摘要:

Model for Analysing Diffusion in Zeolite Crystals BY KLAUS FIEDLER AND DAVID GELBIN" Central Institute of Physical Chemistry, Academy of Sciences of the German Democratic Republic, 1 199-Berlin-Adlershof, Berlin, D.D.R. Received 6th April, 1977 A model is presented which describes the concentration dependence of the effective diffusion coefficient in a zeolite crystal on the basis of a statistical thermodynamic equilibrium analysis. If there is a distribution of cavities occupied by differing numbers of molecules at any average level of adsorption, a large number of rate parameters is involved, since intrinsic diffusion coefficients from one cavity to another are able to vary with the number of molecules adsorbed per cavity. The experimentally determined effective dHusivity depends 011 concentration in a manner determined by the values of the intrinsic diffusion coefficients and the thermodynamic parameters.Only if rather restrictive assumptions are made does our model reduce to Darken's law. reported in the literature are interpreted by our correlation. Adsorption- rate data EQUILIBRIUM CONSIDERATIONS developed and applied by Hilly1 Bakaev,2 RuthvenY3 Fiedler therms are correlated by eqn (1) A statistical-thermodynamic method of analysing adsorption f' iQili m i = 1 = N , 8, = N,O, a = N , ~ i = l I + QiAi i = 1 where e, = f ie, i = 1 and equilibria has been and B r a ~ e r . ~ Iso- l = exp (p/RT). (4) Eqn (1) permits different numbers of molecules i to occupy the cavities with different standard canonical partition functions Qi.The Oi, 0 d i d my are the fractions of the I?, cavities occupied by i molecules. The standard values of Q, p and L are related to the gas state at the temperature T and the molar volume equal to RTo/Po, with Po = 101 325 Pa and To = 273.15 K. Since at equilibrium pads = pgas, for an ideal gas 1-77 24232424 DIFFUSION MODEL FOR ZEOLITE CRYSTALS In addition, The constants N,, Si and Ei can be determined by curve-fitting over a range of experimental temperatures and pressures. Qi = exp [i(SjT-Ei)/RT]. (6) MASS TRANSFER MODEL In our kinetic model we will consider molecules inside the crystal lattice to be in two different states ; (1) a localised or adsorbed state at sites of minimum free energy within the cavities and (2) a mobile state at sites close to or within the windows connecting cavities.Localised molecules will not jump directly between positions of minimum free energy in adjacent cavities, but are assumed to move in two separate steps : a change of position within the cavity from a site of minimum free energy to a site close to the window, followed by a jump through the window to the next cavity. At any moment in time only a small number of molecules will be in the mobile state, The symbol Ci indicates the concentration of cavities holding i molecules of adsorbate, one of which is in the mobile state, where i will be called the occupation level. Further, qi is the concentration of cavities holding i molecules, all of which are in the adsorbed state. In accordance with the basic assumptions of statistical mechanics, the mole- cules are indistinguishable and there is a continuous exchange of molecules between the two states.The localisation or adsorption reaction is Ci 4 qi* (7) Ci + qi (8) whereas exchange of a mobile molecule between a cavity holding i molecules, one of which is mobile, and a cavity holding j-1 molecules, all of which are adsorbed is Ci +qj-l + Q i - l f C j . We neglect the possibility of more than one mobile molecule existing within a cavity. The rate of eqn (9) will be described by a diffusion mechanism. It can easily be shown that if the adsorption reaction, eqn (8), is the rate limiting step, the calculation of diffusion coefficients from sorption rate data will lead to a strong dependence of the apparent diffusivity on crystal size. This aspect of the problem will not be treated in the current work, we will assume instead that local equilibrium is established between the mobile and adsorbed phases, (9) where pi is the probability that one of i molecules in a cavity will be in the mobile state. The model proposed is similar to that of Ruthven and Derrah,6 except that their " activated transition state " is in equilibrium with the entire adsorbed phase irres- pective of occupation level distribution whereas in eqn (10) the equilibrium fraction of mobile molecules is allowed to vary with cavity occupation level.Referring to eqn (1)-(3)9 Oi is the fraction of cavities holding i molecules relative to the total number of cavities.K. FIEDLER AND D. GELBIN 2425 The flux from cavities at a given occupation level will be proportional to Ci; the fraction of mobile molecules entering cavities at a given occupation level will be proportional to Oi.The net flux according to eqn (9) between two adjacent layers of cavities separated by a distance of AZ, (see fig. I), is Di,j-1 is the intrinsic diffusivity of the mobile phase moving from cavities occupied by i to those occupied by j - 1 molecules. The diffusivity is considered to depend on occupation level since molecules adsorbed within the cavity may impede passage of the mobile phase. The prime is chosen to denote the gradient. I df FIG. 1.