its Applica- tions (SOC. Chem. Ind., London, 1955). T. G. Parker, Ph.D. Thesis (University of Strathclyde, Glasgow, 1969). P. J. Flory, Principles ofPolyrner Chemistry (Cornell University Press, Ithaca, 1953). Newman (Plenum, Chicago, 1970). 1964). lo J. A. Love, Ph.D. Thesis (University of Strathclyde, Glasgow, 1968). l 2 M. Gordon, T. C. Ward and R. S . Whitney, Polymer Networks, ed. A. J. Chompff and S. l3 A. M. North, The Collision Theory of Chemical Reactionsin Liquids (Methuen, London, l4 K. J. Laidler, Chemical Kinetics (McGraw-Hill, New York, 1950). Lauric AcidiPentaerythrityl Monolaurate : A Model Melt Esterification Part 2.-Statistical Distribution of Products BY MANFRED GORDON AND CONSTANTINE G.LEONIS Department of Chemistry, University of Essex, Wivenhoe Park, Colchester C04 3SQ Received 31st May, 1974 The esterification of lauric acid, LA, with pentaerythrityl monolaurate (PEML) has previously been shown to exhibit a positive kinetic substitution effect in the PEML moiety : each OH previously esterified in PEML (or in pentaerythritol, PE, itself) accelerates the esterification of any remaining OH in the same PEML unit (first-shell substitution effect, FSSE) by a factor of about 1.3-1.4. This corresponds to a small difference in activation free energy (2-3 kJmol-I), but a similar effect in polycondensations of PE with dibasic acids causes substantial changes in gel points, network structure and physical properties, so that the thorough investigation of the simple model system LA/PEML is of value.The substitution effect is here confirmed by comparing gel permeation chromatographic measurements of the composition as a function of conversion with the statistical theory of the FSSE. The mechanism of esterification in undiluted melts is briefly reviewed. In ungelled systems, no evidence for diffusion control, for effects due to the size of reagent species, or due to the change in medium with increasing conversion, is generally found. The occurrence of a positive substitution effect of an ester link on the rate of formation on another such link on the same pentaerythrityl repeat unit was confirmed in Part 1 by precise kinetic measurements on the esterification in melts of lauric acid (LA) with pentaerythritol (PE) and its monolaurate (PEML).A similar effect had been found earlier in polycondensations of PE or tri(hydroxymethy1)ethane with adipic acid. The motivation behind the careful measurement of even rather small substitution effects of this kind lies in the unexpectedly large changes they can cause in the physical properties of polycondensates, and especially in model gel systems. Such changes were illustrated in a recent theoretical calculation by Dugek on the swelling behaviour of gels formed under a regime of a linear first shell substitution effect The general importance of the FSSE model in physical chemistry is underlined by its history.The first formal treatment we have found was that of Pauling for the binding of oxygen by haemoglobin; and Bjerrum formulated the thermodynamic FSSE theory of ligand binding as the central theme of his book on metal ammines. The result of kinetic measurements in Part 1 was felt to be in need of confirmation by an independent method based on the analysis of the statistical distribution of the ester products. Since the FSSE found was relatively small, amounting to a difference in activation free energy of about 2.3 kJ mol-1 at 170°C, there remained some doubt in case the rate acceleration attributed to the FSSE was simulated by contributions from several experimental sources, even though individually these had been proved to be negligible, e.g.the solubility in the reaction mixture of the steam produced, the escape of a little LA into the vapour phase (followed by its redissolution as the (FSSE). 178M. GORDON AND C. G . LEONIS 179 reaction proceeds), the sorption of water on the glass surfaces, etc. These doubts are resolved by analysis of reaction mixtures using gel permeation chromatography (g.p.c.1. THE PRODUCT DISTRIBUTION I N ABSENCE AND PRESENCE OF SUBSTITUTION EFFECT The mde fractions pi of products carrying i ester groups in the random reaction, free from FSSE, between PEML and a monocarboxylic acid, are given by the Bernouilli distribution : where a is the fractional conversion of the functionalities. Eqn (1) is generalised and usefully expressed in terms of p 1 by eliminating the time from eqn (2)-(6) of the previous paper,l and integrating them, so that (in the same notation) 6NPl 6p2"3 6pY2I3 p 3 = ( 3 - 2N)(3 - N 2 ) - ( 3 - 2;)(2 - N ) (3 - N2)(2 - N ) ~ N ~ P ~ 3 Np: N13 6pY2I3 p4 = - ( 3 - 2N)( 3 - N 2 ) ( 3 - 2N)(2 - N ) - ( 3 - 1V2)(2 - N ) ( 3 ) (4) and the fractional conversion of lauric acid becomes : ( 5 ) 2( 1 - N)p:N13 2p72'3 (2N3-N2-4N+3)pl = ( 3 - 2 N ) ( 2 - N ) + ( 3 - N 2 ) ( 2 - N ) + ( 3 - N 2 ) ( 3 - 2 N ) ' Eqn (2)-(5) revert to (1) for the random case ( N = l), since then This work is concerned with experimental testing of these equations.Two comple- mentary methods were used : one to measure the overall conversion a as a function of time, and the other to measure the distribution pi as a function of time.1 -G! = p = p1 +$p, + i p s . (6) EXPERIMENTAL MATERIALS Pentaerythrityl tetralaurate (PETEL) was obtained from Eastman Organic Chemicals and Naphthalene (NL) was obtained from British Drug Houses Lid. (microanalytical grade). Tetrahydrofuran (THF) was supplied by the East Anglia Chemical Company sufficiently pure as g.p.c. solvent (refractive index at 20°C : 1.4076). The preparation and purification of pentaerythrityl monolaurate (PEML) has been described in the previous paper,l as has the source and purification of lauric acid LA. Mixtures of esters of pentaerythritol and LA were produced by carrying out a reaction between LA and PEML of stoichiometric ratio 1 : 1 in the block thermostat as described.l The reaction was stopped at the desired time and the reaction vessel-pressure transducer assembly was taken out of the oven and the reaction vessel end immediately quenched in a Dewar vessel containing liquid nitrogen.This part of the vessel, containing the reaction mixture was cut off and put in a silica gel desiccator, evacuated and kept in a deep freeze until analysed. recrystallized from petroleum ether (m.p. found 50"C, lit. 49°C).180 MODEL MELT ESTERIFICATION APPARATUS Apart from its use for measuring molecular weight distributions of polymers, g.p.c. is an excellent tool for studying oligomer and low molecular weight mixtures6 The prospect of analysing reaction mixtures quantitatively by g.p.c. was one of the main factors for starting this work. The technique was used not merely to analyse compositions of reaction mixtures as a function of reaction progress, but to supplement titration procedures for assessing purity of the reactants, and for checking their initial concentrations in pellets made up by weighing.In the latter case, agreement was generally of the order of accuracy of the g.p.c. calibration ( N 4 %). A Waters Associates model 200 instrument equipped with differential refractometer, Leeds and Northrup Speedomax W recorder, and the usual accessories was used. Six columns, each 4 ft long with inner diameter of 3 inch with nominal permeability limits of 6, 10, 17, 10, 10 and 20x loF7 cm were used in that order. The last of these six columns was packed with Poragel WA200 using a method developed in this laboratory,' found to improve resolution R by about 25 %, as assessed from the formula : (7) R1,2 = (K- V d / ( K + W2) 1 I * 45 ' 4 0 35 30 elution volume (as 5 cm3 counts) I I .45 '4a 35 30 elution volume (as 5 cm3 counts) elution volume (as 5 cm3 counts) FIG. 1.-Gel permeation chromatogram of reactants and products, (a) at reaction time 77 min : I, naphthalene ; 11, LA ; 111, PEML ; IV, PEDL ; V, PETRL ; VI, PETEL. Length of original recorder trace: 75 cm. (b) As (a) at time 133.33 min. (c) As (a) at 944.33 min.M. GORDON AND C. G. LEONIS 181 where Vi is the elution volume and Wi the width of the peak of substance i. The gel was dispersed in acetone (or methanol), a non-solvent (to restrict swelling), of density less than that of the gel. The suspension was introduced into a column and the settling was accelerated by a simple vertical rocking machine, which tapped the column from below and slowly rotated it.Finally a good solvent was pumped in slowly to displace the non-solvent and to allow the complete swelling of the gel. This procedure gives close packing, good performance and reproducible results. All solutions for g.p.c. were made up at room temperature to ca. 1 % (w/v) in THF as solvent, taken directly from the g.p.c. output end. Each sample was inserted with a hypo- dermic needle, via a fdter over a period of ca. 1 min which still gives adequate resolution, but broadens the peaks a little to assist in the measurements of peak areas (see below). The maximum flow rate used was 2 cm3 m i d . Typical chromatograms obtained at 20°C are shown in fig.1. To reduce errors from a variety of sources, a known weight fraction of a reference compound was added to all mixtures analysed. Naphthalene was chosen, because it is easily available in high purity, it is inert, soluble in THF and of refractive index substantially higher than the sample, thus giving relatively large peaks. It was also well resolved from all compounds to be analysed. MEASUREMENTS OF PEAK AREAS A Dupont 310 curve resolver (essentially an analogue computer) was used to measure peak areas. First the naphthalene reference peak was measured in the usual way by fitting to it a nearly Gaussian curve.8 The result was then used to set the integrator meter to 100 units so as to scale the measurements for the remaining 5 compounds. The peak of lauric acid was always completely resolved, and was determined next, and finally the partly overlapping peaks of the four esters were fitted and resolved together. The peak skewing facility was used to a minor extent, if necessary.The procedure was repeated 4-5 times for each chromatogram and the mean of these measurements for each component was used as the final result. The reproducibility of these measurements was found to be within 4 %. Average characteristics of the measured peaks are shown in table 1 ; the calibration procedure is outlined in the next section. TABLE 1 .