摘要:

Effects of Ionisation on Adsorption from SolutionBY HENRY M. RENDALL“ AND ALEC L. SMITHUnilever Research, Port Sunlight Laboratory, Port Sunlight,Wirral, Merseyside L62 4XNReceived in revised form, 6th August, 1976The adsorption of y-picoline (4-methyl pyridine) at the silica-water interface, as a function of pH,is reported. A general model for the adsorption is developed, which allows for the possibility thatthe ionised (HPic+) and the neutral (pic) forms of the molecule may both adsorb. For the limit ofzero coverage, explicit expressions are derived which give a simultaneous fit of adsorption andelectrokinetic measurements, and the model is extended to consider the complete adsorption isotherms.The magnitudes of the initial slopes of the isotherms, and the Occurrence and position of a maximumin the adsorption with pH, are explained. The two forms of the picoline molecule have specificadsorption potentials of - -4 kT, with the neutral molecule slightly the more strongly adsorbedby - 0.3 kT.The adsorption of the ionised and neutral components of an ionisable moleculehas been widely discussed, both in relation to studies of practical problems involvedin flotation,’ corrosion inhibition,2 and biological activity and from a theoretical~tandpoint.~ It is not normally possible to determine by direct measurement therelative adsorption densities of the two species in the equilibriumBH++H,O + B+H30+in the pH range where both are present in significant quantities.’’ Conway andhis co-workers have studied the separate adsorption of the neutral and the cationiccomponents of organic bases at the mercury-water interface under extreme conditionsof pH.Breuer has explained a number of properties of biological systems on theassumption that only the neutral forms of small organic molecules are adsorbed onproteins and similar hydrophobic surface^.^At the air-water interface, however, Betts and Pethica have suggested a surfacedissociation constant for long chain molecules equal to the value obtained in bulksolution, when allowance is made for the surface potential. This would imply thatboth components have a similar intrinsic tendency to adsorb. It is, therefore, ofinterest to obtain information about the effects of ionisation on the adsorption of asimple molecule at the solid-liquid interface.A study has been conducted of the effect of pH on the adsorption of y-picolineat the silica-water interface, in the presence of NaCl to control the ionic strength.The pK, of y-picoline is 6.02,6 and the isoelectric point (ip) of the silica used wasapproximately pH 3.The adsorption of the picolinium ion onto a neutral andincreasingly negatively charged surface may, therefore, be observed, and comparedwith the adsorption of the conjugate base.In the limit of extrapolation to zero coverage, we have sought the simplest model,based on standard double layer theory, and allowing for the possibility that HPicfand Pic might both be adsorbed, to describe the pH dependence of picoline adsorption.We have used the adsorption affinity so derived for the neutral sptcies to predict theconcentration dependence of its adsorption, and in this way have resolved the10102 EFFECTS OF IONISATION ON ADSORPTIONmeasured adsorption into two components throughout the concentration range.Afew measurements have been made of the adsorption of the methyl quaternaryderivative, MePicf, which is not involved in a reversible ionisation, for comparisonwith the adsorption behaviour inferred for the HPicf ion.EXPERIMENTALMATERIALSAerosil 0 silica was prepared by the method of Taylor, Hockey and Pethica.7 Theprocedure is claimed to produce agglomerates of non-porous primary particles which arespherical, fully hydroxylated (3 to 4.6 of hydroxyl groups) and of about 200 A diameter.This was checked by electron microscopy and nitrogen adsorption (B.E.T.area = 176420 m2 g-’), The aggregates used were mainly in the size range 125-180 pm. It has beenassumed that the results were not seriously influenced by any effect due specifically to theaggregated nature of the adsorbent. Adsorption studies have shown that the silica surfaceinvolved is accessible to polyvinylpyridines of quite large molecular weights.y-Picoline (BDH AnalaR grade) was distilled once and stored under refrigeration toreduce decomposition. A sample of N-methyl y-picolinium bromide was prepared byquaternisation of 7-picoline under reflux in methanol, and was recrystallised from acetone.The water used for all solutions was prepared by the double distillation of deionisedwater under nitrogen in an all-glass still with alkaline permanganate in the first stage.All other chemicals were of BDH AnalaR grade.ADSORPTION MEASUREMENTThe solutions contained mol dm-3 of NaCI, to maintain the ionic strength, andsufficient hydrochloric acid to obtain the desired pH.For the highest pH studied (pH 8.7)an ammonia/ammonium chloride buffer, or sodium hydroxide, was added. The resultswere in agreement, but in the latter case were rather less reproducible, possibly as a resultof some dissolution of the silica. Measurements at higher pH were avoided because ofthese experimental difficulties, and because an underlying assumption of our treatment, thatthe adsorption affinity of the neutral molecule for the surface is independent of the doublelayer potential, becomes doubtful as the surface potential becomes large.Buffers were employed to control the pH in the adsorption of the quaternised molecule.As far as possible sodium salts were used at lom2 mol dm-3 to keep the conditions comparablewith the picoline adsorption.Pyrex test tubes, with polythene stoppers, and containing known amounts of adsorbentand solution (normally 1 g and 10 cm3), were shaken in a thermostat at 298 K for at least3 h, which was more than sufficient to obtain equilibrium.The solutions were centrifugedto remove suspended silica. The pH of the equilibrium solution was determined tok0.05 pH unit. Concentrations were determined by U.V. absorption. In general, twoseparate dilutions were made for each solution, and the determinations agreed to k0.5 %.The concentration change was usually in the range 10-30 %, so that the error in the amountadsorbed was 2-5 %.ELECTROPHORESISSome measurements of the mobilities of the silica particles as a function of pH atmol dm-3 ionic strength were made with a Rank microelectrophoresis apparatus.Charge reversal was demonstrated with both the HPic+ and the MePic+ ions, and theisoelectric point of the silica in the presence of MePicBr was at pH 5.0 (fig.1).The ions studied here do not form micelles in solution; published experimental resultsshow only repulsive interactions between similar ions, adsorbed at the mercury-solutioninterface, up to high surface coverage. The observed charge reversal may, therefore, beattributed to a specific interaction with the silica, not to the cchemimicelle ” formationpostulated for long chain ions.gmoH.M. RENDALL AND A . L. SMITH 103THEORETICALDOUBLE LAYER MODELThe simplest useful model for the double layer, due to Grahame,lO is illustratedschematically in fig. 2. The application of this model to describe the surface electricalproperties of oxides, including silica, has been discussed by one of us.ll The doublelayer is represented by three planes, the surface proper (assumed to contain the centresof ionised groups), and boundary of the diffuse layer (defined by the distance ofclosest approach to the surface of hydrated counterions) and a plane containing thecentres of specifically adsorbed ions.2 4 6 8 10PHRG.1.-pH dependence of measured potentials and charges of silica in mol dm-3 electrolyte.(a) and (b), (-potentials in NaCl and MePicBr, respectively; (c) and (d), Ud and - uo, respectively,in NaCl.The charge densities (cT), potentials ($), and integral capacities (a,* whoselocation with respect to those planes is shown in fig. 2, are related by the equations(using rationalised electrical units)a O + a p + a d = 0 (1)@o-Il/s = ao/& (2)$B-$d = (3)- ad = (2kT ICE fzeo) sinh(zeo$* J2kT) (4)KT1 = K-13-K-1 1 2 ( 5 )where 1c is the Debye-Huckel reciprocal distance parameter, z is the valence of thecounterion, eo, k, and T are the electronic charge, the Boltzmann constant and thetemperature , respectively .* Note that integral capacities K carry subscripts to distinguish them from the association constantK introduced in eqn (8)1 04 EFFECTS OF IONISATION ON ADSORPTIONFor silica at the experimental ionic strength, in the absence of picoline, i)d (takenequal to the electrokinetic potential), and hence ad, are known.A capacity Kd of20 pF cm-2 was found to give good agreement between titration and electrokineticdata on silica,12 and a potentiometric titration of the silica sample used here gavevalues of a. (fig. 1) virtually identical with those reported by Bolt.13 Hence, inthe absence of picoline adsorption, only one additional parameter is required todefine completely the double layer model.solid solutionpotentials yo yp v,FIG. 2.-Double layer model.pH O F MAXIMUM ADSORPTIONThe adsorption isotherms reported below show a maximum in the adsorption, atfixed solution concentration, as a function of pH. We develop here an approach tofind the conditions under which such a maximum will be observed, for the generalcase in which the ionised and neutral forms of the molecule may be adsorbedsimultaneously .In the limit of extremely low adsorption density, and neglecting ion self-atmospherepotentials we use the Langmuir-Stern isotherm to give an approximate measure ofa non-electrostatic contribution to adsorption,where n, is the amount adsorbed, N' is the density of adsorption sites, assumedidentical for the two species.x is the mole fraction of the species in solution, and<D is the specific adsorption potential of the species, with subscripts +and I? referringto the ionised and neutral molecules respectively.The mole fractions of the two species in solution may be calculated from the totalconcentration c (mol dm-3), the hydrogen ion activity aH and the pK by the equationswhere K is the association constant ( = K; ').ref.(6).CDrwhere A = N,c/55.51.[dn,/d(pH) = O] becomesA convenient tabulation of the fractions ionised as a function of pH is given inWe will write -e,ts/RT = $r (i.e., in units of - 25 mV at 298 K) and -(D/kT =(10)For a constant total concentration the condition for maximum adsorptionThe total adsorption of picoline at low coverage is given byns = A(1 +a&)-' [aHKexp($r) exp(Qr+) +exp(@rJIexp(#r+A@,,) = [I -p(l +a&)]-' (1 1H .M. RENDALL AND A . L. SMITH I05i.e., the amount, in units of kT, by which the positive species where ACDr =is more strongly adsorbed than the neutral species, andP = (e0P.303 kT) W$9/d(PH)l. (12)Froin eqn (1 1) a maximum will never be observed when y = I . In this case theincreased attraction of the surface for the ion, by eqn (6), always compensates forthe decrease in x+ as given by eqn (8). The rate of change of 4'/s with pH will, ofcourse, always be less than that given by the Nernst factor. It is possible for a Nernstrelation to apply to ~ o , not to $@, and in the case of silica even $,, shows considerabledeviations from Nernstian behaviour. In principle, therefore, an adsorptionmaximum under the defined conditions is to be expected for all systems.RESULTS AND DISCUSSIONEXPERIMENTAL ADSORPTION ISOTHERMSThe pH dependence of the adsorption of y-picoline on silica, as a function ofthe initial solution concentration, is shown in fig.3, where S is the ratio of the amountadsorbed (in mmolg-') to the amount remaining in solution (in moldm-3). Theadsorption passes through a maximum with increasing pH for all the concentrationsstudied.2 4 6 8PHFIG. 3.-Adsorption ratio S against pH for y-picoline on silica at the initial solution concentrationsThe pH dependence of the adsorption of the MePic+ ion, at a constant initialconcentration of 6 x mol dm-3, is shown in fig. 4. The total adsorption ofpicoline, obtained at equivalent equilibrium solution concentrations of picoliniuniions, is given for comparison in fig.4. At low pH, where the picoline is mainly inthe ionised form (e.g., at pH 2, HPic+/Pic = lo4), the picoline adsorption parallelsthat of the MePic+ ion, and the higher adsorption of MePic" ion suggests a strongerindicated (mmol dm-3). - - - , zero coverage extrapolation106 EFFECTS OF IONISATION ON ADSORPTIONspecific interaction that for HPic+ with silica. At higher pH the picoline adsorption,however, greatly exceeds that of the MePic+ ion. It is reasonable to conclude thatin this higher pH region the ionised and the neutral forms of picoline must bothmake a significant contribution to the measured adsorption.IPHpicoline adsorption ; - - - , calculated HPic+ adsorption.FIG. 4.-Adsorption at equivalent cation concentrations. 0, MePic+ ion adsorption ; 0, totalThe position of the adsorption maximum (fig.3) moves to higher pH as theconcentration of picoline is increased. We may discuss the significance of this shiftin qualitative terms only, since the condition for a maximum, eqn (11), was derivedfor the limit of very low coverage, and since the variation of p with p H and coverageis not well enough known. The term t,br+ACDr represents the total amount by whichthe affinity for the surface of the HPic+ ion exceeds that of the Pic molecule, undergiven conditions. Assuming a,, is independent of coverage, then, by eqn (ll), theaffinity of the cation for the surface must decrease with coverage. Such a decreaseis expected, because the specific adsorption of cations will, in general, make t,bp less25 5 0 7 5 100maximum adsorption/pmol g-'FIG. S.-pH of maximum adsorptionH.M. RENDALL AND A. L. SMITH 107negative. A rapid decrease in apparent adsorption affinity with coverage has beenreported for pyridinium ions at the mercury-solution interface.Throughout the experimental concentration range the pH of maximum adsorptionshowed a linear variation with the amount of picoline adsorbed (25-100 pmol g-')at the maximum (fig. 5). From the intercept, the adsorption maximum at zerocoverage would occur at approximately pH 6.1.LIMITING ADSORPTION RATIO AT ZERO COVERAGEIt is reasonable to assume that the potentials $B appropriate to the limit of zerocoverage are determined by the properties of silica measured in the absence of picoline.Hence if a value is assumed for the integral capacity K,, +b may be calculated, at agiven pH, from $d (fig.6), using eqn (3). The position of the adsorption maximumat zero coverage, as given by eqn (11) with Amr = 0, was found to lie at pH 5.9-6.0for values of K, within physically reasonable limits. This is similar to the pH ofmaximum adsorption suggested by empirical extrapolation of the experimentalresults. The difference is in a direction which would imply that lCDnl > I@+,[ by upto about 0.5 kT.- 1 5 0 -6 aPHFIG. 6.-Electrostatic potentials for silica in mol dm-3 NaCl. (a) #d from electrokineticmeasurements ; (6) $p from $d with K2 = 30 pF cm-2 ; (c) $o from #band uo, with Kl = 60 pFcm-2.0, #p from extrapolated adsorption with AD, = 0 (filled points) and AQr = -0.3 (open points).The magnitude of calculated limiting adsorptions, unlike the position of theadsorption maximum, is very sensitive to the value assumed for K,, and hence for$a.We now seek an extrapolation procedure to obtain values of S at zero coverage.From these we will deduce, for different values of har, the variation with pH of$fl which is required to explain the extrapolated adsorption results. We will thenimpose the condition that t,kB must be related to t+9d (fig. 6) by eqn (3), with a singlevalue of K2. The potentials $b calculated from the adsorption results will be virtuallyindependent of A@ at sufficiently low pH, and will become very sensitive to AQr athigh pH.The procedure outlined should, therefore, yield a unique solution.--- , #o calculated from a modified Nernst equation with 0, = 0.0001 and P.Z.C. at pH 3.2108 EFFECTS OF IONISATION ON ADSORPTIONFor low coverage by a single species, the values of In S, by eqn (6), and (7), givea direct indication of adsorption energy. Even for very low adsorption densitieswhich would correspond to the " initial slope " region of a Langmuir-type isotherm,the experimental values of 1nS at low pH decreased rapidly with coverage. Acomparable decrease with coverage in the apparent adsorption energies of similarcations at the mercury-water interface has been reported by Bockris l 5 and Conway.2We have used a linear extrapolation of In S against n,, to evaluate the limiting initialslopes (g) of the isotherms.In the pH range where both species contribute significantly to the measuredadsorption, S may be subdivided asS = aS++(l-a)S, (1 3)where 01 is the fraction ionised.Although, in this case, In S does not provide asimple measure of adsorption energy, the same extrapolation procedure was used toobtain the approximate values for the initial slopes of the isotherms, which are shownin fig. 3.By eqn (6) the limiting slope p+, for cation adsorption at the ip of the silica givesa measure of @+, and for zero coverage at other pH values we have(14) - S+ = g; exp - (eo$s/kT) ;similarly - S , = 5; -A@r.From the extrapolated limiting slopes we may calculate $b using eqn (13), (14)and (15).Consistency with the values obtained from $d using eqn (3) was obtained(fig. 6) with A@, = -0.3 (Lee, the neutral molecule more adsorbed than the cation)and with K2 = 30 pF cm-2. Smaller values of a, gave potentials I$s[ which increasedrapidly at high pH and could not be reproduced by the substitution of any value ofKz (exemplified in fig. 6 by the case A@, = 0), whereas larger values of On madedecrease at high pH.It was confirmed that, using the values of t,bB and hence of p given by eqn (3)for K2 = 30 pF cm-2 (fig. 6), and assuming AQr = -0.3, eqn (11) predicts anadsorption maximum at pH 6.15, which is consistent with the zero coverage extra-polation (fig. 3 and 5).Usingthe experimental values of cro for this ionic strength, the pH dependence of @o wasobtained from eqn (2), as shown in fig.6. The deviation from the Nernst equationof the calculated surface potentials $o is consistent with theoretical predictionsFrom eqn (5), Kl = 60 pF cm-2 for Kd = 20 pF cm-2, K2 = 30 pF cm-2.(fig. 6).ADSORPTION AT FINITE COVERAGEA Langmuir-type adsorption isotherm, with a pre-exponential term modified onthe basis of Flory-Huggins statistics, has been proposed by Parsons.16 This maybe written in a general form,-- - x exp (- AG,,,/kT) 0r(l-Oywhere r is the ratio of the area occupied by adsorbate and solvent molecules, and 8the fractional coverage of the surface by the adsorbate. An exactly equivalentstatistical term has been given by Levine, Mingins and Bell.14 Eqn (16) reduces, atvery low coverage, to a simple linear form as given by eqn (6) and (7)H .M. RENDALL AND A. L. SMITH 109We now consider briefly the complete measured adsorption isotherms, assuminga competitive adsorption of the two species. Values of x, may be obtained for eachexperimental point using eqn (9), and the corresponding nso obtained from eqn (16),but with the total measured adsorption included in the site-blocking term. Bysubtraction, adsorption isotherms for the HPic+ ion may be inferred. isnot sufficiently well known here we are unable to make a detailed comparison withtheoretical predictions. We may, however, compare the calculated HPic+ adsorptionwith the measured MePicf adsorption.As was observed by Conway at the mercurysolution interface, the substitutionI' = 1 (the Langmuir form of the adsorption isotherm) would give a satisfactoryaccount of the experimental results only if CD,, was allowed to decrease with coverage.This could imply either that there is a lateral repulsion between the adsorbed neutralmolecules, or that I' # 1.Since the solute and solvent molecules clearly differconsiderably in size, it is reasonable to examine the latter possibility.Since5 10 15 20concentrationlmmol dm-3FIG. 7.--Observed (filled points) and calculated (open points) cation adsorption. HPici ion at 0,pH 2 ; 'I, pH 4 ; A, pH 4.7; a, pH 5.9; 0, pH 6.8; 0, pH 7.6. MePic+ ion at ($, pH 6.9.- - -, theoretical Pic adsorption isotherm, eqn (16) with AG = -4.2 kT.Taking the areas occupied per molecule of picoline and of water as 40A2 and10 A2, respectively, and assuming that the whole B.E.T.area is available for adsorp-tion, substitution of the value of ST into eqn (16) gives @+ = -3.9 kT. WithA@r = -0.3, this gives (Q, = -4.2 kT. Using these values of Qn and of r in eqn(16), as described, the HPic+ ion adsorption, obtained by subtraction of the calculatedPic adsorption, paralleled that of the MePic+ ion in its dependence on pH (fig. 4)and on concentration (fig. 7). Lower values of an gave too high HPic+ion adsorption,as judged by comparison with the MePic+ ion, whereas higher values increased thecalculated adsorption of the neutral molecule, for small a, above the experimentaladsorption level. The value of AQr required to give a reasonable description of theadsorption at finite coverage was, therefore, the same as that which fitted the extra-polated zero coverage values.A difference (AQr) of this order is predicted by thesimple " image charge " term proposed by Frisch and Stillinger l7 on the basis ofthe Onsager-Samaras model. 110 EFFECTS OF IONISATION ON ADSORPTIONCOMPARISON WITH METHYL PICOLINIUM ADSORPTIONThe measurements which we have reported of the adsorption of the MePic+ ionmay be used to give a more quantitative test of the consistency of the model, and ofthe extrapolation techniques, as follows.1. The displacement of the ip of a surface with the concentration of an ion whichis adsorbed at the interface provides a sensitive measure of the specific adsorptionp0tentia1s.l~ By eqn (3) and (4), $B = 0 at the ip, and eqn (1) and (2) then give-0s = $oKi.(17)If it is assumed that $o (fig. 6) is unchanged in the presence of adsorbed MePic+ ion,os may be calculated from the reported ip shift. Substitution into eqn (16) gives aAG,,,(= @+ since t,hB = 0) of -4.5 kT for the MePicf ion.2. The adsorption isotherm for MePic+ at pH 6.9 was extrapolated, as 1nSagainst coverage, and t,br (froni fig. 6) subtracted from the zero coverage interceptto give ST for the MePic+ ion. Substitution of gz into eqn (16) gave a+ = -4.5 kTfor the MePicf ion.3. The difference (0.6 kT) between the specific adsorption potentials of HPic+and MePic+ would require that approximately twice as much HPic+ as MePic+ wouldwould be needed in solution to achieve the same level of adsorption under identicalconditions.Within experimental error this was found for the MePic+ adsorptionand the observed or calculated HPicf adsorption where a reasonable comparison waspossible, i.e., at pH 2, 4, 4.6 and 6.9. Only in the latter case was this comparisonsignificantly dependent on the calculation of Pic adsorption.We thank Dr. P. J. Anderson, who initiated this project, and Mr. J. R. Brownfor the preparation of the materials.H. C. Li and P. L. de Bruyn, Surface Sci., 1966,5,203.'B. E. Conway, R. G. Barradas, P. G. Hamilton and J. M. Parry, J. Electroanalyt. Chem.,1965, 10, 485.M. M. Breuer, Physico-Chemical and Biophysical Facfors Afecting the Activity of Pesticides(S.C.I. Monograph No. 29, London, 1968), p. 54.G. M. Bell, R. E. Chapman and M. M. Breuer, J. Colloid Interface Sci., 1968, 27, 161,J. J. Betts and B. A. Pethica, Trans. Faraahy Sue., 1956, 52, 1581.A. Albert and E. P. Serjeant, Ionisation Constants of Acids and Bases (Methuen, London, 1962). ' J. A. G. Taylor, J. A. Hockey and B. A. Pethica, Pruc. Brit. Cerarn. Soc., 1965, 5, 133. * J. D. Wagner, Ph.D. Thesis (CNAA, 1974).D. W. Fuerstenau, J. Phys. Chem., 1956, 60,981 ; P. Somasundaran, T. W. Healy and D. W.Fuerstenau, J. Phys. Chem., 1964,68, 3562 ; S. G. Dick, D. W. Fuerstenau and T. W. Healy,J. Colloid Interface Sci., 1971, 31, 595.lo D. C. Grahame, Chem. Rev., 1947, 41,441.l1 A. L. Smith in Dispersions of Powder in Liquids, ed. G. D. Parfitt (Applied Science Publishers,'' B. Lynskey, Ph.D Thesis (Liverpool Polytechnic, 1973).l3 G. H. Bolt, J. Phys. Chem., 1957, 61, 1166.l4 S. Levine, J. Mingins and G. M. Bell, J. Electroanalyt. Chem., 1967, 13, 280.l5 E. Blomgren and J. O'M. Bockris, J. Phys. Chem., 1959, 63,1475.l6 R. Parsons, J. Electroanalyt. Chem., 1964, 8, 93.l7 H. L. Frisch and F. H. Stillinger, J. Phys. Chem., 1962, 66, 823.l8 L. Onsager and N. N. T. Samaras, J. Chem. Phys., 1934,2,528.l9 H. M. Rendall, A. L. Smith and L. A. Williams, to be published.2nd edn., 1973), p. 93 ; S. Levine and A. L. Smith, Disc. Farczday SOC., 1971, 52, 290.(PAPER 4/297

