摘要:

J. Chem. SOC., Faraday Trans. I, 1984,80, 3307-3314 Structural Study of Aerosol-OT-stabilised Microemulsions of Glycerol Dispersed in n-Heptane BY PAUL D. I. FLETCHER, MOHAMED F. GALAL AND BRIAN H. ROBINSON* Chemical Laboratory, University of Kent, Canterbury, Kent CT2 7NH Received 17th February, 1984 Thermodynamically stable Aerosol-OT-stabilised dispersions of glycerol in n-heptane (microemulsions) have been studied using dynamic light scattering and viscometry. Up to five moles of glycerol can be dispersed per mole of aerosol-OT in n-heptane. The resulting solutions consist of discrete spherical droplets of glycerol stabilised by the surfactant. Droplet size is independent of temperature and depends primarily on the mole ratio (R) of glycerol to AOT according to hydrodynamic radius/nm = 1.7( f 0.2) + 0.88( f 0.15) R.The apparent interfacial area occupied per AOT molecule is ca. 20% less in the glycerol dispersion than in the corresponding water dispersion. Attractive interactions between the droplets increase as the microemulsion phase stability limit is approached. Microemulsions have attracted much recent interest, from both theoretical (thermo- dynamics, particle interactions) and practical (potential use as novel reaction media) viewpoints. Microemulsions of water dispersed in heptane using Aerosol-OT as stabiliser are known to consist of a thermodynamically stable, transparent dispersion of discrete water droplets with a surfactant layer in a continuous oil phase. In this paper we describe dynamic light-scattering and viscosity measurements on solutions containing glycerol dispersed in n-heptane in the presence of sodium bis(2-ethylhexyl) sulphosuccinate (AOT).The corresponding dispersed water system has already been extensively investigated, as for example ref. (1)-(3), and hence it is possible to compare the structural properties of the two systems. Two important structural features of the microemulsion systems involving water and glycerol may be considered. First, for the dispersed water system a simple geometrical calculation [eqn (5), vide infra] involving the molar volume of water and the surface area per AOT molecule at the interface provides a reasonable model for the prediction of the equilibrium size of the aggregates. A further test of this simple calculation is provided by glycerol systems since the molar volume of the dispersed phase is considerably different. Secondly, for the dispersed water systems interparticle attractive interactions are known to be present, particularly as the phase stability limit is appr~ached.~ The nature of the attractive interaction is still uncertain but it may be related to surfactant mobility in the interfacial r e g i ~ n .~ It is of interest, therefore, to determine these interactions when AOT is interfacially bound to a high-viscosity dispersed phase such as glycerol. The amount of glycerol that may be solubilised in n-heptane solutions of AOT as a function of temperature has been determined. The structures of the droplets formed have been determined as functions of composition and temperature using dynamic light-scattering and viscosity methods.33073308 MICROEMULSIONS OF GLYCEROL IN n-HEPTANE EXPERIMENTAL The solvent n-heptane, obtained from Fisons, was distilled from sodium metal, stored over type 4A molecular sieve and filtered prior to use. AOT was obtained from Sigma and used without purification. Many samples of AOT contain an impurity with a pK, z 5 which is thought to be present as a result of incomplete esterification during manufacture or partial hydrolysis on storage.6 The batch used for these experiments contained negligible amounts of this impurity, as determined by a titration procedure. Glycerol was obtained from Fisons. Microemulsions were prepared by weighing quantities of glycerol into a volumetric flask, adding AOT solutions in heptane and making up to the mark with n-heptane.Gentle manual shaking produced clear solutions in a few minutes. Dynamic light-scattering measurements were performed using a goniometer constructed in this laboratory in combination with a Spectraphysics model 168 2 W argon-ion laser (operating at 488 nm), a Malvern K7025 correlator and an EM1 9863 photomultiplier tube in a Malvern RR 102 housing system. Sample solutions were filtered through Millipore 0.22 pm filters directly into Hellma fluorescence cells, which were mounted in a transparent dish of toluene. Precision thermostatting (to f 0.1 “C) was achieved by circulating the toluene through an immersion coil in a Haake thermostat. Data which contained signal perturbations caused by the presence of dust in the sample were discriminated against and rejected using computer control of the instrument.Data were collected in ‘burst’ experiments of one or two seconds duration. If the total count collected was outside preset discriminator levels, the data from that ‘burst’ were rejected. The data were analysed according to the method of cumulants.’ The limiting values (as delay time-0) of the first and second derivatives of the semi-logarithmic plot of the intensity autocorrelation functions against time were taken as the first two moments of the cumulants expansion. Data were accepted when good agreement was obtained between values of the baseline calculated from total counts and that measured at long delay times. The baseline agreement was taken as good when the measured difference was found to be < 1% of the autocorrelation amplitude.Refractive indices were determined using a thermostatted Abbe refractometer. Viscosity measurements were made with an Ubbelohde viscometer. Densities were measured using a standard pyknometer. RESULTS AND DISCUSSION MICROEMULSION STABILITY Fig. 1 shows the amount of glycerol that may be solubilised in AOT solutions of n-heptane as a function of temperature. The results are expressed as plots of the molar ratio of glycerol to AOT ( R ) against temperature. The area under the curve shows the clear microemulsion region. Fig. 1 shows the results for 0.1 mol dm-3 AOT but the stability region is independent of AOT concentration in the range 0.02- 0.2 mol dm-3. As the temperature is increased the solution turbidity increases sharply in the region of the phase limit.Further increase in temperature leads to separation of a glycerol-rich phase which sediments. The line shown in fig. 1 is the point at which the solution turbidity sharply increases and it was measured by visual inspection. Ca. 5 mol glycerol can be solubilised per mol AOT at 0 O C , this amount decreasing with increasing temperature. Aggregates with R values of less than two are stable over a very wide temperature range. Primary solvation of the AOT headgroup and the sodium counterion probably requires 2-3 mol glycerol. In the corresponding water microemulsion system, 1 0 w - R ~ ~ ~ (i.e. [H,O]/[AOT] 3 10) structures are also stable over a wide temperature rangel and this RHIO value marks the transition from a hydrated ‘inverse micelle ’ to a microemulsion droplet containing water with properties similar to bulk water.8 This corresponding point would appear to be R = 2 in the glycerol system. The microemulsion map shows no low-temperature microemulsion phase limitP. D.1. FLETCHER, M. F. GALAL AND B. H. ROBINSON 3 309 5 4 R 3 2 1 0 0 20 40 60 80 T/OC Fig. 1. Stability map for the AOT +glycerol + heptane microemulsion system. AOT concen- tration, 0.1 mol dm+. within the range 0-90 "C. This is in contrast to the corresponding water system and suggests that the factors controlling this low-temperature phase separation are altered. There is some evidence to suggest that, in the water system, this process may be associated with desorption of AOT molecules from the oil/water interface.*q DYNAMIC LIGHT-SCATTERING RESULTS From measurements of the intensity autocorrelation function (g(2)) as a function of delay time (t), a value for the measured collective diffusion coefficient (D) and the corresponding correlation length ( I ) were obtained : D = z/2K2 (1) 1 = kT/67tvD (2) where K = (4nn/A) sin 812, q is the solvent viscosity and z is the limiting decay rate given by [ - d In (g(2))/dt] limit as t -+ 0.It was checked experimentally that the measured correlation lengths were inde- pendent of scattering angle (30 < 8/* < 150) for high-R-value dispersions at 10 and 30 "C. Note that critical behaviour of the solution results in the correlation lengths exhibiting an angular dependence.1° The normalised variance of the autocorrelation function was in the range l-lO% for low volume fractions of dispersed phase.At high volume fractions the variance increased and the presence of two exponentials was detected. This type of behaviour has been observed previously and is explained by the appearance of a self-diffusion process (in addition to the collective diffusion process) at high volume fractions.ll In this study only the collective diffusion coefficient is discussed.3310 MICROEMULSIONS OF GLYCEROL IN n-HEPTANE P 10 30 50 T/OC Fig. 2. Correlation length as a function of temperature. AOT concentration 0.1 mol dm-3; R values (a) 0.986, (b) 1.95, (c) 3.08 and (d) 4.26. Fig. 2 shows values of the correlation lengths obtained for various R-value microemulsions as a function of temperature.Correlation lengths increase both with increasing R and with increasing temperature. The measured correlation length, in general, contains a contribution from interparticle interactions and can be equated with the particle hydrodynamic radius only for the case of a spherical particle in the limit of infinite dilution. In order to obtain values for the hydrodynamic radii, data were obtained at different AOTconcentrations but at constant R value and temperature. The data were analysed to yield values of rH (the hydrodynamic radius) and a. a provides a quantitative measure of inter-particle interactions and is defined by D = Do(l +a+) (3) (for small 4) where Do is the infinite-dilution limiting value of D and 4 is the volume fraction of AOT and glycerol in the dispersion.Note that there is an important assumption contained in the above procedure which is that the composition of the aggregates does not change as the system is diluted. Two possible situations may arise. First, if glycerol were to be soluble in the absence of AOT to a significant extent in the heptane oil phase, then the droplets might be expected to shrink upon dilution. This could then offer an explanation for the observed decrease in correlation length with dilution of the particles. However, this is extremely unlikely since the solubility of glycerol in heptane was measured to be < 0.7 mmol dm-3 over the temperature range 20-100 OC.12 This upper limit is insignificant when compared with the lowest glycerol concentration of 20 mmol dm-3 employed in this work.Secondly, AOT may desorb to some significant extent from the glycerol/heptane interface as the AOT concentration is decreased. This effect would cause an increase inP. D. I. FLETCHER, M. F. GALAL AND B. H. ROBINSON 331 1 01 I I I I 0 1 2 3 4 R Fig. 3. Hydrodynamic radius as a function of R. 0, 10 "C; 0, 30 "C. the size of the droplets at low concentrations, but this is not observed experimentally. Also, as will be shown presently, the values obtained for the hydrodynamic radii as a function of R imply that the AOT does not desorb to any large extent. Fig. 3 shows derived values of hydrodynamic radii plotted as a function of R for two temperatures (10 and 30 "C). For both temperatures the data are well described by r,/nm = 1.7( f 0.2) + 0.88( f 0.15)R.(4) The value of the intercept is in good agreement with other measurements of the hydrodynamic radius of 'empty' inverse micelles of AOT.'? l3 The value of the slope of fig. 3 may be compared with the corresponding water system by the following calculation. For a spherical microemulsion droplet containing a core of phase s (volume per molecule = V,) and containing nAOT surfactant molecules which present an interfacial area of aAOT per AOT molecule, then, assuming all AOT is interfacially bound particle surface area = 4nr2 = ~AOTLZAOT particle core volume = 4nr3 = nAOT RV, J where r is the radius of the central droplet core Combining the two equations yields 3R Vgl y cerol r = ~ A O T (not the overall particle for the core radius as a function of R, where molecule (0.121 nm3 calculated from the bulk density).The model also assumes a monodisperse collection of droplets. The slope of fig. 3 may be equated with (3Glycerol/aAOT) to yield an apparent value for CIAOT. Values of 0.41 f0.07 and 0.51 k0.08 nm2 may be calculated in this way for the glycerol and water [data from ref. (2)] systems, respectively. At face value, the figures imply that either the AOT cfesorbs from the glycerol interface more than from the water interface (by up to 20%) is the volume of a single radius). ( 5 ) glycerol3312 15 10 -ff 5 0 MICROEMULSIONS OF GLYCEROL IN n-HEPTANE 0 1 2 3 4 Fig. 4. Interaction coefficient a as a function of R. 0, 30 "C; 0, 10 "C. R or that the AOT is more closely packed at the glycerol interface.The model of the particle system used in these calculations is very crude and ignores, for example, any possible polydispersity in the system. For this reason it is felt that the similarity of the two systems is more significant than the relatively minor difference revealed by the calculation. Fig. 4 shows the variation of a with R at 10 and 30 "C. For hard spheres with purely repulsive interactions a is thought to be ca. 1.S4 whilst it is predicted to be negative in the case of attractive interactions. It can be seen that a becomes negative as the microemulsion phase limit is approached by increasing either R or the temperature. This result is still valid even if it is assumed that the particles have expanded by 20% on dilution. It is therefore concluded that the observed increase in correlation length with temperature is caused by increasingly attractive interactions between the particles and not by an increase in size of the particles.The value of a for the corresponding water microemulsion system is - 2.1 f 0.4 for all RHZO values (1 1-50) at 25 oC.2 This corresponds approximately with the low-R limiting value observed in this work. Small-angle neutron-scattering data have been obtained for the water-droplet system in the region of the phase-stability limit. It was concluded that the droplet size does not change much but critical scattering behaviour, which is a manifestation of attractive interactions, was 0bserved.~9 lo, l5 VISCOSITY MEASUREMENTS The viscosity of dispersions is sensitive in general to particle shape and interparticle interactions.The method is relatively insensitive to particle size.16 It is, therefore, a useful complementary technique to dynamic light scattering for this type of system. Fig. 5 shows plots of qsp/C against C for a glycerol microemulsion (R = 3.00 at 10 and 30 "C). The data were fitted (at low C) toP. D. I. FLETCHER, M. F. GALAL AND B. H. ROBINSON 3313 .. 4 c W Fig. 0 1 I I I 0 0.05 0.1 0.15 C/g ~ r n - ~ 5. Reduced viscosity plots. R = 3.00. 0, 30 "C; x , 10 "C. where Cis the concentration (g ~ m - ~ ) of the dispersed phase, qsp is the specific viscosity [ = (v -qsolvent)/qsolvent], kH is the Huggins coefficient and [q] is the intrinsic viscosity. It can be seen that both plots have the same intercept ([q]) but that the 30 "C data show a significantly higher slope (kH[q12). The intrinsic viscosity is dependent on both particle shape and solvation as (7) [~ll = 4Oparticle + dU,olvent) where v are the partial specific volumes of the subscripted species, 6 is the weight of solvent associated with 1 g of particles and v is a shape parameter, which is 2.5 for spheres.Partial specific volumes were calculated from measured density data [ i i ~ h ~ = 1.07 0.04 (temperature/"C) g cmP3; o $ ~ ~ ~ ~ ~ ~ = 1.3 1 k 0.05 g ~ r n - ~ (inde- pendent of temperature)]. The measured values of [q] are 2.8 k0.3 and 2.7 k0.3 cm3 8-l at 10 and 30 "C, respectively. If it is assumed that 6 = 0, then the corresponding values of v are 3.4 f 0.4 and 3.0 f 0.4. These values imply axial ratios for the particles of ca.2-3.15 If, however, v is assumed to have a value of 2.5 (corresponding to a spherical shape) then 6 is calculated to be 1&20%. Since the particle must be solvated to some extent, it is concluded that the particles must be close to spherical in shape. Values of k , are found to be 3.8 f 0.9 and 6.4 f 1.5 at 10 and 30 "C, respectively. Theoretical estimates for the Huggins coefficient in the case of hard spheres range from 0.7-0.8.17 The experimental values clearly deviate from the hard-sphere value, the larger deviation being found closer to the phase-separation limit. The conclusion from the viscosity data is that the shape of the particles is constant with increasing temperatures and close to spherical. However, interdroplet interactions clearly increase with temperature.These results are totally consistent with the picture emerging from the dynamic light-scattering data.33 14 MICROEMULSIONS OF GLYCEROL IN n-HEPTANE To summarise, AOT-stabilised glycerol dispersions in a heptane continuous phase consist of discrete droplets which are close to spherical in shape. The hydrodynamic radius of the droplets is a linear function of R and is in the range 1-10 nm. Attractive interdroplet interactions increase as the microemulsion phase limit is approached. We thank the S.E.R.C. (Biotechnology) for financial support. M. Zulauf and H. F. Eicke, J. Phys. Chem., 1979,83,480. J. D. Nicholson and J. H. R. Clarke, in Surfactants in Solution, ed. K. Mittal (Plenum Press, New York, 1983) vol. 3, p. 1663. B. H. Robinson, C. Toprakcioglu and J. C. Dore, J. Chem. SOC., Faraday Trans. I , 1984, 80, 13. 4 C. Toprakcioglu, J. C. Dore, B. H. Robinson, A. M. Howe and P. Chieux, J. Chem. Soc., Faraday Trans. I , 1984, 80, 413. P. G. De Gennes and C. Taupin, J. Phys. Chem., 1982, 86, 2294. P. D. I. Fletcher, N. M. Perrins, B. H. Robinson and C. Toprakcioglu, in Biological and Technological Relevance of Reverse Micelles and other Amphiphilic Structures in Apolar Media, ed. P. L. Luisi (Plenum Press, New York, 1983), p. 69. D. E. Koppel, J. Chem. Phys., 1972, 57,4814. R. Kubik and H. F. Eicke, Helv. Chim. Acta, 1982, 65, 170. P. D. I. Fletcher, A. M. Howe, N. M. Perrins, B. H. Robinson, C. Toprakcioglu and J. C. Dore, in Surfactants in Solution, ed. K. Mittal (Plenum Press, New York, 1983), vol. 3, p. 1745. lo J. S. Huang and M. W. Kim, Phys. Rev. Lett., 1981, 47, 1462. l1 A. M. Cazabat, D. Chatenay, D. Langevin and J. Meunier, in Surfactants in Solution, ed. K. Mittal l2 L. A. K. Staveley and G. L. Milward, J. Chem. SOC., 1957,4369. l3 E. Gulari and B. Bedwell, in Solution Behaviour of Surfactants, ed. K. Mittal and E. J. Fendler l4 A. M. Cazabat and D. Langevin, .I. Chem. Phys., 1981,74, 3148. l5 M. Kotlarcyk, S. H. Chen and J. S. Huang, Phys. Rev. A , 1983, 28, 508. l6 C. Tanford Physical Chemistry of Macromolecules (Wiley, New York, 1961). (Plenum Press, New York, 1983), vol. 3, p. 1729. (Plenum Press, New York, 1982), vol. 2, p. 833. M. Muthukumar and K. F. Freed, J. Chem. Phys., 1982,76, 6195. (PAPER 4/277)