-AVERAGE CHARACTERISTICS OF THE MEASURED PEAKS compound i Ve,i/5 NL 45.5 LA 36.6 PEML 33.5 PEDL 31 PETRL 29.3 PETEL 28 cm3 Ni 7959 4.8 (LA) 5937 1.8 (PEML) 4974 1.3 (PEDL) 4259 0.85 (PETRL) 3805 0.65 (PETEL) 3475 Ni = 16(vqi/Wi)2, theoretical plate number for the compound i with elution volume Ve,i.CALIBRATION OF G.P.C. Of the five compounds, only LA, PEML and PETEL were available in pure form. Accordingly the diester (PEDL) and the triester (PETRL) had their calibration constant determined by interpolation. The calibration constant ki,r of the ith compound available in pure form, relative to the reference compound Y (naphthalene) is defined by AJA, = ki,,wi/w, where A denotes peak area and w weight. According to theory, ki,, should be proportional to the difference An; between the refractive indices of the ith compound and the solvent THF in their pure liquid states, provided effects due to non-ideality of mixing may be neglected. Accordingly, the refractive182 MODEL MELT ESTERIFICATION indices of PEML and PETEL were measured at 74°C (above their melting points), and that of THF at the same temperature was found by extrapolation.The results are given in table 2. The calibration g.p.c. spectrum shown in fig. 2 is one of several taken with different weights of naphthalene, LA, PEML and PETEL, in the range to be expected when analysing the products of kinetic runs. Using two different methods for assessing the effective areas under the peaks of these calibration spectra, fig. 3 and 4 were produced to determine the ki,r [eqn (S)]. Fig. 3 was produced by use of the curve analyser following each peak with the optimal Gaussian curve closely all the way to its well-defined baseline. Fig. 4 was obtained by calculating the areas under the trace by numerical integration between data pairs which were read from the chromatogram without any restriction to obey a specified distribution.TABLE 2.-REFRACTIVE INDICES, AND SPECIFIC REFRACTIVE INCREMENTS FROM G.P.C. DATA kr.rx 102 k;.,x 102 III$& x 102 method 1 method 2 compound nl4'C PEML 1 . 4 5 3 1 7.46 2 6 . 3 5 27.30 PETEL 1 , 4 4 0 3 6 . 1 8 26.04 24.15 LA 1 . 4 2 0 8 4 . 2 3 16.80 1 5 . 9 6 THF 1 . 3 7 8 5 (extr) 0.0 0.0 0.0 , I 45 40 35 30 elution time (as 5 cm3 counts) FIG. 2.-Typical calibration chromatogram : I, NL ; 11, LA ; 111, PEML ; IV, PETEL. ' O t wi/mg FIG. 3.-Linearity of the specific refractive increment for the peaks as estimated by the curve resolver as function of concentration (mg/5 cm3) used. 0, LA ; A, PETEL ; 0, PEML.The second procedure leads to values of kj,r, which are more nearly proportional to Ani (table 2). Nevertheless, we adopt the ki.r obtained from fig. 3 for the following reasons. The differences between the two procedures lead to only small effects on kinetic parameters, especially since the same procedure is applied both to the calibration spectra and to those of reaction products to be analysed. The small error, if any, will be in the direction of decreas- ing the apparent substitution effect, so that the main aim, that of testing for the existence of aM . GORDON AND C . G . LEONIS 183 substitution effect, cannot be prejudiced. Finally, of course, the second method is incon- venient, especially in reaction products where neighbouring peaks may partly overlap (fig.1). The ki,, values of the pantaerythritol dilaurate (PEDL) and trilaurate (PETRL) were taken by linear interpolation between those of PEML and PETEL (which lie very close to each other, column 2, table 3). The analysis of unknown mixtures (products of kinetic runs) was based on eqn (8), using the ki,? thus determined. 0 10 20 30 wilmg FIG. 4.-Linearity of the specific refractive increment for the same peaks as in fig. 3, as estimated by numerical integration using Simpson's method. 0, LA; A, PETEL; 0, PEML. For testing the integrated rate equations (2)-(5), the number of moles ni are required rather than the weights wj. We have : Ai/A, = ki,,wilw, = ki,rMini/w, = k&ni/w,. (9) The new calibration constants kzr thus defined are tabulated in column 3, table 3.The areas Ai and A , are measured by the curve resolver, and wr is the weight of naphthalene added to the reaction product; hence ni is calculated. Finally the ni are converted to the pi by normalisation. The pi (and the original ni) are subject to a further stoichiornetric constraint, viz. the second equality in eqn (6). This condition was used as a very minor constraint in adapting the pattern of the original g.p.c. trace to the output of the curve analyser, which was always easily satisfied without doing violence to the data. This is direct evidence that the linear interpolation used for calibrating g.p.c. peaks of PEDL and PETRL is satisfactory. TABLE 3 .-CALIBRATION CONSTANTS compound ki.t kp*.+ PEML 26.35 83.9 PEDL 26.257 131.57 PETRL 26.14t 178.6T PETEL 26.04 225.3 LA 16.80 36.65 4 interpolated TRANSESTERIFICATION All our results and those on analogous systems with polyfunctional acids can be explained on the assumption that, at least in the absence of strong acid catalysts, any transesterification component superimposed on the irreversible esterification reaction can be neglected. In this work, transesterification would lead to formation of some free PE when starting with PEML.PE is insoluble in THF, but no residue or turbidity was observed when preparing samples for g.p.c. analysis. In addition, the normalization condition of the solutes was always very closely obeyed, confirming the absence of loss of material by way of PE.184 MODEL MELT ESTERIFICATION R E S U L T S Seven samples of an equifunctional mixture of LA and PEML at 160°C were The results of prepared as described by stopping at various stages of esterification. the analyses are given in table 4.TABLE 4.-MEASURED DISTRIBUTION OF REACTANTS AND REACTION PRODUCTS timelmin compound AiIAr PEML 12.3 PEDL 24.8 PETRL 18.5 LA 31.0 N(aver age) PETEL 7.65 wrlmg, eqn (8) 77 n i x 1 0 3 Pi N 16.13 0.310 20.75 0.3g9 1.25 11.39 0.219 1.10 3.73 0.072 1.35 101.33 0.649 1.30 11 .oo 1 .Z5 timelmin compound PEML PEDL PETRL PETEL LA N(average) wrhg time/min compound PEML PEDL PETRL PETEL LA N(average) wr Img 195.66 Ai/Ar n i x 1 0 3 Pi N 5.3 2.84 o.140 19.0 6.50 0.319 1.30 26.75 6.74 0.331 1.41 21.4 4.27 0.210 1.32 21.2 28.35 0.464 1-30 1.33 4.50 400.33 Ai/Ar nix103 Pi N 2.75 3.31 0.062 17.45 13.41 0.253 1.11 29.1 16.46 0.310 1.47 44.3 19.86 0.374 1.32 17.75 53.27 0.335 1.25 1 .24 10.10 133.33 Ai/Ar ni X 103 Pi N 8.95 9.87 0.210 22.9 16.11 0.343 1.39 26.85 13.91 0.296 1.45 17.3 7.10 0.151 1.43 25.55 75.73 0.537 1.42 1.42 9.25 324.66 Pi N Ai/Ar ni X lo3 5.55 3.5, 0.0S3 28.3 ll.62 0.270 1.19 52.35 12.55 0.291 1.29 50.7 15.33 0.356 1.35 30.8 49.42 0.382 l.z3 1.26 5.40 645.33 timelmin compound AiIAr PEML 2.05 PEDL 9.8 PETRL 32.9 LA 13.7 N( average) wrlmg PETEL 73.75 944.33 n i x 103 Pi N 2.22 0.040 6.77 0.122 1.30 16.73 0.302 1.21 29.72 0.536 1.22 36.96 0.222 1.25 1-24 9.08 Next eqn (2)-(5) are utilised to determine the value of the parameter N.For the seven different times, the measured values of the four couples ( p , pl), ( p 2 , pl), ( p 3 , pl), (p4,p1) are substituted in these equations.Through a computer program the calculated values of N for each of these couples were obtained and the results are shown in table 4. The average value for the parameter N is 1.3 0.07. We now compare the g.p.c. results with the kinetic results. The comparison is based on the following tests : (i) the individual p i normalized as mentioned as function of time ;M. GORDON AND C. G . LEONIS 185 (ii) the recalculation of the conversion from the measured p , using the identity a = 1 - p [eqn (6)] and the comparison with the a measured from the steam pressure, where a denotes the extent of the reaction. Fig. 5 shows that a(t) compares favourably with that obtained from the steam pressure. In particular, there is no systematic deviation between the two sets of a values, as would result from faults introduced by the approximations mentioned in connection with the calibration procedure. The steam pressure measurements averaged over seven runs are more accurate, and as expected, they define a smoother curve.The triangles are sample points from the single runs which led to g.p.c. samples, where a(t) values are indicated as circles. od 250 500 750 time /min FIG. 5.