ISSN:0300-9599    

DOI:10.1039/F19777300101

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Heterogeneous Recombination of AtomsTheory of the Smith-Linnett MethodBY ALEKSANDER JABLO~SKIDepartment of Catalysis on Metals, Institute of Physical Chemistry,Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224 Warszawa, PolandReceived 2 1 st November, 1975A general differential equation has been derived which describes the concentration of atomsdiffusing and recombining in a cylindrical tube. It is shown that the previously published equationsare particular cases of that equation. The boundary conditions have also been generalized. In thecase of the Smith-Linnett method the simplifications of the general equation, leading to the one-dimensional linear equation, are the cause of a systematic error in calculation of the recombinationcoefficient. This error is considerable for very active and slightly active surfaces.In the case ofrecombination of atomic hydrogen, the error due to omission of the homogeneous reaction in theanalysis of experimental data is negligibly small when the pressure is lower than 0.1 Torr and theconcentration of atoms is lower than 10 %.The atomic hydrogen recombination coefficient y has been calculated for nickel films and forPyrex on the basis of the one-dimensional linear equation and on the basis of the model proposed inthe present work. It was found that the two methods of calculation differ by 3-6 % in the case ofsurfaces having the high activity (7 over and by 30-40 % in the case of surfaces having lowactivity (y below lo-"). Both methods give approximately the same fit to the experimental data.Heterogeneous recombination of atoms, one of the simplest catalytic reactions,has been reviewed in several pub1ications.l. Kinetic studies have shown that thisreaction is usually of the first order and that it takes place mainly according to theRideal me~hanism.~ A convenient measure of the rate of this reaction and of theactivity of the surface is the recombination coefficient, y, which is the ratio of thenumber of atoms reacting on the surface to the total number of collisions of atomswith the same surface.The kinetics of heterogeneous recombination is usuallyinvestigated by diffusion methods, an example of which is the Smith-Linnettmethod.4* This method has been used in studies on recombination of atomichydr~gen,~~ ' 9 9* 12* l 5 oxygen 5 * 6 * '* lo* 11* l4 and nitrogen.13 It consists ofmeasuring the decrease of concentration of atoms along the axis of a cylindricaItube (side arm) the wall of which is covered with the material to be examined. Theknowledge of this concentration profile makes possible the computation of therecombination coefficient for the material under examination.DISTRIBUTION OF ATOMS IN THE CYLINDRICAL TUBEIn this section we derive the differential equation describing the concentration ofatoms inside the cylindrical tube, and show that the previously published equationsare particular cases of this more general equation.The starting point is the equationof mass conservation in a multicomponent system :16h i p t = - div (nivi) +C VikUk,k11112 HETEROGENEOUS RECOMBINATION OF ATOMSwhere n, is the molar concentration of the ith component ; ol is the resultant velocityof the ith component ; V i k is the stoichiometric coefficient of the ith component in thekth reaction, and 24, is the rate of the kth reaction.Let the recombination reactionproceed in the stationary state and have the form : mA -+ A,,,. During this reactionthe number of particles decreases. The flow of atoms nu is accompanied by thedecrease of the number of moles of the atomic gas equal to no(m-- l)/m. 111 orderto maintain the constant pressure this decrease must be compensated for by con-vection of the gas filling the tube, i.e.,nu(nz- l)/in = N w, (2)where N is the total concentration of atoms and molecules, and w is the velocity ofconvection.Since the total flow of atoms, no, is the sum of convection flow. kiw,and diffusion flow, J, the following relationship results from eqn (2) :NmNm - n(nz - 1)Taking into account the first Fick law, J = -Dgrad?z, and assuming the inde-pendence of concentration of the diffusion coefficient D, eqn (l), considering atomsas the component “ i ”, is transformed into :lltr = J .r 1grad n = mu, J 1 NmD div 1 Nm - n(nz - 1)where u is the homogeneous recombination rate. Introducing cylindrical coordinatesx, r, we obtain finally the equation :U. (3)a2n 1 an a2n tn-1 -+--++,+ ax2 r ar 8r Nm-n(m-I)Let index “ s ” denote the component of a vector, perpendicular to the wall ofthe tube. For the stationary state at the wall the following equation must be obeyed :The number of collisions 2 of the flux of atoms with the unit surface area of the wallis equal to :yz = nu,.(4)I1 E4Z = - exp (- t2/2) + nv,Q(t),where t = ( v , , / G ) / C ; C is the mean velocity of atoms, and @(t) is the normaldistribution function. As a result eqn (4) becomes :Let t = t ( y ) be the root of eqn (5). Then on the boundary between the wall and thegas the following condition must be fulfilled :- -Usually it is assumed that the atomic gas is stationary with respect to the wall of thetube. Then 2 = nS;/4? and eqn (4) can be simplified to: t = y/J2n 2: g. As thesecond approximation l 7 only the first term in the series on the right side of eqn (5)A. J A B L O ~ S K I 113t.Hence the condition (6) is considered.can be rewritten a s :We obtain then : t = y[(l -y/2) Jz.)grad, n = - n[m - (m - l)n/N]/(SmR), (7)where 6 = 4D/(yFR) or 6 = 40(1 -y/2)/(yER) for the first or second approximationrespectively; R is the tube radius. Thus, the boundary conditions of eqn (3) forthe tube having the finite length, L, are as follows :an/& = 0 for r = 0 ;n = no = const. for x = 0 ;a??/ar = -n[m-(m- l)n/N]/(GmR) for Y = R ;[condition (7) for the wall of the tube]dn/dx = -n[m- (m- l)n/N]/(G’mR) for x = L.[condition (7) for the plate closing the tube]In the case of an infinitely long tube the first three conditions remain unchanged,whereas the fourth one becomes : n = 0 for x = co.The solution of eqn (3) is a very complex problem and, for this reason, in practicecertain simplifications are introduced.One of them is the assumption that an/dr = 0,which leads to a one-dimensional differential equation, has shown that insuch a case the catalytic activity of the wall of the tube must not be very high. Thesecond simplification consists in assuming that convection is absent. It follows fromeqn (2) that this is equivalent to the assumption that m = 1 . This simplification canbe inade when the concentration of atoms is low. The homogeneous recombinationis usually also omitted, i.e., it is accepted that u = 0 for a two-dimensional equation.In the case of a onedimensional equation it can be shown that u = yZn/2Rm+kn2(N-n), where k is the rate constant.Neglecting the homogeneous recombinationin this case leads to the relation : u = yEn/2Rrn.Table 1 shows the simplifications which should be made in eqn (3) in order toobtain the equations previously derived and solved. The most convenient methodSmithTABLE 1 .-LIST OF SIMPLIFICATIONS OF DIFFERENTIAL EQN (3) LEADINGTO THE PUBLISHED EQUATIONSlength ofauthor cylinder I?l 14 remarksSmith4Shuler, LaidlerTsu, BoudartMelin, Madix 2oGreaves, Linnett 21Wise, Ablow 22Dickens, Schofield,Walsh 23one-dimensional equationsinfinite 1 yFn/2Rfinite 1 yFn/2Rinfinite 2 yCn/4Rfinite 1 0 nonactive wall offinite 2 0 nonactive wall ofcylindercylindertwo-dimensional equationsWise, Ablow 2 2 finite 1 0Wise, Ablow 22 infinite 1 0Dickens, Schofield, finite 2 0Walsh 23Dickens, Schofield, infinite 2 0Walsh 2 114 HETEROGENEOUS RECOMBINATION OF ATOMSof analysis of experimental data is based on the linear one-dimensional equation foran infinitely long tube (first item in table 1).The solution of this equation can bepresented in the form :where b = yE/2RD. From the slope of the straight line obtained in the system ofcoordinates (In n, x> the value of y can be determined. This procedure is associatedwith the Smith-Linnett method.n/n0 = exp(- Jbx), (8)ANALYSIS OF APPLICABILITY OF THE ONE-DIMENSIONAL LINEAR EQUATIONThe published values of the recombination coefficient, determined by the Smith-Linnett method, range from to 10-l. This method cannot give correct resultsin the whole range of values of y since all the simplifying assumptions leading to theone-dimensional linear equation are not always valid. In order to evaluate quanti-tatively the systematic errors connected with the recombination coefficient determinedon the basis of eqn (8) we will use a model which is more similar to the actual structureof the side arm (fig.1). It is a cylinder consisting of two sections. The catalyticactivity of the first section is given by parameters y1 or 61 and its dimensions are :R,-radius and y-length. The second section corresponds to the examined surface.It is characterized by a similar set of parameters-?, 6, R and L respectively. Thecylinder is closed with the guide piston of the movable probe; the activity of thissurface is given by y' or 6'.The disturbing effect of the junction of the thermocoupleprobe is neglected, because in the case of the Smith-Linnett method the area of thisjunction is made as small as possible (-1 mm2). The analysis given below isaccomplished in the range of values of y between loA5 and 1, where the losses of atomson the wall are supposed to predominate over losses of atoms on the j ~ n c t i o n . ~ - ~This analysis is limited to recombination of atomic hydrogen only.s e c t i o n 2 s e c t i o n 1FIG. 1.-Model of the side arm.28Let us assume that the concentration of atoms is so low that the homogeneousreaction and the convection can be neglected. Then it is described by the equation[m = l , u = 01d2n 1 dn a2n -+--+- = o .dz2 r dr dr2 (9)This equation is subject to boundary conditions determined by the geometry of theintroduced model.n = no for z = 0,avt/dr = 0 for I' = 0,dn/dr = -n/R16,anfar = -n/R6dnpz = -n/R6' for z = L+y.for r = R1,O < z < y ,for r = R , y < z < L+yA.JABLONSKI 115It is also assumed that the function n and the derivatives an/ar and an/dz are con-tinuous. Let n(r, z, L) be the solution of the above boundary problem. Then thefunction n'(x) = n(0, y + x, d+ x ) describes the concentration of atoms at the thermo-couple junction as a function of its position, x. The function In [n'(x)/n'(O)] turnedout to be nearly linear,24 although having a different slope from the linear function (8),In [n(x)/n,] = - Jz x. This enabled the comparison of two methods of computationof recombination coefficient, i.e., on the basis of function (8), (ysL), and on the basisof the presented model (y).Fig. 2 shows the dependence of quantity (y-ySL)/y ontemperature and activity of the examined surface. It can be seen that in the case of f 0 --101 I ! 1 I I10-5 I 0-4 10-3 10-2 10-1 IYFIG. 2.-Relative difference between the atomic hydrogen recombination coefficient calculated on thebasis of proposed model and that resulting from eqn (8), (y-ySL)/y, as a function of surface activity.28It was assumed that y = d = 30 cm, R = 1.6 cm, R1 = 1.75 cm. The diffusion coefficient wascalculated from the Chapman-Enskog formula ;25 the H-H2 interaction was described by theLennard-Jones (6-12) potential with the parameters given by Khouw et ~ 1 .~ ~ Pressurep = 0.08 Torr.0 80 60 3 ns90 40 2010-5 10-4 10-3 10-2 10-1 0.5YFIG. 3.-Dependence of the relative concentration of atomic hydrogen, n'(0)/no, on the activity ofthe examined surface. The concentrations of hydrogen atoms measured at x = 0 in the case ofnickel film are fitted to the theoretical curves : (0) T = 298 K, (0) T = 245 K, (A) T = 215 K116 HETEROGENEOUS RECOMBINATION OF ATOMSvery active surfaces and in the case of surfaces having low activity the deviations areconsiderable. For very active surfaces the cause of deviation is the radial distributionof atomic hydrogen concentration, i.e., an/ar # 0. On the other hand, the assump-tion that the tube is infinitely long is valid since atoms quickly disappear along theactive surface.In the case of surfaces having low activity the value of derivativedn/ar is close to zero, but the assumption that the tube is infinitely long is no longervalid. This is the cause of deviation in the low activity region. It follows fromfig. 2 that the two methods of analysis of experimental data become equivalent whenthe activity of the examined surface is in the region 5 x(213 K < T < 453 K).Fig. 3 shows the dependence of the relative concentration n’(0)/no on the catalyticactivity of the examined surface. A decrease of activity at a constant temperatureshould be accompanied by an increase of the response of the probe in the positionx = 0, recording the concentration of atoms between sections of the cylinder.< y < 5 xTHE EFFECT OF HOMOGENEOUS RECOMBINATIONWe now evaluate the error arising from neglect of the homogeneous recombination.We assume that the relative concentration of atomic gas, a = n/N, does not exceed10 %.Let us introduce into eqn (3) the same simplifications as in the case of the one-dimensional linear equation (&/& = 0, zn = l), but let us also take into account thehomogeneous reaction, i.e., let u = ycn/2R+ kn2(N-n). The solution of theresulting equation for an infinitely long tube is given by the formula :1x = ---=In[; J b1 2 b + a y + 2[ b( b + a y - dy2)]*2b + a + 2[b(b + a - CI)]~]’where y = n/no, a = 2Nkno/3D, b = yZ/2RD, d = kn$/2D. As in the previoussection the calculations consist of the determination of the recombination coefficienton the basis of eqn (8), (ysL), and the comparison with the recombination coefficientdetermined on the basis of eqn (lo), (y).The rate constant of homogeneous recom-bination equal to 1.2 x 1OI6 cm6 mo1-2 s - ~ was used in these calculations. This valuehas been obtained by Larkin 27 for moist hydrogen which is usually used in theSmith-Linnett method. Fig. 4 shows plots of the dependence of deviation (ysL - y)/yon the total pressure of the gas in the side arm and the concentration of atomichydrogen at the inlet to the tube, ao. These plots make it possible to choose such apressure that this deviation becomes negligibly small. It can be seen that homo-geneous recombination may be neglected when the pressure is lower than 0.1 Torr,the recombination coefficient of the examined surface is greater than lo-’, and theconcentration of atomic hydrogen does not exceed 10%.Similar results could beexpected for other temperatures since the rate constant of homogeneous recombi-nation depends only slightly on temperature. According to Larkin 27 the activationenergy of this reaction in the temperature range 190-350 K is 1.1 3- 0.3 kcalfmol-l.The above calculations were carried out for 273 K.APPLICATION OF THE THEORY TO EXPERIMENTAL DATAA typical experimental apparatus was used for determining the activity of thinmetal films.24* 28 Hydrogen was prepared electrolytically, and was freed fromoxygen by passing the gas over heated palladinized asbestos.It was then saturatedwith water vapour up to -2%, to facilitate the dissociation of inolecules. Atomswere produced by pumping a steady stream of hydrogen at the pressure 0.08-0.09 Torrthrough an electrodeless radio-frequency discharge, 13.5 MHz. Surfaces having verA. JABLONSKI 117! I I :01 0 2 0 5 I 2 5 10p/Torrlo--\ cplTorr100x 10 ---.3a,=OI01 a, = 005a,=oo15(4-a0 2 0 5 I 2 5 10 O.O!o'Ip/TorrFIG. 4.-Relative difference between the atomic hydrogen recombination coefficient resulting fromeqn (8) and that resulting from eqn (lo), (~sL--"/)/Y, as a function of the pressure of the mixture ofatomic and molecular hydrogen. a. = tzo/N, R = 1.6 cm. (a)-"/ = ( b ) y = (c)y = lod33 4lo3 KITFIG.5.-Comparison of the temperature dependence of atomic hydrogen recombination coefficientfor nickel film on Pyrex, (0) ,with that for Pyrex, (A).*118 HETEROGENEOUS RECOMBINATION OF ATOMShigh and very low activity were chosen as examples of the application of the theorypresented above. It has been found that thin nickel films (thinner than loo&, attemperatures above room temperature, have a very high activity for the recombinationof atomic hydrogen.24* 28 Their activity is higher than that of thick films and foils.It has been also found that thin nickel films are poisoned at low temperatures (245 and215 K) as a result of the formation of the nickel hydride P - p h a ~ e . ~ ~ . 28 The recom-bination coefficient decreases then to the order ofA program was developed for calculating the recombination coefficient on thebasis of eqn (8) and on the basis of the proposed model.In this program the sumsof squares of deviations(fig. 5).S&) = [ln(n,/n*) + &I2 and S2(y) = (ln(ni/izO) - ln[n’(~,>/n’(O)]>~were minimized. Here the nf are the experimentally measured concentrations ofatoms, xi are the corresponding positions of the thermocouple probe, and no is theconcentration recorded for x = 0. The results of the calculations for nickel filmand for Pyrex are presented in tables 2 and 3. Those results, obtained on the basisof eqn (9), are also plotted in fig. 5 as a function of temperature. Fig. 6 shows some ofthe experimentally determined concentration profiles of atomic hydrogen covering thewhole range of observed values of y.This figure also indicates the correspondingdeviations between both methods of computation of the recombination coefficient.1 iTABLE COR VALUES OF ATOMIC HYDROGEN RECOMBINATION COEFFICIENT FOR NICKEL FILM. THESURFACE CONCENTRATION OF NICKEL = 2.6 pug cm-’no.1234567891011124534533 633 6329829824524521521 54534530.0900.0900.0900.0900.0900.0900.0900.8900.0900.0900.0900.090coefficient of 1calc. on the basis>f presented model3.68 x lo-‘3.01 x lo-’2 . 4 2 ~ lo-’2.02x lo-’1.26 x lo-’9.47 x 10-31.46 x 10-41 . 5 0 ~ 10-41.06 x 10-41.27 x 10-42.17 x2.09 x lo-’:econibination, ycalc. on the basisof eqn (8)3.46 x lo-’2.85 x lo-’2.28 x lo-’1.93 x1.21 x lo-’9 .1 4 ~ 10-31.07 x 10-41 . 1 0 ~ 10-47 . 5 5 ~ 10-59.36 x 10-52.08 x2.00x lo-’TABLE 3 .-VALUES OF ATOMIC HYDROGEN RECOMBINATION COEFFICIENT FOR PYREXp/Torr coefficient of recombination, ycalc. on the basisof presented modelcalc. on the basisof eqn (8)no. T / K12345678910111245345345336336329829829824524521521 50.0890.0910.0910.0910.0910.0920.0920.0920.0920.0920.0920.0929.46 x 10-51 . 1 4 ~ 10-41 . 0 6 ~ 10-41.62 x 10-41 . 1 9 ~ 10-49 . 4 9 ~ 10-51.11 x 10-41 . 1 2 ~ 10-48.88 x 10-59.11 x 10-59.18 x 10-58.88 x5 . 4 6 ~ 10-57.01 x 10-56 . 3 7 ~ 10-56.27 x 10-57.66 x 10-56.05 x 10-56 .2 4 ~ 10-56.46 x 10-56 . 2 2 ~ 10-51.13 x7.85 X lO-’7 . 5 8 A. JABLONS KI 119Those values are in good agreement with fig. 2. In the case of a surface having theactivity 1-4 x deviations within the range 3-6 % are observed. Larger deviationscan be seen in the case of surfaces having a low activity : about 30 % in the case ofpoisoned nickel film, and 30-40% with Pyrex. The poisoning of the nickel film at245 K resulted in an almost four-fold increase in the response of the movable probe,placed in the position x = 0. Such an increase in the concentration of atoms waspredicted earlier (fig. 3). This phenomenon also proves that the losses of atomson the probe are insignificant, because the nickel film was entirely behind the junctionof the thermocouple probe at the moment of poisoning.The validity of the theorydeveloped previously is confirmed more quantitatively by fitting the experimentallydetermined concentrations of hydrogen atoms at x = 0 and corresponding values ofy for nickel film to calculated curves on fig. 3. An excellent agreement can beobserved.Ni/Pyrex1460 2 4 6 8x/cmFIG. 6.-Concentration profiles of atomic hydrogen for nickel film.deviation = 6 % ; curve 4, y = 2.02 x lo-', deviation = 4.5 % ; curve 6, y = 9.47 x= 3.5 % ; curve 8, y = 1.50 xCurve 1, y = 3.68 xdeviationdeviation =28.8 %. The numbers of the curves are the same as in the fist columns of table 2 and 3.In order to determine which method gives a better fit to the experimental data theminimum sums of squares, S1(ysL) and S&), were computed and compared.Theywere nearly equal for most of the measurements. This stems from the fact that theshapes of the functions n(x)/n, = exp( -,/% x ) and n'(x)/n'(O) are almost identical ;as was stated earlier, in semilogarithmic coordinates the first function is linear, thesecond one is nearly linear. For this reason it cannot be decided experimentallywhich method of computation of y is more accurate. However, one can expect thatthe recombination coefficient calculated on the basis of the model presented in fig. 1is closer to its true value than that resulting from eqn (8), because this model is moresimilar to the real structure of the side arm than is the model of a catalytically uniformcylinder of infinite length.deviation = 26.7 % ; curve 9, y = 1.06 120 HETEROGENEOUS RECOMBINATION OF ATOMSCONCLUSIONSThe previously published differential equations describing the stationary stateconcentration of atoms diffusing and recombining inside a cylindrical tube areparticular cases of the more general equation which was derived in this work.Calculation of the recombination coefficient on the basis of the one-dimensionallinear equation gives correct results in the case of surfaces having moderate activity.In the case considered here, of heterogeneous recombination of atomic hydrogen, therecombination coefficient should be in the range 5 x When theactivity of the surface is outside this range a systematic error results from simplifica-tions made in the general equation.In the case of high activities this error is due tothe radial distribution of the atom concentration YE/& # 0) ; with low activities theerror is due to the fact that the length of the cylinder is finite.At pressures lower than 0.1 Ton and concentrations of atomic hydrogen lowerthan lo%, the error in the calculation of the recombination coefficient due to theneglected homogeneous recombination is negligibly small.< y < 5 xH. Wise and B. J. Wood, Adv. Atom. Mol. Phys., 1967, 3, 291. ’ V. A. Lavrenko, Recombination of Hydrogen Atoms on the Surfaces of Solids (Russ.) (Nauk.Dumka, Kiev, 1973).W. A. Hardy and J. W. Linnett, 11th Symp. Combust., Berkeley, 1966 (The CombustionInstitute, Pittsburgh, Pensylvania, 1967), p. 167.W.V. Smith, J. Chetn. Phps., 1943, 11, 110.J. W. Linnett and D. G. H. Marsden, Proc. Roy. SOC. A, 1956,254,489, 504.J. C. Greaves and J. W. Linnett, Trans. Faraday Soc., 1958, 54, 1323 ; 1959, 55, 1346, 1355.M. Green, K. R. Jennings, J. W. Linnett and D. Schofield, Trans. Faraday SOC., 1959,55,2152.P. G. Dickens and M. B. Sutcliffe, Trans. Faraday SOC., 1964, 60, 1272.P. G. Dickens, J. W. Linnett and W. Palczewska, J . Catalysis, 1965, 4, 140.lo P. G. Dickens and M. S. Whittingham, Trans. Faraday SOC., 1965, 61, 1226.l1 P. J. Crane, P. G. Dickens and R. E. Thomas, Trans. Faraday Soc., 1967, 63,693.l2 W. A. Hardy and J. W. Linnett, Trans. Faraday SOC., 1970,66,447.l3 M. L. Rahman and J. W. Linnett, Trans. Faraday Soc., 1971, 67, 170, 179, 183.l4 J. W. Linnett and M. M. Rahman, Trans. Furahy SOC., 1971, 67,191.l 5 W. Palczewska, Adu. Catalysis, 1975, 24, 245, and references contained therein.R. Haase, Thermodynamik der irreuersiblen Prozesse (Dietrich Steinkopf Verlag, Darinstadt,1963), p. 249; S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, London, 1969), p. 12.l7 H. Motz and H. Wise, J. Chem. Phys., 1960, 32, 1893.K. E. Shuler and K. J. Laidler, J. Chem. Phys., 1949, 17, 1212.l 9 K. Tsu and M. Boudart, Canad. J. Chem., 1961,39, 1239.2o G. A. Melin and R. J. Madix, Trans. Faraday SOC., 1971, 67, 198.21 J. C. Greaves and J. W. Linnett, Tram. Faraday SOC., 1959, 55, 1338.22 H. Wise and C. M. Ablow, J. Chem. Phys., 1958,29, 634.23 P. G. Dickens, D. Schofield and J. Walsh, Trans. Faraday Soc., 1960,56,225.24 A. JaModski, Thesis (Institute of Physical Chemistry, Polish Academy of Sciences, 1975).2 5 J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases andLiquids (J. Wiley,26 B. Khouw, J. E. Morgan and H. 1. Schiff, J. Chem. Phys., 1969,50, 66.27 F. S. Larkin, Canad. J. Chem., 1968,46, 1005.28 A, Jablodski and W. Palczewska, Bid. Acad. Polon. Sci., Ser. Sci. ?him., 1976, 24, 239.New York, 1954), p. 527.(PAPER 5/2277

