摘要:

J . Chem. Soc., Faraday Trans. 1, 1985,81, 1577-1587 Redox Properties of Copper Tetra(4-NJV”’N’’- trimethylani1inium)porphyrin Elect roc hemical and Spectral Studies BY ARMAND BETTELHEIM,* DAN OZER AND RACHEL HARTH Nuclear Research Center-Negev, P.0.B 9001, Beer-Sheva 84190, Israel Received 16th July, 1984 The redox behaviour of the copper tetra(4-N,N’,N”-trimethylanilinium)porphyrin (abbrevi- ated as CuTMAP) has been studied in acetonitrile and aqueous solutions using differential pulse polarography, cyclic voltammetry, a rotating ring-disc electrode and spectroelectrochemical methods. The reduction of Cuu is characterized by a two-step one-electron reduction. The CulI/CulTMAP and Cull/CuUITMAP couples show reversible redox behaviour in acetonitrile and have redox potentials of -0.18 and +0.45 V, respectively.In aqueous solutions and at low concentrations, the Cu”TMAP complex is characterized by a Soret band at 412 nm and is reduced at (- 0.56 - 0.057 pH) V, while a band in the 393-398 nm range and a reduction peak at (-0.79-0.057 pH) V predominate at high CuTMAP concentrations. Ej for the oxidation of CuIITMAP is +0.87 V in aqueous solutions and is independent of pH. The decomposition of water is described in terms of a catalytic cycle which involves the CulIITMAP complex. Copper ions often function as redox catalysts in chemical systems and copper complexes have been implicated in oxidation-reduction reactions in biological systems.’ The redox properties of the porphyrins play a key role in their biological function as activators of molecular oxygen and electron mediators.2 Some redox properties of the water-soluble iron,3 manganese4 and cobalt5 ( 4 - N , N , N - t rimethylani1inium)porphyrins (FeTMAP, MnTMAP and CoTMAP) have been reported and correlated to their catalytic effect on the electroreduction of oxygen.In this paper we report some spectral and electrochemical properties of Cu”TMAP as well as of its reduced and oxidized derivatives in acetonitrile and aqueous solutions. The results will be discussed in the context of other copper macrocyclic compounds. EXPERIMENTAL The chloride salt of copper(1r) te tra(4-N, N’,N”- trime thylani1inium)porphyrin (Cull TM AP) was obtained from Man-Win Chemicals. Unlike the iron(rrr) and cobalt(rrr) TMAP complexes, which were soluble in aqueous solutions only at pH < 2 , 3 9 the copper salt was soluble over the entire pH range. The solubility of CuIITMAP in acetonitrile was estimated by adding a known amount of the copper porphyrin to the CH,CN solution and removing the undissolved excess of the complex by centrifugation.The portion which precipitated was calculated by water dissolution and using the experimental extinction coefficient of the Soret band in these conditions. Tetrabutylammonium perchlorate (TBAP) was used as electrolyte for the electrochemical measurements in acetonitrile. A glassy carbon/glassy carbon rotating ring-disc electrode (RRDE, Pine Instrument Co.) was used. The area of the disc was 0.41 cm2. The RRDE was pretreated mechanically and electrochemically. The electrode was polished with alumina powder, washed with 1 mol dmP3 15771578 REDOX PROPERTIES OF CUTMAP HC1 and distilled water, and then introduced into an argon-saturated 1 mol dm-3 KC1 solution.The potentials of the disc and ring electrodes were then cycled in the range from + 0.3 to - 0.8 V until a minimum residual current density was obtained (ca. 1 pA cm-2). The same disc electrode was used for the cyclic-voltammetric (c.v.) experiments. Spectroelectrochemistry was conducted using a thin-layer cell constructed with a gold minigrid optically transparent electrode (OTE) sandwiched between two quartz plates separated by Teflon tape spacers along the edges. The pathlength of the thin cell (ca. 0.1 mm) was determined by measuring the absorbance of a K,Fe(CN), solution.A Cary 17 spectrophotometer, with a cell compartment modified to permit introduction of electrical leads, was used for the spectropo tentios tatic experiments. Cyclic voltammetry and spectroelectrochemistry were performed using a PAR 174 potentiostat coupled with a PAR 175 sweep generator. The RRDE experiments were performed using a double potentiostat (RRDE 3, Pine Instrument Co.) and differential pulse polarography (d.p.p.) using a PAR 173 polarograph with a PAR 303 static mercury drop electrode (SMDE). This apparatus served as a hanging mercury electrode (HME) as well as a dropping mercury electrode (DME). Experiments were conducted at room temperature (20 k 1 "C). All reported potentials are with respect to a saturated calomel electrode (SCE). For measurements in CH,CN solutions, an aqueous SCE was separated from the rest of the cell by an asbestos plug and a salt bridge of lop2 mol dmb3 TBAP in acetonitrile.This was sufficient to prevent leakage of water to the cell. The potential of the aqueous SCE in CH,CN was found to be steady (k 1 mV) over the timescale of the electrochemical experiments. RESULTS AND DISCUSSION ELECTROCHEMICAL MEASUREMENTS ACETONITRILE SOLUTIONS Fig. 1 shows a differential pulse polarogram at a dropping mercury electrode for a deaerated acetonitrile solution of CuIITMAP. Three reduction peaks appear at -0.18, -0.63 and -0.85 V. The peaks at -0.18 and -0.63 V [(a) and (b)] are assigned to reduction of the central metal ion. The maximum peak currents of processes ( a ) and (b) are similar while the maximum peak current of process (c) is considerably larger [ i p ( c ) z 8ip(a)]; this is probably due to reduction of the TMAP ligand.3-5 Cyclic voltammetry at a hanging mercury electrode was used to test the reversibility of the various electrodic reactions.C.V. reveals (fig. 2) that only process (a) approaches Nernstian behaviour. The half-wave potential is -0.18 V and the peak potential separation (Ep, - Ep, = 80-1 20 mV) is consistent with a transfer of one electron. The broadness of the anodic peak suggests the interference of mercury oxidation at potentials close to 0 V. Assuming n = 1 for the electrodic reactions [peaks (a) and (b)], the d.p.p. and C.V. results can be interpreted as follows: (1) (2) process (a) CuIITMAP + e -+ CuITMAP process (6) Cu' TMAP + e -+ Cuo + TMAP.The potential was scanned anodically using glassy carbon as the indicating electrode. As can be seen in fig. 3, C.V. from 0 to 0.8 V reveals a reversible one-electron reaction (Ep, a - Ep, = 60 mV). Assuming stabilization of the CulI1 ion in acetonitrile, as already suggested for other copper macrocyclic compounds,6-8 the anodic process is assigned to a CulI + CulI1 transition: CuIITMAP -+ CulIITMAP+e. (3)A. BETTELHEIM, D. OZER AND R. HARTH 1579 Fig. 1. Differential pulse polarogram (5 mV s-l, 25 mV modulation) at the DME for a deaerated CH,CN solution containing and 1.8 x lob5 mol dm-3 TBAP and CuIITMAP, respectively. A n Fig. 2. Cyclic voltammogram (100 mV s-l) at the HMDE for the same solution as fig. 1. The inset of fig. 3 shows the peak currents as a function of the square root of the scan rate.The cathodic and anodic peak currents (ip,, and ip,a, respectively) are linearly proportional to d, as expected from a diffusion-controlled process. The diffusion coefficient of the CuIITMAP and CuII'TMAP complexes was estimated using the Randles-Sevcik equationg and assuming n = 1 to be (1.8 kO.2) x cm2 s-l. This1580 REDOX PROPERTIES OF CUTMAP 0 0.2 0.4 Fig. 3. Cyclic voltammograms obtained when the potential of a glassy carbon electrode is scanned anodically in a solution of the same composition as in fig. 1. Scan rates are 20, 50, 100 and 200 mV s-' for curves 1-4, respectively. Inset: plot of peak currents as function of the square root of the scan rate. value is similar to that cited in the literature for a similar porphyrin.lO9 l1 The half-wave potential [E; = (EP,.+Ep, ,)/2] of reaction (3) is +0.45 V, which is ca.0.7 V less positive than reported for other Cu"' macrocyclic compounds also studied in acetonitrile solutions.63 This is probably due to larger stabilization of the CuI1' ion for the CulIITMAP/CulITMAP couple. This is also consistent with the results obtained for the Cu"/Cu'TMAP couple. E; of this couple is ca. 0.7 V more positive than for the C U ~ ~ / C U ~ (trans- 1,4-diene) The oxidation of CuIITMAP was also studied using a glassy carbon/glassy carbon rotating ring-disc electrode. In fig. 4, curves (a)-(c) are the disc currents ( i u ) obtained at different rotation speeds when the disc potential is scanned anodically. The half-wave potential for the oxidation of CuIITMAP in acetonitrile (E! = +0.44 V) is in good agreement with that found in the C.V.experiments. The plot ofthe disc limiting current against the square root of the rotation speed (mi) was linear (inset of fig. 4)A. BETTELHEIM, D. OZER AND R. HARTH 1581 Fig. 4. RRDE voltammograms (ER = 0 V, scan rate of disc potential 2 V min-l) for the same solutions as in fig. 1 [curves (a), (b) and (c) at 400, 600 and 800 r.p.m., respectively) and after the addition of 4 vol% water [curves (d), (e) and (f) at 400, 600 and 800 r.p.m., respectively]. (u')-Cf') are the ring curves corresponding to the ( a t C f ) disc curves. Inset: Levich plots for data obtained from curves (u)-(c). with a correlation factor of 0.995. The number of electrons, the n value, involved in the oxidation of the CuIITMAP complex was calculated using the Levich equation:12 in, = 0.62nFADi V-iwi Cb where V is the kinematic viscosity (cm2 s-l), w is the rotation speed (rad s-l), Cb is the complex bulk concentration (mol ~ m - ~ ) , D is the diffusion coefficient (cm2 s-l) and the other variables have their usual meaning.Using the D value obtained in the C.V. measurements, an n value of 1.2 k0.2 was obtained, thus confirming that only one electron is involved in reaction (3).1582 REDOX PROPERTIES OF CUTMAP Fig. 5. Cyclic voltammograms at a glassy carbon electrode (100 mV s-l) for a deaerated CH,CN solution containing mol dm-3 TBAP and Cu'ITMAP, respectively, upon addition of 1, 1.2, 1.6, 2.4 and 4 vol% water (curves 1-5, respectively).and 1.8 x The ring potential was set at 0 V to reduce the Cu1I1TMAP formed at the disc. Curves (ak(c) in fig. 4 correspond to the ring currents (iR) as a function of the disc potential. The ratio iR/iD = 0.4 was found to be independent of rotation speed. Since the collection coefficient of the RRDE was also determined [using the Fe(CN);4/Fe(CN),3 couple] to be 0.4, it can be concluded that the CuIIlTMAP complex is chemically stable in acetonitrile solutions, at least on the timescale of the RRDE experiments, ACETONITRILE AND WATER MIXTURES The effect of the addition of water to an acetonitrile solution of CuIITMAP was studied using the C.V. and RRDE techniques. The gradual addition of water causes the following changes in the C.V. curves (fig.5): (a) E; of the electrodic process shifts gradually to more positive potentials and (b) the broadness of the peaks and the increase of the potential peak separation indicate the irreversibility of the Cull -+ CulI1 reaction at high water concentrations. The same trend for E; was also found in the RRDE voltammograms [cf. curves ( d w ) and (a)--(c) in fig. 41. Moreover, the iR/iD value decreases when the water content in acetonitrile is increased. In the presence of 4 vol% water, Ei is +0.62 V (compared with +0.44 V in pure acetonitrile) and iR/iD drops to 0.33, which corresponds to a CuIIITMAP yield of ca. 80%. AQUEOUS SOLUTIONS Electrochemical measurements on copper porphyrin were also conducted in aqueous solutions at an ionic strength of 1 mol dm-3 using NaCl as electrolyte andA.BETTELHEIM, D. OZER AND R. HARTH 1583 I I I I I I I I I I I I I I I 1 / I I I 1 V I 1 c) -0.9 - 1 . 1 -1.3 -1.5 - 1 . I E/V Fig. 6. Differential pulse polarograms (5 mV s-l, 25 mV modulation) for a deaerated solution containing and 1 mol dm-3 phosphate buffer and NaCl (pH 6), respectively, in the presence of (-) 4 x and (---) 2 x mol dm-3 CuTMAP. in the presence of mol dm-3 phosphate buffer. Scanning cathodically the potential of a DME using the d.p.p. method yields reduction curves as shown in fig. 6. The currents of the peaks appearing at potentials more negative than - 1.4 V (regions 111, IV and V) are linearly dependent on the concentration of CuTMAP and are attributed to ligand However, the reduction of the copper ion centre (regions I and 11) shows complex behaviour.The current of peak I increases linearly over the range (0-1.5) x lop4 mol dm-3, while at higher concentrations peak I1 appears, the height of which is proportional to the CuTMAP concentration up to 5 x mol dm-3 (higher values could not be obtained due to precipitation of the complex). From fig. 7 it can be seen that the potentials of peaks I and I1 are pH dependent: Ep = ( - 0.56 - 0.057 pH) and (- 0.79 - 0.057 pH) V, respectively. More- over, the approximate decrease of 57 mV per pH unit indicates a reduction which involves one electron per proton. On the grounds of similar results, the electrochemical mechanism of Cu**(trans- 1,4-diene) reduction was given as follows Cu"L+H+ +e --* [Cu'L, (4) Polarization curves obtained at a glassy carbon electrode in the anodic potential1584 -1.4 -1 .2 - 1 .o > G - O * 8 - 0 .6 - 0 . 4 REDOX PROPERTIES OF CUTMAP 0 2 4 6 8 10 PH Fig. 7. Potential of peaks I and 11, as obtained from d.p.p. curves, as function of pH. EIV +0.2 +0.4 +0.6 +0.8 +1.0 t 1 I I , \ \ \ 0.8 - 0 2 4 6 8 1 0 PH 2 Fig. 8. Polarization curves obtained when the potential of a glassy carbon electrode is scanned anodically in a deaerated solution containing lo-* and 1 rnol dm-3 phosphate buffer and NaCI, respectively, at pH 1.9 and 1 1.5 [dashed curves (a) and (b), respectively]. The curves (a'k(e') are obtained in the presence of 2 x lop4 mol dmP3 Cu"TMAP (pH 1.9, 9.0, 9.6, 10.2 and 11.5, respectively). Inset: theoretical oxidation potential of water (curve 1) and E! of CuI'TMAP oxidation (curve 2) as function of pH.A.BETTELHEIM, D . OZER AND R. HARTH 1585 range are shown in fig. 8. The oxidation of CuIITMAP proceeds at E; = +0.87 V and is independent of pH. While the limiting current of the wave is constant at pH d 1.9, a gradual increase of current is observed at higher pH values. Moreover, comparing the potential of water oxidation in low and high pH in the absence and presence of CuTMAP [compare curves (a) and (6) with (a') and (e'), respectively], it can be concluded that the water oxidation overpotential is decreased by a much larger amount at pH 11.5 than at pH 1.9 (the oxidation of water proceeds at potentials 150 and 70 less positive in the presence of the complex at the two pH values). These results suggest that oxidation of water is essentially determined by an electrochemical-chemical catalytic mechanism : CuI1TMAP+CuI1lTMAP+e 2Cu"'TMAP + H,O- 2CuIITMAP + $02 + 2H+ \ ( 5 ) where CuIITMAP is oxidized at the electrode to CuII'TMAP, which is unstable and reacts with water to regenerate the CuIITMAP complex.It can be seen from the inset of fig. 8 that catalysis can occur only at pH 2 1.9 since only at these pH values is the potential of Cull oxidation more positive than the theoretical potential of water oxidation. The role of the Culll ion as a catalyst for the decomposition of water was also reported for the copper (trans- 1,4-diene) complex.8 SPECTRAL MEASUREMENTS Table 1 lists the main absorption maxima and extinction coefficients of Cu'ITMAP in acetonitrile and in aqueous solutions.The complex displays the characteristic metalloporphyrin spectrum13 with a visible peak at 538 nm and a very intense Soret band in the near-u.v. Beer's law experiments were conducted in acetonitrile solutions at A, = 538 and 412 nm and linear plots were obtained for both wavelengths. However, only the 538 nm band obeyed Beer's law in aqueous solutions. At low CuIITMAP concentrations (< 8 x mol dmV3) only the 412 nm band appeared in the near-u.v. while a band with 3,,,, in the range 392-398 nm was dominant at high concentrations ( 2 4 x mol dm-3). The two Soret bands appeared at intermediate concentrations. Similar Amax as well as were obtained over the entire range of pH from 0 to 12. Other experiments conducted with the same ionic strength but with other electrolytes than indicated in table 1 did not show any specific electrolyte effect.The results in aqueous solutions suggest an equilibrium involving more than one Table 1. Spectra data for Cu"TMAP in acetonitrile and aqueous solutions absorption extinction coefficient solution [CuTMAP]/mol dm-3 maxima/nm / lo5 dm3 mol-l cm-l ~ 2 x 10-7-2 x 10-5 { i;; CH3CN + 10-l mol dm-3 TBAP d 8 x lo-' i 0.85 0.1 1 1.95 17.0 and 10-1 mol dm-3 I f 538 0.11 4 x 10-5 2 4 x 10-4 phosphate buffer and NaCl, respectively, pH 7.9 OD4,,:OD,,, = 0.73 0.12 1.281586 REDOX PROPERTIES OF CUTMAP chromophore with spectral characteristics which are similar in the visible region but differ in the Soret region. Moreover, these are consistent with the effect of CuTMAP concentration on the potential and current of peaks I and I1 in the d.p.p.curves. A dimeric species was suggested for an iron porphyrin which showed similar spectral and electrochemical behaviour in aqueous Optical spectra as well as magnetic observations were reported in the literature to distinguish between metal and ligand oxidation of a series of tetrapheny1p0rphyrins.l~ Unfortunately, e.p.r. experiments on the CuTMAP complex under the same conditions as used in the electrochemical experiments were unsuccessful because of the broad signal of the copper ion. The optical spectra obtained during electroreduction and oxidation of CuIITMAP in acetonitrile were followed using an OTE thin-layer cell. Irreproducible results were obtained for the reduced species, owing partly to the sensitivity to trace amounts of oxygen in the solution. Moreover, the Cu'TMAP complex was found to be relatively stable only when produced at a mercury electrode, while reduction to metallic copper occurred at solid electrodes (gold-OTE, glassy carbon).The oxidation of CuIITMAP caused a gradual increase in the optical density at A, = 412 nm. The extinction coefficient of CulI'TMAP at this wavelength was determined to be 3.6 x lo6 dm3 mol-1 crn-'. Both the original and oxidized complexes were stable in acetonitrile, as evidenced by the reproducibility of the respective spectra. l4 CONCLUSIONS The electrochemical results demonstrate that Cull TMAP undergoes a two-step, one-electron reduction of the metal-ion centre. The half-wave potential of the Cul'/Cul couple is - 0.18 V in acetonitrile.In contrast to other Cull porphyrins, in which the ligand is reduced in more positive potentials than the copper centre,16 the reduction of copper in CuTMAP is uncomplicated by ligand reduction. The anodic shift of the CuI1/Cul potential compared with other N, marocyclic compounds6~ could result from destabilization of planar Cull and/or stabilization of non-planar Cu1.17 This makes it possible to oxidize or reduce the metal centre with little change in the coordination geometry. The FeTMAP, MnTMAP and CoTMAP complexes have been found to be effective catalysts for the electroreduction of ~ x y g e n . ~ - ~ The potential of the CulI/Cul couple is too negative to reduce the overpotential of oxygen reduction. However, CuIr1TMAP has sufficient positive potential for water decomposition at pH > 1.9 (E; = +0.87 V).The catalytic electro-oxidation of water is proposed to occur through an electrochemical-chemical mechanism, similar to that suggested for the effect of porphyrins on the reduction of o ~ y g e n . ~ - ~ ' We thank the referees for their helpful suggestions and D. Weinraub for technical assistance. J. Peisach, P. Aisen and W. E. Blumberg, The Biochemistry of Copper (Academic Press, New York, 1966). D. Dolphin, B. R. James and H. C . Wellorn, Adc. Chem. Ser., 1982, 201, 563. A. Bettelheim, R. Parah and D. Ozer, J . Electrochem. Soc., 1982, 129, 2247. A. Bettelheim, D. Ozer and R. Parash, J . Chem. SOC.. Faraday Trans. 1, 1983, 79, 1555. D. Ozer, R. Parash, F. Broitman, U. Mor and A. Bettelheim, J . Chem. SOC., Faraday Trans. 1, 1984, 80, 1139. D. C. Olson and J. Vasilevskis, Znorg. Chem., 1971, 10, 463. M. Felhendler, G. Ginzburg and D. Meyerstein, J . Electroanul. Chem., 1980, 112, 295. ' D. P. Rillema, J. F. Endicott and E. Papaconstantinou, Inorg. Chem., 1971, 10, 1939.A. BETTELHEIM, D . OZER AND R. HARTH 1587 @ (a) J. E. Randles, Trans. Faraday Soc., 1948,44, 327; (b) A. Sevcik, Collect. Czech. Chem. Commun., lo T. Kuwana, M. Fujihara, K. Sunakawa and T. Osa, J. Electroanal. Chem., 1978,88, 299. l2 H. R. Thirsk and J. A. Hamson, A Guide to the Study of Electrode Kinetics (Academic Press, London, l 3 K. M. Smith, Porphyrins and Metalloporphyrins (Elsevier, New York, 1975). l4 R. F. Pasternack, H. Lee, P. Malek and C. Spencer, J . Znorg. Nucl. Chem., 1977,39, 1865. l5 A. Wolberg and J. Manassen, J. Am. Chem. SOC., 1970, 92, 2982. l8 R. H. Felton and H. Linschitz, J. Am. Chem. Soc., 1966, 88, 1 1 13. *' G. S. Patterson and R. H. Holm, Bioinorg. Chem., 1975, 4, 257. l8 P. A. Forshey and T. Kuwana, Znorg. Chem., 1983, 22, 699. 1948, 13, 349. P. A. Forshey and T. Kuwana, Znorg. Chem., 1981, 20, 693. 1972), p. 84. (PAPER 4/ 1225)