-Sketch of mass balance section. The assumption of local equilibrium requires that the exchange of molecules among cavities does not alter the distribution of occupation levels, so that in accord- ance with the Onsager relation Eqn (13) may be more readily understood when, after introducing eqn (10) and rearranging, it is written as Di,j-i ciej-, = Dj,i-1 cjOi-1.(1 3) This is the well-known relation where the equilibrium constant K is equal to the ratio of the rate constants for the forward and reverse reactions. It should be noted that the Di,j-l terms have been defined as the intrinsic diffusivities of the mobile phase. Having assumed rapid establishment of local adsorption equilibrium, we may call the Di,j-lpi terms the intrinsic diffusivities of the adsorbed phase. On the basis of adsorption uptake experiments it should not be possible to determine Di,j-l and p i separately, but only their products. The introduction of the product of two constants as a symbol for the diffusivity of the adsorbed phase may appear to be a purely formal step, and will have no effect on the interpretation of experimental results below.However, as has been mentioned, the concept can be useful in explaining the dependence of the apparent diffusivity on crystal size if local equilibrium is not rapidly established. Substituting eqn (lo), (11) and (13) into eqn (12) and gathering the terms,2426 DIFFUSION MODEL FOR ZEOLITE CRYSTALS The relation between chemical potential gradient and concentration gradient will now be treated. On the basis of eqn (1)-(4) we readily derive ae. 1 -' = -(i - Oa)Oi ap RT so that e! 1 ei RT 2 = -(i-O&'. Calculating on the basis of the total amount adsorbed, or, referring again to eqn (l), fl' a' _ - m - N , C i(i-Oa)Oi RT i = 1 From eqn (15) and (17) P' J ~ , ~ - .= -N=D;,~- lpieioj- - RT The fluxes at the individual occupation levels have now been related to the common chemical potential gradient, so they may be summed to give the total flux Introducing eqn (19) ni m C i ( k O a ) 8 i i = l For evaluation of the adsorption uptake experiments Fick's law is usually applied in the form where D, is the effective or overall diffusion coefficient. J, = -D,a' (23) Comparing eqn (22) and (23) m m C i(i-0a)6i i = 1 Owing to the equilibrium restriction, eqn (1 3), not all intrinsic diffusivities in eqn (24) may be chosen independently. Combining eqn (24) and (13) m m i - 1K . FIEDLER AND D . GELBlN 2427 Eqn (25) is the working equation of our model, permitting interpretation of experi- mental effective diffusivities at different adsorption concentrations on a sound thermodynamic basis.The intrinsic diffusivities in eqn (25) are all independent. The first sum in the numerator includes all diffusivities between cavities at occupation levels differing by only one, i.e. where the right- and left-hand sides of the reaction equation are identical. This is eqn (9) for j = i. Exchange of molecules between these cavities does not affect occupation level distribution and the diffusivities are not restricted by eqn (13). The second sum in the numerator of eqn (25) includes the diffusivities between cavities at occupation levels differing by more than one. Exchange of molecules between these cavities influences occupation level distribution, but since eqn (13) has been applied, the diffusivities within the summation limits are independent.The numerator requires the summation over all cavities of the intrinsic diffusivities of the mobile phase, multiplied by p i , the probability that a molecule is mobile, multiplied by 8i8j-l, the probability that a cavity occupied by i molecules will have a neighbour occupied by j - 1 molecules. The denominator of eqn (25) is the reciprocal of the chemical potential gradient with respect to total amount adsorbed, eqn (19). Before analysing experimental results with eqn (25), the compatibility