-Comparison of the extent of reaction a between steam pressure results and g.p.c. [eqn (6)]. Solid line represents the mean kinetic curve for the same run conditions.' A, from p.t.d. ; 0, from g.p.c. ; -, mean experimental curve. In this way the calibration procedure adapted for g.p.c. is again validated. Fig. 6 shows all the p 1 , p 2 , p 3 , p 4 values obtained for the seven different runs at different times.For comparison the changes of these fractions with time are represented by smooth curves obtained by a computer program, using the differential equations (2)-(6) with parameters k* = 477 g2 mo1-2 min-l, and N = 1.34 which give the best fit for the same system for the kinetic study.l The g.p.c. results strongly support the existence of a positive substitution effect of about N = 1.3, by comparing the fit in fig. 6 with the attempted fit of the measurements to the curves for N = 1. This conclusion is unaffected even by attempts to readjust the rate constant k* as a free parameter, i.e. by a rescaling of the time axis in fig. 6, since the degree of fit of the measured p1 and p4 respond in opposite manner to such readjustment of the time scale.DISCUSSION The kinetic analysis supports the substitution effect strongly, and the statistical analysis of the g.p.c. data conclusively. The statistical data on the molecular distribution of ester species obtained by g.p.c., show that the distribution differs significantly from a Bernouilli distribution [eqn (l)]. The only conclusion to be drawn is that the chance of reaction of the hydroxyl groups within any one PE unit are not independent; a conclusion quite independent of the form of the rate law (e.g. the order of the reaction, whether it was steady or periodic, etc.). Thus the data on the distribution show that the definition of a substitution effect is fulfilled. Of course the data go much further, to show that the effect is positive ( N = 1.30,P1 0.5 0 - 8 J I 250 500 750 1000 timelmin 0 250 500 750 1000 P4 time /min 0.5 - 0 250 500 750 1000 time/min FIG.6.--See caption opposite.M. GORDON AND C. G. LEONIS 187 increase of chance of reaction with increasing substitution) and nearly of the same magnitude as deduced completely independently from the kinetics alone ( N = 1.37). Moreover, this effect is comparable in sign and magnitude to that deduced earlier 2 - for polyfunctional analogues of LA from kinetic and statistical data. The statistical data there represented gel points rather than g.p.c. analysis. On the basis of the rigorous statistical analysis, we are in a position to discuss the assumed absence of any disturbance of the random reaction scheme other than the substitution effect during the course of a single reaction run.THE ABSENCE OF REAGENT SIZE EFFECTS I N MELTS In polyfunctional melts, e.g. adipic acid (AA) + pentaerythritol (PE)2* or decane-1,lO-diol (DMB) + benzene-1,3,5-triacetic acid (BTA),1° it has been shown that polyesterification kinetics are described accurately by the same basically third- order scheme supported by the present analysis of a system using a monofunctional acid. Allowance had to be made for a positive substitution effect, of similar order to that observed here, in the case of AA+PE, and some small allowance for intra- molecular esterification in AA + PE and DMG + BTA. These reactions lead to gelation at points very close to those predicted by the classical theory of Flory." The operative size of a reagent molecule in such systems is the weight average, i.e.the mean size of molecule to which a randomly chosen free functionality is attached. This weight average and the viscosity diverge to infinity at the gel point. The esterification kinetics is not measurably changed from the simple third-order scheme up to and some way beyond l 2 the gel point before diffusion control is found to set in (as expected), and, therefore, there can be no measurable effect of reagent size on reaction velocity. Of course, the modern view of the process l 3 includes segmental motions inside a macromolecule as a mechanics whereby a functionality finds a partner for reaction; within the gel molecule, this must be the only cause, since wholesale translation of the molecule does not occur. In the present study, only small molecules are involved, there being a modest increase in reagent size when passing from mainly PEML at the beginning of a run to mainly PETEL near the end of a run.In view of the discussion of polyfunctional analogues, we may exclude the possibility of any effect of the size of the reagent on the kinetics of esterification in LA + PE systems, and of effects of viscosity of the medium, or diffusion of reagent molecules. THE ABSENCE OF MEDIUM EFFECT I N THE COURSE OF A KINETIC RUN There are systematic differences in esterification rate constants when passing from one melt system to another, even when changes in chemical structure of the reagents occur only at considerable distance from the reacting functionalities, e.g.in the series AA, sebacic acid, tridecanoic acid, k increases by ca. 30 %. If k is recalculated in units of dm6 mol-2 min-', which are more appropriate for a detailed comparison, the systematic difference is increased further. Thus a change in the medium brought about by additional CH, groups increases the reaction velocity, by amounts com- parable to the substitution effect deduced for PE and PEML. It is thus tempting to FIG. 6.-Plot I : calculated rate curve for PEML for random model [eqn (2)-(6) of ref. (1) ; k* = 799 g2 mok2 min-', N = 11. Plot I1 : calculated rate curve for FSSE model (same equations, k* = 477 gz mok2 min-', N = 1.34), i.e., the optimal parameter values from kinetic measurements.' Points : (a) experimental p 1 values from g.p.c., using the calibration eqn (9), and normalization 4 1 pi = ni/Ci ni ; (b) ~2 ; (c) ~3 ; (4 ~ 4 -188 MODEL MELT ESTERIFICATION attribute the observed acceleration of the rate during a run, relative to a pure third order scheme, to a medium effect caused by the removal of COOH and OH in favour of ester links (rendering the surroundings perhaps less polar), rather than to a substitu- tion effect within the PE molecular unit.However, in the kinetic analysis,' a medium effect would result in a progressive change in rate during a run, represented to a first approximation by an apparent drop in overall reaction order. The best fit of a single overall order was found for an order of 2.8 instead of 3 ; however, the initial part of the rate curve deviates markedly from 2.8 order (plot 3, fig. 10 of Part l).' The fit of the kinetic data by the alternative single-parameter substitution effect scheme was noticeably better (fig. 11 of Part 1).l The crude collision theory has been largely superseded by the transition state theory [cf. ref. (13), (14)] of chemical kinetics. The observed third order kinetics perturbed by the linear first shell substitution effect is compatible with modern theory. No substitution effect is measurable in the esterification of decamethylene glycol,1o so that some specific cause inherent in the structure of PE is indicated. Only a specula- tive explanation has been given,2 which is still the most likely. The OH groups in PE and its derivatives may be partly intramolecularly H-bonded (6-membered rings) rendering them less accessible to esterification in proportion to the number of partners available for intramolecular H-bonding of a given OH. M. Gordon and C. G. Leonis, J.C.S. Faraday I, 1975, 71, 161. M. Gordon and G. R. Scantlebury, J. Chem. SOC. B, 1967, 1. K. DuSek, J. Polymer Sci. A, 1974, 2, in press ; Faraday Disc. Chem. SOC., 1974, 57, in press. L. Pauling, Proc. Nat. Acad. Sci. U.S.A., 1935, 21, 186. J. Bjerrum, Metalammine Formation in Aqueous Solution (Haase, Copenhagen, 1957). (a) J. Kalal, M. Gordon and C. Devoy, Makrornol. Chem., 1972, 152, 233 ; (b) W. Heitz, B. Bomer and H. Ullner, Makromol. Chem., 1969, 121, 102 ; (c) J. G. Hendrickson and J. C. Moore, J. Polymer Sci. A-1, 1966,4, 167 ; (d) G. D. Edwards and Q. Y . Ng, J. Polymer Sci. C, 1968, 21, 105. ' M. Iguchi and R. J. Ranson, personal communication. * (a) L. H. Tung, J. Appl. Polymer Sci., 1966, 10, 375. (b) L. H. Tung, J. C. Moore and G. W. Knight, J. Appl. Polymer Sci., 1966,10,1261 ; (c) E. Gleuckauf, Ion Exchange and its Applica- tions (SOC. Chem. Ind., London, 1955). T. G. Parker, Ph.D. Thesis (University of Strathclyde, Glasgow, 1969). P. J. Flory, Principles ofPolyrner Chemistry (Cornell University Press, Ithaca, 1953). Newman (Plenum, Chicago, 1970). 1964). lo J. A. Love, Ph.D. Thesis (University of Strathclyde, Glasgow, 1968). l 2 M. Gordon, T. C. Ward and R. S . Whitney, Polymer Networks, ed. A. J. Chompff and S. l3 A. M. North, The Collision Theory of Chemical Reactionsin Liquids (Methuen, London, l4 K. J. Laidler, Chemical Kinetics (McGraw-Hill, New York, 1950).