ISSN:0300-9599    

DOI:10.1039/F19777300111

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Thermodynamic Study of the Vaporization ofCerium OrthophosphateBY M. GUIDO, G. BALDUCCI,* G. DE MARIA AND G. GIGLIIstituto di Chimica Fisica, Universith di Roma,CittA Universitaria-00185 Rome, ItalyReceived 27th November, 1975The high temperature Knudsen cell mass spectrometric technique has been used to study theFrom the second- and third-law analyses of the equilibrium reaction : CeP04(s) = CeOz(g) + vaporization behaviour of solid cerium orthophosphate over the temperature range 1700-1 850 K.PO,(g), the following standard heat of formation of &PO&) has been derived :AHZg8,f [CeP04(s)] = - 1898.5k31.5 kJ mol-l.These results are discussed and compared with those obtained by other authors for other LnP04compounds.Rare earth orthophosphates form an interesting class of compounds for whichevaluations of thermodynamic data of value, e.g., in determining the best conditionsin chemical transport processes,'.have been very limited ; few such data areavailable in standard compilations. Rat'kovskii et aZ.3-5 carried out mass spectro-metric studies of the thermal dissociation of LaPO, and other orthophosphates ofthe yttrium group adopting the same decomposition scheme as that for AlP04,5 forall the compounds studied. Other thermodynamic data available refer to themeasurements of the enthalpies and heat capacities of solid lanthanum, neodymiumand yttrium orthophosphates, as reported by Tsagareishvili et aL6 However, nosuch data are available for CePO, ; vaporization behaviour under equilibriumconditions is reported in this paper.EXPERIMENTALThe vaporization mode of cerium orthophosphate was investigated by the Knudseneffusion mass-spectrometric technique.A Nuclyde Analysis Associated magnetic massspectrometer coupled with a conventional Knudsen cell source was used. Details of theexperimental apparatus and procedure are as described previ~usly.~ *Preliminary vaporization experiments carried out using different Knudsen cells to selectthe crucible material showed that noticeable interaction of the sample with the containeroccurred when using tantalum, tungsten and molybdenum metal crucibles, while reproducibleevaporation conditions were achieved when using an alumina-lined tungsten crucible whichwas subsequently used throughout this work.The Knudsen effusion orifice was 1 mm indiameter and 1.2 mm in length.A sample of powdered anhydrous CeP04 (99.9 % pure from Schilling BHS), checked byX-ray analysis was loaded into the cell together with 2mg of high purity silver metal ascalibrating substance. The cell was heated by radiation and electron bombardment froma tungsten strip. The electron bombardment power regulating system limited temperaturefluctuations to < & 5°C at 1700°C. Temperatures were measured w i t h a k d s andNorthrupoptical pyrometer, periodically checked against a tungsten ribbon standard lamp calibratedby N.B.S. by sighting into a blackbody hole drilled in the bottom of the cell. Temperature12122 VAPORIZATION OFreadings were corrected for window and prism transmission. At an average temperatureof 1300 K, where no detectable vaporization of the sample occurred, the silver was quanti-tatively vaporized in order to obtain the instrument calibration constant.The temperaturewas then raised gradually and the vaporization of the sample was followed for a period ofabout 15 h over the temperature range 1700-1 850 K. The vaporization was then interruptedby rapidly lowering the cell temperature and a portion of the residue sample was checkedby X-ray analysis. Subsequently, the remaining sample was submitted to a second seriesof vaporization measurements for an overall period of about 50 h using the same crucible,and with the same procedure. The residue was again examined by X-ray diffraction (seethe following section).RESULTSIDENTIFICATION OF IONSIn the course of the vaporization experiments, ions at mfq corresponding to P408+,P40T, P406+, P 3 0 t , P30:, P:, PO,’, P;, PO+, P+, O,*, as well as the cerium con-taining species CeO,’, CeOf, and Ce+ were observed in the mass spectra.Of these ions, only CeO;, CeO+, Ce+, PO,’ and PO+, with a shutter profilesimilar to that of Ag+, and also 0,’ with a shutter profile less than 100 %, but narrowand symmetrical, were considered as originating from species effusing from theKnudsen cell.In any case, the intensity of the discarded ions was low enough notto affect the results. The appearance potentials (A.P.) for CeO:, PO:, PO+ and0; were measured to be 9.8 _+ 0.5, 11.7 _+ 0.5, 9.1 _+ 0.5 and 12.1 0.5 eV, respectively,in accord with published values ;9-11 these ions were identified as parent ions.Onlywith PO+ ion did the ionization efficiency curve exhibit a break which indicated thatthe primary ionization was not the only process responsible for the formation ofthis ion. The energy of the observed secondary onset (13.920.5 eV) is consistentwith the dissociative ionization of PO2. Given that &PO;) is the portion of the ionintensity measured at mass 47 due to the fragmentation of PO2, the ratio I(PO&)/I(P0;) in the actual experimental conditions was evaluated to be 0.625 at 98 eV,and the ion intensities measured for PO+ and PO: ions were corrected accordingly.The ions CeO+ and Ce+, [with A.P. of about 13 eV and 20 eV respectively, and forwhich the intensity ratios Z(CeO+)/I(CeO,’) and I(Ce+)/Z(CeO,’) were temperatureindependent and equal to 0.25 and 0.131 were identified as fragment ions from CeO,.The measured CeO; ion intensity was corrected accordingly.X-RAY RESULTSDebye-Scherrer X-ray diffraction patterns of the initial samples and the residuestaken at different stages of the vaporization were made by two different laboratories.In all cases the patterns presented no lines other than those corresponding to themonoclinic structure of the monazite type CeP04.12 The only detectable differencebetween the patterns taken on the initial samples and on the thermally treated residueswas an increased crystallinity shown by sharper diffraction lines.THERMODYNAMICSThe ion intensities of the parent species measured at 98 eV and corrected, whennecessary, for the fragmentation contributions, were converted into the correspondingpartial pressures by use of the well-known relation :8 Pi = Ii+T/Scya,.The instru-mental sensitivity constant, S, was determined, as previously mentioned, through asilver calibration experiment and subsequently through an internal calibrationprocedure * based on the study of the equilibrium reaction (1) as described later inthe text. The electron multiplier efficiency, 7, was assumed for each ion to bM. GUIDO, G . BALDUCCI, G. DE MARIA AND G. GIGLI 123proportional to the inverse of the square root of its mass. The ionizing electronenergies used corresponded in all cases to the maximum of the ionization efficiencycurves of the relative ions; thus the molecular ionization cross sections, cr, werederived from the maximum values of the atomic cross sections given by Mann l3according to a procedure outlined e1~ewhere.l~ The resulting values are : 15.26,7.09, 6.74 and 3.13 for CeO,, PO2, PO and 02, respectively.Values of the partialpressures calculated at various temperatures over the range 1600-1 850 K indicatedfair reproducibility in the case of POz and CeOz as well as for the equilibrium constantof the dissociation reactionbut the partial pressures of PO(g) and 02(g) varied somewhat erratically, dependingon the vaporization conditions.To ascertain that satisfactory equilibrium conditions were attained at least in thegaseous phase, reaction (1) has been studied, especially in the initial part of theexperiment.No direct heat of reaction (1) has been reported previously. However,a value of = 254f 12 k J mol-1 for this reaction is derived by combiningliterature data for AH;,at[PO,(g)] l5 and for D;98(02) l6 and D;98(PO).16 Ourdata have been evaluated by two independent procedures, the so called ‘‘ second-law ”method based on the well known equationand the so called “ third-law ” method, or absolute entropy method, based on theequation :The necessary heat-content functions, (H; - Hig8), and free energy functions,(G$-H,”g8)/T, for PO(g) and O,(g) were taken as reported JANAF Tables,16 andfor PO,(g) the values reported by JANAF Tables l6 were corrected for the vibrationalcontribution as proposed by Drowart et aZ.15The least-square equation representing the temperature dependence of Kp forreaction (1) is :PO,(g) = PO(g) + +02(g) (1)AH298 = -R d In Kp/d(l/n+x(H;- H2098)reactants-~(H~-H2098)~roductsAH2098 = -RT Kp f Tx(Gg -.Hi9 S)/Treactants - Tx(G$ - &9 8)/Tproduets*log Kp(l), atm = (4.165&0.66)-(1.275&0.115) 104/T (2)TABLE 1 ,-THIRD-LAW CALCULATIONS FOR EQUILIBRIUM REACTION (I) :POz(g) = PO(g)++Oz(g)T/K -logm(Kp/atm*) AHi9,/kJ mol-11767 3.01 233.51850 2.76 235.61805 2.87 233.71715 3.205 233.11770 3.06 235.61817 2.895 236.11802 2.815 23 1.41752 3.155 236.41715 3.33 237.21757 3.045 233.41787 3 .OO 235.81757 3.075 234.41730 3.24 236.3average 234.8+ 1.7Note : The quantity A(G~!-HJ,,)/T for reaction (1) is practically constant over the temperaturerange and equal to -74.538 (J K-l mol-I)124 VAPORIZATION OF &Po4where the quoted errors are the standard deviations on the slope and intercept.Thesecond-law heat of reaction (1) is derived to be = 243.1 k22.2 k J mol-f.The individual third-law AHZ98 values corresponding to the experimental points arereported in table 1. These values do not exhibit any temperature trend and theaverage value, AH& = 234.8 & 1.7 k J mol-l, agrees with the second-law resultwithin the reported uncertainties. This was taken as an indication of the internalconsistency of our data. Moreover, the average value between our second- andthird-law results compares well with the aforementioned heat of reaction (1) derivedfrom literature data, so indicating that equilibrium conditions were actually establishedin the vapour phase.Therefore, the value AH2098 = 244f 10 kJ mol-', the averagebetween our value and the literature value, has been selected as the heat of reaction(1) and then used to establish an internal calibration of the instrument. Also, itenabled us to derive the standard heat of formation of PO,(g): AH&8[Po2(g)] =-253.1 & 12.1 kJ mol-l.The temperature dependences of PO,(g) and CeOz(g) partial pressures arerepresented by the least-squares equations :(3)(4)log P(P02), atm = (8.855 k0.25) - (2.6985 0.0435) 104/Tlog P(CeO,), atm = (8.865 kO.47) - (2.841 k0.084) 104/Twhere the associated errors are standard deviations.As long as solid CeP0, at unit activity is present in the Knudsen cell, the reaction(5) CeP04(s) = Ce02(g) + P02(g)can be utilized to derive the standard heat of formatioil of cerium orthophosphate.It is known that natural monazite (orthophosphate of cerium with other lanthaniderare earth elements as constituents) has a stable monoclinic structure.SyntheticCePO, has been found to be dimorphic, with an hexagonal form which transformsat about 500°C into the monazite monoclinic form stable at high temperature.17The transformation is reported to be monotropic and sluggish. As in our experi-ments we found that the initial CePO, samples and the vaporization residues werein the monoclinic form, we assumed that the gas phase we studied was the decom-position product of the monazite type CeP04.With this in mind we derived theheat of reaction (5) by both the aforementioned second-law and third-law procedures.The necessary thermodynamic functions for CePO,(s) were calculated by estimatingthe heat capacity between 298 K and the temperatures of interest through an inter-polation of the experimental C, values reported for LaPO,(s) and NdPO,(s)according to the relation :[C,(Ce) - C,(La)l/l_C,(Nd) - C,Wl =[C,(CePO,) - C,(LaPO,)l/EC,(NdPo,) - Cp(LaP04)I,where the necessary heat capacities for the rare earth elements were taken fromHultgren.18 The standard entropy of CePO,(s) was evaluated to be S;98 =131.25 J K-1 mol-l following the procedure proposed by Tananaev et al. by assumingthat Sg98[CeP04(s)] = *Sg98[Ce,O3(s)] + +S&[P401O(s)].The entropies forCe,O,(s) and P~O~O(S) were taken from the literature.". * l *For CeO,(g), the thermodynamic functions were calculated using the recentresults of Gabelnick et aL2' for the apex angle (146") and for the symmetric andasymmetric frequencies o1 = 75.7 mm-1 and o3 = 73.7 mni-l, while an estimatedbending frequency o2 = 12.0mm-l was assumed, the same value as that used forTh02(g).23 The internuclear distance r(Ce-0) was estimated as 187 prn by com-parison with the ThO(g) and Tho&) molecules.23 By analogy with Tho&), thM. GUIDO, G. BALDUCCI, G . DE MARIA A N D G . GIGLI 125electronic contribution was assumed to be zero. The thermodynamic functions forCe02(g) and CePO,(s) calculated with the above assumptions, are reported in table 3.TABLE 2.-THIRD-LAW CALCULATIONS FOR REACTION (5) :CeP04(s) = CeOz(g)+ PO&)- T/K17171767185017701792181718021752(logio(Kp/atmz)14.5513.62512.18513.5613.1713.0614.0012.805-NGT - Hj: 9 ,)IT) AH;,,371.35 1115.93 70.345 1115.3368.65 1113.63 70.28 5 11 14.9369.845 11 14.8369.32 1116.5369.63 5 1116.6370.64 1118.91.6/J K-1 mol-1 jk J mol-1average 1 1 1 5.8298.15 00,OOO 278.140 000.000 131.2521600 75.228 324.155 1 92.1 71 244.1361700 77.990 326.917 209.849 251.5211800 83.759 329.557 227.8 82 258.6551900 89.533 332.088 246.291 265.5792000 95.3 12 334.5 19 265.056 272.316Third-law calculations for reaction (5) are summarized in table 2.The averagethird-law AH&8 = 1115.8f 1.6 kJ inol-l agrees with the second law AH2098 =1125.1 f 18.4 kJ mol-l resulting from combination of eqn (3) and (4). Therefore,the average value AH;98 = 1120.5 & 18.4 kJ mol-’ was selected as the best valuededucible from our data. The error term corresponds to an estimated standarddeviation equal to that associated with the second-law result. An average value of= 565&21 kJ mol-’ for the standard heat of vaporization of CeO,(s) toCeO,(g), selected from published data 9 p 24 was combined with the standard heat offormation,25 AH;98,f[Ce02(~)] = 1090.3 f 1.3 kJ mol-1 and other thermodynamicdata 26 for CeO,(s), to give a standard heat of formation of CeO,(g) : AH&8,r[CeO,(g)] = -525f21 kJ mol-l.By combining this value with the aforementionedAHz98,f[Po2(g)] and with the selected value for the heat of reaction (5), the followingstandard heat of formation is obtained for CeP04(s) : AH;98,f[CeP04(~)] = - 1898.5k31.5 kJ mol-l.DISCUSSIONThe establishment of equilibrium in the vapours effusing from the Knudsen cellhas been proved by the study of reaction (1). The reproducibility of the PO&) andCe02(g) partial pressures measured in different runs indicates that equilibrium ornear-equilibrium conditions were also reached between the solid phase and the vapourphase. In these conditions the observed non-reproducibility of the partial pressuresof PO(g) and O,(g) could be explained by admitting, e.g., that they originate from th126 VAPORIZATION OF cePo4thermal dissociation of PO, rather than from the evaporation from the sample, andthat a slow interaction occurs between the oxygen and the container.The measured partial pressures of Ce02(g) are reproducible, but somewhat lowerthan required for congruent vaporization.This suggests an enrichment of the samplein cerium and oxygen. A comparison of the CeO,(g) partial pressures here measuredwith those measured by previous authors ’ 9 24 over CeO,,(s) indicates the formationof a cerium oxide phase possibly of the CeO, composition which vaporizes at nearlyunit activity. The relatively small quantity of the sample vaporized from the initialmass may account for the failure to observe the formation of this compound byX-ray analysis.According to the experimental results obtained we are led to conclude that thevaporization of that CePO, crystal modification which is stable in the temperaturerange covered by the measurements could properly be described by the followingreactions : CeP04(s) = CeO,(g) + P02(g) ; [Ce02,J, = CeO,(g) ; and PO,(g) =PO(g)++O,(g), where x is zero or close to zero and a, the activity, is close to unity.Although a definite direct experimental proof that the solid CePO, phase is themonazite monoclinic phase cannot yet be given(no X-ray analyses at high temperatureshave been made) on the basis of the arguments given previously in the text, andconsidering the thermal history of the sample (at the end of each vaporization run thecell temperature was quickly lowered from 1850 K to room temperature), it seems thatfew doubts exist that the solid phase we studied was actually monoclinic.In anyevent, for the purpose of deriving the heat of formation of CePO,(s) through thereaction (9, the uncertainties in the thermodynamic functions should cover theuncertainties in the CeP0, crystal modification actually present at the temperaturesof the experiments and, therefore, the standard heat of formation we reported forthe monazite type CePO, should be reliable within the quoted error.Rat’kovskii et aZ.3-5 have studied the vaporization behaviour of LaPO, and ofother orthophosphates of the lanthanide elements (excluding cerium) using a similarapproach over a similar temperature range to that described here.From theirresults they concluded that rare earth orthophosphates decompose according to thescheme : 2 LnP04(s) = Ln203(s)+2P02(g)+$0,(g). However it seems to us thatthis scheme is not sufficiently supported by the experimental facts. The only partialpressure measured was that of PO,@. The absence of PO(g) from the vapour and,consequently, the ratio of the partial pressure of PO(g) to that of 02(g) as it appearsin the proposed reaction scheme was inferred from having attributed the recordedPO+ ion intensity entirely as due to the fragmentation of P02(g). However theirreported I(PO~)/I(PO~) intensity ratio (about 5 ) is very high compared with thevalue we found, and corresponds to a ratio of the fragmentation cross section to theprimary ionization cross section which is itself unusually high compared with thevalues found in the mass spectrometry of high temperatures molecules with high bondstrength such as that of the P-0 bond in PO2.On the other hand, the A.P. theyfound for the PO+ ion (12.1 k0.5 eV) is somewhat higher than the value we found(9.1 eV) and the value reported by Drowart et aZ.15 (9.5 eV), but rather too low toaccount for the dissociative ionization of PO,(g) to PO+ (the rupture of a OP-0bond requires about 5eV). Therefore, the composition of the gaseous product ofthe decomposition reaction of the lanthanide orthophosphates as reported byRat’kovskii et aZ.3-5 seems questionable. The presence of the Ln203 solid phase asdecomposition product, particularly at unit activity, appears reasonable as a workinghypothesis in default of any experimental information. Were this hypothesis correctin the case of the LnP0, compounds studied by the above authors, we would concludethat the decomposition reaction for GPO, differs from that of the other lanthanidM.GUIDO, G . BALDUCCI, G. DE MARIA AND G. GIGLI 127orthophosphates studied ; this difference could be attributed to the availability of ahigher oxidation state for cerium.The authors are indebted to Dr. G. De Angelis and Dr. P. L. Cignini for theThis work has been supported by the Consiglio Nazionale delle Ricerche throughX-ray analyses.the Centro di Studio per la Termodinamica Chimica alle Alte Temperature.H. Schaefer, V. P. Orlovskii and M. Wiemeyer, 2. anorg. Chem., 1972,390,13.V. P.Orlovskii, Kh. Kurbakov, B. S. Khalikov, V. I. Bugakov and I. V. Tananaev, Izvest.Akad. Nauk S.S.S.R., Neorg. Materialy, 1974, 10, 670; CAY 81(10), 54935.I. A. Rat’kovskii and B. A. Butylin, Vetsi Akad. Navuk Beloruss. S.S.R., Ser. a i m . Navuk,1973, 5, 115.41. A. Rat’kovskii, B. A. Butylin and G. I. Novikov, Doklady Akad. Nauk Beloruss. S.S.R.,1973, 17, 232.I. A. Rat’kovskii, V. A. Ashuiko, V. P. Orlovskii, B. S. Khalikov and G. I. Novikov, DokladyAkad. Nauk S.S.R., 1974,219, 1413.D. Sh. Tsagereishvili, G. G. Gvelesian, V. P. Orlovskii, T. Y. Belyaeskaya and V. P. Repko,Izvest Akad. Nauk. S.S.S.R., Neorg. Materialy, 1972, 8, 1790. ’ G. De Maria, G. Balducci, A. Capalbi and M. Guido, Proc. Brit. Ceram. Soc., 1967, 8, 127.R.T. Grimley in Characterization of High Temperature Vapors, ed. J. L. Margrave (Wiley,New York, 1967).V. Piacente, G. Bardi, L. Malaspina and A. Desideri, J. Chem. Phys., 1973, 59, 31.lo S. Smoes and J. Drowart, Faraday Symp. Chem. Soc., 1974, 8,139.l1 R. W. Kiser, Introduction to Mass Spectrometry and its Applications (Prentice-Hall, Englewoodl2 ASTM Powder Diffraction File, card 11-556, Philadelphia 1960.l3 J. B. Mann, in Proceedings International Conference on Mass Spectroscopy, ed. K. Ogata andl4 M. Guido and G. Gigli, High Temp. Sci., 1975,7,122.Cliffs, N. J. 1965).T. Hayakawa (University Park Press, Tokyo, 1970) p. 814.J. Drowart, C. E. Myers, R. Szwarc, A. Vander Auwera-Mahieu and 0. M. Uy, J.C.S. Faraday11, 1972, 68, 1749.l6 JANAF Thermochemical Tables (2nd edn., NSRDS-NBS 37, 1971) ; JAN& ThermochemicalTables Suppl., J. Phys. Chem. Ref. Data, 1974,3,463.K. Hukuo, Y. Hichiki and N. Ose, Yoyo Kyokai Schi., 1974, 82, 284; K. Hukuo and Y.Hichiki, J. Chem. SOC. Japan, 1975, 4, 622.l 8 R. Hultgren, R. L. Orr and K. K. Kelley, Supplement to selected Values of ThermodynamicProperties of Metals and Alloys (University of California Press, Berkeley, California, 1966).l9 I. V. Tananaev, V. P. Orlovskii, B.S. Khalikov, Sh. Osmanov and V. I. Bulgakov, DokladyAkad. Nauk Tadzh. S.S.R., 1974, 17, 42.‘O B. A. Justice and E. F. Westrum Jr., J. Phys. Chem., 1969,73, 1959.21 W. W. Weller and E. G. King, U.S. Mines Rept. Invest. No. 6245 (1963).22 S. D. Gabelnick, G. T. Reedy and M. G. Chasanov, J. Chem. Phys., 1974, 60, 1167.23 D. L. Hildebrand and E. Murad, J. Chem. Phys., 1974, 61, 1232 and ref. (41) cited therein.24 R. J. Ackermann and E. G. Rauh, J. Chem. Thermodynamics, 1971,3,609.F. B. Baker, E. J. Huber, Jr., C. E. Holley Jr. and N. H. Krikorian, J. Cfiem. Thermodynamics,1971, 3, 77.26 C. E. Wicks and F. E. Block, U.S. Bur. Mines Bull. (1963), 605.(PAPER 5/2317