ISSN:0300-9599    

DOI:10.1039/F19848003307

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. Soc., Faraday Trans. I, 1984, 80, 3315-3329 Generalized Flory-Huggins Isotherms for Adsorption from Solution BY PANAGHIOTIS NIKITAS Laboratory of Physical Chemistry, University of Thessaloniki, Thessaloniki. Greece Received 2 1st February, 1984 A new approach to the study of solutions composed of two kinds of molecules differing in size and shape has been developed on the basis of the lattice statistical model of athermal solutions. The results have been used for determination of the adsorption isotherms of organic compounds adsorbed from solution onto homogeneous surfaces. It is shown that the resulting isotherms are generalized forms of the Flory-Huggins isotherm, to which they are reduced by Flory's approximation. The possible ways of introducing the interactions between adsorbed molecules have also been examined.Finally, a critical examination of the validity of the isotherms is made by comparison with experimental data. The selection of the appropriate adsorption isotherm is one of the fundamental problems faced during analysis of experimental adsorption data. This is because the adsorption isotherm does not just describe the equilibrium between the concentrations of the adsorbate in the adsorption layer and in the bulk of the phase from which the adsorption is taking place. It is also the mathematical expression of a model of the adsorption layer. Therefore correct evaluation of the standard free energy of adsorption and obtaining reliable information about the interaction forces between the adsorbed molecules are only possible when the correct isotherm has been selected.For analysis of experimental adsorption data various isotherms have been emp1oyed.l The most widely used isotherms are those of Fr~mkinl-~ and Langmuir.l* However, these isotherms, though simple and effective, have the disadvantage of not accounting for the presence of the solvent molecules in the adsorption layer. The assumption that adsorption from solution is a substitution process of the pre-adsorbed solvent molecules by the adsorbate has led to the development of isotherms which take into account the size of the adsorbed particle~.~-l~ The most interesting of these isotherms are those of the Flory-Huggins-type:6y (1) 0 (1 -O)rexp(r- 1) pc = 0 exp ( - 2aO) pc = (1 - e y where p is the adsorption equilibrium constant, c is the bulk concentration of the adsorbate, 0 is the surface coverage, r is the molecular size ratio or the area ratio parameter and cc is the interaction parameter.Eqn (1) and (2) have received attention in studies of electrochemical adsorption Eqn (1) results from the assumption that the adsorption layer behaves as an athermal lattice interfacial solution of molecules of different size and by the 33153316 ISOTHERMS FOR ADSORPTION FROM SOLUTION approximation that the coordination number z of the adsorption layer tends to infinity (Flory’s appro~imation~l).~ Although this approximation leads to simple equations it is not accurate, especially when the dimensions of the molecules of the adsorbate and the solvent are significantly different.,l In addition, in eqn (1) the lateral interactions and the adsorbate-adsorbent interactions are included in the equilibrium constant a.Thus it is difficult to obtain information about the intermolecular particle-particle interactions. The term exp (- 2aO) is included in eqn (2) to allow for these interactions. However, the isotherm from eqn (2) deviates from the experimental data. In the present work a new, fairly simple and accurate method is developed for the study of athermal solutions. The results of this method are applied to the study of adsorption from solution and specifically to the determination of the adsorption isotherm. It is proved that the resulting isotherms are generalized forms of the basic Flory-Huggins isotherm, eqn (l), to which they are reduced by Flory’s approximation. Possible ways of introducing molecular interactions into these isotherms are also examined.Finally, the isotherms obtained are critically tested against experimental data for adsorption of methyldiphenylphosphine oxide (MDPO), ethyldiphenylphos- phine oxide (EDPO), triphenylphosphine oxide (TPO), triphenylphosphine (TPP), triphenylarsine (TPAs) and triphenylantimony (TPSb) on Hg from methanolic solution. ADSORPTION ISOTHERMS FOR ATHERMAL INTERFACIAL MIXTURES The lattice theories of the liquid state21922 are based on the assumption that the molecules of a liquid system are arranged in space according to a certain lattice. Each molecule can occupy only one lattice site (monomer) or simultaneously r sites (r-mer). In the case of a binary system of monomers with r-mers, N, and N, will denote the corresponding number of monomers and r-mers in the lattice.Obviously the following relations are valid: N,+N2 = N (3) N, -+ rN, = A4 (4) where N is the total number of the molecules and M is the number of lattice sites. When the binary system of monomers and r-mers has zero mixing energy (athermal solution) then the thermodynamic properties are easily determined provided that the factor a of Guggenheim and McGlashan21g23 has been determined. In principle, a is the ratio of the probability that a group of r sites, congruent with the r-mer, is wholly occupied by a single r-mer to the probability that the group is entirely occupied by monomers. The relative probability a can be determined by the methods of Guggenheim and McGlashan2l9 23 or Brzo~towski,~~ and the method of Guggenheim and McGlashan is considered to be the most accurate.However, it has the disadvantage that for each category of r-mers different and rather complex relationships for a are valid. In the following, a new and simple method for the calculation of a is developed. DETERMINATION OF THE RELATIVE PROBABILITY a ATHERMAL BINARY SOLUTIONS CONTAINING RIGID MOLECULES In order to proceed to a determination of a it is necessary to define first the parameters bi as follows. p denotes the number of allowed distinguishable ways inP. NIKITAS 3317 which an r-mer can be placed in the lattice. Of the r sites which can be occupied by a single r-mer, the 1,2, . . ., i (i < r) sites are already occupied by monomers.Now if the i+ 1 site is occupied by an element of an r-mer, then the number of the available sites for the r-mer in the lattice is not equal to p but to p- bi. If P, is the probability for the group of r sites to be occupied only by monomers, then we have where Pr/l, 2 , ..., ( r - l ) is the conditional probability of the r site being occupied by a monomer when all the remaining r - 1 sites are also occupied by monomers. For the conditional probability we have Pr = q r - 1 ) pr/1,2, ..., (r-1) ( 5 ) where 0 = rN2/(Nl i- rN2). (7) Therefore However, since Pi = 0 / p where Pi is the probability of the group of r sites r-mer, for the relative probability a we will have where b; = b i / p . (9) being completely occupied by an - b; 0) In table 1 the results obtained using eqn (10) are compared with those obtained by the methods of Guggenheim and McGlashan and Brzostowski and also by Flory's approximation.Table 1 also shows the values of b; used for these calculations, determined on the basis of their definition from the geometrical characteristics of the lattice. In certain cases, as for example in the case of a mixture of square tetramers with monomers in a plane lattice, more than one set of b; values were determined. In these cases the set of b; values which minimizes the free energy of the system [eqn (16) below] was selected. Note that the results of eqn (10) are in a good agreement with those of Guggenheim and McGlashan, which means that eqn (10) offers a good approximation of a. Moreover the advantages of eqn (10) are that it is valid for any value of r and it is relatively simple.ATHERMAL BINARY SOLUTIONS CONTAINING FLEXIBLE LINEAR r-MERS In this case prior to a determination of a it is necessary to define the parameter q.21 Consider an r-mer occupying a given group of r sites. Each of these sites has z neighbouring sites. We denote by zq the number of pairs of neighbouring sites of which one is a member of the group occupied by the given r-mer and the other is not. Under the condition that the r-mers are linear and flexible molecules it can be approximately assumed that - b i = b, i = 1,2 ,..., r. (12) The parameter 6can be determined as follows. In a group of r sites, which can be occupied by one r-mer, the r - 1 sites are already occupied by monomers while to the3318 ISOTHERMS FOR ADSORPTION FROM SOLUTION Table 1.Values of the relative probability a in athermal solutionsa ~ mixtures of monomers with trimers on a plane lattice: r = 3, z = p = 6, mixtures of monomers with trimers on a spatial close-packed lattice: and bi = 0.29 bi = 0, b’, = 0.33 and bi = 0.50 r = 3, p = 24, bk = 0, b’, = 0.167 6 I IT I11 IV I I1 I11 IV 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.02 0.02 0.02 0.02 0.0 1 0.06 0.06 0.05 0.07 0.02 0.1 1 0.1 1 0.10 0.15 0.03 0.2 1 0.21 0.18 0.31 0.06 0.42 0.42 0.34 0.67 0.13 0.88 0.89 0.67 1.56 0.29 2.15 2.22 1.55 4.32 0.76 7.33 7.7 1 4.91 16.67 2.77 57.75 62.39 35.65 150.00 23.51 0.0 1 0.02 0.03 0.06 0.13 0.29 0.77 2.8 1 24.07 ~ 0.0 1 0.01 0.0 1 0.02 0.03 0.04 0.06 0.08 0.12 0.17 0.26 0.39 0.66 1.08 2.35 4.17 19.41 37.50 mixtures of monomers with squares on a plane lattice : r = 4, z = p = 4, and bi = 0.75 mixtures of monomers with squares on a simple cubic lattice : r = 4, z = 6, and bi = 0.58 bI, = 0, bi = 0.50, bi = 0.50 p = 12, b; = 0, Bi = 0.33, b; = 0.33 e I I1 I11 IV I I1 I11 IV 0.1 0.03 0.03 0.2 0.08 0.08 0.3 0.18 0.18 0.4 0.35 0.35 0.5 0.71 0.73 0.6 1.58 1.71 0.7 4.34 5.02 0.8 18.00 24.00 0.9 221.20 424.81 0.03 0.07 0.13 0.23 0.41 0.77 1.69 5.33 45.64 0.04 0.12 0.3 1 0.77 2.00 5.86 21.61 125.00 2250.00 0.01 0.01 0.01 0.01 0.03 0.03 0.03 0.04 0.07 0.07 0.06 0.10 0.15 0.15 0.11 0.26 0.33 0.34 0.22 0.67 0.8 1 0.86 0.50 1.95 2.5 1 2.75 1.36 7.20 11.95 13.91 5.62 41.67 174.56 225.06 69.42 750.00 a I, Results of eqn (10); 11, Results of Guggenheim and McGlashan; 111, Results of Brzostowski ; IV, Flory’s approximation.rth site enters the first segment of an r-mer. From the z sites which can be occupied by the second segment of the r-mer only the zq/r are available. However, to the z possible sites for the second segment correspond p possible sites for the whole molecule. Therefore to the zq/r sites available to the second segment of the r-mer correspond p q / r available sites for the whole molecule. Therefore and GuggenheimZ5 and Huggins26 arrived at the same relationship though they used different methods.P. NIKITAS 3319 BASIC THERMODYNAMIC RELATIONS The relative probability a is related to the entropy ASm and the free energy AAm of mixing through:23 AAm - Asm - - ( -joo lna d8+8j01 lna do). RT R r-(r-l)8 In the case of a binary system of monomers with rigid r-mers, from eqn (10) and (1 5 ) we obtain: Xr-l (l-b;O)ln(l -b;8) - O(l-b;)ln(l-b; + B z ( i-0 b; b; where X = 8 / [ r - ( r - 1) 81.comes from eqn (14) and (1 5 ) : The corresponding relationship for a system of monomers with flexible linear r-mers ADSORPTION ISOTHERM FOR A MIXTURE OF MONOMERS WITH RIGID r-MERS For the determination of the theoretical isotherm we use the following adsorption model: (a) the adsorption layer has a regular lattice structure, (b) the N , molecules of the solvent and the N , molecules of the adsorbate occupy the lattice sites of the adsorption layer in exactly the same way as they occupy the lattice sites in an athermal mixture of monomers with r-mers and (c) the adsorption takes place according to: organic (in solution) + r solvent (ads) + organic (ads) + r solvent (in solution).(1 8) The molecules of the solvent and the adsorbate form in the adsorption layer a binary athermal mixture. Therefore the total partition function Q coincides with the partition function of an athermal mixture of monomers with r-mers provided that in the latter the effect of the field of the adsorbing surface is introduced through the internal partition functions qi (i = 1 or 2) of the molecules of the solvent and the adsorbate, respectively. Then we have : In Q = N , In q1 + N , In q2 + ASm/k (19) or In Q = N , In q1 + N , In q2 - N , In ( 1 - 8) - N , In 8 M N1+(1-bb;)rN2 ) -3A1- b;)] (20) +?[qf( 2-0 M b; where Ax) = x In x. and p$ds of the solvent and the adsorbate at the interface are obtained: If eqn (20) is differentiated with respect to Nl and N2, the chemical potentials pgds3320 ISOTHERMS FOR ADSORPTION FROM SOLUTION or and similarly where 0 is obtained from eqn (7) and represents the coverage of the adsorbed layer by the molecules of the adsorbate.For the chemical potentials in the bulk solution the following well known relations are valid: (23) (24) where a,, yi and Xp are the activity, the activity coefficient and the molar fraction, respectively, of the ith component and c and cs are the concentrations of the adsorbate and the solvent, respectively. If we assume that the reference state for the chemical potentials is the unsymmetrical ~ y s t e r n ~ ~ ? ~ ~ then in the region where Henry's law is valid we have PA =/L;+kTInaA =p;+kTIn()'AXb,) X p",kTln(y,c/c,) ps =pg+kTlna, =&+kTln(y,X;) x pg+kTlnys YA=1, YS=l (25) and therefore p A = p i + k T In (c/c,) (26) When thermodynamic equilibrium is established between the adsorbed particles and those in the solution then from the assumption (c) we obtain pi" - rpids = pA - rpS.(28) Now if eqn (21), (22), (26) and (27) are substituted into eqn (28), the adsorption isotherm is obtained : Ll r-1 where W n (I-biO) pc = (1 -6)rexp[-(A+1)] i=o r-l (1 -bi) ln(1 -bi) A = x ( bi i-0 ADSORPTION ISOTHERM FOR A MIXTURE OF MONOMERS WITH LINEAR FLEXIBLE T-MERS Because in this case - - r - 4 ) / r (3 3) b! = b' = b/p = ( the isotherm which is obtained after the substitution of eqn (33) into eqn (29) and (30) has the following form: r-I 0 (1 -0).exp[-(B+ l)] pc = (34) where (3 5 )P. NIKITAS 332 1 PROPERTIES OF EQN (29) AND (34) Eqn (29) and (34) are generalized expressions of the Flory-Huggins isotherm, eqn With Flory's approximation, z -+ co, the following relations are valid: (l), and they can be simplified in the following cases. lim b; = lim[(r-q)/r] = 0 and lim A = limB = - r (36) %-+a z+co and eqn (29) and (34) are reduced to the Flory-Huggins isotherm, eqn (1). When the adsorbate and the solvent have the same size then we have: r = l , b ; = O and A = B = - r . (37) If the above relationships are introduced into eqn (29) and (34) then Langmuir's isotherm is obtained : (38) Langmuir's isotherm is also obtained when the solvent is assumed to be a continuous medium.Then the following relations are valid: 6/( 1 - 6) = (c/cs) exp (- AGo/k7). 41= 1, Ps=O (39) which also lead to Langmuir's isotherm. Finally, when 6 6 1 from eqn (29) and (34) we have pc = 6 (40) which means that these isotherms are reduced to Henry's isotherm. ADSORPTION ISOTHERMS FOR NON-ATHERMAL INTERFACIAL MIXTURES Eqn (29) and (34) are valid when the interfacial mixture of the adsorbate and solvent molecules possesses zero energy of mixing. Therefore these isotherms must be extended in order to include all the possible interactions between the adsorbed particles. This can be achieved if appropriate activity coefficients are introduced into the chemical potentials of the adsorbed molecules. If fA and fs are the activity coefficients of the adsorbate and the solvent in the adsorption layer, then the isotherm resulting from eqn (29) is (41) and similarly from eqn (34) we obtain: (42) On the molecular level the ratiofA/f& can be determined either by the Bragg- Williams approximation21 or by the quasi-chemical approximation.21 homogeneous molecules the Bragg-Williams approximation leads to [n the case of (43) FAR 1 1083322 ISOTHERMS FOR ADSORPTION FROM SOLUTION while the quasi-chemical approximation yields : where u = q6/[q6+r(l -131, v = 1 -U (45) K = 2/(b + l), b = [ 1 + 4uv(v2 - I)]; (46) v = exp(w/2kT).(47) In the above relations, w is defined in such a way that the contribution of each contact of elements of the adsorbate and solvent molecules to the configurational potential energy is (WAA -I- wss + W ) / Z where wAA and wss are the interaction energies between respective contacts of molecules of the same kind.By means of Flory’s approximation, eqn (43) is reduced to The adsorption isotherm in this crude approximation, which results from eqn (41) and (48) or eqn (42) and (48), is 6 exp [a( 1 - 26)] (1 -6)+exp(r- 1) pc = (49) where a = rw/kT. Note that this isotherm is of the same form as eqn (2). At a more general although macroscopic level the ratiofA/’k can be determined in the following way. The introduction of the activity coefficients, fA and fs, is necessarily equivalent to the assumption that there exists an excess free energy g: with respect to the free energy of an athermal binary mixture. Therefore by analogy with the excess free energy ge with respect to an ideal mixture we assume that g: can be expanded as a power series of the molar fractions XA and Xs of the adsorbate and the solvent in the interfacial region:29 In this case the activity coefficients are determined by:29 In the above equations XA and Xs can be expressed as functions of coverage 8 by: XA = 6/[6+r(l-6)] and XA+Xs = 1.(54) This way of introducing particle-particle interactions has also been used by Mohilner et aZ.,8 who instead of gz used ge, i.e. the excess free energy with respect to an ideal mixture. Therefore the values of Bi are expected to be determined by theP. NIKITAS 3323 contribution of the particle-particle interactions and to some extent by the size difference of the adsorbed molecules. On the other hand, in the present work the effect of the size difference is included in the configurational terms of eqn (41) and (42).Consequently in the present approach the values of Bi are mainly determined by the contribution of the particle-particle interactions. COMPARISON WITH EXPERIMENT AND CONCLUSIONS I Eqn (41)-(43) and (49) may be expressed as fl0) = AGo'/RT = AGo/RT+ In (fA/fL) ( 5 5 ) where for the case of rigid r-mersfl8) is given by For the case of the adsorption of flexible linear r-mers we have and finally for the case when Flory's approximation is employed we have From eqn (55) the tests of these isotherms can be performed as follows. First the experimental values of the free energy AG::, = RTfl8) (59) are determined directly from 8 against c data and the values are compared with the corresponding theoretical values obtained from AGE;,, = AGO + RTln CfA/fL). The values of AGO and Bi (or F and a) which are included in this equation can be determined by the least-squares method from AGO' against 6 data.In the case where eqn (53) is employed for the determination of ln(fA/fL) it is obvious that the more Bi terms used the better the fit of the experimental values will be. However, an increase in the number of the Bi terms leads to a decrease in the number of degrees of freedom of the least-squares fit and consequently in the amount of smoothing. Therefore a careful examination of the results of the least-squares fit is required. In this case we can take as a criterion of the fit the value of 0, the root-mean-square deviation between calculated and experimental values of AGO' : N 0' = ~ [ ( A G ~ ~ , , - A G ~ ~ p ) / R T ] 2 / N (61) where N is the number of data points.The fit can be considered as generally satisfactory for r7 values < ca. 0.2. In the present work the isotherms were tested against experimental data for adsorption of MDPO, EDPO, TPO, TPP, TPAs and TPSb on Hg from methanolic solutions of LiCl. The adsorption was studied by means of electrocapillary measure- ments. A description of the experimental apparatus and details of the results have been reported 31 108-23324 ISOTHERMS FOR ADSORPTION FROM SOLUTION Table 2. Data for the adsorption isotherms used in this work isotherm r AGo/RT B,(a or B") B, B2 B3 0 Frumkin Bennes eqn (41) and (43) eqn (53) and (58) eqn (49) eqn (41) and (53) Frumkin Bennes eqn (49) eqn (41) and (43) eqn (53) and (58) eqn (41) and (53) Frumkin Bennes eqn (41) and (43) eqn (53) and (58) eqn (49) eqn (41) and (53) Frumkin Bennes eqn (41) and (43) eqn (53) and (58) eqn (49) eqn (41) and (53) MDPO = 2, b', = 0.333, b; = 0.50 1 -6.61 -0.39 - - - 4.35 -6.09 1.00 - - - 3 -5.89 1.68 3 -6.96 1.07 - - - -6.18 1.46 - - - 3 -5.96 0.99 -0.48 -0.34 -0.11 3 -7.11 1.03 - - - -6.96 0.73 -0.35 -0.38 -0.07 - - - EDPO 4 = 2, b', = 0.333, b; = 0.50 1 -7.11 - 4.75 -6.85 3 - 6.72 3 - 7.78 3 - 6.94 - 6.99 3 - 7.90 - 7.99 - 0.1 1 - 1.33 - - 2.61 - 1.71 1.63 - 1.76 0.16 0.42 1.31 - 1.48 0.29 0.37 - - - - - TPO q = 3, b; = 0.167, b; = 0.333, bj = 0.50 1 -7.65 0.06 - - 5.45 -7.56 1.64 - - 4 -7.05 5.78 - - 4 -8.18 4.15 - - 4 -7.78 2.28 - - 4 -8.67 2.06 - - -7.73 2.37 -0.03 0.56 -8.73 2.12 0.1 1 0.43 TPP q = 3, b; = 0.167, b; = 0.333, bi = 0.50 1 - 10.78 5.51 -10.56 4 - 10.77 4 - 11.70 4 - 10.66 - 10.69 4 - 11.63 -11.69 - 0.07 - - 1.84 - - 5.48 4.16 - 2.46 2.32 -0.09 0.67 2.22 2.06 0.05 0.58 - - - - - - - 0.08 0.09 0.22 0.15 0.08 0.07 0.08 0.07 - 0.1 1 - 0.14 - 0.44 - 0.32 - 0.14 0.09 0.10 - 0.14 0.12 0.10 0.10 - 0.34 - 1.12 - 0.94 - 0.27 0.16 0.09 - 0.27 0.21 0.08 - - 0.17 - 0.82 - 1.80 - 1.55 - 0.60 0.44 0.17 - 0.62 0.49 0.15P.NIKITAS Table 2. (cont.) 3325 isotherm r AG"/RT B,(a or B") B, B2 B3 d Frumkin Bennes eqn (49) eqn (41) and (43) eqn (53) and (58) eqn (41) and (53) Frumkin Bennes eqn (41) and (43) eqn (53) and (58) eqn (49) eqn (41) and (53) TPAs q = 3, b; = 0.167, b; = 0.333, bi = 0.50 1 -10.99 - 5.60 -10.83 4 - 11.00 4 - 11.91 4 - 10.93 - 10.94 4 - 11.90 - 11.94 - - 0.03 1.77 5.56 4.20 - - 2.40 2.32 -0.10 0.62 2.17 2.06 0.04 0.53 - - - - - - - - TPSb = 3, b; = 0.167, 6; = 0.333, bi = 0.50 1 -12.60 0.03 - - 5.82 -12.13 1.97 - - 4 -10.72 9.12 - - 4 -12.16 6.28 - - 4 -12.54 2.47 - - - 12.86 2.26 -0.03 0.26 4 -13.37 2.31 - - -13.84 2.01 0.10 0.3 1 0.09 0.55 1.64 1.36 0.41 0.09 0.41 0.09 0.10 0.82 1.64 1.44 0.63 0.13 0.60 0.13 For the analysis of the experimental data and for the test of the theoretical isotherms the following simplifying assumptions were made.It was assumed that the adsorbed phase consists of a unimolecular layer of adsorbed solvent and adsorbate molecules. In this approximation the parameter Y is equal to the integer closest to the area ratio sA/sS I Y = int (S,/S,) (62) where SA and Ss are the areas covered by an adsorbate and solvent molecule, respectively, on the saturated surface.The values of SA were obtained from ref. (30) and (3 l), while for Ss a value of 0.19 nm2 was used.6 The values of r resulting from eqn (62) are given in table 2. For the calculation of the 6; parameters it was assumed that the adsorbed molecules at the interface occupy the sites of a regular hexagonal lattice. The values of b; are also given in table 2. Fig. 1-3 show plots of the free energy AGO' against the surface coverage 6 at various potentials in the potential range where the isotherms are congruent. The points correspond to experimental values of AGO' while the lines represent theoretical values of AGO' determined from eqn (60).The various parameters required for the calculation of were determined by the least-squares method and are given in table 2, which also gives the data of fitting of Frumkin's isotherm:1~30 (63) PC = [8/( 1 - O)] exp (- 2aO) and Bennes isotherm:10* 303326 ISOTHERMS FOR ADSORPTION FROM SOLUTION -6 -7 -7 h w u 4 --- 0 -9 -1 1 0.5 1.0 e Fig. 1. Tests of the isotherm from eqn (41) and (53) for the adsorption of (a) MDPO and (b) EDPO on Hg at: 0, Emax; 0, -0.5 and A, -0.7 V (us SCE). Points are experimental data plotted according to eqn (56) and (59), solid lines are calculated from eqn (53) and (60) using four Bi terms taken from table 2 and broken lines are calculated according to eqn (43) and (60). - 6 -1 0 h 3 0 u 4 - 14 -9 -13 -17 - 1 8 1 , , -21 0.5 1 .o 8 I 1 0.5 1.0 e Fig.2. Tests of the isotherm from eqn (41) and (53) for the adsorption of (a) TPO and (b) TPP on Hg. Symbols as in fig. 1 with 0, - 0.6 and A, - 0.8 V (us SCE). For TPP, 0 indicates - 0.4 V (us SCE).P. NIKITAS 3327 -1 0 h w "u -15 d . - 20 0.5 0 1.0 -12 -1 7 -22 \ \ \ \ 0.5 1.0 8 Fig. 3. Tests of the isotherm from eqn (41) and (53) for the adsorption of (a) TPAs and (b) TPSb on Hg. Symbols as in fig. 1 and 2. 0.6 0.2 0.0 0.0 0 . 5 1.0 Fig. 4. Change in the excess free energy gz of adsorption of (1) MDPO, (2) EDPO, (3) TPSb and (4) TPO, TPP and TPAs as a function of their molar fraction. gz is calculated from eqn (50) using four Bi terms of eqn (41) and (50) taken from table 2.3328 ISOTHERMS FOR ADSORPTION FROM SOLUTION and as well as the values of 0. From fig.1-3 and from the values of 0 the following conclusions can be drawn. The simple Flory-Huggins isotherm, eqn (49), deviates from the experimental data, with increasing deviation as r increases. The isotherm of eqn (41) and (43) is slightly better than the Flory-Huggins isotherm and it follows the experimental data qualitatively. Essentially identical to the results obtained using eqn (41) and (43) are those obtained using eqn (41) and (44), which is based on the quasi-chemical approximation. This means that in this case the quasi-chemical approximation does not improve the Bragg-Williams approximation. The description of the adsorption layer becomes quantitative only when using eqn (53). Note that three or four Bi terms are enough for the attainment of satisfactory results.It is also characteristic that if only the Bo term is used the results are still better than the results obtained using Bennes isotherm . From the values of Bi and using eqn (50) the excess free energy gz can be calculated. The excess free energy g: can be considered as a measure of the strength of the interactions between the adsorbed molecules. Fig. 4 shows a plot of g: against the molar fraction of the adsorbate in the adsorption layer. Note that gz is positive over the complete range of X , values. Its values for TPP, TPAs, TPSb and TPO are almost the same, while for the phosphinoxides g: decreases in the order TPO > EDPO > MDPO. The positive values of gz reveal that the solvent as well as the adsorbate molecules tend to cluster on the electrode, while the decrease from TPO to MDPO reflects an analogous increase in the interfacial solubility of these substances in the same order.This seems to be reasonable as the decrease of the attractive London interactions and the increase of the repulsive interactions due to the P = 0 dipole are ordered in the same way.3o In addition, it seems reasonable that TPP, TPAs, TPSb and TPO have, within experimental error, the same value of g;. These substances have the same dimensions and they interact with London forces between their phenyl groups. For the case of TPO we expect the dipole-dipole interactions to be markedly weak because the dipoles of the adsorbed molecules of this substance are separated from each other.For the isotherm resulting from eqn (41) and (53) using Flory’s approximation, i.e. eqn (53) and (58), it is seen that, regardless of the difference of the values of the relative probability a (table I), results analogous to those of the generalized isotherm of eqn (41) and (53) are obtained. Therefore this isotherm can be used instead of eqn (41) and (53) or eqn (42) and (53) for the adsorption of substances with unsymmetrical molecules. Note that eqn (41) and (53) provide a good quantitative description of the adsorption of organic substances from solution. The same results are expected to be obtained using eqn (42) and (53). Although these isotherms are complex they have the advantage that the Bi coefficients are determined from the strength of the particle-particle interactions.Therefore the conclusions obtained for these interactions are expected to be more reliable than those obtained using other isotherms. B. Damaskin, 0. Petrii and V. Batrakov, Adsorption of Organic Compounds on Electrodes (Plenum Press, New York, 1971). A. Frumkin, 2. Phys., 1926, 35, 792. R. H. Fowler, Proc. Cambridge Philos. Soc., 1935, 31, 260. R. H. Fowler, Proc. Cambridge Philos. SOC., 1936, 32, 144. J. O’M. Bockris and D. A. J. Swinkels, J . Electrochem. SOC., 1964, 111, 736.P. NIKITAS 3329 J. Lawrence and R. Parsons, J. Phys. Chem., 1969, 73, 3577. H. P. Dhar, B. E. Conway and K. M. Joshi, Electrochim. Acta, 1973, 18, 789. D. M. Mohilner, H. Nakadomari and P. R. Mohilner, J. Phys. Chem., 1977, 81, 244. A. Mazhar, R. Bennes, P. Vane1 and D. Schuhmann, J. Electroanal. Chem., 1979, 100,395. l o R. Bennes, J. Electroanal. Chem., 1979, 105, 85. ' l R. Parsons, J. Electroanal. Chem., 1964, 8, 93. l2 J. M. Parry and R. Parsons, J. Electrochem. SOC., 1966, 113, 992. l3 B. E. Conway and L. G. M. Gordon, J. Phys. Chem., 1969, 73, 3609. l4 S. Trasatti, J. Electroanal. Chem., 1970, 28, 257. l5 B. E. Conway and H. P. Dhar, Surf. Sci., 1974,44, 261. l6 B. E. Conway and H. P. Dhar, J. Colloid Interface Sci., 1974, 48, 73. l7 B. E. Conway and H. P. Dhar, Electrochim. Acta, 1974, 19, 445. la B. E. Conway, H. Angerstein-Kozlowska and H. P. Dhar, Electrochim. Acta, 1974, 19, 455. I g B. E. Conway, J. G. Mathieson and H. P. Dhar, J. Phys. Chem., 1974,78, 1226. 2o K. G. Baikerikar and R. S. Hansen, Surf. Sci., 1975, 50, 527. 41 E. A. Guggenheim, Mixtures (Oxford University Press, London, 1952). 52 J. A. Barker, Lattice Theories of the Liquid State (Pergamon Press, Oxford, 1963). 23 E. A. Guggenheim and M. L. McGlashan, Proc. R. Soc. London, Ser. A, 1950,203,435. 24 W . Brzostowski, Bull. Acad. Polon. Sci., Ser. Sci. Chim., 1963, 11, 407. 25 E. A. Guggenheim, Proc. R. SOC. London, Ser. A, 1944, 183, 203. 26 M. L. Huggins, Ann. N. Y. Acad. Sci., 1942, 43, 9. z'7 A. Sanfeld, in Physical Chemistry, an Advance Treatise, ed. H . Eyring, D. Henderson and W. Jost 28 P. Nikitas, J. Electroanal. Chem., 1984, 170, 335. 29 M. L. McGlashan, J. Chem. Educ., 1963, 10, 516. 30 P. Nikitas, A. Pappa-Louisi and D. Jannakoudakis, J. Electroana!. Chem., 1984, 162, 175. 31 P. Nikitas, A. Anastopoulos and D. Jannakoudakis, J. Electroanal. Chem., 1983, 145, 407. (Academic Press, New York, 1971), vol. 1. (PAPER 4/303)

ISSN:0300-9599    

DOI:10.1039/F19848003315

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1984,80, 3331-3337 USb,O,, as a Catalyst for the Selective Oxidation of Propene Dynamic Interaction of the Oxide Surface with the Gas Phase BY RE& DELOBEL,* HERV~ BAUSSART, MICHEL LE BRAS AND JEAN-MARIE LEROY Laboratoire de Catalyse et de Physicochimie des Solides, E.N.S.C.L., U.S.T.L., B.P. 108, 59652 Villeneuve d'Ascq, France Received 6th March, 1984 The dependence of catalytic performance on the surface dynamics of USb,O,, has been studied. The sequential treatment of USb,O,, with propene, oxygen and the reactant mixture under the experimental oxidation conditions has been studied using the pulse-microreactor method. The existence of two types of active site on the surface is proposed. Sites with highly coordinated oxygen are responsible for complete oxidation.On the other hand, unsaturated sites lead to a selective process. We also discuss the irreversible surface restructuring in relation to the observed low mobility of 0,- ions. As described in our previous paper, propene is oxidized on USb,O,, via a redox niechanism.l An X-ray photoelectron spectroscopic investigation of this mixed metal-oxide catalyst2 has shown that the surface is irreversibly modified by the catalytic process. Previous studies have led us to consider four paths which may be held responsible for the surface dynamics. (i) Oxidation, hydroxylation3 or coke deposition* can block some of the surface sites. (ii) The reversible or irreversible formation of surface structural phases (e.g. two- or three-dimensional cluster^)^ can occur.(iii) There can also be formation of surface polyhedric sites with high or low oxygen coordination.s (iv) Diffusion of different ions in the surface or in the bulk7 can also occur. In this paper we report experiments performed to study these different assumptions by using a pulse microreactor. EXPERIMENTAL The preparation of the mixed oxide USb,O,, has been described previously.' Surface treatments and catalytic-activity tests were carried out with a microcatalytic pulse reactor. The gas chromatograph was an Intersmat IGC 15. The two columns, each 2 m long, were made of 1/8 in. stainless-steel tubing packed with Porapack Q (100-200 mesh). The carbon dioxide yield was determined at room temperature. Propene, water and other oxidation products (mainly C3H40, C,H,O and C,H40) were determined during programming from 20 to 180 "C.Pulses (1.6 cm3) of reactant gases or of a reactant mixture were passed over 80 mg of the catalyst under a pressure of 3 atm in the reactor. Between each pulse the sample was kept under an He flow for 20 min, the time required for chromatographic analysis. To ensure that the catalyst was completely oxidized at our experimental temperatures the sample was pretreated with an oxygen flow (30 cm3 min-') at 400 "C for 16 h and then placed in an helium flow to reach the experimental temperature conditions. Our experiments were carried out at 305 and 370 "C, temperatures for which propene oxidation with C3H, + 0, reactant mixtures presents, respectively, 100 % selectivity for allylic oxidation and a lower selectivity in the kinetic range.33313332 0.2 h E z .- x 0 n REDOX DYNAMICS OF USb,O,, I 5 n Fig. 1. Acrolein yields during propene oxidation in the absence of gaseous oxygen at (a) 305 and (b) 370 "C. 0.1 n E z .- x 0 n 5 n Fig. 2. CO, yields during propene oxidation in the absence of gaseous oxygen at (a) 305 and (6) 370 "C. RESULTS SURFACE RESTRUCTURING DURING PROPENE OXIDATION WITHOUT GASEOUS OXYGEN The yield of propene oxidation as a function of the number of propene pulses is illustrated in fig. 1 and 2 . The fresh catalyst, which is consequently in the higher oxidation state, has the higher activity. Whatever the temperature, a drop in activity is observed between the first and second pulses. The yield of acrolein, which is rapidly stabilized at 305 "C, is low. On the other hand, it increases after the third pulse at 370 "C.Whatever the experimental temperatures, selectivities for acrolein, lower at the first pulse, sharply increase to reach a high and constant value [fig. 3 ( a ) ] . Acetaldehyde and acetone are only found during the first pulse. As shown in a previous i.r. study,8 the reaction proceeds through the removal of lattice oxygen from the catalyst. The amount of oxygen removed after 7 pulses is calculated from the quantity of oxygen transferred to the oxidation products and is related to one compact monolayer of 02- ions, being 6 and 25% at 305 and 370 "C, respectively. TheR . DELOBEL, H. BAUSSART, M. LE BRAS AND J-M. LEROY 3333 n Fig. 3. Selectivities for (a) acrolein and (b) CO, during propene oxidation in the absence of gaseous oxygen at (A) 305 and (B) 370 "C as a function of the number of C,H, pulses.distributions of lattice oxygen among the products at both 305 and 370 "C were calculated on the assumption that a stoichiometric reaction takes place between the lattice oxygens and propene. Fig. 4 shows that the interaction between hydrocarbon and surface atoms involves two different active sites, T and S, responsible for the complete and selective oxidation, respectively, of C,H,. The observed drop in activity may be related to coke formation on the surface of the catalyst. This has previously been observed under experimental conditions by Raman microprobe spectros~opy.~ The change in the oxidation state of Sb surface ions, previously observed by X.P.S.studies, and which is connected with the observed low mobility of lattice oxygens from the bulk to the surface, may also explain the low activity. In order to characterize the phenomena more completely, the reduced catalyst was first treated for 2 h with a He flow to remove all the weakly fixed products. The formation of CO, following the first 0, pulse at 305 or 370 "C corresponds to the oxidation of the coke or of a strongly chemisorbed species. A kinetic study of the reoxidation has not been carried out because the small amount of lattice oxygen removed during the next treatment, together with the oxidation of the fixed carbonaceous species, makes the measurement inaccurate. Nevertheless, qualitative analyses reveal that surface reoxidation is mainly achieved from the first pulse. Indeed, the analysed amount of unconsumed oxygen remains constant for each further pulse and is similar to the amount of oxygen in the pulse.RELATION BETWEEN CATALYTIC PERFORMANCE AND SURFACE RESTRUCTURING A comparison between the performances of (i) the initial USb,O,, (catalyst a), (ii) a catalyst whose surface had been restructured by treatment comprising 15 C,H, pulses (catalyst B) and (iii) a sample of catalyst whose surface had been restructured by a reoxidative treatment (a flow of 0, for 1 h) at 305 or 370 "C (catalyst y ) was3334 REDOX DYNAMICS OF USb,O,, 0 5 n 0 5 n Fig. 4. Lattice-oxygen utilization during propene oxidation in the absence of gaseous oxygen at (A) 305 and (B) 370 "C. carried out.The percentages of propene oxidized on these samples (fig. 5 ) and their selectivities for C,H,O and CO, (fig. 6 and 7) are shown as a function of the number of pulses. Acetaldehyde is always formed, so the values concerning CO, are corrected by taking its formation into account. Whatever the temperatures of the catalytic tests, the action of the reactant mixture on #? leads to an increase in activity as a function of the number of pulses. The activity remains nearly constant from the fifteenth pulse. Under steady-state conditions the amount of oxidized propene on #? remains lower than that observed with a. Only incomplete reoxidation of the surface of #I may be proposed. The same treatment on y leads to a decrease in activity with the number of pulses. The steady-state value observed is always lower than the value obtained for a.For the first pulse the percentage of oxidized propene is highest on catalyst a. This percentage is never obtained again after oxidation treatment of the catalyst. Selectivities for C,H,O under these experimental conditions are always lowest for the first pulse and then quickly reach a high constant value. These results lead us to formulate the following sequences of activity and selectivity. (i) At 305 "C activity follows the order a, > y, > a,, > yst > &, > #?, while selectivity for C&O follows the order a,, > #Ist > y,, > yi > a, > pi. (ii) At 370 "C activity follows the order a, > y, > a,, > yst = fist > pi while selectivity for C,H,O follows the order /Ist > ast > yst > y, > #Ii > ai.(The subscripts i and st indicate initial and steady-state values, respectively.) The results reported here show that the catalyst surface is in dynamic interaction with the gas phase. The catalytic performance of the sample depends directly on the nature of the surface phase.7.5 n E s e = -2 s Q a a ..-I 0 cr 2 2.5 3 C \ R. DELOBEL, H. BAUSSART, M. LE BRAS AND J-M. LEROY 15 n 8 0 P) a L 4- 2 5 s a Y , u 5 10 15 n 3335 5 10 15 n Fig. 5. Influence of the reactant-mixture treatment on the catalysts a, /3 and y at (a) 305 and (b) 370 "C with O,/C,H, = 1 / l . I I 5 10 15 n 1 5 10 15 n Fig. 6. Influence of the reactant-mixture treatment on selectivity for C,H,O of the catalysts a, /3 and y at (a) 305 and (b) 370 "C with O,/C,H, = 1/1.3336 REDOX DYNAMICS OF USb,O,, n 25 h E x +I ..3 .* +I a, - 2 0 Y a 13 5 lb 115 n Fig.7. Influence of the reactant-mixture treatment on selectivity for CO, of the catalysts a, p and y at (a) 305 and (b) 370 "C with O,/C,H, = 1 / 1. DISCUSSION A change in the USb,O,, surface is observed during propene oxidation without gaseous oxygen. In the steady state only one type of site, S, is seen at 305 "C; S seems to lead to allylic oxidation and the formation of C,H,O and C,H,O. At 370 "C a new type of site, T, responsible for complete oxidation coexists with S, the number of S sites being greater than those of T. The type of product obtained thus depends on the type and mutual proportions of these centres. At the first pulse S and T sites are both observed.The following pulses lead to a sharp decrease in the yield of T sites. These T sites may be considered as having highly coordinated oxygen: some of the oxygens in the lattice surrounding such a chemisorption site are activated in order to take part in the oxidation of C,H, to CO,. This oxygen depletion during the first pulse makes most of the sites inactive. Reactivity of the solid for complete oxidation is therefore directly dependent on the rate of regeneration of T sites occurring during the reoxidation step. It may be assumed that S possesses oxygen in low coordination, that propene activated on S reacts and that. the products are then desorbed before un- selective processes can occur. The metal-oxygen bonds on coordinatively unsaturated S sites are stronger than those on T sites, which have more highly coordinated oxygen than the S sites., The presence of stronger bonds is characterized by unlabile oxygens which are expected to bemore selective reactants for olefin oxidation. Such strong bonds are created when surface restructuring occurs.This surface change after the firstR. DELOBEL, H. BAUSSART, M. LE BRAS AND J-M. LEROY 3337 propene pulse has been previously proved by an X.P.S. study2 which characterized the depth profile of the catalyst. C3H6 treatment leads to a change into the antimony oxidation state: the initial Sb5+ is reduced to Sb3+. Cation migration is never observed, so the formation of a defined surface structure cannot be proved. The hypothesis of the formation of unsaturated sites may be considered.The evolution of sites and of the coke deposit on D is confirmed by examination of the structure of this catalyst during and after the action of gaseous oxygen. Raman studies show no coke at the surface of the catalyst, so we may assume that it is burnt off in the presence of gaseous oxygen. If coke is the only reactant responsible for /3 deactivation, the catalytic performance of y should be identical to that of a. In so far as the selectivity of yi for acrolein is much greater than the selectivity of ai, we must consider that S sites are not trapped by reoxidation. Moreover, since the initial catalytic performance of USb30,, is never recovered, we may reject the hypothesis that there is a reversible structural change to the surface.The T sites are not completely regenerated. The role of the reactant mixture on /3 may be analysed as follows. Initially the gaseous mixture reacts with a coked surface on which two types of active sites are present. At the first pulse, the oxygen of the mixture reacts with the coke, and C3H6 is activated on the sites. In this case CO, is the product of coke burning and of the complete catalytic oxidation of the hydrocarbon which takes place via the restructuring of T sites. This hypothesis explains the comparatively high selectivity for CO,. During the following pulses the coke is completely removed and the restructuring of the surface occurs, resulting in the enhancement of selectivity for aerolein. In the steady state at 305 "C the restructured surface possesses essentially unsaturated S sites.At 370 "C two paths leading to complete oxidation may be proposed: a restructuring of the highly coordinated oxygen T sites or a reaction of acrolein or acetaldehyde with the catalyst surface. The latter mechanism involves successive oxidation reactions. CONCLUSION The present study permits the characterization of two types of active sites on the surface of USb,O,,. It is proposed that the difference between these results from the difference in their degree of oxygen coordination. There is only a small amount of active oxygen available. The observed low mobility of oxygen ions from the bulk to the surface or from the surface to the bulk may explain the irreversible surface restructuring. H. Baussart, R. Delobel, M. le Bras, D. le Maguer and J. M. Leroy, J . Chem. SOC., Faraday Trans. 1, 1982, 78, 485. R. Delobel, H. Baussart, J. M. Leroy, J. Grimblot and L. Gengembre, J . Chem. Soc., Faraday Trans. 1 , 1983, 79, 879. B. Levy and B. Degroot, J. Catal., 1982, 76, 385. J. Haber, Kine?. Katal., 1980, 21, 123. J. Haber, in Catalysis by Non-metals, ed. J. P. Bonnelle, B. Delmon and E. Derouane (Reidel, Amsterdam, 1982). James F. Brazdil, D. D. Suresh and R. K. Grasselli, J. Catal., 1980, 66, 347. ' J. C. Bart and N. Giordano, J. Catal., 1980, 64, 356. ' R. Delobel, M. le Bras, M. Traisnel and J. M. Leroy, in Vibrations in Surfaces, ed. R. Caudano, J. M. Gille and A. A. Lucas (Plenum Press, New York, 1982), p. 315. R. Delobel, Y. Schuhl and H. Baussart, Proc. 5th Franco-Soviet Colloquium on Catalysis, ed. J. P. Bonnelle (C.N.R.S., Lille, 1980). (PAPER 4/376)