ISSN:0300-9599    

DOI:10.1039/F19757100178

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Excess Volumes of Mixtures containing o-Dichlorobenzene BY M. S. DHILLON Department of Chemistry, Guru Nanak University, Armitsar, Punjab, India Received 22nd March, 1974 Excess volumes of mixing of o-dichlorobenzene with cyclohexane, benzene, toluene, a-xylene, rn-xylene, and g-xylene have been measured at 303.15 and 308.15 K as a function of composition. The excess volume data have been analysed in the light of refined version of the cell model theory. The refined version of cell model theory of Prigogine has been able to predict correctly the magnitude of excess functions of mixtures. We determined the excess volumes of mixtures of o-dichlorobenzene with cyclohexane, benzene, toluene, o-xylene, m-xylene and p-xylene to analyse the data in the light of a refined version of the cell model theory.EXPERIMENTAL Cyclohexane, benzene, toluene, o-xylene, rn-xylene and p-xylene (B.D.H.) were purified as described ear lie^.^ o-Dichlorobenzene (B.D.H.) was fractionally distilled over PzOs. The purities of the samples were checked by measuring their densities ; the results agreed to within 0.000 02 g C M - ~ with those in literat~re.~. Excess volumes were measured at 303.15 and 308.15 K as a function of composition in a water-filled thermostat controlled to within +O.Ol K by a dilatoinetric methodo3 RESULTS The results are reproducible to within 0.001 cm3 mol-I and are plotted in fig. 1. They were fitted by the method of least squares to the equation : Values of A, B and C are given with standard deviations o( V") in table 1. VE/cm3 = x(1 - x ) ( A +B(2x- 1)+C(2x- (1) TABLE 1 .-VALUES OF PARAMETERS IN EQN (1) AND STANDARD DEVIATIONS a( YE) o-dichlorobenzene+ T,'K cyclohexane 303.15 308.15 benzene 303.15 308.15 toluene 303.15 308.15 o-xylene 303.15 308.15 m-x ylene 303.,15 308.15 p-xylene 303.15 308.15 A 1.1188 1.1781 0.2896 0.2552 - 0.4465 - 0.4831 - 0.341 5 - 0.3694 - 0.5342 -0.5635 - 0.5767 - 0.61 13 189 B - 0.0093 0.0067 0.0108 0.0003 0.0138 0.0161 - 0.0088 - 0.0140 - 0.01 12 -0.0171 0.0486 0.0454 C -0.1686 - 0.0050 - 0.0958 -0.1332 0.1412 0.1344 0.0591 0.0457 0.0871 0.0286 0.1117 0.0174 G( VE)/cm3 mol-1 0.0008 0.001 8 0.0006 0.001 8 0.0033 0.0013 0.0008 0.0007 0.0019 0.0013 0.0012 0.001 1190 EXCESS VOLUMES OF MIXTURES A 0 .0 8 / A 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 (4 X 0.1 0.20.3 0.4 0.5 0.60.7 0.0 0.9 - 0 .0 2 & -0.04 E - 0 . 0 6 w m E - 0 . 0 8 $ -0.10 -0.1 2 - 0.141 I X : I 0.1 0.2 0.3 0.4 0.5 0.60.7 0.6 0.9 (6) X -0.02 -0.0 4 - 0.0 6 -0.08 -0.10 -0.1 2 0.1 0.2 0.30.4 0.50.6 0.7 0-80.9 (4 X 0.1 0.2 0.3 0.4 0.5 0.d 0.7 0.00.9 - 0 . 0 2 ~ 0.04 -0.06 -0.08 - 0 . I 0 -0.12 - 0. I 4 - 0 . 1 6 FIG. 1.-Plots of VE for the mixture x. o-dichlorobenzene + (1 - x ) (a) cyciohexane, (b) benzene, (c) toluene, ( d ) o-xylene, (e) m-xylene, (f)p-xylene. A, 303.15 K ; B. 308.15 K. DISCUSSION The excess volumes are negative for mixtures o-dichlorobenzene + toluene, + o-xylene, + m-xylene, and +p-xylene while positive for the remaining two mixtures. The temperature coefficient a VE/aT, is negative for all mixtures except for o-dichloro- benzene + cyclohexane.Excess volumes V” were calculated using the cell model theory of Prig0gine.l The expression for VE is given by : Y E / X 1 X 2 = 3 V,p[B(x, - x2) + 6/2 + 1 1 p] + T V;[ - 28 + 9p2 + o2 - *a2 + ~ ( i + 2x2) -+Po +$p6 + +pe(x, - x2)3 + $ ~ 2 V;”P - $ 6 2 + ~ ( 1 + 2 4 1 (2)M. S . DHILLON 191 where the terms have the significance as given by Prigogine.' 9 The characteristic parameters for the pure components were evaluated from critical constants s9 assuming that each component of the mixtures obeys the theorem of corresponding states. In computing VE, eqn (2) was simplified for dispersion forces, i.e., 8 = - d2/4. The convergency of eqn (2) was tested. The values of VE thus calculated are in table 3. The probable reason for the poor prediction of VE from cell model theory may be due to the assumption that dispersion forces are operative between the components of these mixtures.TABLE 2.-THE VALUES OF THE PARAMETERS FOR PURE COMPONENTS o-dichlorobenzene (1)+ 61 62 P1 P2 cyclohexane (2) 0.1956 -0.1636 0.0522 - 0.0490 benzene (2) 0.1922 -0.1612 0.121 1 -0.1081 toluene (2) 0.1321 -0.1167 0.0382 - 0.0366 rn-xylene (2) 0.0620 - 0.0590 -0.0196 0.0201 p-xylene (2) 0.0873 - 0.0803 - 0.0100 0.01 11 o-xylene (2) 0.0863 - 0.0799 - 0.0232 0.0290 TABLE 3 .-EXPERIMENTAL AND COMPUTED VE VALUES AT EQUIMOLAR COMPOSITIONS P / c m 3 mol- 1 system o-dichlorobenzene (1)+ 303.15 cyclohexane (2) 308.15 benzene (2) 303.15 308.15 toluene (2) 303.15 308.15 o-xylene (2) 303.15 308.15 rn-xylene (2) 303.15 308.15 p-xylene (2) 303.15 308.15 expt.0.280 0.294 0.072 0.063 -0.112 -0.121 - 0.085 - 0.092 -0.134 -0.141 -0.144 -0.153 cell model theory V," v? 0.596 0.598 3.286 3.333 0.329 0.331 - 0.002 - 0.004 - 0.005 - 0.005 -0.138 - 0.143 0.541 0.542 2.559 2.604 0.347 0.352 0.063 0.069 0.006 0.005 0.064 - 0.067 The author thanks the Head of Chemistry Department for providing laboratory facilities and Y. R. Bhardwaj for experimental assistance. I. Prigogine and V. Mathot, J, Chem. Phys., 1952, 20, 49. I. Prigogine, A. Bellemans and A. Englert-Chowles, J. Chem. Phys., 1956, 24, 518. M. S. Dhillon, J. Chem. Thermodynamics, 1974, 6, in press. J. Timmermans, Physico-Chemical Constants of Pure Organic Liquids (Elsevier, New York, 1950). R. C. Weast, Handbook of Chemistry and Physics (The Chemical Rubber Co., Ohio, 1972).A. G. Williamson and R. L. Scott, J. Phys. Chem., 1960, 64,440. ' R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids (McGraw-Hill, London, 1966). Excess Volumes of Mixtures containing o-Dichlorobenzene BY M. S. DHILLON Department of Chemistry, Guru Nanak University, Armitsar, Punjab, India Received 22nd March, 1974 Excess volumes of mixing of o-dichlorobenzene with cyclohexane, benzene, toluene, a-xylene, rn-xylene, and g-xylene have been measured at 303.15 and 308.15 K as a function of composition. The excess volume data have been analysed in the light of refined version of the cell model theory. The refined version of cell model theory of Prigogine has been able to predict correctly the magnitude of excess functions of mixtures.We determined the excess volumes of mixtures of o-dichlorobenzene with cyclohexane, benzene, toluene, o-xylene, m-xylene and p-xylene to analyse the data in the light of a refined version of the cell model theory. EXPERIMENTAL Cyclohexane, benzene, toluene, o-xylene, rn-xylene and p-xylene (B.D.H.) were purified as described ear lie^.^ o-Dichlorobenzene (B.D.H.) was fractionally distilled over PzOs. The purities of the samples were checked by measuring their densities ; the results agreed to within 0.000 02 g C M - ~ with those in literat~re.~. Excess volumes were measured at 303.15 and 308.15 K as a function of composition in a water-filled thermostat controlled to within +O.Ol K by a dilatoinetric methodo3 RESULTS The results are reproducible to within 0.001 cm3 mol-I and are plotted in fig.1. They were fitted by the method of least squares to the equation : Values of A, B and C are given with standard deviations o( V") in table 1. VE/cm3 = x(1 - x ) ( A +B(2x- 1)+C(2x- (1) TABLE 1 .-VALUES OF PARAMETERS IN EQN (1) AND STANDARD DEVIATIONS a( YE) o-dichlorobenzene+ T,'K cyclohexane 303.15 308.15 benzene 303.15 308.15 toluene 303.15 308.15 o-xylene 303.15 308.15 m-x ylene 303.,15 308.15 p-xylene 303.15 308.15 A 1.1188 1.1781 0.2896 0.2552 - 0.4465 - 0.4831 - 0.341 5 - 0.3694 - 0.5342 -0.5635 - 0.5767 - 0.61 13 189 B - 0.0093 0.0067 0.0108 0.0003 0.0138 0.0161 - 0.0088 - 0.0140 - 0.01 12 -0.0171 0.0486 0.0454 C -0.1686 - 0.0050 - 0.0958 -0.1332 0.1412 0.1344 0.0591 0.0457 0.0871 0.0286 0.1117 0.0174 G( VE)/cm3 mol-1 0.0008 0.001 8 0.0006 0.001 8 0.0033 0.0013 0.0008 0.0007 0.0019 0.0013 0.0012 0.001 1190 EXCESS VOLUMES OF MIXTURES A 0 .0 8 / A 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 (4 X 0.1 0.20.3 0.4 0.5 0.60.7 0.0 0.9 - 0 . 0 2 & -0.04 E - 0 . 0 6 w m E - 0 . 0 8 $ -0.10 -0.1 2 - 0.141 I X : I 0.1 0.2 0.3 0.4 0.5 0.60.7 0.6 0.9 (6) X -0.02 -0.0 4 - 0.0 6 -0.08 -0.10 -0.1 2 0.1 0.2 0.30.4 0.50.6 0.7 0-80.9 (4 X 0.1 0.2 0.3 0.4 0.5 0.d 0.7 0.00.9 - 0 . 0 2 ~ 0.04 -0.06 -0.08 - 0 . I 0 -0.12 - 0. I 4 - 0 . 1 6 FIG. 1.-Plots of VE for the mixture x. o-dichlorobenzene + (1 - x ) (a) cyciohexane, (b) benzene, (c) toluene, ( d ) o-xylene, (e) m-xylene, (f)p-xylene. A, 303.15 K ; B. 308.15 K. DISCUSSION The excess volumes are negative for mixtures o-dichlorobenzene + toluene, + o-xylene, + m-xylene, and +p-xylene while positive for the remaining two mixtures.The temperature coefficient a VE/aT, is negative for all mixtures except for o-dichloro- benzene + cyclohexane. Excess volumes V” were calculated using the cell model theory of Prig0gine.l The expression for VE is given by : Y E / X 1 X 2 = 3 V,p[B(x, - x2) + 6/2 + 1 1 p] + T V;[ - 28 + 9p2 + o2 - *a2 + ~ ( i + 2x2) -+Po +$p6 + +pe(x, - x2)3 + $ ~ 2 V;”P - $ 6 2 + ~ ( 1 + 2 4 1 (2)M. S . DHILLON 191 where the terms have the significance as given by Prigogine.' 9 The characteristic parameters for the pure components were evaluated from critical constants s9 assuming that each component of the mixtures obeys the theorem of corresponding states. In computing VE, eqn (2) was simplified for dispersion forces, i.e., 8 = - d2/4.The convergency of eqn (2) was tested. The values of VE thus calculated are in table 3. The probable reason for the poor prediction of VE from cell model theory may be due to the assumption that dispersion forces are operative between the components of these mixtures. TABLE 2.-THE VALUES OF THE PARAMETERS FOR PURE COMPONENTS o-dichlorobenzene (1)+ 61 62 P1 P2 cyclohexane (2) 0.1956 -0.1636 0.0522 - 0.0490 benzene (2) 0.1922 -0.1612 0.121 1 -0.1081 toluene (2) 0.1321 -0.1167 0.0382 - 0.0366 rn-xylene (2) 0.0620 - 0.0590 -0.0196 0.0201 p-xylene (2) 0.0873 - 0.0803 - 0.0100 0.01 11 o-xylene (2) 0.0863 - 0.0799 - 0.0232 0.0290 TABLE 3 .-EXPERIMENTAL AND COMPUTED VE VALUES AT EQUIMOLAR COMPOSITIONS P / c m 3 mol- 1 system o-dichlorobenzene (1)+ 303.15 cyclohexane (2) 308.15 benzene (2) 303.15 308.15 toluene (2) 303.15 308.15 o-xylene (2) 303.15 308.15 rn-xylene (2) 303.15 308.15 p-xylene (2) 303.15 308.15 expt. 0.280 0.294 0.072 0.063 -0.112 -0.121 - 0.085 - 0.092 -0.134 -0.141 -0.144 -0.153 cell model theory V," v? 0.596 0.598 3.286 3.333 0.329 0.331 - 0.002 - 0.004 - 0.005 - 0.005 -0.138 - 0.143 0.541 0.542 2.559 2.604 0.347 0.352 0.063 0.069 0.006 0.005 0.064 - 0.067 The author thanks the Head of Chemistry Department for providing laboratory facilities and Y. R. Bhardwaj for experimental assistance. I. Prigogine and V. Mathot, J, Chem. Phys., 1952, 20, 49. I. Prigogine, A. Bellemans and A. Englert-Chowles, J. Chem. Phys., 1956, 24, 518. M. S. Dhillon, J. Chem. Thermodynamics, 1974, 6, in press. J. Timmermans, Physico-Chemical Constants of Pure Organic Liquids (Elsevier, New York, 1950). R. C. Weast, Handbook of Chemistry and Physics (The Chemical Rubber Co., Ohio, 1972). A. G. Williamson and R. L. Scott, J. Phys. Chem., 1960, 64,440. ' R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids (McGraw-Hill, London, 1966).