ISSN:0300-9599    

DOI:10.1039/F19777300121

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Mechanics of DispersionsPart 1 .-Identification of Parameters in Structural HysteresisBY ALLAN J. B. SPAULLSchool of Chemistry, Brunel University? Uxbridge: MiddlesexRcceived 9th March, 1976A necessary and sufficient set of parameters that describe the mechanical properties of a perfectthixotropic dispersion is derived using a statistical method.By reference to a study of the viscoelastic and thixotropic properties of carbonblack in mineral oil, Mewis et a2.l have reported on the phenomenon of structuralhysteresis. This work is of interest because of the experimental proof that char-acterization of the structure of thixotropic systems by one parameter is inadequate, asubject about which there has been some controversy.2There are many reported examples of two phase systems of monodisperse and ofheterodisperse dispersions of particulate solids in a liquid phase showing visco-elasticity? or thixotropy, or both.3 The size of the particles has ranged from the lowerlimit to just above the upper limit of what is called the colloidal subdivision ofWhether the elastic response in such viscoelastic systems is entropic orpotential in origin has not been established.It is, therefore, of some importance toexamine the basic theory of two phase dispersions so as to determine the number ofparameters required to describe behaviour observed in the usual kind of rheologicalexperiment, and to inveytigate how the theory could further our understanding of suchdispersions and of related scientific problems. We choose a statistical thermodynamicmethod.ANALYSISThe analysis is based on one given by G~ggenheim.~ The preliminary step insolving a physicochemical problem is the choice of parameters required for an,adequate macrodescription of the system, preference being given to those whichaccord physical significance to underlying theory, and are easily determined experi-mentally.Although thixotropy has been defined somewhat differently by differentauthors,6* we will regzrd it as a time dependent reversible decrease of viscosity undershear, resulting from a reversible breakdown of structure.*-1° To this end, wedescribe a perfect thixotropic model which can be used to compare with real systems.Consider two discrete particles of colloidal dimensions in a liquid continuum. Theirsize is bounded and their (potential, distance) interaction is composite, arising fromattraction (London-van der Waals forces) and repulsion (electrical or steric forces orboth).ll The interaction energy function has two minima, primary and secondary,separated by a potential barrier.The interparticle distance depends on temperature,for if the depth of the secondary minimum is greater than several units kT of thermalenergy, the interaction leads to a permanent physical bond with a fixed interparticledistance between the two particles. On raising the temperature the interparticle12A. J. B. SPAULL 129distance increases until a point is reached when the interaction is so weak in relationto kT that the bond is considered as broken, the translational motion of the particlesbecoming independent of each other.Formation and breaking of bonds can bereversed by varying the temperature. Similarly, interparticle distance can be variedby applying i? shear field. Spzcifically, the physical bond distance between twoparticles in secondary interaction can be increased by increasing the shear field untilultimately the applied couple is sufficient to overcoine the interaction so as to break thephysical bond. To continue the development of the model, let there be N suchparticles in volume V. No restriction is placed on their size or shape, except thatthcj are c~lloidal.~ The barrier between the primary and secondary minima issufficient to prevent primary interaction between particles.Pairwise interactionQCCU~S between nearest neighbours, surrounding particles having no influence on theifiteraction between two given particles. The shear field has 110 effect on the solid-liquid surface structure of the particles, so electrical and steric repulsion potentialsare unchanged in a varying field.Depending on their thermal energy, someparticles will remain unbound, whereas others will form groups of two or moreparticles. Unbound particles will translate in a manner determined by the hydro-dynamic and Brownian interactions with the liquid continuurn, i.e., they could alsobe rotating. Groups of particles may also translate and rotate as a result of hydro-dynamic and Brownian interaction. Further, the geometric configuration of thegroups may be affected by hydrodynamic interaction with the continuum phase ; twolimiting shapes are spherical and linear.Particles located in a group may also berotating : indeed part of a group of particles may rotate in a different way from thatin another part of the same group. However, cz complete description of all possibleand actual physical processes of the particles is not necessary.The relation between the above microdescription and the macrodescription, forprescribed values of the inacroscopic parameters, N, V, energy (thermal plus shearfield) U, and a parameter c7 can be derived statistically by averaging over all accessiblephase space states. The properties of 5 are explored later. The dispersion isassumed to be an assembly of discrete colloidal particles in a liquid continuum,independently distributed in phase space, whenA shear field is applied at constant T.where Ur is the energy (thermal plus shear field) of phase space r, 5, the thermo-dynamic probability of the sth value of 5, Q(t,) a group of values of 5, of weight Rwhich we do not distinguish, and k the Boltzinann constant.Using a concentric cylinder geometry of infinite length, the dispersion is strainedat a constant rate.After infinite time, t (see appendix), < reaches a false thermo-dynamic equilibrium vaIue c:, when the microscale processes of the assembly nolonger change. The equilibrium energy, U", is given by :We conclude that, for i! given geometry, there is a one-to-one correspondence betweenthe equilibrium energies of the assembly and the constant rates of strain applied forinfinite time.1-I30 MECHANICS OF DISPERSIONSAt time to (= l), let us change the equilibrium energy of the assembly by changingthe rate of strain to a higher constant value, so that after infinite time the value ofU ; becomes Uh, and 5: becomes 5;.The instantaneous values of the energy and ofthe parameter 5 at time ti are respectively U: and 5'. At this higher rate of strain,certain changes in the microscale processes take place, compared with those previouslydescribed at equilibrium <:. For example, some bonds will no longer be stable andhence will rupture ; the interparticle distances between the particles forming asecondary bond may increase as a result of the higher potential energy they possess ;accordingly the geometric configuration of many groups will change.Thus, as wellas a change in the energy of the assembly, there is a change in the distribution of theenergy ; since there is a change in the thermodynamic probability of the phase spacesavailable, various values of 5, will contribute to the sum 5,. The change in dis-tribution of energy is time-dependent : physically it is a relaxation process. Oneimportant result of the relaxation is that even when the total energy of the assemblyhas reached a constant value, changes may still occur in its distribution among thephase spaces as changes in their thermodynamic probability occur, Le., we concludethat Ui does not necessarily take the same time to reach U i as ti does to reach <;.The parameter is a measure of the extent to which the assembly has approached athermodynamic equilibrium state.It is, therefore, appropriate to retain the nameDe Donder l 2 gave to the parameter 5, viz. the extent of reaction of a (thixotropic)physicochemical change.From our argument on the microdescription, four macroscopic properties areadequate to describe the rheology of a thixotropic dispersion; a suitable choice isvolume, composition, energy and extent of reaction.If 5 isknown, the parameter U can be determined from measurements of stress, p i j , sinceU = p,VN<, or in differential form (aU/aV),, = p i j , where p i j is a physicalcomponent of the stress tensor. There is difficulty in determining 5.In physico-chemical studies the thermodynamic probability, or partition function (to which < isrelated) is determined from spectroscopic measurement ; it may also be calculated.The analogue in mechanics is to obtain the mechanical spectrum by subjecting thesystem to a series of forcing vibrations having a wide range of frequencies, from whichthe relaxation spectrum may be determined. However, there is at present no simplerelation between 5 and the relaxation spectrum. Furthermore, there are almostcertain to be experimental difficulties : the mechanical technique is necessarilydestructive of what it is being used to determine ; a sufficiently sensitive experimentaldevice for determining a particular microscale process may be elusive.Values of ti, determined from transient spectra taken during a continuous thixo-tropic path from t = 1 to t = co, are required.On such a path the values lie betweenlimits, 0 < ti < I. A physical property of 5' is that it is the instantaneous descriptionof the microscale phase spaces, for prescribed values of N, V, and U ; the relationbetween ti, other macroscopic parameters, and the microscale processes can beobtained statistically and the relation is formally similar to eqn (1). Although wehave indicated that ti can be obtained from the spectral density function formechanical loss, it can, in principle, be obtained from any transient spectra resultingfrom perturbation of the microscale processes. Such perturbation can be achievedby a number of experimental techniques, and, depending on the method used, willgive different information about the physical nature of the microscale processes. Fora simple thixotropic change, e.g., from chains of particles bonded together to free,unbound, discrete particles, to be followed through 5, the spectral technique must beprecise and discriminating enough so as to follow the change in the statistical weightSThe next problem concerns the experimental determination of U and 5A.J. B. SPAULL 132of at least one of the microscale processes, such as the appearance of unboundparticles, or the disappearance of chains. An adequately accurate technique coveringa wide range of frequency would allow the determination of the time dependence of allmicroscale processes, but this is not needed in an evaluation of 5.One example of the mechanical spectra l3 is shown in fig.1. Transient mechanicalspectra taken with the dispersion at rest at one minute and 17 h intervals after thecessation of steady state shear (0.071, 0.71, and 7.1 s-I) are shown. The symbol His the relaxation spectrum (shear),14 and was determined from experiments using aWeissenberg rheogoniometer. In practical applications the time dependence of < isobtained from the variation in the character of spectra with time.log T / SFIG. 1.-Transient relaxation spectra taken during thixotropic build-up at one minute and 17 hintervals after the cessation of flow (0.071, 0.71 and 7.1 s-l), using a 2.7 % carbon black dispersionOther time dependent transient relaxation spectra have been reporfed,15 thus theapproach to dielectric spectra developed by Helsen et aZ.,16 may prove speciallysuitable in the determination of (.in mineral oil (w/w).After one minute -; after 17 h ---.DISCUSSIONWe apply our analysis to the assembly that we have described ; it closely resemblesthixotropic systems encountered in technology. The equilibrium curve, giving thevariation of U, as a function of t,, is shown in fig. 2. For all values of the thermo-dynamic equilibrium parameters dc/dt = 0 ; the function U, = UJ&) lies in thet = co plane, see fig. 2 and represents an infinite number of false thermodynamicequilibrium states. Most research work has been argued on the basis of equilibriumcondition^,'^ so it is not surprising that the one-parameter theory of thixotropy-adistinct one-to-one correspondence between macroscopic properties-has obscuredthe underlying fundamental problem.Non-equilibrium values of U, U', and t, ti,determined during thixotropic build-up and break-down at different values of t areshown in fig. 2 by projecting them on the t = 00 plane. During build-up and break-down, the one-to-one correspondence disappears, when correct analysis allows theemergence of the two-parameter thixotropic theory.Some paths that can be taken during break-down and during build-up are shown.The paths would depend on the mode of application of strain during these processes.For example, starting from the same equilibrium point on the U, = U,((,) curve132 MECHANICS OF DISPERSIONSbuild-up would take different paths depending on whether the dispersion is at rest,under flow or (small amplitude) vibration.This observation could be utilized inchemical engineering design for it is important to note that if energy conservation is adominant factor in the handling of thixotropic systems, equilibrium conditions areto be avoided.J4FIG. 2.-Energy (thermal plus shear field) as a function of extent of reaction. Curve 1, U, = Ue(te)in the t = 00 plane, the plane of the paper. Projected on the f = 00 plane, curves 2, thixotropicbuild-up under flow ; 3, break-down, under flow ; 4, build-up, under low amplitude vibration ; and5, build-up at rest. The t-axis is perpendicular to the plane of the paper.There are two limiting equilibrium cases for which 5 can be calculated.In one,the continuum phase is totally disregarded, when the particulate solid becomes agaseous assembly of structureless identical particles, each of mass m. There is now aunique value of 5 for all rates of strain, and the quantity C Q(5) exp( - U,/RT) is thepartition fuizction of the assembly, which has the value V(27-cmNkT/h2)3, where ti isPlanck's constant.18 We can use the expression,rto show that the stress is independent of the rate of strain and hence to derive the well-known result that the coefficient of viscosity of the assembly is independent ~f stress(which in this relation is equal to the pressure, p , of the gas). Such behaviour isfound in near perfect gases.lg In the other case, again disregarding the liquidcontinuum, we cause the particles to gel to an assembly of N identical lacalizedoscillators regularly spaced on a lattice.The value of 5 is again unique for sr!ch anassembly, and at high temperature the partition function for an oscillator is kT/Av,where v is the natural frequency.20 The response to a siiiusoidal strain i s itselfsinusoidal, falling rapidly to zero when the imposcd frequency is much abovc v.This kind of response is found with crossed-linked polymers and gels,14 as s z m intheir relaxation spectra.Implicit in the statistical method we have used is that 5 is a necessary parameter.It follows, therefore, that is a necessary parameter in any study of the rlheology ofthixotropic dispersions.Since the change in the character of the spectra is employeA. J. B. SPAULL 133to follow the way the model changes with time, we have the iniportant result that theanalysis is not dependent on the model. The only constraint on the model is that itmust be thermodynamically reversible (between true and false or between differentfalse equilibrium states) with respect to U, or the applied stress, in time, whichemphasises, in this light, the physical nature of 5, a relaxation parameter.To conclude, we briefly consider a few illustrations where the basic theory mightbe further exploited. It should be possible to calculate the value of 5 and its timedependence for some systems ; armed with such information we might be in a positionto derive a general theory for thixotropic kinetics, and the seat of elasticity: inparticular it would be interesting to use the theory to contrast the effects stemmingfrom the explanation we give for structural hysteresis with those originating fromthe explanation Everett proposed for the hysteresis found in surface chemistry.211 am indebted to Prof.J. Mewis for hospitality in Belgium, during tenure of aRoyal Society European Science Exchange Programme visiting fellowship.APPENDIXFlow time, zf, is the time basis for defining rate of strain tensor, &(= de/dz,), andrate of stress, fiij(= dpij/dzf).Kinematic or kinetic time, K , is the time used in practical experiments, to measurethixotropic change, during build-up or break-down.Tlzermodynamic (or de Donder) time, t, is that used in thermodynamic discussion.The parameter 5 is a function of time, t, only, 5 = t(t).We find the form of thefunction. For the geometry employed in this paper, the arbitrary law U = U(z,)governing the way the energy of the assembly increases is determined from the rate ofstrain tensor, 6 = l/zf.5 = v ( ~ , t) = v(t, 5) = alt,dtWe need to distinguish between different kinds of tinie in rheology.Thus we know the form of the differential equation :where a is a dimensionless constant [see ref. (7), chap. 1, article 91. We adopt twoboundary conditions. One, the rheological ground and thermodynamic standardequilibrium states, cE*s, is the value of 5 when t = 1, and after the dispersionhas been at rest for infinite time, t.We equate t f 9 S arbitrarily to zero. The otherboundary is that for which d</dt = 0. At this boundary t = c,, a false thermo-dynamic equilibrium. Therefore, < = aln(t). The reference state, t:,', is a truethermodynamic equilibrium [see ref. (7), p. 401, since dtE,s/dt = 0, and the affinity,A:*s, is zero. Other equilibrium values of t are false thermodynamic equilibria,since for these values of 5, though dt,/dt = 0, the affinity has a finite positive value.Thus to each value of 5, in the equilibrium curve U, = Ue(te) corresponds a value ofthe affinity, A,. It should be noted that the values of <, in the t = plane can bereflected in the t = 1 plane, fig. 2. Further we have assumed the convention thatdc/dt is positive in sign when a thixotropic path is from a lower to a higher value ofU and negative in a reverse direction.Arbitrarily, the values of 5 are put equal tozero in the t = 1 plane and to 1 in the t = 01) plane.J. Mewis, A. J. B. Spaull and J. Heken, Nature, 1975, 253, 618.D. C-13. Cheng, J. P/zys. D, 1974, 7, L155.J. Mewis and A. J. B. Spaull, Adv. Colloid. Interface Sci., 1976, 6, 173.D. H. Everett, Pure Appl. Chem., 1972, 31, 579.E. A. Guggenheim, Tlternzodynamics (North-Holland, Amsterdam, 5th revised edn, 1967),chap. 2134 MECHANICS OF DISPERSIONSW. H. Bauer and E. A. Collins, Rheology, Theory and applications, ed. F. R. Eirich (AcademicPress, N.Y., 1967), 4, 423.L. Dintenfass, Proc. 5th Int. Congress of Rheology, ed. S . Onogi (University of Tokyo Press,Tokyo, 1970), vol. 2, p. 281.H. Freundlich, Thixotropy (Hermann, Paris, 1935).Ukr. SSSR, 1972).1973), vol. 1, chap. 5.R. Defay, translated by D. H. Everett (Longman, London, 1973), p. 10.' M. Reiner and G. W. Scott-Blair, see ref. (6), p. 461.lo M. N. Kruglitshii and N. V. Mihailov, Rheology of thixotropic systems (Nauk. Dumka., Kiev,l1 R. H. Ottewill, CoZloid science (Specialist Periodical Reports, The Chemical Society, London,l2 For a bibliography of the work of de Donder see Chemical thermodynamics, I. Prigogine andl3 Personal communication from J. Mewis.l4 J. D. Ferry, Viscoelastic properties of polymers (Wiley, New York, 2nd edn, 1970) ; FarahyDisc. Chem. Soc., 1974, 57.G. Schoukens, J. Mewis and A. J. B. Spaull, report presented at a meeting of the British Societyof Rheology, April, 1975.l6 J. Helsen, G. Schoukens, J. Mewis and A. J. B. Spaull, report presented at a meeting of theFaraday Division, Colloid and Interfacial Science Group, Bristol, April, 1976.l7 J. W. Goodwin, Colloid science (Specialist Periodical Reports, The Chemical Society, London,1975), vol. 2, chap. 7.G. S . Rushbrooke, Introduction to statistical mechanics (Oxford U.P., London, 1949), p. 63.l9 J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular theory ofgases and Ziquids (Wiley,New York, 1954).2o See ref. (18), p. 65.21 D. H. Everett and P. Nordon, Proc. Roy. Soc. A , 1960, 259, 341.Gels and Gelling Processes.(PAPER 6/477

ISSN:0300-9599    

DOI:10.1039/F19777300128

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Sequence Studies in Liquid Phase Hydrocarbon OxidationPart 4.-Hydroperoxide-Alcohol and Hydroperoxide-Ketone Transitions in theOxidation of EthylbenzeneBY &A DAN~CZY, ISTVAN NEMES AND DEZS~ GAL*Central Research Institute for Chemistry of the Hungarian Academy of Sciences,1025 Budapest, Pusztaszeri ut 59-67, HungaryReceived 10th March, 1976The rates of consumption of cc-phenylethylhydroperoxide molecules during the oxidation ofethylbenzene at 120°C: have been measured using radioactive tracer procedures ; balance equationsfor the total activities and concentrations were used for the calculations. In order to obtain a coherentset of rates a hydrogen transfer reaction between hydroperoxide molecules and peroxy radicals had tobe taken into account.It was established that ketone and alcohol molecules were formed mainly as a result of the induceddecomposition of the hydroperoxide and the contribution to their formation by termination pro-cesses was <lo % of their total formation rates.The formation rates of alcohol and ketone viahydroperoxide molecules were very similar.The relative reactivity of hydroperoxide and ethylbenzene molecules toward peroxy radicals wasfound to be two. Further kinetic data, such as ease of oxidation and kinetic chain length both forthe oxidation of the parent hydrocarbon and its main intermediate, have been determined.In previous papers we have reported on the kinetics and mechanism of theconsumption of 1-phenylethanol (ROH) formed during the oxidation of ethylbenzene.In the present work we report on the transformation of the main intermediate, a-phenylethylhydroperoxide (ROOH) in the course of the oxidation.Pritzkow and Holm and Emanuel et aL6 performed earlier studies on the trans-formation of hydroperoxides in oxidative systems.EXPERIMENTALMATERIALSEthylbenzene (RH) was used after careful purification as described previously.1-214GEthylbenzene was prepared by the reduction of 4C-acetophenone (RCOR”) syn-thesized from Ba14C03 by a Grignard reaction followed by a Friedel Crafts process. Theradiochemical purity after distillation was 100 % and the molar activity of the product was3.4 Ci mol-I.14C-a-Phenylethylhydroperoxide was obtained by oxidation of 14C-RH using azobis-isobutyronitrile (AIBN) as initiator or sodium stearate as catalyst.After removal of thewater-soluble 2-cyanoprop-2-ylhydroperoxide, formed from AIBN, the ROOH was pre-cipitated as its sodium salt, washed thoroughly and neutralised with hydrochloric acid. Theproduct so obtained was then dried and its purity checked by gas chromatography. Molaractivity of the 14C-ROOH was 0.8 Ci mol-1 and its radiochemical purity was 92 % ; RCOR”(2.5 %) and ROH (1.2 %) were found as chemical impurities.ANALYSISGas chromatography and radio gas chromatography were used. Working conditionsexcept that in order to obtain a sharp peak for ROOH, the were as previously reported13I36 LIQUID PHASE HYDROCARBON OXIDATIONcolumns were filled with 10 ”/, Ge XE 60 on Gas Chrom S (120-140 mesh) and operated at75°C with argon as carrier gas.REACTION CONDITIONSThe experimental technique has been described previously.‘RESULTSFrom the experiments carried out at 120°C in the presence of 14C-ROOH theamounts of ROOH formed and consumed during the oxidation were calculated bythe kinetic isotope method.’.However, the amounts of ROOH consumed exceededthe equivalent amounts of the products formed from the ROOH and observedanalytically. Possible explanations for this discrepancy may be : (i) During theconsumption of the hydroperoxide further products are formed which have not beendetected by our analytical method, i.e. the expression assumed in Part 3where ARH is the amount of ethylbenzene consumed, is not valid. (ii) The sequencenetwork * assumed in Part 1 does not represent the overall process correctly becauseof unaccounted reactions.[ARH] = [ROQH] + [ROH] + [R’COR] +[phenol] (1)CONTROL OF THE VALIDITY OF THE BALANCE EQN ( I )Labelled ethylbenzene with a total activity of 22.7 mCi dm-3 was oxidized for50 11.Samples were analysed for the total activities of RH, ROOH, ROH and R’CORand for the total amount of the latter three compounds. The amounts of RHconsumed were calculated from its total activity losses and from the activity increases1.6I .4m 1.2Ec) 1.0E .s 0 . 820 . 68I-3& . c -0 -40.20.time/hFIG. I .--Kinetics of product formation in the oxidation of ethylbenzene. [ROOH] + [RC’OR] +[ROHI f [phenol] against time, + sum of product concentrations from total activity increase, x sumof product concentrations from activity decrease of ethylbenzeneE. DANOCZY, I .NEMES AND D. GAL 137of the products, and compared with the total amounts of products determined analy-tically. The results are given in fig. 1 and show that the amounts of ethylbenzeneconsumed as calculated by the balance equation (1) and based on activity measure-ments agree to within + 5 %. The results also indicate that eqn (1) can be used upto 15-20 % conversion.DETERMINATION OF THE FORMATION A N D CONSUMPTION RATES OF THEROOH I N THE OXIDATION OF ETHYLBENZENEThe amounts of labelled ROOH introduced into the system varied between 3.5and 33 x It was established previously that the introduction ofROOH causes a shift to higher conversions, but the kinetic curves can be matchedby a simple translation along the tiEe axis.in01 dm-3.DISCUSSIONPrior to the quantitative calculations we had to determine those processes whichare responsible for the activity decrease of the ROOH without its simultaneous con-centration change.The most likely such process is the hydrogen transfer reaction(2) investigated in detail by Howard and co-workers ’* l owhere RO: are a-phenylethylperoxy radicals. Although this reaction is ari identityprocess in the present system, since ROOH is introduced in labelled form, reactioii(2) might nevertheless result in activity losses if its rate is significant.Ingold and co-workers have fouiid that the rate constant of reaction (2) variedbetween 102-103 dm3 mol-1 s-l.A similar rate constant was obtained by Niki etal.’ 9 l2 at 60°C. Values observed by Thomas and Tolman and by Hiatt, Gouldand Mayo l4 are also -lo2. Consequently we included the hydrogen transfer pro-cess in the sequence network :RO’, + ROOH + ROOH + RO’, (2)w13I RONi -3)K’COR”‘“1 4where ivXy are the corresponding rates and * refer to the transfer processes.Since, the total activities, molar activities and concentrations of the peroxy radicalsare not known, the equations of the kinetic isotope method applied earlier 1 * cannotbe used. Consequently we introduced the balance equations for the total activitiesand concentrations :dA,,,H = - a 2 w 2 3 - a 2 ~ 2 4 - a 2 ~ ~ 1 + a l ~ ~ 2 + a 1 ~ v 1 2 = b,dt (4)r 5 ) d A,,, - = a 2 ~ ~ 2 3 + a l w , , - a 3 w 3 , = b6d138 LIQUID PHASE HYDROCARBON OXIDATION= a 2 ~ ~ 1 - a , w ~ 2 - a l w ~ 3 - a l w , 4 = b, dA,o;dt (7)whers a l , a2 and a3 refer to the molar activities of RO:, ROOH and ROH, respec-tively.Values of al, [RO’,], w ; ~ and wY2 are not known.We expressed certain rates by using reliable rate constants from literature dataand thus obtained the values of al. According to Tsepalov and Shlyapintokh l5k13 varies between 1.9 and 2.2 x lo7 dnl3 mol-1 s-l while Gadelle and Clement l6and Howard et aL9 give k I 3 = 2 x lo7 dm3 mol-’ s-l.Tsepalov and Shlyapintokh foundk12 = 9.6 x lo5 exp(-8500/RT)giving k12 = 18 dm3 mol-1 s-l at 120°C. According to Gadelle and Clement l6k12 = 20.6 dm3 mol-l s-l.In our calculations we have used the average values at120°Ckigo = 2 x lo7 dm3 mol-l s-land= 19.2 dm3 mol-l s-I.In addition, values of w33 given in Part 1Using the above literature data and assuming that a fast equilibrium takes placewere used.in the hydrogen transfer process, i.e. wT2 N wil, eqn (4)-(11) yieldFor long kinetic chains and at not too high conversionsw12 = [al(b2 + b3 + b4)-(a2b2 + b6 + b7)l/(al -a2)* (1 2)w1 = kl 2[RH](~i/2kl 3)9 (1 3)where wi is the total rate of initiation. Since Wdeg, the rate of the degenerate branching,substantially exceeds w ~ , ~ , the rate of primary initiation, the latter can be neglectedOn the other hand, the rate of initiation equals the rate of termination, wi =~ 1 3 + w , ~ . Recent results indicate l7 that ketone molecules can be formed fromperoxy radicals by the isomerization and subsequent decomposition of the latterinto ketone and 6 H radicals.Therefore, we express the rate of termination as 2w13assuming a Russel-type termination mechanism. Thus, wi = 2 ~ ~ 3 .From eqn (4)-(11) values of w13 are given bySO that M’i = Wdeg.w13 = [a2(b3 +W34)-b6-a3w3411(a2-al). (148. DANOCZY, I. NEMES AND D. GAL 139From eqn (12)-(14) we obtain a quadratic equation for al+b3 + b4)2 - al[2(b2 + b3 + b4)(a2b2 + b6 + b7) + c] + (a2b2 + b6 + b7)2 + a2c = 0(15)(16)whereC = (G2CRH12/k13)[bci +a3W34-&(b3 + W34)I.Calculations were carried out for the initial 25 h.After solving eqn (15) for al we can calculate the corresponding rates from eqnSome of the values obtained are given in table 1.(4141 1).TABLE 1 .-MOLAR ACTIVITIES, CHAIN LENGTH (v) AND HYDROGEN TRANSFER RATES CALCULATED[14C-ROOH] = 33 x mol dm-35295132175220270315360410460515570625680735865.51006.3937.11081.41092.31352.81479.51543.51235.61025.5930.0860.8825.3682.8580.2470.2254.7181 .o134.8104.883.369.5659.050.243.237.132.1528.224.9721.9521 5.0184.0157.0146.0137.0132.5128.3123 .O112.0102.094.589.586.583.078.72.73.23.64.24.95.66.37.99.9511.512.613.013.6514.315.56.967.427.267.447.37.37.08.088.89.259.559.79.9Fig. 2 shows the total rate of consumption (giving alcohol and ketone molecules)of ROOH and the formation rates of alcohol and ketone in the pathway, omittingthe intermediate formation of ROOH.The main source of the alcohol and ketoneformation is the transformation of hydroperoxide molecules. The data also showthat ROOH molecules are transformed into alcohol and ketone molecules with similarprobabilities wZ3 - ~ 2 4 .We can calculate the relative reactivities of the hydroperoxide and ethylbenzenemolecules toward the chain carrier radicals, if the following considerations are takeninto account. The total consumption rate of ROOH, ( ~ 2 3 + ~ 2 4 ) consists of threedifferent rates ; thermal decomposition into radicals, induced decomposition andthermal decomposition into molecules. The last one, according to the data of Emanueland co-workers,18 can be neglected.As mentioned already, the rate of the thermaldecomposition into radicals (degenerate branching) is equal to 2w1 3. Consequently,the differences ~ 2 3 + ~ 2 4 - 2wl correspond to the rates of induced decomposition ofthe ROOH molecules, which are plotted in fig. 3 against [ROOH].Comparing fig. 2 and 3 reveals that the consumption of ROOH proceeds mainlyvia an induced decomposition. Since the " correction " values 2wI3 are very small(and consequently bear the highest error) it was necessary to verify the calculationsindirectly1 40 LIQUID PHASE HYDROCARBON OXIDATIONE 1.0100 2 0 0 3 0 0 400 5 0 0 600 7 0 0[ROOH]/103 mol dm-3FIG. 2.-(n) Total consumption rate of ROOH (wz3 + w24) and (b) termination rates ( ~ ~ 3 , w14) againstthe actual [ROOHJ concentrations.According to literature data l8 the decomposition rate constant of ROOH intoradicals at 120°C is 0.56 x s-l.According to our earlier data it lies betweens-l. Present results, calculated from 21v13, yield a value of 4 x lo-'s-l, in good agreement with the above values though somewhat lower than thosemeasured directly using inhibitors,Assuming that the prevailing process which determines the induced decompositionof the ROOH is its reaction with a-phenylethylperoxy radicalsandkROOHRO', + ROOH '-+ product +radicaland knowing the rate of the induced decomposition of ROOH (shown in fig. 3) wecan calculate the ratio kFooH/k~H at 120°C where kFH refers to the processkpRHRO', + RH -+ Ro+ ROOH.The value of this ratio is -2, less than the kFoH/kEH = 4.3 calculated previouslyand should be considered as an average, since the calculations were carried out upto [ROOH] concentrations at which the contribution of dimers in process (17) isvery likely.This assumption is supported by attempts to calculate the absoluterate constant of process (2), where it was established that the k* values, though theirorder of magnitude is in good agreement with literature data, lo3 dm3 mol-l s-I, arenot constant but decrease reproducibly with increasing [ROOH] concentrationsi. DANOCZY, I. NEMES A N D D. GAL 141A similar phenomenon was observed by Niki et aZ.ll* l2 Howard et aZ. attributedWe computed some further values ; the oxidation rate of ethylbenzene, 4.3 xthis to dimer formation.inoI-% dms s-g, and the oxidative decomposition of ROOH, 8.4 xs-?.are given in table 1.mol-3 dm3The changes in the kinetic chain length during the oxidation of ethylbenzeneX13: 233 3 3 3 400 5QE 530 7rJ9[ROOH]/103 mol dm-3FIG.-;.-Rates of the induced decomposition of the hydroperoxide (wZ3 + 1u24-2~v13) against theactual [ROOHJ concentrations.Since the rates of consumption of ROOH are known and the rate of the initiationis constant throughout the whole system, it was possible to calculate the kinetic chainlength of the oxidative consumption of ROOH. These are also given in table 1 andare seen to increase with increasing conversion.We thank Drs. F. Dutka, A. Mirton and T.Komives for preparing the 14C-elhylbenzene.E. Danbczy, G. Vasviri, J. Phys. Chem., 1972, 76,2785.T. Vid6czy. 8. Dan6czy and D. Gh1, J. Phys. Chem., 1974, 78,828.8. Danbczy, I. Nemes, T. Vidbczy and D. Ghl, J.C.S. Faraday I., 1975, 71, 841.' D. GAl, 8. Danbczy, I. Nemes, T. Vidbczy and P. Hajdu, Ann. N. Y. Acad. Sci., 1973,213,51142 LIQUID PHASE HYDROCARBON OXIDATIONW. Pritzkow and I. Holm, J. pvakt. Chem., 1962, 16,287.N. M. Emanuel, Z. K. Maizus and L. G. Privalova, Int. J. Appl. Rad. Isotopes, 1959, 7, 111. ’ M. B. Neiman and D. 681, The Kinetic Isotope Method and its Applications (Elsevier, Amster.dam, 1971).* I. Nemes, L. BotBr, T. Vidbczy and D. Ghl, in press.J. A. Howard, W. J. Schwalm and K. U. Ingold, Adv. Chem. Ser., 1968,75,6.J. A. Howard and J. H. B. Chenier, Canad. J. Chem., 1975,53,624.E. Niki and Y . Kamiya, J. Fac. En.u. Uiiiv. Tokyo, 1972, 31, 4.l2 E. Niki, K. Qkayasu and Y. Kamiya, Int. J. Chem. Kinetics, 1974, 6, 279.l3 J. R. Thomas and C. A. Tolman, J. Amer. Chem. Soc., 1962, 84, 2079.l4 R. Hiatt, C. W. Gould and F. R, Mayo, J. Org. Chem., 1964,29, 3461.V. F. Tsepalov and V. Ya. Shlyapintokh, Kinetika i Kataliz, 1962, 3, 870; V. F. Tsepalov,V. Ya. Shlyapintokh and P. M. Shou, Zhur. Fiz. Khim., 1964, 38, 351.l6 C. Gadelle and G. Clement, Bull. SOC. chim. France, 1967, 1175 ; 1968, 44.l7 G. E. Zaikov, Z . K. Maizus and N. M. Emanuel, Kinefika i Kataliz, 1966, 7, 401.l 8 I. P. Skibida, Z . K. Maizus and N. M. Emanuel, Neftekhimiya, 1964, 4, 82.l9 T. Vidbczy, personal communication.(PAPER 6/482