ISSN:0300-9599    

DOI:10.1039/F19848003331

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1984,80, 3339-3357 Interaction of Water and Oxyethylene Groups in Lyotropic Liquid-crystalline Phases of Poly(oxyethy1ene) n-Dodecyl Ether Surfactants Studied by 2H Nuclear Magnetic Resonance Spectroscopy BY KEVIN RENDALL AND GORDON J. T. TIDDY* Unilever Research Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW Received 9th March, 1984 N.m.r. quadrupole splittings (A-,H) of heavy water have been measured as a function of composition and temperature (268-338 K) in hexagonal (H,) and lamellar (L,) liquid crystals formed from a range of poly(oxyethy1ene) surfactants. Measurements have been made on the L, phase of C,,EO,, C,,EO,, C,,EO,, C,,EO, and C,,EO,OMe, and the H, phase of C,,EO,, C,,EO, and C,,EO,. A few data are presented for the metastable gel phases of C,,EO, and C,,EO, (at 268 K).Increasing the surfactant concentration causes an initial sharp increase in A, followed by a levelling off or a shallow maximum. The values of A generally decrease with increasing temperature at high surfactant concentrations for all the surfactants studied. This is also true at low surfactant concentrations, unless increasing temperature causes a transition from micellar solution (L,) to L, where A may increase with temperature close to this phase boundary. There is a general decrease of A with increasing EO length. The molecular processes contributing to the observed A values are discussed, and t h s is followed by a description of water binding equilibria. The experimental data can be fitted using a model where water binds collectively to the head groups.For each data set three parameters are required, these being the number of bound water molecules (r), the equilibrium constant of binding (KB) and the order parameter of the bound water. A1 k yl pol y( ox ye t h ylene) non-ionic sur fac tan t s [ C H + 1( OCH CH 2)m OH, C EO,] are widely used as emulsifying agents and detergents. Their properties can be changed gradually by incremental steps in either m or n. Thus it is possible to study the relationship between surfactant chemical structure and physical properties using the homologous series of C,EO, derivatives. Recently we investigated the formation of lyotropic liquid crystals by these c0mpounds.l A general description of the major factors responsible for mesophase structures in surfactant systems was used as the basis for discussing the observed phase behaviour of a range of surfactants (n = 8-1 6 , m = 3-12).The most important factors are the area per hydrocarbon chain at the micelle surface, a, which limits possible micelle shapes, plus the formation of ordered arrays of micelles and alterations of micelle shapes at high concentrations of surfactant, owing to the intermicellar repulsions. Additional hypotheses were required to account for the changes of phase structure with temperature and at very low water concentrations (< ca. 20%). We deduced that the hydration of EO groups decreases with increasing temperature. This leads initially to a gradual decrease in a owing to smaller steric repulsions, and then to a sharp increase in a owing to a change in the nature of water/EO binding. The latter occurs at temperatures close to the mesophase 33393340 2H N.M.R.OF NON-IONIC SURFACTANTS melting point. It is also thought to occur at the mesophase/liquid surfactant (L,) boundary where the water concentration is low, again leading to a sharp increase in a. Otherwise, within a particular phase (liquid crystal or micellar solution), a is expected either to remain constant or to decrease with increasing surfactant concentration . To obtain further information on the binding of water to EO groups in these systems we have measured the 2H n.m.r. quadrupole splittings (A) of ,H,O in mesophases prepared from a variety of dodecyl poly(oxyethy1ene) derivatives.These give infor- mation about the fraction of bound water and its ordering, the latter being related to a. In anisotropic media such as non-cubic liquid crystals, nuclei with spin quantum numbers (I) where I 3 1 give multiplet resonances (21 peaks) owing to the interaction of their electric quadrupole moments with non-zero, net electric-field gradients. 2 y For inorganic ions and water [2H,0,1(2H) = 11 in lyotropic liquid crystals it is now generally accepted that these electric-field gradients occur within the surfactant head-group region, close to the alkyl-chain/water interface. The separation between adjacent resonance lines of the multiplet is termed the quadrupole splitting. Neglecting the asymmetry parameter, as is common with these systems, its magnitude (A) for a ‘powder’ sample is given by:,, A = iEQ S .The quadrupole coupling constant (EQ) is dependent on both nuclear properties and the magnitude of the electric-field gradient, while S is an order parameter describing and time-average angle (eDM) between the electric field gradient and the liquid-crystal axis given by s = i ( 3 COS28D&,f-1). (2) Thus for water (,H,O) in non-ionic surfactant mesophases the ,H doublet-splitting arises from the fraction of ,H nuclei ‘bound’ to the head groups (Pb) (where subscript b refers to these nuclei). There is rapid exchange on the n.m.r. time-scale of these nuclei with bulk water to give an average A value In this system we can envisage that water associated with each EO group will have a different value of EQ, b and s b .Also, the terminal hydroxy hydrogen will exchange rapidly with water hydrogens, giving a further contribution to A. Taking into account the existence of i separate types of bound 2H nuclei we have Values of s b , will be related to the degree of order to individual EO groups. For the surfactant hydrocarbon chain the order parameters of CH, groups are fairly constant over the half of the chain next to the head groups and then decrease rapidly towards the terminal methyl g r o ~ p . ~ . ~ With EO chains the barrier to internal rotation about 0-CH, groups is much less than that for CH,-CH, groups,6 while the extra available space from the presence of water results in less hinderance from chain/chain interactions. Thus a wider range of conformations can be adopted than is the case for alkyl chains, hence we can anticipate that Sb(EO) will be large only for a few EO groups next to the hydrocarbon-chain/water interface.The order parameters S(CH,) for the alkyl chain increase with a decrease in surface area per surfactant molecule We can anticipate a qualitatively similar dependence for EO groups. Moreover,K. RENDALL AND G. J. T. TIDDY 3341 the number of water molecules ‘bound’ per head group (nb) is directly related to P b : P b = nbCs/Cw where c, and c, refer to concentrations of surfactant and water. Thus the variation of A with surfactant concentration can be used to obtain information on both P b and S b provided that their separate effects can be distinguished. At very high water concentrations the EO groups are expected to be saturated with water, hence deviations from linear behaviour of plots of A against c,/c, will reflect changes in s b and, by implication, in a.Where we can be sure from other measurements (e.g. X-ray diffraction) that a is reasonably invariant with changes of temperature or composition, then variations of A give information on P b directly, which can be used to assess models for binding of water to EO groups. In the present work we describe measurements of water (,H,O) A values as a function of temperature and composition for the lamellar phase formedl9 lo by Cl2EO3, C,,EO,, C,,EO,, C,,EO, and C,,EO,OMe [n-C,,H,,(OCH,CH,),0CH3]. In addition, measurements were made on the hexagonal phase which occurs with C,,EO,, C,,EO, and C,,EO,.Also available is a previous report of A values for the C1,EO, lamellar phase,ll measurements on C,,EO, and Cl,EO, mesophases made elsewhere12 and unpublished data13 on C,,EO,. EXPERIMENTAL The surfactants were used as received from Nikko Chemicals. Their specified purity was > 98%. In support of this, microscope ‘penetration’ scans of the phase behaviour with water gave transition temperatures in excellent agreement with previous measurements.’ Commercially available heavy water (> 99.7%) was also used as received. Quadrupole splittings were measured using a Bruker BKr-322s pulsed spectrometer and variable-temperature probe operating at 1 1 .O MHz for 2H resonance. The n/2 pulse length was CIZ. 10 ,us. Values of A were determined from the free-induction decay following a z/2 pulse with signal averaging where necessary.The accuracy is estimated as better than + 5 % . Temperatures, measured by inserting a thermometer into the probe before and after the measurements, were constant within & 1 K. RESULTS The dependences of water ,H A values on surfactant concentrations at various temperatures are given in fig. 1-6. Fig. 1 shows the data for Cl2EO3 + water mixtures. This system forms surfactant liquid (L,), lamellar phase (La) and a lamellar phase + water dispersion (La + W) below ca. 300 K, while an isotropic liquid (L3) forms at the water-rich lamellar phase boundary above 300 K.’ The L, liquid is stable only for a limited range of temperatures; it coexists with water and is continuous with L,. As expected, no A values are observed for L, samples.Below 300 K some non- reproducibility was experienced in measurements on high-water-content samples (< 0.03 mole ratio of C,,EO, to H,O). In addition to the doublet from water in the La phase, a narrow singlet was observed. This increased in intensity with the amount of shear used in mixing and decreased with equilibration time before measurement. Obviously the signal arises in part from phase-separated water (the W phase). However, the size of lamellar ‘ crystallites ’ decreases with increasing water content and after shear. Fast diffusion of water between different crystallites leads to an averaging of A giving an ‘isotropic’ signal.’, Thus the isotropic signal cannot be taken as an indication of the L,/W coexistence region in this case.However, the constant A value measured at low surfactant concentration (ca. 400 Hz at 278 K) suggests that the3 342 3 6 30 2 4 s! 5 18 a . 12 6 0 'H N.M.R. OF NON-IONIC SURFACTANTS 0 0 0 o + + + o + + 0 + 8 00 I I 1 I 1 0 0 - 1 0.2 0.3 0 .I 3 6 30 2 4 s! 5 1 8 Q --- 1 2 6 0 mole ratio 0 0 8 0 o + + ( h ) o + + 9 8 0 0 0.1 0 . 2 0.3 0 . 4 0.5 mole ratio Fig. 1. Water 2H A values as a function of surfactant/water mole ratio for the C,,E0.J2H,0 lamellar phase at various temperatures; (a) 0, 278 and +, 308 K; (b) 0, 298 and +, 318 K. boundary lies at about mole ratio 0.03. At all temperatures there is an initial sharp increase in A values with surfactant concentration, followed by a levelling off. At 298 and 308 K the values decrease just before the L,/L, boundary.The decrease either does not happen at 3 18 K, or is only very slight, since the sample with mole ratio 0.256 C,,E0,/2H20, which has the phase structure L, + La, gives a A value of 1.8 kHz. This is the same as those of mole ratios 0.148 and 0.187 shown in fig. 1 (b). At 278 K the decrease is also not observed, perhaps because the boundary has shifted to a surfactant concentration well above those examined. The phase diagram of C,,EO, is very similar to the one of C,,EO,, differing only in that the narrow salient of L, above the La phase is separated from L, and that aK. RENDALL AND G . J. T. TIDDY 2 5 - 2 0 G 2 1 5 - ---- Q 10 5 - 3343 - - 30 r 30 2 5 - 2 0 - - 0 + 0 + O ? + - 0 0 0 0 + + * O + X X + r!J + * o * + * 01 I I I I 0 0.05 0.1 0.15 0.2 mole ratio 0.25 0.3 0 0 + X X I 1 1 I I I 0 0.05 0.1 0.15 0.2 0.25 0.3 mole ratio Fig. 2.Water 2H A values as a function of surfactantlwater mole ratio for the C,2E0,/2H20 lamellar phase at various temperatures: (a) 0, 268; +, 288 and *, 338 K; (b) 0, 278; +, 298 and x , 318 K. micellar solution occurs at low surfactant concentration below ca. 290 K. Values of A at temperatures > 290 K (see fig. 2) show a similar dependence on composition to the C,,EO, data. A definite maximum in the plot of A against concentration occurs at 298 K, but it is not observed at 318 or 338 K. The same A value was obtained at 3 18 K for an L, + La mixture containing mole ratio 0.222 C,,E0,/2H,0 as for an La sample at mole ratio 0.197. Problems were encountered again in obtaining reproducible samples for the La + W boundary at 298 and 318 K.These data points represent average measurements made on several occasions with various mixing and equilibration times. Here the La+W regions appears to exist below mole ratio ca. 0.018 C,,E0,/2H,0. At low temperatures (< 290 K) an L, phase replaces the La dispersion.3344 2H N.M.R. OF NON-IONIC SURFACTANTS 1 5 . s 2 --. 1 0 ' 2 5 r + 0 * 0 1 I I 1 I I I 0 0.05 0.1 0.15 0.2 0 . 2 5 0.3 mole ratio 8 0 8 8 2 o I 8 + + + + x x 9 f X r I I X 0 )0 0.05 0.1 mole 0.15 ratio 0.2 0 . 2 5 0.3 Fig. 3. Water 2H A values as a function of surfactant/water mole ratio for C,,E0,/2H20 hexagonal and lamellar phases at various temperatures: (a) 0, 268 K La; 0, 268 K H, and +, 338 K L,; (b) 0, 278 K La; 0, 278 K H,; +, 298 K La and x , 318 K L,.Dotted lines indicate compositions that contain the cubic (V,) phase at 278 K. The A values show a sharp decrease on approaching the L, phase. Note that measurements at 268 K were made mostly on metastable L, samples. Prolonged storage at this temperature resulted either in the formation of crystalline surfactant or ice. There is excellent agreement between the results in fig. 2 and the reported data of Klason and Henriksson.12 With C12E0, an hexagonal phase occurs below 290 K, while above this temperature the phase diagram1 resembles that of C,,EO, but transition temperatures are increased by up to 20 K. A lamellar-phase dispersion (L, + W) exists over the temperature range ca. 32&338 K, but here we were unable to obtain A values from samples withK. RENDALL AND G.J. T. TIDDY 21 17.5 1 4 2 Z 1 0 . 5 d . 7 - 3 . 5 3345 - - - - - 9 0 + . @ . + + + 8 3 . 5 711-..- 0 0 0 0 0.1 0.2 0.3 0.4 mole ratio t 0 + ( b 1 + o?o O l I I I I 0 0 . 1 0.2 0 . 3 0.4 mole ratio Fig. 4. Water 2H A values as a function of surfactant/water mole ratio for C,2E0,/2H,0 hexagonal and lamellar phases at various temperatures: (a) 0, 268 K La; 0, 268 K H,; +, 298 K La and x , 268 K H,; (b) 0 , 2 7 8 K L,; 0 , 2 7 8 K H, and +, 318 K L,. concentrations below mole ratio 0.03 C,2E0,/2H20. No attempt was made to store samples at this temperature for prolonged equilibration to allow the annealing of defects because of anticipated surfactant decomposition. The maximum in A within the La phase was observed at 318 K (mole ratio 0.196, L2+La, A = 1.65 kHz; mole ratio 0.171, A = 1.69 kHz) but not at 268, 278, 298 and 338 K, where at the highest surfactant concentrations either the A values were constant, or the decrease was within experimental error.Note that the results at 268 K for compositions above mole ratio 0.1 C,2E0,/2H20 are for metastable samples; crystalline surfactant formed within these samples after ca. 20 min. For one sample (mole ratio 0.278) a metastable gel (A = 3.2 kHz) was observed prior to the formation of crystalline C,,EO,.3346 2H N.M.R. OF NON-IONIC SURFACTANTS 8 - 6 - z 5 4 - ---- 4 2 - 2 5 2 0 1 5 - z 2 10- 4 5 - X X a X 0 - - O o o + + o + o + 01 I I I 1 0 0.025 0.05 0.075 0 .I Fig. 5. Water ,H A values as a function of surfactant/water mole ratio for the C,2E0,/2H,0 hexagonal phase at various temperatures: x , 268; 0,278; 0 , 2 9 8 and + , 31 8 K.mole ratio 0 0 0 + + + * 0 + * 0 a 8 d * * 0 0 0.0 5 0.1 0.1 5 0.2 0 . 2 5 mole ratio Fig. 6. Water 2H A values as a functionof surfactant/water mole ratio for the C,,E0,0Me/2H20 lamellar phase at various temperatures: 0, 268; +, 278; * , 288 and 0, 298 K. A ‘bicontinuous’ cubic phase (V,) occurs at compositions between the H, and La phases., No splittings are obtained for this phase since A averages to zero by rapid diffusion of water over the micelle-network surface. Hexagonal-phase samples were examined at 268 and 278 K (fig. 3, open circles). Two samples which fell within the V, + H, and V, + La two-phase areas were examined at 278 K. Thus we have A values (but not compositions) for the H1/La phase transition. These are shown by the dottedK.RENDALL AND G. J. T. TIDDY 3347 lines in fig. 3(b). At 268 K we obtained only a single-phase V, sample within this region, so we do not have A values corresponding exactly to the HJL, transition. For Cl2EO6 the hexagonal phase persists to 310 K and the phase diagram, below ca. 3 13 K resembles that of C,,EO, below 293 K. Above 3 13 K, however, the La phase is surrounded by L,; it extends only down to ca. 60% surfactant with an upper temperature limit of ca. 346 K. Values of A measured at 268,278,298 and 318 K are shown in fig. 4. The concentration range of the La phase is too narrow at 338 K to give reasonable information on changes of A with water content.At 268, 278 and 298 K values of A for both the H, and La phases were measured. At the intermediate compositions the V, phase occurred. The transition values shown were obtained close to the V, region rather than for V,+L, or V,+H, samples. In addition, at these temperatures the maximum in A within the La phase is well established. This is not observed at 3 18 K because of the limited extent of La at high concentrations. At 268 K the mesophases are metastable above ca. 50% surfactant, with solid forming eventually. Metastable gel samples were obtained at mole ratio 0.211 and 0.241 C,,E06/2H,0 having A values of 2.47 and 2.45 kHz, respectively. Only the H, phase was examined for C,,EO, because the La phase has a very tiny region of existence., The A values (fig. 5) show no sign of a maximum with concentration, possibly because this phase is mostly bounded by V, at high concen- trations rather than L,.No gel phase was observed at 268 K, apparently because this H, phase is more stable than that of the shorter EO surfactants. Note that the range of surfactant/water mole ratios is lower here than the other surfactants. No phase diagram has been published for C,,EO,OMe. This surfactant forms10 a lamellar phase below 300 K with L, occurring below 283 K, and a cloud point of ca. 273 K. The La phase is bounded by L, on the high-water side above 296 K. Thus the diagram strongly resembles that of C12E04, but with the temperature spans of L,, L, and La phases compressed by about a half. Measurements on this compound were limited by the small amount available.The water A values are shown in fig. 6. At none of the temperatures was a definite maximum in A against composition plots observed, although the values had levelled off at 268 and 278 K. At both these temperatures a sample with mole ratio 0.24 forms an L, + La mixture, and A for the La phase is the same (to within < 1 %) as that for the La phase sample with mole ratio 0.198. Also, A values at low concentrations were rather difficult to measure, as for C,,EO,-C,,EO, in this region. As a final point we emphasise the excellent agreements between our results for C,,EO, and C,,EO, and those of Klason and Henriksson.12 Some measurements have also been reported15 for a commercial surfactant having an average EO length of 10.4 units. Our results for C,,EO, are also consistent with the data given in this latter study.DISCUSSION In this section we start with a detailed consideration of the molecular mechanisms responsible for A; we then consider particular models to account for the concentration dependence. Finally we discuss whether or not A values provide any support for hypotheses concerning surfactant hydration based on the previous consideration1 of the phase diagrams. MOLECULAR PROCESSES CONTRIBUTING TO A First we examine the dependence of A on the surfactant alkyl chain length. Water A values have been publishedll for the L, phase of C,,EO, at 315 K. These lie just3348 2H N.M.R. OF NON-IONIC SURFACTANTS 3 6 2 7 . 2 El ---. 1 8 . 9 - 0 . I I I 1 I 0 0.08 0.16 0 . 2 4 0.32 0.4 surfactant/water mole ratio Fig.7. Experimental and calculated (continuous curves) water A values for the lamellar phases of: 0, C,,EO,; x , C,,EO,; *, C,,EO,; +, C,,EO, and 0, C,,EO, at 278 K. Theoretical curves were calculated as described in the text using the parameters listed in table 2(a). above the value for C,,EO, at 318 K. From fig. 1 we observe that A for C,,EO, at high concentration decreases in a roughly linear manner by ca 1.6 kHz for a 40 K increase in temperature. Hence a temperature decrease of 3 K increases the values for C,,EO, by ca. 120 Hz. This correction gives superposition of the two sets of data within experimental error. Thus we conclude that, as expected, the alkyl chain makes no direct contribution to A. Now we have to assess the relative contributions of the water bound to different EO groups.In fig. 7 and 8 the variation of A as a function of surfactant concentration at 278 K is compared for the various surfactants (C,,EO, at 279 K). The lamellar-phase values at low concentration (fig. 7) and the hexagonal-phase values (fig. 8) are all fairly close together, but do show a tendency for A to decrease with increasing EO length. At high concentration there is a large decrease in A with increasing EO length. Suppose that water bound to all the EO groups makes a significant contribution to A because of large Sb values at all binding sites. Then we would except larger A values for increased EO size at a given surfactant mole fraction, owing to the larger pb. This is opposite to the experimental observations. Thus we conclude that only water bound to the first one or two EO groups makes a significant contribution to A.This can be understood on the basis of the anticipated large decrease of the order parameters for the OCH, groups on increasing distance from the hydrocarbon chain, as discussed in the introduction. Hence the major effect arises from water bound to the first ether oxygen, with possible smaller contributions from water bound to the second and third oxygens. Finally we consider the contribution of the terminal OH group. Comparison of fig. 2 and 6 shows that C,,EO, and C,,EO,OMe have similar A values, indicating that changing OH for OMe has an insignificant effect. This is to be expected from the tiny order parameter of the 0-H bond caused by EO conformational freedom asK.RENDALL AND G. J. T. TIDDY 3349 I I I I J 0 0.02 0 *04 0.06 0 -08 0.1 surfac tan t/w ater mole ratio Fig, 8. Experimental and calculated (continuous curve) water A values for the hexagonal phases of: +, C,,EO,; 0, C,,EO, and * C,,EO, at 278 K. Theoretical curves were calculated as described in the text using the parameters listed in table 2(b). explained above. To simplify any model for water binding we make the approximation that A values are due to water associated with the first EO group. In this discussion we have assumed that the surfactant micelles (bilayers or rods) are well ordered with respect to each other, i.e. S(micel1e) = 1 . A check on this can be made by comparing the Cl2EO3 and C16E03 systems. At 3 18 K Cl2EO3 is only 7 K below the L, phase melting point, while for C16E03 the La phase transforms on heating to V,, which melts at 334 K.ll Any local disordering of the bilayers would be expected to increase markedly on approaching the La melting point.Thus the effect should be much larger for C,,EO, than for C16E0, and will lead to a decrease in A. That the measured values are so close demonstrates that the assumption of S(micel1e) = 1 is valid. Also, the lamellar phase of C,,EO,OMe melts at 301 K, only 3 K above the highest measurement temperature. That the A values for C,,EO,OMe and C,,EO, lamellar phases are so close at 298 K is further confirmation that the effects of local micelle disorder can be neglected. MODELS FOR WATER BINDING TO SURFACTANT Considering only the contribution to A of water bound to the EO group closest to the alkyl chain (no.l), eqn (4) becomes A = f P b , 1 EQ, b, 1 sb, 1 = ; p b f ( l ) ‘Q, b, 1 sb, 1 ( 5 ) wheref( 1) is the fraction of bound water associated with the first EO group. In the simplest model (A) for water binding to surfactant we can write the equilibrium as w,+s,,so (6) where Wf is free water and S, and So represent unoccupied or occupied binding sites on the surfactant. This model assumes that water molecules bind independently of3350 2H N.M.R. OF NON-IONIC SURFACTANTS each other. It was used successfully to account for ultrasound relaxation measurements on concentrated surfactant systems.16 Differences in EO size simply alter the number of binding sites at a given concentration of surfactant.The equilibrium constant (KA) is given by where the terms in square brackets represent the molefractions of the various species. Thus for a total surfactant concentration of 1 mole, wb and wf, the numbers of moles of bound and free water per mole of surfactant, are related by where q is the number of binding sites per surfactant molecule and wT = wb + wf = total water concentration per mole of surfactant. Neglecting physically unreal solutions to this equation (negative values of wf or wb), wb/wT increases as l/wT increases. This expression is unable to reproduce the maximum in A at high concentrations of surfactant. Also, to account for the A values for hexagonal and lamellar phases of C,,EO, and C,,EO, we require different values of the equilibrium constant for the two phases, an unlikely occurrence with independent binding sites.The model can account for the lower A values for longer EO groups by the smaller fraction of bound water at the EO( 1) group (1 /m) together with a lower value of Sb,l as expected for larger head groups. An alternative model (B) is one where the surfactant/water complex involves several water molecules The equilibrium constant (KB) is given by (9) For one mole of surfactant the relationship between free and bound water concentration can be expressed as It is easy to demonstratel' that this function leads to a maximum in wb/wT (=Pb) as a function of 1 /wT. This occurs at wT = (r - 1) moles of water per mole of surfactant for all r > 1. Theoretical curves to illustrate the variation of&, with surfactant/water mole ratio are shown in fig.9. The graphs show wb/wT as a function of l/wT (the surfactant/water mole ratio). Note that at low surfactant concentration the dependence is linear, with the line passing through the origin. Also, the initial slopes are directly proportional to r for constant KB. For given value of KB, increasing r increases Pb at low values of 1 /w, and decreases Pb at high values of 1 /wt. The latter is presumably a reflection of the unfavourable entropy involved with large r values. Before using this model to derive values of KB and r from the data we discuss some of its inadequacies, and say why, despite these, we feel that it does give some useful insights into the molecular behaviour of non-ionic surfactant/water systems. Major drawbacks of the model are the use of mole fractions in eqn (10) rather than activities, and the neglect of the consequences arising from the ordered arrays of micelles in the mesophases.A third drawback is the existence of three adjustable parameters [r, KB and if(1) EQ, Sb, (the last term is essentially a scaling factor)].K. RENDALL AND G. J. T. TIDDY 3351 0.4 L 0 - 3 0.2 0 0 0.4 0.8 1 . 2 1 . 6 2 .o 1 /Wt Fig. 9. Variation of wb/wt as a function of surfactant/water mole ratio (l/wJ calculated from eqn (11). KB = 1; r = (a) 1, (b) 2 and (c) 8. The use of concentrations rather than activities is necessitated by the absence of activity data. However, both are expected to change monotonically with composition; thus while the absolute values of the derived parameters may be in error, trends with changing EO size or temperature will be accurate.The consequences of ignoring the differences of phase structure is difficult to assess, but this is likely to alter entropic factors. Thus it will lead to errors in KB but not in r. With three adjustable parameters the theory is extremely flexible. However, some constraints can be placed on the ranges of values that are reasonable. The quadrupole coupling constant EQ, b, should be essentially invariant for all the compounds, since the local environments of the first EO groups are likely to be similar. Moreover, it is commonly assumed that the electric-field gradient of the water 0-2H groups arises from intramolecular 3 9 l2 so that the reported EQ value for water of 2 1 4 kHz can be used.Thus variations in this .term are assumed to originate in changes of f( I)&, 1. Theoretical considerations suggest1* that Sb is proportional to 1 /a2(a is the surface area per chain at the interface). X-ray StudieP show that a increases with EO number. Unfortunately we require a for the first EO group, rather than the average value. This should increase with EO number, and decrease or remain constant with increasing surfactant concentration, as for the ‘average’ a. Hence S b , i should decrease with increasing EO size, and increase or remain constant with increased surfactant concentration. In the fitting procedure below, we assume that S b , i is invariant for a given compound over the concentration range considered. As a final check we can compare the values of A with those of ionic surfactants at low concentrations.It is reasonable to expect that the value off( 1) Sb, will be of the same order of magnitude as those for head-group-bound water of ionic surfactants, since the first EO group and ionic head groups all lie in the most ordered part of the mesophase. Examination of published data20* 21 shows that A values reported for sodium dodecyl sulphate and sodium dodecanoate are similar to those of the non-ionics. There are further checks on the values of r and K, since both are expected to increase3352 'H N.M.R. OF NON-IONIC SURFACTANTS with EO length. Including effects due to the terminal OH, one expects that r will be a linear function of m of the type r = cm+b (12) where b and c are constants.It also seems reasonable that if b is small, there will be a linear relationship between r and the free energy of water binding (AGw), given by AGw = rAGb = RTlnK, (13) where AG; is the free energy of water binding per water molecule. Hence both r and KB are required to fall within fairly narrow constraints. In particular, for two different surfactants (1) and (2), r and KB are related by Finally it should be pointed out that while the model assumes a single value for r, in practice surfactant molecules with a range of bound water molecules will occur [ l , 2, . . ., ( r - l), I , ( r + 1). . . etc.]. Thus a calculated value of r will represent an average. Despite all the above limitations, we feel that the model is of value provided that data are fitted for a number of compounds.It offers an opportunity to derive quantitative information on water binding, its variation with temperature, composition, EO size and phase structure. This can be used to check against other information, such as that available from self-diffusion measurements22, 23 or inferred from mesophase transitions. Because three parameters are used in fitting the equations [r, KB and f( 1) s b . i] we have chosen to fit curves at three temperatures only (278,298 and 318 K), where data on a range of compounds are available. We have not included the data on C,,EO,OMe at this stage, since the limited availability of this compound prevented extensive measurements. Also, the temperature range of the La phase is small and Sb,l is expected to alter with composition at 278 K (the only temperature for comparison with other compounds).In fitting individual curves, the data for the hexagonal phase were considered separately from those of the lamellar phase. For surfactants that exhibit phase transitions with increasing concentration (e.g. LJL,, L1/H1/La), a decreases with increased concentration, changing less rapidly at high surfactant levels. Thus sb, , increases with surfactant content. For these cases the curves have been fitted to the high-concentration A values. Considered separately, a range of r, KB andf( 1) s b , , values can be used to fit each data set (quality of fit judged by eye). Typical values are shown in table 1 . The data are not fitted by all the values in the ranges shown, since alteration of the curve by changing one parameter can to some extent be compensated for by adjustment of the others.Thus high values of r and KB correspond to low values off( 1) s b , 1. The most crucial experimental values for fitting the curves are those between the initial linear part and the maximum, since the latter determines r, while the abruptness of the deviations from linearity determines KB. The hexagonal-phase data have a wide range of r and KB values because of the limited composition range. It was possible to fit some of the curves with lower values of r and KB than those shown. These fits gave very low values of pb, requiring unrealistically large values off( 1) Sb, ,. For further limitation of the values in table 1 it is necessary to consider a number of compounds at each temperature.Here the criteria expressed in eqn (12) and (14) are used. Values of r and KB were selected for C,,EO, in the La phase at the lowest temperature (278 K). The remaining values of r and KB (for C,,E03-C,,E0,) were3353 K. RENDALL AND G. J. T. TIDDY Table 1. Parameters used to fit data with model B C&O4 278 (lamellar) 298 318 C12EO6 278 (lamellar) 298 318 C,2EO* 278 (hexagonal) 298 318 4.5-5.5 4.5-5.5 4.5-6.0 6.0-6.5 5.5-6.5 5.5-7.0 11-13 9-1 3 9-17 5- 1 O4 30-lo3 10-103 300- > 105 10-104 30-300 0.3-15 0.5-20 0.3-100 1.84-3.49 1.562.12 I .37-2.37 1.15-1.34 1.25-1.74 1.03-1.49 0.754.80 0.60-2.99 0.3 7-3.74 determined by eqn (1 2) and (1 4), respectively. The experimental points were then fitted by adjustment off(1) s b , ,. Only r values within a small range (40.3) were suitable, while KB could be varied by a factor of ca.2-3. It was not possible to fit the data with b = 0 [eqn (12)]. The fit to the data is reasonable, given the expected decrease of S b , , for C,,EO,-C,,EO, at low surfactant concentrations (see fig. 7). The same r values were then used to fit data at 298 and 318 K, with KB being chosen for C,,EO, and the ratio of KB values again being determined by eqn (14). At 298 K a reasonable fit was obtained, but not at 318 K. Here, only the data for Cl2EO6 could be fitted. For the other compounds a larger r value was required. Note that most of the curves are reasonable fits, but for C,,EO, at 278 K and C,,EO, at 298 K the experimental points at the ‘turnover’ of the curves are off the line.This implies that r may be underestimated in these cases. For the hexagonal phase [table 2(b), fig. 81 values of r and KB were chosen for C,,EO, at 278 K. The values of r for the other compounds were simply calculated from eqn (12) (with b = 0); these were then used in eqn (14) to calculate KB. Again f ( 1 ) Sb, , was used for a final fit of the curves. Because of the limited composition range of the hexagonal phase no attempt was made to fit the curves with b > 0. However, as the values of Y are large, it would be possible to fit the curves with small values of b (i.e. b = 1-2). Note that the data for C,,EO, at 278 K are poorly fitted by the theoretical line, but the additional point available for the H, + V, two-phase sample (mole ratio 0.072, A = 840 Hz) does lie close to the curve.At higher temperatures the same values of r were used with KB being chosen for C,,EO,, followed by final fitting Before considering the derived parameters further, there is a final check possible on the f( 1) s b , values. The value of s b , , is expected to increase by a factor of two at the hexagonal/lamellar transition if a does not alter.2*3 Even if a does alter, we expect s b , ,(lamellar) > Sb, ,(hexagonal) to hold. Thus iff( 1) could be estimated the value of s b , , can be compared. It seems reasonable to expect that either each EO group binds the same number of water molecules, i.e. usingf(1) Sb, 1’ or, allowing for different binding to the terminal OH [eqn (12)], 109 FAR 13354 2H N.M.R. OF NON-IONIC SURFACTANTS Table 2.Parameters used to fit measured 2H A values (a) lamellar phase 279 278 278 278 278 298 298 298 298 318 318 318 318 3.5 143 4.25 412 5.0 1194 5.75 345 5 6.5 10000 4.25 92 5.0 208 5.75 45 1 6.5 1000 6.0 50 6.0 200 6.5 69 6.5 69 3.18 2.43 1.93 1.54 1.23 2.27 1.81 1.46 1.15 1-50 1.46 1.40 1.18 6.36 7.29 7.72 7.70 7.38 6.8 1 7.24 7.30 6.90 4.50 5.84 7.00 7.08 14.8 13.8 12.9 11.8 10.7 12.8 12.1 11.2 10.0 - 10.2 (b) hexagonal phase T/K surfactant r K~ 10-3f(i) sb, 10-2 sb, la 10-2 sb, 278 C12EO5" 8.125 9.2 1.21 6.05 6.05 278 C12E06 9.75 14.4 0.95 5.70 5.70 298 Cl'EO6- 9.75 6.5 0.93 5.58 5.58 298 C12E08 13.0 12.0 0.67 5.36 5.36 318 C12EO8 13.0 4.8 0.67 5.36 5.36 278 C,,EO, 13.0 35 0.65 5.20 5.20 a Calculated fromf(1) = l/m. IJ Calculated fromf(1) = c / r .Fit not good. For the hexagonal phase both give the same result, but for the lamellar phase the values do differ as can be seen from the final columns of table 2. For both calculations s b , ,(lamellar) > s b , ,(hexagonal). Moreover, if eqn (1 5 6) is used then the values do change by ca. 1.7-2.0 at the hexagonal/lamellar transition. Given the many assumptions in the theory, the large range of A values involved (0.5-4.5 Hz) and that the data sets for the two phases were fitted independently, this agreement is remarkable. It does give encouragement that, when used for a series of compounds, the derived parameters have physical significance. While the fit of theoretical curves to experimental results is good in most cases, the theory is unable to reproduce the large decrease in A at concentrations above the maximum value observed in a few cases (e.g.C,,EO, at 279 K, C,,EO, at 298 K). The most probable explanation is that a range of (integer) r values occurs in practice, and that at high surfactant concentration r decreases slightly. That r represents an average is also the reason why non-integer values can occur. Table 2 shows that the decrease in water binding to EO head groups with increasing temperature arises not from aK. RENDALL AND G. J. T. TIDDY 3355 decrease in r but from a decrease in KB. Indeed, the increase in r required to fit Cl,E03-C,,E0, lamellar-phase data at 318 K may well arise because the collective binding of only a few water molecules, which contributes to the low side of the r distribution at lower temperatures, is no longer strong enough to overcome kT.As further evidence of this trend, it was not possible to fit the C,,E040Me data at 278 K with parameters extrapolated from table 2(a) [r = 3, KB = 70, f( 1) s b . , = 0.0321. Values of r = 6-7, KB = 70 andf( l)sb, , = 0.01 7-0.0 19 did fit the data, but the number of experimental measurements is too few to warrant further discussion. Moreover, a change in the distribution of r values will result in values of KB no longer being related by eqn (14). Also, for larger r values it is possible that bound water molecules interact with adjacent EO groups (see below). Thus it is difficult to interpret differences in KB values when eqn (12) and (14) no longer apply. Arrhenius plots of the KB values for C12E08 and C,,EO, (lamellar) are reasonably linear, giving AH, values of 20.6 kcal mol-1 (lamellar) and 8.62 kcal mol-l (hexagonal).Hence the values of AH, per bound water molecule are 3.2 and 0.66 kcal mol-l, respectively. The linear Arrhenius plots give further confidence in the derived parameters. The large difference between the AH, values only serves to emphasise that water binding in lamellar hexagonal phases is completely different according to the parameters in table 1. It does not seem unreasonable that more water should be associated with EO groups in the H, phase than in L, since there is more space available between EO groups for water to fit into. The smaller AH, value per bound water molecule for the H, phase may indicate that the (expected) more disordered conformation of the EO group in this phase is less well able to bind water.A similar conclusion was derived from a consideration of the phase behaviour,l where the hydration of the V, phase was suggested to be stronger than that of L, or H, because of the smaller a value. Note that the larger number of water molecules bound in H, than in La is responsible for the absence of a sharp increase in A across the HJL, transition. [A factor of 2 is expected; see ref. (2) and (3).] This sharp increase is observed with ionic surfactants, implying that water binding to ionic headgroups does not alter significantly across the boundary. The large value of AH, per mole of bound water in the La phase does point to a specific role of the EO group in promoting hydrogen-bond formation of the EO-bound water.A simple explanation for this is that individual water molecules interact with two EO units on adjacent molecules in the La phase and only one EO unit in the H, phase. Most EO oxygens could form two bonds in both cases. The only quantitative data available for comparing our r values is that derived from self-diffusion meas~rements.~~ Comparison with water binding derived from ultra- sound relaxation data1, requires the data to be reanalysed using model B. Nilsson and Lindman measured surfactant22 and water (2H20)23 diffusion in the isotropic phases of Cl2EO, and C,,EO, as functions of composition and temperature. An analysis of their data in terms of a simple ‘bound/free’ model gave r/m in the range 4-6 at low surfactant concentrations (ca.0.01-0.02 mole fraction), decreasing linearly to 0.5-1 at high concentration. According to model B, r/m should be constant at low concentration. However, the self-diffusion technique cannot distinguish between bound water and that merely ‘ trapped’ within the EO network, having a consequently lower diffusion coefficient. Our results are consistent with the diffusion data in that r is lower and is not markedly temperature dependent. The effect of temperature shows up in the variation of KB, which does not have a large influence at low concentrations. At high surfactant concentrations most of the water is bound, while the unbound water will have a self-diffusion coefficient limited by the movement of EO groups. Hence self-diffusion data require careful analysis under these circumstances.109-23356 2H N.M.R. OF NON-IONIC SURFACTANTS It is important to recognise that the model represents a static ' time-average' of the dynamic water binding. In reality there will be a series of equilibria of the type All of these will have individual equilibrium constants K,, Kb, ... etc. such that the populations of the states with Y values close to those given in table 2 are the most favoured. Thus the model should not be taken to imply that Y water molecules all bind to the surfactant head group in a single step. CONCLUSIONS The simple model, B, is able to account for the n.m.r. A values for a series of compounds over wide ranges of composition and temperature. The parameters derived from the model are in good agreement with conclusions based on a consideration of the phase behavi0ur.l Thus water binding is gefierally decreased on increasing temperature and increases with EO size.The decrease in water binding could be expected to lead to a decrease in a. Moreover, deviations from the calculated A values at constant temperature and low surfactant concentrations are observed only for those cases where a was expected to increase. Although the model successfully describes the n.m.r. data, much further work is required to establish its wider validity. Since it allows the calculation of free water concentrations, suitable modifications should enable water activities to be estimated. The latter are related to interbilayer 'hydration' forces.24 The applicability of the model to water activities is currently under investigation. It is a pleasure to acknowledge many fruitful discussions on surfactant hydration with Prof. D. G. Hall. D. J. Mitchell, G. J. T. Tiddy, L. Waring, 'I'. Bostock and M. P. McDonald, J. Chem. Soc., Farnday Trans. I , 1983, 79, 975. A. Johansson and B. Lindman, Liquid Crystals and Plastic Crystals, ed. G. W. Gray and P. A. Winsor (Ellis Harwood, Chichester, 1974), vol. 2, p. 192. H. Wennerstrom, G. Lindblom and B. Lindman, Chern. Scr., 1974,6, 97. J. Charvolin and A. Tardieu, in Solid State Physics, ed. L. Liebert (Academic Press, New York 1978), vol. 14, suppl. p. 209. D. F. Bocian and S. I. Chan, Annu. Rev. Phys. Chem., 1978,29, 307. P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969), chap. V. H. Schindlet and J. Seelig, Biochemistry, 1975, 14, 2283. B. Mely, J. Charvolin and P. Keller, Chem. Phys. Lipids, 1975, 15, 161. ' S. Marcelja, Biochim. Biophys. Acta, 1974, 367, 165. lo K. Rendall and G. J. T. Tiddy, C12E040Me phase diagram, unpublished results. l1 C. D. Adam, J. Durrant, M. Lowry and G. J. T. Tiddy, J. Chem. Soc., Faraday Trans. I , 1984, 80, l2 T. Klason and U. Henriksson, paper presented at the International Symposium on Surface Science, l3 C. D. Adam, K. Rendall and G. J. T. Tiddy, to be published. l4 G. Lindblom, B. Lindman and G. J. T. Tiddy, J. Am. Chem. Soc., 1978, 100, 2299. l5 K. Beyer, J. Colloid Interface Sci., 1982, 86, 73. 789. Lund, Sweden, 1982.K. RENDALL AND G. J. T. TIDDY 3257 l6 G. J. T. Tiddy, M. F. Walsh and E. Wyn-Jones., J. Chem. SOC., Faraday Trans. I , 1982, 78, 389. l7 D. G. Hall, personal communication, May 1983. P. G. de Gennes, Phys. Lett., 1974, 47A, 123. C. D. Adam, I. G. Lyle and G. J. T. Tiddy, unpublished results. Faraday Trans. I , 1981, 77, 2867. 2o I. D. Leigh, M. P. McDonald, R. M. Wood, G. J. T. Tiddy and M. A. Trevethan, J . Chem. SOC., 21 K. Rendall, G. J. T. Tiddy and M. A. Trevethan, J . Chem. SOC., Faraday Trans. I , 1983, 79, 637. 22 P. G. Nilsson, H. Wennerstrom and B. Lindman, J. Phys. Chem., 1983, 87, 1377. 23 P. G. Nilsson and B. Lindman, J. Phys. Chem., 1983, 87,4756. 24 D. M. Le Neveu, R. P. Rand, V. A. Parsegian and D. Gingell, Biophys. J., 1977, 18, 209. (PAPER 4/391)