ISSN:0300-9599    

DOI:10.1039/F19757100189

出版商:RSC    

年代:1975

数据来源: RSC

摘要:

Investigation of Equilibrium Wetting Films of n-Alkanes on a-Alumina By TERENCE D. BLAKE Research Division, Kodak Limited, Headstone Drive, Harrow, Middlesex HA1 4TY Received 3rd April, 1974 A review is given of previous disjoining pressure investigations of liquid films on solids, and the advantages of combining such investigations with corresponding vapour adsorption studies are discussed. The relevant thermodynamic framework is presented in outline. Direct measurements of the disjoining pressure of stable wetting films of n-octane and n-decane on a-alumina are reported for films of from 20-80 nm in thickness. The results obtained, together with data for much thinner films derived from a previous gravimetric study of the vapour adsorption of n-decane on the oxidised surface of aluminium foil, are compared with the predictions of Lifshitz and London-Hamaker theories of dispersion forces.It is found that both theories correctly predict the disjoining pressure and differential free energy of formation of the films, provided the films exceed monolayer coverage, and provided due allowance is made for retardation if the films exceed a thickness of about 5 nm. In making these predictions, it is sufficient to assume that the films have molar volumes, molar entropies and dielectric properties identical with those of the parent bulk liquids. This paper reports a disjoining pressure study of wetting films of n-alkanes on cc-alumina and compares the results with the predictions of Lifshitz and London- Hamaker theories of dispersion forces.Much of the previous work on systems of this type has centred on measurements of vapour adsorption, and there has been a tendency to neglect the disjoining pressure approach. This paper seeks to partly redress the balance and to suggest, through example, that the two approaches are profitably treated as complementary. The paper contains a certain amount of review material and a section is devoted to an outline of an appropriate thermo- dynamic framework. showed that when a gas bubble is pressed against a hydrophilic solid surfaye (such as a plate of mica or glass) immersed in water, the intervening liquid slowly thins to leave a uniform equilibrium film of considerable thickness (fig. 1). The film behaves as though there were an excess pressure, II, acting normal to the film and opposing further reductions in film 'thickness, 1.This excess pressure, originally termed by Derjaguin the " wedging apart " or " disjoining " pressure, represents the difference between the pressure within the bubble, pb, and that in the bulk liquid adjacent to the solid surface,^' : i.e. The original investigations by Derjaguin and co-workers n = y b - p Z . (1) From elementary considerations of mechanical equilibrium, it follows that for stable films, I I > O (2) and (anpl) < 0. 192 (3)T. D . BLAKE 193 If a film is stable at all thicknesses, then the liquid is said to completely wet the solid. Thus a condition for complete wetting is that the function n = II(2) decreases mono- tonically from some positive value at I = 0 and approaches zero as I -+ co.A more general condition for complete wetting is given by; where 07, asz and 0: are the equilibrium tensions of the solid/vapour, solid/liquid and liquid/vapour interfaces respectively, and the subscript indicates saturation vapour pressure. The significance of this expression has been discussed in great detail by Melr~se.~ Discussions of wetting that involve the concept of disjoining pressure have been given by Frumkin and by Derjaguin and Shcherbak~v.~ aso' = cTsz+a;, (4) liquid - 5 Y - L = p b - p l FIG. 1.-Formation of a stable wetting film between a bubble and a plate. The phenomenon of disjoining pressure is believed to result from three different types of solid/liquid interaction : compression of electrostatic double layers within the film; van der Waals forces of attraction between liquid and solid-chiefly London dispersion forces; and forces of a third kind,6 usually assumed to be entropic in character, such as the build-up of solvation layers by hydrogen bonding.Whilst the first two types of interaction have a firm experimental foundation, the significance of the third type is still contr~versial.~ In view of the material importance of solid/liquid interactions, it is surprising that disjoining pressure studies have been so little exploited until quite recently. The bubble-against-plate (b.a.p.) technique is a considerably more direct way of investi- gating solid /liquid interactions than some of the alternative approaches more com- monly employed, such as classical studies of the coagulation of lyophobic colloids.' Presumably, the slow progress has been due to the exceptional experimental difficulties encountered, including non-reproducibility and inhomogeneity of solid surface^,^ greasy contamination, foreign particles, and vibration.l0.Thus, for example, Elton l2 and Evans l 3 were unable to repeat the Russian results and respectively attri- buted them to electroviscous effects and contamination. 1 - 7194 n-ALKANE FILMS ON a-ALUMINA More recently, however, Kitchener and co-workers lo* 0 l4 successfully applied the method to show that thick ( I > 20 nm) aqueous films on silica are stabilised principally by electrostatic forces, and are not significantly influenced by forces of a third kind. Detailed studies by Schulze and Ciclios l 5 lead to essentially the same conclusions, although the thinnest films reported (10 to 15 nm, at high ionic strengths) may have been stabilised by dispersion forces.In addition, Tabor and Roberts 16* l7 have shown that electrostatic double layer theory accounts reasonably well for the behaviour of aqueous films at disjoining pressures as high as 6 x lo4 N m-2. In these experiments, which involved a glass substrate and a transparent rubber ball in place of a bubble, dispersion forces, considered alone, probably produced a nett attraction between the materials on either side of the film and hence a negative contribution to the total disjoining pressure. Calculations l7 indicate that this contribution is about - 4 x lo2 N m-2, i.e. about two orders of magnitude less than the total pressure.In the new experimental work presented here, the b.a.p. technique has been used to investigate a system in which dispersion forces alone are responsible for the forma- tion of stable wetting films. A simple system was chosen so that results could be compared unambiguously with theory. Synthetic a-alumina was selected as the solid substrate because of its simple dispersion properties (see below), high refractive index and therefore high dispersion interaction ; it had the additional advantages of being rigid, chemically inert and crystallographically well-defined. n-Octane and n-decane were selected as the liquids because they are non-polar and have low refrac- tive indices. Preliminary calculations indicated that even with such a favourable system, films of substantial thickness would exist only at very low disjoining pressures.Measurements were therefore made over the range 0.5 to 50 N m-2. Previous disjoining pressure studies of well-characterised systems of this type are few. However, Scheludko and Platikanov l8 reported a 24 nm thick equilibrium film of benzene on mercury at II E 70 N m-2, and Schulze l9 reported a 28 nm equilibrium film of n-octane on silica at 16.2 N m-2. This last value is in good agreement with dispersion force calculations.20 The formation of wetting films on solids has, of course, been investigated many times before by conventional vapour adsorption techniques. However, because of capillary condensation, these investigations have usually been restricted to films of a few monolayers or less.Where this difficulty has been overcome (as, for example, in the ellipsometric study of adsorption on silica by Derjaguin and Zorin 21), then the very precise temperature control necessary at very high relative pressures has still restricted equilibrium measurements to comparatively thin films. Recent investiga- tions 22* 23 of the adsorption of liquid helium on alkaline-earth metal fluorides were exceptional. Because of the unusual properties of liquid helium, it was possible to use an acoustic phonon spectrometer 24 to investigate helium films of from 1 to 20 nm in thickness. The results obtained were shown to be in excellent agreement with dispersion force calculations. 25 With more conventional systems, it would appear that the most profitable course is to treat vapour adsorption studies and disjoining pressure measurements by the b.a.p.technique as complementary. For, whilst adsorption measurements are usually restricted to films of less than, say, 10 nm in thickness, the b.a.p. technique is most conveniently applied to much thicker films. This dual approach is exemplified in the discussion section of this paper where results, both from the present investigation and from a previous vapour adsorption study, are compared with the results of dispersion force calculations. For the purpose of this comparison it is necessary to employ a thermodynamic framework appropriate to both b.a.p. and adsorption(b) PLATE 1.-(u) Appearance of a typical film when viewed from beneath by reflected monochromatic light.