ISSN:0300-9599    

DOI:10.1039/F19777300135

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Electroreduction of Cobalt-Amino Peroxs ComplexesPart 1.-The Reduction of Oxygen in the CO(II) + Ammonia System-/-BY ARMAND BETTELHEIM,* M. FARAGGI, 1. HODARA AND J. MANASSEN:Atomic Energy Commission, Nuclear Research Centre-Negev,P.O.B. 9001, Beer-Sheva, IsraelReceived 19th March, 1976The electroreduction of O2 in Co(@ + NH3 solutions has been investigated using the rotatingdisc electrode technique. It was found that the electroactive species, in the potential range 0 to- 1 V against s.c.e., are O2 and the peroxo complex [(NH3)5Co-02-Co(NH3)5]+4. The electro-activity of the complex was shown by the appearance of a new cathodic wave and by the linearincrease of the limiting current of this wave with the peroxo complex concentration. It is suggestedthat four electrons are involved in the reduction of the complex on a Pt rotating disc electrode.Its diffusion coefficient was calculated to be 8 .6 ~ cm2 s-I. The decomposition of the peroxocomplex to form a mononuclear complex of Co(n1) was a slow process (k = 3 . 0 ~ s-l).Synthetic reversible oxygen carrying chelates have been of interest as modelcompounds in the study of the reversible oxygenation mechanisms involved in naturaloxygen carriers, e.g., the haemoglobins and haemocyanins.It is well known that many CO(II) complexes take up molecular oxygen readilyin aqueous solutions to give binuclear peroxo c~mplexes.l-~ The best knowncomplex is [(NH3)5C~-02-C~(NH3)5]f4. The reversibility of the reaction withoxygen and the rate of oxygen uptake have been investigated by numerous authorsin the past using spectroscopic, potentioinetric and kinetic methods.3*This work deals with the electroreduction of oxygen in the presence of the CO(II) +ammonia system, using the rotating disc electrode (r.d.e.) technique.EXPERIMENTALU7ater was triple distilled.Merck pro analysis Co(N03)2, NH4N03 and NH3 wereused without further purification. All other materials were of analytical grade. Matheson“ extra dry ” oxygen and ‘‘ high purity ” nitrogen were used for the saturation of thesolutions.The solutions were prepared by mixing 6.3 mol dm-3 NH3 and 2 rnol dm-3 NH4N03 atpH 10.3 with 0-10 mmol dm-3 CO(NO,)~ shortly before the experiments. Saturation of thesolutions by the appropriate gas was carried out by continuous bubbling for at least 30 min.through a trap of aqueous ammonia (6.3 mol dm-3).Two types of solutions were prepared :Solutions A; these were saturated with oxygen before the addition of the Co(u) ion and nofurther oxygen was introduced afterwards.Solutions B ; oxygen saturation was carried out after the addition of the Co(u) ion and wascontinued for a further 30 min.In the type A solutions, the total concentration of oxygen is constant and equal to thesolubility of oxygen in the 6.3 rnol dm-3 NH3 and 2 mol dm-3 NH4N03 solutions :(1) [OJ+ [CO-O~-CQ~ = constant (solutions A).7 Based on A.B.3 Ph.D.Thesis submitted to the Weizmann Institute of Science, Rehovoth, Israel.1 Present address : The Weizmann Institute, Rehovoth, Israel.14144 ELECTROREDUCTION OF O2 I N C ~ ( I I ) + N H ,In the type B solutions, it is assumed that the Concentration of the free oxygen [not boundto Co(n) complex] is constant, its value being determined by its solubility in the 4.3 mol dm-3NH3 and 2 mol dm-3 NH4N03 solutions :(2)The peroxo coixentration in solutions B increases as the Co(rr) ion concentration is increased.The maximum concentration of the peroxo complex is half the concentration of the addedCO(II) ion.The rotating disc electrode (r.d.e.) consisted of a platinum cylinder pressed into teAon(supplied by Pine Tnst.Co.) The area of the electrode was 0.458 cm2. The electrodc wasrotated at 340r.p.m. by means of a Pir-Rotator (Pine Tnst. Go., serial 35"). The counterelectrode was a platinum wire, separated from the solution by a porous glass sinter.Thereference electrode was a saturated calomel electrode (s.c.e.) made according to Meitesand Thomas." All the potentials were measured against this electrode. Pretreatmentof the Ft-r.d.e. was according to Bockris and CO-workers.'Potentiostatic current against potential curves were obtained by applying to the cell apotential sweep of 0.45 V min-l using a potentiostat (both the potential ramp generator andthe poteiitiostat were built at the electronics laboratory of the Nuclear Research Centre-Negev).Coulometric measurements at a controlled potential were made with the aid of a voltageto pulse rate converter unit [Elron-model A(PRC I-B)] and an electron scaler (Elron-modelPolarographic experiments were performed with a Radiometer-PoIariter Type PO 4d.Excess of dissolved oxygen was removed by bubbling nitrogen for 20 min before recordingpolarograms.The dropping mercury electrode (d.m.e.) was a capillary electrode (suppliedby Sargent and Co.). The capillary characteristics were In = 1.799 mg s-l, t = 4.69 sand in3 t i = 1.91 mg3 s-3 under a mercury head of 850 nrn at a potential of -0.5 V aginsts.c.e.fO,] = constant (solutions B).N r s- 1 4-PI.All measurements were performed at 25°C (& 0.l"C).RESULTS AND DISCUSSIONIn arninoniacal solutions, the deca-amine complex [(NH3)5Co-0,-Co(NH3)5]+4is most stable in the pH range 10-12 and high ammonia concentration ([NH3]-7 moldm-3).3* This is presumably the range of pH in which the aquo-pcnta-amine CO(II) coinplex predominates in the absence of oxygen.The significance ofthis is clear, in view of the equilibrium~ C Q ( N H ~ ) ~ ( H ~ O ) + ~ + 0 2 + [(NH~)~CO-O~-CO(NH~)~]+~ + 2H28. (3)It is of interest to know whether oxygen is the only electroactive species in thepotential range 0 to - 1 V in the above equilibrium.Fig. 1 describes typical current against voltage curves measured in oxygensaturated ammoniacal solutions. Curve C is a voltammogram of oxygen reductionin the NH3/NH4N03 base electrolyte saturated with oxygen. The reduction ofoxygen on a Pt electrode in the above ammoniacal solutions is thus characterized bya single wave with a value of E3 = -0.24 17. In the presence of Co(n), two waves(waves 1 and 11) are observed.The first wave (wave I) has a similar value of E, asbefore and the half wave potential value of the second wave (wave 11) is -0.58 V.Voltammograms Al, A, and A3 (fig. 1) describing reduction in type A solutions[saturated with oxygen before adding Co(r1) ion] indicate that the total limiting currentdecreases as the concentration of CO(II) ion is increased. The opposite effect isobserved in typz B solutions [saturated with oxygen after the Co(11) addition] : thetotal limiting current increases as the Co(~r) ion concentration is increased (curves B1,13, and B3).The single wave of cathodic reduction of oxygen in 6.3 mol d n r 3 NH, anA . BETTELHEIM, M . FARAGGI, I . HODARA AND J . MANASSEN 1452 rnol d n ~ - ~ NH4N03 solutions is explained as a reduction involving the transfer of 4electrons.This was shown by a coulometric collecting charge at a controlledpotential of -0.6 V. The charge collected under these conditions was 2.8 C ascompared with the theoretical value of 0.73 C per electron. Similar results in acidsolutions were reported by Bockris and co-workers.'It should be noted that wave I appears in solution with and without the presenceof Co(rr) ion. Its potential is independent of the cation presence. This seems toindicate that this wave is related to the reduction of free oxygen.The dependence of the limiting current of wave I was plotted aga,inst the CO(II)ion coilcentration (fig. 2). In this figure, it is clearly demonstrated that, whcreas thet , ,-0.3 -0.6 -0.3voltage against s.c.e.FIG.1.---R.d.e. voltainniograms ( w = 340 r.p.m.) of 6.3 mol d ~ n - ~ NH3 and 2 mol dm-3 NH4N03oxygen saturated solutions. Curve C, no Co(r1j ion present; curves Al, A2 and A3, type Asolutions with 2, 4 and 8 mmol dm-3 Co(NO3j2 respectively ; curves B1, B2 and B3, type €3solutions with 2, 4 and 8 minol dm-3 CO(NO,)~ respectively.0.60 4 8[CO(IOl /mMFIG. 2.-The dependence of the limiting current of wave I on CO(NO,)~ concentration in 6.3 niol d1n-3NH3 and 2 mol dm-3 NH4N03 solutions : curve A1, type A air saturated solutions ; curve AZ,type A oxygen saturated solutions ; curve B1, type B air saturated solutions ; curve BZ, type B oxygensaturated solutions146 ELECTROREDUCTION OF 0 2 IN CO(II)+NH~limiting current in type A solutions decreases with the total Co(n) ion concentration,in type B solutions it has apparently a constant value.This strengthens the suggestionthat the first wave (wave I) is related to the free oxygen reduction. In the type Asolutions, the overall oxygen concentration is constant (and equal to the solubilityof oxygen in 6.3 mol dm-3 NH3 and 2 mol dm-3 NH4N03), therefore the productionof the peroxo complex decreases the free oxygen concentration and thus decreases thelimiting current. In the type B solutions, the free oxygen concentration is constantand thus one would expect a constant limiting current for the reduction of free oxygen.[peroxo] x 104/mol dm-3FIG. 3.--The dependence of the total limiting current on peroxo concentration for type B, air (curveBJ and oxygen (curve B,) saturated solutions.TABLE EQUILIBRIUM CONCENTRATIONS OF FREE OXYGEN AND OF THE PEROXO COMPLEX INTYPE A AND B SOLUTIONS CONTAINING 6.3 mol dm-3 NH3 AND 2 mol dm--3 NH4N03.type A solutions type B solutionsair oxygen air oxygen[Coltot.1021, beroxol 1021, [peroxol [Od, tperoxol [Od, Iperoxol/mmol dm-3 X lO-4/mol dm-3 x lO-4/mol dm-3 x lO-4/mol dm-3 x lO-4/mol dm-30 1.50 0 6.00 0 1.50 0 6.00 02 0.92 0.58 4.14 1.86 1.50 0.85 6.00 2.354 0.38 1.12 2.16 3.54 1.50 2.95 6.00 6.956 0.23 1.27 1.07 4.93 1.50 5.90 6.00 12.506.00 18.65 8 0.16 1.34 0.40 5.60 1.50 9.50In fig. 3, the total limiting current (wave I+wave 11) was plotted against theequilibrium concentrations of the peroxo complex. These concentrations, given intable 1, were calculated on the basis of Simplicio and Wilkin’s data for the equilibriumgiven in reaction (3) and :CO(NH~)~(H~O)+~ +NH3 + Co(NH3); +H,O (4)2Co(NH,): + 0 2 + [(NH~)~CO-O~-CO(NH~)~]+~ +2NH3. (5)The equilibrium constants of reactions (3), (4) and (5) are 1.6 x lo6 dm6 mok2,0.25 dm3 mol-1 and 2.5 x lo7, respectively.’ In view of the small concentrationchanges in the equilibrium components during the experiment, we assume that thereis no shift in the above equilibria, the voltage sweep being fast enough to preventdepletion of electroactive species by electrolysisA .BETTELHEIM, M. FARAGGI, I . HODARA AND J . MANASSEN 147Wave I1 appears only in solutions containing CO(II) ions. This fact together withthe linear correlation between the overall limiting current and the equilibrium peroxoconcentration suggests that wave I1 characterizes the reduction of the peroxocomplex. The extrapolated value ([peroxo] -+ 0) of the limiting current is the valueexpected for wave I in the absence of Co(11) ion (fig.1, curve C). The values obtainedin fig. 3 for air and oxygen saturated solutions are in agreement (within the experi-mental error) with the limiting current found for wave I in the above solutions.The limiting current for the r.d.e. system is given by :8iL = 0.62 nE;ACD2!3v-1i6~112where iL is the limiting current (expressed in A), n is the number of electrons, Fis theFaraday constant (in C mol-l), A is the electrode area (in cm2), C is the bulk con-centration (in mol ~ r n - ~ ) , D is the diffusion coefficient (in cm2 s-'), v is the kinematicviscosity (in cm2 s-l) and cr) is the rotating velocity (in rad s-l).From the aboveequation, it is expected that parallel linear curves will be obtained for air and oxygentype B saturated solutions (curves B1 and B2 respectively), the ratio iJC being aconstant value for a given electroactive species and a constant speed of rotation.For oxygen, the calculated value of the ratio iL/C (iL is taken from r.d.e. volt-ammograms and C is taken from table 1) is 0.88 A dm3 mol-l. For the peroxocomplex, this value calculated from the slope of the paraller linear curves B1 and B2(fig. 3) is 0.42 A dm3 mol-l. The experimental value of the ratio :nperoxoD&roxo = 0.48.As no, and Do, are known (no, = 4 and Doz = 2.6 x s-'),nperoxoD~eroxo = 1.68 xThe number of electrons involved in the reduction of the peroxo complex(NH3)5Co-0,-Co(NH3)5 could not be determined by our techniques (because offree oxygen reduction interference) as was done for the peroxo complexes of CO(II)ion and ethylenediamine and triethylenetramine as ligand~.~ However, assumingnperoxo = 1 and 2, the value of Dperoxo obtained is greater or equal to that of Do2.It is rather unlikely that the peroxo molecule, which has a greater size than theoxygen molecule, would have a similar diffusion coefficient.Assuming nperoxo = 4,then the value of Dperoxo is 8.6 x cm2 s-l. This value is to be compared with thevalue for the superoxo complex of CO(III) estimated in the literature to be 6.0 xcm2 s-l.l0The small value of the diffusion coefficient of the peroxo complex can explain thedecrease in the total limiting current with CO(II) ion addition in type A solutions :the increase in wave I1 (caused by the increase of peroxo concentration) is smallerthan the decrease of wave I (caused by the decrease of free oxygen concentration).Hence, there is a net decrease in total limiting current (curves A', A, and A3 infig.1). In type B solutions, the peroxo concentrations are high and the oxygenconcentration is constant when CO(II) ion is added. Hence, a total increase oflimiting current is observed (curves B1, B2 and B3 in fig. 1).THE RATE CONSTANT OF THE DECOMPOSITION OF THE PEROXO COMPLEXIt is known that CO(II) complexes lose their properties as oxygen carriers by aside reaction ; the peroxo binuclear complex dissociates to yield a mononuclearCO(III) complex :39(6) LCO-O,-COL + 2H+ + 2CO"'L + H202148 ELECTROREDUCTION OF O2 I N CO(II)+NH~The unknown decomposition rate of (NH3)sC~-02-C~(NH3)5 has been investi-gated using the different polarographic behaviour of the peroxo and the CO(III)amino complexes.When an oxygen saturated ammoniacal solution containing Co(11) ion is bubbledwith nitrogen, oxygen is expelled.The equilibrium, represented by reactions (3) and(5), is shifted towards the dissociation of the peroxo complex. The Co(11) complexesare not reduced in the potential range investigated (0 to - 1.0 V). The CO(III)complex(es) obtained via reaction (6) is the only electroactive species which could bereduced at the d.m.e.in the above potential range. Fig. 4 describes a typicalpolarogram of the CO(III) complex (E4 = -0.35 V). The rate of decomposition ofthe peroxo complex was determined by plotting log iL (iL being the limiting currentof the polarographic wave) against time of exposure to oxygen atmosphere (fig. 5).2 0.4-I IIvoltage against s.c.e.F~G. 4.--D.m.e. polarograms of Co(rrr) + NH3 complex produced after hh (curve A), 71 h (curve B)from the decomposition of [(NH3)5C~-02-C~(NH3)51'1.'\I I ItlhFIG. 5.-The time dependence of the polarographic limiting current for the Co(m)+ aiiiinonia complex.The reaction is first order with respect to the Co(n11) complex concentration, with arate constant of 3.0 x In contrast to the rapid oxygenation reaction whichyields the peroxo complex, reactions (3) and (5) with k3 = 2.1 x lo4 dm3 mo1-l s-I,kV3 = 69 s-l and k s - 1 x lo3 dm3 inol-1 s - I , ~ the decomposition of the oxygenatedcomplex to yield Co(rr1) is a slow process.Therefore, the decomposition reactiondoes not interfere in the measurements related to equilibrium (3).s-lA . BETTELHEIM, M. FARAGGI, 1. HODARA AND J . MANASSEN 149CONCLUSIONThe use of the complex [(NH3)5Co-02-Co(NH3)5]+4 increases the limitingcurrent of oxygen reduction without showing any decrease in overpotential. Thisresult can be explained as an increasing effect of the oxygen dissolving capacity of theammoniacal Co(n) solution. A similar effect has been described by Dinkevich andKsenzhek l2 in the Co(11) + histidine system.R. G. Wilkins, Bioinorg. Chem., 1970, 100, 111.k. H. Vogt, H. M. Faigenbaum and S. E. Wiberly, Chem. Rev., 1963, 63, 269.A. G. Sykes and A. J. Weil, Inorganic Reaction Mechanisms, Progress in Inorganic Chemistry,ed. J. 0. Edwards (Interscience, N.Y. 1970), vol. 13, p. 1.E. Bayer and P. Schretzmann, Structure and Bonding, ed. C . K. Jsrgensen (Springer Verlag,Berlin, 1967), vol. 2, p. 181.J. Simplicio and R. G. Wilkins, J. Amer. Chem. Suc., 1969, 91, 1325.L. Meites and H. C. Thomas, Advanced Analytical Chemistry (McGraw Hill, N.Y., 1958), p. 34.A. Damjanovic, M. A. Genshaw and J. O’M. Bockris, J. Electrochem. Soc., 1967,114,466.H. R. Thirsk and J. A. Harrison, A Guide to the Study of Electrode Kinetics (Academic Press,London, 1972), p. 83.A. Bettelheim, M. Faraggi, I. Hodara and J. Manassen, J.C.S. Faraday I, 1977,73,150.(Amer. Chem. SOC., Wash., D.C., 1968), no. 83, p. 79.F. E. Dinkevich and 0. S. Ksenzhek, Trudy Ukrain. Respub. Konf. Elektrokinr., 1973, 1, 39.lo M. Anbar and E. J. Hart, Radiation Chemistry, Advances in Chemistry Series, ed. R. F. Gouldl 1 M. S. Michailidis and R. B. Martin, J. Amer. Chem. Soc., 1969, 91,4683.(PAPER 6/529