ISSN:0300-9599    

DOI:10.1039/F19848003339

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J . Chem. Soc., Faraday Trans. I, 1984,80, 3359-3363 Chemical Equilibria and Related Isochoric Functions BY MICHAEL J. BLANDAMER,* JOHN BURGESS AND BARBARA CLARK Department of Chemistry, The University, Leicester LE1 7RH AND JOHN M. W. SCOTT Department of Chemistry, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada Received 16th March, 1984 The meaning is examined of the term ‘isochoric’ when used in examination of the dependence of equilibrium parameters on temperature and pressure. A number of terms which identify the extrinsic nature of this term are defined. The question of a definition of the standard and reference states is considered. For the most part, the chemical literature describes properties of liquids and solutions at constant temperature and pressure.Certainly equilibrium and rate constants for chemical reaction in solution are usually documented for isobaric- isothermal conditions. In the next stage of an analysis the corresponding derivatives of these constants are examined with respect to temperature at constant pressure and with respect to pressure at constant temperature. Nevertheless many claims are made for derivatives calculated at constant volume,l i.e. isochoric constraint. For the most part these claims are advanced in connection with thermodynamic activation parameters based on the formalism of transition-state theory2 and calculated from the rate constants for chemical reactions in solution. For example, in discussing kinetic data for the solvolysis of t-butyl chloride in methyl alcohol, Hills and Viana3 argue that the isobaric activation parameters are more complicated than the isochoric set.This view is echoed by Whalley and coworkers in their analysis of the dependence of activation parameters on solvent composition for reactions in binary aqueous For example, Gay and Whalley6 conclude that constant-volume activation parameters are more appropriate for fundamental discussion. A marked difference between trends in isochoric and isobaric parameters as a function of solvent composition is borne out by kinetic data reported recently by Holterman and Engbert~.~ These claims for the usefulness of isochoric activation parameters have attracted our interest over the years despite the fact that we have continued to concentrate attention on isobaric-isothermal activation parameters.Part of our hesitancy over isochoric parameters can be understood by attempts to answer two questions : (i) what volume is held constant and (ii) what are the reference (or standard) states for solutes (reactants and transition state) referred to in derived parameters such as the isochoric thermodynamic energy and isochoric heat capacity of activation? Various answers are to be found in the literature. For example, Whalley states8 that the isochoric condition is ‘the volume of an equilibrium mixture of initial and transition state’. [n the form applied to kinetic data for reactions in solution, transition-state theory2 uses the language of equilibrium thermodynamics for chemical equilibria in solutions. The answer to the questions posed above might develop therefore from a consideration 33593360 CHEMICAL EQUILIBRIA AND ISOCHORIC FUNCTIONS of the treatments using classical equilibrium thermodynamics. The literature does not, however, offer the complete answer.Indeed various puzzling statements are encountered. For example, Lown et al.,g in an analysis of the dependence of acid dissociation constants in water on temperature and pressure, write ' At constant volume, the volume of ionisation becomes more negative with increasing temperature '. In the following analysis we examine the definition of isochoric functions from the standpoint of chemical equilibria in solutions. For example, we show that the statement quoted above can be understood if it is reworded to read 'If the pressure is changed such that the molar volume of the solvent remains constant with increasing temperature, the volume of ionisation of acetic acid in water, A, P, decreases with increasing temperature'.The aim of the present paper is to provide a framework for the analysis of kinetic data. CHEMICAL EQUILIBRIUM Consider a closed system at fixed temperature and pressure. Within this system there exists a chemical equilibrium between solutes (j = 2 to j = i) in solvent 1. At chemical equilibrium, where the Gibbs function G is a minimum, the chemical composition is related to the standard equilibrium constant K* (T) by In Ke(T) = In Q(T;p)+jp pe q d p RT where Q( T;p) = ng' = 2 ; j = i) (mi"" yFQ/m*)vj ( 2 ) A,Vm(T;p) = X U = 2 ; j = i)viVy(T;p) (3) and vj is the stoichiometry.The standard equilibrium constant is defined in terms of the chemical potentials of the substances involved in the chemical equilibrium in their corresponding solution standard states at temperature T and standard pressure p*. For a given system the composition quotient Q(T;p) can be defined by the two independent intensive variables T and p . The quotient Q is related to the chemical potentials of solutes in reference states; i.e. the ideal solution where mi = 1, yi = 1 at temperature T and pressure p . The dependence of Q on T and p describes a surface in the In Q-T-p domain: In Q = lnQ[T;p]. (4) At a given temperature 6 and pressure z there exists Q(0; n). Two orthogonal gradients describe the dependence of Q on Tat fixed pressure and on pressure at fixed temperature.MOLAR VOLUME OF SOLVENT The molar volume of the pure solvent c can be defined by the two independent variables T and p : v = V[T;pl. ( 5 ) In other words at a given temperature 0 and pressure z there exists a characteristic molar volume for the solvent, c(6; z).M. J. BLANDAMER, J. BURGESS, B. CLARK AND J. M. W. SCOTT 336 1 COMPARISON The nub of the argument presented here draws together the two sets of data described by eqn (4) and (5). Consider a given temperature 8 and a given pressure n together with the two quantities Q(8; n) and q(O;n). Consider a change in temperature from 8 to 8+A8. According to eqn ( 5 ) there exists a pressure n+Anl where ( 6 ) v(8; n) = v(8+A8; n+Anl) and the pressure increment, An1, is characteristic of pure liquid 1.According to eqn (4) there exists a corresponding equilibrium quotient Q(O+ A8; n + An1). In other words the two quotients Q(8; n) and Q(O+ A8; n + Anl) characterise chemical equilibria in solutions which are individually at minima in Gibbs functions G under conditions where the molar volume of the solvent is the same. Hence the isochoric condition is given by eqn (6) rather than the volumes of the solutions containing the chemical equilibria. For any function of state X which is a function of both T and p, the total differential can be expressed as dX= ( 3 p d T + ( 3 d p . (7) Here we set X = In Q and use the ‘chain rule’ to expand (ap/aT),: and its inverse. condition can be calculated from the properties of the pure solvent: The gradient of the tangent in In Q-7‘-p domain conforming to the isochoric where a,* and ic? are the thermal-expansion coefficient and isothermal compressibility of the solvent at temperature T and pressure p.Another isochoric condition can be formulated with reference to the solvent. Again we start with the two quantities Q(9;n) and q ( 8 ; n ) at temperature 8 and pressure n. With reference to the molar-volume data, consider a change in pressure from n to n+An. According to eqn (4) there exists a temperature O+A8,, characteristic of the solvent, where q ( 8 ; n ) = q(O+A8,;n+An). (9) This isochoric condition leads to the identification of two equilibrium quotients Q(8; n) and Q(O+AO,; n+ An). The gradient of the tangent in the In Q-T-p domain conforming to the isochoric condition [eqn (9)] is given by RELATED PARAMETERS The analysis outlined above can be repeated with reference to the thermodynamic parameters characterising the chemical equilibrium at temperature T and pressure p.Thus the dependence of Ar Vm on T and p can be written in the following form: Ar Ifrn = Ar Vrn[T;p].3362 CHEMICAL EQUILIBRIA AND ISOCHORIC FUNCTIONS The isochoric condition given in eqn (7) can be incorporated in an analysis of the dependence described by eqn (1 1). This in turn leads to the analogue of eqn (8): The derivative calculated by eqn (12) describes the dependence of A, Vm on temperature at constant c. The isochoric condition applies therefore to the solvent and not to either the system under examination or some ideal solution containing unit molalities of the solutes.DERIVED PARAMETERS The van't Hoff equations express the isobaric dependence of Q on temperature in terms of the enthalpy parameter A,Hm and the isothermal dependence of Q on pressure in terms of the volume quantity, A, Vm [eqn (5)]. In analogous fashion we may use the isochoric quantities calculated in eqn (8) and (10) to define two further terms : and Dimensional analysis shows that Ary is expressed in J mol-l and A4 in m3 mol-l, i.e. a volume per mole. DISCUSSION In the introduction we posed two questions concerning isochoric parameters. The analysis presented here and comparison with equations quoted in the references cited in the introduction show that the term 'isochoric' can be understood in terms of variations in T and p which preserve constant molar volume of the pure solvent.In these terms the meaning is unambiguous and leads to a simple connection between the extrinsic isochoric condition and intrinsic isothermal and isobaric dependences of equilibrium parameters. In other words, isochoric conditions are extrinsic to the equilibrium characterised by the quotient Q and standard equilibrium constant Ke( T>. The term isochoric is not used in the present context to signify a thermodynamic change at constant volume, e.g. where the Helmholtz function is the isochoric- isothermal thermodynamic potential function. Under the latter circumstances the condition isochoric is intrinsic to the chemical processes under consideration. By extrinsic we signify above that the isochoric condition refers to another system, i.e.the solvent rather than the solution. This distinction is important because the chemical equilibrium [eqn (l)] describes a system at a minimum in G and the reference states for the solutes are isobaric-isothermal. These comments raise the question as to the significance to be attached to Ary and A4 [eqn (13) and (14)]. The quantity A4 does not seem to have been calculated from experimental data. In contrast Aw is often written as A U e and its temperature dependence as the isochoric heat capacity of reaction. We caution against such practice. The point can be supported as follows. Consider a plot of Arc$, the isobaric heat capacity of reaction, against temperature. With increasing temperature, so the molar volume of the solvent changes (at fixed p ) . Consider the corresponding plot of the isochoric heat-capacity term against temperature. Each point on the plot is calculated for a local isochoric condition for a characteristic change in pressure [cf.M.J. BLANDAMER, J. BURGESS, B. CLARK AND J. M. W. SCOTT 3363 Anl in eqn (7)]. Hence across the plot neither the volume of the solvent nor the local pressure increments are constant. Similar features can be identified in isochoric parameters derived from kinetic data. This point will be explored in another paper. We thank the S.E.R.C. for a grant to B.C. E. Whalley, Adv. Phys. Org. Chem., 1964, 2, 93. S. Glasstone, K. J. Laidler and H. Eyring, Theory of Rate Processes (McGraw-Hill, New York, 1941). G. J. Hills and C. A. Viana, in Hydrogen-bonded Solvent Systems, ed. A. K. Covington and P. Jones (Taylor and Francis, London, 1968), p. 261. B. T. Baliga and E. Whalley, J. Phys. Chem., 1967,71, 1166. B. T. Baliga, R. J. Withey, D. Poulton and E. Whalley, Trans. Furaduy Soc., 1965, 61, 517. D. L. Gay and E. Whalley, J. Phys. Chem., 1968,72, 4145. E. Whalley, Ber. Bunsenges. Phys. Chem., 1966, 70, 958. ' H. A. J. Holterman and J. B. F. N. Engberts, J. Am. Chem. SOC., 1982, 104, 6382. 9 D. A. Lown, H. R. Thirsk and Lord Wynne-Jones, Trans. Furaduy SOC., 1970,66, 51. (PAPER 4/426)