(6) Type of interference pattern obtained when the bubbles are positioned just sufficiently above the alumina surface for no flattening to occur. [To face page 194T. D. BLAKE 195 systems. This framework, which involves certain assumptions about the nature of films, is therefore outlined in the following section. Only planar wetting films of a single component are considered. A general account of the thermodynamics of films has been given by Rusanov.26 THERMODYNAMIC FRAMEWORK According to the classical view of interface^,^^ whilst the coniponent of the pressure tensor normal to a plane interface is equal to the pressure in the contiguous bulk phases, the tangential component takes a different value which varies with position along the normal.It is this anisotropy of the stress tensor that gives rise to the phenomena of surface tension and surface pressure. In the case of a film in equili- brium with its parent bulk liquid (as in the b.a.p. system), the mechanical anisotropy is manifest not only in the form of a film tension, but also as an apparent excess pressure acting normal to the film, i.e. the disjoining pressure. Nevertheless, the mechanical properties of a plane film, like those of a plane interface, may be adequately described in terms of a single film tension and a single isotropic pressure, pf, equal to the normal pressure exerted by the contiguous bulk phases.26 For a film on a solid, the film tension may be identified with 0'. For a film in the b.a.p. system, pf = pb, whereas for an adsorbed film in equilibrium with its pure vapour at pressure p", pf = p'.The magnitudes of the extensive thermodynamic properties of a film depend upon the choice of the positions of the two principal dividing surfaces that constitute its boundaries. Although in principle this choice is quite arbitrary, in practice it will be operational. That is to say, it will be determined by the nature of the experimental method and the system. For present purposes, it is convenient to assume that the density of the solid remains constant up to a dividing surface chosen so that all the molecules of the solid component are in the solid and none are in the film. For a rigid, inert solid such as u-alumina, this is a realistic choice. The position of the second dividing surface relative to the first is fixed by either ascribing a value to the molar volume of the film component, or by employing the experimentally determined film thickness.Provided one is not concerned with the detailed structure of a film, it may be treated as a mechanically anisotropic but otherwise homogeneous phase. Thus, by making use of Gibbs' thermodynamic treatment of bulk phases,28 the partial molar Helmholtz free energy of a single-component film can be expressed as : where Uf, Sf, V', Af and nf are respectively the internal energy, entropy, volume, area and number of moles of the film at chemical potential pf and temperature T. Simi- larly, for the parent bulk liquid at the same temperature,196 I1-ALKANE FILMS ON a-ALUMINA whence, on subtracting (6) from (5), one obtains the differential Helmholtz free energy of film formation : This expression gives the coefficients for variations in free energy resulting from iso- thermal transfer of molecules between film and bulk liquid at specified pressures.The expression is equally applicable to both experimental systems under consideration. Consider the b.a.p. system. If the liquid is assumed to be incompressible so that film and bulk liquid have the same molar volume, i.e. ($)T,Af = r$)T = d, then, since the film is in equilibrium with its parent bulk liquid, pf = p' and (7) reduces to ATf = - d(pf - p'). (8) IT = -Affiu! (9) But, pf = pb, hence pf -p' is equal to the disjoining pressure, n, and Now consider the adsorption system. The film is in equilibrium with its vapour, which may be assumed to be a perfect gas.Moreover, away from the critical point where p: is the saturation vapour pressure of the liquid. (7) reduces to : Hence, for this system, ATf = RT In pvIp& (10) Eqn (7), (9) and (10) provide the thermodynamic relationships required for the discussion section of this paper. EXPERIMENTAL METHOD The techniques used in this study were similar to those described previously." However, they were employed with greater precision. The apparatus, which was mounted on an antivibration table of low periodicity, is shown schematically in fig. 2. A bubble of purified nitrogen held in an inverted cup (D) was lowered slowly with a micromanipulator (A) to press lightly against an optically-polished, flat, a-alumina disk (F) immersed in the test liquid (E).Films formed between bubble and disk were observed from beneath by reflected monochromatic light (wavelength A = 435 or 547 nm), using a low-powered microscope (x 100 or x 200 magnification). The appearance of a typical film together with its surround- ing " Newton's rings " interference pattern is shown in plate l(a). The disjoining pressure was varied over the required range by varying the size of the bubble, using bubble holders of from 2 to 25 mm diameter. Most experiments were carried out at 294& 1 K.T . D . BLAKE 197 Q FIG. 2.-Schematic representation of the disjoining pressure apparatus : A, micromanipulator ; B, Perspex resin enclosure ; C, fused silica cell ; D, bubble holder ; E, n-alkane ; F, optically-polished a-alumina disc ; G, optical window; H, x 10 microscope objective; I, interference ater (435 or 547 nm) ; J, heat filter ; K, condenser ; L, 250 W, high-pressure mercury lamp ; My silica plate ; N, collimator ; 0, beam-splitter ; P, prism ; Q, 35 mm camera ; R, eyepiece.Disjoining pressures were determined from photographs of the interference pattern obtained when the bubbles were positioned just sufficiently above the alumina surface for no flattening to occur [plate l(b)]. Since the base of each bubble was then essentially spherical, the pressure drop across its surface was given simply by Ap = 2azv/rb. The radius of curvature, rb, was calculated from the expression where ri and ri are the radii of the ith and jth interference fringes, and R! is the refractive index of the liquid.On pressing the bubble against the alumina surface, providing the radius of the film so formed was much less than rb, the pressure in the bubble was negligibly altered and Ap was equal to II ; in practice, film radii were always less than rb/lO. The thickness of each film was determined from its reflectivity 29 I (4sf)2 + (4fb)2 + 24sf4fb cos 6 = I, = 1 +(#sf4fb)2 + 2#sf4fb cos 6 ' where Pf = ( & - H ~ ) / ( N ~ + + ~ ~ ) , fifb = ( ~ ~ - + w ~ ) / ( ~ ~ + & b ) and 6 = 47c~~Z/A. I. and I are the intensities of incident and reflected light, and &, wzf and are the refractive indices of solid, film and bubble respectively. The refractive index of the film was assumed to be the same as that of the bulk liquid. Fig. 3 shows p as a function of I for films of n-decane on a-alumina at the two wavelengths used.The interference order was established by observing the shift in p on changing from one wavelength to the other. To measure p, fine-grain photographs of the films and their surrounding interference patterns were taken using a 35 mm camera attachment. The negatives were developed under standard conditions and scanned with a calibrated Joyce-Loebel double-beam micro- densitometer to give density profiles similar to that shown in fig. 4. The reflectivity of each198 ll-ALKANE FILMS ON CI-ALUMINA film was found by comparing its image density, d, with dmax and dmin, the densities of the maxima and minima, Pmax and pmin, given by eqn (11). Over the small density range involved, (P max + Pel (P + P,) ’ dmax- d = log and The term pe, which accounts for any extraneous light entering the microscope, is easily eliminated from these equations to give p.Use of the appropriate p against I curve (fig. 3) then gives I directly. 1 I I I I I 5 0 100 1 5 0 200 2 5 0 300 V Ilnm FIG. 3.-Variation of reflectivity, p, with film thickness, Z, for films of n-decane on a-alumina; curves calculated using eqn (11) for experimental wavelengths, A, of 435 and 547 nm. t d (direction of scan FIG. 4.-Image density profile of a film and its surrounding Newton’s rings interference pattern. This profile corresponds to a film thickness of 46 _+ 4 nm. Because of fluctuations in lo, it was necessary to determine d, dm, and &in from the same photograph. However, as can be seen from fig.4, the contrast between succeeding maxima and minima gradually decayed as one scanned away from the fdm, with even the first minimum being slightly affected. This attenuation was due to the increasing curvature of the bubble. Nevertheless, examination of the density profiles of very thin films and slowly thinning films exhibiting broad central maxima or minima, showed that sufficiently accurate values of dmax and &in could be obtained by linear extrapolation of the attenuated valuesT . D . BLAKE 199 The microdensitometer was calibrated for the chosen combination of wavelength, photographic film and development by first exposing a sample of the film to light of the appropriate wavelength through a linear density wedge of known slope. The film was then developed in the given way and scanned with the microdensitometer to give the required calibration curve.MATERIALS AND PREPARATION Synthetic a-alumina disks, 20mm in diameter and 2mm thick, were supplied by Fred Lee and Co. Ltd. They were ground flat and optically polished by the Department of Mining and Mineral Technology, Imperial College, London. Interferometric examination showed that the resulting surfaces were sensibly flat and free of visible irregularities apart from a few fine scratches. Fused silica cells (C, fig. 2) were supplied by Jencons Ltd. with 50-mm diameter optically flat bases. Before use, a cell containing an alumina disk was ultrasonically scoured with Teepol solutions followed by freshly distilled water. The cell was then covered and baked in an oven at about 1000 K for 12 h.After cooling, the cell was immediately filled with the test liquid. The n-octance and n-decane (99 % by g.l.c., as supplied by B.D.H. Ltd.) were exhaustively dried over molecular sieve, percolated through a column of activated alumina to remove any traces of polar impurities and distilled directly into the cells as required. White Spot nitrogen from a compressed gas cylinder was purified over activated charcoal and filtered to remove particles. The gas was inserted into the bubble holders via a micro- pippette. For the remaining materials, the values listed in table 1 were used. The refractive index of nitrogen was taken to be 1.000. TABLE 1 .-REFRACTIVE INDICES 435 1.777 1.406 1.421 547 1.767 1.399 1.414 0 a-alumina is bi-refringent ; values listed are arithmetic means.t/nm a-aluminaaJo n-octane 31 n-decane 31 RESULTS As expected, both n-octane and n-decane gave equilibrium wetting films that persisted, apparently indefinitely, at all disjoining pressures investigated. The films were evidently stable, since equilibrium thickness could be approached from either direction and films were not disrupted even by severe vibration. The experimental data are shown in fig. 5, with ll plotted as a function of I for both liquids. At the highest pressures (> 30 N m-2), equilibrium thickness was effectively attained within 10 min. At the lowest pressures (< 1 N m-2), equilibrium was approached only after 1 to 2 h. Usually, films were monitored for extended periods (more than 15 h in a few cases) after the attainment of equilibrium.The uncertainty associated with measurement of I is difficult to assess. The error bars on each datum point in fig. 5 represent an attempt to estimate the maximum probable error from a number of sources. These include uneven illumination of the film and photographic noise ; however, residual roughness of the alumina surface, and uncertainty in the extrapolated value of dmax are thought to be the main sources of error, especially for I < 30 nm. Larger surface defects and dust particles did not present a problem as these were clearly visible and could be avoided. One of the advantages of the photographic method is that it enables one to select only representa- tive areas of the film for measurement. For films thicker than about 60nm, the disjoining pressures were so low that bubbles became very susceptible to mechanical vibration; hence it was difficult to2,OO n-ALKANE FILMS ON CC-ALUMINA ensure that films were at equilibrium.Measurements of II were also affected by vibration. However, reproducibility was usually better than 2 %. Consequently, the contribution to the overall error was negligible. 