ISSN:0300-9599    

DOI:10.1039/F19858101577

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I . 1985,81, 1589-1609 Relaxation Processes on Graphitic Surfaces Part 1.-In the Absence and Presence of Adsorbed 4He on Spheron and Grafoil with Increasing Temperature BY ANTONIOS A. ANTONIOU Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR6 Received 24th July, 1984 An analysis of the time dependence (after-periods) of heat capacities measured for Spheron and Grafoil in the presence and absence of adsorbed 4He (and Ne) reveals the existence of slow first-order relaxation processes. For low temperatures these are endothermic but above 19.6 and 11.5 K for Spheron and Grafoil, respectively, they are exothermic. The rate at which these processes occur is determined by thermoelastic stresses associated with relatively small readjustments in the disordered surface geometry.In the absence of adsorbates the dimensional expansion in the c direction and contraction parallel to the surface can lead, respectively, to endothermic (dominant at low temperatures) and exothermic processes. In the presence of adsorbed *He the superimposition of two endothermic processes is attributed to thermal expansion of the superimposed film and of the surface layers. The decrease, with increasing coverage of adsorbate, of the temperature above which the exothermic processes are observed is attributed to the effect of adsorbate on the structure of the surface layers of graphite. The increased deformation in the substrate lattice due to the interaction of the superimposed film results in the longer relaxation times and the higher ‘relaxed heat capacities’ of these processes.Different types of graphitic substrates have been used extensively to study the adsorption of gases in the past. Experimental evidence for the surface lattice distortions of these materials and for changes in their structure in the presence of adsorbates is therefore important. Such evidence is provided from the analysis of the after-periods of calorimetric data, heat capacities and heats of adsorption, which have been determined on the graphitic materials Spheron and Grafoil in the absence and presence of the adsorbates 4He172 and Ne394 between 2 and 30 K and at higher temperatures on Grafoil.2 Analysis indicates that thermodynamic equilibration within these systems with increasing temperature, and in the presence of the adsorbate with increasing coverage, occurs with first-order relaxation processes.These time-dependent processes are observed after the initial exponential decay of temperature caused by heat diffusion within the system. In Part 1 the relaxation processes observed from the heat-capacity measurements determined for Spheron and Grafoil in the presence and absence of adsorbed 4He are related to the particular thermal properties of graphite and to those of the superimposed film. Similar information is provided from the heat capacities determined for adsorbed neon on Spheron., In Part 2 the processes related to the ‘trapping’ of the adatoms at the ‘ high-energy ’ sites of these substrates and the formation of the superimposed film are described. In this case these processes are observed during the after-periods of measurements of the calorimetric heat of adsorption.Information on similar relaxation processes has been reported from specific-heat data determined for amorphous materials such as LaZn alloy by Ravex et al.,5 for SiO, 15891590 RELAXATION ON GRAPHITIC SURFACES and other materials by Loponen et a1.,6 as well as from the heat release during the cooling of vitreous silica' and polycrystalline copper8 at helium and sub-helium temperatures. These processes have been attributed to the relaxation of thermoelastic stresses, especially for polycrystalline copper, by Trofimov.8 This is the first time that calorimetric data determined on adsorbates have been analysed in this way.However, there is previous experimental evidence to indicate that processes similar to those presented in Part 2 (related to the migration and 'trapping' of the adatoms at the 'high-energy' sites) have been observed in the past during calorimetric studies of the adsorption of nitrogen and neon on r ~ t i l e . ~ EXPERIMENTAL MATERIAL Two different types of adsorbents were used, Spheron and Grafoil. Spheron, a carbon black graphitized at 2700 "C (supplied by the Cabot Corporation) had a particle size at the surface of the native aggregate of ca. 300-800& as determined by scanning microscopy. The agglomerates themselves were 1-2 mm in diameter.3 Each particle consists of stacks of graphite platelets whose inner interplanar distance is expected to be larger than in the natural graphite.10 These particles are connected within the aggregate with ' non-hexagonal aromatic bridging regions between aromatic hexagon regions'.ll At the edges of these aggregates the disparity between the links of the carbon atoms should also be expected to be even more pronounced.The Grafoil (Union Carbide) consists of rolled sheets 0.015 in. thick manufactured out of compressed graphitic powder. Discs of ca. 1: in. diameter with a 4 in. centre hole were cut from these sheets. The c stallites within these sheets have an orientation of ca. 30" and lengths in the range 100-150 l3 In both cases the adsorbent was first placed in a high-purity graphite crucible, heated under vacuum for > 2 days to ca. 900 "C and transferred to the calorimeter vessel.The lid of the vessel was welded in place and the whole assembly was soldered to the filling line of the cryostat. The transfer of the sample to the calorimeter, weighing of the sample, welding and the soldering of the whole assembly to the filling line of the cryostat and testing for leaks were performed under an argon atm~sphere.~ CRYOSTAT AND CALORIMETER VESSEL The adiabatic calorimeter and the experimental procedure used have already been de~cribed.~ The main features and procedures which permit the calorimeter's use in the study of long relaxation processes at graphitic surfaces are briefly reviewed for the convenience of the reader. The main feature of this cryostat is the use of a three-stage refrigeration set-up which, together with its larger size than most conventional cryostats, allows the sample to be maintained at temperatures < 4 K for a number of days with a single charge of liquid helium in the lower container.[See ref. (14) of ref. (3).] In that way the slow rate processes that take place during either the cooling or the heating of the systems studied at these low temperatures (especially at liquid-helium temperatures) during the calorimetric measurements can be detected and investigated over a sufficiently long period of time. Special attention was also given to minimize stray energy input due to vibrations, so the cryostat was placed on a concrete base bearing on natural rock. The calorimeter vessel used for the graphitized carbon adsorbent was machined out of high-purity aluminium. For the Grafoil adsorbent the vessel was made out of high-purity copper (gold plated).In both cases each of the vessels was suspended with nylon threads within the envelope surrounding the calorimeter. The temperature of the envelope was controlled by a differential thermocouple attached to the inner surface of the envelope and to the outer surface of the calorimeter. The temperature difference between the envelope and the calorimeter was adjusted so that the final steady-state drift rate in the calorimetric measurements was kept to a minimum. In most cases this driftA. A. ANTONIOU 1591 rate averaged to c 2-3 mK in 30 min. This procedure proved to be essential in the determination of the final temperature in the calorimetric measurements, in which thermodynamic equilibration takes place with relatively long relaxation processes. RESULTS GENERAL ANALYSIS OF THE AFTER-PERIODS The analysis of the after-periods of the heat capacities determined for both Spheron and Grafoil in the presence and absence of adsorbed 4He (and similarly for Ne on Spheron2) shows that thermodynamic equilibration occurs with first-order relaxation processes. Within the lower temperature range, which depends on the system, these are endothermic processes, but above a certain temperature they are exothermic.In the absence of adsorbate the change from endothermic to an exothermic process takes place on Spheron near 19.6 K and on Grafoil near 1 1.5 K. However, in the presence of the adsorbates this 'crossover' temperature decreases progressively with the increasing coverage.An example of the behaviour at temperatures close to the 'crossover' temperature is shown in fig. 1 ( a ) for Spheron without the adsorbate and in fig. 1 (b) for 4He on Grafoil at a coverage of 0.88 cm3 (s.t.p.) g-' adsorbent. Furthermore, in the after-periods of the heat capacities determined at low tem- peratures in the presence of adsorbate two, rather than one, superimposed first-order endothermic processes take place. Originally, only the endothermic process with the longer relaxation time was observed and reported.' The period required for the data to follow the straight line of the logarithmic plot in this process, which in some cases lasted for > 100 min, was at the time attributed to thermal equalization within the system. However, the present analysis clearly indicates that thermal equalization takes place within a shorter time interval and that this first part of the after-period is associated with two superimposed endothermic processes.In the analysis of the after-periods of the heat-capacity measurements determined in the presence and absence of the adsorbate, the following equations are used. In the case in which only one process, endothermic or exothermic, takes place the equation is used, where A T = T,- T (or T- T,) and AT = &- Tnf (or &-To) for an endothermic (or exothermic) process, respectively, and z is the relaxation time of the process. Tis the temperature at time t (corrected for the steady-state drift rate of the after-period) and qnf is the temperature at infinite time. T, is the temperature determined from the logarithmic plot of In ( T - Tnf) [or 11; ( qnf - T)] against t for an endothermic (or exothermic) process, respectively, by extrapolation of the linear section to zero time.A typical logarithmic plot of a heat-capacity run obtained for Spheron at 4.17 K where an endothermic process takes place is shown in fig. 2(a). Fig. 2(b) shows the behaviour of Grafoil at 29.19 K, where an exothermic process occurs. These logarithmic plots provide information on the relaxation times and the energy involved in these processes. When two superimposed (in parallel) endothermic processes take place the equation A T = A7Jl -exp(-t/z)] (1) A T = AT,[l -exp(-z/z,)]+AT,[l -exp(-t/z,)] is used. In this equation AT = T,, - &, , and AT, = &, , - qnf, 2.T,, is the temperature determined by extrapolation of the linear section of the logarithmic plot of the first part of the after-period to zero time (with the shorter relaxation time zl), T,,, is the1592 RELAXATION ON GRAPHITIC SURFACES 20.5791- 20.570 I (=) 20.577 /- I 20.576 i * 20.575 c i 19.5491 I I tlmin 12.426 1 12.424 12.422 12.420 11.317 / 10.329 10.328 Lr g * 7 0 t L I r L . L 20 t/min 30 4 0 9.703 Fig. 1. After-periods of consecutive heat-capacity measurements determined (a) for Spheron close to the crossover temperature and (b) for 4He adsorbed on Grafoil at 0.88 cm3 (s.t.p.) g-' adsorbent coverage and at temperatures close to the crossover temperature. temperature determined again by extrapolation to zero time of the subsequent linear section of the logarithmic plot (related to the longer relaxation time z,), and Tnf,, is the temperature approached at infinite time.As a first approximation, which is considered sufficient for this presentation, the following procedure was followed. First, the data obtained from the after-periods, T as a function of t, were plotted in the form In ( T - Tnf, ,) against t. A linear relationship was observed in these logarithmic plots, but only after the first part of the after-period mentioned above.A. A. ANTONIOU 1593 t/min Fig. 2. Logarithmic plots of the after-periods in which (a) an endothermic and (6) an exothermic process is observed. (a) 7 = 22 min, qnf = 4.1718 K ; (b) 7 = 24.9 min, qnf = 29.1900 K. Secondly, the T against t data obtained within the first part of the after-period were replotted in a similar manner, but with determined from the temperature close to that at which an approach to the straight line in the logarithmic plot (with the longer relaxation time) was observed.In this way both the relaxation times and the energies involved in these processes were determined. The general behaviour of these prolonged after-periods has already been presented in fig. 3 of ref. (1). An example of the logarithmic plots of the two superimposed processes is shown in fig. 3 (a) and (6). The initial decay of T with time at the lower temperatures is not directly related to the processes but to heat diffusion within the system [fig. 3(a)]. An analysis of the after-periods of the heat capacities for Spheron is presented here between 2 and 30 K.Between the first and second series of these measurements the calorimetric data for neon adsorbed on Spheron took place over a period of more than a year. For Grafoil this analysis is presented between 2 and 40 K. These data correspond to those determined from the heat capacities for Grafoil (in the absence of adsorbates) obtained after calorimetric measurements of 4He adsorbed on this substrate had been completed and the system had been kept at room temperature for more than two years. The same data determined prior to the calorimetric measurements on 4He confirm the data presented here. In the presence of 4He adsorbed on Spheron these data were determined between 2 and 15 K and for Grafoil from 8 to over 30 K. Because of the different temperature ranges in which the calorimetric data were determined for Spheron and Grafoil the endothermic processes presented here refer to results for 4He on Spheron and the exothermic ones mainly to 4He on Grafoil.RELAXATION TIMES The relaxation times of the endothermic and exothermic processes as determined for Spheron (in the absence of the adsorbate) are shown in fig. 4(a) and 5(a). The corresponding relaxation times for Grafoil are shown in fig. 6(a) and 7(a), respectively.1594 RELAXATION ON GRAPHITIC SURFACES t 0 -5.0 - I I I I I I00 200 300 400 500 600 -6.0 tlmin Fig. 3. *He adsorbed on Spheron. Logarithmic plots of the after-period of a heat-capacity measurement during which two superimposed endothermic processes are observed. (a) Loga- rithmic plot of the first part of the after-period with the shorter relaxation time (z,) (superimposed on that with the longer relaxation time) and determined with Tnf, as described in the text. (The initial exponential decay of the temperature is related to heat diffusion within the system: coverage = 22.26 cm3 (s.t.p.) g-’ adsorbent, z1 = 39 min, qnf, = 3.560 K.) (6) Logarithmic plot of the after-period with the longer relaxation time (z,) and determined with Tnf, (the temperature the system approaches at infinite time: coverage = 22.26 cm3 (s.t.p.) g-l adsorbent, z, = 153 min, qnf.= 3.482 K). For both substrates the relaxation times of the endothermic processes at first increase with increasing temperature ; after passing through a peak they decrease sharply as the temperature approaches the ‘crossover’ temperature where the change from an endothermic to an exothermic process occurs. For Spheron the peak occurs at ca.10 K with relaxation times of ca. 15 and > 20 min for the first and second series of measurements, respectively. For Grafoil the peak increases to higher values of > 40 min at ca. 3 K. The relaxation times of the exothermic processes for both substrates increase with increasing temperature. Such an increase is more evident for Grafoil, since these data were determined over a wider temperature range than for Spheron. A comparison ofA. A. ANTONIOU 1595 \ 1.5- I M I " M 2 1.0 - G 1 0 a 0.5 - - 0 3 T/ K Fig. 4. (a) Relaxation times and (b) relaxed heat capacities of the endothermic processes (Cendo) observed for Spheron in two series of measurements. The arrow indicates the crossover temperature (see text).0, First series; 0, second series. the relaxation times of the exothermic processes at similar temperatures indicates that the values for Spheron are lower than those for Grafoil. Fig. 8(a) shows the relaxation times of the endothermic processes in the presence of 4He adsorbed on Spheron for the 7.93cm3 (s.t.p.)g-l adsorbent coverage but only at temperatures close to the crossover temperature. For the two higher coverages (fig. 9 and 10) the data were determined at lower temperatures and the relaxation times of the two superimposed processes are presented. Again these increase at first with increasing temperature. Above a certain temperature, however, a decrease in the values of both z, and z, is observed with increasing temperature, reaching the crossover temperature at which the change from endothermic to exothermic processes takes place.Furthermore, at a particular coverage the values of z, are seen to be higher than the corresponding values of 7,. The data for the lowe! 4.88 cm3 (s.t.p.) g-l adsorbent coverage are not presented here. These data are not as precise because these were the first in which the prolonged after-periods were observed. It is only mentioned here that the average z, and z, values are ca. 22 and 75 min, respectively. The isosteres of the relaxation times of the exothermic processes for 4He on Spheron1596 RELAXATION ON GRAPHITIC SURFACES I I 0 20 25 30 35 TI K Fig. 5.(a) Relaxation times and (b) relaxed heat capacities of the exothermic processes (C,,,) observed for Spheron. W and 4He on Grafoil are shown in fig. 11 (a) and 12, respectively. In the case of 4He on Spheron their values, determined within the monolayer region, are shown to decrease with increasing temperature within the small temperature range in which these are determined. On the other hand, in the case of 4He on Grafoil a similar decrease is observed but only at the lower coverages and within a small temperature range, for reasons discussed below. Above this coverage and temperature range, the relaxation times increase with increasing temperature. RELAXED HEAT CAPACITY The relaxed heat capacity, i.e. the energy involved in the endothermic or exothermic process observed during the heat-capaci ty measurements and calculated per degree increase in the temperature, is defined here as Cendo or Cexo, respectively.In the absence of adsorbates their values are calculated using the equation where Ccal+graph is the heat capacity of the calorimeter with the graphitic adsorbent, AT = T, - Tnf for an endothermic process and qnf - T, for an exothermic one. TnitA. A. ANTONIOU 1597 50 40 E .- $ 30 .- : ; 20 c, E .- U w Q) 10 0 0.10 - I 00 " I Y E 0.05 h 1 0 'c) Lie 0.0 0 TI K Fig. 6. 50< 20 O. 0 10 TI K Fig. 7. Fig. 6. (a) Relaxation times and (b) relaxed heat capacities of the endothermic processes (Cendo) observed for Grafoil. The arrow indicates the crossover temperatures (see text). Fig. 7. (a) As fig. 6 but for the exothermic processes (Cexo).is the temperature of the system before the electrical energy, Q, is applied. In this calculation it is assumed that Ccal+graph is equal to Q/(T,- Tnit), i.e. to the energy adsorbed by the vibrational modes of the graphitic material before the endo- or exo-thermic process takes place. The Centlo values for Spheron and Grafoil calculated using eqn (3) are shown in fig. 4(6) and 6(b), respectively. Starting from the lowest temperature of measurement (ca. 2 K) the Cendo values for Spheron and Grafoil increase with increasing tempera- ture, pass through a maximum at ca. 15 K for Spheron and 7 K for Grafoil, and then decline as the temperature approaches the crossover temperature, above which exothermic processes are observed. Comparison of the Cendo values for the two types of graphite at temperatures where the increase in Cendo with increasing temperature occurs in both cases, shows considerably larger values for Spheron than for Grafoil.The Cendo values of the second series of measurements on Spheron are higher than those observed during the previous set of measurements. The C,,,, values for Spheron between 20 and 30 K and for Grafoil between 12 and1598 RELAXATION ON GRAPHITIC SURFACES 6 8 10 T K Fig. 8. 4He adsorbed on Spheron. (a) Relaxation times and (b) relaxed heat capacities of the endothermic processes (Cendo) observed during the after-periods of the heat capacities determined at 7.93 cm3 (s.t.p.) g-' adsorbent coverage but at temperatures close to the crossover temperature (indicated by the arrow).40 K are shown in fig. 5 (b) and 7 (b), respectively. In both cases Cexo is seen to increase with increasing temperature. This behaviour is similar to that already mentioned for the relaxation times. However, the values presented for Spheron are lower than those for Grafoil in the same temperature range. The percentage contribution of Cendo and Cexo to the heat capacities of Spheron and Grafoil can only be estimated within a few percent from the present data. (The heat capacity of the surrounding vessel has not been determined experimentally as yet.) In this estimation the heat capacity of the vessel was calculated using the heat-capacity values of high-purity aluminium for Spheron and high-purity copper for Grafoil. For Spheron the Cendo values increase from CQ.10 to 20% of the estimated heat capacity of Spheron between 3 and 15 K during the first series of measurements. During the second series the Cendo values are higher and these vary from ca. 35% at 3 K to 22% at 10 K and 35% at 15 K. For Grafoil the values are found to vary from ca. &lo% between 3 and 7 K. Above 15 K for Spheron and 7 K for Grafoil these values decline, as shown in fig. 4(b) and 6(b), respectively. The C,,, values for Spheron increase progressively up to CQ. 24% for the estimated heat capacity of this material between 20 and 30 K. For Grafoil these values increase above 12 K up to ca. 13, 23 and 50% at 20, 30 and 40 K, respectively. In the presence of the adsorbate, Cendo (or Cexo) is calculated using the equation In the cases in which only one process takes place, AT = T, - Tnf (or Tnf - T,) for an endothermic (or exothermic) process.For the after-periods in which two super- imposed endothermic processes are observed the energies associated with the twoA. A. ANTONIOU 1599 0 5 10 Tl K Fig. 9. *He adsorbed on Spheron. (a) Relaxation times (0, T~ and 0, 72) and (b) relaxed heat capacities of the two superimposed endothermic processes (0, Cendo.1 and 0, Cendo,2) observed during the after-periods of the heat capacities determined at the 12.30 cm3 (s.t.p.) g-l adsorbent coverage. The arrow indicates the crossover temperature at this coverage. superimposed endothermic processes presented here per degree increase of tempera- ture, which correspond to z, and z, are defined here as Cendo,, and Cendo,?, respectively.For Cendo, , AT = &, , - &, ,, for Cendo, AT = &, - qnif, and in thls case qnf = I;nf,2. Cads is the heat capacity of the adsorbed gas and Cg is the heat capacity of the gas in the calorimeter dead space. qst is the isosteric heat of adsorption. The values of qst which correspond to 4He on Grafoil were determined at a particular coverage and temperature from the pressure isotherms at 1 K difference.2 An is the1600 RELAXATION ON GRAPHITIC SURFACES 2oo I 0 5 10 TIK Fig. 10. As fig. 9 but for 22.26 cm3 (s.t.p.) ggl coverage. number of moles adsorbed (desorbed) during the endothermic (exothermic) process, 5 is the dead space in the calorimeter and P is the pressure. In this calculation the total value of (Cca,+graph + Cads + C,) was calculated according to the equation where A T = T,, 1- Tnit for an endothermic process and AT, = T,- qnit for an exothermic one.By inserting in this calculation the value for the endothermic processes (and the T, values for the exothermic ones) it is assumed that the energy absorbed by the graphitic material (including the adsorbate) corresponds to the energy absorbed by the vibrational modes only before the endo- or exo-thermic process takes place. In this equation An is the number of moles desorbed with the increase of temperature from Tnit to T, (T,, l). For 4He on Spheron the Cendo values for the 7.93 cm3 (s.t.p.) ggl adsorbent coverage are shown in fig. 8 (b) at temperatures close to the crossover temperature. For the two higher coverages the Cendo, and Cendo, values (which correspond to the relaxation times z, and z, respectively), calculated according to eqn (4), are shown in fig.9(b) and lO(b).A. A. ANTONIOU 1601 15 .4 6 10 --.. .- ; 3 5 + c: .- + 0 I .5 -i 1.0 M E b. 0.5 M d I h --. 0.0 ,c $1 t I J 15 Fig. 11, 4He adsorbed on Spheron. (a) Relaxation times and (b) relaxed heat capacities of the exothermic processes (C,,,,) observed during the after-periods of the heat capacities at different coverages. The arrows indicate the decrease of the crossover temperature with increasing coverage. In general these energies increase with increasing temperature, from the lowest temperature at which these processes are observed, following the similar trend of the corresponding relaxation times. Above a certain temperature a decrease in these energies towards zero with increasing temperature is observed as the crossover temperature is approached. Unlike their corresponding relaxation times, the Cendo, values are shown to be higher than the corresponding Cendo, values, and the latter reach a maximum value at approximately the same temperature at which the corresponding relaxation times reach their higher values.For the lower 4.88 cm3 (s.t.p.) g-l adsorbent coverage, for which the data are not as precise for reasons mentioned above, the average Cendo, and Cendo, values are ca. 1.5 and 0.7 mJ K-l g-l, respectively. The relatively high equilibrium pressures observed in the adsorption of 4He on Grafoil, within the temperature range for the exothermic processes, result in a decrease of coverage for a series of heat-capacity measurements. For this reason data determined from the logarithmic plots, i.e.the relaxation times and the corresponding C,,, values, together with the coverages at which these are observed, were first plotted against T. From these plots relaxation times and the corresponding C,,, values were determined as a function of coverage at constant temperature (isotherms), and the 53 FAR 11602 RELAXATION ON GRAPHITIC SURFACES Fig. 12. 4He adsorbed on Grafoil. Relaxation times plotted against temperature (at constant coverage) of the exothermic processes observed during the after-periods of the heat-capacity measurements at different coverages [denoted in cm3 (s.t.p.) g-l adsorbent]. data were then replotted as a function of temperature at a constant coverage (isosteres).The isosteres of the Cexo values for *He on Spheron and on Grafoil are shown in fig. 11 ( b ) and 13, respectively. For both systems the Cexo values of these isosteres increase with increasing temperature. Within the temperature and coverage range in which the completion and formation of the second monolayer takes place this increase is even more pronounced. DISCUSSION RELAXATION PROCESSES ON SPHERON AND GRAFOIL In general, relaxation processes observed during the after-periods of the calorimetric measurements on the graphitic materials Spheron and Grafoil should be related to the particular thermal properties of graphite, especially to those at the outermost surface layers. The thermoelastic stresses in these layers caused by the irregular distribution of atoms on sites8 might contribute to the rate at which both the endothermic and exothermic processes occur. This disorder differs between Spheron and Grafoil owing to their different structures and results in the differences in the processes described here for these graphitic materials.ENDOTHERMIC PROCESSES The particular thermal properties of graphite, especially at low temperatures, are attributed to the excitation of the lower limiting frequency of the out-of-plane modesA. A. ANTONIOU 1603 L L 0 4.65 3.88 3.10 L i b 30 T/K Fig. 13. 4He adsorbed on Grafoil. Relaxed heat capacities of the exothermic processes (Cexo) plotted against temperature (at constant coverage) which take place during the after-periods of heat-capacity measurements at different coverages [denoted in cm3 (s.t.p.) g-l adsorbent]. in comparison with the higher in-plane modes.l*v l5 For lower temperatures most of the energy is absorbed by the out-of-plane modes, so it is reasonable to correlate the endothermic processes that are observed during the after-periods of the low-temper- ature heat-capacity measurements with the thermal expansion along the c axis of these graphitic substrates, and especially with the excess of thermal expansion at the outermost surface layers. The surface thermal expansion excess is related to the anharmonicity,16 and the coefficient of the surface thermal expansion has been found to pass through a high peak at low temperatures.l7* l8 At 0 K atoms within the graphitic materials are expected to be located at their closest approach.However, with increasing temperature ‘ for carbon materials of different graphitic perfection there will be different limiting distances of closest approach between the layers’.19 The distribution of limiting distances of closest approach results in thermoelastic stresses especially in the outermost surface layers. The relatively high relaxation times of the endothermic processes could thus be related to the change in the interlayer force distribution caused by a rearrangement of the carbon atoms within the disordered regions of these graphitic planes with increasing temperature. The corresponding Cendo values could also be ascribed to the energy involved in these processes. The increase in the relaxation times and Cendo values with increasing temperature 53-21604 RELAXATION ON GRAPHITIC SURFACES (fig.4 and 6 ) may be attributed to the ‘frozen-in defects (which) can have relatively large effects in the heat capacity and thermal expansion’.20 These defects result in an increase in stress inhomogeneities and a corresponding increase in the relaxation times. However, above a definite temperature, owing to the expanding interplanar distance (which reduces the forces between these layers), a decrease in both the relaxation times and Cendo values with increasing temperature occurs, as should be expected. Thermal expansion continues above the temperatures at which the endothermic processes are observed. These processes occur at a faster rate during the period in which electrical energy is applied (i.e.the heat-capacity measurement) and are not observed in the after-periods. CHANGES IN THE STRUCTURE OF SPHERON The higher Cendo values observed for Spheron in the second series of these measurements, as compared with those in the first, together with the higher relaxation times (fig. 4), may be related to a change in the structure of Spheron. This change takes place when the system is brought to liquid-helium temperatures between these two series of measurements and the calorimetric data on adsorbed neon are obtained as mentioned above. The heat capacity of Spheron determined, as usual, from the initial temperature and final temperature which the system approaches during thermodynamic equili- bration is referred to here as Ctotal.In this case where Ccal is the heat capacity of the calorimeter vessel. As a first approximation Ctotal is the sum of c v i b (the heat capacity from the absorption of energy by the vibrational modes only, before the endo- or exo-thermic process takes place) and Cendo (or Cexo), as given by the equation where Calorimetric data estimated for Spheron indicate that, at ca. 2 K, the Cvib values during the second series of measurements are ca. 1 5-20 % lower than the corresponding values of the first series. This difference decreases towards zero with increasing temperature to and above 15 K. However, the corresponding C,,,,, values of Spheron, including the heat capacity of the calorimeter vessel during the second series of these measurements at temperatures below 15 K, are from 0.5 to 1% higher than the corresponding values of the first series.These higher Ctotal values are related to the corresponding higher Cendo values. At these low temperatures most of the energy is absorbed by the out-of-plane modes, and the lower Cvib values suggest that on average the interplanar distance (especially at the outermost layers) is less in the sample used in the second series of measurements. In other words, the surface structure of Spheron was irreversibly changed by the contraction to which the system was subjected when brought to liquid-helium temperatures. Therefore both the increased Cendo values and relaxation times observed during the second series of measurements should be related to the increased interplanar forces and defects.A.A. ANTONIOU 1605 COMPARISON OF THE ENDOTHERMIC PROCESSES OBSERVED ON SPHERON AND GRAFOIL The difference in magnitude of the relaxation times of the endothermic processes in the lower temperature range, above 2 K, which are higher for Grafoil than for Spheron [fig. 4(a) and 6(a)], might be related to differences in their structure. For Grafoil, which is a compressed powder, the strong misalignment of the basal planes parallel to the Grafoil surface, together with their shorter interplanar distances, might result in the larger differences in the interplanar forces; for Spheron these differences may be ascribed mainly to the non-hexagon regions. The lower Cendo values for Grafoil as compared with those for Spheron [fig. 4(b) and 6(b)] may be attributed partly to the smaller surface area in the case of Grafoil.[The surface area is related to the coverage at which the calorimetric heat of adsorption of an adsorbate, qst, declines steeply. For 4He on Spheronl and 4He on GrafoiP the qst values decline at 12 K at coverages of ca. 22 and 8 cm3 (s.t.p.) g-' adsorbent, respectively.] Since the interplanar forces are stronger in the case of Grafoil (a compressed powder) than for Spheron,1° these lower values also indicate that the coefficient of thermal expansion of Grafoil should be smaller than that of Spheron. The decrease in the temperature of the peaks of both relaxation times and Cendo values which is observed for Grafoil as compared with Spheron could also be influenced (in addition to the decrease in the interplanar force with increasing temperature, as mentioned above) by the energy absorbed by the in-plane modes, whose frequency is lower in Grafoil than in Spheron.This energy results in the exothermic processes discussed below. The results presented here provide clear evidence that the thermal conductivity in these graphitic materials is not the dominating factor in the slow processes observed in the after-periods. It is known that surface atoms are arranged in a different way from those in the bulk material.21 With increasing temperature the rearrangement of the atoms in the outermost surface layers (especially for Spheron and Grafoil because of their lattice distortions) may result in surface disturbances which spread as surface waves and which may contribute to heat diffusion within these materials.EXOTHERMIC PROCESSES The thermal expansion parallel to the c axis of graphite is accompanied by a contraction along the basal planes which occurs at these low temperature^.'^ The structural irregularitiss which exist in both Spheron and Grafoil, especially within their outermost surface layers, might result in the increased relaxation times with which this contraction occurs. In these surface layers the thermal expansion excess decreases the in-plane interatomic distances more for the upper than the lower surface layers. The exothermic processes are observed at higher temperatures than the endothermic ones because the limiting vibrational frequency of the in-plane modes is higher than that of the out-of-plane modes. For the same reason, these processes occur at higher temperatures for Spheron than for Grafoil.For Spheron the in-plane interatomic distances are expected to be smaller than those of Grafoil because the interplanar distances in this materiallo are larger than in the compressed powder. In fact, similar data obtained in the presence of 4He and Ne2 adsorbed on these substrates indicate that the structure of the outermost surface layers of these adsorbents is modified in a similar way through the forces exerted by the superimposed films. The increase in the relaxation times with increasing temperature observed for both Spheron and Grafoil [fig. 5 ( a ) and 7 (a)] may be attributed to structural changes within the disordered regions, especially of the outer surface layers. The corresponding increase in the C,,, values [fig.5 (6) and 7 (b)] indicates a strong increase of the in-plane1606 RELAXATION ON GRAPHITIC SURFACES interatomic energy caused by the decreasing interatomic distances and the increase in the mean-square vibrational amplitude of the in-plane modes. The increasing negative coefficient of thermal expansion perpendicular to the c axis of graphite above the temperatures reported here15 suggests that these values may increase even more at higher temperatures within the temperature range in which this coefficient is negative. RELAXATION PROCESSES IN THE PRESENCE OF ADSORBED 4He ENDOTHERMIC PROCESSES The two superimposed first-order endothermic processes which are observed for 4He adsorbed on Spheron at low temperatures [fig.9 and 101 have relatively high relaxation times which probably arise from thermal-expansion processes : the faster (tl) process from the expansion of the 4He film and the longer (z,) process from the expansion of the outermost surface graphitic layers. The reasons for this are as follows. The formation of the 4He films superimposed on the graphitic substrates is characterized by endothermic processes which are observed during the after-periods of the calorimetric qst, as will be discussed in Part 2. Although these qst values were determined at temperatures > 10 K for both Spheron and Grafoil, it is reasonable to assume that the superimposed film on this substrate remains as such even at the lowest temperatures at which the present calorimetric data are obtained. The relatively long relaxation times of these processes might result from the interaction of the adatoms, especially those ‘trapped’ at ‘ high-energy ’ sites, with the substrate.This interaction deforms the substrate lattice2, and results in longer relaxation times and higher ‘relaxed heat capacities’ for these processes. A similar, but smaller, increase in relaxation times is observed during the after-periods of the heat capacities determined for neon adsorbed on Spheron., The binding energy between the 4He films and the graphitic substrate is considerably lower (varying between 1 . 1 and 0.95 kJ mol-l depending on coverage)’ than the binding energy between graphitic layers (ca. 33 kJ m ~ l - ~ ) . ~ ~ The density of the 4He films is also lower than the density of the graphitic layers.These differences, together with the increased deformations of the substrate lattice of the outermost surface layers mentioned above, should result in the larger variation of stresses between the outermost graphitic layers as compared with the corresponding layers of the superimposed film. The relaxation times are related to the activation energy, Q, by an Arrhenius equation23 z = zo exp(Qlk7‘). (7) Since this energy depends on a variation in stress, the thermal expansion within the films is expected to occur with shorter relaxation times (z,) rather than the longer z, of the outermost graphitic layers. However, the higher energies absorbed during the endothermic processes which correspond to the expansion of the 4He films, Cendo, ,, as compared with the lower Cendo,, values of the graphitic layers, together with the weaker forces exerted between this film and the substrate, as compared with the corresponding forces between the graphitic layers, indicate that the coefficient of thermal expansion of these films is higher than that of the outermost graphitic layers, as expected.This is also indicated from the steeper decline of the z, and Cendo, curves to lower temperatures as compared with the corresponding z2 and Cendo, , curves above the temperature at which these increase to a maximum (fig. 9 and 10). At temperatures close to the crossover temperature a single endothermic process is observed, as shown in fig. 8. The higher z2 and Cendo,, values observed within the lower temperature range inA.A. ANTONIOU 1607 which these increase with increasing temperature, as compared with the corresponding values for Spheron (in the absence of adsorbate), together with the lower temperature above which these values decline (and the lower crossover temperature above which the exothermic processes are observed), may be attributed to the increase in the coefficient of thermal expansion, especially of the outermost surface graphitic layers, in the presence of the superimposed film. The reasons for this are as follows. The decrease of the crossover temperature above which the exothermic processes are observed with increasing coverage should be attributed to the increase of the in-plane interatomic distances of the carbon atoms within the outermost surface graphitic layers caused by the presence of the superimposed film.The increase of the in-plane interatomic distances decreases the limiting vibrational frequency of the in-plane modes and consequently the temperature at which energy is absorbed by these modes. At 0 K this increase should also result in a corresponding decrease of the interplanar distance (Poisson's contraction) and the consequent increase of the interplanar forces. The increase in lattice deformations in the presence of the adsorbate,22 together with the increase in the interplanar forces, might contribute to the increase in defects which lead to larger Cendo, values.2o Similarly, the increased stress inhomogeneity increases the relaxation times with which these processes occur.The present data indicate clearly that the coefficient of thermal expansion of the outermost graphitic surface layers increases in the presence of the film. This increase is controlled by the difference in the binding energy of the film to the substrate, on the one hand, and the corresponding binding energy between the graphitic layers, on the other. At lower temperatures the z, and Cendo,B values are higher, but above a certain temperature the increase in the coefficient of thermal expansion of the outermost surface graphitic layers decreases the interplanar forces at lower tempera- tures, and this decrease results in the corresponding decrease of the z2 and Cendo,z values. The same behaviour is observed for similar calorimetric data determined on adsorbed neon on the same substrate, Spheron.In this case, however, the temperature at which these data decline towards zero and above which the exothermic processes are observed is higher than the corresponding one in the presence of adsorbed 4He.2 The relaxation times, z, which correspond to the coverages reported here indicate that these are also influenced by the density of the superimposed 4He films. The maximum relaxation times at a coverage of 12.3 cm3 (s.t.p.) g-l adsorbent [fig. 9(a) are > 200 min, whereas those determined at the lower [4.9 cm3 (s.t.p) g-l absorbent] and the higher [22.3 cm3 (s.t.p.) g-l adsorbent] coverages increase to ca. 75 and 150 min, respectively. Similar behaviour is observed in the relaxation times of the exothermic processes observed for 4He on this substrate [see fig.11 (a)]. EXOTHERMIC PROCESSES The increase in Cex0 values with increasing coverage (at constant temperature) and with increasing temperature (at constant coverage), as observed for both substrates [fig. 11 (b) and 131, is similar to that in the absence of adsorbates. This increase should also be related to the increase of the mean-square displacement of the carbon atoms caused by the lowering of the limiting vibrational frequency with increasing coverage (at constant temperature) and to a similar increase accompanying an increase in temperature. The higher relaxation times characteristic of the exothermic processes that occur in the presence of 4He on Grafoil as compared with those in the absence of the adsorbate should again be attributed to the increased deformation of the substrate lattice.,,1608 RELAXATION ON GRAPHITIC SURFACES The decrease in relaxation times with increasing temperature observed within the lower temperature range for both systems, 4He on Spheron and on Grafoil, may be related to the decrease in the number of adatoms ‘ trapped’ at the ‘high energy’ sites with increasing temperature, as will be discussed in Part 2.This number is considerably higher on Spheron than on Grafoil. For 4He on Spheron, within the relatively small temperature range in which exothermic processes are observed, only a decrease in the relaxation times with increasing temperature is observed. However, at higher temperatures than those reported here an increase in these relaxation times should be expected for this system with increasing temperature.For 4He on Grafoil a decrease in relaxation times with increasing temperature is observed from the present data within the lower coverage range only. However, if these data were determined at lower temperatures (below 8-9 K) this decrease would be expected to be observed at higher coverages also. LONG-TIME HEAT RELEASE DURING THE COOLING PROCESS In the present cryostat the cooling of the calorimeter to low, especially liquid-helium, temperatures takes place by heat conduction along the electrical leads between the calorimeter and the surrounding envelope. The rate at which heat is released from the calorimeter thus depends on the heat-leakage modulus along these leads and the temperature difference between the calorimeter and the envelope.Under these conditions the cooling of Spheron from 4.5 to 1.7 K required a period of ca. 9 h, but that of Grafoil, from 4 to ca. 2.2 K, required > 26 h, although the total heat capacity of the calorimeter (including the Grafoil sample) was ca. 10% lower than that with the Spheron sample in the same temperature range. The cooling of the system *He on Spheron from 4 to 2 K, especially at coverages of 12.3 and 22.26 cm3 (s.t.p.) g-l adsorbent, required ca. two days, as already reported [see ref. (24) of ref. (l)]. If during this cooling the temperature difference between the calorimeter and the envelope was reduced below a certain value by a few hundredths of a degree, the temperature of the calorimeter increased slowly, indicating heat release within the system.In some cases this release lasted for a few hours, especially at helium and sub-helium temperatures. The longer periods which were required to cool Grafoil as compared with Spheron, especially at sub-helium temperatures, together with the slow rate of heat release when the calorimeter-envelope temperature difference is small, might be attributed to the long-time heat release which takes place during the cooling of this system. This heat release may result from the thermoelastic cooling due to the reorientation of the short crystallites in Grafoil; for Spheron, especially in the presence of adsorbed 4He, it may be due to substrate-lattice deformations. A similar heat release is also observed when the system is subjected to vibrations. These vibrations occur when liquid nitrogen is transferred to the Dewar surrounding the cryostat. In the case of 4He on Spheron and on Grafoil this heat release was again longer than on Spheron (in the absence of adsorbate) and lasted for 2-3 h. A. A. Antoniou, J . Chem. Phys., 1975, 62, 779. A. A. Antoniou, unpublished results. A. A. Antoniou, P. H. Scaife and J. M. Peacock, J . Chem. Phys., 1971, 54, 5403. A. A. Antoniou, J . Chem. Phys., 1976, 64, 4901. A. Ravex, J. C. Lasjaunias and D. Thoulouze, J. Phys. (Paris), 1980, 41, 749. M. T. Loponen, R. C. Dynes, V. Narayanamurti and J. P. Garno, Phys. Reu. B, 1982, 25, 1161 J. Zimmermann and G. Weber, Phys. Rev. Lett., 1981, 46, 661. V. N. Trofimov, J . Low Temp. Phys., 1984, 54, 555.A. A. ANTONIOU 1609 G. L. Kington and J. G. Aston, J. Am. Chem. Soc., 1951,73, 1929; J. A. Morrison and G. J. Szasz, J. Chem. Phys., 1947, 16, 280; R. J. Tykodi, J. G. Aston and G. D. L. Schreiner, J. Am. Chem. SOC., 1955, 77, 2168. B. T. Kelly, Proc. 4th Znt. ConJ Carbon and Graphite (Society of Chemical Industry, London, 1976), p. 598. H. Taub, K. Carneiro, J. K. Kjems, L. Passel and J. P. McTague, Phys. Rev. B, 1977, 16, 4551. l 3 M. Nielsen, and J. P. McTague, Phys. Rev. B, 1979, 19, 3096. l 4 J. B. Nelson and D. P. Riley, Proc. Phys. SOC. London, 1945, 57, 477; D. P. Riley, Proc. Phys. Soc. l5 B. T. Kelly, Physics of Graphite (Applied Science Publishers, London, 1981), chap. 4. l 6 M. G. Lagally, in Surface Physics of Materials, ed. J . M. Blakely (Academic Press, New York, 1975). l 7 V. E. Kenner and R. E. Allen, Phys. Rev. B, 1973, 8, 2916. lo W. D. Schaeffer, W. R. Smith and M. H. Polley, Ind. Eng. Chem., 1953,45, 1721. London, 1945, 57, 486. L. Dobrzynski and A. A. Maradudin, Phys. Rev. B, 1973, 7, 1207. E. A. Kellet and B. P. Richards, J. Appl. Crystallogr., 1971, 4, 1. "O T. H. K. Barron, J. G. Collins and G. K. White, Ado. Phys., 1980, 29, 609. 'I P. Bak, Physica, 1980, WB, 325. 22 M. B. Webb and L. W. Bruch, in Interfacial Aspects of Phase Transformations, ed. B. Mutaftschiev 23 A. S. Nowick and B. S. Berry, Anelastic Relaxation in Crystalline Solids (Academic Press, New York, (Reidel, Dordrecht, 1982), p. 365. 1972), p. 58. (PAPER 4/ 1293)