ISSN:0300-9599    

DOI:10.1039/F19848003359

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1984, 80, 3365-3378 Adsorption of Benzene on Platinum Black A Neutron Scattering Study BY DOUGLAS GRAHAM AND JOSEPH HOWARD* Department of Chemistry, University of Durham, Science Laboratories, South Road, Durham DHl 3LE Received 19th March. 1984 Incoherent inelastic neutron scattering spectra (0-1000 cm-l) of benzene adsorbed on platinum black (0.1 < 8 < 2.0) are reported. The spectra, which vary markedly with coverage, indicate that the plane of the C,H, molecule is lying parallel to the metal surface. Shifts in the low-wavenumber intramolecular modes also indicate that the interaction of C,H, is stronger with platinum than with nickel. Some of the vibrations of adsorbed C,H, relative to the substrate have been assigned, e.g. at 8 = 0.75 the Pt-C,H, stretching and tilting modes occur at 522 and 638 cm-l, respectively. While the interaction between organic species and precious-metal catalysts has been studied frequently, knowledge of the structure and dynamics of the adsorbed species is limited.Vibrational spectroscopy has contributed significantly to this work,l particularly for supported metals and for single-crystal surfaces. In order to obtain vibrational-spectroscopic data relevant to hydrocarbon catalysis on unsupported polycrystalline metals we have studied the adsorption of benzene on platinum black using incoherent inelastic neutron scattering (i.i.n.s.) spectroscopy. Although the resolution of i.i.n.s. spectroscopy is low compared with optical techniques it is comparable with that of low-energy electron energy-loss (1.e.e.l.) spectroscopy.2 1.i.n.s.is usually only applied to the study of hydrogeneous species adsorbed on high-surface-area non-hydrogeneous adsorbents. The i.i.n.s. spectrum is then dominated by those normal modes which involve hydrogen-atom motion. This is a consequence of the large incoherent scattering cross-spection of H when compared with that of any common element and of its low mass. 1.i.n.s. is therefore not a surface-specific technique and depends upon the difference in cross-sections of the adsorbate and adsorbent. For i.i.n.s. there are no electromagnetic selection rules to be obeyed and in particular the ‘surface selection rule’ does not apply. There are difficulties associated with the use of i.r. Raman and 1.e.e.l.spectroscopies for surface studies below ca. 300 cm-l. These difficulties do not obtain for i.i.n.s. studies of this region, which in many cases contain the vibrations of the adsorbate relative to the adsorbent. There have been many studies of the benzene-platinum and the related benzene- nickel systems. Low-energy electron diffraction (1.e.e.d.) has been employed to study benzene on Pt( 11 1 ) 3 7 and at low coverage each benzene molecule appeared to lie above a single platinum atom parallel to the surface plane, whereas at high coverage it was concluded that the c6 rings were tilted with respect to the surface. The data gathered by Lehwald et aL5 and Bertollini et aL6 for the nickel systems using 1.e.e.l. spectroscopy were similar but the assignments differed significantly and this led to 33653366 ADSORPTION OF BENZENE ON Pt BLACK / Fig.1. Hindered rotations ( T ~ , z, and z3) and translations ( K , & and G) of an adsorbed C6H6 molecule. conflicting models for the position of the benzene above the nickel surface. The study on the platinum surface5 indicated, in agreement with the 1.e.e.d. data, a parallel- to-the-surface structure involving a chemisorbed benzene state on Pt( 1 1 1) bound to the surface metal atoms through interactions of the n and n* benzene orbitals with the appropriate platinum orbitals. From the increased frequency, relative to the gas phase, of v,, (the out-of-plane CH deformation) and its assignment to two observed bands it was proposed that at sub-monolayer coverages there were two coexisting benzene- platinum geometries, one with the c6 centroid above a platinum atom and the other with the centroid above a three-fold hollow site.Since the frequency shifts of both species were greater on the platinum than on the nickel surface it was postulated that benzene was more strongly adsorbed in the former case. For 8 > 1 the band positions were found to be similar to those of gaseous benzene, although there was still a contribution from the chemisorbed C&,. This disappears at high coverages. At low (0 < 1) coverage of benzene on platinum, Lehwald et aL5 assigned bands at 360 and 570 cm-l to C-Pt stretching modes. An i.i.n.s. study of C&, adsorbed on Raney Pt has been reported by Jobic et al.’ These authors reassign some of the 1.e.e.l.data and consider that their i.i.n.s. data are in good agreement with these. In fact Jobic et al. failed to consider that Lehwald5 observed different relative intensities, as a function of coverage, for the two bands assigned to v,, (at different sites). Jobic et al. reassigned them to dzflerent modes of the same molecule on a particular site without offering an explanation of the relative-intensity changes. This is clearly unsatisfactory. Detailed comparison between single-crystal Pt( 1 1 1),5 Raney Pt7 and Pt black data for adsorbed C,H, are difficult. The latter surfaces are not simple, and the Raney method in particular is known to produce very complex materials. For example the Raney Pt used by Jobic was stated to be ‘porous material’ and its surface area was 50 m2 s-l compared with 8 m2 s-l for the Pt black.The adsorption of a benzene molecule introduces 6 new normal modes: 3 hindered rotations and 3 hindered translations (fig. 1). Corresponding modes have been observed by i.i.n.s., infrared and Raman techiques in organometallic compounds. We include data (see later) on various benzene-containing n complexes to assist in the assignment of the benzene-platinum-black system. Such compounds have been considered by various authors as possible models of surface complexes formed during chemisorp tion. 9D. GRAHAM AND J. HOWARD 3367 Table 1. Summary of sample and experimental conditions benzene platinum amount adsorption surface black of C6H6 overpressure coverage sample adsorbed/g /Torr (monola yers) (a) sample temperature : 77 K; spectrometer : b.f.d.(Pluto); wavenumber range: 95-1060 cm-2 - - 1 1 0.85 40 0.75 1 1.9 100 1.75 - (b) sample temperature: 103 K; spectrometer: 4H5 (Dido); wavenumber range: 0-400 cm-l 2 2 0.6 5 0.5 (c) sample temperature: 5 K; spectrometer: IN4 (I.L.L.); wavenumber range: 0.240 cm-l 3 3 0.1 2 0.1 3 0.7 25 0.5 3 2 100 2 - - - - - - EXPERIMENTAL The platinum black (platinum powder no. 4) was obtained from Engelhard Sales Ltd and had a surface area of 8 m2 g-l. Cu. 100 g of the powder was employed in any one i.i.n.s. experiment. Prior to the adsorption the surface of the powder was cleaned in a vacuum system,lo capable of evacuating to lo-* Torr,* utilizing hydrogen (99.9% pure and supplied by B.O.C. Ltd) to remove chemisorbed oxygen. Cleaning and degassing were carried out at 200 "C because above this temperature sintering would have reduced the surface area to an unacceptable level.Water production during the cleaning process was monitored using a quadrupole mass spectrometer, and up to four reduction treatments were required before, upon the admittance of hydrogen, the partial pressure of water vapour was unchanged from the system background. The benzene, supplied by Hopkin and Williams Ltd, was dried using sodium wire and distilled under a P20,-dried nitrogen atmosphere from fresh sodium wire onto type-3A molecular sieve. Immediately prior to an absorption experiment the benzene was further purified by the freeze-thaw technique to remove dissolved gases then sealed in glass phials fitted with glass break-seals.The technique of benzene adsorption has been described in more detail elsewhere;" however, the error in measured coverage is ca. & 5%. All adsorptions were carried out at room temperature. The i.i.n.s. spectra were measured with the powdered platinum contained in thin-walled aluminium cells which were fitted with glass break-seals so that the benzene could be admitted after the background spectrum had been run. Neutron energy-loss spectra (77 K) were obtained in the 95-1060 cm-l range using the beryllium-filter detector (b.f.d.) spectrometer at A.E.R.E. Harwel1.l2J3 Neutron energy-loss time-of-flight (t.0.f.) spectra ( 5 K) were obtained in the 0-240 cm-l range using the IN4 spectrometer at the I.L.L. in Grenoble,14 in its down-scattering mode.Lower-resolution t.0.f. spectra were obtained using the 4H5 spectrometer at A.E.R.E. Har~e1l.l~ Unlike b.f.d. data, which can be obtained in a form [S(Q, a)] immediately comparable with optical spectra by plotting 'detected neutron counts per n monitor counts ' against energy, raw * 1 Torr = 101 325/760 Pa.3368 ADSORPTION OF BENZENE ON Pt BLACK 500 1000 time of flightlps m-’ Fig. 2. Time-of-flight (4H5 spectrometer) spectra (103 K) of (a) Pt black, (b) Pt black+C,H, (0 = 0.5) and ( c ) adsorbed C,H, obtained by subtracting (a) from (b). t.0.f. data require several corrections to be made and formulation in terms of various useful functions before comparison.2 Standard computer programs are available for the calculation of these functions.1s. l7 For the comparison of t.0.f.and optical data the function P(a,p) is used in this work. In the b.f.d. spectra the transition frequencies were obtained for the band maxima using published correction factors.12 Table 1 gives details of the conditions under which the samples were prepared and the spectra collected. Spectra of the adsorbed species have had a background, corresponding to the sample cell and the cleaned platinum surface, subtracted from them. RESULTS AND DISCUSSION PLATINUM BLACK ONLY 1.i.n.s. spectra of the clean platinum black were primarly obtained so that they could be subtracted from the platinum black + benzene spectra to give the spectra due to the adsorbed species only. However, the background spectra were also analysed to check the surface for hydrogeneous impurities.Two low-frequency maxima were obtained at 87 and 165 cm-1 and at 91 and 175 cm-1 using the t.0.f. [fig. 2(a)] and b.f.d. (fig. 3) spectrometers, respectively. This compares well with previous platinum- black data of 97 and 169 cm-l gained using the A.E.R.E. t.0.f. spectrometer, 6H.18 Since the b.f.d. spectrometer was not designed to operate in the low-frequency region and the resolution functions of the b.f.d. and t.0.f. spectrometers are very different then the frequency differences between the two sets of data are within experimental error. The bands are assigned to the low-frequency density-of-states of bulk platinum.D. GRAHAM AND J. HOWARD 3369 200 400 600 800 incident neutron energy/cm-' Fig. 3. B.f.d. spectrum (77 K) of Pt black. and x denote data collected using the Al(111) and Al(311) monochromator planes.The numbers within the figure are the transition wavenum bers. No other low-frequency maxima were identified in the t.0.f. spectra. In the b.f.d. spectrum a shoulder and a band are found at 269 and 381 cm-l, respectively. The former feature may well be a combination mode, 9 1 + 175 = 266 cm-l. The very broad band peaking at 381 cm-l will certainly contain a contribution from the overtone of the band at 175 cm-l, but it clearly contains at least one other contribution. One possibility is that the additional scattering arises from contaminants on or in the platinum black, e.g. H, H20 or C1. Studies of the Pt/H20 systems by Howard et al.19 and Sexton20 showed that Pt-H,O and Pt-OH vibrations did not occur in the 200-450 cm-l region.The manufacturer of the Pt black indicated that there was a possibility of up to 0.1 % impurity which may have included a substantial proportion of chlorine (incoherent cross-section 3.5 barn*). Since Pt-Cl and Pt-C1-Pt stretches have been assigned at 315 and 350 cm-l, respectively,21 the likelihood that the bands in the i.i.n.s. spectrum of platinum black at 269 and 381 cm-l contain contributions from Pt-C1 vibrations cannot be dismissed. B.F.D. SPECTRA OF BENZENE ADSORBED ON PLATINUM BLACK The b.f.d. spectra of benzene adsorbed to low ( B = 0.75) and high coverages (0 = 1.75) on Pt black are shown in fig. 4 and the frequencies derived from these spectra are displayed in table 2. It is immediately apparent that there are substantial differences between these spectra.The b.f.d. spectrum of solid benzene (141 K) is shown in fig. 5 while information from the spectrum is also given in table 2 along with relevant optical data for the gaseous and solid phase~.,~-,~ The assignment of the intramolecular benzene modes of vibration follows the notation of Wilson.25 * 1 barn = m2.3370 ADSORPTION OF BENZENE ON Pt BLACK 686 647j I 871 a 0 0 a 4-l I L11 F t I I 200 400 600 800 1000 incident neutron energylcm-' Fig. 4. B.f.d. spectra (77 K) of C,H, adsorbed onto Pt black with Pt background subtracted. (a) 0 = 0.75 and (b) 6 = 1.75. Symbols as for fig. 3. On the basis of their intensities and frequencies compared with the i.i.n.s. spectrum of solid benzene the bands at 41 1, 686 and 871 cm-l in the spectrum of the adsorbed species [fig.4(b)] are best assigned to v16, vll and vl0, respectively. In solid benzene the out-of-plane intramolecular modes generally increase in frequency compared with those found in the gas phase. Thus one finds v,, increasing from 671 in gaseous to 686 cm-I in solid benzene. A similar increase was found in vl0. Increases in frequency of v,, and vl0 at high benzene coverage on Pt black are also observed in the present work. Note that for adsorbed C6H6 [fig. 4(b)] the intensities of v,, and v,, relative to v,, are very much lower than in the i.i.n.s. spectrum of solid C6H, (fig. 5). A detailed explanation of this must await calculations based on a full normal coordinate analysis which must in turn await i.i.n.s. data obtained over the full wavenumber range (to 4000 cm-l).Lehwald et al. observed that with increasing coverage they obtained spectra containing weak bands due to chemisorbed benzene together with the more intense spectrum of the condensed phase. In view of the similarities and differences between fig. 4(b) on the one hand and fig. 4(a) and 5 on the other we are probably observing something rather similar in our i.i.n.s. data (0 = 1.75). In the gas phase24 the in-plane ring deformation, v6, is assigned at 606 cm-l and corresponding bands are observed in the optical and i.i.n.s. spectra of solid benzene. In the latter spectrum (fig. 5 ) the band assigned at 602 cm-l has medium intensity. In fig. 4(b) a weak shoulder is observed at 647 cm-l which we assign to v6 in this case.At the lower coverage of benzene (0 = 0.75), the i.i.n.s. spectrum [fig. 4(a)] differs quite considerably from that at higher coverage. The strong bands at 41 1 and 686 cm-l in fig. 4(b) are absent and have been replaced by bands at 638 and 810 cm-l and a number of other features in the 400-600 cm-l region. The dominating i.i.n.s. bandD. GRAHAM AND J. HOWARD 337 1 Table 2. Summary of the observed transitions (70-900 cm-l) in and assignments of the spectra of solid benzene and of benzene adsorbed on Pt black at various coverages C6H6 platinum + C,H, : i.r . / Raman i.i.n.s. i.i.n.s. - b.f.d. solid gas Pt only 8 = 0.75 8 = 1.75 (a) (b) (4 assignment ~~ ~ - - 75 175 157 168 - - 91 269 272 270 - - 38 1 41 1 - 47 1 - - - - - 522 543 647 638 - 810 686 - - - - - 882 87 1 97 1 49 203 280 - - 40 1 490 540 602 700 766 858 - - - - - C,H, lattice modes - - Pt density-of-states - Pt density-of-states Pt-c,H, torsion/deformations combinations/overtones - C,H, lattice mode Pt-Cl stretch(?) ;I - - - 400 404 vI6 (E2u 0.p.ring def.) intramolecular/lat tice - - mode combinations of - benzene Pt-C,H, stretch (A) 607 606 v, (E2g i.p. ring def.) - - Pt-C,H, Tilt (E) 686 671 v,, (A2u 0.p. CH def.) - - combination band 856 849 vl0 (Elg 0.p. CH def.) -1 - - - - (e.g. 700 + 68) a Ref. (10). Ref. (22) and (23). Ref. (24). 200 400 600 800 incident neutron energylcm-' Fig. 5. B.f.d. spectrum of benzene (77 K). Symbols as for fig. 3.3372 ADSORPTION OF BENZENE ON Pt BLACK Table 3. Assignments of v16, Vg, vll and vl0 (benzene intramolecular modes of vibration) in some benzene model compounds and related benzene-surface systems system technique '16 '6 v11 vl,, reference C,H,+Pt black, 10W 8 C6H6 4- Pt black, high 8 i.i.n.s.i.i.n.s. i.r. i.r. i.i.n.s. i.i.n.s. i.r. i.r. l.e.e.1. 1.e.e.l. i.i.n.s. I.e.e.1. l.e.e.1. i.i.n.s. i.i.n.s. 40 1 429 423 424 414 394 - - - - 41 1 - - c;; 41 1 602 700 62 1 81 1 615 764 600 775 610 790 623 737 758 748 - - - {;;: - c:: 769 613 714 - (830 1920 - 810 647 686 - 858 892 890 - - - - - - - 768 - - 88 1 87 1 this work 26 27 27 10 10 28 28 5 697 29 5 5 this work this work at 810 cm-1 may be assigned to v,, owing to its intensity, its similar frequency to v,, as assigned in benzene organometallic complexes (table 3) and the studies of Lehwald et al.,5 who considered v,, to occur at 830cm-l (c6 above a single Pt atom) and 920 cm-l (c6 above a 3-fold hollow) at low coverage.At higher coverage (0 > 1) v,, was found5 at 700 cm-l, in agreement with the present work. In view of the increase in frequency of vll on adsorption it is reasonable to assume that the other out-of-plane modes will also increase in frequency. We therefore assign v,, to the i.i.n.s. band at 8 8 2 ~ m - l ~ whereas v16 could be assigned to either 422 or 471 cm-l. These assignments of v,,, v,, and v16, respectively, are supported by i.i.n.s. and optical spectra of benzene-organometallic compounds and other benzene-surface ~ y ~ t e m ~ . ~ - ~ ~ ~ ~ ~ ~ ~ - ~ ~ Table 3 lists some of these data. Note that the high value of vll (810 cm-l) for benzene on platinum black (8 -c 1) may be an indication of a strong platinum-benzene bond compared with that of ni~kel-benzene.~~ 29 This, perhaps, arises from the greater ability of platinum to accept the benzene ;n-electron density caused by the greater spatial extent of the 5d orbitals of platinum.Therefore we agree with Lehwald et aL5 in assigning a band in the 800-830 cm-l region to v,,; however, we did not observe an analogue of their 920 cm-l band for benzene adsorbed in a different position. This indicates that a single form of benzene is predominant on platinum black. This is not surprising if in Lehwald's work the second band was due to benzene adsorbed above 3-fold sites since only a small percentage of these 3-fold sites would be available on platinum black where the highest density crystal planes of low surface free energy are (1 1 l), (1 10) and (100) and in the latter pair no such 3-fold sites are available.The available evidence indicates that C,H, is bonded parallel to the Pt surface. This reduces the molecular symmetry from D6h to C,, in the case of a featureless plane. If the benzene interacts with a single platinum atom on the (1 1 1) surface two possible orientations exist, both of c6, symmetry, whereas on the (100) and (1 lo) planesD. GRAHAM AND J. HOWARD 3373 68 126 184 energy transfer/ cm -' Fig. 6. Time-of-flight (4H5 spectrometer) spectra of C,H, adsorbed onto Pt (0 = 0.5), with the Pt background subtracted, at scattering angles of (a) 82 and (b) 90". although again two structures are possible, the maximum attainable symmetry is C,,.Thus, at least C,, symmetry would be held by benzene on the three most common crystal planes likely on platinum black. If the benzene-surface interaction is weak, splitting of the doubly degenerate modes would be unlikely to be observed if it occurred. If the interaction is strong then some splitting may be observed. Of the E modes in the region of interest, v6 is not observed, vl0 is in a poorly resolved region at higher wavenumber but v16, an E,, mode, lies in a region where there are 2 bands (422 and 471 cm-l) at low benzene coverage. We postulate that these two bands represent the split components of v16 and this is evidence that the majority of the adsorbed benzene (0 < 1) is residing in a position of C,, symmetry and that this position is above a single platinum atom.Note that there are features at 522 and 638 cm-1 in fig. 4 which cannot be explained as being due to benzene intramolecular modes or combination/difference vibrations. There are also similar bands in the t.0.f. spectra which cannot be explained as being due to benzene intermolecular modes. These bands must therefore be associated with normal modes of vibration of benzene relative to the surface. TIME-OF-FLIGHT SPECTRA OF BENZENE ADSORBED ON PLATINUM BLACK The i.i.n.s. t.0.f. spectra of benzene adsorbed on Pt black (0 % 0.5) collected using the 4H5 spectrometer are shown in fig. 2 and 6 while those collected using IN4 (ca. 0.1, ca. 0.5 and ca. 2 monolayers) are shown in fig. 7. The data are summarised in table 4. Also included in the table are data from t.o.f., i.r.and Raman spectra of solid The i.i.n.s. data on solid benzene collected by ourselvesll and Bokhenkov et aZ.30 are very similar. At high benzene coverages on Pt black there are also some similarities, in the low-wavenumber region, with the i.i.n.s. spectra of the benzene lattice modes. benZene.lls23, 30-323374 ADSORPTION OF BENZENE ON Pt BLACK 218 182 1L5 110 75 40 energy transferlcm-' Fig. 7. Time-of-flight (IN4 spectrometer) spectra (5 K) of C6H6 adsorbed on Pt black, with the Pt background subtracted: (i) 8 = 0.1, (ii) 8 = 0.5 and (iii) 8 = 2.0. However, the ca. 2 monolayer coverage of platinum black cannot model a three- dimensional benzene lattice unless large mu1 tilayer domains of benzene were formed and the higher-wavenumber spectra indicate that this is unlikely.Thus, although those bands below 100 cm-l are of a similar frequency to the solid-benzene lattice modes and are undoubtedly due to benzene-benzene interactions they cannot, with any certainty, be assigned to specific benzene lattice modes owing to the effect of the platinum surface. The bands in the spectra at > 100 cm-l are discussed below. VIBRATIONS DUE TO THE BENZENE-PLATINUM INTERACTION At low benzene coverage [fig. 7 (a)] there are two poorly resolved bands at 175 and 217 cm-l which appear to be better resolved at 6 = 0.5 [fig. 7(b)]. Two further bands appear in fig. 7(b): one at 153 cm-l, similar in intensity to that at 171 cm-l, and one of much greater intensity at 121 cm-l. At ca. 2 monolayer coverage, [fig.7(c)], there is broadening in the 115-130 and 150-180 cm-l regions. The bands at 121, 153 and 17 1 cm-l [fig. 7 (b)] cannot be associated with benzene-benzene interactions since the coverage was so low (6 = 0.5). Further, the spectrum at 6 = 0.5 [fig. 7(b)] bears little relationship to that found at much higher coverage (6 = 2), where benzene-benzene interactions may well be expected.Table 4. Summary of the observed transitions (0-400 cm-l) and assignments of the spectra of solid benzene, Pt black and benzene adsorbed on Pt black at various coverages platinum black + C,H6 C6H5 i.i.n.s. Raman i.r. (4 (4 assignment C6H6 lattice modes Pt density-of-states C6H6 lattice modes Pt-C6H6 torsion ( A ) C6H6 lattice modes/combination/overtones Pt-C,H6 deformation Pt density-of-states Pt-C6H6 deformation C6H6 lattice modes/combination/overtones '16 a Ref.(10). Ref. (30). Ref (31). Ref. (32). Ref. (23).3376 ADSORPTION OF BENZENE ON Pt BLACK Table 5. Correlation table for the rotations and translations of benzene on a platinum surface mode D6h c 2 v 71 Aw A2 A2 A, A2 A' r, A2u A, A1 A1 A1 A' 72, z3 El, El E E B, + B2 A'+ A" r,, r, El u El E E A, +A2 A'+ A" There are similar bands in the b.f.d. spectra which cannot be explained in terms of benzene-only fundamental modes of vibration. There is a weak band at 543 cm-l at high coverage [fig. 4(a)] which may be related with the weak band at 540 cm-l in solid benzene (fig. 5). The latter can be assigned to a combination of a high-intensity internal mode with a high-intensity lattice mode.Similar features have been observed by Thomas and G h ~ s h ~ ~ and Jobic et aZ.29 in other systems. However, at low coverage [fig. 4(b)] the band at 522 cm-l has medium intensity and is unlikely to be an overtone or combination band. Further, at low coverage there is a stronger band at 638 cm-l [fig. 4(a)] which cannot be assigned to v, since it does not increase in intensity, viz. v16 and vll, at greater benzene coverage [fig. 4(b)]. These new bands, not associated with benzene inter- and intra-molecular vibrational modes, are produced by the benzene-platinum interaction (fig. 1). The stretch and the torsion are A modes while the tilts and deformations are possibly doubly degenerate, depending upon the symmetry. From studies of the vibrational spectra of C,H, rings n-complexed with metals the torsion and deformation are usually found at low frequency (< 200 cm-l) whereas the tilts and stretch are found generally at higher frequencies (> 200 cm-l).Further, in the i.i.n.s. spectra the (approximate) relative intensity of the E modes to the A (or B) modes is 2: 1. The correlation table for the reduction in symmetry of the hindered rotations and translations of benzene is shown in table 5. We concluded earlier that the adsorbate lay in a position of C,, symmetry and that this was sufficient to split the E mode, v16. At low frequency there are three major bands in fig. 7(b) which have yet to be assigned. The two intense bands at 153 and 171 cm-l may be assigned to the split ( E ) deformation mode and, following on from this, the A-mode torsion, which will involve a considerable amplitude of vibration of the benzene hydrogen nuclei, may be reasonably assigned to the single intense feature at 121 cm-l. This assignment is reasonable since generally in i.i.n.s.spectra the intensity of the torsional mode (A) is found to be greater than half the observed intensity of the deformation mode(s) At higher frequency the two major bands yet to be assigned in fig. 4(a) may be similarly treated. The most intense band at 638 cm-l may be assigned to the tilt ( E ) while the medium intense band at 522 cm-l is assigned to the stretch (A). The doubly degenerate tilt should also be split; however, the resolution of the b.f.d. instrument is poorer than IN4. At 638 cm-l the b.f.d.instrument resolution is not better than 40 cm-l using the A 1 (1 1 1) monochromator plane, and this could not have differentiated bands separated by only ca. 18 cm-l (the estimate of the resolution includes experimental as well as calculated uncertainties12). Table 6 lists the assignments of the benzene-platinum vibrational modes. The evidence for a strong benzene-platinum bond is further substantiated by the high frequency of the tilt and stretching modes at 638 and 522 cm-l, respectively. These (E).D. GRAHAM AND J. HOWARD 3377 Table 6. Assignments of the rotations and translations of benzene interacting with the platinum black surface (C2v symmetry) frequency/cm-l vibrational mode mode symmetry 121 torsion A2 '"I- 171 deformations 522 stretch 638 tilts A,, A,a A1 B,, B,b a Resolved.Unresolved. values are substantially higher than those reported by Lehwald et aL5 on Pt(l1 l), i.e. 570 and 360 cm-l. Jobic et in their study of C6H6+Raney Pt, reassigned the 570 cm-l 1.e.e.l. band [Pt(l 1 l)] to Y6. This suggests that vg is reduced by some 32 cm-l on adsorption compared with solid C&?6. In fact, as table 3 shows, this mode normally increases in wavenumber on adsorption and complexation. The low-wavenumber i.i.n.s. data of Jobic et al. are not in fact in particularly good agreement with their calculated spectrum. For example, their data contain a shoulder on the higher- wavenumber side of the 470 cm-l band and the observed relative intensities of the bands between 300 and 600 cm-l do not agree at all well with those calculated.We therefore prefer the assignment of Lehwald. Jobic et aZ.,29 in their study of benzene on Raney nickel, also found high values for the tilt and stretching modes, 548 and 440 cm-l, and compared the frequencies with those reported by Bertolini et a1.6 for benzene on Ni(100) and Ni(l1 l), i.e. 363 and 290 cm-l, respectively. Our work supports the postulate of Jobic et al.29 that the nature of the substrate plays an important part in determining the frequency of the skeletal vibrational modes. Thus with Raney nickel and platinum black, both polycrystalline powders showing numerous Miller-index planes, there is a higher heat of adsorption and a stronger benzene-metal bond resulting in increases in the benzene-metal force constant and the frequencies of the skeletal vibrations compared with the Ni( 1 1 l), Ni( 100) and Pt( 1 1 1).We thank both the S.E.R.C. and A.E.R.E. Harwell for the award of a CASE studentship and for the provision of access to neutron-beam facilities. Vibrational Spectroscopy of Adsorbates, ed. R. F. Willis, Springer Series in Chemical Physics, (Springer Verlag, Berlin, 1980), vol. 15. J. Howard and T. C. Waddington, Advances in Infrared and Raman Spectroscopy, ed. R. J. H. Clark and R. E. Hester (Heyden, London, 1980), vol. 7 , chap. 3 . J. L. Gland and G. A. Somorjai, Surf. Sci., 1973, 38, 157. P. C. Stair and G. A. Somorjai, J. Chem. Phys., 1977, 67,4361. S . Lehwald, H. Ibach and J. E. Demuth, Surf. Sci., 1978, 78, 577. J. C. Bertollini, G. Dalmai-Imelik and J. Rousseau, Surf.Sci., 1977, 67, 478; J. C . Bertollini and J. Rousseau, Surf. Sci., 1979, 89, 467. E. L. Muetterties, T. N. Thosin, E. Band, C. F. Brucker and W. R. Pretzer, Chem. Rev., 1979,79,91. M. Privet, J. M. Bassett, E. Labowski and M. V. Matthieu, J. Am. Chem. SOC., 1975, W, 3655. lo J. Howard, Ph.D. Thesis (University of Durham, 1976). D. Graham, Ph.D. Thesis (University of Durham, 1980). l 2 A. D. Taylor and J. Howard, J. Phys. E, 1982, 15, 1359. l3 A. H. Baston, D. H. C. Harris, A.E.R.E. Harwell Report R9278 MPDINBSI97, 1978 (unpublished). l4 B. Maier, Neutron Beam Facilities at the HFR Available for Users (I.L.L., Grenoble, 1981). ' H. Jobic and A. Renouprez, Surf. Sci., 1981, 111, 53.3378 ADSORPTION OF BENZENE ON Pt BLACK l5 M. B. H. Harryman, J. B. Hayter, A.E.R.E. Harwell Report USSIP23, 1972 (unpublished). l6 A. H. Baston, A.E.R.E. Harwell Report A42570 (H.M.S.O., London, 1972). R. E. Ghosh, A.E.R.E. Harwell Report USS/P19(REV), 1974 (unpublished). J. Howard and T. C. Waddington, J. Chem. Phys., 1976, 64, 3897. J. Howard, T. C. Waddington and C. J. Wright, Int. Symp. Neutron Inelastic Scattering (International Atomic Energy Agency, Vienna, 1977). 2o B. A. Sexton, Surf. Sci., 1980, 94, 435. 21 D. M. Adams, P. J. Chandler and R. G. Churchill, J. Chem. SOC. A, 1967, 1272. 22 R. D. Mair and D. F. Hornig, J. Chem. Phys., 1949, 17, 1236. 23 M. Ito and T. Shigeoka, Spectrochim. Acta, 1966, 22, 1029. 24 G. Herzberg, Infared and Raman Spectra of Pofyatomic Molecules (Van Nostrand, New York, 1945). 25 E. B. Wilson, Phys. Rev., 1934, 45, 706. 26 J. Howard, K. Robson and T. C. Waddington, J. Chem. Soc., Dalton Trans., 1982, 967. 27 B. V. Lokshin, E. B. Rusach, V. S. Kaganovich, V. V. Krivykh, A. N. Artemov and N. I. Sirotkin, 28 H. F. Efner, D. E. Tevault, W. B. Fox and R. R. Smardzewski, J. Organomet. Chem., 1978,146,45. 29 H. Jobic, J. Tomkinson, J. P. Candy, P. Fouilloux and A. J. Renouprez, Surf. Sci., 1980, 95, 496. 30 E. L. Bokhenkov, V. G. Fedotov, E. K. Sheka, I. Natkaniec, M. Sudnik-Hrynkiewicz, S. Califano 31 I. Harada and T. Shimanouchi, J. Chem. Phys., 1967,46,2708. 32 H. Bonadeo, M. P. Marzocchi, E. Castelluci and S. Califano, J. Chem. Phys., 1972, 57, 4299. 33 M. W. Thomas and R. E. Ghosh, Mol. Phys., 1975,29, 1489. Zh. Strukt. Khim., 1975, 16, 553. and R. Righini, Nuovo Cimento B, 1978, 44N2, 3241. (PAPER 41442)