ISSN:0300-9599    

DOI:10.1039/F19777300143

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Electroreduction of Cobalt-Amino Peroxo ComplexesPart 2.-The Reduction of Oxygen in the Co(II)-Ethylenediamine andCo(I1)-Triethylenetetramine SystemsBY ARMAND BETTELHEIM," M. FARAGGI, 1. HODARA AND J. MANASSEN tAtomic Energy Commission, Nuclear Research Centre-Negev, P.O.B. 9001,Beer-Sheva, IsraelReceived 19th March, 1976The cathodic reduction and the optical properties of the peroxo-complexes [LCO-O~--COL]+~with L = en (ethylenediamine) and L = trien (triethylenetetramine) have been studied. It wasfound that four electrons are involved in the reduction of the peroxo-complexes. The diffusioncoefficients of the above complexes were calculated to be 7.0 x cm2 s-l respectively.The redox potentials are -0.57 V and -0.50 V (us. s.c.e.) respectively. These complexes areunsuitable as catalysts for the cathodic reduction of oxygen because they have lower redox potentialsthan that of oxygen.A different behaviour was found in the cobalt-ethylenediamine system whenthe ratio [en] : [Co(n)] = 1. The redox potential of the complex formed in this case is - 0.17 Vand its optical spectrum showed two absorption bands (Amax at 350 and 310nm.) Therefore, itis suggested that a CO(III) en complex is formed, one which was found to be a suitable homogeneouscatalyst for the cathodic reduction of oxygen.and 8.8 xPeroxo complexes of Co(n)-ethylenediamine (en) and Co(I1)-triethylenetetramine(trien) have been prepared. The interaction between oxygen and CO(II) complexesof en and trien were studied by spectroscopic, potentiometric and kinetic r n e t h ~ d s .~ ~ ~The spectrum of the complex [(en)2Co-0,-Co(en)2]+4 is characterized by two ab-sorption bands : Amax = 355nm and A,,, = 270nm, both with an approximate extinctioncoefficient of 5 x lo3 dm3 mol-1 ~ m - l . ~ Those of the complex [trien Co-0,-Cotrien]+4 are : A,,, = 360 nm and A, = 220 nm with extinction coefficients of 6.4 x lo3and 1.5 x lo5 dm3 mol-1 cm-l respectively.6 From oxygen absorption and cryoscopymeasurements, it was concluded that the peroxo complexes are bin~clear.~~Kinetic studies indicate that the reaction of the CO(II) complexes and oxygen is firstorder with respect to oxygen.4- 9 9 lo Magnetic susceptibility measurements indicatethat the peroxo complexes are diamagnetic1 Miller and Wilkins assumed p hydroxobridged intermediates in the formation of the oxygen complex of Co(~r)-trien.~Also Michailidis and Martin have indicated that a p-hydroxo bridge may be presentin the oxygen complex of bis ethylenediamine CO(II).Stability constants of theoxygenated and oxygen-free complexes were found 2* using potentiometrictechniques.The increasing reactivity of molecular oxygen upon coordination (activation ofthe oxygen molecule) was suggested. According to Valentine,l three explanationsare possible :1. Coordinated oxygen being diamagnetic, reactions with diamagnetic substratesto form diamagnetic substrates are not hindered by the requirement for spinconservation.t present address : The Weizmann Institute, Rehovoth, Israel.15A .BETTELHEIM, M. FARAGGI, I . HODARA A N D J . MANASSEN 1512. The metal may hold the oxygen molecule and the substrate in a cis position,lowering the activation energy for the oxidation of the substrate.3. Coordinated O2 is, in most cases, partially reduced; increasing the electrondensity of the oxygen may activate it.In this paper, the Co(II)-en and Co(u)-trien systems were studied by electro-chemical methods. In view of the suggested activation mechanism, these systemsmight be used as possible catalysts for the cathodic reduction of oxygen in aqueoussolutions.EXPERIMENTALWater was triple distilled. Merck pro analysis CoCl2, Baker " analysed " trien andFluka " puriss " en were used without further purification. All other materials were ofanalytical grade.Matheson " extra dry " oxygen and " high purity " nitrogen were usedfor the saturation of the solutions.The working electrode for the coulometric measurements was a mercury pool ( A =20 cm2) or a platinum gauze ( A = 30 cm2). The electrochemical apparatus has beendescribed previously. Spectroscopic measurements were performed using a Cary 17spectropho tometer.The peroxo complexes were prepared by mixing 75 cm3 of water containing appropriateamounts of electrolyte with en or trien. These solutions were brought to pH 5 under oxygenbubbling. Co@) ions were added and the pH 5 adjusted by dropwise addition of 1 mol dm-3NaOH. After pH stabilization, the solutions were diluted to 100 cm3 in volumetric flasks.All potentials were measured against the s.c.e.as reference at 25 +O.l"C.RESULTSTHE CO(II)-EN SYSTEMPOLAROGRAPHYPolarography of the peroxo complex [(en>,C~-O~-Co~(en),]+~ in alkalinesolutions and in excess en shows a single polarographic wave with a half wavepotential of -0.57 V [fig. l(B)]. This is to be compared with the two polaro-graphic waves of oxygen saturated alkaline solutions not containing Co(n) ionIV against s.c.e.FIG. 1.-Polarograms of: (A) an oxygen saturated solution at pH 9 containing 1 mol dm-3 NaCI.(B) mol dm-3 peroxo complex [(en)zCo-02-Co(en)2]+4 and 1 mol dm-3 NaCl at pH 9.Polarogram B was recorded after removal of the free dissolved oxygenI52 ELECTROREDUCTION OF 0, I N C O ( I I ) + N H ~[fig. I(A)]. These waves are attributed to the reduction of O2 to hydrogen peroxideand to water.14 The single wave of the cathodic reduction of the peroxo complexis explained as a redaction involving the transfer of four electrons.This was shownby a coulometric collecting charge at a controlled potential of -0.9 V with a mercurypool as the working electrode. The charge collected for 25 pmol of the peroxocomplex was 12.7k0.2 C as compared with the theoretical value of 3.1 C per electron.Other pzroxo complexes of Co(11) behaving similarly have been investigated bySprieck.lcquation The diffusion polarographic current as given by the iniproved IlkovicThis equation differs from the usual Ilkovic equation by the term 1 +39 D3 f* nr*,which represents the influence of the electrode curvature. In this equation, id is thediffusion current (in PA); n, the number of electrons; f , the drop time (in seconds);D, the diffusion coefficient (in cm2 s-I); 712, the weight of the mercury flowing perunit time (in mg s-l) and C, the buIk concentration (in mol ~ m - ~ ) .For the peroxocomplex [(en)2Co-02 - C~(en),]+~, the value of the diffusion coefficient (D),calculated from the above equation, is 7.0 x cm2 s-I.ROTATING DISC ELECTRODE ( R . D.E.) EXPERIMENTSThe polarographic study shows that the peroxo complex in solutions where[en]/[Co(xr)] > 2, is reduced at a more negative potential than that of oxygen.Changes in the redox potential of the peroxo complex as function of the en concentra-tion at a constant value of CO(II) ion concentration were recorded by r.d.e.voltammo-grams.The redox potential of the yeroxo complex of CO(II) (which is partially at theCO(III) state) is expected t o shift towards that of oxygen, when the [en] : [Co(11)]ratio is decreased.17~ l8 Thus, Rock l7 stated that the redox potential of the @o(II~)complex is related to the thermodynamic stabilization of the CO(III) ions. Henneyet d . l S found thzt the potential shifts towards more negative values when the[en] : [CO(III)] ratio is increased.Fig. 2 shows the r.d.e. voltammograms obtained for [en]/[Co(~r)] = 2 (curve A)and for [en]/[Co(11)1 = 1 (curve B). Curve A shows the single wave of the pzroxoV against s.c.e.FIG. 2.-Pt -r.d.c. voltaminograim ( w = 340 r.p.m.) of : (A) lop3 tnol d n r 3 peroxo complex[(en)2Co-f2,-Co(en),]-4 and 1 rnoI d ~ r a - ~ NaCI at pH 9. (B) 2 x 1W3 mol dm-3 Co(III) en com-plex and 1 12201 dm-3 NaCl at pH 9.Voltaiixnograms were recorded after removal of the freedissolved oxygenA . BETTELHEIM, M. FARAGGI, 1. HODARA AND J . MANASSEN 153complex. In agreement with our spectroscopic and electrochemical results, the firstwave in curve B (curve B,) is attributed to the mononuclear salt of Co(rr1)-en. Thesecond wave (wave B,) is suggested to be due to H202 reduction, hydrogen peroxidebeing a product of the reaction of Co(rI)-en with oxygen (wave B2 appears at the samepotential as that of H20J :The half wave potentials of the various species are given in table 1.2Co(11)-en+0, +2H,O 3 2Co(r11)-en+H,O,+20H-. (1)TABLE 1 .-EXPERIMENTAL DATA OF VARIOUS CQ(1II) SPECIES AND OXYGENsystemEL no. of D X 106 experimenta 1/V againzt s.c.e.electrons ,kmz s- method[(NH~)~CO-O~-CO(NH~)~]+~ - 0.58 4 8.6 r.d.e.4 7.0 d.m.e.[trien Co-02--Co trien]+' - 0.50 4 8.8 d.m.e.Co(nI)eii -0.17 1 2.0 r.d.e.0 2 - 0.38 4 26 l4 r.d.e.[Cen)2Co-02 - C ~ ( e n ) ~ ] + ~ - 0.57In a separate experiment, a nitrogen-saturated solution of the Co(r1)-en complex(cquimolar concentrations) was oxidized electrolytically in the absence of oxygen :The oxidation was carried out at a controlled potential of +0.9 V on a Pt gauze asthe working electrode.Co(II)-en + Co(rrr)-en + e (2)SPECTRQSCOPIC MEASUREMENTSThe spectrum of the peroxo complex (en)2Co-02-Co(en)z is shown in fig. 3(curve A). It is similar to that given in the literat~re.~ When the [en]/[Co(rr)]ratio is reduced to 1 : 1, the spectrum obtained is shown in fig.3, curve B. It ischaracterized by two absorption bands, one at Amax = 350 nm and the other at Amax =310 nm. The spectrum obtained by electrolytic oxidation of a nitrogen saturatedsolution containing equimolar concentrations of Co(11) ions and en, as describedabove, has similar absorption bands (Amax at 350 and 310nm, fig. 3 curve C).Spectroscopic titratioii at II, = 355 nm of Co(11) ion oxygen-saturated solutions as afunction of en concentration shows a two step curve. The first occurs at a ratio of[en] : [Co(rr)] = 1 and the second at a ratio of 2. Thus it is suggested that twodifferent species are formed in the two [en] : [CO(II)] ratios.When the ratio is 2,the peroxo complex is formed. When it is 1 , the Co(rI1)-ethylenediamine complexis generated. Similar results have been recently reported by Bijl and De V r i e ~ . ~Moreover, acidifying the peroxo complex (pH = 2) liberates bound oxygen ashydrogen peroxide or free oxygen.6 Acidification causes the disappearance of theabsorption band at il = 350 nm. This is not the case when the ratio equals unity,no changes are observed upon acidifying to pH 2. This strengthens the abovesuggestion.THE CO(II)-TRIEN SYSTEMThe peroxo complex with trien as ligand ([trien Co-0,-Co t r i e ~ ~ ] + ~ ) shows thesame characteristics as found in the polarography of the peroxo complex with en asthe ligand. One polarographic wave is formed (E3 = -OSOV, table 1) and fourelectrons are involved in the complex reduction, as confirmed by constant potentialcouloinetry at -0.9 V.The reduction potential was found to be independent o154 ELECTROREDUCTION OF 0 2 I N CO(II)+NH,the ligand-to-Co(n) ratio. The limiting current of the polarographic wave for solu-tions containing CO(II) ions increased linearly with trien concentration. A constantcurrent value was obtained in solutions where [trien] 2 [CO(II)]. This is similar toresults obtained by spectroscopic methods in a similar system.lgThe 1 : 1 trien/Co(rr> +02 complex is polarographically equivalent to the 2 : 1en/Co(u)+O, complex. This similarity can be explained by the fact that at leastthree nitrogen atoms are needed for the formation of a stable cobalt peroxo complex.'In the present study, the ligands can supply four nitrogen atoms, by a single trien ord01I250 300I 1350 4A /nm0FIG.3.-U.V. spectra ( I = 1 cm) of (A) 2 xand 1 mol dm-3 NaCl at pH 9, (3) 4 xpH 9, (C) a nitrogen saturated solution containingmol dm-3 peroxo complex [(en)zCo--02-Co(en)]~+4mol dm-3 Co(1II) en complex and 1 mol dm-3 NaCl atmol dmd3 CoflII) en obtained by constantpotential electrolysis at +0.9 V (against s.c.e.) at a Pt-gauze (A = 30 cmz).by two en molecules. These results suggest that only liganded CO(II) ions react withoxygen to form the peroxo complex. Decreasing the ligand to CO(II) ratio causes adecrease of peroxo complex concentration; no other species are formed when[trien] : [CO(II)] < 1.Using the improved Ilkovic equation (I), the calculated valueof the diffusion coefficient of the peroxo complex of CO(II) ion with trien as ligand is8.8 x cm2 s-l.HOMOGENEOUS CATALYSIS OF OXYGEN CATHODIC REDUCTIONThe peroxo complexes of CO(II) with ammonia,l ethylenediamine and triethylene-tetramine are reduced at a more negative potential than that of oxygen (table 1).This makes them unsuitable as possible catalysts for oxygen reduction. However,the complex Co(m)-en formed in oxygen-saturated solutions containing equimolarconcentrations of Co(n) ions and en is reduced at a more positive potential than thatof oxygen (table 1). Moreover, in these solutions ([en] : [CO(II)] = 1), coulometricexperiments show that it is possible to keep a constant value of cathodic current at apotential where free dissolved oxygen is insignificantly reduced at the electrode(fig.4). At a potential of -0.2 V in solutions at pH = 9, the cathodic current iA . BETTELHEIM, M. FARAGGI, I . HODARA AND J. MANASSEN 155stable, even when the number of Coulombs recorded is 10 times the charge requiredto reduce all CO(III) species present in solution (10 C).The steady state current was plotted as a function of the potential. Fig. 5,curve A, shows the results obtained in oxygen saturated solutions at pH 9. Curve Bin fig. 5 represents the potentiostatic current against potential curve for solutionscontaining equimolar concentrations of Co(11) ions and en. At a current density of0.05 mA c r r 2 an overvoltage decrease of 200 mV is observed.Thus, this Co(II)-ensystem is a suitable homogeneous catalyst for the cathodic reduction of oxygen.0 ,. f6 34 52 70FIG. 4.-Coulometric plots of-0.2 V (against s.c.e.) and pHflhsolutions (50 cm3) continuously saturated with oxygen (bubbling) at9 containing : (A) 1 mol dm-3 NaCl ; (B) 2 x mol dm-3 Co(m) encomplex and 1 rnol dm-3 NaCl.r IV against s.c.e.FIG. 5.-Current density against potential curves with a Pt-gauze as the working electrode ( A =30 cm2) of solutions at pH 9 continuously saturated with oxygen (bubbling) and containing :(A) 1 mol dnr3 NaCl ; (B) 2 x rnol dm-3 Co(m) en complexland Ibniol dm-3 NaCl.DISCUSSIONThe diffusion coefficients, the number of electrons involved in the reduction andthe reduction potentials of the peroxo complexes [(NJ33),Co-0,-Co(NH3)5]+4, a[(en),Co--O,-C~(en),]+~ and [trien Co-02 -Co trier^]+^ as well as the complexCo(m)-en are summarized in table 1 and are compared to that of oxygen.A mechanism commonly mentioned in the literature is called " oxygen activa-tion ' ' .1 2 5 20* 21 This term means that oxygen bound in the complex is partiallyreduced. A partial electron transfer from the metal ion to the n* orbitals of theoxygen causes a negative polarization of the oxygen molecule.21 However, th156 ELECTROREDUCTION OF 0 2 I N CO(II)+NH~peroxo complexes we investigated are reduced at more negative potentials than thatof free oxygen, so that they cannot be used as homogeneous catalysts for oxygenreduction.The only catalytic effect in these cobalt complexes was found in the cobalt-ethylenediamine system when the ratio [en] : [CO(II)] = 1.In this catalytic cycle,the reducing agent (the electron from the electrode) reacts with the oxidized state,giving the reduced state. The reduced state of the catalyst then reacts with oxygenreducing it to hydrogen peroxide [reaction (l)] and regenerating the oxidized state ofthe catalyst to react with the primary reducing agent once again. Coulometricexperiments show that the steady state current obtained in oxygen-saturated solutionsis obtained after collecting a certain amount of charge. In the experimental set-updescribed in this study, this charge (which may depend on the cell geometry) wasabout 20 C .It is kiiown that the first step of oxygen reduction to produce the HOzradical :02+H++e 3 HQi (3)is unfavourable from thermodynamic considerations (E" = - 0.32 V).22 However,the two-equivalent reduction of oxygen to produce H202 is more favourable(E" = +0.68 V) :It is suggested that the coulometric results indicate that a constant current value isobserved after a steady state concentration of species is obtained. This species isreduced with two electrons :Q2+2H++2e -+ H202. (4)2Co(11r)en+2e -+= 2Co(11)en ( 5 )-0;- J. + 0 2L- [en CO(III)-O~---CO(III)~~]+~The species [en Co(rn)-0$--Co(rrr) en]+" seems to be an unstable intermediate incontrast to the well known stable peroxo coniplex [(en)2Co(~r~)-Qq--Co(~~~)(en)2]+4.A. G.Sykes and J. A. Weil in Inorganic Reaction Mechanisms, Progress in Inorganic C/iemistry,ed. J. 0. Edwards (Interscience, N.Y., 1970), vol. 13, p. 1 .R. Nakon and A. E. Martell, J. Inorg. Nuclear Cheni., 1972, 34, 1365.R. Nakon and A. E. Martell, J. Amer. Chem. SOC., 1972, 94, 3026.F. Miller and R. G. Wilkins, J. Amer. Chenz. SOC., 1970, 92, 2687.P. Bijl and G. De Vries, J.C.S. Dalton, 1972, 303.S. Fallab, Chimia, 1970, 24, 76.R. S. Nakon, Ph. D. Thesis (Texas A and M University, 1971).S. G. Abrahamson, Ph.D. Thesis (University of Idaho, 1964).J. Simplicio and R. G. Wilkins, J. Amer. Chem. SOC., 1967, 89, 6092.lo F. Miller, J. Simplicio and R. G. Wilkins, J. Amer. Chem. Soc., 1969, 91, 1962.l1 M. S. Michailidis and R. B. Martin, J. Amer. Clzem. Suc., 1969, 91,4683.l2 J. S. Valentine, Chem. Rev., 1973, 73, 235.l3 A. Bettelheim, M. Faraggi, I. Kodara and J. Manassen, J.C.S. Faraduy I , 1977,73,143.l4 J. M. Kolthoff and J. J. Lingane, Polarography (Interscience, N.Y., 1952), vol. I, P. 105.l5 T. Sprieck, Ph.D. Thesis (University of Nebraska-Lincoln, 1972).l6 Ref. (14), p. 44.l7 P. A. Rock, Inorg. Chem., 1968,7, 837.l 9 A. Bondoli and V. Carunchio, J. Iizorg. Nuclear Chem., 1972, 34, 3491.2o G. Henrici Olive and S. Oliv6, Angew. Chem. Internat. Edn, 1974, 13, 29.22 P. Georgz in Oxidases and Reluted Redox Systems, ed. T. E. King (John Wiley, N.Y., 19651,R. C. Henney, H. F. Holtzclaw Jr. and R. C. Larson, J. Electroanalyt. Clzem., 1967, 14, 435.H. Alt, H. Binder and G. Sandstede, J. Catalysis, 1973, 28, 8.vol. 1, p. 3.(PAPER 6/530