ISSN:0300-9599    

DOI:10.1039/F19858101589

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1985,81, 1611-1622 Relaxation Processes on Graphitic Surfaces Part 2.-Adsorption of 4He on Spheron and Grafoil BY ANTONIOS A. ANTONIOU Division of Chemistry, National Research Council of Canada, Ottawa, Canada KIA OR6 Received 24th July, 1984 An analysis of the after-periods of the calorimetric heat of adsorption determined for 4He on Spheron at temperatures close to 12 K and for 4He on Grafoil between 8 and 12 K provides information on the processes by which adsorption takes place with increasing coverage. Within the lower coverage range the exothermic processes which follow the steep rise of temperature occurring when the adatoms come into contact with the adsorbent surface are related to the migration and ‘trapping’ of the adatoms at the ‘high-energy’ sites of these adsorbents.Above a certain coverage, depending on structure (especially of the outermost surface layers of the substrate), the steep rise of temperature is followed by endothermic processes. These processes are related to the rearrangement of the adatoms in different configurations within the films superimposed on the surface of the adsorbent. At higher coverages, during the completion of the first monolayer and the formation of the second, both the relaxation times and the energies involved in the endothermic processes provide information on the processes by which the formation of the superimposed second monolayer takes place. In this paper the data obtained from the after-periods of measurements of calorimetric isosteric heats of adsorption, qst, for the systems 4He on Spheron and 4He on Grafoil are presented and discussed.For both systems these qst values were determined within and up to the completion of the first monolayer. For Spheron these data were determined between 1 1 and 13 K in three successive series of measurements. The first two were carried out only within the lower coverage range. For Grafoil qst values were determined between 9 and 13 K together with a few data points close to 8 K, but only within the higher coverage range during the completion of the first monolayer .2 The initial steep decline of the qst values (as well as those determined for neon on Spheron3) within the lower coverage range was attributed to the adsorption of adatoms at the ‘ higher-energy ’ sites of the adsorbent.’. The pressure isotherms for these systems determined at the same temperatures are convex to the pressure axis in this range for the same ~eason.~ The after-periods of these qst reveal that, following the sharp increase of temperature of the whole assembly (calorimeter + adsorbent + adsorbate) which occurs as soon as the gas is adsorbed onto the surface of the adsorbent, thermodynamic equilibrium is approached through an exothermic process.The sharp increase of temperature and the exothermic process which follows are shown schematically in fig. 1 (a). At higher coverages, above the coverage at which the qst decline sharply, the sharp increase in temperature of the whole system mentioned above is followed by a cooling process, which suggests that the thermodynamic equilibrium takes place through an endothermic process.This is shown in fig. l(6). 161 11612 RELAXATION ON GRAPHITIC SURFACES t I Fig. 1. (a) Schematic diagram showing the sharp increase in temperature of the whole assembly (calorimeter+adsorbent+adsorbate) as soon as the gas is adsorbed on the surface of the adsorbent, followed by a gradual increase due to the warming (exothermic) process with which thermodynamic equilibrium takes place within the system. (b) As (a), but here thermodynamic equilibrium takes place through an endothermic process. There is experimental evidence5 which indicates that exothermic processes similar to those reported here occur during the adsorption of nitrogen and neon on rutile. This is discussed later. RESULTS EXOTHERMIC PROCESSES The logarithmic plots of In (&- T ) against t for an exothermic process [or In ( T - Tnf) against t for an endothermic one] derived from the recorded qst after- periods for 4He on Spheron and Grafoil fall on a straight line (see fig. 2 and 3).This indicates the first-order kinetics with which the exo- and endo-thermic processes take place during these after-periods. The only exception to this behaviour is observed during the after-period of the first dose in each series of measurements. The logarithmic plots for these measurements suggest that two consecutive exothermic processes take place with different rate constants, as shown in fig. 4. The first process takes place with the longer relaxation time and the energy evolved is larger than in the consecutive process. For 4He on Spheron there is similar behaviour during the after-periods of the first dose of each of the three series of measurements within the temperature range 11-1 3 K.The same behaviour is also observed for 4He on Grafoil as well as for neon on Spheron.2 RATE CONSTANTS The rate constants, k , of the exothermic processes (determined from the slope of the above-mentioned logarithmic plots) are plotted in fig. 5 as Ink against 1/T. For the first part of the first dose k falls along a straight line, whereas for the second part it lies on a separate line with larger slope. The rate constants of the consecutive doses again fall on a separate line but with a higher slope than the previous ones. The activation energies determined from the slopes of these lines increase with increasing coverage from ca.1060 J mol-1 for the first part of the first doses to ca. 1600 J mol-l for subsequent doses.A. A. ANTONIOU 1613 11.34 tlmin Fig. 2. 4He adsorbed on Spheron. Logarithmic plot of the after-period of a calorimetric heat of adsorption measurement (second dose, first series). The corresponding temperature rise of the whole assembly (calorimeter + adsorbent + adsorbate) is also shown. (The initial steep temperature decay is due to the heat diffusion within the system. This decay is steeper at higher temperatures.) Fig. 3. 4He adsorbed on Grafoil. Logarithmic plot of the after-period of a calorimeter heat of adsorption measurement during which an endothermic process takes place. The corresponding decrease of the temperature of the whole assembly (calorimeter + adsorbent + adsorbate) is also shown.1614 RELAXATION ON GRAPHITIC SURFACES -l-oK----- 111.70 I 11.65 11.60 M 2 11.55 11.50 11.45 1.40 t/min Fig.4. As fig. 2 but for the first dose, first series. -2.0 - * E I - -3.0 - K/ T Fig. 5. 4He adsorbed on Spheron. Rate constants (k) of the exothermic processes which take place during the after-periods of the calorimetric heat of adsorption measurements plotted against 1 / T (Arrhenius plot). series 1 2 3 k,, first dose O A U k,, first dose O A W k, subsequent doses * A . IA. A. ANTONIOU 1615 ENERGIES INVOLVED IN THE EXOTHERMIC PROCESSES The energy involved per mole of adsorbate in the exothermic (or endothermic) processes, defined here as Qaft, was calculated using the equation where AT = Tnf - T, for an exothermic process (and T, - Tnf for an endothermic one), T, is the temperature determined by extrapolation of the logarithmic plot to zero time, [i.e.the time at which the valve on the top of the cryostat was opened and a certain amount of gas (dose) was introduced into the calorimeter], An is the number of moles desorbed (adsorbed) during the exothermic (endothermic process) and AN is the number of moles adsorbed per dose during the calorimetric 4st measurement. In this calculation the total value of (Ccal+graph + Cads + Cg) was determined as follows. First, these values [calculated in a series of heat-capacity measurements using eqn (5) of Part 11 were plotted against T. From these plots and from the corresponding plots of coverage against temperature the value of (Ccal+graph + Cads + C,) was plotted against coverage at constant temperature (isotherms).From these isotherms the values at a particular coverage and temperature were determined by graphical interpolation. In the calculation of the energy evolved for each of the two successive exothermic processes observed during the first dose (see fig. 4) the following procedure was followed as a first approximation, For the first process (with the longer relaxation time) the value of I;;nf was assumed to be close to the temperature at which the logarithmic plot changes slope. The corresponding T, value is the temperature determined by extrapolation to zero time, as mentioned above. For the second process (with the shorter relaxation time) qnf corresponds to the temperature approached at infinite time.In this process T, is assumed to equal Tnf of the first part of the after-period. Energies involved in the exothermic processes of 4He on Spheron and calculated according to eqn (1) are shown in fig. 6, together with the temperatures at which these processes are observed. This demonstrates the dependence on temperature of the coverage at which the change from an exothermic to an endothermic process occurs. This change occurs at lower coverages with increasing temperature. In the first series of qst measurements this change took place at ca. 1 1 . 1 K for a coverage of ca. 1.6 cm3 (s.t.p.) g-l adsorbent. In the third series the same change took place at ca. 12.6 K for a coverage of ca.1.2 cm3 (s.t.p.) g-l adsorbent. For 4He on Grafoil the change from an exothermic to an endothermic process is observed at ca. 10.4 K but at a considerably lower coverage than on Spheron, ca. 0.1 cm3 (s.t.p.) g-l adsorbent. Similar behaviour is observed for neon on Spheron.2 In this case the after-periods of the calorimetric qst, determined close to 24 K, indicate that the exothermic processes occur at coverages up to ca. 3.7 cm3 (s.t.p.) g-l adsorbent. However, close to 29 K the same processes are observed only up to about half this coverage. The energy released during the process which occurs during the first part of the after-period of the first dose (with the longer relaxation time) is ca. 250 J mol-1 for 4He on Spheron in all three series of measurements (fig.6). However, the energy which corresponds to the second part of the after-period (with the faster relaxation time) is only ca. 60 J mol-l and decreases with increasing coverage. For 4He on Grafoil the energies involved during the first and second parts of this after-period are ca. 190 and 65 J mol-l, respectively. These processes are discussed below.1616 RELAXATION ON GRAPHITIC SURFACES 12.99 4:; - - 12.2 'i4 13.01 0" 11.7 V/cm3 (s.t.p.) g-' adsorbent Fig. 6. 'He adsorbed on Spheron. Energies (Q,,,) involved during the exothermic processes which take place during the calorimetric heat of adsorption measurements. The numbers signifiy the temperatures at which these processes were observed. ., First series; 0, second series; A, third series.ENDOTHERMIC PROCESSES RELAXATION TIMES The relaxation times with which the endothermic processes occur during the after-periods for 4He on Spheron between I 1 and 13 K and for *He on Grafoil between 8 and 12 K are shown in fig. 7 ( a ) and 8(a), respectively. In general, the relaxation times observed for 4He on Spheron are lower than the corresponding values for 4He on Grafoil. At the coverages at which the qst decline steeply, during the completion of the first monolayer and the formation of the second, the data, especially those determined for 4He on Grafoil (for which more results were obtained within this coverage range), show an increase in relaxation time with increasing coverage. The coverage at which the increase occurs is temperature dependent : at higher temperatures this increase occurs at lower coverages.ENERGIES INVOLVED IN THE ENDOTHERMIC PROCESSES The energies involved in the endothermic processes, QaPt, for 4He on Spheron and 4He on Grafoil calculated using eqn ( I ) are shown in fig. 7(6) and 8 (b), respectively.A. A. ANTONIOU i- 0 0’ 0 10 20 1617 0 0 I I I 1 I 0 10 20 V/cm3 (s.t.p.) g-’ adsorbent Fig. 7. *He adsorbed on Spheron. (a) Relaxation times and (b) energies (Q,,,) involved during the endothermic processes which take place during the after-periods of the calorimetric heat of adsorption measurements. T = 12 1 K. The last two terms on the right-hand side of eqn (1) contribute appreciably to the Qaft value within the coverage range in which the equilibrium pressures increase appreciably.For 4He on Spheron, at temperatures close to 12 K and coverages within the range 10-21.4 cm3 (s.t.p.) g-I adsorbent, the term qst An contributes from ca. 6 to ca. 40%, and the value of the term GAP ranges from ca. 1 to 4% of the Qaft value. For 4He on Grafoil, for which more data were obtained during the completion of the first monolayer, the contribution of these terms to Qaft is higher. At temperatures close to 12 K and coverages between 5 and 8 cm3 (s.t.p.) 8-l adsorbent, qst An increases from ca. 16 to 80% and the value of G A P is from ca. 1 to 8% of Q,,,. At temperatures close to 10 K, within the same coverage range, the contribution of qst An is between 5 and 50% and the corresponding contribution of G A P from ca. 0.5 to 4% of Qaft. At lower temperatures the values of these terms decrease. Within the submonolayer region the average Qaft value for 4He on Spheron is ca.15 J mol-I. These values are lower than the corresponding ones for 4He on Grafoil, which decrease progressively from ca. 80 to 60 J mol-1 with increasing coverage within the lower coverage range. At higher coverages, during the completion of the first monolayer and the formation of the second, the Qaft values (together with the corresponding relaxation times mentioned above) increase steeply, especially for 4He on Grafoil. At higher temperatures this increase occurs at lower coverages, the same behaviour as observed for the relaxation times mentioned above. For 4He on Spheron only the initial part of the qst decrease during the completion of the first monolayer was determined [see fig. 1 of ref.(l)]. It may be for this reason that the increase in the relaxation times and the corresponding Qaft values at this coverage is not as large as in the case of 4He on Grafoil.1618 RELAXATION ON GRAPHITIC SURFACES 0 5 90 t 80b: O \ . 50t P I ! 1;:: 100 90 80 70 60 50 DISCUSSION ' TRAPPING ' OF ADATOMS AT ' HIGH-ENERGY ' SITES The initial steep decline of the calorimetric qst is attributed, as mentioned above, to the adsorption at the so-called ' high-energy ' sites. The rate-determined exothermic processes which take place during the after-periods of these calorimetric qst should thus be related to the adsorption, and in particular to the 'trapping', of the adatoms at these sites. This trapping takes place after the gas atoms come into contact with the surface of the adsorbent and have migrated by diffusion to the high-energy sites. The driving force for this migration can be the potential gradient along the surface.6 The activation barriers to these processes may be found in the existence of dipole moments of ledges and single adatoms,6T especially at the lowest coverages.The first of the two successive exothermic processes which are observed following the first calorimetric qst measurement of each series (which is associated with the higher energy and the longer relaxation time, as compared with those of the consecutive ones) may be related to the trapping of the adatoms at the sites at which the binding energy is stronger. In this process the activation energy is ca.1060 J mol-1 and may be controlled by the dipole moments of ledges at these sites. In the subsequent exothermicA. A. ANTONIOU 1619 processes this activation energy increases to ca. 1600 J mol-l (fig. 5). The increase in the activation energies, together with the lower binding energies with which the trapping takes place in the subsequent processes, suggests that the migration and trapping occur by hopping of the adatoms amongst the substrate sites with different binding energies. In this case the activation energies may be related to ‘ the difference between the binding energy in different substrate sites’ (the ‘hopping potential’as suggested by Einstein and Schrieffer8 for chemisorption on metals) which is of the order of the surface diffusion barrier and some moderate fraction of the binding energy.The decrease in the number of atoms trapped at the high-energy sites with increasing temperature should be expected because of the increasing mean-square displacement of these adatoms. This decrease is also observed from an extrapolation of the pressure against coverage isotherms to zero pre~sure.~ This extrapolation indicates that at I 1 K the coverage is ca. 0.08 cm3 (s.t.p.) g-l adsorbent, whereas at ca. 29 K it is ca. 0.008 cm3 (s.t.p.) g-’ adsorbent.2 Similar behaviour has also been reported concerning the ‘trapping’ of Re atoms on tungsten.1° In this case, however, the trapped Re atoms escaped from the surface above the temperature at which migration of the adatoms is induced.” The change in surface potential of the graphitic substrate with increasing number of adatoms trapped at the high-energy sites becomes apparent from the change in the energy evolved when the gas atoms first come in contact with the adsorbent surface.This energy, denoted here as Qsurf, results in a steep rise in temperature of the whole system, as shown schematically in fig. l ( a ) , and is related to the corresponding qst by the equation Values of Qsurf calculated according to eqn (2) for 4He on Spheron, shown in fig. 9, decline with increasing coverage. Similar behaviour is seen in the adsorption of rare gases on metals.l2V l3 In all cases the work function (the change of which is equal and opposite in sign to the change in surface potential)14 decreases with increasing coverage within the submonolayer region.On graphitic surfaces, however, the decrease in Qsurf occurs only within the lower coverage range. The decrease in Qsurf with coverage suggests that the binding energy of 4He on Spheron (or the surface potential of this substrate) depends on the number of gas atoms trapped at the high-energy sites of the adsorbent. The change in the surface potential energy from the interaction of two adsorbed atoms which share itinerant electrons has already been discussed by Grimleyl5 for metallic surfaces. The present data indicate that a similar change also occurs on graphitic surfaces in the presence of adsorbed 4He and Ne2 owing to their semimetallic electronic structure.16 Finally, similar results to those for the exothermic processes reported here exist in the literature.Kington and Aston5 reported that ‘when N, was adsorbed on rutile a quick rise was followed by a very slow increase in temperature’. A similar process has also been reported by Morrison and Szasz5 for the same system and by Tykodi et aL5 for Ne on rutile. In these experiments an adiabatic type of calorimeter was used. Owing to the increased non-uniformity of the rutile surface (which is observed from the progressive decline of the calorimetric qst with increasing coverage)” as compared with that of Spheron and Grafoil the exothermic processes are expected to take place within a considerably larger coverage range than for the graphitic substrates.1620 I70( I I30C 0 I RELAXATION ON GRAPHITIC SURFACES - \ \& \ \ \ - \ \ 0.5 I .o 1.5 V/cm3 (s.t.p.1 g-’ adsorbent Fig.9. Qsurf for 4He adsorbed on Spheron calculated as described in the text. 0, First series; A, second series; 0, third series. FORMATION OF FILMS SUPERIMPOSED ON THE SUBSTRATE The endothermic processes which are observed during the after-periods of the calorimetric qst within the submonolayer region may be related to a repulsive interaction between the adatoms within the film superimposed on the substrate for the following reasons. First, these processes cannot be attributed to thermal equalization within the systems. The presence of the adsorbate and the increase in the equilibrium pressures with increasing coverage increase the rate of heat diffusion within the system. (For 4He on Grafoil the equilibrium pressures increase to ca. 40 Torr for the higher coverages at which the relaxation times of these processes also increase to relatively high values.) Secondly, the formation of a film superimposed on the substrate has been attributed to the lateral adatom-adatom interaction.‘* The present data indicate that this interaction occurs above the coverage range within which the ‘trapping’ of the adatoms at the high-energy sites takes place, as has been pointed out by Ying.lg The indirect interaction of adsorbed atoms on a metallic surface by sharing electrons between the adatoms and the metal has been discussed by Grimley.15 Einstein and Schrieffer8 have also proposed that this adlayer superstructure is related to the indirect oscillatory interaction of the adatoms on a metallic surface.This interaction may also be expected on graphitic surfaces because of their semimetallic electronic structure,16 which may be influenced by the variation of the substrate surface potential. An increase in the repulsive interaction of inert adatoms, as compared with that in the bulk state, has been suggested by Sinanoglou and Pitzer20 and by Freeman.21 For helium atoms the attractive interaction in the bulk state is weak, and thisA.A. ANTONIOU 1621 interaction becomes weaker in the adsorbed state. The endothermic processes with which the adsorption of 4He on graphite takes place can thus be related to the repulsive interaction of the adatoms during their rearrangement into different configuration within the films. Recently experimental evidence of an interaction between silicon atoms on the (1 10) plane of tungsten and the formation of an adlayer superstructure has been reported by Tsong22 from field-ion microscopy.The relaxation times with which these processes occur may be attributed to changes in the interplanar forces between the film and the substrate with increasing coverage. These are related to changes in geometry, especially of the outermost graphitic surface layers, with the increasing density of the superimposed film. The changes in geometry become apparent from the lowering of the ‘crossover’ temperature above which exothermic processes are observed and the increase in the C,,, values with increasing coverage (at constant temperature) (see Part 1). As already discussed, these data indicate an increase in the intraplanar distances of the carbon atoms within the basal planes and a corresponding decrease in the interplanar distances of the outermost surface layers.The energy absorbed during the endothermic processes within the submonolayer region is ca. 15 J mol-1 on Spheron but between 80 and 60 J mol-l on Grafoil, where it decreases with increasing coverage within the lower coverage range. The relaxation times of these processes at temperatures close to 12 K are also smaller on Spheron (ca. 12 min) than on Grafoil (ca. 15 mins). These differences may be due to differences in structure. The stronger potential field to which 4He is subjected on Grafoil as compared with Spheron (the binding energy for *He on Grafoil is ca. 80-100 J mol-1 larger than on Spheron)2 may result in the stronger repulsive energies associated with these 21 The strong misorientation of the small crystallites on Grafoil may also result in the larger variation of surface potential and longer relaxation times.Within the higher coverage range the observed increase in relaxation times with increasing coverage might be related to the rate with which the completion of the first monolayer and the formation of the second occurs. These data correspond to the after-periods of the calorimetric qst at coverages at which these decline steeply. At these coverages this rate may be controlled by the potential field exerted by the superimposed second monolayer to the first one, together with the change in the distribution of the interplanar forces between the first monolayer and the substrate.The corresponding increase of the Qaft values in these endothermic processes, fig. 8(b), which is mainly observed from the data determined on Grafoil, suggests the removal of adatoms from the first to the second monolayer. This removal could result from the increase in the repulsive interactions of the adatoms within the first monolayer (and the corresponding decrease in their density) with increasing coverage of the superimposed second monolayer. The present data, relaxation times and (Iaft values reported for 4He on Grafoil, together with the corresponding calorimetric qst values, indicate that the density of the monolayer is also temperature dependent. At higher temperatures both the relaxation times and the Qaft increase at lower coverages at which the calorimetric qst decline steeply.This behaviour is to be expected owing to the increase in the mean square amplitude of vibration of the adatoms with the increasing temperature. I thank Dr D. W. Davidson for advice and critically reading the manuscript, Drs S. K. Garg and J. S . Tse for valuable discussion during the preparation of the work and Dr G. Paraskevopoulos for advice in the analysis of the data.1622 RELAXATION ON GRAPHITIC SURFACES A. A. Antoniou, J. Chem. Phys., 1975, 62, 779. A. A. Antoniou, unpublished results. A. A. Antoniou, J. Chem. Phys., 1976,64, 4901. D. Graham, J. Phys. Chem., 1957,61,1310; F . A. Putman and Tomlinson Fort, J. Phys. Chem., 1975, 79, 459. G. L. Kington and J. G. Aston, J. Am. Chem. Soc., 1951,73, 1929; J. A. Morrison and G. J. Szasz, J. Chem. Phys., 1947,16,280; R. J . Tykodi, J. G. Aston and G. D. L. Schreiner, J. Am. Chem. Soc., 1955, 77, 2168. H. P. Bonzel, Crit. Rev. Solid State Sci., 1976, 6, 171. T. L. Einstein and J. R. Schrieffer, Phys. Rev. B, 1973,7, 3629. T. L. Einstein, in Chemistry and Physics of Solid Surfaces, ed. R. Vanselow (CRC, Florida, 1979), vol. 11, p. 181. J. Klafter and R. Silbey, Surf. Sci., 1980, 92, 393. ’ K. Besocke, B. Krahl-Urban and H. Wagner, Surf. Sci., 1977, 68, 39. lo T. T. Tsong, Phys. Rev. B, 1972, 6, 417. l2 T. Engel and R. Gomer, J. Chem. Phys., 1970,52, 5572. l3 C. Lea and R. Gomer, J. Chem. Phys., 1971,54, 3349. l4 G. Wedler, Chemisorption: An Experimental Approach, translated by D. F. Klemperer (Butterworths, l5 T. B. Grimley, Proc. Phys. Soc., 1967,90, 751. T. B. Grimley and S. M. Walker, Surf. Sci., 1969,14, l6 G. S. Painter and D. E. Ellis, Phys. Rev. B, 1970, 1, 4747. l7 W. A. Steele and J. G. Aston, J. Am. Chem. Soc., 1957, 79, 2393. l 0 S. C. Ying, Phys. Rev. B, 1971, 3, 4160; A. D. Novaco and J. P. McTague, Phys. Rev. Lett., 1977, l9 S. C. Ying, J. Vac. Sci. Technol., 1981, 18, 500. 2o 0. Sinanoglou and K. S. Pitzer, J. Chem. Phys., 1960, 32, 1279. ** T. T. Tsong, Phys. Scr., 1983, T4, 17. London, 1976). 395. 38, 1286. D. L. Freeman, J. Chem. Phys., 1975, 62, 941. (PAPER 4/ 1294)