ISSN:0300-9599    

DOI:10.1039/F19848003365

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. 1, 1984, 80, 3379-3390 Transport of Acetate and Chloroacetate Weak Electrolytes through a Thin Porous Membrane in Counter-current Electrolysis BY KYOSTI KONTTURI,* TUOMO OJALA AND RRKKO FORSSELL Department of Chemistry, Helsinki University of Technology, SF-02150 ES 15, Finland Received 19th March, 1984 The transport of weak electrolytes through a porous membrane during counter-current electrolysis has been studied both theoretically and experimentally. The theoretical model is based on the Nernst-Planck equations and the obtained transport equations for the ion constituents are used to solve the fluxes of the ion constituents. Expressions for the diffusion coefficients and transport numbers are also presented. Experiments and calculations for two binary systems (acetic acid in water and monochloroacetic acid in water) and for three ternary systems (acetic acid and sodium acetate in water, monochloroacetic acid and sodium mono- chloroacetate in water and acetic acid and monochloroacetic acid in water) were performed at a total concentration of 0.01 mol dm-3 or less.The theoretically obtained fluxes of the ion constituents are compared with the experimental fluxes and it is shown that the theoretical model is able to predict the transport phenomena. It has been shown that counter-current electrolysis in a thin porous membrane can be used to separate ions of different In these studies only strong electrolytes in water were considered. It has been verified both theoretically and experimentally that the ionic equivalent conductance determines the order in which the ions can be separated and that the separation efficiency is exponentially dependent on solvent flow through the porous membrane (convection).Furthermore, the small contribution of electric migration to separation in the case of strong electrolytes has been deduced. For weak electrolytes the case is different. It is obvious that electric migration has a significant effect on the transport phenomena occurring in a mixture of several weak electrolytes of different dissociation constants. This becomes clear when it is realized that the transport number depends directly on the amount of ionic species present. In the present work three different kinds of weak electrolyte system were studied. The first system [a weak acid (acetic acid or monochloroacetic acid) in water] was studied to test the feasibility of the Nernst-Planck equations derived from a kinetic The second system [a weak acid and its sodium salt (acetic acid and sodium acetate or monochloroacetic acid and sodium monochloroacetate) in water] was studied because it forms an interesting buffer solution, i.e.a system in which there can be different pH values on either side of the porous membrane. This arrangement may have useful applications in the separation of zwitterions, which have different isoelectric points. The third system [two weak acids (acetic acid and monochloroacetic acid) in water] was studied in order to verify that by using counter-current electrolysis in a thin porous membrane weak acids can be separated efficiently when their dissociation constants differ from each other.33793380 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE THEORY TRANSPORT EQUATIONS The transport processes of weak electrolytes can be described by equations obtained by a macroscopic approach such as the thermodynamics of irreversible processes.6-8 These transport equations are analogous to those used to describe the transport of strong electrolytes except that the concept of the ion must be replaced by the conept of the ion constituent, as defined by Noyes and Falk.g However, these transport equations, in spite of their general nature and applicability, are not as useful in practice since the dependences of diffusion coefficients and transport numbers on concentrations are rarely known.1° Because the Nernst-Planck equations for dilute solutions describe the transport phenomena through a thin porous membrane in counter-current electrolysis fairly accurately for the case of strong electrolytes,ll the same treatment is also used for systems of weak electrolytes.For every ionic species i we have a Nernst-Planck equation of the form where ji is the flux of ion i, Ai its molar conductivity, zi its charge number, ci its concentration and v the velocity of the solvent in a fixed coordinate system. There is one Nernst-Planck equation for every ion, with each equation containing the common quantity usually denoted by d$/dx and interpreted as the gradient of the electric potential. The concentrations of the ions are subject to the condition of electroneutrality: and the ionic fluxes must obey the n i-1 c zici = 0 equation for electric current ( I ) : n i-1 zi ji = I/F.(3) For every undissociated species of weak electrolyte we may write Fick’s law in the form where the subscript u denotes the undissociated species of the weak electrolyte j and Duj is its diffusion coefficient. Duj cannot be measured but it can be estimated by linear extrapolation of the data at high concentrations,12 because in a concentrated solution the degree of dissociation of weak electrolytes is vanishingly small. The dissociation constants form a link between the ionic species and undissociated species and, when only monovalent weak acids are considered, we have where Ki is the dissociation constant, cH+ is the concentration of hydrogen ion and ci and cuj are the concentrations of the ionic and undissociated species of the weak acid, respectively.For the ionic species and for the undissociated species the fluxes in eqn (1) and (4) are not stationary, i.e. constant, because of the changes in concentration in the porousK. KONTTURI, T. OJALA AND P. FORSSELL 3381 membrane. This is the case even though the transport process itself is in a stationary state. The fluxes are constant only for the ionic constituents. For instance, in the system of acetic acid (HOAc) + sodium acetate (NaOAc) +water the fluxes in eqn (1) and (4) are jH+, joAc-, jNa+ and juHOAc. and the stationary fluxes are j H =jH++juHOAc, Before deriving the transport equations with the aid of eqn (1)-(5) the following notation is presented.The subscripts T1 and T2 denote acetic acid and monochloro- acetic acid, - 1 and ul the dissociated anion and undissociated species of acetic acid, and - 2 and u2 the dissociated anion and undissociated species of monochloroacetic acid, respectively. With this notation the following expressions for the concentrations and fluxes of the ion constituents can be written. j o ~ c = jOAc- +juHOAc and jNa = jNaf- Binary systems : cT1 = CH = cH++c,,; jH = jH++jul for acetic acid in water. To obtain the corresponding expressions for the system of monochloroacetic acid in water subscript 1 is replaced by subscript 2. Ternary systems : cT1 = CH = cH+ + c,,; CNa = CNa+; jNa =ha+ j H = j H + +jul for acetic acid + sodium acetate + water. Again the corresponding expressions for monochloroacetic acid + sodium monochloroacetate + water are obtained by re- placing subscript 1 by subscript 2.For the system acetic acid + monochloroacetic acid+water we have c, = cT1 = c-, + c,, ; j, = j-, +jul c, = cTZ = c2+jU2; j, = j-,+j,,. The concentrations c, ahd c, are the concentrations of the acetate-ion constituent and monochloroacetate-ion constituent, respectively. The symbols for the dissociation constants are chosen to be K , for acetic acid and K, for monochloroacetic acid (Kl = 1.75 x Taking into account the condition of electroneutrality, eqn (2), the relationship between the ionic fluxes and electric current, eqn (3), the dissociation constants, eqn (9, the Nernst-Planck equations, eqn (l), Fick's law, eqn (4), and the Nernst-Einstein relation for ions and K2 = 1.36 x mol dmP3).we obtain, after the elimination of the electric-potential gradient, the transport equations for the different systems. For the binary system acetic acid + water we obtain where the transport number of the hydrogen-ion constituent has the form and the diffusion coefficient of acetic acid is3382 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE The diffusion coefficient as expressed by eqn (9) is the weak electrolyte analogue of the Nernst-Hartley equation. It gives the same numerical values for the diffusion coefficient as the equation presented by Muller and Stokes,13 indicating that the same assumptions were made when deriving both of these equations. The transport equation and estimates for the transport quantities in the case of monochloroacetic acid + water are obtained from eqn (7)-(9) by substituting subscript 1 with subscript 2.The values for the ionic diffusion coefficients or ionic conductivities have been presented by Robinson and Stokes14 and the values for the diffusion coefficients of undissociated species have been presented by Vitagliano and Lyons12 and Holt and Lyons15 in the case of acetic acid and by Garland et aZ.lS in the case of monochloroacetic acid. The numerical values are presented in table 1 . Using the numerical data of table 1 and eqn (8 b) the estimates for diffusion coefficients were calculated and were found to be in a good agreement with measured data.l2? 14-16 For the ternary system consisting of acetic acid + sodium acetate +water the transport equations are where the transport numbers of the hydrogen-ion constituent and sodium ion are tNa = and the expressions for the diffusion coefficients are In eqn (1 2) and (1 3) the concentrations of the hydrogen and acetate ions are obtained using and the condition of electroneutrality. The corresponding equations for the system of monochloroacetic acid + sodium monochloroacetate + water are obtained by sub- stituting subscript 1 with subscript 2.The diffusion coefficients in the system acetic acid + sodium acetate + water have cH+ = +{ 'd K1 + (CNa+ + K1)21 - (K1 + cNa+)) (14)K. KONTTURI, T. OJALA AND P. FORSSELL 3383 Table 1. Diffusion coefficients of the species at infinite dilution at 25 "C species Oil cm2 s-l ref.H+ 9.3 1 14 Na+ 1.33 14 OAc- 1.09 14 CH2C1C00- 1.12 14 HOAc" 1.20 12 CH,ClCOOH" 1.08 16 a Undissociated species. been measured at different concentrations by Leaist and Lyons." They also developed a theoretical model to estimate the diffusion coefficients, and good agreement was found between calculated and measured values. Even though Leaist and Lyons used the methodology of the thermodynamics of irreversible processes their assumptions and results are almost the same as ours. The small differences are due to the fact that Leaist and Lyons took into account the influence of activity coefficients, but we do not. However, the results obtained are not essentially different. For the ternary system acetic acid + monochloroacetic acid + water the transport equations are where the transport numbers of the acetate-ion constituent and monochloroacetate- ion constituent are3384 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE where A = (Kl + K2) cH+ + c$+ + K , c-, + Kl cT2 + cH+(c-, + c-,) + K, K2.The concen- trations of hydrogen ion, acetate ion and monochloroacetate ion in eqn (1 7) and (1 8) are obtained as follows. The concentration of acetate ion (eel) is calculated from (19) Eqn (19) has three roots, of which the one existing in the concentration range (0, cT1) is the value of the acetate-ion concentration required. After obtaining the value of c-, the hydrogen-ion concentration can be calculated from and the condition of electroneutrality is used to obtain the concentration of the monochloroacetate ion. The diffusion coefficients in eqn (13) and (18) are ternary analogues of the Nernst-Hartley equations for weak electrolyte systems.The transport numbers in eqn (8), (12) and (17) are estimates of the stoichiometric transport numbers, which are measured by Hittorf s method, i.e. the only measurable transport numbers in the above systems [cf. ref. (18)]. TRANSPORT PROCESSES The above equations are now used to model the transport processes through a thin porous membrane which is part of the counter-current electrolysis cell presented schematically in fig. 1 . In the stationary state the mass balance for ion constituent i, which cannot go through the ion-exchange membrane, in compartment a is simply -Aji = cf F/a (21) where A is the surface area of the porous membrane and cf is the concentration of ion constituent i in compartment a.Using eqn (21) we can, after analysing the concentration of ion constituent i and after measuring the volume flow determine the experimental value ofj,. Comparing this value with the theoretically obtained value of ji we are able to deduce the feasibility of the theory. Solving for the fluxes ji in the above equations leads us to a two-point boundary value problem of a set of ordinary differential equations. This problem does not have an analytical solution, except in the binary case, and therefore numerical methods have to be used. Two different procedures for solving the problem have been p r e ~ e n t e d l ~ ? ~ ~ and are used in the present calculations, that based on the shooting method described in the ref.(19) being applied most often. These numerical methods are also applied to the binary case, because the form of the analytical solution is dependent on the parameter to be solved and therefore its use is unwieldy. As mentioned above, the binary systems are studied only to find out how well the Nernst-Planck equations approximate the diffusion coefficient and transport number. In the ternary systems our main interest is in studying the separation of weak electrolytes. The separation efficiency is characterized by the selectivity ratio ( S ) where subscripts 1 and 2 denote ion constituents chosen so that S 3 1 and superscriptsK. KONTTURI, T. OJALA AND P. FORSSELL 3385 Fig. 1. Schematic drawing of the counter-current electrolysis cell. A thin porous membrane (M) divides the cell into two compartments a and p.The solutions in compartments a and pare well mixed. When cations are separated the polarity of electric current is chosen as presented in the figure and anionexchange membranes (AM) are used to separate the electrode compartments (E) from the a and j? compartments. If anions are separated the polarity must be changed and AM must be replaced by cation-exchange membranes. This means that the counterion in the ion-exchange membrane is the common ion of the system studied. In the binary case we have only one cation, i.e. H+, which moves towards the cathode and no separation exists. vf denotes the stream into compartment of the weak electrolyte solution being studied and Vb the flow out of the compartment.The concentrations in compartment /3 are kept constant by circulating the weak-electrolyte solution being studied so rapidly that no essential changes in concentration take place. Vo denotes the water flow jnto compartment a. Part of this water flows out of the compartment on the product stream ( Va) while. the rest flows as convection through the porous membrane ( Vc = Vo - Va). a and /3 denote the compartments a and /3. Unfortunately, unlike in strong-electrolyte systems where the selectivity ratio is exponentially dependent on convection,23 no simple relationship was found for the selectivity ratio in weak-electrolyte systems. EXPERIMENTAL The weak-electrolyte systems studied were HOAc + H,O, CH,ClCOOH + H,O, HOAc + NaOAc + H,O, CH,ClCOOH + CH,ClCOONa + H,O and HOAc + CH,ClCOOH + H,O.The apparatus used in the measurements is schematically described in fig. 1. A detailed representation of the experimental set-up has been presented previ~usly.~ For every measurement the total concentration in compartment p was kept constant (ca. 0.01 mol dmP3). The concentratjons in compartment a were determined by analysing the concentrations in the outflow stream Va. The system was deduced to have reached the stationary state when the concentrations in the outflow stream Va remained unchanged. For the binary systems the measurements were carried out by changing the electric current and convection as well as the outflow rate so that large variations in the magnitude of the flux through the membrane could be obtained. In the ternary systems the electric current and convection were changed while the outflow rate was kept constant.Sodium was analysed by flame photometry and the acids were mostly analysed by potentiometric titration. When the concentration of hydrogen was too small for potentiometric determination the acid concentration was calculated from pH measurements. In the case of two weak acids a computer program of Partanen21 was used to interpret the titration curve and to obtain the concentrations of the individual acids. The accuracy of these analyses was estimated to be better than 5% in every case. 110 F A R 13386 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE RESULTS AND DISCUSSION BINARY SYSTEMS The results of the measurements in the binary systems HOAc+H,O and CH,ClCOOH + H,O with varying electric current, convection and outflow rate are reported in table 2, which also includes the quantity N calculated with the help of eqn (7)-(9).The quantity N is defined as N = N,+t,I, where NH is the dimensionless flux of the hydrogen-ion constituent and I, is the dimensionless electric current (for the definition of N , and I, see the footnote to table 2). The theoretical value of NH is calculated using the experimental value of I,, which is very accurate. The last column of table 2 is the ratio of the difference in experimental and theoretical hydrogen flux to electric current. This quantity is designated by qH (a type of current efficiency of ion-exchange membranes) and can be explained as follows. In the measurements we have to use ion-exchange membranes to separate the products of the electrode reactions from the rest of the system (see fig.1). For our binary systems these membranes were anion-exchange membranes through which hydrogen ions always leak introducing extra flux into the balance equation, eqn (21). This leakage is a complicated function of the electric current, the concentrations in compartment a and the electrode compartments (cg, cg) and the time of equilibration t,, i.e. VH =Ar, CF, c?, tE)- Usually tE differs from t g , which is the time required to reach the stationary state in the membrane. This difference is due to the fact that it was impossible to maintain constant values of the parameters ( vo, vc, 3 and A / l ) when the measuring time was lengthened (the usual measuring time in these experiments was a few days).The effect of electro-osmosis for the various v is ca. 0.1 % or less (assuming that 20 mol water are transported for 1F) and it can therefore be neglected as a source of error. Other souces of error are the theoretical model itself, the analysis of hydrogen in dilute solutions and the determination of the flow rates. The membrane constant ( A / l ) , needed in the calculation of fluxes, depends on convection and stirring in compartments a and a, and for acetic acid and monochloroacetic acid slow changes in the structure of the porous membrane (made of cellulose acetate or nylon) caused variations in membrane constant. The effect of the changes in A / l was studied with the aid of a theoretical model and it was found to be small for binary systems but large for ternary systems.In table 2 the membrane constant A/Z is taken to be 13.1 cm, which corresponds to the geometric value.29 22 Taking into account these errors we conclude that the theoretical approach based on the Nernst-Planck equations describes the behaviour of the system sufficiently well. Furthermore, note that theoretical calculations can be arranged to fit the experimental data exactly by changing the boundary concentrations on both sides of the porous membrane within the range of experimental error. However, this procedure always decreases the boundary concentration in compartment a and therefore it cannot be interpreted merely as an experimental error. On the other hand, the leakage of hydrogen through the anion-exchange membrane always occurs and so exact corres- pondence between measured and theoretical data is not possible.system -4 UC Ye YP measured theoretical measured theoretical H20 0.95 0.48 0.78 0.93 0.48 0.31 0.37 0.54 0.08 1 .oo 0.50 0.35 0.35 0.50 0.95 4.45 2.85 0.60 1.45 0.98 1.66 1.04 0.89 1.51 2.85 4.35 0.26 1 .oo 1 S O 1.13 1.05 1.42 7.60 4.66 0.71 1 .oo 3.93 3.31 2.87 3.49 9.49 1.91 1.17 1 .oo 2.55 2.25 5.95 6.25 2.85 0.98 1.03 0.94 1.59 1.03 0.95 1.515 Definitions of dimensionless parameters when c, = 0.01 .mol dm3, Do = 2 x lop5 cm2 s-l, A / l = 13.1 cm, Fis Faraday's constant and 1 membrane: uc = VCl/(ADo) (convection); ua = Val/(AD,) (outflow); I,.= Il/(c,D,F) (electric-current density); & = CJC, (//(Do co); N = NH + t , I,.; N,(measured) = uaca/co; AN, = N,(measured) - N,(theoretical).CH2C1COOH + H,O 0.95 1 .oo 0.43 1 .oo 0.45 0.27 0.40 0.57 2.85 4.35 0.30 1 .oo 1.29 1.29 1.26 1.263388 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE TERNARY SYSTEMS The results of our measurements for the three different ternary systems HOAc + NaOAc + H20, CH2C1COOH + CH2C1COONa + H20 and HOAc + CH2C1COOH + H20 are reported in table 3, which also includes the theoretically calculated fluxes. In every measurement the outflow rate via had the same value and A/Z was taken as 13.1 cm. The sources of error are essentially the same as in the binary case. As can be seen from the results the theoretical model predicts the course of the transport phenomena. The model fails to explain the smaller fluxes quantitatively, but gives results of the same order of magnitude.HOAc + NaOAc + H,O Since acetic acid is very poorly dissociated at the studied concentrations (ca. 0.01 mol dm-3), its transport through a porous membrane in counter-current electrolysis consists mainly of diffusion and convection, the contribution from electric migration being small. However, some contribution from electric migration exists, as can be seen when inspecting the first three measurements in table 3. When the electric current is doubled and the convection is kept constant, the concentrations of acetic acid and sodium acetate are also doubled. The amount of totally dissociated sodium acetate in compartment a increases. This increase is due to electric migration, i.e. to the much greater transport number of the sodium-ion compared with the hydrogen-ion constituent (note that the concentration of hydrogen is ten times greater than that of sodium in compartment p).Diffusion and convection alone cannot explain this increase. In the last three measurements for the system HOAc + NaOAc + H20 the selectivity ratio S [see eqn (22)] is very high (in fact infinite): no hydrogen is left in compartment a because it has been partially neutralized by hydroxide ions, the products of the hydrolysis of sodium acetate. This means that the acetic acid concentrations in these three measurements are calculated not real values. Nevertheless, they demonstrate the flow of the hydrogen-ion constituent through the porous membrane. However, we must remember that the tabulated, rather inaccurate theoretical values for the flux of the hydrogen ion are obtained using a poor theoretical model, since the model does not take hydrolysis into account.Hydrolysis can be included in our model but it complicates the problem too much compared with the advantage gained. The measurements for the system HOAc + NaOAc + H20 show that using counter- current electrolysis with a thin porous membrane different buffer solutions of different pH values can be maintained on both sides of the porous membrane. This may be of use in the separation of zwitterions and pH-dependent complexes. CH2C1COOH + CH,ClCOONa + H 2 0 The behaviour of this system is very similar to that of the previous one, but because the dissociation constant of monochloroacetic acid is approximately a hundred times greater than that of acetic acid the contribution of electric migration to the transport is much stronger. To verify this, compartment p was filled with a solution containing a hundred times more acid than its sodium salt.Thus in this solution we have more hydrogen ions than sodium ions. Furthermore, the transport number of the hydrogen ion ought to be greater since A,+ 7A,,+. According to the calculations and the measurements the amount of acid in compartment a is increased. This is due to electric migration and both diffusion and convection have only a small effect on this increase. The theoretical model predicts the behaviour of this weak electrolyte system fairly well, but the increasing influence of activity coefficients can clearly be seen.Our modelTable 3. Experimental and calculated results for the ternary systems measured theoretical system - I , vc Yp Yg yz" y! Nl N2 Nl N2 S (1) HOAC+ 1.98 1.22 3.96 1.16 (2) NaOAc + H 2 0 3.96 2.12 7.91 4.18 11.87 4.18 15.43 4.37 (1) CH2C1COOH + 3.96 1.87 3.96 4.12 (2) NaOAc + H,O 7.91 1.94 7.91 4.22 (2) CH2C1COOH + H 2 0 11.87 4.24 (1) CH2C1COOH + 5.93 4.45 0.12 0.2 1 0.10 0.004 0.005 0.003 0.76 0.49 1.43 0.9 1 0.025 0.014 1 .oo 1 .oo 0.98 0.96 0.95 0.98 0.97 0.90 0.95 0.95 1.02 1 .oo 0.25 0.52 0.41 0.62 0.89 1.07 0.0016 0.000 8 1 0.0045 0.00 16 0.063 0.17 0.096 0.095 0.097 0.088 0.088 0.089 0.01 1 0.012 0.012 0.012 0.94 0.93 0.25 0.50 0.36 0.41 1 .oo 0.45 0.20 0.82 0.13 9.8 x 1.75 6.6 x 7.1 x 10-4 1.21 8.2x 10-3 5.9 x 10-4 2.17 5 . 4 ~ 10-3 1.68 3.5 x 10-3 2.1 1 3.03 9.5 x 10-3 4.20 1.91 3.5 x 10-3 3.22 1.10 1.8 x lob3 1.49 0.048 0.12 - 0.098 0.028 0.34 - 0.052 0.53 1.17 1.13 1.78 2.8 1 3.81 5.5 x 10-4 -2.2 x 10-4 16.6 x 10-4 2.4x 10-4 0.36 0.56 ?? 21.3" * 26.1" 41.0" 5 18 700" 19 400" Y 5 40 600" 5.4b 8.3b $ 4.0b > 2 6.6b $ 2.7" 13.3" 6 B ? Definitions of dimensionless parameters, when c, = 0.01 mol dmP3, Do = 2 x lop5 cm2 sP3, A / l = 13.1 cm, Fis Faraday's constant and I is the thickness of the membrane: uc = VCI/(AD,) (convection); ua = Val/(AD,) (outflow, ca. 2.0); I, = Il/(c,D,F) (electric-current density); 6 = ci/co (concentration); Ni (theoretical) = JiI/(Doco); N,(measured) = uac$/co; the meaning of subscripts 1 or 2 can be seen in the first column.a S = Y; Yf/Y,f'Y;. s = Yp Y!/ Yg Yz". w w 00 \o3390 COUNTER-CURRENT ELECTROLYSIS IN A POROUS MEMBRANE does not take into account the dependence of the activity coefficients on concentration and therefore greater deviations between theoretical and experimental results compared with the system HOAc + NaOAc + H20 can be expected.Monochloracetic acid is a stronger electrolyte than acetic acid, which is why the effect of activity coefficients is more pronounced in the system CH,ClCOOH + CH,ClCOONa + H20. HOAc + CH2C1COOH + H,O This system was studied in order to show that counter-current electrolysis can be used efficiently when separating weak acids from each other. In spite of the great difficulties in the analysis of these acids we are able to achieve our goal, i.e. to show that separation by this method is possible.The selectivity ratios ( S ) are much lower than predicted by calculations (note that N , > 0), which can be partly explained by the leakage of acetic acid through the cation-exchange membrane from the electrode compartment to compartment a. To obtain more quantitative results the experimental set-up must be improved. CONCLUSIONS Our theoretical model predicts the transport of weak electrolytes through a thin porous membrane in counter-current electrolysis when the total concentration is ca. 0.01 mol dm-3. In the case of weak electrolytes transport across a porous membrane is characterized mainly by electric migration, i.e. the separation can be estimated by considering transport numbers, and diffusion and convection determine the separation only in the case where the transport numbers of the individual ion constituents are of the same order of magnitude as in the case of strong electrolytes. A. Ekman, P. Forssell, K. Kontturi and B. Sundholm, J. Membr. Sci., 1982, 11, 65. K. Kontturi, P. Forssell and A. Ekman, Sep. Sci., 1982, 17, 1195. P. Forssell and K. Kontturi, Sep. Sci., 1983, 18, 205. W. Nernst, Z. Phys. Chem., 1888, 2, 613; 1889,4, 129. M. Planck, Ann. Phys., 1890, 40, 561. D. G. Miller, J. Phys. Chem., 1966, 70, 2639; 1967, 71, 616; 1967, 71, 3588. A. Ekman, S. Liukkonen and K. Kontturi, Electrochim. Acta, 1978, 23, 243. K. Kontturi, Acta Polytech. Scand., 1983, 152. A. Noyes and K. Falk, J. Am. Chem. Soc., 191 1, 33, 1437. lo E. Cussler, Multicomponent Dryusion (Elsevier, Amsterdam, 1976). l1 K. Kontturi, P. Forssell and A. H. Sipila, J. Chem. Soc., Faraday Trans. 1, 1982, 78, 3613. l2 V. Vitagliano and P. A. Lyons, J. Am. Chem. Sac., 1956, 78, 4538. l3 G. T. Miiller and R. H. Stokes, Trans. Faraday Soc., 1957, 53, 642. l4 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 2nd edn, 1959). l5 E. L. Holt and P. A. Lyons, J. Phys. Chem., 1965, 69, 2341. l6 C. W. Garland, S. Tong and W. A. Stockmayer, J. Phys. Chem., 1965, 69, 2469. l7 D. G. Leaist and P. A. Lyons, J. Phys. Chem., 1981, 85, 1756. l9 A. H. Sipila, A. Ekman and K. Kontturi, Finn. Chem. Lett., 1979, 97. 2o K. Kontturi and A. H. Sipila, Finn. Chem. Lett., 1983, 1. 21 J. Partanen, to be published. 22 T. Hashitani and R. Tamamushi, Trans. Faraday SOC., 1967, 63, 369. R. Haase, Thermodynamics of Irreversible Processes (Addison-Wesley, London, 1969). (PAPER 4/443)