of this expression with the commonly used Darken equation Ci + qi- 1 + 4i- 1 + Ci will be investigated. D* is generally termed the self-diffusivity.It is necessary to make rather restrictive assumptions to derive eqn (26) from (25). We do not necessarily consider the following assumptions to be either likely or plausible. On the contrary, we are pointing out that, accepting the validity of our derivation, authors using the Darken equation for zeolitic systems involving multiple occupation levels are themselves tacitly making these assumptions. (1) The Di, i-lpi term will be assumed proportional to the occupation level, Di,i-Ipi = i Dx.x-1Px (27) where Dx,x-l and p x are constants. specific function of Dx,x-lpx, Eqn (28) is appropriate in the sense that it leads to the desired result, since eqn (14) and (28) yield (2) The remaining intrinsic diffusion coefficients will be expressed as an appropriate Di,j-IPi = ~ D x , x - i P x ( i + j K j , i - I , i , j - i ) * (28) which is useful in simplifying the numerator of eqn (25).Introducing eqn (1 S ) , (27) and (29) into eqn (25), rearranging, and gathering terms, Since the summation over i equals 8, and that over j equals2428 DIFFUSION MODEL FOR ZEOLITE CRYSTALS (3) The application of eqn (31) will be restricted to concentration ranges where 8, < 1. One might also assume that cavities apparently saturated with m molecules within the experimental range of temperatures and pressures still permit passage of one additional mobile molecule, so that all cavities contribute to the total flux. Then, the limits for j in eqn (30) become 1 < j < m+ 1, and which is equivalent to Darken’s law, eqn (26), with Eqn (33) relates Darken’s self-diffusivity to our intrinsic diffusivity, if eqn (27) and Considering the nature of the restrictions involved, it appears unlikely that Darken’s equation should be applied to zeolitic systems with multiple occupation levels.Another simplified, but not necessarily more plausible, equation is derived if, instead of eqn (27) and (28), it is assumed that the Di, i-lpi terms are independent of occupation level, lI* = Dx,x-lpx* (33) (28) apply. and Introducing eqn (18), (34) and (35) into eqn (25) Since only one diffusivity is needed for the simplified eqn (31) and (36), they may be useful for curve-fitting the concentration dependence of the measured effective diffusivity where computer routines are not available, or where insufficient data do not warrant detailed analysis.COMPARISON WITH PUBLISHED DATA Recently Ruthven and Doetsch published thermodynamic and kinetic data for four hydrocarbons in 13X zeolite crystals at four different temperatures. Of particular interest are the diffusivities of n-heptane which go through a minimum with increasing sorbate concentration. This behaviour cannot be explained satis- factorily by the Darken equation. Below we demonstrate the ability of our model to analyse data read from photographic enlargements of the figures in ref. (7). TABLE 1 .-THERMODYNAMIC CONSTANTS N ~ l p i si Ei 0.49 1 -56.8 -53 600 2 -77.0 -63 000 3 -91.6 -66300 The thermodynamic constants obtained by fitting the equilibrium isotherms between 409 and 488 K to eqn (1)-(6) are listed in table 1.Both the entropy and the adsorption energy increase negatively with loading. The number of effective cavities per unit weight NJp is only0.82 of the theoreticalvalue given in ref. (7) ; the saturationK . FIEDLER A N D D. GELBIN 2429 occupation level is m = 3. With these constants and eqn (1)-(6) the Bi values have been calculated for all experimental conditions; an example is given in fig. 2 at 458 K. Cavity loading varies from zero to three molecules, and over the entire concentration range different occupation levels exist side by side, as was also observed in ref. (5). 1 0 eCd-1 FIG. 2.-Distribution of cavity occupation densities against total amount adsorbed ; n-heptane and zeolite 13X at 458 K.7 In fitting eqn (25) to the rate data in ref.(7) it was not possible to determine the intrinsic diffusivities between cavities at occupation levels differing by more than one to any satisfactory degree of statistical significance. Average values were either close to zero or negative; the standard deviation was extremely large. The accuracy of the remaining diffusivities also suffered from the error in the faulty coefficients. TABLE 2.