ISSN:0300-9599    

DOI:10.1039/F19858101611

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1985, 81, 1623-1630 A Nuclear Magnetic Resonance Study of the Sodium Cryptate Formed by 4,7,13,18-Tetraoxa-l, l0-diazabicyclo[8.5.5]eicosane (C211) in Various Solvents BY STEPHEN F. LINCOLN* Department of Physical and Inorganic Chemistry, University of Adelaide, South Australia 5001, Australia AND IAN M. BRERETON AND THOMAS M. SPOTSWOOD Department of Organic Chemistry, University of Adelaide, South Australia 500 1, Australia Received 6th August, 1984 Sodium-23 n.m.r. studies of the exchange of Na+ between the solvated and Na+.C211 environments show that the cryptate dissociation rate constant k , (335 K) = 1053.6 & 4.1, 832.7 & 5.0 and 554.8 k 3.2, AHt = 67.2 k0.3, 69.5 k0.4 and 83.5 k0.5 kJ mo1-I and A S = 12.6k0.7, 17.4k 1.2 and 55.9+ 1.2 J K-I rno1-I in water, dimethyl sulphoxide and dimethylformamide, respectively.Both 13C and 23Na n.m.r. studies indicate that Na+.C211 exists predominantly in the exclusive form in solution whereas Li+ .C211 exists predominantly in the inclusive form. These data are discussed in terms of the two sequential equilibria: k i k2 M++C211 M+-C211 M+-C211. k - l (exclusive) k - , (inclusive) Mechanistic discussion is also extended to larger cryptates. Since Lehn first introduced the poly(oxadiazabicycloa1kane) or cryptand ligands, the inclusion complexes or cryptates formed between metal ions and these ligands, as exemplified by kf M++C21l’M+*C211 K = k f / k , kd for the cryptand C211 (4,7,13,18-tetraoxa-l,10-diazabicyclo[8.5.5]eicosane), have been the subject of a considerable number of kinetic and equilibrium Broad trends in the variation of k , and kf have been discerned, among which it is apparent that the cryptates formed by C211, probably as a consequence of its smaller size and lower flexibility, do not fit the broad kinetic pattern of those formed by the larger cryptands.6 Thus k, for Li -C211+ (which has been particularly thoroughly studied3 and for which most of the surprisingly few activation parameters for cryptate systems are available) is substantially less than expected from a simple comparison of the k, values characterizing the cryptates formed by C221 and C222.To a lesser extent this is also the case for the less studied Na+-C211, which is the subject of this variable-temperature n.m.r. investigation that seeks further insight into the factors determining the lability ofcryptates formed by C2 1 1 and thereby a better understanding of the mechanism of cryptate dissociation and formation in general.I6231624 N.M.R. STUDY OF THE CRYPTATE Na+-C211 EXPERIMENTAL REAGENTS Cryptand C211 (Merck) was redistilled, then dried under high vacuum for 24 h before use and stored under nitrogen. Sodium perchlorate was dried under high vacuum for 24 h. Dimethyl sulphoxide (DMSO) and dimethylformamide (DMF) were fractionally distilled from calcium hydride under reduced pressure and dried over Linde 4A molecular sieves. Deuteriochloroform (MSD) was dried over Linde 4A molecular sieves. INSTRUMENTAL Solutions of sodium cryptate Na+ * C2 1 1 were prepared under dry nitrogen and sealed under vacuum in 5 mm n.m.r.tubes, which were coaxially inserted in a 10 mm n.m.r. tube containing either D,O, [2H,]acetone or [2H,]DMS0 lock solvent. Sodium-23 n.m.r. measurements were recorded on a Bruker CXP-300 n.m.r. spectrometer operating at 79.39 MHz or on a modified Bruker HX-90E n.m.r. spectrometer operating at 23.81 MHz. An average of 6000 transients was accumulated into a 2048-point data base at temperature intervals of 5 K. The sample temperature was controlled with a Bruker B-VT1000 variable-temperature unit to within f 0.3 K. The Fourier-transformed spectra were subjected to complete lineshape analysisg on a BNC-12 minicomputer. The 23Na chemical shifts were referenced to an external 3.0 mol dm-3 aqueous sodium chloride solution at 298.7 K and corrected for differences in bulk diamagnetic susceptibilities.lo Carbon-1 3 n.m.r. measurements were recorded on a Bruker WP-80 n.m.r. spectrometer operating at 20.1 MHz equipped with a microprobe facility. An average of 30000 transients were accumulated into a 16384-point data base. RESULTS AND DISCUSSION STRUCTURAL ASPECTS In the solid statell and in solution8* 1 2 ~ l 3 cryptate complexes of the alkali-metal ions may exist either in the ‘inclusive’ form, in which the metal ion resides in the centre of the cavity formed by the cryptand, or in the ‘exclusive’ form, in which the metal ion resides approximately in the centre of one of the poly(oxadiazacycloa1kane) rings of the cryptand. Solid-state X-ray studies1’ show that Na+.C221, in which the fit of Na+ in the C221 cavity is optimal, exists in the inclusive form, whereas complexation of the larger K+ by C221 produces the exclusive form of K+ * C221, in which K+ is sited just outside the centre of the 18-membered ring of C221.The 13C n.m.r. spectra of these two species in deuteriochloroform solution differ substantially and have been interpreted in terms of the structures observed in the solid state persisting in solution.8 On the basis of the optimisation of fit between the alkali-metal ion and the cryptate cavity, Li+ C2 1 1 and Na+ * C211 resemble Na+ - C22 1 and K+ * C221, respectively, and solid-state X-ray studies1** l5 of Li+ C2 1 1 and Na+ C211 show these cryptates to exist in the inclusive and exclusive forms, respectively. The 13C n.m.r. spectrum of Na+ -C211 and that of its Li+ analogue shown in fig.1 differ markedly (and are very similar to the spectra of K+.C211 and Na+-C221) and are also consistent with Na+ - C2 1 1 and Li+ * C2 1 1 existing predominantly in the exclusive and inclusive forms, respectively, in deuteriochloroform solution. The assignments of the resonances arising from carbons 3, 4 and 5 in C211 are self-evident, and the assignments of resonances to carbons 1 and 2 are made by comparison with those reported* for C22 1. The shifts of all of the Li+ - C2 1 1 resonances are upfield of those of Na+ * C211 and the separations of the resonances in the two spectra differ substantially and qualitatively in a similar manner to those observed for Na+ - C22 1 and K+ - C22 1. Such differences are consistent with the changes in bond angles of the cryptand in forming exclusiveS.F. LINCOLN, 1. M. BRERETON AND T. M. SPOTSWOOD 1 c 211 5 1625 1 . 1 . 1 . , . , . , . I . , . , . ~ . ~ . , . , . , . I . I 80 78 76 74 72 70 68 66 64 62 60 58 56 54 52 50 48 PPm Fig. 1. 20.1 MHz 13C-(lH) n.m.r. spectra of (a) free C211 and its (b) LiSCN and (c) NaSCN complexes in deuteriochloroform solution at 305.2 K. Chemical shifts are referenced to the centre peak of deuteriochloroform (77.25 ppm). The cryptand and cryptate concentrations were 0.213 mol dm-3. The peaks are assigned by the numbers shown on the cryptand. Na+ - C2 1 1 and inclusive Li+ - C2 1 1 complexes. The observation that the 23Na chemical shift of Na+ C211 is sensitive to the nature of the solvent? is consistent with contact between the complexed Na+ and solvent occurring as anticipated for an exclusive cryptate, whereas the insensitivity of the 7Li shift of Li+ -C211 to the nature of the so1vent17 is consistent with this cryptate existing predominantly in the inclusive form.These conclusions are of substantial importance in subsequent mechanistic discussion. KINETIC AND MECHANISTIC ASPECTS At 298.2 K exchange of Na+ between Na+.C211 and the solvated state is slow on the n.m.r. timescale, and the greater width of the 23Na resonance of Na+ - C211 (fig. 2) t H,O, 12.06 and - 1.01; DMF, 10.82 and -4.12; DMSO, 10.52 and -0.24 ppm, where the shift of Na+.C211 and Na+ (solvated) appear first and second, respectively. Under the experimental conditions of this study the chemical shifts differ from those reported elsewhere,lG but the trends are similar.1626 N.M.R.STUDY OF THE CRYPTATE Na+.C211 340.3 335.2 330.1 325.0 314.9 Fig. 2. Typical exchange-modified 23Na n.m.r. (23.8 MHz) spectra of a DMF solution of NaClO, (0.100 mol drnp3) and C211 (0.067 mol dm-3). Experimental temperatures are shown to the left of the figure. Best-fit lineshapes and the derived z, values appear to the right of the figure. is a consequence of quadrupolar-induced relaxation arising from the non-cubic symmetry experienced by 23Na in the cryptate environment. At 79.39 MHz coalescence of the resonances arising from Na+ sC211 and solvated Na+ similar to that shown in fig. 2 is only observed for the water and DMSO systems. At the slower timescale available at 23.81 MHz this coalescence phenomenon is also observed for the DMF system (fig.2), but in pyridine, acetonitrile, methanol, acetone and propylene carbonate the exchange process is still too slow at this frequency to produce similar coalescences in the accessible temperature ranges. Subsequent discussion is accordingly restricted to water, DMSO and DMF solutions such that direct comparison may be made with Li+ -C211 under similar conditions. The mean lifetimes of Na+ -C211, z, were derived using complete lineshape analysis methods which incorporate the non-exchange-induced temperature variations of the 23Na linewidths and chemical shift^,^ and typical best-fit lineshapes are shown in fig. 2. The relationship between k,, the dissociation rate constant, and z, is given by in which z, is the mean lifetime of solvated Na+, xc and x, are the appropriate mole fractions and the other symbols have their usual meanings.Eyring plots of Tz, against 1/T are shown in fig. 3, and the derived k,, AH' and A S values appear in table 1, as do the compositions of the solutions studied. Within experimental error integration of the Na+ - C211 and Na+ (solvated) resonances under slow exchange conditions showed all of the cryptand to be complexed, consistent with reported stability constants K = 103e2, 104.6 and 105e2 in water, DMSO and DMF, respectively.' The most reliable kinetic parameters are obtained in the midst of the coalescence temperature range, when the widths and amplitudes of the coalescing resonances are similar, and this imposes a limitation on the range over which xc and xs may be varied.ThusX, andXs were varied in the ranges 0.30-0.63 and 0.70-0.37, respectively, in water,S. F. LINCOLN, I. M. BRERETON AND T. M. SPOTSWOOD 1627 1 o2 10' v1 M 2 b" 1 oo lo-' lo-* 2.8 3.0 3.2 lo3 KIT Fig. 3. Plots of 7, T against 1/T for (A) DMF ( x lo2), where solutions (viii) represented by 0 and +, respectively, (B) H,O ( x lo), where solutions (i), (ii) represented by 0, + and A, respectively, and (C) DMSO, where solutions (v), are represented by 0, + and A, respectively. and (ix) are and (iii) are (vi) and (vii) 0.33-0.67 and 0.67-0.33 in DMSO and 0.495-0.665 and 0.523-0.335 in DMF. Fig. 3 and table 1 show that k, is invariant under these conditions, consistent with the rate-determining step for exchange being the dissociation of Na+ eC211, as has also been reported to be the case for Na+-C222.4 Protonation of both cryptates and cryptands can occur in water,'* and accordingly in addition to the three solutions of Na+.C211 studied in water at pH 10.5 another solution was studied at pH 11.8.Table 1 shows that this pH variation induces no significant variation in the kinetic parameters, and it is concluded that the data reported here refer to the unprotonated form of Na+ * C211. Comparisons between the kinetic parameters characterizing Na+ C211 and Li+ sC211 may be made from the data collected in table 2. The positive A S values characterizing Na+ - C211 contrast with the negative values characterizing Li+ sC211 and are the sole source of the greater Na+ aC211 k, values in DMSO and DMF1628 N.M.R.STUDY OF THE CRYPTATE Na+ - c211 Table 1. Kinetic parameters for Na+ exchange on Na+-C21 1 in various solvents [Na+(solvated)] [Na+.C211] k, (335 K) AH1 A S solvent /mol dm-3 /mol dmP3 /s-l /kJ mol-l /J K-' mol-I (i) H,O (pH 10.5) (ii) H,O (pH 10.5) (iii) H,O (PH 10.5) (i)-(iii) combined (iv) H,O (pH 11.8) (v) DMSO (vi) DMSO (vii) DMSO (v)-(vii) combined (viii) DMF (ix) DMF (viii)-(ix) combined 0.052 0.037 0.070 0.049 0.05 1 0.033 0.067 0.052 0.033 - - - 0.048 0.063 0.030 0.05 1 0.049 0.067 0.033 0.048 0.067 - - - 1054.8k8.2 67.5f0.5 13.5+ 1.3 1061.8k7.1 67.2k0.4 12.6k 1.1 1044.4k4.8 66.9k0.3 11.7k0.9 1053.6f4.1 67.2f0.3 12.6k0.7 1058.3k9.5 67.3fO.l 12.9f 1.6 837.4 & 6.2 69.1 k 0.5 16.4 & 1.4 827.9 _+ 9.0 71.1 k 0.9 22.1 & 2.5 840.3 k 8.2 68.3 0.7 14.0 k 1.8 832.7 k 5.0 69.5 f 0.4 17.4+ 1.2 550.2 f.3.0 84.2 k 0.4 57.7 & 1.3 558.3 k 5.0 83.1 f 0.7 54.9 k 1.8 554.8 & 3.2 83.5 k 0.5 55.9 f 1.2 Table 2. Kinetic parameters for Li+ and Na+ exchange on cryptate in various solvents k,(298.2 K)" k,(298.2 K) AH& AS& M+ cryptand solvent 103 s-1 /S-1 /kJ mol-1 /J K-l mol-1 ref. Li+ C211 Li+ C211 Li+ C211 Na+ C211 Na+ C211 Na+ C211 Na+ C221 Na+ C221 Na+ C221 K+ c22 1 Na+ C222 K+ c222 HZO HZO HZO HZO H2O HZO DMSO DMF DMSO DMF DMSO DMF 1.55 16.1 75.4 127 1450 1920 3 600 7 200 1 8 000 1 8 000 1 400 2 000 0.0049 & 0.002 0.0232 4 0.0054 0.0 13 f 0.0033 47.6 f 0.5 34.0 f 0.7 12.1 k0.2 14.5 0.75 0.25 2000 7.5 147.6 4 2.6 86.6 f 4.6 64.8 k 2.5 64.4 f 2.5 67.2 & 0.3 69.5 0.4 83.5 k0.5 - 67.4k0.8 1.7+ 13.0 b -57.7f5.8 b -63.2k5.8 b 12.6k0.7 c 17.4k1.2 c 55.9f 1.2 c d d d d 22.2*3.3 e d - - - - - a k, = k,Kusing Kvalues from ref. (7).Ref. (3). Ref. (6) quotes k, = 0.025, 0.0212 and 0.0145 s-' for H,O, DMSO and DMF, respectively. These values were determined using a stopped-flow technique and the origin of the discrepancy between the H,O values is not obvious. However, this discrepancy does not affect the arguments presented. This study. For H,O and DMSO ref. (18) and (6), respectively, quote k, (298.2 K) = 140 and ca. 5 s-l, determined by temperature-jump spectrophotometric and stopped-flow spectrophotometric methods. The origins of these discrepancies are not apparent but they do not affect the arguments presented.Ref. (6). ' Ref. (4). solvents. In water the greater k, value characterizing Na+ -C211 arises from both a smaller AH1 value and more positive A,!$ value than are observed for Li+ * C211. These differences in the activation parameters characterizing the Li+ and Na+ cryptates probably reflect the different sizes and solvation of the two metal ions to some extent, but in addition may also reflect the differing propensities of the two cryptates to exist in the exclusive and inclusive forms, as is discussed below. The modest dependence of k, characterizing both Na+ eC211 and Li+-C211 on the nature of the solventS. F. LINCOLN, I. M. BRERETON AND T. M. SPOTSWOOD 1629 indicates some involvement of solvent in the transition state, but the dependence of kf ( i e .Kk,, table 2) on the nature of the solvent is greater. This suggests that the transition state for alkali-metal ion exchange is more similar to M+.C211 than to solvated M+ and C211, that in the formation reaction M+ becomes substantially desolvated and that any C211 solvational changes are close to completion when the transition state is attained. These observations are contrary to those made for the larger and more flexible cryptands and probably reflect the greater rigidity of the C211 structure by comparison with its larger homologues.6 Discussion of these data is complicated by the multistep nature of the cryptate formation process, and it is now appropriate to consider the mechanistic aspects in more detail. (The dependence of the relative magnitudes of k, characterizing Na+ .C21 I on solvent is similar to that observed for other cryptates, and as this aspect has been discussed extensively elsewhere6 it is not further considered here.) As cryptates exist in exclusive and inclusive forms in solution a minimum of two kl k2 steps, i.e.M++C211+ M+*C211+ M+*C211 (3) k-, (exclusive) k-, (inclusive) must be considered in discussion of dissociation and formation processes. This scheme is over-simplified as it does not specifically include solvation and conformational changes, and the diffusion-controlled formation of the encounter complex generally considered to precede metal complex formation reactions is not shown. Nevertheless, reaction (3) provides a convenient basis for the ensuing mechanistic discussion and raises the possibility that the rate-determining step for dissociation of M+ mC211 may involve either the exclusive or the inclusive cryptate as the nature of M+ is varied (or the nature of the cryptate is varied). The previously discussed data indicate that Na+ * C2 I 1 exists predominantly in the exclusive form in solution such that k , @ k-,.Under these circumstances it is probable that k-, characterizes the rate-determining step for dissociation of Na+ eC211, so that k, z k - , / ( k , / k - , + 1) z k-, and similarly k , = Kkd z k,. (Note that if significant amounts of Na+-C21 1 were to exist in the inclusive form and k-, > k-, the 23Na resonance of this species would appear superimposed on the coalescing resonances of Na+ and Naf mC211.) In contrast L,i+ - C211 exists predominantly in the inclusive form such that k, 9 k+.A stopped-flow calorimetric study of the formation of Li+-C211 in water detected two kinetic processes consistent with the fast formation of the exclusive form followed by the slower formation of the inclusive It was not possible to separate individual rate constants from these data, and the k, values determined by 7Li n.m.r.3 (table 2) cannot be unambiguously identified with k-, or k-, in reaction ( 3 ) . Intuitively it seems plausible that as a consequence of the smaller ionic radius of Li+ compared with that of Na+ the rate-determining step in the dissociation of Li+ involves inclusive Li+ C211 such that k, z k-z. (An alternative possibility that k-, characterizes the rate- determining step results in k, = k - , k P 2 / k 2 .) When log k , is plotted against log K the Li+. C211 k , values are found to be lo3-lo4 smaller than expected by comparison with similar data for the dissociation of Na+ and K+ from larger cryptates, and this has been attributed6 largely to the lower flexibility of C211. In DMF, DMSO and water k, for Na+ sC211 is found to be 10-102 smaller than anticipated from a similar comparison. These observations are consistent with the earlier deduction (based on the solvent dependence of k, being greater than of k , ) that both Li+ and Na+ in the transition state are substantially desolvated. Thus it appears that the relative rigidity of C211 restricts the sequential displacement or acquisition of solvent molecules in the metal-ion solvation sheath in comparison with more flexible complexones, and as a consequence k, and k, characterizing Li+-C211 and Na+ eC211 are quite small.1630 N.M.R.STUDY OF THE CRYPTATE Na+ -C211 It is appropriate briefly to extend the discussion to the data pertaining to the other Na+ and K+ cryptates in table 2. A comparison of the k, and k, values determined in water for Na+-C221 and K+*C221 (which 13C n.m.r. studies indicate exist predominantly in the inclusive and exclusive forms, respectively, in solution) shows that the kf and kd values characterizing Na+ * C221 are substantially less than those characterizing K+ - C22 1. It is expected that for K+ - C22 1 k, % k-, and for Na+ - C22 1 k, x k-, on the basis of the arguments advanced above for the C211 cryptates.In both pairs of exclusive and inclusive cryptates the latter is seen to be the least labile towards exchange of M+ between the solvated and complexed environments. The kd and k, values characterizing K+ - C222, which is expected to exist predom- inantly in the inclusive form, are decreased in comparison with those characterizing K+ - C221, consistent with the above observations. However, such comparisons between cryptates formed with different cryptands must be made with caution as the flexibility of the cryptand increases with size. Thus it is seen that in contrast to Na+ * C2 1 1 and Li+ - C2 1 1 the k, values characterizing Na+ - C22 1 are more dependent on the nature of the solvent (table 2) than are the kf values; this is consistent with the transition state for Na+ exchange resembling the solvated Na+ and the cryptand more than the cryptate in comparison with the C211 cryptates, where the reverse situation prevails. It is therefore likely that the variation of the k, and kf values in water for Na+-C211, Na+ * C221 and Na+ - C222 not only reflects the change from the exclusive to the inclusive species on going from the first to the second cryptand, but also the increasing flexibility of the cryptand with size and the non-optimal fit of Na+ into the large cavity of C222.This discussion is based on data obtained in a limited range of solvents, but it is nevertheless apparent that the predominance of the factors determining the lability of the cryptands varies as the metal ion and the cryptand are varied. We thank the Australian Research Grants Scheme for supporting this research and Dr E. H. Williams for valuable assistance. The award of a Commonwealth Postgraduate Research Award to I. M. B. is gratefully acknowledged. J. M. Lehn, Struct. Bonding (Berlin), 1973, 16, 1. J. M. Lehn, Acc. Chem. Res., 1978, 11, 49. Y. M. Cahen, J. L. Dye and A. I. Popov, J. Phys. Chem., 1975, 79, 1292. J. M. Ceraso, P. B. Smith, J. S. Landers and J. L. Dye, J. Phys. Chem., 1977, 81, 760. G. W. Leisegang, J. Am. Chem. SOC., 1981, 103,953. B. G. Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. SOC., 1981, 103, 1054. B. G. Cox, J. Garcia-Rosas and H. Schneider, J. Am. Chem. SOC., 1981, 103, 1384. E. Schmidt, J. M. Temillon, J. P. Kitzinger and A. 1. Popov, J. Am. Chem. SOC., 1983, 105, 7563. S. F. Lincoln, Prog. React. Kinet., 1977, 9, 1 . lo D. H. Live and S. I. Chan, Anal. Chem., 1970, 42, 791. l 1 F. Mathieu, B. Metz, D. Moras and R. Weiss, J . Am. Chem. SOC., 1978, 100, 4412. l2 A. I. Popov, Pure Appl. Chem., 1979, 51, 101. l 3 E. Mei, A. I. Popov and J. L. Dye, J. Am. Chem. SOC., 1977,99, 6532. l4 D. Moras and R. Weiss, Acta Crystallogr., Sect. B, 1973, 29, 400. I. M. Brereton, personal communication. J. D. Lin and A. I. Popov, J. Am. Chern. SOC., 1981, 103, 3773. Y. M. Cahen, J. L. Dye and A. I. Popov, J. Phys. Chem., 1975,79, 1289. K. Henco, B. Tummler and G. Maass, Angew. Chem., 1977, 89, 567. (PAPER 4/ 1389)