ISSN:0300-9599    

DOI:10.1039/F19848003379

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1984,80, 3391-3398 Reactions of Methyl Radicals with 3-Methyloxetane, 3,3-Dimethyloxetane and 2,2-Dime thyloxe tane BY MARTIN G. DUKE AND KENNETH A. HOLBROOK* Department of Chemistry, University of Hull, Hull HU6 7RX Received 19th March, 1984 The reactions of methyl radicals with 3-methyloxetane, 3,3-dimethyloxetane and 2,2- dimethyloxetane have been studied. The overall rates of hydrogen-atom abstraction from these three compounds have been obtained over the temperature range 100-200 "C by assuming the value of Quinn and coworkers (J. Chem. SOC., Faraday Trans. 1, 1976, 72, 1935) for the rate of recombination of methyl radicals. The following rate expressions were found : loglo(k4/cm3 mol-l s-1)(30x) = 11.69 (kO.20)-38.23 (k0.84) kJ mol-l/2.303RT loglo(k4/cm3 mol-1 s-1)(3,30x) = 1 1.72 ( f 0.20) - 39.47 (& 1.0) kJ mol-l/2.303RT loglo(k4/cm3 mol-l s-1)(2,20x) = 1 1.99 ( k 0.23) -41.24 ( f 1.13) kJ mol-l/2.303RT.From these rate expressions and those obtained previously for three other oxetane molecules, the rate parameters for hydrogen-atom abstraction from five distinct sites in the substituted oxetane molecules have been obtained. Very little information is available concerning the abstraction reactions of methyl radicals with cyclic molecules.' In an attempt to remedy the deficiency, and in connection particularly with studies of the thermolysis of various oxetane molecules, we reported previously the results of work on hydrogen abstraction by methyl radicals from oxetane, 2-methyloxetane and 2,4-dimeth~loxetane.~ Two different types of ring hydrogen atom were distinguished, namely secondary and tertiary hydrogen atoms, and Arrhenius parameters for their removal were obtained by assuming those for removal of primary hydrogen atoms in the methyl groups to be similar to the parameters for removal of primary hydrogen in ~ r o p a n e .~ In the present paper this work is extended to three other oxetane molecules. Five types of hydrogen-atom sites can now be distinguished, and by analysing the present and previous results it was hoped to obtain individual Arrhenius parameters for abstraction from all five types of site assuming only a value for the rate of recombination of methyl radicals. EXPERIMENTAL APPARATUS AND PROCEDURE All reactions were carried out in the gas phase by photolysing reaction mixtures in a Pyrex cell (volume 180cm3) with a plane glass window.The apparatus and procedure have been described previously. MATERIALS Acetone (A.R.) was supplied by Koch-Light Ltd, and, after thorough degassing and on-line distillation, was found to be > 99.5% pure. The oxetane samples were prepared in these laboratories by Mrs B. Worthington. The 2,2-dimethyloxetane was prepared from 3- 339 13392 REACTIONS OF METHYL RADICALS WITH OXETANES Poxetanelpacetone Fig. 1. Plots for calculation of k,lkf: (-A-) 3-methyloxetane at 2,2-dimethyloxetane at 197.0 "C and (-n-) 3,3-dimethyloxetane at 192.0 "C. 197.2 "C, (---O---) bromoethylpropionate by reacting it with methylmagnesium iodide to form 2-methyl-4- bromopropan-2-01.This was then ring-closed using tributyltin ethoxide to give the product. A sample of 3,3-dimethyloxetane was prepared by ring-closing 2,2-dimethylpropan- 1,3-diol using concentrated sulphuric acid and sodium hydroxide. The 3-methyloxetane was prepared from diethylmonomethyl malonate which was reduced to 2-methylpropan- 1,3-diol using lithium aluminium hydride. The diol was then converted by acetyl chloride to the chloroester, which was ring-closed using a concentrated solution of sodium and potassium hydroxides. After purification by preparative g.1.c. and on-line distillation, all samples of oxetanes were found to be > 99.5% pure. RESULTS REACTIONS BETWEEN METHYL RADICALS AND OXETANES The results for the photolysis of acetone between temperatures of 100 and 192 "C have been reported previously2 and were shown to be in good agreement with the results of other workers.When acetone is photolysed in the presence of an oxetane, the following reactions occur : hv CH,COCH, + X H , + CO k, CH, + CH,COCH, --+ CH, + CH,COCH, k, CH, + CH,COCH, -+ C,H,COCH, k, 2CH, --+ C2H, k4 CH, + oxetane + CH, + oxetanyl.M. G. DUKE AND K . A. HOLBROOK 3393 Table 1. Analytical results and rate constant ratios for the methyl radical + 3-methyloxetane reaction Pacetone P3-methyloxetane PCH4 PCzHs (k4lkb T/"C /Torr /Torr Torr /lov2 Torr /cm: mol; s-4 104.3 104.8 105.5 117.5 1 1 7.5a 118.2 124.1 124.3 132.8 132.9 134.9 150.2 150.2 150.3 150.7 167.7 168.2 168.2 168.8 182.9 183.1 183.2 183.3 197.2 197.3b 197.4 30.9 31.1 30.8 31.3 31.3 31.3 32.2 32.1 32.7 32.9 32.6 34.2 34.2 34.0 33.9 36.2 36.2 36.2 36.2 36.5 36.9 36.5 36.8 38.3 37.8 38.1 30.1 30.3 30.6 31.3 31.3 31.3 31.8 31.9 32.1 32.2 32.6 24.8 17.9 33.7 33.9 17.6 22.5 36.2 36.3 36.5 15.8 36.5 36.6 26.2 37.8 18.7 2.99 3.02 3.07 4.02 4.14 3.79 4.50 4.50 5.34 5.14 5.58 6.37 5.73 7.44 7.41 7.3 1 7.81 8.99 8.89 9.56 8.32 9.56 10.1 10.2 11.6 9.12 2.48 2.52 2.48 1.97 2.0 1 1.87 1.65 1.59 1.47 1.39 1.48 1.19 1.44 1.02 1 .oo 0.93 0.79 0.54 0.53 0.29 0.63 0.32 0.29 0.32 0.24 0.39 0.538 0.534 0.542 0.784 0.776 0.753 0.955 0.970 1.16 1.16 1.21 1.87 1.86 1.92 1.92 3.00 3.03 3.03 3.03 4.52 4.55 4.55 4.47 5.47 5.33 5.32 a Photolysis time = 1920 s.Photolysis time = 2040 s. It can be shown that this leads to the expression k, k, Poxetane x Pacetone G ki Pacetone =-T+-€x- RCH4 where RCHl and RCzHs are the rates of formation of methane and ethane, respectively.Plots of the left-hand side of this expression against poxetane/pacetone are shown for the three oxetanes studied in fig. 1. This expression predicts linear plots provided that poxetane and pa,,,,,, are not depleted by formation of products during the experiment. This is shown by the data in table 1. In all three cases the oxetane under study was illuminated alone for 1 h at 150 "C and no products were detected. The three oxetanes were also put separately and admixed with acetone into the furnace and left for 1 h without illumination, to check that there was no thermal decomposition; no breakdown products were detected . 3-METHY LOXETANE An initial pressure of 30 Torr* of 3-methyloxetane at 100 "C was used and the pressure adjusted accordingly to keep the initial concentration constant as the3394 REACTIONS OF METHYL RADICALS WITH OXETANES Table 2. Equivalence of propene and carbon monoxide pco from 3-methyloxetane T/"C / 1 0-2 Torr pCIH/ 1 0-2 Torr 105.5 117.5 132.8 150.7 168.2 183.2 0.20 0.43 1.04 2.61 4.20 8.14 0.23 0.45 1 .oo 2.58 5.60 9.95 temperature was raised.Although most reactions were carried out at a 3- methyloxetane: acetone ratio of 1 .O, several were carried out at a ratio < 1 .O to show that k,/kt was independent of this ratio (see fig. 1). From a series of 26 photolyses in the temperature range 104.3-197 "C, and assuming the value of k, from the work of Quinn and c o ~ o r k e r s , ~ the rate constant (k4)3-0x for the overall abstraction of hydrogen from 3-methyloxetane is given by loglo(k4/cm3 mol-l s - ~ ) ( , . ~ ~ ) = 1 1.69 (k 0.20) - 38.23 ( f 0.84) kJ mol-l/2.303RT the error limits being the 95% confidence limits.The values of k,/k: * used for the Arrhenius plot (fig. 2) are shown in table 1. As well as methane and ethane, propene, carbon monoxide and hydrogen were found in the reaction products. Propene and carbon monoxide were determined quantitatively, but hydrogen was only detected at temperatures above 170 "C and no accurate quantitative work could be carried out. Determination of carbon monoxide formed due to the presence of 3-methyloxetane was made by subtracting the pressure of CO measured by the photolysis of acetone alone.Owing to the small pressures of CO involved and the method of measurement, errors are likely to be quite large. However, at all temperatures, the propene pressure was equal, within experimental error, to the CO pressure, as shown for 6 temperatures in table 2. This is in accordance with the breakdown of the 3-methyloxetanyl radical as shown below: C3H6 + HkO HkO - CO+H 3,3-DIMETHYLOXETANE AND 2,2-DIMETHYLOXETANE Similar procedures were used for the other two oxetanes studied. From a series of 30 photolyses in the temperature range 100.4-192.3 "C, the rate constant (~k~),.,~~ for overall hydrogen abstraction by methyl radicals from 3,3-dimethyloxetane is given by loglo(k4/cm3 mol-1 s-1)(3.30x) = 1 1.72 (k0.20) - 39.47 (& 1 .O) kJ mol-l/2.303RT the error limits being the 95 % confidence limits.Isobutene and carbon monoxide were analysed quantitatively and it was found that reasonable agreement was obtained between the amounts of these products. For 2,2-dimethyloxetane, 2 1 photolyses were carried out in the temperature rangeM. G. DUKE AND K. A. HOLBROOK 3395 103 KIT Fig. 2. Arrhenius plots: (a) 3-methyloxetane and (b) 3,3-dimethyloxetane. The plot for 2,2-dimethyloxetane is very similar to that for 3,3-dimethyloxetane and has been omitted for clarity. 100.1-197.8 "C and the rate constant (k4)2.20x for overall hydrogen abstraction by methyl radicals is given by loglo(k4/cm3 mol-l s-1)(2,20x) = I 1.99 (f 0.23) -41.24 (If: 1.13) kJ mol-l/2.303RT the error limits being the 95% confidence limits. Isobutene and carbon monoxide and hydrogen were also detected in the reaction products, but ethene was absent, unlike the reaction of methyl radicals with 2-methyloxetane.DISCUSSION The Arrhenius parameters for the abstraction of a hydrogen atom by methyl radicals from three oxetane molecules have been obtained, and these supplement the previous results that we have reported.2 A summary of all the results and the overall rate constants at 164 "C are given in table 3. Although it is evident that both 2-methyloxetane and 2,4-dimethyloxetane have a higher rate constant at 164 "C than the other four oxetanes studied, it must be realised that this overall rate constant is the sum of H-atom abstraction from all sites in the molecules. We have shown previously that the tertiary H atoms in the 2-position are removed much faster than the secondary methylene H atoms.From the results obtained in this present work, the rate constants for H-atom abstraction by methyl radicals at all positions in the oxetane ring can be calculated. If it is assumed that the overall rate constant can be calculated by addition of the3396 REACTIONS OF METHYL RADICALS WITH OXETANES Table 3. Comparison of rate parameters for hydrogen abstraction log,o(k log,o(A /cm3 mol-l s-l) substrate /cm3 mol-I s-l) E/kJ mo1-I at 164 "C ref. 11.29 35.22 7.08 11.42 34.04 7.35 11.51 33.52 7.51 11.69 38.23 7.12 11.72 39.47 7.00 11.99 41.24 7.06 9 t! DO 2 2 2 this work this work this work rate constants for attack at all sites in the molecules, five H-atom sites may be distinguished in the six oxetanes studied.These may be labelled a, b, c, d and e as shown below, and rate constants for their abstraction by k,, k,, kc, kd and k,: C c b a b b CH Z-CH 2 CH2-CH CH,-CH CHZ-0 I I CH,-o I Is /CH-0 a a CH3 I Is C Assuming that the rate constants are additive, it can be shown that the individual rate constants are given by k~ = ( k 3 , 3 0 X -k 'OX- k Z , Z O X ) / 6M. G. DUKE AND K. A. HOLBROOK 3397 Table 4. Rate parameters for H-atom abstraction from oxetane molecules a 10.2 33.0 b 11.0 38.5 C 12.5 56.9 d 11.6 41.3 e 10.7 30.4 6.26 6.40 5.70 6.67 7.07 Table 5. Arrhenius parameters for the H-atom-abstraction reactions of methyl radicals (per H atom) species log,,A/cm3 mol-1 s-l E/kJ mol-l ref. CH3CH20H A A Ha (adj. to 0) H, (remote from 0) He (adj.to 0) H, (remote from 0) primary C-H 11.25 10.20 10.8 10.20 12.5 11.52 11.12 1 1.30 10.89 10.49 10.22 11.01 10.39 9.80 11.43 10.2 11.0 tertiary C-H 11.38 10.98 10.7 11.6 secondary C-H 50.2 41.8 49.4 39.7 56.9 42.4 41.8 40.5 43.5 38.9 43.1 55.2 40.2 37.7 49.5 33.0 38.5 33.6 33.0 30.4 41.3 7 8 5 8 this work 9 5 10 5 11 11 5 12 13 6 this work this work 9 5 this work this work * 1 Torr = 133.33 Pa. Values of these rate constants per H atom have been calculated at temperatures between 100 and 200 "C, and the corresponding Arrhenius parameters are given in table 4 with the rate constants per H atom at 164 "C. The rate of H-atom abstraction follows the expected order of tertiary > secondary > primary since He, H, > Ha, H, > H,. A comparison of the rate constants for H-atom abstraction from the sites in oxetane molecules with those from other molecules is given in table 5.Comparison of the Arrhenius parameters in table 5 reveals some interesting facts. Secondary H atoms in small-ring compounds have slightly lower A factors and3398 REACTIONS OF METHYL RADICALS WITH OXETANES activation energies for abstraction by methyl radicals compared with secondary H atoms in comparable open-chain compounds. The presence of an adjacent oxygen atom lowers the activation energy to approximately the same extent in both 3-membered and 4-membered rings; thus E(*, [ref. ( ~ ) ] - E , A , , [ref. (6)] = 55.2-49.5 = 5.7f3.0 kJ mol-1 E,o, [ref. ( 5 ) ] - E , (this work) = 43.5-33.0 = 10.5f2.7 kJ mol-l. The parameters from ref. ( 5 ) have been used in this comparison as they are considered more reliable than those from earlier work cited in table 5 .A similar lowering of the activation energy for removal of a tertiary hydrogen atom adjacent to oxygen is noted when comparing values for the hydrogen atoms He and H,. Baldwin et have recently shown that an Evans-Polanyi type equation which fits the variation of activation energy with bond dissociation energy for methyl attack on alkanes, viz. : E = 30.0 + 0.504[D(R-H) - 38 1.51 kJ mol-1 can be extended to include data for cycloalkanes, oxirane and oxetane. Applying this equation to the activation energies derived here for hydrogen abstraction at the various sites we obtain the following values of dissociation energies in kJ mol-l: D, = 387.5, D, = 398.4, D, = 434.9, Dd = 403.9, D, = 382.3.From these data it can be shown that the relative ease of removal of secondary and tertiary H atoms in an oxetane ring is comparable to the difference between such atoms in open-chain analogues, i.e. D, (sec)- D, (tert) = 5.2 kJ mol-1 cp4 The least reliable of our data are the Arrhenius parameters for the removal of primary H atoms in the methyl side-groups where the A factor and activation energy appear too high by comparison with previously measured values on hydrocarbon^.^ We hope to obtain more reliable values for these parameters from a study of H-atom abstraction from the fully methylated compound hexamethyloxetane in the near future. P. Gray, A. A. Herod and A. Jones, Chem. Rev., 1971, 71, 247. M. G. Duke and K. A. Holbrook, J. Chem. Soc., Faraday Trans. I , 1980, 76, 1232. J. R. McNesby and A. S. Gordon, J. Am. Chem. Soc., 1950,72, 101. D. A. Parkes, D. M. Paul and C. P. Quinn, J . Chem. Soc., Faraday Trans. I , 1976,72, 1935. J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas-phase Hydrogen Transfer Reactions of Methyl Radicals (Butterworths, London, 1976). R. R. Baldwin, Annette Keen and R. W. Walker, J. Chem. SOC., Faraday Trans. I , 1984, 80, 435. ' J. A. Kerr and D. Timlin, J . Chem. SOC. A , 1959, 1241. * A. F. Trotman-Dickenson, J. R. Birchard and E. W. Steacie, J . Chem. Phys., 1951, 19, 163. * W. M. Jackson, J. R. McNesby and B. de B. Darwent, J . Chem. Phys., 1962,37, 1610 and references therein. lo P. Gray and A. A. Herod, Trans. Faraday SOC., 1968, 64, 1568. l1 A. F. Trotman-Dickenson and E. W. R. Steacie, J . Chem. Phys., 1951, 19, 329. '* M. K. Phibbs and B. de B. Darwent, Can. J . Res., Sect. B, 1950, 28, 395. l 3 R. Gomer and W. A. Noyes, J. Am. Chem. Soc., 1950, 72, 101. l4 J. A. Kerr and A. F. Trotman-Dickenson, in Handbook of Chemistry and Physics, ed. C. R. Weast (C.R.C. Press, Boca Raton, 62nd edn, 1982), p. F192. (PAPER 4/445)