2 0 4 0 6 0 8 0 100 FIG. 5.-Dependence of disjoining pressure, lI, on film thickness, I, for films of n-alkanes ona-alumina. Experimental data : 0, n-decane ; a, n-decane after irradiation ; 0, n-octane. Curves indicate theoretical contribution of dispersion forces to TI calculated according to : -, Lifshitz theory ; -- , London-Hamaker theory ; - - - - , London-Hamaker theory, but allowing for retardation.Theoretical curves are shown for n-decane only. DISCUSSION Before comparing the experimental results with the predictions of contemporary theories of dispersion forces, it is useful to consider some of the assumptions under- lying both the theories themselves and their application. There are currently two fundamentally different approaches to the calculation of dispersion forces between condensed media. One of these, the microscopic approach of London 32 and Hamaker,33 is based on the summation of individual, molecular interactions. The other, which is due to Lifshitz and co-w~rkers,~~ treats the inter- acting media as continua and therefore involves only their macroscopic, electro- dynamic properties. Both have been the subject of recent review^.^^-^^ A number of authors have used the microscopic approach to calculate the contribu- tion of dispersion forces to the disjoining pressure of a liquid film on a solid.Schel~dko,~ for example, has integrated London's expression for the energy of interaction between two molecules separated by a distance r, over all pairs of molecules, to obtain U = - B r 6 , (1 3)T . D. BLAKE 20 1 where dsl and dL1 are the Hamaker constants for solid/liquid and liquid/liquid interactions respectively : and dl' = nz(N/v')2B" dsL = T C ~ ( N ~ / U ~ V ~ ) B ~ ~ . Like eqn (9), these expressions contain the simplifying assumption that (a Vf/dnpT,Af = v'. If a corresponding assumption is made about the entropy of the film,g9 39 i.e. (> = (??)T = sl, anf T,Af where s1 is the molar entropy of the liquid, then it follows from (7) and (14) that Hence, from (9) AJf = - ~'(d'' - d1')/6nl '.(1 5 ) II = ( d s ' - d " ) / 6 ~ Z 3 , (16) whilst, from (lo), for an adsorbed layer, In p'/p; = - v z ( d S L - d11)/6n RT 13. Eqn (17) is essentially that proposed by Frenkel,39 Halsey 40 and Hill 41 for the multi- layer adsorption of gases. Because the propagation of electromagnetic radiation is not instantaneous, dispersion forces fall off more rapidly with distance than predicted by eqn (13). The effect, which is known as retardation, has been investigated theoretically by Casimir and Polder.42 They have shown that at sufficiently large separations, U varies as r7 rather than rr6. In general, retardation can be allowed for by applying a correction function, f(#), to the London expression, whence where # = 2nr/LC and Ac is the characteristic wavelength of the interaction. Although no simple expression for f (j4) exists, Overbeek 43 has given the following analytical formulae : U = - B r 6 f @ ) , (18) 0 < b < 3, 3 < b < a, f(b) = 1.01-0.14fi; f(b) = 2.45b-1-2.04jh-2.Overbeek and others ' 9 lo* 3 5 9 44 have used these formulae to integrate (18) and obtain what amount to retardation correction functions for Hamaker constants. If this procedure is carried out for a liquid film on a solid, then the following, rather lengthy, expressions are obtained for Aiif : 1 < 3;1,/2n, V1 6n13 Afif = -~ (dsz[ 1.01 - 0.28#" + 0.0143(p)3 - 0.0193(~")4] - d z z [ l . O l -0.28fi12+0.0143(#2z)3 -0.0193(#')4]]; (20a) V l 6n13 Aiif = - ---(d"'[:1.470(+is2)- ' -0.S16(#,")-2] -202 n-ALKANE FILMS ON CC-ALUMINA where flz = 2nZ/A",' and f i 1 2 = 2n2/ALz.Hence one may obtain expressions, in terms of retarded forces, analogous to (15), (16) and (17). In the fully-retarded limit, II = (dy- d%",'/79l4. (21) It has been argued 45-5 that the microscopic approach is, in many cases, inadequate for the calculation of dispersion forces between condensed media, and that the Lifshitz, macroscopic approach is both more general and more accurate. For a liquid film on a semi-infinite solid, the Lifshitz theory gives where a = ( X 2 - 1 + E ~ / E ~ ) and are those of the bulk solid and bulk liquid respectively, and are functions of the imaginary frequency icy = 2nivkT/k.The quantity Xis an integration variable and the summation index v takes values 0, 1,2, 3, etc. The prime on the summation symbol in (22) means that the term for which v = 0 must be multiplied by 3. As with the simplified microscopic approach, it is assumed that ( 8 v f / i h ~ ~ , , ~ = d , and Aff and IJ follow on the further assumption that (8Sf/8n9,,,f = s2. Although expression (22) is complicated, it can be evaluated numerically providing suitable data are available. The present author is grateful to Dr. P. Richmond 52 who has carried out this operation for n-octane and n-decane films on a-alumina. The calculations were simplified by the fact that each of these materials has one major absorption frequency centred in the ultra-violet. Consequently, below this frequency, it is possible to represent the dielectric constant of each material by a simple expression involving the characteristic frequency v, = c/A0 and the limiting dielectric constant in the visible region, co : = ( X 2 - 1 + 1 / & I ) .The dielectric constants and &,-1 1 + (t/2nv,)2' &(it) = l + Furthermore, by restricting calculations to relatively thick films (I -c 10 nm), it is possible to neglect contributions from frequencies greater than the absorption frequency. Both v, and E~ were determined in the manner discussed by Gregory 37 from the variation of refractive index with frequency. Necessary data were obtained from the literat~re,~,. 31 and the resulting values are listed in table 2 below. TABLE 2.-DISPERSION DATA a-alumina n-octane n-decane EO 3.056 1.927 1.967 v,/s-l 4 .1 6 ~ 1015 3.470 x 1015 3 . 4 2 9 ~ 1015 The calculated dependence of II on I for n-decane is shown by the solid curve superimposed on the data in fig. 5. Calculations for n-octane give disjoining pressures only 1 to 2 % higher. Agreement between theory and experiment is excellent, as can be seen even more clearly from the log-log plot in fig. 6. Presented in this way, the best straight line (by linear regression giving 96 % correlation) through the experimental points deviates from the theoretical curve by less than 2 % of I over the entire experimental range. In addition, the line has a slope of -3.77, as compared with a mean value of about -3.9 for the theoretical curve in this region.T. D. BLAKE 203 These slopes may be compared, in turn, with limiting theoretical slopes for fully retarded and unretarded forces of - 4 and - 3 respectively.The single, filled-in point in each of fig. 5 and 6 was obtained 20 min after exposing the system to more than 20 mrad of ionising radiation from an l3II source. The radiation had no significant effect on film thickness, and it was therefore concluded that electrostatic forces arising from tribolectric effects were not contributory to measured disjoining pressures. I , I , \ , \ IC 2C) 3 0 5 0 7 0 100 200 300 FIG. 6.-Log-log plot of the dependence of disjoining pressure, n, on film thickness, I, for films of n-alkanes on a-alumina. Data and theoretical curves as for fig. 5 ; - -, best straight line (96 % correlation) through experimental points.Fig. 5 and 6 also show disjoining pressure curves calculated on the basis of the microscopic theory, using eqn (16) and equivalent expressions derived from (20a) and (20b). Again, calculations are simplified by the simple dielectric properties of a-alumina and the n-alkanes, which allow the necessary Hamaker constants to be obtained in terms of v, and go according to the formulae given by Gregory 37 : and where vzl = 2v~v~/(v”,”vvl,l>. Again, the values of v, and co listed in table 2 were used. These gave for n-decane, atsz = 10.40 x J, and for n-octane, dS’ = 10.15 x It is clear from fig. 5 and 6, that over the range of film thicknesses studied, neglect J and &I1 = 5.68 x J and atzz = 5 . 4 0 ~ J.204 11-ALKANE FILMS ON CI-ALUMINA of retardation leads to large errors.It is also clear that when retardation is allowed for, the predictions of the microscopic theory are only slightly different from those of the macroscopic theory. Indeed, on the basis of the present data, it is not possible to distinguish which is the more accurate. It has been argued,53 that the simple additive approach of the London-Hamaker theory is not valid for condensed media because it neglects any perturbation of pair-wise interactions by neighbouring molecules. However, the above results suggest either that this objection is unimportant for dispersion interactions in the high frequency region, or that any non-additivity is effectively accounted for by the use of macroscopic dielectric properties, v, and E ~ , to calculate the Hamaker constants.In either case, a significant part of the success of the microscopic approach with this system can be attributed to the simple dielectric properties of the materials involved. With more complex dielectrics, such as water, in which orientation and inductive effects are important, the microscopic approach appears to be much less success- As noted in the Introduction, measurements of disjoining pressure and vapour phase adsorption are complementary. It is therefore of interest to compare theory not only with the present results, but also with some earlier data 54 for much thinner films obtained by gravimetric measurement of the adsorption of n-decane on the oxidised surface of aluminium foil. For the purposes of such a comparison, ATf is a more appropriate parameter than II.Accordingly, fig. 7 shows a log-log plot of the theoretical dependence of -Aff on I for I between 0.1 and 100 nm. On this extended scale, it can be seen that the curves for the retarded region merge with the line for un-retarded forces at I = 5 nm. Superimposed on the theoretical curves in fig. 7 are the experimental points. The lower group were derived from the disjoining pressure measurements for decane using eqn (9), taking v z = 1.95 x m3 mol-l. The upper group were derived from the adsorption data using (10) and on the assumption that I = u'nf/Af. B.E.T. treatment of the adsorption data gave 0.72 nm2 for the molecular area of n-decane and 0.45 nm for the thickness of the first monolayer. The latter value has been used to express I in terms of an equivalent number of monolayers for the top scale of fig.7. However, the scale is somewhat artificial, since the molecular