ISSN:0300-9599    

DOI:10.1039/F19858101623

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1985, 81, 1631-1636 Rotational Degrees of Freedom in the Adsorption of Hydrocarbons on Aerosil BY JOAQU~N CORTI&,* GLORIA TRONCOSO, LUIS ALZAMORA AND ELIANA VALENCIA Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago, Chile Received 7th August, 1984 A study has been made of the different contributions to the entropy of adsorption in Henry's zone of several hydrocarbons on Aerosil with different degrees of hydrophobicity. The statistical-mechanical interpretation of the experiments on the adsorption of isobutene on hydroxylated Aerosil shows that there is mobile adsorption with loss of one rotational degree of freedom. A recent paper from this laboratory' reported the results of the adsorption of a series of saturated and unsaturated four-carbon hydrocarbons in the low-pressure region on the surface of Aerosil with different degrees of hydrophobicity, as defined by the concentration of OH groups on the surface.The confirmation of the fact that the experiments reached Henry's zone in every case allowed calculation of the heat of adsorption, qst(O-+O), and the entropy of desorption, AP(0+0), in the low- adsorption region (0 3 0) and discussion of the macroscopic behaviour of the system in that region, where phenomena such as lateral interactions and effects caused by the porosity of the solid can be excluded from the analysis. This paper deals with the analysis of the entropic contributions to the different degrees of freedom of the adsorbate molecule. The following paper2 gives calculations of the adsorption potential from the viewpoint of models of amorphous solids, such as these silicas.CONTRIBUTIONS TO THE ENTROPY OF ADSORPTION Table 1 gives details of the calculation of the different entropic contributions of the adsorbate molecule at 25 "C according to the ideas of Kembal13 and de Boer and K r ~ y e r . ~ The first three columns, which are the same as those reported previously,l correspond to the description of the system, the heat of adsorption, qst(O -+ 0), and the experimental entropy of desorption, ASe(0 -P 0), calculated from Henry's constant, KH, using Pe = 1 Torr as a reference for the gas phase and rI* = 0.338 dyn cm-2 for the adsorbed phase, as suggested by de Boer.4 The nomenclature A1 10, A600 and AlOOO refers to the treatment of Aerosil200 (Degussa) under a pressure of Torr at temperatures of 110, 600 and 1000 "C, respectively.If it is assumed that in Henry's region the configurational entropy is negligible, the entropy of desorption of the adsorbed molecule may be interpreted as separable into contributions due to translation (AS,), rotation (AS,) and vibration normal to the surface (Sv), assuming that the internal molecular vibrations are not altered by the process of adsorption, i.e. A S ' = AS, -+ AS, - Sv. (1) 16311632 ADSORPTION OF HYDROCARBONS ON AEROSIL The fourth and fifth columns of table 1 show the values of the translational entropies of the gas phase, Sig)(P = P), and the absorbed phase, Sis) (n = He), for the corresponding reference states, calculated from5 and (2rcmkT)ikT ( h3P@ S$g)(P = P) = R In )+2R (27tmkT) k T ( h2H* SlS)(n = lie) = R In (3) where m is the mass of one molecule of adsorbate, k is Boltzmann’s constant, h is Planck’s constant and T is the absolute temperature.The variation of the rotational entropy shown in the last column of table 1 was calculated from the difference between eqn (1) and the assumption of mobile adsorption if (4) ASt = Slg’ (P = Pe) - S$’) (Il = ne). The vibrational entropy was calculated from where 8, = hv/k. The frequency v perpendicular to the surface was determined using the approximation of the classical harmonic oscillator, assuming that the adsorbate’s internal rotational and vibrational degrees of freedom are not affected by the process of adsorption. In this case, Henry’s constant KH is given by6 1 2nmk Tv2 KH = ( exp ( -cmin/kT).The frequency, v, is thus derived directly from the position coefficient of the straight line that is obtained when In K , is plotted against 1/T, assuming that the variation of the coefficient with temperature is negligible. ROTATIONAL ENTROPY The localized adsorption model of Kembal13 and de Boer and Kruyer4 assumes that ASt = Stg) (P = P) and that the vibrational entropy is of the order of three times that of the mobile case. Therefore, from the values of table 1 it is evident that the systems considered correspond to mobile adsorption. The change in rotational entropy (7) that appears in the last column of table 1 corresponds to this assumption. Note that the values obtained are in agreement with those views presented in ref.(1) for all systems. Within the restrictions imposed by the experiment and by the theoretical calculations, only isobutene shows a significant rotational contribution. Therefore negative values should be interpreted as being equal to zero. An attempt will thus be made to analyse this variation in the light of statistical mechanics. As far as we are aware, this has been done only for the adsorption of simple molecules such as water’? 13 and not for the physisorption of more complex molecules. AS, = ,’j’$g) - S(S)Table 1. Thermodynamic parameters in Henry's region isobutene/A 1 10 9694 19.4 26.0 38.0 1.14 x 1015 0 7.40 buta- 1,3-diene/A I 10 8005 13.8 26.0 37.9 7.38 x 1013 0 1.90 isobutene/A600 6129 9.8 26.0 38.0 9.44 x 10'2 0.67 - 1.53 n- butane/A600 6072 10.6 26.1 38.1 1.43 x 1013 0.72 - 0.68 isobutene/A 1000 4312 4.7 26.0 38.0 7.44 x 10" 6.20 - 1.10 Table 2.Coordinates of the isobutene atoms of fig. 1 x(i) -0.6765 0.6765 1.4115 1.4115 -1.212 -1.212 0.7025 2.0387 2.0387 2.4841 1.1479 1.1479 x(i) 0 0 - 1.273 1 1.273 1 0.9275 -0.9275 2.1023 1.3309 1.3309 - 1.0737 - 1.8452 - 1.8452 z(i) 0 0 0 0 0 0 0 -0.6299 0.6299 0 - 0.6299 0.6299 4 m. rn L Q\ w w1634 ADSORPTION OF HYDROCARBONS ON AEROSIL 44 n8 Fig. 1. Schematic diagram of the isobutene molecule. Table 3. Rotational entropy at 25 "C degrees of freedom, n In x 4 n (entropy units) 1 22.638 x g cm2 72.6 9.50 2 14.809 x g cm2 1097.8 15.89 3 144.283 x g3 cm6 42 972.0 24.17 The following equations correspond to the rotational partition function, q;, of a molecule with n degrees of rotational freedom:'9 * where the moments of inertia, I,, are calculated with respect to the rotational axes in each case.Fig. 1 is a schematic representation of the isobutene molecule showing a system of perpendicular Cartesian coordinates in which the x axis coincides with the direction of the double bond and the origin of the coordinates is at its centre. Atoms H,, H,, H,, C,, C , and C , are on the xy plane, while the z axis is perpendicular to the plane of the paper. Table 2 includes the coordinates of all the atoms in the system, and it is then easy to calculate the centre of mass of the molecule, with x = 0.7325,~ = z = 0 and using 12.01 amu for the mass of the carbon atom and 1.008 amu for that of the hydrogen atom.J.CORTES, G. TRONCOSO, L. ALZAMORA AND E. VALENCIA 1635 The partition function, q;, corresponds to the isobutene molecule in the gas phase, when it has three rotational degrees of freedom. The calculation of qi can be done 13 = I, I b using eqn (lo), where if I,, I b and I , are the moments of inertia for rotation about the three principal axes of rotation. If these are not known, the calculation can (1 1) be performed using the expression where if the sums take into account all the atoms, i, in the molecule and the coordinates are considered relative to any set of mutually perpendicular axes that go through the centre of mass. The products of inertia, which cancel out if the axes are chosen as the principal axes of inertia, are calculated from Ixz = C mi xi zi (17) i The coordinates of the atoms that must be taken into account in the calculation of eqn (1 2)-( 18) must have their origin at the centre of mass, so that after performing the translation xi = xi + 0.7325 of the coordinates corresponding to axis x, they will be those of table 2.Table 3 includes, in addition to the results for the gas phase, two possibilities for the molecule in the adsorbed phase corresponding to one and two degrees of rotational freedom. In the first case, it is assumed that the molecule of adsorbate is rotating in the xy plane, parallel to the surface, with respect to the z axis that goes through the middle of the double bond. Physically, as was discussed in a macroscopic analysis of these systems,' this case takes into account the interaction of the molecule's double bond with the OH group on the surface of Aerosil.The calculation of qi is performed using eqn (8), in which the moment of inertia is I1 = C mi(x:+y;) (19) i if the coordinates are now those given in table 2. The case of two degrees of freedom for the adsorbate takes into account the previous rotation together with the simultaneous rotation of the molecule with respect to the x axis. The calculation of qi was made using eqn (9), where I, is obtained from and the coordinates of table 2. 54-21636 ADSORPTION OF HYDROCARBONS ON AEROSIL In all the cases, the entropy Sp, corresponding to n degrees of rotational freedom, was calculated from the expression :5 The results for the moments of inertia, partition functions and rotational entropies are shown in table 3.CONCLUSIONS Within the limitations imposed by the approximations and assumptions made in the calculations, we obtain a microscopic view of these systems, which were described macroscopically in a previous paper. The adsorbates show behaviour associated with a mechanism of mobile adsorption, with no variation in the degrees of rotational freedom during the process of adsorption, except in the isobutene/Al 10 system, where the adsorbed molecule loses some of them as it goes from the gas phase to the adsorbed phase. This change of 7.40 entropy units in table 1 differs from the value of $ - 3 = 14.67 entropy units, but, within experimental error, it agrees with the value of q-8 = 8.28 entropy units if the values of table 3 are considered.The symmetry number o has not been included in eqn (21). This does not affect the values of AS?' if we suppose that o of the adsorbed molecule is equal to that of the gas phase. It could be stated, then, that in the adsorbed phase, even within the framework of mobile adsorption and as a result of the interactions between the double bond and the OH groups of Aerosil, when the isobutene molecule moves from site to site on the surface it still possesses two degrees of rotational freedom, having lost only one of those it had in the gas phase. We may thus view it as a rolling helix. * J. Cortes, L. Alzamora, G. Troncoso, A. L. Prieto and E. Valencia, J . Chem. Soc., Faraday Trans. I , 1984, 80, 2127. J. Cortes, G. Troncoso and E. Valencia, J . Chem. Soc., Faraday Trans. I , 1985, 81, 1637. G. Kemball, Advances in Catalysis (Academic Press, New York, 1950), vol. 11. S. Ross and J. P. Oliver, On Physical Adsorption (Interscience, New York, 1964). W. A. Steele, The Interaction of Gases with Solid Surfaces (Pergamon Press, Oxford, 1974). * J. H. de Boer and S. Kruyer, K . Ned. Akad. Wet. Proc., 1952,55B, 451. ? E. McCafferty and A. C. Zettlemoyer, J. Colloid Interface Sci., 1970, 34, 452. * J. H. Knox, Molecular Thermodynamics (Wiley, Chichester, 1978). (PAPER 4/ 1396)

ISSN:0300-9599    

DOI:10.1039/F19858101631

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraduy Trans. I, 1985, 81, 1637-1646 Calculation of the Adsorption Potential of Argon on Dehydroxylated Aerosil BY JOAQU~N COR&S,* GLORIA TRONCOSO AND ELIANA VALENCIA Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago, Chile Received 7th August, 1984 The adsorption potential of argon on an amorphous solid such as dehydroxylated Aerosil has been calculated by considering a model of the solid that takes into account only two characteristics: the stoichiometry and the sizes of its atoms. The adsorption potential has also been calculated for the crystalline solids tridymite and cristobalite. The values are compared with those from experiments on the adsorption of argon on dehydroxylated Aerosil in the intermediate adsorption zone. Much work has been done in recent years on the molecular theory of adsorption, partly because of the current development of computers.However, as far as we are aware, the solids that have been used are crystalline and most of the work has been done with graphitized carbon as the adsorbent. The crystallinity of the solid allows the exact location of every particle of the system to be known and also determines some sort of periodicity of the coordinates of each atom, thereby facilitating the computer programming for the calculation of the adsorption potential. The problem becomes more complicated when the adsorbent is an amorphous solid such as Aerosil, which is of special interest in this laboratory. As a preliminary step leading to the study of more complex adsorbates, an attempt has been made to calculate the adsorption potential of argon on amorphous solids using a procedure for the calculation which represents the adsorbent by means of a mathematical model that utilizes a minimum number of the solid's properties.THE ADSORPTION POTENTIAL A semi-empirical method for calculating the adsorption potential, 4, of an adsorbate molecule has been developed by Kiselev and co~orkers,~-~ following the first attempts by bar re^,^ by treating the various types of interaction that occur in the system independently. When only non-specific interactions are present, the energy potential between two atoms or groups of atoms may be separated into a repulsive term and an attractive term. The best known example is the Lennard-Jones (6-12) p~tential.~ If pair additivity is also assumed, then the adsorption potential may be considered as the sum of the interactions of each atom of the adsorbate and each atom of the solid.In the case of the system under discussion, in which the adsorbate is the argon atom, only non-specific interactions exist. After Kiselev and coworkers,' the adsorption potential can be calculated from the following expression, similar to that of the Lennard-Jones potential: 16371638 ADSORPTION OF ARGON ON AEROSIL where rij represents the distance between the ith atom (or atom group) of the adsorbate molecule and thejth atom (or atom group) centre of the adsorbent. The attractive force constants, Cij, can be expressed as functions of the polarizabilities, ai, and susceptibilities, xi, of the respective atoms.Cij would then be given by Kirkwood’s6 and Muller’s’ equations and the other two constants by the analogous expressions of Kiselev and coworkers:l 1 Cijl = 6mc2aiaj ( Yi + Yj) 1 + c. =--- aj2 2 Yj/ Yi + 1 2 Yi/ Yj + 1 Yi Yj + 1 05h4 Yi + “j3 = 256n4m3c2 ai ai ( 3 Y j / Yi + 1 4( Yi + Yj) 3 Yi/ yj + 1 (3) (4) where Yi = ai/xi, c is the speed of light, m is the mass of the electron and h is Planck’s constant. The repulsive part of eqn (1) is that suggested by Lennard-J~nes,~ and Bij is the repulsion constant. An expression similar to eqn ( 1 ) may be given with the repulsive part equal to other functions such as that of Buckingham.* GEOMETRIC MODELS FOR AMORPHOUS SILICA The summations of eqn (1) should, in principle, extend over the total volume of the solid.However, since the potential energy decreases very sharply with distance, it is sufficient to consider a reasonable number of atoms so that the calculation may be performed without difficulty on an ordinary computer. This has been done by Vidal-Madjar et al. for the case of crystalline solids like graphiteg or ice,l0 where the exact spatial location of each atom can be determined easily. In this paper, this type of calculation is applied to dehydroxylated Aerosil, an amorphous solid. The first possible approach is, naturally, to relate the amorphous solid to some known crystalline form. For example, amorphous silica has been associated with cristobalite, as shown through X-ray studies by Krejci and Ott,ll or its surface structure is believed to be similar to that ofD-tridymite.l2 Fig.1 and 2 are schematic representations of top views of P-cristobalite and P-tridymite, including the superficial oxygen atoms. These atoms result from the expected dehydroxylation of the surface of the silica by dehydration at 1000 “C, involving the loss of one molecule of water from every two superficial OH groups. Since it is known that the OH groups have disappeared, we have supposed a probable distribution of the remaining oxygen atoms which is shown in the figures for the three models discussed in this paper. Regarding the tridymite, we have assumed, as suggested Hockey and Pethica,13 that the oxygen atoms of the strained Si-0-Si surface bridges formed on dehydration of silica can fit into the vacant spaces between the oxygen atoms of the first layer and therefore fill half of the available holes.The distance of the superficial oxygens layer related to the first layer of silicons for tridymite, cristobalite and the ‘mathematical model’ is 0.7045, 0 and 1.212 A, respectively. Fig. 3 shows a model, which we call a ‘mathematical model’, constructed from two sets of data: the stoichiometry of the macromolecule and the sizes of the atoms, given the van der Waals radii. Thus, this model tries to interpret average values of the properties of the system, similarly to what is done by statistical thermodynamics. The stoichiometry of the macromolecule requires the existence of two oxygen atoms for every silicon atom in the bulk of the solid. This can be reproduced in the model makingJ.CORTES, G. TRONCOSO AND E. VALENCIA 1639 Fig. 1. Schematic model of P-cristobalite: 0, silicon atom of the first layer; 0, oxygen atom of the first layer; 0, oxygen atom of the outer layer; 0, superficial site. Fig. 2. Schematic model of P-tridymite: 0, silicon atom; 0, oxygen atom; 0, superficial site; 0, silicon atoms below surface.1640 ADSORPTION OF ARGON ON AEROSIL Fig. 3. Schematic model of the ‘mathematical model’: 0, silicon atom of the first layer; 0, oxygen atom; 0, oxygen atom of the first layer; 0 , superficial site. Table 1. Solid atom coordinates for the mathematical model without the oxygen atoms of the outer layern x(Si) = K , a + Ma/2 + J a / 4 y(Si) = 4K,a 2/3+tJa2/3 z(Si) = -La/2 x(0,) = x(Si)+a/2 y ( 0 , ) = y(Si) + Qav’3 z(0,) = z(Si)-a/4 W,) = 40,) y(0,) = y(Si) - Aav’3 Z(0,) = Z(O1) K , = - N , , -(N1- l), ..., - 1, 0, 1 , . . . (N1- I), N , K , = -&, --(N,- l), . . ., - 1, 0, 1 . . . ( N 2 - l), N , L=O, 1 , 2 ,..., N , Ni &IN” M = 0 if K , even M = 1 if K , odd J = 0 if L even J = 1 ifLodd a Si, silicon atoms; 0,, 0,, oxygen atoms; a, side of the triangle of fig. 3.J. CORTkS, G. TRONCOSO AND E. VALENCIA 1641 use of the geometric property of the equilateral triangle framework of fig. 3, where the number of triangle centres is twice the number of vertices. Each vertex could then represent a silicon atom, while the oxygen atoms would be located at the centres of the triangles. As a representation of the average situation, the sides of the triangles would be determined by the van der Waals diameters of oxygen and silicon, giving a value of 4.85 A.From this value, aoH = 4.91 hydroxyl groups per 100 A2, which is in a reement with the experimental ~a1ues.l~ The oxygen layer would be located first and displaced with respect to it along the z and y coordinates, as represented in the equations of the table 1, where x i , yi and zi are the coordinates of particle i. 1.21 3 w below the silicon layer. The second silicon layer would be 2.424 A from the CALCULATION OF THE ADSORPTION POTENTIAL The calculation of the adsorption potential for the three models referred to above was done according to the considerations of the previous sections, locating the argon atoms at the sites defined in the figures of the model of the solid.The calculation has also been done for the different distances between the adsorbate atom and the superficial xy plane. The location of each of the atoms, i, of the solid is given by the coordinates (xi, 37i, zi) and is expressed, as in table 1, as a function of the geometric parameters of the system and of certain indices, Kk, that enable the computer to go over each one of the atoms of the system in its calculation. Even though the attractive constants can be calculated from the properties of the respective atoms by means of the equations given above, the current state of molecular theory does not provide similar expressions for the repulsive constant, Bij. To determine it in graphitized carbon, Kiselev and c o ~ o r k e r s ~ - ~ have used the equilibrium condition ($) = o z - 2 0 where zo would be the value of z at equilibrium, and it would also be equal to the sum of the van der Walls radii of the atoms involved. If the solid is made of more than one kind of atom, as with silica, this condition is not sufficient because now there are two constants that must be determined. To solve this situation, Mayorga and used This semiempirical expression results from considering the condition established by eqn (5) and an expression of the Lennard-Jones type for 4 in the interaction between two particles, i andj.We have applied the same approximation but using eqn (1) for 4, resulting in Bij = !J'ijl(ri + rj)6 + gCij2(ri + rj)4 +ECij3(ri + rj)2. (7) Thus Bij can be calculated approximately, starting from the known Cij constants, using eqn (2)-(4).Table 2 shows the physical properties and the attractive constants of all the atoms and table 3 gives the values of 4 against coordinate z for the 'mathematical model' and for each site shown in fig. 3. The minimum values of the potential 4, together with the corresponding values of z , are shown in table 4 for each of the models discussed. Table 4 also includes the1642 ADSORPTION OF ARGON ON AEROSIL Table 2. Physical properties of the atoms diamagnetic van der Waals polariza bili ty , susceptibility , radius, ai/cm3 mol-l xi/ cm3 mol-l r i / A A 0.981 0 19.39 0 0.994 0 12.58 Si 0.0 12 04 1 .o 1.91 1.40 0.42 Table 3. Energy of adsorption of the mathematical model for different z values ~~ site I site I1 site I11 site IV z 4 z 4 Z 4 Z 4 1.50 1.60 1.62 1.66 1.670 1.673 1.676 1.677 1.678 1.679 1.69 1.70 1.80 2970 1.60 3183 1.62 3202 1.64 3222 1.660 3223 1.662 3223.20 1.665 3223.30 1.68 3223.33 1.70 3223.32 1.72 3223.30 1.74 3222 1.76 3220 1.90 3153 2.10 3791 3806 3815 3818.2 3818.2 3818.2 3816 3810 3800 3787 3770 3596 3269 1.40 1.50 1.60 1.62 1.640 1.646 1.648 1.650 1.66 1.68 1.70 1.80 1.90 2899 3144 3236 3242 3244.90 3245.20 3245.27 3245.28 3244.9 3242 3238 3188 3109 1.40 1 s o 1.52 1.54 1.560 1.566 1.5669 1.569 1.58 1.60 1.68 1.70 - 3387 3580 3598 3607 3611.5 361 1.78 361 1.79 361 1.77 361 1 3604 3550 3525 - x = 2.425 x = -0.606 x = -0.809 x = 3.232 y = 0.0 y = -1.050 I' = - 1.401 y = 0.0 value of the frequency, v, determined under the assumption that the adsorbed molecules perform harmonic oscillations perpendicular to the surface and move freely parallel to the surface.16 In this case, the frequency is given by where the constant k, for motion in the z direction is equal to the second derivative (a2~/i3z2)2-,o for the value of z that corresponds to the minimum potential.The x and y coordinates are those that belong to the sites defined in the figures. 4 was calculated from eqn (1) using a computer, increasing the number of atoms until the last term of the summation had a negligible effect on the result. This required taking into account ca. 50000 atoms in each case. The calculated density for this model was 2.01 g cmW3, in good agreement with the experimental value of 2.2 gJ. CORl%S, G. TRONCOSO AND E. VALENCIA 1643 Table 4. Adsorption energy and frequency values for the different models site I site I1 4 Z v 4 Z v tridymite 5604 1.54 1.862 5604 1.54 1.862 cris to bali te 3619 1.80 1.433 408 1 1.72 1.760 mathematical 3223 1.68 1.758 3818 1.66 1.804 model site I11 site IV 4 Z V 4 Z V tridymi te 3680 2.29 1.975 3912 2.28 2.016 cristo bali te 3542 2.11 1.885 mathematical 3245 1.65 1.336 3612 1.57 1.785 - - - model EXPERIMENTAL The adsorbent was the same as that used earlier under the label A1000.'* It was prepared from Aerosil 200 (Degussa), which has a nominal surface area of 200+25 m2 g-l.It was agglomerated by treatment with benzene (E. Merck, Darmstadt, Puriss.) and cleaned as described previously.l** l9 The complete removal of benzene was confirmed by i.r. spectroscopy after keeping it overnight at 110 "C and mmHg.* The sample was then treated for 4 h at 1000 "C and mmHg.The B.E.T. surface area20 was determined with argon and was found to have an average value of 143 m2 g-l if, as has been recommended,21 the area covered by the argon molecule is taken as 13.8 A2. The argon adsorbate was analysed by chromatography and found to consist of 99.924% argon, 0.076% nitrogen and 0.001 % of hydrocarbon traces. Adsorption isotherms were determined using the conventional borosilicate-glass volumetric apparatus described previously.18* l9 The equilibrium pressures were taken with a Universal vaccum gauge with a range of 0-25 mmHg (Todd Scientific Co.) in the low-pressure region and with an MKS digital manometer in the high-pressure region. Liquid-nitrogen, oxygen and air baths were used to obtain the temperatures of the isotherms.The equilibrium pressure readings were made every hour, which was sufficient time for equilibrium to be reached. Because the adsorbed quantities are relatively small, the amount of Aerosil sample used was > 0.4 g. RESULTS AND DISCUSSION Fig. 4 and 5 show the experimental values of the different isotherms for the system at various pressure ranges. Good reproducibility and low errors were obtained in the high- and middle-pressure regions corresponding to fig. 4 and 5 (a), respectively. The greater dispersion seen in fig. 5(b) reflects the experimental limitations set by the increased error in the low-pressure region. It is also observed that Henry's zone cannot be reached for this system in the range covered by this work, in agreement with other Hobson has clarified several aspects related to that section of the isotherm. For example, he 'measured the adsorption isotherms of argon, krypton and xenon on the 23 * 1 mmHg = 133.322 Pa.1644 - I an 5 5.0 E f -2 s1 m 3.0 2 5 --.7 2 0) -5 C - 1 .c ADSORPTION OF ARGON ON AEROSIL '0 05 10 amount absorbed 1 I I 50 150 2 50 P/mmHg Fig. 4. Adsorption isotherms for argon on dehydroxylated Aerosil: 0, 77.86 K ; A, 81.36 K; 0, 90.16 K. P/ m in Hg P/ 1 0-2 mmHg Fig. 5. Adsorption isotherms for argon on dehydroxylated Aerosil: 0, 77.86 K; A, 81.36 K; 0, 90.16 K. (a) Intermediate-pressure zone and (h) low-pressure zone. heterogeneous adsorbent.porous silver at 77.4 K over a pressure range from vapour pressure to ultrahigh vacuum and did not find Henry's law at the lowest pressure measured '.24 Fig.4 also shows the isosteric heat of adsorption, qst, curve determined from the isotherms of fig. 4 and 5(a), and the equationJ. CORTES, G. TRONCOSO AND E. VALENCIA Table 5. B.E.T. parameters for the system studied 1645 ng) EL+ RTln c Es+ RTln c T/K /mmolg-' C /cal mol-l /cal mol-l A(P/P,) correlation ~~ ~ ~~ ~ 77.86 1.66 48.7 2191 248 1 (O.OM.37) 0.9991 81.36 1.71 36.3 2170 2460 (0.05-0.37) 0.9997 90.16 1.79 25.7 2171 246 1 (0.035-0.26) 0.9985 Table 5 shows the B.E.T. parameters for the isotherms of fig. 4, together with the relative pressure intervals and the correlations with the B.E.T. plot for each case. The heat of the first layer obtained from the value of parameter C and the heats of liquefaction, EL, or sublimation, Es, are calculated. CONCLUSIONS A method has been proposed for calculating the adsorption potential of argon on an amorphous solid such as dehydroxylated Aerosil.This is shown to be possible by making use of only two characteristics of the solid : its stoichiometry and the sizes of its atoms. As a reference, the calculation was also made for tridymite and cristobalite, since some analogies have been reported in the literature between these crystalline solids and amorphous silica. The determination of experimental adsorption isotherms for argon on dehydroxy- lated Aerosil provides a reference for discussing this method of calculating the adsorption potential. In addition to giving a macroscopic view of the system in terms of the B.E.T.parameters and the isosteric heat plot, these data allow one to show that the proposed model, in spite of using a minimal number of assumptions, leads to the best value of 4 with respect to the heat of adsorption plot, as compared with the other solids. Because of experimental restrictions, the data do not include Henry's zone, and it is therefore not possible to obtain a better fit of the results. The proposed model is thus a tool for the statistical-mechanical calculation of adsorption on an amorphous solid such as Aerosil that can be applied to other situations, e.g. the adsorption of hydrocarbons.18 N. N. Avgul, A. A. Isirikyan, A. V. Kiselev, I. A. Lygina and D. P. Poshkus, Bull. Acad. Sci. USSR, Div. Chem. Sci. (Engl. Transl.), 1957. 11, 1334.A. V. Kiselev and D. P. Poshkus, Trans. Farahy SOC., 1963, 59, 176; 428; 1438. A. V. Kiselev, D. P. Poshkus and A. Y. Afreimovich, Russ. J. Phys. Chem., 1970, 44, 545. R. M. Barrer, Proc. R. SOC. London, Ser. A, 1937, 161, 476. J. E. Lennard-Jones, Trans. Faraday SOC., 1932, 28, 333. fi J. G. Kirkwood, Phys. Z., 1932, 33, 57. ' H. R. Muller, Proc. R. SOC. London, Ser. A , 1936, 154, 624. J. 0. Hirschfelder, C. F. Curtis and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954). C. Vidal-Madjar, L. Jacob and G. Guiochon, Buff. SOC. Chim. Fr., 1971; 3105. lo C. Vidal-Madjar, G. Guiochon and B. L. Karger, J . Phys. Chem., 1976, 80, 394. l1 L. Krejci and E. Ott, J . Phys. Chem., 1931, 35, 2061. l 3 J. A. Hockey and B. A. Pethica, Trans. Faraday SOC., 1961, 57, 2247. l4 W. J. Eakins, Ind. Eng. Chem. Prod. Res. Dev., 1968, 7, 39. l5 G. D. Mayorga and D. L. Peterson, J. Phys. Chem., 1972, 76, 1641. lfi A. V. Kiselev and D. P. Poshkus, Trans. Faraday SOC., 1963,59, 176. R. K. Iler, The Colloid Chemistry of Silica and Silicates (Cornell University Press, Ithaca, 1955).1646 ADSORPTION OF ARGON ON AEROSIL l7 Technical Bulletin Pigments no. 1 1 (Degussa, 1982). J. Cortes, L. Alzamora, G. Troncoso, A. L. Prieto and E. Valencia, J . Chem. Sac., Faraday Trans. I , 1984,830,2127. L. Alzamora, S. Contreras and J. Cortes, J . Colloid Interface Sci., 1975, 50, 503. 2o S. Brunauer, P. H. Emmett and E. Teller, J . Am. Chem. SOC., 1938, 60, 309. 21 A. L. McClellan and H. F. Harnsberger, J. Colloid Interface Sci., 1967, 23, 577. 22 W. A. House, J. Chem. Soc., Faraday Trans. I , 1978,14, 1045. 23 C. A. Leng and A. T. Clark., J . Chem. SOC., Faraday Trans. 1, 1982,78, 3163. 24 J. P. Hobson and R. Chapman, in Akorption-Desorption Phenomena, ed. F. Ricca (Academic Press, London, 1972). (PAPER 4/1397)