-DATA FOR COMBINATIONS OF CAVITY OCCUPATION LEVELS, T = 437 K occupation levels r i, j - 1 10 20 30 21 31 32 average .elative - weight Fj 0.234 0.175 0.01 8 0.195 0.040 0.338 equilibrium constant e i e j - , p j e i - , 1 1.37 0.092 1 0.067 1 It appears that major contributions to flow are derived only from molecules jumping between cavities differing by one in occupation level.This fact may be partly explained by an examination of the factors Fj,j-l = Fi,j-l/( Fi,j-l), S J where F;, j - 1 are the relative weights of the intrinsic diffusivities according to eqn (25). The average values F ; , j - 1 over the entire concentration range at 437 K are listed in table 2. Since the relative weight of D30p3 is only 0.018 and that of D31p3 only2430 DIFFUSION MODEL FOR ZEOLITE CRYSTALS 0.040, that is, < 5 % of the total contribution, it is not surprising that these diffusivities cannot be determined by curve-fitting to any degree of accuracy. However, the relative weight of DZ0pZ is 17.5 % of the total. The equilibrium constants have also been calculated according to eqn (3), (6) and (14) and the data in table 1, and are given in the last column of table 2.Whereas the ratio 8380/8182 is only 0.092 and 0301/8~ is only 0.067, the equilibrium ratio 6,8,/8? is determined to be 1.37. The values at the other temperatures are related to each other in a similar manner. The extremely low diffusivity DZ0p2 determined by curve-fitting the kinetic data is a result of the high relative weighting factor. There is a discrepancy between the thermo- dynamic results, indicating a high probability that cavities occupied by two molecules have empty neighbours, and the kinetic results, indicating that jumps from cavities holding two molecules into empty cavities are not contributing appreciably to total flow. In eqn (12) we have assumed that a cavity holding i molecules will have a number of neighbours holding j - 1 molecules proportional to 6,-1.Fowler-Guggenheim statistics * however would lead to a higher probability that empty cavities have neighbours holding one molecule than those holding two, without necessarily changing appreciably the total cavity distribution as determined by eqn (1)-(6). The possibility of applying Fowler-Guggenheim statistics to our kinetic model warrants further study. Neglecting the second sum in the numerator of eqn (25) and limiting curve fitting to determination of the Di,i-Ipi values, the accuracy of the individual diffusivities is very good, see table 3. TABLE 3.-INTRINSIC DIFFUSION COEFFICIENTS (lo-' Cm2 S-I) T 409K 438K 458K 488K DlOPl 0.65 1.02 1.51 2.14 f 0.11 0.04 0.04 0.05 D21P2 0.71 1.14 1.53 1.99 - + 0.07 0.04 0.07 0.08 D32P3 0.68 0.85 1.14 1.71 0.01 0.01 0.03 0.08 CT curve 0.03 0.02 0.04 0.04 The overall dependence of D, on sorbate concentration calculated with the constants given in tables 1 and 3 for the four temperatures studied is shown as solid lines in fig.3 and compared with the experimental points. The standard deviation of the entire curve is listed in the last row of table 3. Agreement is highly satisfactory, except for slight deviations near 8, = 1 at 458 K. The three intrinsic diffusion coefficients in table 3 are about equal at the lowest temperature, but there is a clear tendency for D3,p3 to drop behind the other values as the temperature increases. This may mean that at 488 K the vibration of sorbate molecules within the cavity has increased to a point where passage through the cavity at high occupation level is impeded.Neglecting differences in the Di, i-lpi, the minimum in the effective diffusion coefficient with increasing concentration is caused by the nature of the total weighting factor m i= 1K . FIEDLER AND D. GELBIN 243 1 This is the total probability that a cavity will have a neighbour occupied by one less molecule than itself, multiplied by the statistical thermodynamic expression for the rate of change of chemical potential with respect to cavity loading. Darken's law cannot give a good description of the results, since the intrinsic diffusivities of the adsorbed phase do not increase proportionally to occupation level, 1.2- 7.0- ~ 0.8- I, 3 I 2 6 0.6- 0.4 - 0.2- as required by eqn (27), but The average activation 0.4 kcal mol-1 in agreement actually decrease slightly.energy of the intrinsic diffusion coefficients is 6.0+ with the activation energy of D, given in ref. (7). 0 -pe49J a I c o- 2.b 3.0 42[-1 FIG, 3.