ISSN:0300-9599    

DOI:10.1039/F19777300150

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Spectrophotometric Investigations in Aqueous Solutionat Elevated TemperaturesThe Effect of Temperature on the Ionisation Constant of the 2,2' Bipyridyl CationBY DAVID €3. BUISSON-~ AND ROGER J. IRVISG'~Department of Chemistry, University of Surrey, Guild ford, Surrey GU2 5XHReceived 30th April, 1976The ionisation constant, Ka, of the 2,2' bipyridyl cation has been determined at various tempera-tures between 298 and 473 K from spectrophotometric data. The results, expressed as a functionof absolute temperature, are given by the equationpKa = (968.58/T)+0.735 53+0.001 131 1 T.The increase in ionisation with increasing temperature is attributed to increasing solvation of thehydronium ion relative to the 2,2' bipyridyl cation.The changes of enthalpy, entropy and heat capacity for the ionisation reaction have been calculatedfrom the temperature coefficients of the ionisation constant at each of the experimental temperatures.'There have been a number of determinations of the acid dissociation constant(K,) of thc 2,2' bipyridyl cation (Bipy H+) under a variety of experimental csndi-tions 2 v but only up to a temperature of 323 K4 A knowledge of the behaviourof compounds such as bipyridyl in water at high temperatures is desirable becauseof their potential use as ligands to chelate metal ions which could otherwise causeprobleins in high pressure steam generating plants.This paper reports the determination of K, of Bipy H+ over the temperaturerange 298-473 K.EXPERIMENTALAnalytical grade 2,2' bipyridyl (Koch Light) and AnalaR perchloric acid were usedwithout further purification, water was twice aistilled and deionised.For determinations in the range 298-333 K a Unicam SP3000 spectrophotometer fittedwith a 1 cm flow-through cell and thermostatted cell block was used.In the temperaturerange 353-373 K a Unicam SP1800 U.V. spectrophotometer fitted for digital readout inabsorbance was used. The temperature was maintained to kO.5"C using a thermostattedelectrically heated aluminium block. Matched 1 cm Spectrosil cells were used in each ofthese series of experiments.At temperatures above 373 K spectroscopic measurements were carried out using a hightemperature, Teflon lined cell between quartz windows, heated in an aluminium furnace asdescribed pre~iously.~ The temperature in the cell, which was controlled to kl"C, wasmeasured by means of an iron-constantan thermocouple which extended to the surface ofihe inner cell.In a typical series of experiments at temperatures below 373 K one cell contained waterand the other a series of solutions of varying hydrogen ion cencentration (adjusted usingAnalaR perchloric acid) suitable for the determination of the ionisation constant.Afteran equilibration period the absorbance of each solution was measured and corrected forthe appropriate cell blank. The extinction coefficient of the Bipy was determined for usepresent address : Chemistry Division, DSIR, Private Bag, Pstone, New Zealand.15158 SPECTROPHOTOMETRY AT ELEVATED TEMPERATURESin calculations rather than HBipy+ as experimental determinations showed that withincreasing acid concentrations there was a progressive shift in the spectral peaks of a solutionof 2,2’ bipyridyl.This has been attributed by McBrycie to a second stage protonation of2,2’ bipyridyl. Measurements in the high temperature cell entailed measurements of theseries of solutions only : it was not necessary to know the background absorbance of thecell and optical path length provided these were constant within very small limits from oneexperiment to the next. A level of reproducibility of 0.5-1 % was maintained over the wholetemperature range. Variations in pressure of as much as 100 bar had a negligible effect onabsorbance readings, so for convenience the pressure was maintained at just above thesaturation vapour pressure of water at the appropriate temperature.RESULTS AND DISCUSSIONThe equilibrium for the dissociation of HBipy+ may be writtenH Bipy+ + H+ + Bipy.HenceIn order to avoid the difficulty of estimating activity coefficients, the present workhas been carried out in solutions having ionic strengths of the order of where itis reasonable to assume, within experimental error, that all activity coefficients areunity.Thus K, was considered to be equal to K,.The calculation of K, was based on the equations, due to Maroni and Calmanand revised by Albert and Serjeant as follows :where D is the absorbance of a solution of Bipy of hydrogen ion concentration H+.Letting EO and 8, represent the extinction coefficients of Bipy and BipyH+ respectivelyat wavelength A thenDo = c o d and D, = E,CZwhere c is the total concentration of 2,2’ bipyridyl and Zis the optical path length in cm.Usingthis value of D, and eqn (2), pKa is calculated for each hydrogen ion concentrationand an average value of pK, determined.In view of the discussion of Quist andMarshall the molar concentration scale was used throughout. Concentrations of2,2’ bipyridyl and perchloric acid were, therefore, corrected for expansion of thesolutions on heating assuming that the solutions were sufficiently dilute SO as toexpand as pure water.l0. l1 The determinations of pK, were carried out at a numberof different wavelengths and at least two parallel determinations were carried out ateach temperature.The experimental data were incorporated in a least squares computer programand processed on an ICL 1905F computer.Absorbance values and the results ofcalculations to determine Ka at 298 K and 423 K are given in table 1. These aretypical calculations at widely different temperatures. Table 2 contains values of K8calculated for the full temperature range 298 K (pKa = 4.323) to 473 K (PKa = 3.32).Eqn (3) l2 in the form proposed by Harned and Robinson,13 expresses the pK, valuesas a function of absolute temperature :From eqn (1) a plot of D against (D-D,)/[H+] has an intercept D,.pKa = A/T-B+CT (3D. H. BUISSON AND R. J . IRVING 159where A = 968.58, B = -0.735 53 and C = 0.001 131 1. Thermodynamic quan-tities for the dissociation were computed from the coefficients of eqn (3) using thefollowing :AGO = 2.3026 R ( A - BT+ CT2)AHo = 2.3026 R (A-CT2)(4)(5)AS" = 2.3026 R (B-2CT)AC; = 2.3026 R (-ZCT).TABLE ACIDITY CONSTANT OF 2,2' BIPYRIDYL CATION AT 298 AND 423 K2 = 310.0 nm ; c = 6 .0 ~ mol dmA3 ; Do = 0.0058T = 298 K D , = 0.750104[HC104]/mol dm-3 D 104[H+]/mol dm-3 M a 1 0 5 ~ ~1.960 0.572 1.502 4.323 4.7482.450 0.605 1.965 4.321 4.7723.430 0.646 2.91 1 4.326 4.7264.900 0.678 4.354 4.329 4.6829.800 0.71 3 9.219 4.313 4.861average PKa = 4.322 apKa = 0.005average Ka = 4.785 x aKa = 0.066~ lo5A, = 310.0 nm ; c = 6.0 x mol dm-3 ; Do = 0.0203T = 423K D , = 0.7652.082 0.280 1.720 3.492 32.203.644 0.394 3.077 3.514 30.625.205 0.456 4.461 3.499 31.706.767 0.501 5.861 3.492 32.2210.41 0.573 9.158 3.497 31.84average PKa = 3.499 up& = 0.009average Ka = 31.72 x UKa = 0.65 xThese are also included in table 2.It has been assumed that the pressure remainsconstant over the whole temperature range as the effect it would have on the thermo-dynamic constants would be expected to be small.TABLE 2.-THERMODYNAMIC CONSTANTS OF THE DISSOCIATION OF THE 2,2' BIPYRIDYL CATIONPKS PKU AG" AH" AS" A&temp/K lO4Ka (expt) OpKa (calc) /kJ mol-1 /kJ mol-1 /J K-1 mol-1 /J K-1 mol-12983083183383593803984234484730.47580.59420.72731.0391.4451.8912.373.174.054.784.3234.2264.1383.983.843.723.623.503.393.320.0050.0050.0050.010.010.010.010.010.010.014.3214.2274.1403.983.853.713.623.503.403.3224.7 _+ 0.0125.0 f 0.0125.2 f 0.0125.8 -t 0.0126.4 -t 0.0127.1 k 0.0127.6 -t 0.0128.4 k 0.0129.2 k 0.0130.1 & 0.0216.6-tO.0416.5 k 0.0416.4 k 0.0316.1 & 0.1015.8 f 0.0715.4 f 0.0515.1 k0.0714.7k 0.1014.2 f 0.2013.7k0.2- 27.0 & 0.1- 27.4 & 0.1- 27.9 f 0.1- 28.7 f 0.3- 29.7 -t 0.2-30.6k0.1-31.3k0.2- 32.4 f 0.3- 33.5 & 0.4- 34.6 & 0.5- 12.9 & 0.4-13.4f0.4-13.8k0.4-14.7t-2-15.652-16.5+2-17.3k4- 18.3 f 5- 19.4k 5-20.5f160 SPECTROPHOTOMETRY AT ELEVATED TEMPERATURESComparison of the pK,'s in table 2 with other data is not possible as measurementshave not been attcmpted before on 2,2' bipyridyl at elevated temperatures.Potentio-metric neasurements, however, at 298 K and at ionic strengths ( I ) of 0.025 and" extrapolated to zero " gave pK,'s of 4.33 l4 and 4.35 respectively and a spectro-photomeirk determination at an I of 0.01 gave a pK, OF 4.34 ; I s all in agreement withthe value obtained in this study. Calorimetric studies at 293 K ( I = 0.1) and 303 K( I = 1.0) gave values of AH" of 15.3 l 5 and 16.8k2.1 l7 kJ mol-1 respectivelycompared with values of 16.7 and 16.6 kJ m01-~ calculated using eqn (5) and AS'of - 34.3 l6 J K-' mol-1 compared with -25.1 J 3C-l mob1 calculated using eqn (6).The plot of AHagainst TAS" shown in fig. 1 is a straight line and is an excelleiitexample for a single compound of tbe so called " Compensation Law ".Theimportance of the concept of this linear enthalpy-entropy effect was emphasized byHaanmett.' * It has been proposed that the major source of this effect of compensationin solutions is attributable to solvation changes.lg The fact that the plot in fig. 1is a straight line shows that the same principles apply to a single compound over arange of temperatures, and lends support to the explanation of the " compensationlaw * ' in ternis o f solvation, which in this case is a function of temperature.1.71.63 - I0 E2dt 1.5 2L,\I.?\I I I I I t I 1 0- TAS/J mol-'FIG. 1.-Variation of AH" with TAS" for the ionisation of the 2,2' bipyridyl cation.The process of ionisation is usually divided into two parts, one, the reaction part,a function of the solute and the other, the hydration part, a function o f the solvent.20In ionisation reactions Ives and Marsden 2o suggested that the enthalpy and entropyof hydration make the major contribution to the total AH" and AS" of the reactionand hence the coinpensation law is believed to have its main application to reactionswhich differ from each other principally in the extent of solvation changes whichaccompany them.For an isoelectric process a plot of -log K, against 1/T will be a straight lineassuming the "reaction part " work done in the proton transfer is independent oftemperature, and the hydration part work is zero or close to zero.21 Such a plotshown in fig.2 is a straight line indicating that these assumptions are justifiedD .H . BUISSON AND R. J . IRVINGI _ _-2 I I2.5 3.0 3.5d2 .clo3 KITFIG. 2.-Variation of log Ka with 1/T for the ionisation of the 2,2' bipyridyl cation.000I I I I2.2 2.L 2.6 2.0161lo2 DklFIG, 3.-Variation of TpKa with as derived from the Born equation AG,l = B+A/&(T) forthe cations of the following: aminopyrine 2 2 x , 2,2' bipyridyl (this work) 0, aniline (in aqueous 220, and methanol + water 24 0 mixtures), and 4 aminoantipyrine 22 + .1-162 SPECTROPHOTOMETRY AT ELEVATED TEMPERATURESFor many reactions the electrostatic or hydration contribution to the free energy(AG,,) of dissociation can be expressed in terms of the Born or Bjerrum equationswhere Dk is the dielectric constant at temperature T and A and B are constants.Hence, over a variable temperature range there should be a linear relationshipbetween TpKa and l / D k .Fig.3 shows plots of TpKa against l / D k for a number of isoelectric ionisations.Over a relatively small temperature range 288-323 K TpK, against l / D k is very closeto a straight line for anilinium, 4-aminoantipyrine, aminopyrine 22 and 2,2' bipyridylbut over the full temperature range (298-473 K) the plot for the latter substance showsa marked curvature. There are no studies over a comparable temperature rangefor similar compounds but, through the use of mixed solvents, the dielectric constant(Dk) can be varied over a similar range to that covered by the temperature change.Thus for water+methanol mixtures at 25"C, Dk changes from 78 in pure water to36.8 in 10 % water+%) % methanol.At 473 K water has a D, of 3 4 . C ~ ~ ~ Acomparison can be made of the pKa of the anilinium ion of 4.45 in 20 % methanol/80 % water 24 with a Dk of 71 and the pK, of 4.25 of the anilinium ion in water at319 K ( D , = 71) interpolated using eqn (3).The difference in slope of the plots of TpKa against l/Dk for the anilinium ion,where the change in one case is due to variation of Dk with temperature and in theother with variation of solvent composition, is largely due to selective hydration inthe latter case so that although comparisons can be made, a detailed analysis of thedifference would be fruitless.We thank the Central Electricity Generating Board for financial support of thiswork.Previous paper in this series.A. W. L. Dudeney and R. J. Irving, J.C.S. Faraday I, 1975,71, 1215.Stability Constants, Special Publication No. 17 (The Chemical Society, London, 1964).Stability Constants, Supplement No. 1, Special Publication 25 (The Chemical Society, London,1971).R. Nasanen, Suomen Kemi., 1955, 28, 161.R. D. Alexander, A. W. L. Dudeney and R. J. Irving, J. Phys. E, 1974,7,522.W. A. E. McBryde, Canad. J .Chem., 1965, 43,3472.A. Albert and E. P. Serjeant, The Determination ofIonisation Constants (Chapman and Hall,London, 2nd edn., 1971).A. S. Quist and W. L. Marshall, J, Phys. Chem., 1968, 72, 684.lo R. E. Mesmer, F. H. Sweeton, B. F. Hitch and C. F. Baes, Proc. Int. Conf. High Temp. HighPress. Electrochem. in Aq. Soh. (University of Surrey, Guildford, 1973).l1 G. S. Kell, in Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, 49thedn., 1968).l 2 The constants were calculated by fitting a set of data points as a series of Chebyshev poly-nomials : E. Stiefel, Numerical Methods of Chebyshev Approximation in On NumericalApproximation ed. R. E. Langer (U. of Wisconsin Press, Madison, 1959).' P. Maroni and J. P. Calman, Bull. SOC. Chim. France, 1964, 519.l3 H. S. Harned and R. A. Robinson, Trans Faraday Soc., 1940, 36,973.l4 J. H. Baxendale and P. George, Trans. Faraday SOC., 1950, 46, 55.l5 M. T. Falqui, Gazetta, 1958, 88, 57.l6 G. Anderegg, Helv. Chim. Acta, 1963, 46, 2813.l7 R. L. Davies and K. W. Dunning, J. Chem. Sac., 1965, 4168.l8 L. P. Hammett, Trans. Faraday SOC., 1938, 34, 156.l9 K. J. Laidler, Trans. Faraday SOC., 1959, 55, 1725.2o D. J. G. Ives and P. D. Marsden, J. Chem. Suc., 1965, 649D. H. BUISSON AND R . J . IRVING 16321 R. W. Gurney, Ionic Processes in Solution (Dover Publications, New York, 1962).2 2 Data taken from F. Kopecky, M. Pesak and J. Celechovsky, COIL Czech. Chem. Camm.,23 G. C . Akeslof and H. I. Oshry, J. Arner. Chern. SOC., 1950,72,2844.1970, 35, 576.R. A. Robinson and R. H. Stokes, EZectroZyte Solution (Butterworth, London, 1959).(PAPER 6/833

ISSN:0300-9599    

DOI:10.1039/F19777300157

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Kinetics of Methylene Addition to cis- and trans-But-2-eneFurther Evidence for the Energy Separation between Triplet and Singlet MtlthyleneBY HENRY M. FREY* AND GORDON J. KENNEDYChemistry Department, The University of Reading, Whiteknights,Reading, Berkshire, RG6 2ADReceived 3rd June, 1976The reactions of triplet and singlet methylene with cis- and trans-but-2-ene have been studiedover the temperature range 350-473 K. The results yield a value of (36.5& 3.2) kJ mol-' for theenergy separation between singlet and triplet methylene, and provide further confirmation of theassumption that singlet methylene reactions with hydrocarbons proceed with activation energiesclose to zero. Previous evidence for the similar reactivities of triplet methylene and the methylradical receives additional support.Recent theoretical calculations of the energy separation between the triplet (3B1)and the singlet (lA,) states of methylene lead to a value of (4658) kJ 11101-l.Areinterpretation of earlier experimental data yielded a lower limit of 34 kJ mol-Ifor this separation, in sharp contrast to the much smaller values of 4-10 kJ 11101-1derived earlier.3 In a preliminary report of this work a value of 38 kJ mol-' wasobtained. The additional studies reported here provide further confirmation of thisvalue.EXPERIMENTALMATERIALSKeten was prepared by the pyrolysis of acetic anhydride and purified by several trap-to-trap distillations from -130 to -160°C. It was stored as a gas at pressures below100 Torr in blackened glass vessels.It was degassed before each run at - 196°C.Nitrogen (B.O.C. oxygen free grade) was used without purification.Cis-but-Zene and trans-but-Zene (Matheson Instrument Grade) were better than 99 %pure and were used without further purification.APPARATUSA conventional high vacuum line was used for all gas handling. Teflon-glass stopcockswere used throughout to minimise absorption problems.All photolyses were carried out in a Pyrex reaction cell using the unfiltered output of anOsram HBO 200 W super pressure mercury lamp. The cell was thermostatted in analuminium furnace. Temperature variations over the cell surface were less than +_ 1°C fromthe mean temperature of the cell. Temperature measurements were made using chromel-alumel thermocouples.ANALYSISAll quantitative analyses were by gas chromatography, using a Perkin Elmer 452 gaschromatograph with a flame ionisation detector.A 100m PPG capillary column at 0°Cwas used. The retention times of all the products of interest were determined from puresamples. The detector response to the products, all C5 hydrocarbons, was assumed to beequal. The product ratios were determined by peak height measurements, corrected forretention times.16H . M. FREY AND G . J . KENNEDY 165PROCEDUREPhotolysis mixtures consisted of keten, cis- or trans-but-2-ene and nitrogen in the ratio1 : 2 : 30. Total pressures were in the range 600-700 Torr. A few experiments were carriedout using a ratio 1 : 2 : 200. The mixtures were photolysed and the non-condensable gasesremoved at - 196°C.Most runs yielded sufficient products for two analyses ; for all runsreported, the product ratios for duplicate analyses were reproducible to better than _f5 %.The product ratios were reproducible to & 10 % from separate runs under identical conditions.RESULTSThe following reaction scheme represents the important processes occurring :A vCH2CO --+ CH2 + CO3CH, + M + lCH2 + M3CH2 + cis-but-2-ene -+ cis- + trans-dimethyl cyclopropane(CB2) (DMCP)'CHz + CB2 + cis-DMCPlCH2 + CB2 -+ 2-methylbut-2-ene (2MB2)lCH2 + CB2 --+ cis-pent-2-ene (CP2)3CH2 + CB2 -+ CH3- + (butenyl).3CH2 + trans-but-2-ene (TB2) --+ cis- + trans-DMCP' CHz + TB2 --+ trans-DMCPlCHz +TB2 -+ 2MB2'CH, + TB2 -+ trans-pent-2-ene (TP2)3CH2 +TB2 -+ CH3- + (butenyl).CH3= + (butenyl).--+ 3-methylbut-1-ene (3MBl)CH3- + (butenyl). + CP2CH3- + (butenyl). -+ TP2CH3* + CH3- -+ ethane2(butenyl)* -+ C8 hydrocarbons.On the assumption, discussed below, that reactions (2) and ( - 2 ) maintain anequilibrium ratio of singlet to triplet methylene in the presence of a thirty-fold excessQf inert gas the following relations may be derived :log[(cis-DMCP/trarzs-DMCP) - 0.301 = log(O.43~f~~/A~~) -(AEZ - E3,)/2.303 RT (1)(AE2 -E3,)/2.303 RT (2)andlog[(traizs-DMCP/ciDMCP) - 3.401 = log( 1 .45A4b/A 3b) -where AE, is the energy separation between the two spin states of methylene, E3aand EBb are the energies of activation of reactions (3a) and (3b) respectively and A3a,A3b, A4a and A4, are the Arrhenius pre-exponential factors for reactions (3a), (3b),(4a) and (4b) respectively. In the derivation of relations (1) and (2) the same valuefor the ratio (trans-DMCPlcis-DMCP) has been assumed in reactions (3a) and (3b).The value (3.40) for this isomer ratio has been taken from Montague's study of th166 KINETICS OF METHYLENE ADDITIONmercury photosensitised isomerisation of 3-methylb~t-l-ene.~ Thus the 1.h.s.in eqn(1) and (2) are corrected for the fraction of stereospecific product arising from thetriplet reactions (3a) and (3b) respectively. It has also been assumed that the singletaddition reactions (4a) and (4b) proceed with zero activation energies. Plots of theleft hand sides of eqn (1) and (2) against 1/T are shown in fig.1.103 KITFIG. 1 .-Ratio of geometric isomers of 1,2-dimethyl-cyclopropane as a function of temperature.0, Using CB2 (1.h. axis): A, using TB2 (r.h. axis).Accepting the value of 1.39 for the ratios(TP2/CP2) produced by reactions (9)and (10) the contribution from triplet reaction to the product CP2 in the CB2 systemand to the product TP2 in the TB2 system may be separated from the singlet contri-bution to these products arising from reactions (6a) and (6b) : the two contributions tothese products will be designated s- and t-CP2 and TP2. The triplet contribution tocis-DMCP (CB2 system) and to trans-DMCP (TB2 system) may be separated fromthe yields of these products arising from the singlet reactions (4a) and (4b) : the twocontributions to the total yield of these products may be similarly distinguished.According to the reaction scheme above 2MB2 arises only from the singlet reactions(5a) and (5b).The following relations may then be derived for the CB2 system:~o~(s-CP~/S-C~S-DMCP) = log(A Ga/A4J - (E6a - E,,)/2.303 RT (3)log(2MB2/s-cis-DMCP) = - (Esa- E4a)/2.303 RT. (4)Analogous relations may be derived for the TB2 system.Representative data for the temperature dependence of the ratios 2MB2/s-cis-DMCP and s-CP2/s-cis-DMCP, (CB2 system) and 2MB2ls-trans-DMCP and s-TP2/s-trans-DMCP, (TB2 system) are shown in table 1. The data indicate no systematicvariation of these product ratios with temperature.103 KIT2.302.412.472.522.572.632.742.86TABLE 1.-PRODUCT RATIOS AS A FUNCTION OF TEMPERATURE2MBZ/s-cis-DMCP s-CP2/s-cis-DMCP ~MBZ~S-~~U~S-DMCP S-TPZ~S-~~U~S-DMCP0.380.330.340.300.320.310.3 10.300.740.700.780.710.720.700.690.270.200.230.180.880.840.830.8H .M. FREY A N D G . J . KENNEDY 167Adding t-cis-DMCP to the measured trans-DMCP in the CB2 system gives thetotal yield of reaction (3a); the yield of reaction (3b) in the TB2 system may besimilarly determined. If is is assumed that the activation energies of the radical-radical reactions (8)-(12) are close to zero the following relation may be derived forthe CB2 system :An analogous relation may be derived for the TB2 system. Plots of the left handsides of these equations are shown in fig. 2.log 3MB1 /(t-cis-DMCP+ trans-DMCP) = log(A,,/A,,) - (E,,-E3,)/2.303 RT.( 5 )L103 KITFIG. 2.-Ratio of 3-methylbut-1-ene to t-1,2-dimethylcyclopropane as a function of temperature.In order to evaluate AE, from the values of (AEz - E3,) and (A& - E3J given byeqn (1) and (2) we have previously assumed that E3, and E3b are equal to theexperimentally determined activation energies for methyl radical addition to CB2and TB2 respectively. If the additional assumption is made that A3, and A3b areequal to the A factors for methyl radical addition to the two olefins the evaluation ofthe ratios (A4JA3,) and (A4JASb) on the basis of eqn (1) and (2) permits an evaluationof A4, and A4b as a fraction of the collisional rate.,,The values of the parameters derived from the above analysis are summarised intable 2.0, Using CB2 : A, using TB2.TABLE 2.-ACTIVATION ENERGY DIFFERENCES AND A-FACTOR RATIOSA-factor ratios activation energy differences/kJ mol-1AE,-E3, = 5.3k0.2 ' 9 bA E z - E3b = 3.450.5a AE2 is the energy separation between the two spin states ; if Esa and E3b are assumed to be(30.6 f 2.0) kJ mol-I and (33.8 k 2.0) kJ mol-l respectively, then values of (35.9 k 2.1) kJ mol-I and(37.252.5) kJ mol-l for AE2 result.The mean value of AE2 from the two systems is thus (36.523.2) kJ mol-1 (see text) ; C if values of dm3 mol-1 s-I are assumedfor AJa and A3b respectively, values of 5 . 6 ~ for the ratios of A4a and A4brespectively to the collisional rate result.dm3 mol-I s-' andand 6.8 168 KINETICS OF METHYLENE ADDITIONDISCUSSIONIt is well known that the photolysis of keten (1) at wavelengths shorter than366nm produces methylene in both triplet and singlet states, the latter spin stateiiicseasingly predominating at shorter wavelengths.We assume, on the basis ofC a d s work,l0 that in the presence of a thirtyfold excess of nitrogen the non-equilibrium ratio of the spin states produced by (1) is brought to equilibrium by theinter-system crossing reaction (2) and (-2) and, thus, that the subsequent reactions(3)-(12) involve equilibrium populations of the two spin states. Runs carried out inthe presence of a hundred-fold excess of nitrogen gave product distributions identicalto those reported using a thirtyfold excess, confirming this assumption.Though the products of reactions (3a)-(6a) and (3b)-(6b) are chemically activatedupon formation, there is ample evidence from other work that the half-pressuresfor stabilisation of the hot molecules are 70 Torr or less.Thus at the pressures usedin this work (600-700 Torr), chemically activated decoinpositioiis and isomerisationsof the products of reactions (3n)-(6a) and (3b)-(6b) will not occur to a significant extent.has shown that the isomer ratio (trans-DMCPlcis-DMCP) arisingfrom the ring closure of the biradical initially formed in reactions (3a) and (3b) ispressure-dependent. If it is assumed that the triplet biradical is in conformationalequilibrium at each energy level during collisional deactivation, then the pressuredependence of the isomer ratio will reflect the pressure dependence of the meanenergy level from which the final deactivating collision occurs.On the basis of thisinterpretation the initial excess energy of the biradical is unimportant and the tempera-ture dependence of the ratio is unlikely to be strong. We have thus used the value3.4 for the product ratio (trans-DMCPlcis-DMCP) arising from reactions (3a) and(3b), as determined by Montague for the pressure range of this study.Since it is known that the activation energies for hydrogen abstraction from cis-and trans-but-2-ene by methyl radicals are similar to the activation energies foraddition, on the basis of the similar reactivities of triplet methylene and the methylradical discussed below, reactions (7a) and (7b) are expected to occur at ratescomparable to those of reactions (3a) and (3b) respectively. The presence of ethanein the product mixture is evidence for methyl radical participation and, as notedabove, it is unlikely to be produced in significant amounts by decomposition of thebiradical intermediate of reactions (3a) and (3b) in the pressure range of this study.The addition of 10 % of oxygen to the reactant mixture suppresses completely theproduction of ethane and 3MBl in both the CB2 and the TB2 systems, TP2 in theCB2 system and CP2 in the TB2 system.Since oxygen is known to suppress thereactions of triplet methylene very efficiently this further confirms that the abovescheme represents all the significant reactions occurring in the two systems.We thus derive values of (36+2) and (3712) kJ mol-1 from the CB2 and TB2systems respectively for the energy separation between singlet and triplet methylene.These values are in good agreement both with the results of recent theoreticalcalculations and with the experimental results of Hase et a2.,l2 Simons and Curry l3and Lahmani.14 The key difference between our interpretation of these systems andthe earlier interpretations which led to very much lower values for the energyseparation is our assumption that collisional reactivation of the triplet to the singlet,reaction (2), is significant.Thus, in the presence of a sufficient excess of inert gas,the reactions of an equilibrium population ratio of the two spin states can be studied.That earlier work reveals the presence of insertion products in the presence ofan excess of inert gas sufficient lo, l 6 to deactivate the singlet quantitatively to thetriplet is evidence for the occurrence of reaction (2).That a substantial change inMontaguH . M. FREY ,4ND G . 3 . KENNEDY 169the inert gas/substrate ratio produces no change in the product ratios, as reportedabove, is evidence that an equilibrium ratio of the two spin states is being studicd.The major assumption made in the derivation of the above values is the use ofArrhenius parameters for triplet methylene derived from analogous reactions of themethyl radical. The evidence for the validity of this assumption is less direct.However, on the basis of this assumption we have derived values of the r2iiosA4,/collision rate and A,,/collision rate which are in good agreement with the vaiueof 5 x for the irrsertion of singletmethylene into methane.The values derived for the activation energy differecee(E3,-&J viz., (2.0-)0.7) kJ mol-', for addition to the two olefins and forthedifferences(E7a-E3u) and (E,h-E3b) viz., 5 and 10 kJ mol-1 respectively are of comparablemagnitude to the relative activation energies determined * for the analogous methylradical reactions. The magnitudes of these assumed activation energies for thetriplet are also in general agreement with the results of Carr's BEBOFinally, Lahmani's result of (3 1.4f 3.0) kJ mol-1 for the energy separation is derivedfrom an experimentally determined rate ratio of ( 5 5 2 x 10") for the followingreactionsderived from flash photolysis studies'CHz+C3Hs -+ C4Hio3CH2 + C3Hs + CHS*C3H7*.Precise agreement with our derived value for the energy separation would requirea value of 1.9 x lo5 for this rate ratio.Rowland et aL1* derive a value > lo7 forthis ratio, which is close to the value derived using the experimental Arrheniusparameters for the analogous reaction of the methyl radical with propane.lg A valueof lo7 in Lahmani's calculation yields a value for the energy separation of 44.5 kJmol-I. Thus, pmding a direct determination of the Arrhenius parameters for thetriplet reaction, our present assumption is vindicated by its consistency with theresults of these other studies.We have derived values for the relative rates of the three possible singlet reactionswith the two olefins.Our results indicate no temperature dependence of theserelative rates within the limits of the experimental accuracy. Further, the ratio ofvinylic to methyl C-H bond insertion is close to 0.33 in both olefins, as anticipatedif' insertion proceeds with equal probability in all C-H bonds. Taken in conjunctionwith the agreement of the singlet addition rates with the absolute value of Braun,Bass and Pilling I 7 for methane, these results support the commonly held assumptionthat singlet methylene reactions with hydrocarbons procecd with activation energiesclose to zero.J. F. Harrison, Accounts Chem. Rex, 1974, 7, 378.H. M. Frey, J.C.S. Chem. Comm., 1972, 1024.R. W. Carr, T. W. Eder and M. G. Topor, J. Chem. Plzys., 1970, 53, 4716.H. M. Frey and G. J . Kennedy, J.C.S. Chcin. Comm., 1975, 233.A. D. Jenkins, J. Chem. SOC., 1952, 2563.D. C. Montague, hit. J. Chem. Kinetics, 1973, 5, 513.R. J. Cvetanovic and R. S. Irwin, J. Chem. Phys., 1967, 46, 1694; N. Yokoyania and R. K.Brinton, Canad. J. Chenr., 1969, 47, 2987.P. M. Kelley and W. L. Hase, Chem. Phys. Letters, 1975, 35, 57.H. M. Frey, Proc. Roy. Soc. A , 1959, 251, 575 ; D. C . Montague and F. S. Rowland, J.C.S.Chem. Comm., 1972, 193.' D. C. Montague, J.C.S. Chem. Comm., 1972, 615.l o T. W. Eder and R. W. Carr, J. Chem. Phys., 1970, 53,2258.l 2 W. L. Hase, R. J. Phillips and J. W. Simons, Chem. Phys. Letters, 1971, 12, 161.l 3 J . W. Simons and R. Curry, Chem. Phys. Letters, 1976, 38, 171.l4 F. Lahmani, J. Php. Chem., in press170 KINETICS OF METHYLENE ADDITIONl 5 S . H. Ho and W. A. Noyes, f. Amer. Chern. Soc., 1967, 89, 5091 ; D. F. Ring and B. S.l6 W. Braun, A. M. Bass and M. Pilling, J. Chem. Phys., 1970, 52, 5131.l 7 R. W. Carr, J. Phys. Chem., 1972, 76, 1581.l 8 F. S. Rowland, P. S. T. Lee, D. C . Montague and R. L. Russell, Faraday Disc. Chem. SOC.,l9 W. M. Jackson, J. R. McNesby and B. de B. Derwent, J. Chem. Phys., 1962, 37, 1610.Rabinovitch, Canad. J. Chem., 1968, 46, 2435.1972, 53, 111.(PAPER 6/1052