ISSN:0300-9599    

DOI:10.1039/F19858101637

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1985,81, 1647-1654 Kinetic Models for the Development of Density in Photographic and Radiographic Film BY BRIAN W. DARVELL Dental Materials Science Unit, Faculty of Dentistry, University of Hong Kong, Prince Philip Dental Hospital, 34 Hospital Road, Hong Kong Received 13th August, 1984 The behaviour of radiographic and photographic films is usually described in terms of a plot of optical density against log (exposure). This form, based on a desired ‘ideal’ rather than any theory of the actual process, leads to difficulties of interpretation and arbitrary ‘speed’ determinations. Data collected have been shown to fit chemical kinetic models of differing order, depending on film and radiation type, with the rate constant providing a rational speed parameter.The order of the model seems to be associated with the number of quantum hits required for grain developability. A rational contrast index is proposed The relationship between exposure and developed density in photographic emulsions has been the subject of investigation for over a hundred years, and yet no more than ‘tolerable’ agreement with ‘inadequate’ theory has been achieved.’ It is usually conceded that the biggest advance was made by Hurter and Driffield,2 who produced what has since been termed the ‘characteristic’ or ‘H-D’ curve, being a plot of optical density (D) against the logarithm of the exposure (a. This particular graphical presentation arises directly from their definition of a perfect negative, uiz. ‘the amounts of silver deposited in the various parts are proportional to the logarithms of the intensities of the light.. . ’. They then posed the question of whether such a negative can be produced in practice, and sought as evidence for the answer a straight-line segment in the D against log E curve (see fig. 1). This ‘characteristic curve’ plot, still o \inertia 1 2 log (relative exposure) Fig. 1. Terminology of the characteristic curve as applied to photographic and radiographc emulsions. 16471648 KINETIC MODELS FOR PHOTOGRAPHIC DEVELOPING the basis of discussions in ph~tography,~ X-ray crystallography4 and radi~graphy,~ thus depends on an unsupported premise rather than theory or observation of the actual process. This spurious use of the logarithmic transformation is the root cause of the difficulties experienced in attempts to fit multiparameter equations to characteristic curves.' No evidence has been found that the validity of that plot has ever been seriously questioned.Curve-fitting will always be successful with an arbitrarily high-order polynomial. However, while such approaches may yield equations of value in some contexts, they neither provide any insights into the nature of the process, nor do they necessarily recognize and take into account physical characteristics. THEORETICAL DEVELOPMENT From Lambert's law, we can write for the dispersion of silver particles in a developed photographic emulsion that D = px log,, e where D is the optical density, p is the linear absorption coefficient and x is the emulsion thickness.x is fixed for a given film and p depends only on the number of silver particles, which in turn depends on the exposure, the interaction probability and the processes of development. However, once converted into a developable state, a halide grain is unavailable for further contributions to developed density. Then, assuming only that the probability of the formation of an individual developable latent-image centre is proportional to the concentration of available sites (i.e. grains), the optical density in the developed film due to (deliberate) exposure, D,, would be expected to be given by D, = Q[l - ~ X P (-BE)] (1) where Q is the saturation density, E is the exposure and is a parameter combining photon-halide interaction efficiency and development factors. (All densities are expressed as ' above base '.) To allow for film 'fog' density, Df, which may for convenience (despite multiple causes) be considered as being due to an unknown equivalent pre-exposure, Ef (as some halide is used up), and to facilitate analysis, eqn (1) is extended and transformed into the following form: where D is the measured density ( D = D , +Of).However, eqn (1) is simply the form of expression for a first-order reaction process. Higher-order reaction schemes were also considered as models, using D , = Q{ 1 - [ 1 +PE(n - 1) en-' 1 (3) where n is the order, n # 1 . Incorporating the fog density in a similar manner to that used for eqn (2) we get from eqn (3): 1 - 1 ) =BE. ((Q - D)n-l (Q - Df)'+l (4) In these equations p is the equivalent of the rate constant and expresses the sensitivity or speed of the emulsion for any given exposure and development conditions.B. W.DARVELL 1649 EXPERIMENTAL The applicability of eqn (2) was tested with three dental radiographic films (Kodak Ektaspeed, Kodak Ultraspeed and Agfa Dentus) using X-radiation from a tungsten target operated at 70 kV (peak) and 15 mA, varying only the time of exposure, in a commercial dental radiographic apparatus. Standard automatic film processing was used (developer: Agfa G 138 at 27 "C). As the saturation density of the latter two of those double-coated films (Q > 7) was not measurable directly on the densitometer to hand (Parry DT 1405) the value of Q was estimated graphically and then refined iteratively using as a guide the coefficient of determination ( r 2 ) in a least-squares regression analysis with origin constrained (no significant intercept being detected in a prior analysis), estimating p simultaneously.The value of Q for the Ektaspeed film was accessible (ca. 6 OD units) and was used directly to estimate p. A test of emulsion behaviour with visible light was conducted using the above radiographic films and an ordinary photographic negative film (Ilford Pan 135, 64 ASA) and an electronic flash (Metz 40CT-4, colour temperature ca. 5600 K). Multiple exposures of a white diffusing surface were made through an operating microscope (Zeiss OPMI 1). The flash duration was controlled by a sensor measuring the light received at one port of the microscope, the camera back being attached in an equivalent position.Flash illumination was used as it was the most reproducible illumination source available. The recycle time was ca. 7-8 s and the flash duration was 0.3 1 0.02 ms. Ordinary commercial film processing was used for the Pan F135 (developer: Kodak HC110 at 22 "C); the radiographic films were developed as above. In the case of the Pan F135 film Q could be measured directly on an overexposed section of the film (avoiding reversal) so that estimation of the apparent order of the interaction could be made iteratively using the same regression technique as above, again estimating simultaneously. The values of Q obtained for the radiographic film with X-rays were used in estimating n and /? for their response to visible light. RESULTS The results of the radiographic film X-radiation exposures are given in fig.2. The data are well explained by the first-order model. This result seems to be paralleled by the response to a-particles,' although it was found then that extension could not be made to visible light. Indeed, from the satisfactory fit of the model of eqn (4) to the data from the photographic film with visible light (fig. 3 shows some representative results), with a fitted order of ca. 2.7, it is evident that there is a marked difference in behaviour. This difference is emphasised by a fitted order of ca. 2 for the three radiographic films with visible light (fig. 4), the fit to the model of order 1 having been found to be quite unsatisfactory. (The values for obtained in these tests are not reported here as the absolute exposures could not be determined, and the values are therefore essentially arbitrary.This does not detract from the theoretical import of the parameter.) DISCUSSION The application of the kinetic models is successful at least insofar as they achieve a good fit to experimental data with a minimum of parameters, four in total: the two physical limits of the available range of optical density (Of and Q), a naturally emerging speed parameter, p, and the order, n, which is associated with the nature of the exposing radiation. Evidently this number is irreducible. Effective though these four parameters are in defining emulsion behaviour, there yet remains a perceived film property of evident practical importance and utility, i.e.1650 KINETIC MODELS FOR PHOTOGRAPHIC DEVELOPING 1 2 3 4 5 exposure time/s Fig.2. Plot according to eqn (2) for radiographic films: (a) Kodak Ektaspeed, (6) Kodak Ultraspeed and (c) Agfa Dentus (displaced by + 1 s for clarity). 1.0- E $ Q+ Q .- U \" I -0 0.5- ,z - no. of flashes Fig. 3. Plot according to eqn (4) for Ilford Pan-F photographic film at three arbitrary camera- port apertures. Estimated order of model: (a) 2.6, (b) 2.75 and (c) 2.7. contrast. If this is defined simply as the rate of change of density with exposure, we have from eqn (1)B. W. DARVELL 1651 / /a /' 1' 1 5 10 15 20 25 no. of flashes Fig. 4. Plot according to eqn (4) for radiographic films (estimated order of model in parentheses): (a) Kodak Ektaspeed (2.05)' (b) Kodak Ultraspeed (2.4) and (c) Agfa Dentus (2.05).(b) and (c) are displaced by + 5 flashes for clarity. Camera-port apertures and ordinate scales are arbitrary. As n = 1 in eqn (5) we can generalise these results to (7) dD -=Ben at E = 0 . dE It is proposed that the value of this derivative be used as a 'contrast index' to define this aspect of behaviour, and as such it is seen to be a derived quantity, using the more fundamental, but plainly controlling, emulsion parameters. In practical terms it may be more useful to use the actual initial slope by taking into account fog: although the numerical difference will be slight. The generally accepted mechanism for the formation of the latent image follows the Gurney-Mott This involves the generation of clusters of Ago by the sequential reaction of photoelectrons and Ag+ ions.A minimum of two Ago is required for the cluster to be stable, but estimates of the minimum number for the centre to be developable lie in the range 3-4, although this number may depend upon, inter uliu, the redox potential of the developer. As visible light produces only one photoelectron per quantum absorbed (and not all such photoelectrons may result in Ago formation; indeed, not all Ago may survive to join a cluster) several quanta are involved in producing a developable centre. With an a-particle or an X-ray quantum, many Ago may be formed in each of several halide grains; consequently many clusters may be formed. There is then a striking parallel between the observed order of the fitted models and the known differences in the interaction of the two types of radiation with halide crystals.It is tempting therefore to identify the apparent order of the process withI652 KINETIC MODELS FOR PHOTOGRAPHIC DEVELOPING the number of effective quantum hits required for stable-cluster formation and therefore developability. In the case of visible light this would be equivalent to the (average) number of Ago in a developable cluster. This would not pertain to a- or X-radiation, which would imply that this system is then better termed pseudo-first order. However, irrespective of whether this speculation is tenable now, the goodness of fit of the present models is enough to warrant a more detailed investigation of these processes from the kinetic standpoint. The parameter B automatically subsumes changes in response due to factors which affect the photon-detection efficiency of the halide, and as such is independent of the other parameters even though they may also be affected by the same factors./I is then a true sensitivity measure. OTHER MODELS Many attempts at explaining the D against log E curve have been based on more or less detailed analysis of the statistics of interaction and latent-image formation and decay.’ Some representative examples are (expressed where possible in the present notation) : (9) where E,, is a reference exposure and n is the minimum number of Ago in a cluster required for developability ;8 D, = Q@[a-l In (E/EO)] (10) where @ is the cumulative distribution function for the lognormal case and CT is to be derived from 6 estimated emulsion parameter^;^ where q is the number of incident quanta per grain, assuming 1000/;; efficiency, and f(P) is a Poisson-based function;6 and (12) D, = Q[l -exp ( - z ) ] where z is a latent-image site density number, itself to be derived from seven estimated emulsion parameters and distributions.1° All these equations depend on assumptions concerning factors such as grain-size distribution, exposure variation with emulsion depth, latent-image site-development probability distribution and quantum-sensitivity distribution.Eqn (9) and (I 0) require in particular a reference exposure, E,, corresponding to a point in the ‘straight-line’ region of the D against log E curve; it can, however, only be determined by reference to the curve itselfg (an arbitrary procedure) or by the use of emulsion parameters dependent on the assumptions referred to above, which must themelves be estimated.8 The summation in eqn (9) reduces to 1 for X-radiation (n = I), revealing that l/Eo is equivalent to B of the present notation, although the simple dependence of D on E (not log E ) was overlooked8 and thereby its explicit determination experimentally.Similarly, if the threshold and saturation levels involved in f(P) of eqn ( 1 1) are set to one, and by reading q as the effective number of quanta (i.e. introducing an efficiency parameter /3), this too reduces to eqn (1) and again the non-logarithmic relationship was overlooked.6 Eqn (1 2) can evidently be viewed in a similar manner, but is difficult to solve from a distributional standpoint.None of these equations is algebraically equivalent to eqn (3), although there are structural similarities; however, in no case has experimental confirmation of anyB. W. DARWLL 1653 theoretical result been obtained beyond inspection of numerical examples to yield remarks such as ‘qualitative agreement’lO and ‘expected shape’.8 Eqn (10) was said to be usable directly, but no demonstration of anything other than agreement with its own assumptions was made.g Even so, its practical application and interpretation is limited because of the extensive series of assumptions and approximations which lead to it and the numerous emulsion parameters required for Rs evaluation. Unfortunately, lacking values for relevant emulsion parameters, the present data cannot be tested for fit under these alternative models except as indicated above where they reduce to equivalence.The authors of eqn (1 1) are guided in their development of it and an equation for ‘gamma’ by the observation that ‘in practice image-density characteristics are usually expressed as a function of the logarithm of the exposure’, and go on to say that the slope of the D against log Ecurve ‘ often is fairly constant over a large exposure range’s even though ‘there are a multitude of photographic materials which do not exhibit straight lines’.ll However, note that only one of the examples given above9 is inherently logarithmic in exposure (and the least easy of application), which returns to the original question as to why the D against log E plot is used at all.As remarked earlier, arbitrary polynomial curve fitting can be successful, but at the expense of extraordinary complexity and numerous parameters. Even then, success is judged on ‘satisfactory shape’ and whether the curve does or does not ‘look like D against log Ecurves ’.12 Another approach is the use of principal-component analysis13 whereby experimental data can be succinctly ‘explained’ by a small number of vectors fitted in a least-squares process. As the author remarks, there is no guarantee that the vectors will mean anything or be related to causal ~ariab1es.l~ However, when the only input variable is log (exposure), which of necessity is treated at a finite number of discrete points, the vectors obtained relate only the reconstruction of the original density data and are intrinsically meaningless. They cannot be used in any predictive fashion and, strictly speaking, do not give any information on points lying between or outside the original data points. A more relevant procedure for generating descriptive (continuous) functions would be that of Fourier analysis, but, in the present context, it is equally unhelpful in attempts to understand the process of density development.The success of the present models may be surprising in view of the amount of previous work and the awareness of some of the same basic points as are used here. However, if the proposition that the original definition of a perfect negative has biassed thinking is correct, then much difficulty in the interpretation of characteristic curves is explained.It is now clear that, given the unavoidable asymptotic approach to the saturation density Q in any case, a logarithmic transformation for exposure must produce a sigmoid curve, and the region around the inflection must then approximate the straight line desired by Hurter and Driffield.2 The inappropriateness of their interpretation is apparent, especially as the range of densities most appropriate to visual inspection, i.e. ca. 0.5-2 OD, is fortuitously coincident with this region. Major simplification of the description of film behaviour becomes possible under the present model. In particular, the ‘speed’ of a film may be expressed simply as the rate constant, B, using appropriate exposure units under defined processing conditions. This compares with the present arbitrary methods based on characteristic c ~ r v e s .~ ~ l 1 9 14-17 Equally, the variation of 8,Q and n with emulsion formulation and processing conditions is accessible from this point of view and would seem to offer much scope for study. The practice of referring speed to a particular density ‘above fog’ is shown to be quite inappropriate, as fog is better considered as equivalent to a ‘ pre-exposure’ which *1654 KINETIC MODELS FOR PHOTOGRAPHIC DEVELOPING has depleted the available halide, since Q for a given emulsion is essentially fixed. Another simplification is possible in practice: the form of eqn (2), (4) and (8) shows that the densities (D, D, and Q) can be used ‘including base’, as this cancels out. Accordingly, the base density does not have to be separately determined in this context, avoiding the complications that the boundaries between the several layers of a modern film introduce and ensuring comparable histories for all processed films in a test series.The definitions of ‘ working range’ and its complement ‘latitude’, as corresponding to the straight-line portion of the characteristic curve, are redundant and have no physical bases. In radiographic usage ‘inertia’ is still interpreted as ‘speed’ and ‘gamma’ as ‘contrast’ ; both are artefactual. Contrast may, however, be expressed through the contrast index, pen, which is directly accessible experimentally, avoiding assumptions and arbitrary definitions as are essential to the usual method^.^^ 11, 14-17 The calibration of X-ray crystallographic films over a wider range may also be facilitated on the present model, providing a wider range of useful densities and enhanced precision. CONCLUSIONS A kinetic model for the behaviour of silver halide emulsions has been developed with the minimum of parameters.The apparent order of the model is associated with the known behaviour of the exposing radiation and may represent the number of effective quantum hits required for grain developability. Speed and a contrast index may be defined rationally. On this basis the model has no arbitrary or uninterpretable constants and offers the possibility of direct investigation of the two characteristics of speed and order independently. Bearing as they do on a wide range of photographic questions, the results presented here indicate the need for a reappraisal of the photographic process. Certainly, the abandonment of the characteristic curve of Hurter and Driffield is warranted.I acknowledge the technical assistance of Mr D. Brown of the Radiographic Unit of this Faculty and valuable discussions with Dr C. F. Ng of the Department of Chemistry, University of Hong Kong. I am indebted to a referee for helpful remarks. The Theory of the Photographic Process, ed. C. E. K. Mees (Macmillan, New York, 1954). F. Hurter and V. C. Driffield, J. SOC. Chem. Ind., London, 1890,9,455. SPSE Handbook of Photographic Science and Engineering, ed. W. Thomas (Wiley, New York, 1973). H. P. Klug and L. E. Alexander, X-Ray Dzflraction Procedures (Wiley, New York, 2nd edn, 1974). D. Jenkins, Radiographic Photography and Imaging Processes (MTP Press, Lancaster, 1980). J. C. Dainty and R. Shaw, Image Science (Academic Press, London, 1974). R. L. Dixon and K. E. Ekstrand, Med. Phys. 1976, 3, 340. E. F. Haugh, Photogr. Sci. Eng., 1962, 6, 370. ’ The Theory of the Photographic Process, ed. T. H. James (Macmillan, New York, 3rd edn, 1966). lo E. Gerth, Ann. Phys., 1971, 27, 126. l1 J. C. Compton, J. Appl. Photogr. Eng., 1977, 3, 199. l2 G. Pittman, SPSE News, 1966, 9, 6. l3 J. L. Simonds, J . Opt. SOC. Amer., 1963, 53, 968. l4 British Standard 1380: 1973 Part 1 (British Standards Institution, London). l5 British Standard 5230: 1975 (British Standards Institution, London). l6 Australian Standard 1 139: 1971 (Standards Association of Australia, Sydney). l7 M. P. Chong and A. R. Docking, Aust. Dent. J., 1965, 10, 354. (PAPER 4/ 1430)