-Experimental diffusion coefficient against total amount adsorbed ; n-heptane and zeolite 13X at 0,488 ; a, 458 ; 0,438 and A, 409 K.' CONCLUSIONS (1) A model has been presented and equations derived which interpret adsorption rate data on the basis of a statistical thermodynamic approach, taking into account2432 DIFFUSION MODEL FOR ZEOLITE CRYSTALS the discrete cavity structure of zeolites. In contrast to previous kinetic models, the diffusion coefficients may vary with local cavity occupation level. (2) The validity of the Darken equation in zeolitic systems involving multiple occupation levels is dependent on restrictive assumptions compared with the general model.(3) In one system reported in the literature, contribution to flow appears to come mainly from molecular jumps between pairs of cavities differing in occupation level by just one. At elevated temperatures intrinsic diffusivity decreases if occupation level is high, indicating blockage of passage by previously adsorbed molecules. Nevertheless, the effective overall diffusion coefficient goes through a minimum with increasing concentration and then rises at higher zeolite loading. This behaviour is determined by the total probability that a cavity will have a neighbour occupied by one less molecule than itself, multiplied by the rate of change of chemical potential with respect to zeolite loading.T. L. Hill, Thermodynamics ojSmall Systems (N.Y.-Amsterdam, 1964), part 11. V. A. Bakaev, Doklady Acad. Nauk S.S.S.R., 1967,167,369. D. M. Ruthven, Nature, Phys. Sci., 1971,232, 70. (Liblice/CSSR, 1975), p. 194-223. P. Brauer, A. Lopatkin and G. Stepanez, Adv. Chem., 1971, 102,97. D. M. Ruthven and R. I. Derrah, J.C.S. Faraday Z, 1972, 68, 2332. R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, New York, 1939). 4K. Fiedler, H. Stach and W. Schirmer, Proc. 2nd Czechoslovak Con5 Physical Adsorption ' D. M. Ruthven and I. H. Doetsch, Amer. Znst.Chem.Eng. J., 1976, 22, 882. (PAPER 7/609) NOMENCLATURE a Ci D" Di, j - 1 &,x- 1 D Z E F i J K AI rn Nc p g a s Q Pi 4i total amount adsorbed, eqn (1) concentration of cavities holding i molecules, one of which is mobile self diffusivity in the Darken equation (26) intrinsic diffusivity of molecules moving from cavity with i mole- cules to one with j - 1 molecules intrinsic diffusivity between all pairs of cavities differing in occupa- tion level by one, assumed constant effective overall diffusivity measured in adsorption uptake experi- ment energy of adsorption relative weighting factor, eqn (37) number of molecules in cavity, also called occupation level flux adsorption equilibrium const ant distance between cavities saturation number of molecules per cavity total number of cavities gas pressure probability that one of i molecules in cavity will be mobile standard canonic partition function concentration of cavities holding i molecules, all of which are adsorbed rnol ~ m - ~ rnol CM-~ cm2 s-l cm2 s-l cm2 s-l cm2 s-l J mo1-1 I mol cm-2 s-l cm rnol CM-~ Pa - - - - rnol ~ m - ~K.FIEDLER AND D. GELBIN R gas constant r radial coordinate S standard entropy T temperature 8i a standard chemical activity P standard chemical potential P fraction of cavities holding i molecules, eqn (1 1) specific gravity of zeolite crystal 2433 J K-' mo1-I cm J K-' mol-I K - - J mol-' g C M - ~ Model for Analysing Diffusion in Zeolite Crystals BY KLAUS FIEDLER AND DAVID GELBIN" Central Institute of Physical Chemistry, Academy of Sciences of the German Democratic Republic, 1 199-Berlin-Adlershof, Berlin, D.D.R. Received 6th April, 1977 A model is presented which describes the concentration dependence of the effective diffusion coefficient in a zeolite crystal on the basis of a statistical thermodynamic equilibrium analysis.If there is a distribution of cavities occupied by differing numbers of molecules at any average level of adsorption, a large number of rate parameters is involved, since intrinsic diffusion coefficients from one cavity to another are able to vary with the number of molecules adsorbed per cavity. The experimentally determined effective dHusivity depends 011 concentration in a manner determined by the values of the intrinsic diffusion coefficients and the thermodynamic parameters. Only if rather restrictive assumptions are made does our model reduce to Darken's law. reported in the literature are interpreted by our correlation.Adsorption- rate data EQUILIBRIUM CONSIDERATIONS developed and applied by Hilly1 Bakaev,2 RuthvenY3 Fiedler therms are correlated by eqn (1) A statistical-thermodynamic method of analysing adsorption f' iQili m i = 1 = N , 8, = N,O, a = N , ~ i = l I + QiAi i = 1 where e, = f ie, i = 1 and equilibria has been and B r a ~ e r . ~ Iso- l = exp (p/RT). (4) Eqn (1) permits different numbers of molecules i to occupy the cavities with different standard canonical partition