area is consistent with molecular orientation parallel to the surface,55 and this is unlikely to be preserved much beyond the first layer. For films of between 1 and 5 monolayers, the adsorption data lie reasonably close to the theoretical line and have a similar slope. In fact, theory underestimates I by about 15 %. Electron diffraction 56* 57 indicates that the oxide layer on aluminium is amorphous, and hence has a slightly lower density and dispersion interaction than a-alumina. At worst, this would lead to a further 10 % underestimate of I. Such discrepancies could be explained by a comparable underestimate of adsorbent area, as this was determined 5 8 by the B.E.T. method using an adsorbate (tetramethyl- silane) having large, approximately spherical molecules (area 0.46 nm2), and gave a roughness factor of only 1.08.This value is 16 % lower than that obtained by Bowers 59 using nitrogen (area 0.162 nm2). An alternative possibility is that the extra adsorption was due to the substrate aluminium. However, the alumina layer resulting from oxidation at normal temperatures is at least 5 nm 57 so any contribution from imaging forces should have been small. One additional consideration is that the alumina layer has a small surface dipole which may be expected to generate induced dipole interactions with at least the first monolayer of decane. Taking a value of 5.7 V nm-1 for the surface field,60 and 8 x nm3 for the polarisability of the n-decane molecule in the direction normal fu1.469 48, 51T.D. BLAKE 205 to the Clo chain,61 and ignoring lateral interactions, one arrives at a contribution to ASf of about - 8.8 x lo3 J mol-1 at monolayer coverage. As this is about one and a half times the calculated contribution from dispersion forces, one would expect the experimental dependence of Aff on I shown in fig. 7 to become steeper in this region. In fact, the opposite occurs, with Aff declining increasingly slowly as zero coverage is approached. One possible explanation is that the induced dipole contribution is being submerged in compensating for the obvious inadequacies of the present calcula- tions for films of molecular thickness.The identification of I in these calculations with v'nf/Af is one such inadequacy, and is probably the initial reason for the sharp divergence between experiment and theory below monolayer coverage. number of statistical monolayers f/nm FIG. 7.-Log-log plot of the dependence of differential free energy of film formation, Aff, on film thickness, 1 : 0, n-decane on a-alumina calculated from the experimental data of fig. 5 ; A, n-decane 011 oxidised aluminium foil calculated from vapour adsorption measurement~.~~ Curves indicate the theoretical contribution of dispersion forces to Aff calculated according to : -, Lifshitz theory ; - -, London-Hamaker theory ; - - - -, London-Hamaker theory, but allowing for retardation. Whilst more appropriate calculations for the monolayer region are beyond the scope of the present work, it is evident that they can only follow detailed knowledge of the material and electrical properties of both the film and the solid surface.In particular, the dependence of the molar entropy of the film on its thickness can no longer be neglected, and it must be decided whether one may treat a film of molecular dimensions as a continuum or whether one must, of necessity, consider individual molecular interactions. For filiiis of more than 5 monolayers, fig. 7 shows a gradual divergence between theory and experiment. However, over this regionp'/p; > 0.96, and it is therefore very likely that an increasing part of the measured adsorption was in the form of206 n-ALKANE FILMS ON Q-ALUMINA interlaminar condensate within the adsorbent sample.* In consequence, there seems no reason to doubt that dispersion force theory adequately accounts for the inter- mediate range of film thicknesses not investigated experimentally. CONCLUSIONS (i) n-Octane and n-decane form stable wetting films on a-alumina. (ii) The combined use of disjoining pressure and adsorption measurements provides a convenient way of investigating the properties of these films over a very wide range of film thicknesses. (iii) Both Lifshitz and London-Hamaker theories of dispersion forces correctly predict the disjoining pressure and differential free energy of formation of the films, provided the films exceed monolayer coverage and provided due allowance is made for retardation if the films exceed a thickness of about 5 nm.(iv) In making these predictions, it is sufficient to assume throughout that the films have molar volumes, molar entropies and dielectric properties identical with those of the parent bulk liquids. SYMBOLS area Hamaker constant London constant index for bubble speed of light (2.998 x lo8 m s-l) image density Helmholtz free energy index for film differential Helmholtz free energy of film formation Planck constant h/2n intensity of reflected light intensity of incident light general numerical indices (i # j ) Boltzmann constant film thickness index for liquid Avogadro’s number number of moles refractive index pressure saturation vapour pressure 2n3/AC in (1 8) and (19) ; 27d/Ac in (20) gas constant radius of curvature of bubble at its base radius of ith or jth interference fringe intermolecular distance J-1 4 S s S T U Ailf V 0 V X a! D 6 &O A.& A, P v, V i t IT P P e n 0 Fresnel coefficient in (1 1) entropy molar entropy index for solid temperature internal energy differential internal energy of film formation volume molar volume index for vapour integration variable in (22) ( x2 - 1 + &S/&I) ( x2 - 1 + 1 / E l ) 4niwf2/A. in (1 1) dielectric constant limiting dielectric constant wavelength characteristic dispersion wave- length chemical potential summation index in (22) characteristic dispersion frequency imaginary part of complex frequency disjoining pressure 3.1416 reflectivity of film correction term for extraneous light in eqn (12) interfacial tensionT. D. BLAKE 207 The author gratefully acknowledges many helpful discussions with Dr.J. F. Padday, and is especially grateful to Dr. P. Richmond for carrying out the calcula- tions involving Lifshitz theory and for making the results available for publication. B. V. Derjaguin and M . Kussakov, Acta Physicochim., 1939, 10, 25, 153. €3. V. Derjaguin, M. Kussakov and L. Lebedeva, Compt. rend. U.R.S.S., 1939, 23, 671. J. C. Melrose, Soc. Chem. Ind. Monograph, 1967, no. 25, p. 123. A. N. Frumkin, Acta Physicochim., 1938,9,313 ; Zhur. fiz. Khim., 1938, 12, 337. B. V. Derjaguin and L. M . Shcherbakov, Colloid J. U.S.S.R. (trans.), 1961, 23, 33. B. V. Derjaguin, Disc. Faraday SOC., 1966,42, 109. 1971). Colloid Science, ed. H. R. Kruyt (Elsevier, London, 1952). A. Scheludko, Colloid Chemistry (Elsevier, London, 1966). ' e.g.Spec. Disc. Faraday Soc.: Thin Liquid Films and Boundary Layers (Academic Press, London, lo A. D. Read and J. A. Kitchener, SOC. Chem. Ind. Monograph, 1967, no. 25, p. 300. l1 T. D. Blake and J. A. Kitchener, J.C.S. Faraday I, 1972, 68, 1435. l2 G. A. H. Elton, Proc. Roy. SOC. A, 1948,194,259. l 3 L. F. Evans, Nature, 1953,172,776. l4 A. D. Read and J. A. Kitchener, J. Colloid Interface Sci., 1969,30, 391. l5 H. J. Schulze and C. Cichos, 2. phys. Chem. (Leipzu), 1972,251,145,252. l 6 A. D. Roberts and D. Tabor, Nature, 1968,219, 1122 ; Spec. Disc. Faraday Soc.: Thin Liquid l7 A. D. Roberts, J. Colloid Interface Sci., 1972, 41, 23. l 8 A. Scheludko and D. Platikanov, Kolloid-Z., 1961, 175, 150. l9 H. J. Schulze, Naturwiss., 1972, 59, 119.2o T. D. Blake, unpublished results. 21 B. V. Derjaguin and 2. M. 20x51, Proc. 2nd Int. Congr. Surface Activity, 1957, 2, 145. 22 C. H. Anderson and E. S. Sabisky, Phys. Rev. Letters, 1970, 24, 1049. 23 C. H. Anderson and E. S. Sabisky, Phys. Rev. A, 1973, 7,790. 24 C. H. Anderson and E. S. Sabisky, J. Acoust. SOC. Amer., 1971,49, 1052. 2 5 P. Richmond and B. W. Ninham, J. Low Temp. Phys., 1971,5,177. 26 A. I. Rusanov, Colloid J. U.S.S.R. (trans.), 1966, 28, 583 ; 1967, 29, 118, 183 ; Res. Surf. Forces, 1971, 3, 103. 27 e.g. R. Defay, I. Prigogine, A. Bellemans and D. H. Everett, Surface Tension and Adsorption (Longman, London, 1966), chap. I and 11, and papers cited therein. 28 J . W. Gibbs, Scientific Papers (Dover, New York, 1961), vol. 1. 29 A. Vasicek, Optics of Thin Films (North Holland, Amsterdam, 1960).30 M. A. Jeppesen, J. Opt. SOC. Amer., 1958,48,629. Films and Boundary Layers (Academic Press, London, 1971), p. 243. J. Timmermans , Physico-Chemical Constants of Pure Organic Compounds (Elsevier, Amsterdam, 1950, suppl. 1965). 32 F. London, 2. Phys, 1930,63, 245 ; Trans. Faraday SOC., 1937,33, 8. 3 3 H. C. Hamaker, Physica, 1937,4, 1058. 34 E. M. Lifshitz, Suuiet Phys. J.E.T.P., 1956,2, 73 ; I. E. Dzyaloshinskii, E. M. Lifshitz and L. P. 35 A. van Silfhout, Proc. k. ned. Akad. Wetenschap. B, 1966, 69, 501, 516, 533. 36 H. Krupp, Adv. Colloid Interface Sci., 1967, 1, 111. 37 J. Gregory, Adv. Colloid Interface Sci., 1969, 2, 396. 38 J. Visser, Adv. Colloid Interface Sci., 1972, 3, 331. 39 J . Frenkel, Kinetic Theory of Liquids (Oxford University Press, 1946), p. 332-342. 40 G. D. Halsey, J. Chem. Phys., 1948, 16, 931. 41 T. L. Hill, J. Chem. Phys., 1949, 17, 590, 668. 42 H. B. G. Casimir and D. PoIder, Phys. Rev., 1948, 73, 360. 43 J. Th. G. Overbeek in ref. (8), p. 266-267. 44 E. J. Clayfield, E. C. Lumb and P. H . Mackey, J. Colloid Interface Sci., 1971, 37, 382. 45 B. W. Ninham and V. A. Parsegian, J. Chem. Phys., 1970,52,4578. 46 V. A. Parsegian and B. W. Ninham, Biophys. J., 1970, 10, 664. 47 B. W. Ninham and V. A. Parsegian, J. Chem. Phys., 1970,53,3398. 48 V. A. Parsegian and B. W. Ninham, J. Colloid Interface Sci., 1971, 37,332. 49 D. J. Mitchell and B. W. Ninham, J. Chem. Phys., 1972,56, 1117. 5 0 B. W. Ninham and P. Richmond, J.C.S. F'raday II, 1973, 69,658. 51 P. Richmond, B. W. Ninham and R. H. Ottewill, J. Colloid Interface Sci., 1973,45,69. Pitaevskii, Soviet Phys. J.E.T.P., 1960,37, 161.208 n-ALKANE FILMS ON a-ALUMINA 5 2 P. Richmond, personal communication. 53 e.g. E. M. Lifshitz 34; M. J. Sparnaay, Physica, 1959, 25, 217. 54 T. D. Blake, J. L. Cayias, W. H. Wade and J. A. Zerdecki, J. Colloid Interface Sci., 1971, 37, 5 5 J. H. Clint, J.C.S. Faraday I, 1972, 68, 2239. 56 M. S. Hunter and P . Fowle, J. Electrochem. Soc., 1956, 103, 482. 5 7 S. Wernick and R. Pinner, The Surface Treatment and Finishing of Aluminium and its Alloys (Draper, Teddington, 4th edn., 1972). 58 T. D. Blake and W. H . Wade, J. Plzys. Chem., 1971, 75, 1887. 5 9 R. Bowers, Phil. Nag., 1953, 44, 467. 6o D. J. A. Dear, D. D. Eley and B. C . Johnson, Trans. Faraday SOC., 1963,59,713. 61 T. Smith, Hydrophobic Surfaces (Academic Press, New York, 1969), 189. 678.

ISSN:0300-9599    

DOI:10.1039/F19757100192

出版商:RSC    

年代:1975

数据来源: RSC