ISSN:0300-9599    

DOI:10.1039/F19858101647

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1985,81, 1655-1667 Characterization of Sulphided Molybdenum-containing Hydroprocessing Catalysts by Oxygen and Hydrogen Chemisorption BY BENJARMAHIPAL REDDY, KOMANDUR V. R. CHARY AND VARANASI SURYA SUBRAHMANYAM* Catalysis Section, Regional Research Laboratory, Hyderabad 500 007, India AND NABIN K. NAG* Department of Fuels Engineering, University of Utah, Salt Lake City, Utah 841 12, U.S.A. Received 22nd August, 1984 Low-temperature oxygen (- 78 "C) and hydrogen (300 "C) chemisorption have been applied to characterize a series of sulphided Mo/Al and Co-Mo/Al hydroprocessing catalysts containing up to 12% Mo. Three commercial Co-Mo/Al catalysts have also been studied. Attention has been focussed mainly on the merit of oxygen chemisorption as a surface-specific probe for characterizing hydroprocessing catalysts.From the results it appears that while oxygen chemisorbed at - 78 "C can titrate the number of coordinately unsaturated sites (CUS) irrespective of the nature of the support they are on, it cannot distinguish between two CUS with different intrinsic hydrodesulphurization (HDS) activity (arising either because of carrier-catalyst interaction or because of the influence of a promoter) or between a hydrogenation (HYD) and a HDS site. Hydrogen-chemisorption results are also found to throw some light on the structural growth of MoS, crystallites on the support. The results strongly indicate that hydrogen first dissociates on the CUS on the edge planes of MoS, prior to its migration to the basal planes where it remains as SH groups.There is also evidence that the van der Waals gap between two MoS, ' sandwiches ' cannot accommodate hydrogen. Oxygen chemisorption at temperatures ranging from - 78 to 60 "C has recently been applied to characterize sulphided Mo-containing hydroprocessing ~ata1ysts.l-l~ In these studies advantage has been taken of the surface-specific adsorption behaviour of oxygen on the edge planes of MoS, crystallites14 to determine a correlation (or otherwise) between the amount of oxygen chemisorbed and the hydrodesulphurization (HDS) or hydrogenation (HYD) activities of these catalysts. Chemisorption of hydrogen and hydrogen sulphide at higher temperatures has also been applied to elucidate the structure of Mo and W sulphide c a t a l y s t ~ .~ ~ - ~ ~ While some workers'. ** 6 , found a correlation between oxygen chemisorption (presumably occurring on the edge planes of MoS, crystallites) and HDS activity, otherss7 failed to do so. Even the basic concept that HDS reactions occur on the edge planes, rather than on the basal planes, has been the subject of considerable debate.22-24 The difficulty encountered in unifying the oxygen chemisorption results of various workers, as referred to above, and coming to a definite conclusion regarding the merit of the technique as a surface-specific probe is the lack of uniformity in the techniques applied to generate the data. For instance, oxygen chemisorption has been performed by static12 or dynamic flow9 and pulse methods1? 4 9 5 * 6 v l2 and at temperatures varying between - 78 and 60 "C.Additionally, 16551656 SULPHIDED Mo-CONTAINING CATALYSTS catalysts with various compositions including pure MoS, and pre-sulphided supported (sometimes with different support materials) Co-Mo and Ni-Mo have been used in these studies. Lastly, different catalyst treatment procedures have also added to the difficulties mentioned above. Only in a few s t ~ d i e s ~ - ~ has the Mo loading been varied systematically on the same support and oxygen chemisorption on these catalysts has been applied to correlate with HDS activity. The present work was undertaken against this background. The major purpose was to evaluate the merit of oxygen chemisorption as a surface-specific probe by conducting chemisorption of oxygen on a series of catalysts based on the same support and at a sufficiently low temperature that oxygen would not attack the bulk of MoS, crystallites.Any secondary effect arising through carrier<atalyst interaction and leading to a possible change in the intrinsic activities of the HDS and HYD sites was eliminated by this procedure. Attention was also focussed on the surface structure of the catalysts derived from the hydrogen chemisorption data. EXPERIMENTAL CATALYSTS A series of Mo/Al catalysts with Mo loadings ranging from 2 to 12% was prepared by incipient wetting of y-alumina (precalcined at 540 "C for 16 h) with solutions (at pH 8) of appropriate concentrations of ammonium heptamolybdate. The impregnated samples were dried in air at 120 "C for 16 h and then calcined in air at 540 "C for 16 h.The Co-promoted catalysts were prepared from the oven-dried 8 % Mo/Al catalyst by impregnation with cobalt nitrate solutions of appropriate concentration in an identical manner, drying at 120 "C followed by calcining at 540 "C, both for 16 h. Three commercial catalysts were also used in this investigation. The compositions and the physicochemical properties of all the catalysts are given in table 1. CHEMISORPTION MEASUREMENTS A conventional high-vacuum system was modified in order to be able to sulphide the catalysts in situ prior to chemisorption measurements. The details of the set-up have been given el~ewhere.,~ In a typical experiment ca. 0.5 g of catalyst was placed in the catalyst chamber and heated to 100 "C in a flow of nitrogen.Sulphiding was then carried out using a mixture of CS, and H, as follows. A stream of H, (40cm3min-', pretreated by Pd 'Deoxo' and 4A molecular-sieve zeolite) saturated with CS, vapour at 25 "C was passed through the catalyst bed and the temperature was raised to 400 "C at a rate of 4 "C min-'. Sulphiding was continued for 2 h at 400 "C, after which the sulphiding gas flow was stopped and the system was evacuated at 400 "C for 4 h at lop6 Torr. The catalyst chamber was then cooled to -78 "C by a dry-ice+ acetone bath and the evacuation Torr) was continued at this temperature for 1 h. The catalyst was now ready for oxygen chemisorption, which was carried out as follows. Oxygen from a reservoir, connected to the high-vacuum manifold, was allowed to enter the catalyst chamber with known dead space.An initial quick fall in the pressure was followed by a levelling off within ca. 10 min and the equilibrium pressure was noted. This process was repeated with different initial pressures and the first adsorption isotherm, representing both the chemisorbed and physisorbed oxygen, was generated. After this the catalyst was evacuated at -78 "C for 3 h at Torr to remove the physisorbed oxygen, and the second isotherm, representing only the physisorbed oxygen, was generated in an identical manner. From these two linear and parallel isotherms the amount of chemisorbed oxygen was determined by the method of Parekh and Weller.26 The adsorption equilibrium pressure varied between 200 and 400 Torr. A fresh sample was used to determine the uptake of hydrogen in an identical manner.In this case, however, a higher temperature of adsorption, namely 300 "C, was to be applied in order to obtain appreciable chemisorption. After the chemisorption experiment the B.E.T. surface area of the catalyst was determined by N, adsorption at - 196 "C by taking 0.162 nm2B. M. REDDY, K. v. R. CHARY, v. s. SUBRAHMANYAM AND N. K. NAG 1657 Table 1. Composition and the B.E.T. surface areas of various catalysts composition B.E.T. surface area (wt %I" /m2 g-l fresh sulphidedb catalyst Mo Co SiO, catalyst catalyst 1 2 3 4 5 6 7 8 Ketjenfine- 124 Ketjenfine-742 Harshaw-HT-400 2.0 4.0 6.0 8.0 10.0 12.0 8.0 8.0 7.7 10.0 10.0 - 199.0 - 191.0 - - 184.0 - 175.0 - - 169.0 - 162.0 3 .O - 171.0 5.0 - 169.0 2.44 1.16 267.0 3.34 0.91 253.0 2.36 - 200.0 - - - - 181.0 187.0 189.0 189.0 170.0 158.0 168.0 157.0 249.0 239.0 187.0 a The balance was A1,03.The B.E.T. surface area of the calcined alumina (Harshaw Measured after the oxygen Al-1 1 1-61) which was used to prepare catalysts 1-8 was 204 m2 g-l. chemisorption experiment. as the area of cross-section of N,. The B.E.T. surface areas of the fresh and sulphided catalysts are given in table 1. ACTIVITY MEASUREMENTS A differential flow microreactor, operating under normal atmospheric pressure and interfaced to a gas chromatograph by a six-way gas-sampling valve, was used to measure the activities of the catalysts. In a typical experiment ca. 0.2 g of a catalyst sample was secured between two plugs of Pyrex glass wool inside the glass reactor (Pyrex glass tube, 0.5 cm i.d.) and was sulphided at 400 "C for 2 h following the procedure described in the previous section.After sulphidation the reactor temperature was adjusted to 400 "C for thiophene HDS and 350 "C for cyclohexene HYD. The sulphiding gas mixture was then replaced by nitrogen and the reactor was flushed by N, at the reaction temperature for 0.5 h. At this stage the catalyst was contacted with the reaction mixture, which consisted of a stream of hydrogen saturated with thiophene (Fluka, 99 % ) or cyclohexene (Merck-Schuchrdt) at 25 "C. The partial pressures of thiophene and cyclohexene were 80.0 and 85.0 Torr, respectively. All rates were measured under steady-state conditions and in the absence of any diffusion effects with the help of the equation x = r(W/F) where r is the rate in mol h-l g-' catalyst, x is the fractional conversion, W is the weight of catalyst in g and F is the total flow rate of gas in mol h-l.The conversion was maintained below 10% and a straight line was obtained by plotting x against W/F for each catalyst. The rate was calculated from the slope of this line. ANALYSIS The HDS products of thiophene were butene and butane and were analysed by gas chromatography with the help of a 2 m stainless-steel column packed with 10% OV-17, maintained at 100 "C. Cyclohexane was the only product found for the HYD of cyclohexene under the experimental conditions and was analysed with 20% PEG-1500 (2m column maintained at 90 "C). A carrier-gas (nitrogen) flow of 40 cm3 min-l and an FID were used in both cases.1658 SULPHIDED Mo-CONTAINING CATALYSTS -200 -100 0 100 temperature of chemisorption/'C Fig.1. Oxygen uptake plotted as a function of the temperature of chemisorption. Data are taken from various sources: 0, this work; 0, ref. (6); V, ref. (7); A, ref. (8); and 0, ref. 9. All points represent CQ. 8% Mo on alumina (sulphided) with comparable catalyst surface area. RESULTS OXYGEN AND HYDROGEN CHEMISORPTION The choice of the temperature at which oxygen chemisorption could give useful information on the surface structure of the catalysts was deemed crucial. Zmierczak et aL9 have found that -78 "C is the most suitable temperature for oxygen chemisorption, and that at higher temperatures the state of oxygen could be uncertain. Bodrero and Bartholomew,12 from extensive studies on supported and unsupported MoS, catalysts, have come to a similar conclusion and have advocated - 78 "C as the most realistic temperature for chemisorption of oxygen as a surface-selective probe for characterizing sulphided hydroprocessing catalysts.As noted by Parekh and Weller,26 we observed that even at 0 "C the pressure of oxygen in contact with the catalysts showed a continuous and slow decrease with time (indicative of the slow chemical interaction of oxygen with the MoS, bulk), whereas at -78 "C the adsorption equilibrium was attained within a few minutes. By conducting chemisorption at - 196 "C (with evacuation at -78 "C between two isotherms) it was found that the amount of chemisorbed oxygen was virtually equal to that obtained at -78 "C.In order to appreciate the temperature effect fig. 1 has been drawn from the results obtained by various w ~ r k e r s . ~ - ~ The oxygen-uptake values shown in fig. 1 correspond to ca. 8 % Mo on A1,0,. The effect of the temperature of chemisorption on the amount of oxygen uptake is clearly seen. The sharp rise in oxygen uptake above -78 "C is probably due to the attack of the bulk of MoS,, thus stressing the fact that a temperature higher than -78 "C should be cautiously used to draw any conclusions about the surface structure of the catalysts. In view of these facts all our oxygen chemisorption experiments were carried out at -78 "C and under static conditions. The oxygen-uptake values as a function of catalyst composition are given in fig.2. Oxygen uptake per gram of catalyst is found to level off at an Mo loading of ca. lo%, and the results pertaining to all the catalysts, including the unpromoted, promotedB. M. REDDY, K. V. R. CHARY, V. S. SUBRAHMANYAM AND N. K. NAG 1659 Fig. 2. Oxygen uptake at -78 "C plotted as a function of catalyst composition: 0, Mo/Al catalysts; 0, 3:8 Co-Mo/Al; v, 5:8 Co-Mo/Al; ., Ketjenfine-124; 4, Ketjenfine-742 and A, Harshaw HT-400. and commercial ones, fall approximately on the same curve. Pure y-Al,O, was found by an independent experiment to chemisorb some oxygen under our experimental conditions. Therefore, the amount of chemisorbed oxygen corresponding to the amount of alumina present in each catalyst was subtracted from the oxygen-uptake values of the catalysts before reporting the results.Chemisorption of hydrogen on dichalcogenides like MoS, is an activated p r o c e s ~ , ~ ~ - ~ ~ and a higher temperature, 300 "C, was necessary to obtain appreciable chemisorption. The results are given in fig. 3. Unlike the case of oxygen, a sharp maximum in hydrogen uptake is observed at a loading of ca. 8% Mo on A1,0,. Wright et aL.l5 have also noted that hydrogen uptake at 300°C increases with increasing Mo loading and passes through a maximum for supported MoS, catalysts. This, and their other observation that the promoter does not lead to a higher hydrogen uptake, are in accord with our results. Hydrogen uptake by a pure alumina support under identical experimental conditions was taken into account to make necessary corrections for the hydrogen- uptake data of all the catalysts.OXYGEN CHEMISORPTION versus HDS AND HYD ACTIVITIES HDS activity of the catalysts, reported as the steady-state rate of HDS of thiophene, has been plotted as a function of oxygen uptake in fig. 4. There is a good correlation between oxygen uptake and HDS activity for the unpromoted catalysts, at least up to a certain level of Mo loading. This level corresponds to an Mo loading that is generally reported to give the monolayer c ~ v e r a g e ~ ~ ~ ~ ~ of the support surface. At higher oxygen uptakes the activity seems to level off. Similarly, the promoted catalysts show a rough correlation amongst themselves [fig. 4 (B)]. Note that the correlation line representing the promoted catalysts has a 3-4 times higher slope than that representing the unpromoted catalysts.This implies that the activity per oxygen atom1660 Y x ; V M 0 " I - \ 3 Y a 5i E 'p x c 20 10 SULPHIDED Mo-CONTAINING CATALYSTS Mo on A1203 (wt %) Fig. 3. Hydrogen uptake at 300 "C plotted as a function of catalyst composition. Symbols as fig. 2. 40 2c A 0 0 20 40 oxygen uptake at -78 'C/pmol g-' catalyst Fig. 4. HDS activity at 400 "C of various catalysts plotted as a function of oxygen uptake at -78 "C. Symbols as fig. 2.B. M. REDDY, K. v. R. CHARY, v. s. SUBRAHMANYAM AND N. K. NAG 1661 oxygen uptake at -78 'C/pmol g-I catalyst Fig. 5. HYD activity at 350 "C of various catalysts plotted as a function of oxygen uptake at -78 "C. Symbols as fig. 2. 0 100 2 00 hydrogen uptake at 300 "C/pmol g-' catalyst Fig.6. HDS activity at 400 "C of various catalysts plotted as a function of hydrogen uptake at 300 "C. Symbols as fig. 2. chemisorbed on the promoted catalysts is 3-4 times higher than that on the unpromo ted catalysts. The hydrogenation activity of the catalysts as a function of oxygen uptake is shown in fig. 5 . Unlike the case of the HDS reaction, both the promoted and unpromoted catalysts fall on the same correlation line. HYDROGEN CHEMISORPTION uersus HDS AND HYD ACTIVITIES HDS and HYD activities of the various catalysts are plotted as a function of hydrogen uptake in fig. 6 and 7, respectively. It is observed from fig. 6 that the1662 SULPHIDED Mo-CONTAINING CATALYSTS hydrogen uptake at 300 'C/pmol g-' catalyst Fig. 7. HYD activity at 350 "C of various catalysts plotted as a function of hydrogen uptake at 300 "C.Symbols as fig. 2. unpromoted catalysts show an initial linear increase in HDS activity that levels off beyond a certain limit of hydrogen uptake [fig. 6(A)]. The promoted catalysts do not show any correlation with the unpromoted catalysts. However, with the exception of the laboratory-made 5 : 8 Co-Mo/Al, a reasonable correlation similar to that observed for the unpromoted catalysts is observed amongst the promoted catalysts. The promotional effect of Co on the HDS reaction is again reflected by the data presented in fig. 6. The correlation between HYD activity and hydrogen uptake is shown in fig. 7. All the laboratory-made catalysts, including the promoted ones, show a good correlation between HYD activity and hydrogen uptake.The commercial catalysts show some scatter, probably owing to the diversity of their source and slight differences in the composition of the support. The promoted catalysts do not show any significantly higher HYD activity than the unpromoted catalysts. DISCUSSION CATALYST COMPOSITION versus OXYGEN AND HYDROGEN CHEMISORPTION All the oxygen chemisorption studies, as referred to earlier,l-13 are based on two very important ideas: first that oxygen chemisorbs selectively on the edge planes of MoS, crystallites and secondly that the active sites for HDS and HYD reactions are also located on the edge planes'l 2 v 2 7 9 29 as coordinately unsaturated Mo ions. Although the second premise, especially in connection with HDS reactions, has been the subject of some contro~ersy,~~-~* the importance of the edge planes, where sulphur anion vacancies are automatically formed in order to maintain the electrical neutrality of small MoS, cry~tallites,~~ can hardly be overemphasized.Therefore, surface-specific oxygen chemisorption should, in principle, offer the opportunity to evaluate critically the merit of this technique for correlating the activity of the sulphided catalysts with the edge-plane area (or more precisely, the oxygen area). As shown in fig. 2, a good correlation is observed between Mo loading and oxygen uptake up to a loading of ca. 10% (a loading which corresponds to monolayer coverage). This linear correlation can be explained in the light of the structural model of sulphided Mo catalysts as proposed by T o p s ~ l e .~ ~ The model, based on MossbauerB. M. REDDY, K. v. R. CHARY, v. s. SUBRAHMANYAM AND N. K. NAG 1663 emission spectroscopy, EXAFS and other studies, depicts the catalyst as a highly dispersed two-dimensional MoS,-like structure which remains on the support surface as small patches (10 A) of one ‘sandwich’ of MoS,. The promoter, Co or Ni, does not alter this basic structure, but substitutes for Mo and/or occupies a neighbouring interstitial position on the edge planes. This combination has been identified as a separate phase (the Co-Mo-S phase) by MES spectroscopy and is claimed to be responsible for the HDS-associated reactions.,’ Under the tenet of this model we envisage that with increasing Mo loading the number, and not the size, of such crystallites increases on the freely available alumina surface with a concomitant increase in the edge surface for oxygen chemisorption. As our results indicate, this goes on up to an Mo loading of ca.10% (fig. 2) and explains the linear correlation between oxygen uptake and Mo loading in this region. However, above this Mo level the uptake of oxygen levels off. This is probably due to the increase in size of the individual MoS, patches in the crystallographic a-direction (i.e. parallel to the basal plane). This growth in size of the small patches, rather than in number, is expected not to add to the edge surface area per unit Mo as a function of Mo loading. In order to rationalize the hydrogen chemisorption results, as shown in fig.3, it is necessary to understand the way hydrogen binds with MoS, under the experimental conditions. From studies on MoS, and WS, catalysts by inelastic neutron-scattering spectroscopy, Wright et al.159 l6 have considered the possibility that hydrogen first dissociates on the exposed metal atoms on the edges and corners (which, incidentally, are also the sites for oxygen chemisorption) and then migrates (possibly via a spillover mechanism) to the basal planes, whefe it binds with S atoms and remains as SH groups. Chadwick and Breysse22 made a similar proposal while rationalizing some HDS results in another context. The important point to note here is that although the edge planes of MoS, are indirectly involved in the hydrogen-chemisorption process, it is the basal planes which are the actual ‘seat’ of hydrogen.Therefore, the sharp rise in hydrogen uptake can be explained by the corresponding increase in the basal-plane area generated by the increase in the number of two-dimensional MoS, patches. However, unlike the case of oxygen, the maximum hydrogen uptake occurs at a slightly lower Mo loading, namely 8%. One plausible explanation for this phenomenon could be that at this level a multilayer growth of MoS, crystallites sets in along the crystallographic c-direction (i.e. perpendicular to the basal plane). This results in a drastic decrease in the exposed basal-plane area without much affecting the edge-plane area. So, although new edge planes are created in the range &lo% loading, as indicated by the uninterrupted increase in oxygen uptake in this range (fig.2), the basal-plane area per unit Mo loading starts to decrease from 8% loading owing to multilayer growth. This decline may be confirmed by plotting (not shown) hydrogen uptake per mol of Mo against Mo loading, when a maximum is again observed at a loading of 8% Mo. This decline in the basal-plane area results in a decrease in the hydrogen-uptake value. Topsare and Tops0e31 have given evidence for the formation of three-dimensional MoS, under certain experimental conditions. We failed to detect any X.r.d. lines due to large MoS, crystallites even with 12% Mo/Al catalyst, although this does not rule out the ossibility of formation of up to 6-7 layers of MoS, The departure of 5 : 8 Co-Mo/Al (laboratory-made) and Ketjen- 124 catalysts from the correlation curve might stem from their higher Co and SiO, contents, respectively. corresponding to the ca.40 K limit of the detection capability of the X.r.d. technique. OXYGEN CHEMISORPTION versus HDS AND HYD ACTIVITIES The correlation between oxygen uptake and HDS activity of the unpromoted catalysts is found to be linear and quite strong, as shown in fig. 4(A). The promoted1664 SULPHIDED Mo-CONTAINING CATALYSTS catalysts, both laboratory-made and commercial, also show a similar trend amongst themselves [fig. 4(B)]. By comparing the results shown by curves (A) and (B) of fig. 4 it is observed that the promoted catalysts are associated with about four times higher activity per unit of chemisorbed oxygen, as compared with the unpromoted catalysts.A similar conclusion is inherent in the results of Zmierzcak et where the promoted catalysts showed ca. 5-6 times higher activity than showed by the unpromoted ones. This is a clear indication that the role of promoter is primarily to increase the intrinsic activity of the HDS sites and not to increase their number. This observation is in accord with other reported 9 p 32 As discussed earlier, a difference of opinion exists, however, as to whether the amount of oxygen chemisorbed at low temperatures around -78 "C does correlate with HDS activity. Zmierzcak et aL9 found only a rough correlation between oxygen uptake (at - 78 "C) and HDS activity of a series of catalysts containing 8 % Mo and 8 % Mo plus 3 % Co on various supports, including y-Al,03, SiO,, 10-75 % SiO,-AI,O,, Zn-doped Al,O, and TiO,.They ascribed the appreciable scatter in their correlation curve to different degrees of the promoting effect of Co for different catalysts. In general, carrier-catalyst interactions can lead to a change in the dispersion as well as in the intrinsic activity of the active sites when the same catalyst is supported on different carriers.33 The findings of Tops0e31 that Mo has a lower electron density when supported on SiO, than when supported on Al,03 is a case in point. Since supports with widely differing acidities were used in the study by Zmierzcak et aL9 it is quite likely that the latter's failure to find a smooth correlation was due to the non-uniformity in the intrinsic activity of the sites assokiated with different supports.It is known that oxygen chemisorbs at low temperatures on the coordinately unsaturated (CUS) Mo sites located on the edge but there is no reason to believe that while doing so it should 'see' any difference between CUS (which are also the HDS sites) with different intrinsic HDS activity. The HDS rate, on the other hand, is a function of both the number and the intrinsic activity of the sites. The monotonic decrease in the oxygen-uptake capacity of Mo and Co-Mo catalysts with increasing SiO, content of the SO,-Al,O, supports [ref. (9), table 2, first 5 catalysts] is thus a dispersion effect, whereas the decrease in HDS activity of the same catalysts [ref. (9), fig. 4(A) and 5(A)] is partly due to dispersion and partly due to the change in the intrinsic activity stemming from the carrier-catalyst interaction.Therefore, we recommend that the secondary effects arising due to carrier-catalyst interaction should be carefully considered while correlating oxygen chemisorption data with HDS activity of hydroprocessing catalysts. By doing this, we observe a good linear correlation (fig. 4) between oxygen uptake and HDS activity of the catalysts. The correlation between oxygen uptake and HYD activity, as shown in fig. 5, agrees well with other Both the promoted and unpromoted catalysts conform to the same correlation line, thus showing that unlike HDS in the case of HDS sites, the promoter does not alter the intrinsic activity of the HYD sites. This enables a direct correlation to be obtained between hydrogen uptake and HYD activity of all the catalysts, promoted or unpromoted. The results discussed above are significant and stimulate further thoughts concerning the active sites.The current notion about the nature of different functionalities of hydroprocessing catalysts is that HDS and HYD sites are structurally different.32 It is also believed that these sites are located on the edge planes of MoS,-like structures27~2g~32~37 as CUS. The necessary condition for oxygen to be able to chemisorb on the catalysts at -78 "C is the presence of CUS on the edge planes. As long as these are available oxygen cannot distinguish between two CUS with different intrinsic HDS activities or one with HDS and the other with HYD activity. In viewB. M. REDDY, K. v. R . CHARY, v.s. SUBRAHMANYAM AND N. K. NAG 1665 of the results discussed above we propose that both HDS and HYD sites are indistinguishable, geometrically speaking. However, when the question of functionality of these sites (CUS in general) arises, the HYD activity appears to be a function of only the extensive property (i.e. the number of sites) and is subject to only a dispersion effect, whereas the HDS activity appears to be a function of both an extensive and an intensive property (i.e. the intrinsic activity that is sensitive to the carrier<atalyst interaction). Co as a promoter changes the intrinsic activity of the HDS sites by altering the electron density3' around Mo. Therefore, the promoted catalysts have a higher HDS activity per site (CUS) than the unpromoted catalysts.This is the reason why HDS activities of the promoted catalysts do not correlate with those of the unpromoted catalysts. This change in the intrinsic activity of the HDS sites is also envisaged for Mo catalysts supported on different materials, which is indeed observed in pra~tice.~ In contrast, the universal curve correlating oxygen uptake and the HYD activities (fig. 5 ) of promoted, unpromoted and commercial catalysts implies that the HYD reaction is less sensitive, if at all, to the intensive property (intrinsic activity) of the catalysts. This difference in sensitivity of HDS and HYD reactions towards the intensive property of the CUS is quite significant and can be understood properly only when the mechanisms of these reactions are fully understood.However, it is worth remembering that since the HDS reactions involve C-S bond scission they are more demanding than the HYD reactions, which require the saturation of double bonds. HYDROGEN CHEMISORPTION versus HDS AND HY D ACTIVITIES In the light of the hydrogen chemisorption mechanism, as proposed by Wright et l6 and elaborated in the text, the initial increase and subsequent levelling off in HDS activity as a function of hydrogen uptake [fig. 6(A)] indicate that only a fraction of chemisorbed hydrogen takes part in HYD reactions. It is possible that only those H atoms that are bound as SH groups in the immediate neighbourhood of the edge planes (where the HDS sites are also located) actually take part in the reaction, while a large fraction of hydrogen remains unavailable owing to its location on the distant part of the basal planes.In the case of the promoted catalysts the correlation [fig. 6(B)], with the exception of the 5% Co-Mo/Al sample, shows a definite trend similar to that observed with the unpromoted catalysts. The higher intrinsic HDS activity of the promoted catalysts is again demonstrated by the hydrogen chemisorption data, as depicted in fig. 6. Fig. 7 shows a reasonable correlation between hydrogen uptake and HYD activities of the catalysts. Unlike in the case of HDS, all the chemisorbed hydrogen, irrespective of its location on the basal plane, correlate with the HYD activity. This implies that the role of hydrogen is different for the HDS and HYD reactions. A similar approach has recently been applied by Nag38 to understanding the HDS-associated reactions, where the reactions have been envisaged as occurring via two independent routes.Nevertheless, the real significance of these results is not clear at this stage. RELATIONSHIP BETWEEN OXYGEN AND HYDROGEN CHEMISORPTION SITES In the earlier part of our discussion it was speculated that certain sites (CUS) on the edges of MoS, act as centres for the initial dissociation of hydrogen prior to its migration to the basal plane. Recalling also the fact that oxygen too chemisorbs on these sites, interesting information can be derived by plotting hydrogen-uptake values against oxygen-uptake data. This has been done in fig. 8. Two important features are worth noting: the first is a very sharp rise in hydrogen uptake at an oxygen uptake of ca.25 pmol g-l catalyst and an equally sharp decrease in hydrogen uptake beyond this level, and the second is that all the catalysts, unpromoted, promoted and 55 FAR 11666 200 0 4 a SULPHIDED Mo-CONTAINING CATALYSTS C oxygen uptake at -78 OCIpmol g-l catalyst Fig. 8. Hydrogen uptake at 300 "C plotted as a function of oxygen uptake at - 78 "C. Symbols as fig. 2. commercial, conform to the volcano-shaped curve. We have also noted earlier that this maximum in hydrogen uptake occurs just before the three-dimensional multilayer growth of MoS, sets in. This leads to a decrease in the exposed basal-plane area without affecting the edge-plane area. The sharp fall in hydrogen-uptake capacity as a function of oxygen-uptake capacity then indicates that hydrogen can only be accommodated on the basal planes which are exposed; the van der Waals gap between two MoS, layers cannot accommodate hydrogen.In conclusion, we stress that oxygen chemisorption at low temperatures can be used as a valuable surface-specific probe for characterizing sulphided hydroprocessing catalysts, provided care is taken to eliminate the complications arising owing to carrier-catalyst interaction or owing to the inclusion of the promoters such as Co. When this is done, oxygen uptake can be correlated directly with HDS activity of the catalysts. This restriction does not apply to HYD reactions, where the oxygen chemisorption data can directly be correlated with the HYD activity of all the catalysts irrespective of the vigour of the carrier-catalyst interaction or the electronic changes brought about by the promoter on the CUS.Finally, hydrogen chemisorption can also be exploited to derive some valuable information on the structure of the sulphided catalysts. We thank Drs G. Thyagarajan, R. Vaidyeswaran and E. R. Saxena, all of the Regional Research Laboratory, Hyderabad, India for their support and encourage- ment. Thanks are also due to Dr B. Rama Rao for his help in obtaining the X.r.d. data. Constructive suggestions by the referees are gratefully acknowledged.B. M. REDDY, K. V. R. CHARY, V. S. SUBRAHMANYAM AND N. K. NAG 1667 S. J. Tauster, T. A. Pecoraro and R. R. Chianelli, J. Catal., 1980, 63, 51 5. K. S. Chung and F. E. Massoth, J. Catal., 1980, 64, 332. F. E. Massoth and K.S. Chung, in Proc. 7th Znt. Congr. Catal., Tokyo, 1980, ed. T. Seiyama and K. Tanabe (Elsevier, Amsterdam, 1981), vol. 7A, p. 629. S. J. Tauster and K. L. Riley, J. Catal., 1981, 67, 250. J. Bachelier, J. C. Duchet and D. Cornet, Bull. Soc. Chim. Belg., 1981, 19, 1301. J. Bachelier, M. J. Tilliette, J. C. Duchet and D. Cornet, J. Catal., 1982, 76, 300. H. J. Jung, J. L. Schmitt and H. Ando, in Proc. 4th Climax Znt. Conf. Chem. and Uses of Molybdenum, ed. H. F. Barry and P. C. H. Mitchell (Climax Molybdenum Co., Ann Arbor, Michigan, 1982), p. 246. 8 R. Burch and A. Collins, in Proc. 4th Climax Znt. Con$ Chem. and Uses of Molybdenum, ed. N. F. Barry and P. C. H. Mitchell (Climax Molybdenum Co., Ann Arbor, Michigan, 1982), p. 379. 9 W. Zmierzcak, G. Muralidhar and F.E. Massoth, J. Catal., 1982, 77, 432. l o T. A. Bodrero, C. H. Bartholomew and K. C. Pratt, J. Catal., 1982, 78, 253. B. Concha and C. H. Bartholomew, J. Cataf., 1983, 79, 327. l 2 T. A. Bodrero and C. H. Bartholomew, J. Catal., 1983, 84, 145. 13 V. Vyskocil and D. Tomonova, React. Kinet. Catal. Lett., 1979, 10, 37. l5 C. J. Wright, C. Sampson, D. Fraser, R. Moyes, P. B. Wells and C. Rickel, J. Chem. SOC., Faraday l6 C. J. Wright, D. Farser, R. Moyes and P. B. Wells, Appf. Catal., 1981, I, 49. l 7 E. E. Donath, Adv. Catal., 1956, 8, 245. C. Sampson, J. M. Thomas, S. Vasudevan and C. J. Wright, Bull. Soc. Chim. Belg., 1981,90, 1215. l9 D. Fraser, R. B. Moyes and P. B. Wells, in Proc. 7th Znt. Congr. Catal., Tokyo, 1980, ed. T. Seiyama and K. Tanabe (Elsevier, Amsterdam, 1981), vol. 7A, p. 1424. *O A. L. Dicks, R. L. Ensell, T. R. Phillips, A. K. Szczepura, M. Thornley, A. Williams and R. D. Wragg, J. Catal., 1981, 67, 266. 21 E. H. M. Badger, R. H. Griffith and W. S. Newling, Proc. R. Soc. London, Ser. A, 1949, 197, 184. 22 D. Chadwick and M. Breysse, J. Catal., 1981, 71, 226. 23 R. R. Chianelli and S. J. Tauster, J. Catal., 1981, 71, 228. 24 G. C. Stevens and T. Edmonds, J. Catal., 1981, 71, 230. 25 N. K. Nag, K. V. R. Chary, B. 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ISSN:0300-9599    