ISSN:0300-9599    

DOI:10.1039/F19848003391

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1984,80, 3399-3408 Application of Microelectrodes to the Study of the Li,Li+ Couple in Ether Solvents Part 1 BY J. DAVID GENDERS, WILLIAM M. HEDGES AND DEREK PLETCHER* Department of Chemistry, The University, Southampton SO9 5NH Received 21st March, 1984 The electrodeposition and anodic dissolution of lithium metal in ether *solvents, including tetrahydrofuran, 2-methyltetrahydrofuran, diethyl ether, dioxolane and mixtures of these solvents, each containing LiAsF,, have been studied. It is demonstrated that experiments with microelectrodes (in this work copper discs, area 5 x cm2) lead to high-quality data, free of effects from IR drop even in these low-dielectric-constant solvents. As a result, cyclic- voltammetric and potential-step experiments show that at a freshly deposited lithium surface the Li,Li+ couple is rapid and a film is formed on the surface only relatively slowly.The mechanism and kinetics of the nucleation and growth of lithium metal on a copper substrate have been probed by potential-step experiments from 0 V vs the Li,Li+ reference electrode to values in the range from -40 to -500 mV; well defined rising I against t transients were recorded in response to these potential steps. Double-potential-step experiments have been used to obtain further data for the deposition of lithium and also in a study of the anodic oxidation of the electrodeposited lithium metal. Probably the most significant and exciting development in the battery industry over the last two decades has been that of lithium batteries; batteries based on many solvent/electrolyte combinations and also positive electrode reactions have been investigated and some have reached the market place.These developments have been thoroughly re~iewed.l-~ Many of the lithium secondary batteries employ an aprotic medium containing a lithium salt. There is often uncertainty as to the stability of the media to lithium metal, the kinetics of the Li,Li+ couple, the role of water and other impurities in the electrolyte and the identity and role of surface films on the lithium metal. In fact, solvents have generally been chosen empirically on the basis of lithium cycling efficiency measured by repetitive galvanostatic dissolution and electrodeposition of the lithium metal, e.g. the work of Koch and c o ~ o r k e r s .~ ~ ~ Although many attempts have been made to use modern electrochemical techniques to gain more fundamental knowledge of the Li,Li+ couple, the data are clearly distorted by experimental problems, particularly uncompensated IR drops in the low-dielectric-constant ether solvents and water in the electrolyte medium; recent examples of reports of such studies include those of Takei' and Irr.* Hence our understanding of the Li,Li+ couple lags far behind its practical application in batteries.' In this paper we describe experiments using microelectrodes designed to overcome the problems of uncompensated IR drop even in ether solvents. The use of micro- electrodes for kinetic investigations is on the increaseg and it has been shown that (a) high-quality data may be obtained in poorly conducting media,lo? l1 (b) high rates of steady-state diffusion (of the order DC/r, where D is the diffusion coefficient, C is the 33993400 THE Li,Li+ COUPLE IN ETHER SOLVENTS concentration of electroactive species and r is the radius of the microelectrode) may be obtained, thus allowing the study of fast coupled chemical reactions,12-14 (c) the use of a microelectrode reduces the charging time of the cell and the non-faradaic currents in sweep experiment^,^^^^^ and ( d ) it is possible to form and grow a single nucleus of a meta1l77 and to use the single nucleus for studies of electro~atalysis.~~ It is properties (a) and (c) which make microelectrodes particularly attractive for the present study.Indeed, we shall show that it is possible to obtain high-quality data for the electrodeposition and anodic dissolution of lithium in a range of ether solvents.Moreover, the experiments require only a two-electrode cell and simple instrumentation because the experimental currents (not current densities) are very small; the electrodes were constructed from Cu wires (40 and 80 pm diameter) by sealing into soda glass and polishing so that only a small-area disc was exposed to the electrolyte solution. EXPERIMENTAL Tetrahydrofuran (East Anglia Chemicals), diethyl ether (May and Baker), 2-methyltetra- hydrofuran (Aldrich Chemicals) and 1,3-dioxolane (Aldrich Chemicals) were distilled from sodium metal under a nitrogen atmosphere and propylene carbonate (Aldrich Chemicals) was distilled under reduced pressure from calcium hydride.All the solvents were used immediately after distillation. The electrolyte was always Electrochemical Grade lithium hexafluoroarsonate (USS Agri-Chemicals) and it was used without purification. The solutions were prepared in an Ar circulating atmosphere dry box but the experiments were performed in a closed cell outside the box. Solutions were deoxygenated with high-purity argon (B.O.C. Ltd). All experiments were carried out in a two-electrode cell. The working electrode was prepared from 80 pm diameter (also sometimes 40 pm) copper wire. It was sealed into soda glass using a vacuum pump to collapse the glass on to the wire so that only the end of the wire was exposed. This copper microdisc was polished with 12 pm dry polishing cloth (Wetordry Production) and then repolished between every experiment.The other electrode was prepared by pressing lithium foil (Foote Mineral Co.) onto a platinum wire under an argon atmosphere. The cell was undivided with a volume of ca. 10 cm3. Throughout the paper potentials are quoted uersus the Li,Li+ couple in the same medium as the working electrode. The resistance of the experimental cell filled with THF + LiAsF, (0.6 mol dm-3) was measured using an a.c. bridge and was found to be 5000 n. In this paper only cell currents below 3 pA (current density 60 mA cm-2) have been analysed quantitatively so that the maximum IR drop is 15 mV (in most experiments the currents were lower); note that while the currents are low, the current densities are well into the region of interest in battery technology.In many ways a better test of the absence of significant IR drops is to repeat the experiment with an electrode of different area when only the current should change and there should be no shift in peak potential or changes in shape of transients. In this work two electrodes with areas differing by a factor of four were used for such checks. The potential of the copper microelectrode was programmed using a Hi-Tek function generator model PPR 1. The currents passing through the cell were amplified using a home-built amplifier whose output was displayed either directly on a Farnell XY recorder or stored in a Gould digital oscilloscope type 0s 4100 and then displayed on the XY recorder. RESULTS Fig. 1 shows a cyclic voltammogram run at 100 mV s-l for a Cu microelectrode ( r = 40 pm) in THF + LiAsF, (0.6 mol dm-3) recorded between + 500 and - 200 mV us the Li,Li+ reference electrode in the same solution.It is very similar in shape to a voltammogram reported by Fraser20 for a nickel electrode in propylene carbonate + LiC10, although the current densities obtainable were much lower than in the present study despite the use of a much more highly conducting medium. TheJ. D. GENDERS, W. M. HEDGES AND D. PLETCHER 340 1 Fig. 1. Cyclic voltammogram for a Cu microelectrode (area 5 x cm2) in THF+LiAsF, (0.6 mol dm-3). Potential scan rate 100 mV s-l. first features to be noted are the current-density scale and the nucleation loop at negative potentials. At the potential scan rate used, current is not observed until -90 mV on the forward sweep, but on the reverse scan the current is always higher and reduction continues until almost OmV.This loop is good evidence that the cathodic current is due to lithium deposition; this is confirmed by the shape of the anodic peak on the reverse scan, clearly that for the stripping of a surface layer. The charge for lithium deposition is 0.1 1 C cm-2 and the stripping efficiency ca. 85 % . Other features to be noted are the very low background and charging currents on the forward scan and that the I against E curve on the back sweep passes directly from reduction to oxidation close to 0 mV without a potential region with a low current, good evidence that the Li,Li+ couple is rapid under these conditions.Variation of the negative limit or the potential scan rate had the effects expected on an I against E curve for a metal-deposition process. Making the former more negative increased the charge associated with both the deposition process and the anodic dissolution peak, while increasing the potential scan rate caused nucleation to occur only at more negative potentials and hence led to a decrease in charge for both deposition and dissolution. Experiments on solutions of LiAsF, in dioxolane, 2-methyltetrahydrofuran, prop- ylene carbonate, diethyl ether and a range of THF+diethyl ether mixtures led to I against E curves with very similar characteristics, although the potential where nucleation occurs varies leading to different current densities for the deposition and dissolution processes.The stripping efficiencies, as measured from the curves, generally exceed 80%. Fig. 2 shows the I against E characteristic for a linear potential-sweep experiment where the potential is scanned from + 500 to - 1000 mV at 100 mV s-l. A well formed reduction wave is observed with E; = - 210 mV and a limiting current of 0.18 A ern+ ; the limiting current estimated by assuming spherical diffusion to the Cu microdisc is 0.15 A cm-2 but some additional contribution is to be expected from migration. At more negative potentials the further rise in current is presumably caused by direct cathodic reduction of the solvent. The nucleation and growth of the lithium phase on the copper substrate were3402 THE Li,Li+ COUPLE IN ETHER SOLVENTS 0.5 0 - 0.5 -1.0 E/V vs Li, Li’ Fig.2. Linear potential scan for a Cu microelectrode (area 5 x 1 0-5 cm2) in THF + LiAsF, (0.8 mol drnp3). Potential scan rate 100 mV s-l. studied by a series of potential steps from 0 mV. Currents which increased with time could be recorded when the potential was stepped to any value in the range from - 100 to -400 mV; typical sets of transients at higher overpotentials are shown in fig. 3. Note that the currents start from close to zero (no charging current is observed) and increase over a timescale of 10 ms to 10 s. The rise time of the transients decreases as the potential is made more negative and either the current reaches a plateau value which increases as the overpotential is made more negative or at very negative potentials the current passes through a peak and then decreases towards a steady value. The steady-state currents at the most negative potentials, 0.11 A cm-2, are again close to those expected for mass-transport control.Overall the transients have the features expected for a nucleation and growth process. Analysis of the early part of the rising I against t transients suggests that they follow an I against t2 growth law at low overpotentials and an I against t law at more negative potentials. This might indicate two-dimensional growth but the limiting currents clearly show that continuous growth occurs and deposits equivalent to 10 C cm-2 can readily be formed as coherent layers. In fact, on a much longer timescale than that shown in fig. 3, ca. 50-200 s, the current again increases with time.The plateau current corresponds to the rate of thickening of the lithium layer into the solution. The further increase in current may arise when the lithium layer becomes thick enough for it to grow three-dimensionally, in a macroscopic sense, by extending beyond the bounds of the copper microdisc and over the glass surrounds. When the deposition potential is less negative than - 80 mV, the timescale of the first rising part of the transient extends to 20 s or more and the plateau becomes less well defined; the current continues to increase slowly. At even less negative potentials it becomes increasingly difficult to define a plateau as the ‘short’ and ‘long’ timescale increases in current begin to overlap. Finally at -40 mV a very slowly increasing current is observed (over hundreds of seconds) but the current rises to a value well beyond that expected at such a low overpotential.At -30 mV no nucleation was observed. These experimental observations prevented analysis of the steady-state current as a function of overpotential within the interesting range from 0 to - 100 mV. Hence a series of double-potential-step experiments was carried out. The potential was stepped from 0 to - 150 mV for 4 s and then pulsed back to the potential of interest. Effectively the first pulse is used to form a layer of lithium onJ. D. GENDERS, W. M. HEDGES AND D. PLETCHER h 200 - n Eo 4 150- E ---. U .r( A 100- m c U k 2 5 0 - 0 - 3403 . 5 40-- 2.0 .I -100mV - 80mV -70mV I t 0 1 2 3 4 5 tl s -0.40V -0.30V - 0 .2 5 V - 0 . 2 0 v -0.15V -0.13V -0.1ov I 1 I I 0 1 2 3 4 tls Fig. 3. Plots of current against time responses to potential steps from 0 mV to the potential shown (us the Li,Li+ reference electrode). THF + LiAsF, (0.37 mol dm-9. Cu microelectrode (area 5 x cm2). the copper microdisc and then the rate of growth at the lower negative overpotential can be observed. In such experiments the lithium was found to grow at a steady rate over at least 50 s and the deposition current could be determined over the range from - 10 to - 100 mV. These data, together with the plateau currents from fig. 3, are plotted in fig. 5 and will be discussed later. The anodic dissolution of lithium metal was studied further by a series of double-potential-step experiments. A layer of metal was deposited by applying - 120 mV for 30 s (deposition charge 1.5 C cmP2) and the potential was then stepped to a value in the range 20-600 mV.A set of transients from such experiments is shown in fig. 4. It can be seen that over the potential range 20-175 mV the lithium metal3404 A 70 - PI 60 - 5 5 0 - 4 E ‘x Y 40 c-’ 30-‘ t: .r( E a b) 2 20-< 10 - 0 THE Li,Li+ COUPLE IN ETHER SOLVENTS \ c -120mV 1 0 5 10 15 20 25 30 35 40 45 50 1 , X x x X X . I I I I I I I 1 deposition X X 0 0 0 0 0 0 0 X 8 8 0 0 0 0 0 0 0 0 0 0 0 dissolutionJ. D. GENDERS, W. M. HEDGES AND D. PLETCHER 3405 70 10 0 t 0 10 20 30 40 50 60 70 80 90 100 ti S Fig. 6. Plots of current against time responses for the oxidation of filmed lithium surfaces. Potential step sequence 0 + - 70 mV (30 s) -, open circuit (time shown) + 120 mV.THF+LiAsF, (0.82 mol dmP3); Cu microelectrode (area 5 x cm2). oxidises at an approximately uniform rate at each potential until the layer is depleted. At more positive overpotentials, the I against t transients are more complex and there is evidence that pitting corrosion occurs since initially the current passes through a peak which becomes more marked with increasing overpotential. Fig. 5 shows plots of steady-state current against overpotential for the deposition of lithium and its anodic dissolution. The former are either the plateau values taken from the experiments of the type shown in fig. 3 or the steady-state current immediately the potential has been stepped back to the potential of interest following the deposition of a lithium layer (0.3 C cm-2) at - 150 mV.The anodic currents are taken early in the transients resulting from the double-potential-step experiments, such as those illustrated in fig. 4. The log I against E characteristic in fig. 5 is clearly that for a rapid electron-transfer couple. The current densities are high even at low overpotentials and both log I against ‘I plots are curves which asymptote to the axis. Moreover, at high overpotentials the currents tend to a plateau value, as expected for mass-transport control. Indeed this is the expected form of the curves if the surface electron transfer is in equilibrium on the timescale of the experiment and surface concentrations are determined only by the Nernst equation, i.e. no kinetic information is obtainable or k e > cm s-l.The plateau value of the current density at negative overpotentials corresponds closely to the value predicted by spherical diffusion to the microdisc. On the other hand, at large positive overpotentials the plateau is both higher and less convincing because of the interference of the pitting phenomenon noted above. On standing at open circuit, however, the lithium surface slowly becomes covered with a layer, from reaction with THF, water or the hexafluoroarsonate anion. This is shown by the data in fig. 6, where the deposition of the lithium and its dissolution are separated by periods at open circuit. It can be seen that even a period of 60 s on open circuit causes the dissolution of the lithium to occur at a lower rate.By 120 s the film is apparently fully formed.3406 THE Li,Li+ COUPLE IN ETHER SOLVENTS Table 1. Data taken from cyclic voltammograms recorded between + 500 and - 140 mV at a Cu microelectrode in diethyl ether + THF mixtures. Potential scan rate 30 mV s-l. % diethyl ether in THF [Li+] /mol dm-3 deposition nucleation current at potential - 140 mV /mV /mAcm-2 stripping peak stripping I p efficiency E,/mV /mA cm-2 (%) 0 0.54 10 0.6 25 0.56 50 0.56 60 0.55 90 1 .o 100 0.57 - 90 41 - 70 36 - 80 32 - 70 19 - 80 18 - 60 35 - 60 4 + 170 40 91 +210 35 97 + 190 31 98 + 185 22 86 + 205 16 80 + 195 35 93 + 185 5 80 0.4pA I + 500mV I - 500mV -700mV +1100mV Fig. 7. Cyclic voltammograms as a function of temperature. THF (lO%)+diethyl ether (90% ) + LiAsF, (1.3 mol dmP3); Cu microelectrode (area 5 x cm2); temperatures (a) 290, (6) 270 and ( c ) 213 K.J.D. GENDERS, W. M. HEDGES AND D. PLETCHER 3407 Table 2. Influence of temperature on the deposition and dissolution of lithium metal onto Cu from 90% diethyl ether+ 10% THF containing 1.3 mol dmV3 LiAsF,. Data taken from cyclic voltammograms run at 30 mV s-' potentials where I = 2 mA cm-2/mV nucleation potential/mV deposition dissolution T/K 213 250 290 - 420 -210 - 70 - 520 - 280 - 30 + 590 + 370 + 30 A range of experiments was also carried out in THF+diethyl ether mixtures. The cyclic voltammograms, as reported above, have the same form as that shown in fig. 1 and the similarities are also emphasised by table 1. Pure diethyl ether gave curves of the same general shape but the deposition currents were low.On the other hand, the addition of only 10% THF gave results comparable to those in pure THF and, indeed, may be superior to mixtures containing ca. 50 : 50 THF +ether. Furthermore potential-step experiments carried out in 90 % diethyl ether + 10 % THF gave transients very similar to those of fig. 3. Finally we decided to investigate the influence of temperature on the kinetics of the Li,Li+ couple in one solvent and the 90% diethyl ether+10% THF mixture was selected. Fig. 7 shows cyclic voltammograms run at 30 mV s-l and at temperatures of 213, 250 and 290 K. It is clear that temperature has a very strong influence on the nucleation potential, the rate of mass transport and the kinetics of the Li,Li+ couple, as demonstrated by the form of the I against E curves on the reverse scans.Indeed, in order to see the deposition and dissolution currents it is necessary to extend both the positive and negative potential limits as the temperature is reduced. The influence of temperature can also be seen clearly from the summary in table 2. DISCUSSION The objective of this first study was not to solve particular lithium-battery problems but rather to demonstrate the range of experiments possible with microelectrodes, which are capable of giving an insight into the fundamental electrochemistry of the lithium electrode. Most importantly, therefore, the experiments in this study have shown that it is possible to carry out meaningful and reproducible experiments using the ether-type solvents commonly of interest in rechargeable lithium batteries.Moreover, the experiments employ only a two-electrode cell, the electrodes are easily manufactured and the control circuit is simple and cheap. Such simplicity results from the very low currents passing through the cell with a working-electrode of area 5 x cm2 even when the current density is 0.2 A cmP2; the small electrode area also discriminates for the faradaic current and against the charging current. The use of an even smaller area electrode (here 20 pm radius with area 1.25 x lop5 cm2) is the best test that the results at the 40 pm radius disc were not significantly influenced by IR drop. The cyclic-voltammetry and potential-step experiments all show the kinetics of the Li,Li+ couple on a freshly deposited lithium surface to be very fast.Indeed, the plot of log1 against q shown in fig. 5 suggests that the current is always mass-transport controlled. More practically, the overpotentials required for current densities of 103408 THE Li,Li+ COUPLE IN ETHER SOLVENTS and 100 mA cm-2 are only ca. 80 and 200 mV, respectively, for deposition and dissolution of the metal in THF. The results of fig. 6, however, show that a film readily forms on the lithium surface within a few minutes. Such films have been extensively discussed in the literat~rel-~ and it remains unclear whether the film arises from reaction of the lithium surface with the solvent, trace water or the electrolyte. Even the question as to whether the reaction of the metal with an ether is thermodynamically favourable is yet to be decided but it is unclear whether experiments with microelec- trodes can give a definitive answer.It appears, however, that no film forms during the deposition of the lithium layer. This may be because the metal is cathodically protected at the negative overpotentials or because each surface is fully covered with further lithium before any film can form. The experiments at low temperatures show the kinetics of the Li,Li+ couple to be very strongly influenced by temperature and it is to be expected that the performance of lithium batteries in such solvents would deteriorate substantially as the temperature is lowered. This is, indeed, the case. The form of the I against t responses in the potential-step experiments to negative potentials confirms the essential role of nucleation of the new phase in the deposition of lithium and also that the number density of nuclei is sufficiently large that many nuclei are formed on the microelectrode [cf.ref. (1 8)]. The early part of the transients at low negative potentials can be replotted to give linear I against t2 plots while at more negative potentials the form of the response changes to I against t. This indicates a change from progressive to instantaneous nucleation. Hence it must be concluded that the growth is two-dimensional although the plateau current at longer times confirms that continuous growth occurs. Later papers will consider specific aspects of the lithium electrode in non-aqueous solvents in greater detail. Lithium Batteries, ed. J-P. Gabano (Academic Press, London, 1983). A. N. Dey, Thin Solid Films, 1977, 43, 13 1. N. A. Hampson, M. Hughes and S. A. G. R. Karunathilaka, J. Power Sources, in press. V. R. Koch, J. Power Sources, 1981, 6, 357. J. R. Goldman, R. M. Mank, J. H. Young and V. R. Koch, J. Electrochem. SOC., 1980, 127, 1461. V. R. Koch, J. R. Goldman, C. J. Mattos and M. Mulvaney, J. Electrochem. SOC., 1982, 129, 1. T. Takei, J. Appl. Electrochem., 1979, 9, 587. L. G. Irr, Electrochim. Acta, 1984, 29, 1. R. M. Wightman, Anal. Chem., 1981,53, 1125A. lo R. Lines and V. D. Parker, Acta Chem. Scand. B, 1977, 31, 369. l1 A. M. Bond, M. Fleischmann and J. Robinson, J. Am. Chem. SOC., in press. l2 M. A. Dayton, A. G. Ewing and R. M. Wightman, Anal. Chem., 1980,52, 2392. l3 M. Fleischmann, F. Lasserre, J. Robinson and D. Swan, J. Electroanal. Chem., in press. M. Fleischmann, F. Lasserre and J. Robinson, J. Electroanaf. Chem., in press. l5 R. S. Robinson and R. L. McCreery, Anal. Chem., 1981, 53, 997. l6 R. S. Robinson, C. W. McCurdy and R. L. McCreery, Anal. Chem., 1982,54, 2356. E. Budevski, W. Bostanoff, T. Witanoff, Z. Stoinoff, Z. Kotzewa and R. Kaishev, Electrochim. Acta, 1966, 11, 1697. l8 B. Scharifker and G. J. Hills, J. Electroanal. Chem., 1981, 130, 81. l9 G. A. Gunawardena, D. Pletcher and A. Razaq, unpublished results. 2o E. J. Frazer, J. Electroanal. Chem., 1981, 121, 329. (PAPER 4/463)

ISSN:0300-9599    

DOI:10.1039/F19848003399

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1984,80, 3409-3417 Multiplicity for Isothermal Autocatalytic Reactions in Open Systems Influence of Reversibility and Detailed Balance BY BRIAN F. GRAY AND STEPHEN K. SCOTT* School of Chemistry, Macquarie University, North Ryde, N.S.W. 21 13, Australia AND PETER GRAY Department of Physical Chemistry, University of Leeds, Leeds LS2 9JT Received 27th March, 1984 The prototype autocatalytic reaction A + 2B --+ 3B (rate = k, ab2) leads to a variety of exotic patterns of behaviour, including multistability, ignition, extinction and hysteresis. It also lies at the heart of the simplest models which display sustained oscillatory reaction under well-stirred, isothermal conditions in an open system. The lower-order catalysis A + B -+ 2B (rate = k,ab) and the uncatalysed step A -+ B (rate = k,a) have the same overall stoichiometry and may occur in parallel with the above reaction.The rate constants k, and k, influence the range of residence times over which the exotic patterns can be found. As these two additional steps become more important, such features disappear leaving a monotonic dependence of the stationary-state concentrations on residence time. The conditions for multiplicity etc. in this augmented model can be evaluated analytically in terms of the quotients k,/k,a, and ku/kca;, where a, is the concentration of reactant A in the feed to the reactor. Reversibility also affects the range over which these patterns arise. Each of the three reactions is subject to the same equilibrium constant K, = k,/k-, = k,/k-, = k,/k-,.The influence of K, is revealed clearly by the use of a graphical or flow-diagram approach. The cubic autocatalytic reaction A + 2B -+ 3B, rate = k, ab2 (1) leads to multiple stationary-state extents of conversion under well stirred, isothermal c~nditionsl-~ in an open system. When the autocatalyst B is stable, the dependence of ass on the flow-rate or residence time forms an S-shaped curve. If, however, B participates in a subsequent reaction, such as B + C , rate = k2b more exotic patterns2 such as isolas and mushrooms may be found. Another feature of this two-step scheme is the occurrence of sustained oscillations4 about one or more of the stationary-state solutions. The simplicity of this prototype mechanism is such that the algebra remains tractable throughout, thus allowing a great deal of physical insight into the effects of changing, for example, the catalyst lifetime or the concen- tration of the different species in the feed to the reactor.The same simplicity, however, also leaves this model open to a number of criticisms. One should, for instance, recognize that the lower-order, quadratic analogue of step (1) A+B -+ 2B, rate = k,ab (2) 34093410 ISOTHERMAL AUTOCATALYTIC REACTIONS and the uncatalysed process A -+ B, rate = k,a (3) also have non-zero rates. Furthermore, all chemical reactions are reversible to some greater or lesser extent. Each of steps (1H3) has the same net stoichiometry and hence will have the same changes in the various thermodynamic quantities, A H e , A G e etc.They must also have the same equilibrium constant: This relationship between the rate constants is independent of the concentrations of A and B and will therefore apply away from equilibrium. The inclusion of these three steps, their reverse reactions and the principle of detailed balance [eqn (4)] greatly increases the algebraic effort. However, the flow-diagram approach introduced by Gray and Scott4 affords a very compact route to evaluating the conditions under which multistability is possible even in this more general case. We shall consider a reactor fed by a stream of pure reactant A and from which there is an outflow of all species present. This distinguishes our model from the so-called ‘pool-chemical’ approach5 in which the concentration of the reactant is assumed to be somehow held constant.Our results provide an unequivocal counterexample to the suggestion6 that more than one independent concentration is necessary for multiple stationary states in an isothermal open system. INFLUENCE OF QUADRATIC AND UNCATALYSED REACTIONS ON CONDITIONS FOR MULTIPLICITY : IRREVERSIBLE STEPS The system of irreversible reactions (1)-(3) leads to the governing equation for the rate of change of the reactant concentration in the reactor da - = - k,ab2 - k,ab - k,a+ kf(a, -a) dt where k,, the inverse of the mean residence time z,,,, plays the role of a first-order rate constant and a, is the concentration of A in the inflow. If the autocatalyst is stable and undergoes no further reaction, its concentration is determined uniquely by a and a, at all times.If we assume that no uncatalysed reaction occurs in the inflow before the reactant enters the reactor (we might, for instance, provide the inlet tubes with a cooling jacket) this relationship becomes b = a,-a. (6) The concentration of B cannot vary independently from that of A, so we have a one-variable system. At a stationary state daldt is zero. Eqn (5) and (6) may then be combined to give the condition kf(a,- = kc + kQ ass) -k k,ass* (7) Eqn (7) apparently has five parameters: the rate constants k,, k, and k,, the flow-term kf and the inlet concentration a,. More important, however, are the ratios of theseB. F. GRAY, S. K. SCOTT AND P. GRAY 341 1 Fig. 1. Flow diagram for the autocatalytic reactions (1x3). The reaction-rate curve has a cubic dependence on the extent of conversion (1 -a): it passes through R = z;' for the state of no conversion [( 1 -a) = 01 and through R = 0 for the state of complete conversion [( 1 -a) = 11.For locations of extrema see text. The flow term L has a linear dependence on (1 -a) with a gradient given by z&. The intersections of R and L represent the stationary states of the system. different terms, and we may reduce the number of parameters by introducing the following dimensionless groups : a = a/a, dimensionless reactant concentration zq = k, a,/k, characteristic timescale for quadratic step z, = k , a i / k , characteristic timescale for uncatalysed step zreS = k , a i / k f dimensionless residence time. The stationary-state condition then becomes O r L = R.The right-hand side of this equation, designated R, represents the rate at which A is converted to B via the reaction; the left-hand side, L, gives the net rate of inflow of A to the reactor. These two terms may be plotted as functions of a, or the extent of conversion (1 -a), on a flow diagram (fig. 1). The cubic curve R is zero for the state of complete conversion a = 0 (i.e. a = 0 or 1 -a = 1); it has two extrema, whose locations are given by the roots of the quadratic 3a2 - 2(2 + zsl) a + (1 + zql+ zi1) = 0. For a system such that the quadratic and uncatalysed reactions are slow, and hence z, and z, are large, R has a maximum in the vicinity of a = +ao, i.e. a = or 1 -a = $, and a minimum near to zero conversion, a = a, or 1 -a = 0. If the uncatalysed reaction has a longer characteristic timescale than the quadratic step (k, < kqa, and z, > zq), the minimum in R is achieved for reactant concentrations in excess of the inlet a > a,, 1 -a > 0 and hence to the left of the origin in fig.1. If the timescales for these two steps are equal, zq = z,, the minimum is located at the origin, 1 -a = 0. For zq > z,, the minimum in R occurs at some positive extent of conversion, 1 -a > 0.3412 ISOTHERMAL AUTOCATALYTIC REACTIONS 1 0 Fig. 2. Dependence of the stationary-state extent of conversion (1 - ass) on residence time z,,, : (a) system displaying multiple solutions over some range of residence time; (b) system displaying a unique stationary state for all z,,,. The flow term L is a straight line, with a slope given by 1 /zreS, passing through zero for the state of no conversion when the inflow and outflow would have the same composition. Stationary-state solutions of eqn (8) are given by the intersections of R and L.For very short or for very long residence times (corresponding to flow lines with very steep and very low gradients, respectively), L cuts R once only. These systems have a unique stationary state. In between these extremes, R and L may intersect three times, giving multiple solutions. A typical dependence of the extent of conversion (1 - ass) on the residence time swept out in this way is shown in fig. 2(a). The region of multiplicity is bounded by points of extinction (at low residence times) and ‘ignition’ (at high residence time). The points correspond to values of z,,, at which R and L become tangential. Thus we may identify the condition for multiple stationary states over some range of the residence time with the condition for tangency of the reaction and flow curves.This condition turns out to be independent of z,,,, so the requirements for multiplicity can be expressed in terms of the two chemical timescales z, and zq. Fig. 2(a) is typical of values of z, and zq which permit multiple solutions: fig. 2(b) corresponds to z, and zq such that R and L can nowhere become tangential. Tangency of the reaction-rate curve and flow line arises when R = L andB. F. GRAY, S. K. SCOTT AND P. GRAY 341 3 4 rq-l 2 0 stationary states 1 2 3 4 102 r;1 Fig. 3. Division of zq-z, plane by the marginal condition for tangency for irreversible reaction.System which lie below the locus display multiple stationary states over some range of residence time: those lying above have only unique solutions. 0, Points at which the locus cuts the zq and z, axes, at z ~ l = 1 and at z;' = 1/27, respectively. simultaneously. This leads to the cubic equation 2a3 - ( 5 + oil) a2 + 2(2 + zql) a + ( 1 + z i l + z;') = 0 (9) which has one or three real positive roots. One root exceeds unity, corresponding to negative extents of conversion, and hence is physically unacceptable. The other two roots lie in the range 0 < a < 1 and thus correspond to the points of ignition and extinction. The condition for these to be real is that the discriminant of eqn (9) should be negative, and the corresponding marginal condition for the onset of multiplicity is that the discriminant should become zero.After some manipulation this leads to the following requirement : Gray and Scott have previously considered' selected cases in which steps (1) and (3) occur in parallel but for which step (2) has zero rate (i.e. with zsl + 0). For such a system we see from inequality (10) that multiple stationary states arise if T~ > 27, i.e. k,a: > 27k,. (1 1) If the quadratic step has non-zero rate, but the uncatalysed reaction is ignored (z;l-+ 0) the requirement for multiplicity is zq > 1, i.e. kcao > k,. (12)3414 ISOTHERMAL AUTOCATALYTIC REACTIONS For general non-zero values of k, and k,, inequality (10) divides the z,--zq plane into two regions (fig.3), one for systems which have multiple stationary states and one for systems with unique solutions at all residence times. INFLUENCE OF REVERSIBILITY AND DETAILED BALANCE ON CONDITIONS FOR MULTIPLICITY For a real chemical system with a finite rather than infinite enthalpy change the reverse of steps (1)-(3) will have non-zero rates. The principle of detailed balance also requires that the relationship given by eqn (4) exists between the forward and backward rate constants. The mass-balance equation now gives for the rate of change of reactant concentration * = - k,ab2 + k-, b3 - k,ab+ k-, b2 - k,a+ k-, b+k,(a, -a). dt The stationary-state condition may be written in the form kf(ao-a) = k,b2 ( a - - k i L b ) + k q b ( a - y ) + k , ( a - $ $ ) . (14) Using eqn (4) we see that the terms on the right-hand side of eqn (14) have a common factor and hence (15) kf(a, - a ) = (a - K;' b) (k, b2 + k, b + k,) where K , is the equilibrium constant for the three reactions.Again we have for a stable catalyst b = (a, -a), so eqn (I 5 ) becomes in dimensionless terms (16) 1 % -(1 -a) = [(l +K;')a-K;'] (1 -a)'+-(l -a)+- 1 zres L = R. Using the same approach as before we identify the requirement for multiple solutions with the requirements for tangency of the curves R and L. The condition for tangency is now 2( 1 + K:') a3 - [5 + 7;' + (6 + 7;') K;'] a2 + [2(2 + ~6') + 2(3 + 0;') Kgl] a - ( I +T;'+Z,~)-(~+Z,')K;' = 0. (17) Again, the marginal condition for multiple stationary states is that the discriminant of this cubic equation should vanish.Thus the requirement for multiplicity becomes 27( 1 + K;1)2 z;l < 18( 1 + K;l) [5 + z;l+ (6 + z6') K;'] x [2 + z;' + ( 3 + z;') K;'] - [5 + z;' + (6 + zs') K;'I3 - 54( 1 + Kg')2 [ 1 + ZS' + (2 + ~6') K;']. (18) In the special case that the rate of the quadratic step becomes zero (z;' --+ 0), the right-hand side of eqn (18) reduces to unity and we obtain the simple form z, > 27(1 KC')^, i.e. k,ai > 27k,(l + K L ' ) ~ . (19) The loci corresponding to eqn (1 8) for various values of the equilibrium constant Ke are shown in fig. 4. In general, an increase in the reversibility of the reaction leadsB. F. GRAY, S. K. SCOTT AND P. GRAY 341 5 1 0 2 4 Fig. 4. Division of the zq-z, plane by the marginal condition for tangency for reversible reactions, with equilibrium constants K, = 100, 10 and 1.The limiting form of these loci as K, -, co (irreversible system, see fig. 3) is shown as a dashed line. 1 o2 ‘;I to a decrease in the range of the parameter zq and z, over which multiplicity can be found. For the case in which the forward and reverse rate constants are equal for each step, i.e. for which K, is equal to unity, multiple stationary states require zq > 2 and z, > 108. DISCUSSION The visualization of the condition for multiple stationary states in terms of the tangency of two curves on a flow diagram has been of great help for a system in which the autocatalyst is completely stable. The results emerge in terms of certain inequalities between the forward rate constant for the three different steps and the equilibrium constant. For the simpler, irreversible case, multiplicity requires k,af > kqa, and k,ai > 27k,.The first of these requires that the product of a termolecular rate constant and an initial concentration exceeds a bimolecular rate constant. For collisional processes in general this is not commonly the case. Thus multiple solutions will only be observed for systems which display strong catalytic properties, where the uncatalysed and quadratic processes are very much unfavoured compared with the higher-order step. In circumstances where the autocatalyst B may react further (or decay), this3416 ISOTHERMAL AUTOCATALYTIC REACTIONS approach is still useful. The slope of the loss-line L then becomes a more complicated function2 of the dimensionless residence time and more than two tangencies are possible.This gives rise to isolas or mushrooms for the dependence of the extent of conversion on z,,,. The same inequalities derived above apply to the ranges of zq and z, over which multiplicity may be found, but an additional consideration is the characteristic lifetime or half-life of the catalyst. The appropriate dimensionless measure of this is given by z, = k,ai/k2. Our model applies rigorously to a simple autocatalytic scheme proceeding in a continuously fed, well-stirred reactor (the CSTR). The reactor is fed by a supply consisting of pure reactant A, although we may easily generalize this approach to cover a wider range of inlet compositions. There is a matching outflow of reactants, products and intermediates: the composition of the outflow is the same as that in the reactor.The multiplicity of stationary states displayed here arises because the constant influx of fresh material allows the system to be held away from the unique state of chemical equilibrium appropriate to a closed vessel. An alternative, theoretical framework, commonly invoked to discuss ' open' systems, is the pool-chemical approach, where the concentrations of the major reactants are assumed to be held at some constant level. This is clearly an approximation at best. It also leads to qualitatively different results. Karmann and Hinze have shown6 that the correctly balanced set of reactions (1)-(3) [i.e. these reactions with their reverse steps and rate constants satisfying eqn (4)] taken with A as a pool chemical can have only one real, positive ' stationary state'.For general, non-zero flow rates (non-infinite residence times) our model may give rise to one or three stationary-state extents of conversion, which differ from the state of chemical equilibrium. In the limit of vanishingly small flows (k, -+ a), however, the solution is unique and smoothly approaches the equilibrium composition. Even if the catalyst is not perfectly stable this is the case, and we find that the stationary state has nodal character. The time-dependent concentration histories converge to equilibrium monotonically, without any overshoot, as required.8 If the irreversible quadratic autocatalysis (2) is considered on its own, this limiting form is not obtained2 as k, tends to zero: furthermore the solution may have focal character (damped oscillatory approach) and, for more complex decay rates of the auto~atalyst,~ may even display undamped oscillations. We may regard it as axiomatic that any acceptable chemical model must go over to a unique equilibrium solution which has nodal stability in this closed vessel limit. Such behaviour is achieved by these autocatalytic schemes provided either the reverse rate constants or the rate of the uncatalysed step (or both) are non-zero, no matter how small. It does not arise if all these terms are set equal to zero, even if some autocatalyst is included in the feed. S.K.S. is grateful for an award under the Queen Elizabeth I1 Post-doctoral Fellowship Scheme.B. F. GRAY, S. K. SCOTT AND P. GRAY 3417 K. F. Lin, Can. J. Chem. Eng., 1979, 56,476. P. Gray and S. K. Scott, Chem. Eng. Sci., 1983, 38, 29. S. K. Scott, Chem. Eng. Sci., 1983, 38, 1701. P. Gray and S. K. Scott, Chem. Eng. Sci., 1984, in press. See, e.g., R. J. Field and R. M. Noyes, J. Chem. Phys., 1974, 60, 1877. K-P. Karmann and J. Hinze, J. Chem. Phys., 1980, 72, 5476. P. Gray and S. K. Scott, J. Phys. Chem., 1983, 87, 1835. G. R. Gavalas, Non-linear Differential Equations of Chemically Reacting Systems, Springer Tracts in Natural Philosophy, vol. 17 (Springer, Berlin, 1968). S. K. Scott, J. Chem. SOC., Faraday Trans. 2, 1985, 81, in press. (PAPER 4/504) 111

ISSN:0300-9599    

DOI:10.1039/F19848003409

出版商:RSC    

年代:1984

数据来源: RSC