ISSN:0300-9599    

DOI:10.1039/F19777300164

出版商:RSC    

年代:1977

数据来源: RSC

摘要:

Experimental and Theoretical Aspects of Hydration Isothermsfor BiomoleculesB Y PETER R. C. GASCOYNE AND RONALD PETHIG"School of Electronic Engineering Science, University College of North Wales, Bangor,Gwynedd, WalesReceived 5th May, 1976A resonating quartz crystal microbalance technique has been used to obtain room temperaturewater sorption isotherms for cytochrome-c, DNA, lecithin, lysozyme and serum albumin. Theresults compare favowably with earlier work using more conventional techniques. A completelygeneral formula describing the sorption isotherms is derived. With the assumption of identical andnon-interacting primary sorption sites, this general formula gives exact values for the monolayersite capacity and the thermodynamic activities of all the hydration states.However, it is shown thatat least one of these assumptions is not valid for the materials studied here, accordingly only limitedinformation can be derived using this theory. This restricted usefulness also applies to other sorptiontheories described in the literature, most of which are based on purely modelistic or kinetic con-siderations. The significance of a sorption activity parameter having values greater or less thanunity is discussed for the materials examined.The experimental and theoretical aspects of protein hydration have receivedconsiderable attention, and are the subject of recent reviews.l* A recent advance inthe measurement technique for obtaining sorption isotherms of biological materialsis the use of a resonating quartz crystal mi~robalance.~~ This technique has beenused for the studies described here and confirms the earlier conclusions 39 regardingits advantages over more conventional methods.Numerous theoretical treatmentshave been proposed to describe the hydration processes of proteins. Many of thesetheories can, however, be considered to be based on models of doubtful physicaljustification. Guggenheim has shown that the original isotherm formulae ofLangmuir,6 Freundlich,' and Brunauer, Emmett and Teller (B.E.T.),8 which arebased entirely on kinetic considerations, may be derived from general statisticalmechanical treatments using Grand Partition Functions. The use of such fuiictionsis extended here to derive a completely general equation describing sorption isotherms,and the applicability and usefulness of this treatment, and of others described in theliterature, is discussed.EXPERIMENTALThe following materials were used: Bovine Serum Albumin (Fraction V), SigmaChemical Co. ; Cytochrome-c (Horse heart), Type VI, Sigma Chemical Co.; L-a-Lecithin(egg yolk), Sigma Chemical Co. ; Lysozyme (egg white), Sigma Chemical Co. ; NaDNA (calfthymus), BDH.A thin film (approximate area 20 mm2 x 25 pm thick) of the material under investigationwas applied to the centre of one side of a fundamental AT-cut 2 MHz quartz crystal oscillator(Cathodeon Crystals). For such a crystal of mass m, the addition of a small mass Am willcause the resonant frequency f to change by an amount Af according to the relationshipA f / f = - K h / m (1 )17172 HYDRATION ISOTHERMS FOR BIOMOLECULESwhere K is a mechanical constant for the crystal and normally has a value very close to unity.A full discussion of the validity of eqn (1) has been given recently by P ~ l k e r .~The test crystal was enclosed inside a vacuum cell within a constant temperature environ-ment, and connected to a frequency comparator circuit as outlined in fig. 1. This electricalcircuit provided the necessary conditions for the crystal to resonate in its fundamental mode.The resulting oscillating signal was mixed with that from a standard 2 MHz oscillator andthe resultant beat frequency detected. This beat frequency was measured to within 0.1 Hzusing a digital frequency counter (Venner Type TSA 6636/2M).If the crystal with no filmattached has a resonant frequency of exactly 2 MHz, then this beat frequency of the loadedcrystal corresponds to Af of eqn (1) with Am being the test film mass. In practice, exactmatching of the standard 2 MHz oscillator with clean 2 MHz crystals was not possible, anda small correction was required to account for this.rnanom t prFIG. 1 .-Outline of the experimental arrangement used for determining the water sorption isotherms.The water vapour used in the hydration studies was provided from a water reservoircontaining triply distilled de-ionised water which had been degassed by redistilling andfreezing under vacuum. The water vapour pressure was determined usicg a calibratedsilicon-oil manometer allowing an accuracy of better than 13 Pa.Before a hydration runwas commenced, the system was evacuated to about Pa and the partial pressure ofwater was further reduced using liquid nitrogen and P205 traps. Temperatures to within40.15 K were determined using a thermocouple, and temperature stability to within 0.5 Kwas achieved by immersing the vacuum cell in an oil bath. The vacuum cell accommodatedfour crystals which could be independently switched into circuit, so allowing for simultaneousobservations of different test materials.It follows from eqn (1) that for a small mass increase am associated with a uniformadsorption of water molecules on the test film, the corresponding change af in the crystalfrequency is given bywhich is independent of any crystal constants.Apart from lecithin, which was suppliedin hexane solution, the biological materials were dissolved in doubly distilled de-ionisedwater and applied to the crystal surface using a clean nylon brush. The mass of the depositedfilm, when dry, was such that on average the crystal resonant frequency decreased by about3 kHz, and was typically reduced further by about 1 kHz as a result of water adsorbed atpartial pressures of the order of 0.8. Thus the maximuni change in crystal resonant frequencydue to the attached hydrated sample was about 4 kHz, well within the accepted range ofvalidity of eqn (1).Effects associated with mechanical coupling to the ambient atmosphere, and with theadsorption of water on the quartz crystal surfaces themselves, were found to be negligible,corresponding at most to a 6 Hz shift at partial pressures of the order 0.8.Eqn (2) is validd f l A f = dm/Am (2P . R . C . GASCOYNE AND R . PETHIG 173so long as the mechanical coupling between the test film and the crystal remains constant.At the higher relative humidities (- 0.9) the DNA samples became gelatinous and it wasconsidered doubtful that the mechanical coupling had remained unchanged compared withthe dry and moderately hydrated condition. For this reason the sorption isothermsdescribed here were restricted to an upper limit of relative humidity of 0.9. With therelatively unsophisticated experimental arrangement described here, these sorption isothermswere determined to resolutions of 5 parts in lo5 change in mass and 4 x partial pressure,which compares very favourably with other more conventional techniques.THEORETICALFollowing the treatments of Hill l o and Guggenheim,' the Grand Partitionfunction for Ns identical primary sorption sites may be writtenwhere x is the activity of the sorbed gas which may, without loss of generality, beidentified with the relative pressure of the gas.The coefficients ni refer to the activityof sorbed molecules in the ith layer. The total sorption O(x) will be the sum of theoccupations of all layers of sites, when, writing the partition function for a singlesite as.f(x) = F(x)'JNSwe have, as shown by Dole,ll thatF(x) = (1 +alx+ala2x2 +a1a2a3x3 + . . . )Ns (3)Dividing both sides of this equation by x and integrating, and noting that for anypartition function describing sorptionf(0) = 1, we may write 1; F) dx = In f ( x ' ) .Now O(x) js the ratio of the total sorption, v(x), to the monolayer sorption capacityof the primary sites, u,, hence finallyThis equation, which to our knowledge has not previously been derived, may bzwritten in the alternative formd( 5 ) v(x) = v,x - In f ( x ) .axSubstitution for f (x) in eqn (5) allows the corresponding sorption isotherm toFor example, setting the activities of sorption sites in the second andSubstitutionbe established.subsequent layers to zero leads to the partition functionf(x) = 1 +ax.into eqn ( 5 ) yields the isotherm equationv,ax1+axu(x) = ___.This is the well known Langmuir equation for monolayer adsorption.An interesting case, previously analysed by Anderson,12 Hill l3 and Halsey,I4occurs when the activities of the second and subsequent layers are equal.Theresulting partition function is a geometrical progression(7) f(x) = 1 + abx+a(bxI2 + a ( b ~ ) ~ + . . 174 HYDRATION ISOTHERMS FOR BIOMOLECULESwhere (ab) is the activity of gas sorbed in the first layer, and b is the activity in allsubsequent layers. Substitution of f(x) in eqn (5) yields the isotherm equationv,abx(1 - bx)[l +(a- b)x]'v(x) =In the special case of the activity in the second and subsequent sorption layers beingequal to that of the bulk condensed gas, b becomes unity. In this case eqn (8) reducesto the well known and much used B.E.T. isotherm equation *av,x(1 - x)[ 1 + ( a - 1)xl'v(x) = (9)Eqn (4) allows the partition function for the sorption sites to be determined directlyfrom sorption isotherm data.The treatment is completely general and, unlike othertheoretical treatments, involves no assumptions regarding the form of f(x). Byusing, for example, an orthogonal Chebyshev polynomial curve fitting technique theactivities of all sorption layers may be obtained directly from the partition function.To complete the analysis, however, it will be noted that a value for vm is required ineqn (4). It is clear that any partition function for multilayer sorption will approachthe form f(x) = 1 +ax at sufficiently small values of x. All sorption isotherms forthe case of identical primary sites will, therefore, be described by eqn (6) when x isvery small.A plot of x/u(x) against x will have a gradient 1 /v, at very low hydrations.The factor vm can, therefore, without loss of generality be defined fromprovided a 9 1.Eqn (4) and (5) apply only to sorption isotherms of materials whose primarysorption sites are identical. It may readily be demonstrated that an extended formof eqn (4) which describes sorption by materials with N different types of primarysites isN n [fj(x')]um~ = exp {Jr dx) j = 1where vmj are the primary site capacities of the N different types of sites whoserespective partition functions are fj(x).Hydration isotherms for materials such as the naturally occurring polypeptidesare described by eqn (1 l), since several different types of water sorption sites will bepresent.Unfortunately, this equation is insoluble unless information regarding thesorption sites is available. On the other hand it is useful to note that the left handside of eqn (11) may be approximated to the form of eqn (7). It must be stressed,however, that because the form of the partition function is assumed, an analysis interms of eqn (7) represents only an approximation to the true isotherm equation.For this reason the value obtained for v, will be an effective value and unlikely tobe identical with vmj, the true primary site monolayer capacity. The valueobtained for the activity of the sites will also be no more than an effective value.However, it can be seen from eqn (1 1) that if members of the set of functions fj(x)are sufficiently similar, the treatment may yield reasonable approximations to thetrue values.Nj = P.R. C . GASCOYNE AND R. PETHIG 175RESULTS AND DISCUSSIONA typical water sorption isotherm for the materials studied is that of BovineSerum Albumin (BSA) illustrated in fig. 2.Mpartial pressure, x0, This work (296.5 K).(298 K).FIG. 2.-Water sorption isotherm for BSA. @, Isotherm data of Bull l 6To analyse the experimental data it was found convenient to write eqn (8) in theformwhereA = (v,ab)-l; B = a-2b and C = b(a-b). (1 3)A least squares computer routine was used to fit eqn (12) to the experimenta1sorption isotherms obtained for the various biological materials. The values of v,,u and b are given in table 1, together with results obtained from conventional B.E.T.analyses of the isotherms.It can be seen that the results obtained here for BSA,DNA and lysozyme using the crystal microbalance technique give B.E.T.-derivedvalues for v, and (ab) in good agreement with earlier work using more conventionalsorption techniques. We cannot explain the disparity between our B.E.T. values forcytochrome-c and lecithin and those derived from the isotherms given in ref. (17),but wish to make the comment that for cytochrome-c at least, close inspection of theisotherm of ref. (17) reveals deviations from the characteristic shape commonly foundfor proteins. Our use of lecithin prepared from hexane solution may account forthe observed differences for this material.For all the freshly prepared samples, ourresults consistently gave the same values for v, (k 0.1) and ab (& 0.2) for each material.There are two cases of interest regarding the activity parameter b. A value of bgreater than or equal to unity implies that the activity of sorption sites in the secondand subsequent sorbed layers is respectively greater than or equal to that of the sorbat176 HYDRATION ISOTHERMS FOR BIOMOLECULESin its pure bulk state. Eqn (8) implies that materials with such a property will attaininfinite hydration at a vapour pressure below p o (x less than unity). The onlymaterial investigated which yielded a value for b greater than unity was DNA, andit is interesting to note that the sample films of this material exhibited deliquescentproperties at a partial pressure of about 0.9.Conversely, a value of b less than unityTABLE VALUES OF THE PERCENTAGE HYDRATION urn AND ACTIVITIES (ab) FOR THE FIRSTFOR THE PARAMETER b REQUIRED TO GIVE THE BEST LINEAR PLOTS AS FOR FIG. 3 AND 4.VALUES DERIVED FROM THE CONVENTIONAL B.E.T. GRAPHICAL ANALYSIS ARE INCLUDED FORBOUND MONOLAYERS DERIVED FROM A COMPUTER FIT OF EQN (12), TOGETHER WITH THE VALUESCOMPARISONB.E.T. ( b = 1)- [eqn ( 1 311material Cln ( ~ b ) b Crn ( ~ b )BSA 7.87 9.63 0.81 6.5 12.26.7 12.56.7 11.3cytochrome-c 8.27 13.4 0.88 7.5 9.86.3 14.1"DNA 11.5 17.3 1.05 12.1 13.312.2* 13.6"12.5" 12.9*4.6 6.2*7.2* 1 8 9lecithin 7.18 3.79 0.88 5.2 8.51 y sozyme 8.15 10.5 0.82 7.4 14.9ref.this work15t16this work17this work1718this work17this work19t Bovine plasma albumin (BPA) ; * calculated from B.E.T.plots derived from isotherm datagiven in reference. Measurements for " this work " were made at 296.5 (kO.1) K.implies finite hydration at the saturated vapour pressure po. Such a value of b wa5obtained for all the materials investigated with the exception of DNA. This findingis in agreement with the observation that when the sample films of the proteins wereleft in a saturated water vapour atmosphere deliquescence did not occur.A consistent trend seen in the results derived from the computer fit of eqn (12)is that the values obtained for the monolayer hydration capacities exceed the B.E.T.-derived values when b is less than unity, whereas for DNA, with b greater than mity,the value of urn is reduced.Eqn (8) may be rearranged to allow convenient graphical representation of theexperimental results. Theresults obtained for BSA using the quartz crystal microbalance technique are showntogether with those of Bull obtained using a conventional weighing-bottle technique.A straight line fit to the data over the entire partial pressure range is obtained withan appropriate value for b found from the computer fit of eqn (12).The effect ofvarying the parameter b is clearly demonstrated in fig. 3. The plot for b = Icorresponds to the conventional B.E.T. plot, and the characteristic deviation from astraight line plot, as remarked upon by a number of workers,l* 2o occurs because ofthe assumption that water sorbed in the second and subsequent hydration layersbehaves as pure bulk water. Such an assumption leads to the prediction that morewater is sorbed than is measured experimentally for BSA.It can be seen that onlya single value for b results in a good linear plot of the experimental data, over thewhole partial pressure range, as can also be seen in fig. 4 for the results of DNA.Fig. 3 shows a plot of x/[u(x)( 1 /b -x>] against x for BSAP . R. C. GASCOYNE AND R. PETHIGi ’177partial pressure, xFIG. 3.-Plots of the function x / [ u ( x ) . (l/b-x)] against x for BSA, where x is the partial pressurep / p o , for various values of the parameter 0. 1, h = 1.0; 2, b = 0.81 ; 3, 0.67. 0 This workIsotherm data of Bull l 6 (298 K).(296.5 K).partial pressure, xFIG. 4.-Plots as for fig. 3 for DNA (296.5 I<). 1, b = 1.17 ; 2, b = 1.05 ; 3, b = 0.95.Eqn (4) represents the most general description of the partition function f(x) forbound water in all the multilayers, with Ihe restriction that all the primary monolayersorption sites are identical and non-interacting. Such a restriction is in fact thebasis for all the sorption theories reviewed by Kuntz and Kauzmann.l A test fo178 HYDRATION ISOTHERMS FOR BIOMOLECULESthe validity of this assumption was made by using a Chebyshev orthogonal curvefitting computer technique for the experimental isotherm data to check for theplausibility of the derived activity parameters. The results of such a curve fittingprocedure gave negative values for some of the activity coefficients, which can haveno physical meaning.Typically, consistent values were obtained for the activitiesof the primary sorption layers, negative values for the second layers and unreasonablylarge values for the third layers.CONCLUSIONSWe consider that the isotherm results obtained here confirm the earlier conclusionsof Kennerley regarding the useful applicability of the resonating quartz crystalmicrobalance technique for hydration studies. Even with a relatively unsophisticatedexperimental arrangement the sensitivity and speed that the method affords comparesvery favourably with the more conventional ‘‘ weighing bottle and salt solution ”and gravimetric methods, for example.-3c Ipartial pressure, xFIG.5.-The mean deviation A from the best linear plots of the form of fig. 3 and 4, for all thematerials investigated here (296.5 K).The partition functionf(x) described by eqn (7), which is similar to that proposedby G~ggenheim,~ can be regarded as a geometrical series approximation to the moregeneral description off(x) given by eqn (4) derived here. We find that a geometricseries does not exactly fit the experimentally derived sorption data. Close inspectionof fig. 3 for example indicates that the experimental data tend to deviate from the beststraight line plots in a consistent periodic manner. The form of such periodicdeviations is illustrated more clearly in fig. 5, which shows the mean deviation fromthe best straight line plots ofeqn (8) for all the biological materials studied here.Thisshows that the treatment of eqn (7), and hence of Guggenheim, is only an approxima-tion, and that the values given in table 1 should only be treated as such. The B.E.T.-derived values will be of very much greater inaccuracy due to the erroneous assumptionof having b = 1.Also, an attempt to make an exact fit of a polynomial of the formj-(X) = 1 + a x + ~ X 2 + y X 3 + . . .to the experimental data using a Chebyshev orthogonal curve fitting techniquP. R. C . GASCOYNE AND R. PETHIG 179resulted in physically unrealizable activity coefficients a, p, y, . . . This implies forthe samples studied here that either there are several different types of primarysorption sites, or that the primary sites interact with one another.Either of theseeffects negates the basic assumptions used to derive the various sorption theoriesdescribed in the literature and reviewed by Kuntz and Kauzmann. Hence withoutmore specific information regarding the partition functions fj(x) or the monolayerhydration capacities umj [see eqn (ll)] for the various types of sites, more detailedinformation regarding the sorption site activities cannot be derived from experimentalisotherm data. For biological materials it is reasonable to expect different types ofprimary sorption sites to be present ; the conclusions above serve to indicate that thisfact severely restricts the information that can be derived from the analysis of sorptionisotherms.For synthetic polypeptides however, where the different kinds of sorptionsites can be more clearly defined, analysis using eqn (4) can be expected to be morefruitful.A further complication which will effect the usefulness of any sorption theory canbe appreciated from eqn (3). The Grand Partition Function described by thisequation implicitly assumes that the activity of any one sorbed layer is not altered bythe sorption of subsequent laysrs upon them. This restriction can be overcome byrewriting eqn (3) in the formF(x) = (1+a,x+a;a,x2+a';a;a,x3+ . . .>Nswhich can be shown to lead to results of the same form as eqn (4) and (5). Eqn (3)and (1 4) are therefore thermodynamically equivalent so that without other physicaldata, sorption measurements cannot provide information regarding the individualactivities of sorption layers beyond the first.In applying eqn (4) it is important to be able to assess how experimental errorsin u(x) and x effect the accuracy Gf the derived activity coefficients.A detailedanalysis of this problem will not be given here, it being sufficient to indicate that forthe first few sorption layers errors in ai are comparable to, if not less than, the rootmean square experimental errors in determining u(x) and x.The observation that the activity parameter b of eqn (8) is less than unity for theproteins studied, but of value greater than unity for DNA, we consider to be ofsignificance regarding their behaviour in solution. The value of b less than unity forthe proteins implies that their outermost hydration layer is formed by water moleculesof lower activity than bulk water, so that extra layers of water are required to beassociated with the hydrated macromolecule before it can become fully accommodatedinto normal bulk water.For materials such as DNA, with a value b greater thanunity, the outermost hydration shell is already indistinguishable from bulk waterand no such additional modification of the bulk water is required. These considera-tions may be of direct relevance to such phenomena as salting-in and salting-out,and to other macroinolecular interactions in solution.Finally we wish to add that favourable attention is often given in the literatureregarding certain isotherm equations which give good descriptions of experimentalisotherm data.Such good agreement should not, we feel, be considered to lead toaccurate physical sorption parameters. For example eqn (12) is identical in form tothat obtained by Hailwood and Horrobin,21 and eqn (8) can be compared to thatobtained by Enderby.22 The restrictions described here regarding the derivation ofaccurate sorption parameters should also be considered pertinent to these theories.We acknowiedge the invaluable mathematical zdvice of Messrs. T. P. T. Williamsand D. Everett, and the S.R.C. for the award of a studentship to P. K. C. G1 so HYDRATION ISOTHERMS FOR BIOMOLECULESD. Kuntz and W. Kauzmann, Adu. Proteiri Chem., 1974, 28, 239.R. Cooke and I. D. Kuntz, Ann. Rev. Biophys. Bioeng., 1974, 3, 95.M. G. Kennerley, Polymer, 1969, 10, 833.M. M. Breuer and M. G. Kennerley, J. Colloid Interface Sci., 1971, 37, 124.chap. 11, pp. 186-206.' E. A. Guggenheim, Applications of Statistical Mechartics (Oxford, Clarendon Press, 1966)-' I. Langmuir, J. Amer. Chein. SOC., 1918, 40, 1361. ' H. Freundlich, Kapillarchernie (Leipzig, 1909).' H. K. Pulker, Thin Solid Films, 1976, 32, 27.S. Brunauer, P. H. Emmett and E. Teller, J. Amer. Chem. Soc., 1938, 68, 309.l o T. L. Hill, J. Chem. Phys., 1946, 14, 263.l 2 R. B. Anderson, J. Amer. Chem. SOC., 1946, 68, 686.I 3 T. E. Hiil, Adv. Catalysis, 1952, 4, 211. *' G. D. Halsey, A h . Catalysis, 1952, 4, 259.l 5 D. D. Eley and R. B. Leslie, in Electronic Asp~cts of Biochemisfry, ed. B. Pullman (AcademicM. Dole, Infroductiort to Statistical Thermodynamics (Prentice-Hall, N.Y., 19541, p. 200.Press, N.Y., 1964), pp. 105-117.H. B. Bull, J. Amer. Chem. SOC., 1944, 66, 1499.M. R. Powell and B. Rosenbzrg, J. Bioenergetics, 1970, 1, 493.l 8 M. Falk, K. A. Hartman and R. C. Lord, J. Amer. Chem. Sac., 1962, 84, 3844.I 9 W. S. Hnojewyj and L. H. Reyerson, J. Phys. Chem., 1959, 63, 1653.2o P. J. Killion, L. H. Reyerson and B. F. Cameron, J. Colloid Interface Sci., 1970, 34, 495.2 1 A. J. Hailwood and S . Horrobin, Trans. Faraday SOC., 1946, 42, 84.2 2 J. A. Enderby, Trans. Famday Soc., 1954, 51, 106.(PAPER 6/858

ISSN:0300-9599    

DOI:10.1039/F19777300171

出版商:RSC    

年代:1977

数据来源: RSC