DOI:10.1039/F19858101655

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1985, 81, 1669-1676 Photochemical Behaviour of N,N,N' ,"-Tetramet hylbenzidine and its Pro tonated Forms in Sodium Dodecyl Sulphate Anionic Micelles under 337 nm Laser Irradiation BY RAFAEL ARCE~ AND LARRY KEVAN* Department of Chemistry, University of Houston, Houston, Texas 77004, U.S.A. Received 29th August, 1984 Continuous 337 nm laser excitation of N,N,N',N'-tetramethylbenzidine (TMB) in 0.1 mol dmP3 sodium dodecyl sulphate micelles produces monophotonic ionization of the molecule. A study of the photoionization process has resulted in the following new results: (1) the radical-cation quantum yield decreases with adsorbed light because of its spectral overlap with TMB and its simultaneous photodestruction during irradiation, ( 2 ) partial regeneration of the TMB absorption band after radical-cation decay suggests that a principal mode of radical decay is through a disproportionation reaction, (3) the photoionization yield is affected by the degree of protonation of TMB, increasing with increasing bulk pH, and (4) diprotonated TMB, TMBHi+, photodecomposes into TMB2+.Surfactant micelles and vesicles serve as structural and functional models for complex bioaggregates, artificial photosynthesis and for the photochemical utilization of light energy through photoionization of molecules solubilized in these systems. Photoionization of organic molecules is enhanced in these organized systems as compared with homogeneous solutions, as shown in the work of Alkaitis et a1.,lt2 Wallace et ~ l . , ~ Gratzel and tho ma^,^ Alkaitis and Gratze15 and Atik and Thomas.6 This increased efficiency seems to be caused by prevention of the photoejected- electron-cation-radical recombination by the electrostatic barrier at the micelle/water interface. The kinetic aspects of the initial charge separation process in the photo- ionization of N,N,N',N'-tetramethylbenzidine (TMB) have been studied by optical detection of the reactive intermediates using flash-photolysis experiments5 and by transient spontaneous Raman spectroscopy.Fluorescence and laser spectroscopic methods8 have recently been used to obtain information on the TMB and TMBH+ singlet decay pathways in anionic micelles. Recently, electron spin echo and electron spin resonance spectroscopies have been used to obtain information on the structural aspects which affect the optimization of TMB photoionization in micelles and vesicle^.^-^^ In this paper we report on the steady-state photochemical behaviour of TMB in sodium dodecyl sulphate (SDS) anionic micelles and on the effect of protonation on the photoionization of TMB.EXPERIMENTAL SDS and TMB were obtained from Eastman Kodak Co. and used as received. Aqueous solutions of the surfactants were prepared with triply distilled and deoxygenated water. TMB was solubilized (0.14.3 mol dmW3) in deoxygenated 0.1 mol dm-3 SDS by stirring at 60 "C for 7 On sabbatical leave from the University of Puerto Rico, Rio Piedras, Puerto Rico. 16691670 1 .o 0.8 a, 5 0.6 e 9 0.4 0.2 PHOTOIONIZATION OF TMB IN SDS 240 280 320 360 400 440 480 520 wavelength/nm Fig.1. Ultraviolet-visible absorption spectrum of 2.8 x mol dm-3 TMB in 0.1 mol dm-3 SDS: (-) before and (---) after 15 s irradiation at 337 nm. The laser power was 2.8 x W. 3 h. The stock solution was quantitatively diluted with 0.1 rnol dm-3 SDS deoxygenated aqueous solution to give an absorbance of 0.9-1.1 at 305 nm in a 1 cm pathlength Suprasil quartz optical cell [(2.6-2.9) x mol dm-3 in TMB]. Aliquots of 2.2 mm3 of this solution were transferred to I cm Suprasil optical cells and sealed with Parafilm under a nitrogen atmosphere. Absorbance measurements before and after irradiation were made with a Cary 14 spectrophotometer. No difference in absorbance without irradiation over the same period as an experiment indicated that any oxygen diffusion into the sample produced negligible effects on the absorbance.The e.s.r. samples for room-temperature measurements were contained in 75 mm3 pipettes and the spectra were recorded with a Varian E-4 e.s.r. spectrometer. The pH of the micellar solutions was changed by adding small drops of 0.1 mol dm-3 HCl or 0.1 mol dm-3 NaOH and measuring with a pH meter. Irradiations were performed with the optical cell in a cell holder at a distance of 16 cm from the exit port of a Lumonics model 861-T excimer laser operated at 337 nm with a nitrogen + helium mixture at 100 Hz. The absorption spectrum of the photolysed sample was recorded 130-140 s after irradiation. The laser power was measured with a Scientech model 36001 laser-power meter. The laser power was varied with screen filters.RESULTS AND DISCUSSION PHOTOCHEMICAL BEHAVIOUR OF TMB AT NEUTRAL pH Upon laser irradiation at 337 nm, a (2-3) x lop5 mol dm-3 TMB solution in 0.1 rnol dm-3 SDS turns yellow. Its absorption spectrum (fig. 1) shows a band with an onset at 5 10 nm extending into the near-u.v. region with maxima at 473,455,435 and 420 nm which has been assigned to the TMB+ radical ~ a t i o n . ~ A molar absorption coefficientR. ARCE AND L. KEVAN 1671 0 1 2 3 4 5 Fig. 2. Changes in absorbance at the (a) TMB (305 nm) and (6) TMB+ (473 nm) wavelengths of maximum absorbance as a function of absorbed light. labs/ 10-3 J of 4 x lo4 dm3 mol-1 cm-l at 473 nm has been previously reported for this cation5 A simultaneous decrease in absorbance of the TMB band at 305 nm is also observed.Photoionization of TMB in SDS has been detected for excitation wavelengths shorter than or equal to 360 nm.15 Fig. 2 shows that the rate of decrease with adsorbed light in the 305 nm absorption assigned to TMB is less than the rate of increase in the 473 nm absorption assigned to TMB+. This difference can be rationalized if the TMB+ absorption band has a U.V. tail which extends through 305 nm, where TMB absorbs. The dependence of TMB+ absorbance at 473 nm on laser power suggests mono- photonic photoionization, as has been deduced previ~usly.~ An apparent change in the light-intensity dependence of the photoionization of pyrene is SDS micelles from biphotonic to monophotonic has been interpreted by HalP as being caused by inhibition of the geminate ion-recombination back reaction.Hirata et a1.l’ have suggested that the mechanism of monophotonic ionization of TMB in acetonitrile occurs through a solvent-solute exciplex interaction leading to electron transfer and producing long-lived ion pairs. Absorbance values of the TMB+ radical cation at 473 nm together with values of the absorbed light were used to calculate the TMB+ quantum yields. The TMB+ quantum yield decreases with absorbed light, as shown in fig. 3. An extrapolated TMB+ quantum yield of 0.085 is obtained for the limit zero absorbed light. This value is not corrected for TMB+ radical-cation decay in the time interval between the end of irradiation and the absorbance measurement at 473 nm, which is estimated as < 15%. Hashimoto and Thomas* found a TMB+ quantum yield of 0.25 in single-pulse (6 ns) laser experiments.The lower yield determined in these steady-state experiments is probably due to rapid recombination of the radical cation and the photoejected electron and possibly to other radical decay processes. The decrease in quantum yield with increase in light absorbed suggests that the photochemical mechanism is more complex than a single monophotonic photoionization process. A possible explanation for the observed decrease in TMB+ yield with absorbed light is that the TMB+ radical cation absorbs in the same U.V. region (300-400 nm) where TMB absorbs. Thus, as the radical-cation concentration grows with irradiation time, the cation radicals begin to compete with the neutral TMB molecules for the excitation light and the rate of light absorption by the neutral species decreases, resulting in a1672 PHOTOIONIZATION OF TMB IN SDS I 1 I .I h + m 0.04 0.02 *-.- I I I I I I -*.--------A 0 1 2 3 I labs/ 1 0 - 3 J Fig. 3. Dependence of TMB+ quantum yield at 473 nm on absorbed light. decrease in the radical-cation yield. Excitation photons absorbed by the radical cation could also result in its photodestruction and decrease its rate of formation. In prolonged laser irradiation (fig. 4) the TMB+ radical-cation visible absorption band decreases in intensity with irradiation time and new bands appear in the visible (480-350 nm) and U.V. (350-240 nm). The bands with a maximum around 380 nm could be due to a dictation dimer, TMB;+, previously observed for irradiated solutions of TMB in SDS at concentrations equal to or higher than 4 x mol dm-3,15 in vesicles13 and in low-temperature matrices.ls This photochemical behaviour of TMB is a limitation for light-energy conversion since the yield of TMB+ decreases with irradiation time.A longer effective lifetime for TMB+ in SDS micelles has been observed in D20 solutions compared with H 2 0 s01ution.l~ However, within experimental error no effect of deuterated water on the photoionization yield is observed. In photolysed TMB solutions, the TMB+ radical cation slowly decays and after complete decay only regenerates half of the original neutral TMB molecule absorption (fig. 5). This behaviour is also observed in oxygen-saturated solutions. This partial regeneration of TMB suggests that one path for TMB+ radical decay is through the disproportionation reaction TMB++TMB+ +TMB+TMB2+ (1) in which probable further reaction of TMB2+ occurs at neutral pH.It has been reportedz0 that TMB2+ has an absorption maximum at 469 nm with an extinction coefficient of 7 x lop4 cm3 mol-1 cm-l, and we have observed this absorption in irradiations of TMB in 0.1 mol dm-3 SDS at pH 3. However, at neutral pH no new absorption in this wavelength region is observed during or after TMB+ decays on our observation timescale of minutes. However, on a timescale of 100 p s or less, Beck and Brus7 observed the disappearance of a Raman spectrum assigned to TMB+R. ARCE AND L. KEVAN 1673 0.8 0.7 0.6 0 . 5 e, u C ; 0.1 0, 9 m 0.3 0.2 0.1 TMB' 220 260 300 310 380 120 160 500 wavelength/nm Fig.4. Plot of changes in the ultraviolet-visible absorption spectrum of TMB in 0.1 mol dm-3 SDS against 337 nm irradiation time: (-) 0, (---) 2, ( a - ) 5, (-) 15 min, (---) 25 and (0-0) 30 min. 240 280 320 360 400 440 180 wavelength/nm Fig. 5. Changes in absorption spectrum TMB in 0.1 M SDS solution: (-) before irradiation, (---) immediately after 60 s of 337 nm irradiation and (--) 24 h after 60s of 337nm irradiation.1674 PHOTOIONIZATION OF TMB IN SDS 1.0 0 . 8 2 0.6 e 0, P 0 4 0.2 0 - TMB:+ 220 260 300 340 380 420 460 500 waveleng t h/nm Fig. 6. Absorption spectra of TMB in 0.1 mol dm-3 SDS at pH 3 to give TMBi+: (-) before irradiation and (---) after 30 s irradiation at 337 nm. and the growth of a spectrum assigned to TMB2+.Thus we conclude that reaction (1) is probable for TMB+ decay in neutral SDS micellar solutions and that TMB2+ decays further before it can be observed in our experiments on a timescale of minutes. EFFECT OF BULK pH ON THE PHOTOIONIZATION EFFICIENCY OF TMB In aqueous or micellar solutions TMB can exist in different ionic forms depending on the pH of the ~ ~ I u t i o n . ~ ~ ~ ~ The equilibria involved in these protonation- deprotonation reactions are H+ H+ TMBmTMBH+ -TMBHi+. The neutral, mono- and di-protonated forms show different absorption spectra in the U.V. Neutral TMB has a maximum at 305 nm, TMBH+ has a maximum red-shifted to 315 nm and diprotonated TMBHi+ has a maximum at 250 nm. The diprotonated species shows a tail extending in the near-u.v. region to 380 nm7920 (fig. 6).Beck and Brus7 reported a pKal value of 6 and pKaz value of 4.2 for TMB in SDS micelles. These are smaller than the corresponding pKa values in water + alcohol s~lution,~ implying that in SDS micelles the equilibrium is shifted toward the protonated forms. Protonation of TMB has been found to affect the relative importance of its excited-singlet decay channels.* The effect of bulk pH on the yield of radical cation measured after laser irradiation and at the same incident laser power is given in fig. 7. In the pH range from 4 to 6, where TMBH+ exists as the main species, the photoionization yield shows a plateau at #(TMB+) = 0.025. In this pH range excitation of the protonated species TMBH+R. ARCE AND L. KEVAN 1675 I I I I I I I ! I I I 1 I I I 0 1 2 3 4 5 6 7 8 9 1 0 1 1 Fig.7. TMB+ quantum yield at 473 nm in 0.1 mol dm-3 SDS solution containing TMB as a function of bulk pH. The point at pH 3 actually corresponds to TMBZ+ but it has a similar extinction coefficient to that of TMB+. PH produces a band in the visible region with absorption features similar to the TMB+ radical cation observed in irradiated solutions at neutral pH. This spectrum could result from (a) the TMB+ radical cation formed via H atom ejection by the excited protonated species according to TMBH+-%TMBH+*-TMB++H (3) or (b) TMBH2+ if it has a similar absorption spectrum to the TMB+ radical cation.’ We favour explanation (a). At pH < 4, the diprotonated species TMBHi+ is dominant and shows a lower photoionization yield. Laser excitation at 337 nm produces a decrease in the absorbance of the band assigned to TMBHi+ and the appearance of a broad band in the visible region of 467 nm (fig.6) assigned to TMB2+. No vibronic structure is observed on this band, in contrast to the band in the same wavelength range assigned to TMB+ (fig. 1). The structureless band at 467 nm can also be generated by adding a drop of 0.1 mol dm3 HCI to a previously laser-irradiated solution of TMB in 0.1 mol dm-3 SDS at neutral pH. In addition, the e.s.r. spectrum of TMB+ disappears on addition of acid. This demonstrates that TMB+ can be converted into TMB2+ by added protons 2TMB + 2H+ -P TMB2+ + TMBHi+ (4) as also reported by Beck and Brus.’ The band characteristic of the TMBHi+ is also observed in this experiment, consistent with reaction (4).At pH < 6 TMB exists as either a mono- or di-positively charged species. Thus one could expect on an electrostatic basis that the positively charged TMB species might move toward the negatively charged micellar surface. This effect plus partial neutralization of the surface negative charge density resulting from the addition of hydronium ions could lead to a higher photoelectron and cation recombination rate in solution and thus result in a lower net cation yield. Protonation of the TMB1676 PHOTOIONIZATION OF TMB IN SDS molecule also affects the rates of excited-singlet decay channels, increasing the fluorescence At pH > 6 neutral TMB exists as the principal absorbing species. In this pH region the radical-cation yield increases linearly with pH and shows a sharp drop at pH > 10.The increase in yield might be explained as a pH effect on the relative probability of excited-singlet decay, which increases the photoionization channel probability. CONCLUSIONS This study of the photoionization process of TMB in SDS micelles has given the following new results: (1) the radical-cation quantum yield decreases with absorbed light because of its spectral overlap with TMB and its simultaneous photodestruction during irradiation, (2) partial regeneration of the TMB absorption band after radical-cation decay suggests that a principal mode of radical decay is through a disproportionation reaction, (3) the photoionization yield is affected by the degree of protonation of TMB, increasing with increasing bulk pH, and (4) diprotonated TMB, TMBHi+, photodecomposes into TMB2+.This research was supported by the U.S. Department of Energy under contract DE-ASO5-80ER 10745. S. A. Alkaitis, G. B. Beck and M. Gratzel, J. Am. Chem. SOC., 1975, 97, 5723. S. A. Alkaitis, M. Gratzel and A. Henglein, Ber. Bunsenges. Phys. Chem., 1975, 79, 541. S. C. Wallace, M. Gratzel and J. K. Thomas, Chem. Phys. Lett., 1973, 23, 359. M. Gratzel and J. K. Thomas, J. Phys. Chem., 1974, 78, 2248. S. A. Alkaitis and M. Gratzel, J. Am. Chem. SOC., 1976, 98, 3549. S. S. Atik and J. K. Thomas, J. Am. Chem. SOC., 1981, 103, 3550. ' S. M. Beck and L. E. Brus, J. Am. Chem. SOC., 1983, 105, 1106. Hashimoto and J. K. Thomas, J. Phys. Chem., 1983, 88,4044. P. A. Narayana, A. S. W. Li and L. Kevan, J. Am. Chem. SOC., 1981, 103, 3603. lo P. A. Narayana, A. S. W. Li and L. Kevan, J. Am. Chem. SOC., 1982, 104, 6502. l 1 P. A. Narayana, A. S. W. Li and L. Kevan, J. Phys. Chem., 1982, 86, 3. l2 P. A. Narayana and L. Kevan, Photochem. Photobiol., 1983, 37, 105. l 3 A. S. W. Li and L. Kevan, J. Am. Chem. SOC., 1983, 105, 5752. l4 E. Szajdzinska-Pietek, R. Maldonado, L. Kevan and R. R. M. Jones, J. Am. Chem. SOC., 1984, 106, l5 A. Bernas, D. Grand, S. Hautecloque and A. Chambaudet, J. Phys. Chem., 1981,85, 3684. l6 G. E. Hall, J. Am. Chem. SOC., 1978, 100, 8263. l7 Y. Hirata, M. Takimoto and N. Mataga, Chem. Phys. Lett., 1976, 97, 569. 4675. K. Takemoto, H. Mutsusaka, S. Nakayama, K. Suzuki and Y. Ooshika, Bull. Chem SOC. Jpn, 1968, 41, 764. A. Plonka and L. Kevan, J. Phys. Chem., 1984, 88, 6348. 2o J. P. Saget and V. Plichon, Bull. SOC. Chim. Fr., 1964, 4, 1395. (PAPER 4/1497)

ISSN:0300-9599    

DOI:10.1039/F19858101669

出版商:RSC    

年代:1985

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1985, 81, 1677-1684 Thermodynamics of Ion-exchange Equilibria in Polyelectrolyte Systems BY HANS VINK Institute of Physical Chemistry, University of Uppsala, Box 532, S-751 21 Uppsala 1, Sweden Received 5th September, 1984 A general, simplified thermodynamic treatment of ion-exchange equilibria in polyelectrolyte systems is presented. The treatment unifies the approaches based on the Gibbs-Donnan phase equilibrium and the mass-action law. The ion-exchange equilibrium depends essentially on two effects, the electrostatic Donnan effect and specific local interactions manifest in the activity coefficients. If ions with different valences are present the Donnan effect dominates in dilute solutions, and in the limit of infinite dilution the exchange equilibrium is completely in favour of the counterion having the highest valence.In very dilute solutions effects arising from the self-ionisation of water are important and the system becomes partially hydrolysed. An equation for the quantitative evaluation of this effect is derived. The equilibrium distribution of a simple salt between a polyelectrolyte phase (an ion-exchange gel or a polyelectrolyte solution contained by a membrane) and an ambient solution is essentially governed by the Donnan effect.' In multicomponent solutions the effect becomes more complex and also involves selective ion-exchange equilibria between the phases. As an alternative to the treatment based on the Gibbs-Donnan phase equilibrium, the approach based on the mass-action law has been extensively Thus, for a binary exchange reaction between the cations A$i+ and Aj5+ we have (1) zj AiZ'i +- zi A f'j zj A f'i +- zi A;Z+j and where ai and aj are the activities of the ions, K is the thermodynamic equilibrium constant and unprimed and primed quantities refer to the polyelectrolyte phase and the ambient solution, respectively.This approach seems unexceptionable when the ions form well defined compounds with the polyelectrolyte (e.g. when the polyelectrolyte phase can be considered as a solid solution from which coions are completely excluded or when ion exchange occurs at the surface of a porous solid). However, if these conditions are not fulfilled the treatment based on eqn (1) and (2) becomes purely formal and needs substantiation by more general thermodynamic considerations.Although much work has been devoted to the formulation of a rigorous thermodynamic theory for ion-exchange equilibria,8 many aspects of the theory have remained unsettled and need further clarification. In the present article a unified thermodynamic treatment of ion-exchange processes in multicomponent electrolyte solutions is presented and special consider- ation is given to the limiting behaviour of ion-exchange equilibria at infinite dilution of the ambient solution and effects arising from the self-ionisation of water. 16771678 ION EXCHANGE IN POLYELECTROLYTE SYSTEMS THEORY Choosing a system of sufficient generality we consider a two-phase system (polyelectrolyte phase and ambient solution phase) consisting of solutions of an anionic polyelectrolyte (alternatively fixed charges on a gel matrix) and an arbitrary number of permeable ions.The thermodynamic condition for phase equilibria stipulates the equality of the chemical potentials of the permeable components in the two phases. For the ionic species we use the electrochemical potential pi = p:+RTln ai+zi Fry (3) where ai is the activity and zi the charge number of the ith ionic species and ry is the electrical potential. If the hydrostatic pressure in the two phases is different it is appropriate to refer the activities and standard chemical potentials to a common reference pressure po. The pressure dependence of the chemical potential is where 6 is the partial molar volume of the ith ionic species at the actual composition of the phase.Integrating eqn (4) at constant composition we obtain where is the average partial molar volume (corrected for compressibility) by j+- 6 dp. Expressing pi (Po) in terms of eqn (3), we obtain from eqn ( 5 ) pi (P) = (Po) + RT lnai ( P o ) + (P -pol + zi Fy/ where it is expedient to incorporate the pressure term with the activity (because it is concentration dependent it cannot be incorporated with the constant standard chemical potential p:). Thus pi@) = py(Po)+RTlniii+ziFy/ (8) where iii = ai exp( c (P-Po) RT ). (9) Using unprimed quantities for the polyelectrolyte phase and primed quantities for the ambient solution we have at equilibrium pi = pi. (10) Substituting from eqn (8) we obtainH. VINK 1679 To eliminate the unknown Donnan potential (I,/- v / ) we may combine eqn (1 1) for two ions i and j and obtain or where In eqn (13) the ions i and j may have charges of equal or opposite sign.If the ions are oppositely charged eqn (1 3) represents the equation for Donnan equilibrium of the neutral salt S,. If i and j are counterions we find that eqn (1 3) is a generalisation of the mass-action law, eqn (2), as it includes effects arising from the pressure difference between the phases. Obviously the mass-action law is of general validity and also holds for the coions. We now express activities in terms of ionic concentrations and activity coefficients and specify the standard chemical potentials in the above equations. According to eqn (9) we write (15) ai = yipo exp( UP RT -Po) ) c i = Tici where yi is the activity coefficient, yi the pressure-corrected activity coefficient and ci the molar concentration of the ith ion (as all concentrations are referred to the same pressure po, it is immaterial if molar or molal concentrations are used).The polyelectrolyte concentration is denoted cp and is expressed as the molar concentration of the univalent fixed-charged groups ( z , = - 1). To avoid any confusion concerning the choice of reference states in eqn (13), we note that the reference states may be chosen at will and are determined either by fixing the values of the standard potentials (pi) or the activity coefficients (pi) for a particular solution. From eqn (8) and (1 5) we find that a transformation changing the standard potential p: to changes the value of the activity coefficient Ti to p:* = pi-+ Ap: (16) Thus no real significance can be attached to the choice of reference states in eqn (1 3).For the ambient solution we choose as usual the infinitely dilute solution as reference by fixing the value of the activity coefficient at unity. We also choose the pressure of the ambient solution as the reference pressure (p’ = po). Then 7; = y; + 1 for c; -, 0 (for i = 1,. . .n). (1 8) Accordingly the standard potentials have definite values pi’. It is appropriate to choose the same standard potentials for the polyelectrolyte phase. Thus pi = p i ’ (for i = 1 , . . .n). (19) The corresponding activity coefficient is a function of all solute concentrations and the pressure, Ti = j j i (p, cp, c, . . . cn). Obviously in this case the activity coefficient tends1680 ION EXCHANGE IN POLYELECTROLYTE SYSTEMS to unity when the concentrations of all solutes (including the polyelectrolyte) tend to zero and p = po.Normally we are concerned with situations when cp remains finite when the ambient solution is infinitely diluted. In this case the activity coefficient tends to a limit different from unity. Thus 7~-,y~=7i(p,cp,cy...con) (fori= 1 ,... n) where at least one of the limiting concentrations cy ... con remains finite. choice of reference states the exponent in eqn (14) is zero, K E 1 and eqn the form (20) With this (1 3) takes The importance of the effect of pressure on the activity coefficient Ti in eqn (1 5 ) has often been overrated in the p a ~ t . ~ - l ~ If the polyelectrolyte phase is a solution contained by a membrane, the pressure difference eqdals the osmotic pressure and is measurable.In general it is sufficiently low to be neglected in eqn ( 1 5). If the polyelectrolyte phase represents a gel, the pressure difference is in general not measurable. However, if the gel is flexible and freely swelling it follows from thermodynamic arguments that the pressure in the gel phase is equal to the pressure in the ambient s01ution.l~ Therefore, the pressure term in eqn (15) has in general only a marginal effect on partition equilibria. In eqn (21) some uncertainty still remains concerning the definition of the counterion concentrations when counterions are bound to the polyion. According to some models for polyelectrolyte systems some counterions may be bound to the polyion by ion-pairing (Rice and Harris14) or electrostatic condensation (Manning15).The counterions may then be considered as 'free' and 'bound' having the concen- trations c: and cp, respectively. Calling c, the stoichiometric concentration, we have ci = c;+c:. (22) As this classification does not affect the activity of the counterion we arrive at two different expressions for the activity coefficient or where 7, is the stoichiometric activity coefficient, 7; the free-ion activity coefficient and a, the fraction of free counterions. From eqn (21) and (23) we find that either set of concentrations and activity coefficients may be used in eqn (21). Although the concept of ion binding constitutes a useful basis for the theoretical treatment of specific interactions between counterions and the fixed charges, it is not possible from a thermodynamic standpoint to distinguish the binding effect from other changes in the activity coefficient.16 In the present general thermodynamic treatment it is therefore appropriate to use the stoichiometric activity coefficients.In the following we use the indexes k and I as general notations for cations and anions, respectively. For the salt sk1 eqn (21) yields Introducing the partition coefficient for the coion Kl : c1 = Kl C;H. VINK 1681 and For eqn observing that z1 is negative, we obtain two counterions i and j we obtain from eqn (27) the separation factor8 by dividing (27) for k = i and k = j If the counterions i and j have the same valence, Kl drops out from eqn (28) and we obtain the simple relation which implies that the counterion concentration ratio in the polyelectrolyte phase is uniquely determined by the corresponding concentration ratio in the ambient solution and by specific interactions manifest in the activity coefficients.However, if the counterions have different valences the situation is entirely different. Assuming we find that Kl is retained with a positive exponent in eqn (28). It is well known that the exclusion of coions from the polyelectrolyte phase increases when the ambient solution is diluted, which indicates that Kl decreases on dilution. The asymptotic form of the concentration dependence of Kl is obtained from the electroneutrality condition for the polyelectrolyte phase: zj > zi (30) Substituting for ck from eqn (27) we obtain Since at infinite dilution all concentrations c;, tend to zero, eqn (32) can be true only if KL also tends to zero [the activity coefficients remain finite because of eqn (20)].If z j is the highest charge number we find that terms containing this charge number dominate in eqn (32). Assuming, for simplicity, that only one ionic species has the charge number zj we obtain the following asymptotic expression for K,: The limiting law for ion-exchange equilibria is now obtained by inserting eqn (33) into eqn (28): At infinite dilution c; and ci tend to zero and, provided the ratio c;/cj remains finite, the counterion concentration ratio ci/cj also tends to zero according to eqn (34). Thus, eqn (34) quantifies the finding of earlier investigati~nsl~y l8 that in the limit of infinite dilution the ion-exchange equilibrium is completely in favour of the counterion having1682 ION EXCHANGE IN POLYELECTROLYTE SYSTEMS the highest valence.Obviously the asymptotic expression for the separation factor is independent of the coions present in the system. The limiting law for the distribution of coions is obtained from eqn (26) and (33). For two coions I = m, n we obtain Thus, the coion having the higher valence is more strongly excluded from the polyelectrolyte phase. Note that the coion distribution depends on the type of counterion present in the polyelectrolyte phase. HYDROLYSIS OF THE POLYELECTROLYTE PHASE In the range of limiting concentrations of the permeable electrolytes the self- ionisation of solvent cannot in general be neglected.Using the present formalism the effect is investigated for aqueous solutions. It is shown that the polyelectrolyte phase is always hydrolysed when in contact with a very dilute ambient solution. An equation for the quantitative evaluation of this effect is derived. Considering the equilibrium between a polyelectrolyte phase (with univalent counterions) and water, we denote the volumes of the phases by V and V‘ and use the following notations for the ionic concentrations (mol drn-,) in the respective phases: c, and c’ for the counterion M+, c2 and c; for the counterion H+, c, and c j for the coion OH- and cp for the fixed negative charges. The concentrations have to satisfy the following equations : the equation for ion-exchange equilibria [eqn (29)] the ionic product for water yz y3 c, c, = 10-14 the condition of electroneutrality c1+c, = c,+cp (39) c; + c; = c; (40) vcp = YCl+ V’c;.(41) and the equation for material balance An iterative solution of this equation system may be obtained in the variable c;. Combining eqn (36) and (38) and observing that in this range of concentrations the numerical values of y;, y; and y j are unity, we obtain 72 c; c; c, - - 10-14. 71 Cl c; = c;(l-E) where = 10-14/~;2. From eqn (38) and (40) we get (43) (44)H. VINK 1683 From eqn (37), (39), (41) and (43) we obtain vc; - Vq1-E) V(1-E’) - V(1-e’) C‘, = ~ where Finally, from eqn (39) we obtain E’ = 10-14/y2 jj3 c;. c, = cp (1 - E N ) &” = -. ‘2 - ‘3 where Thus, eqn (42)-(48) yield CP Yc, (1-&’)(l-E”) 3 - 7 2 v (1-&)2 - c’3 - (45) (46) (47) (48) (49) An approximate solution of eqn (49) is obtained by deleting the last term in eqn (49).More accurate solutions may be obtained by successive approximation using eqn (44), (46) and (48) to evaluate E , E’ and E”. The procedure is normally rapidly convergent. Only in the limit Vcp/V = 0 or 00 does eqn (49) become inapplicable, as then E and e’ = 1. Direct solutions of the equation system may then be obtained. For Vcp/V‘ = 0 the trivial solution c, = c; = 0 is obtained, implying that the polyelectrolyte phase is completely hydrolysed. For Vcp/ V’ = m we have c, = cp and c2 = c3 and obtain from eqn (37), (42) and (43) It follows from eqn (49) and (50) that in the absence of permeable electrolytes the ambient water phase becomes strongly alkaline.For Vc,/V‘ = 1 we thus find for a poiysulphonate solution or gel (jjl = y2), pH 9.33 in the ambient solution. For a polycarboxylate solution 7, 4 jjl and the pH value is considerably higher. This effect is of course very important when polyelectrolytes are purified by dialysis. To prevent hydrolysis the dialysate solution has to be alkaline to the extent predicted by eqn (49). Also, some anomalies8 in ion-exchange equilibria found at high dilution of the ambient solution may be due to the hydrolytic effect. The hydrolysis is depressed by the presence of permeable electrolytes. Assuming that an univalent coion is present and has the concentration c j in the ambient phase, the following approximate equation holds for dilute solutions A similar analysis carried out for a polyelectrolyte with multivalent counterions shows that in this case the extent of hydrolysis, as a consequence of eqn (34), is considerably reduced. F. G. Donnan, 2. Electrochem., 1911, 17, 572. E. Ekedahl, E. Hogfeldt and L. G. Sillen, Acta Chem. Scand., 1950, 4, 556. E. Hogfeldt, Ark. Kemi, 1952, 5, 147. 0. D. Bonner, W. J. Argersinger Jr and A. W. Davidson, J . Am. Chem. Soc., 1952,74, 1044. S. Fronaeus, Acta Chem. Scand., 1953,7, 469. G. L. Gains Jr and H. C. Thomas, J . Chem. Phys., 1953, 21, 714.1684 ION EXCHANGE IN POLYELECTROLYTE SYSTEMS R. M. Barrer and R. P. Townsend, J . Chem. Soc., Faraday Trans. 2, 1984,80, 629. F. Helfferich, Ion Exchange (McGraw-Hill, New York, 1962), chap. 5. H. P. Gregor, J. Am. Chem. Soc., 1951,73, 643. lo G. E. Boyd and B. A. Soldano, Z. Electrochem., 1953, 57, 162. l1 G. Dickel, 2. Phys Chem. (N.F.), 1960, 25, 233. l2 B. Z. Ginzburg and D. Cohen, Trans Faraday Soc., 1964, 60, 185. l3 H. Vink, Acta Chem. Scand., Ser. A , 1983, 37, 187. l4 S. A. Rice and F. E. Harris, Z. Phys. Chem. (N.F.), 1956, 8, 207. l5 G. S. Manning. J . Chem. Phys., 1969, 51, 924. l6 H. Vink, J . Chem. Soc., Faraday Trans. I , 1979, 75. 1207. l7 H. C. Subba Rao and M. M. David, AIChE J.. 1957, 3, 187. R. M. Barrer and J. Klinowski, J . Chem. SOC., Faraday Trans. 1 , 1974, 70, 2080. (PAPER 4/ 1537)

ISSN:0300-9599    

DOI:10.1039/F19858101677

出版商:RSC    

年代:1985

数据来源: RSC