functions Qi. The Oi, 0 d i d my are the fractions of the I?, cavities occupied by i molecules. The standard values of Q, p and L are related to the gas state at the temperature T and the molar volume equal to RTo/Po, with Po = 101 325 Pa and To = 273.15 K. Since at equilibrium pads = pgas, for an ideal gas 1-77 24232424 DIFFUSION MODEL FOR ZEOLITE CRYSTALS In addition, The constants N,, Si and Ei can be determined by curve-fitting over a range of experimental temperatures and pressures.Qi = exp [i(SjT-Ei)/RT]. (6) MASS TRANSFER MODEL In our kinetic model we will consider molecules inside the crystal lattice to be in two different states ; (1) a localised or adsorbed state at sites of minimum free energy within the cavities and (2) a mobile state at sites close to or within the windows connecting cavities. Localised molecules will not jump directly between positions of minimum free energy in adjacent cavities, but are assumed to move in two separate steps : a change of position within the cavity from a site of minimum free energy to a site close to the window, followed by a jump through the window to the next cavity.At any moment in time only a small number of molecules will be in the mobile state, The symbol Ci indicates the concentration of cavities holding i molecules of adsorbate, one of which is in the mobile state, where i will be called the occupation level. Further, qi is the concentration of cavities holding i molecules, all of which are in the adsorbed state. In accordance with the basic assumptions of statistical mechanics, the mole- cules are indistinguishable and there is a continuous exchange of molecules between the two states. The localisation or adsorption reaction is Ci 4 qi* (7) Ci + qi (8) whereas exchange of a mobile molecule between a cavity holding i molecules, one of which is mobile, and a cavity holding j-1 molecules, all of which are adsorbed is Ci +qj-l + Q i - l f C j .We neglect the possibility of more than one mobile molecule existing within a cavity. The rate of eqn (9) will be described by a diffusion mechanism. It can easily be shown that if the adsorption reaction, eqn (8), is the rate limiting step, the calculation of diffusion coefficients from sorption rate data will lead to a strong dependence of the apparent diffusivity on crystal size. This aspect of the problem will not be treated in the current work, we will assume instead that local equilibrium is established between the mobile and adsorbed phases, (9) where pi is the probability that one of i molecules in a cavity will be in the mobile state.The model proposed is similar to that of Ruthven and Derrah,6 except that their " activated transition state " is in equilibrium with the entire adsorbed phase irres- pective of occupation level distribution whereas in eqn (10) the equilibrium fraction of mobile molecules is allowed to vary with cavity occupation level. Referring to eqn (1)-(3)9 Oi is the fraction of cavities holding i molecules relative to the total number of cavities.K. FIEDLER AND D. GELBIN 2425 The flux from cavities at a given occupation level will be proportional to Ci; the fraction of mobile molecules entering cavities at a given occupation level will be proportional to Oi. The net flux according to eqn (9) between two adjacent layers of cavities separated by a distance of AZ, (see fig.I), is Di,j-1 is the intrinsic diffusivity of the mobile phase moving from cavities occupied by i to those occupied by j - 1 molecules. The diffusivity is considered to depend on occupation level since molecules adsorbed within the cavity may impede passage of the mobile phase. The prime is chosen to denote the gradient. I df FIG. 1.-Sketch of mass balance section. The assumption of local equilibrium requires that the exchange of molecules among cavities does not alter the distribution of occupation levels, so that in accord- ance with the Onsager relation Eqn (13) may be more readily understood when, after introducing eqn (10) and rearranging, it is written as Di,j-i ciej-, = Dj,i-1 cjOi-1. (1 3) This is the well-known relation where the equilibrium constant K is equal to the ratio of the rate constants for the forward and reverse reactions.It should be noted that the Di,j-l terms have been defined as the intrinsic diffusivities of the mobile phase. Having assumed rapid establishment of local adsorption equilibrium, we may call the Di,j-lpi terms the intrinsic diffusivities of the adsorbed phase. On the basis of adsorption uptake experiments it should not be possible to determine Di,j-l and p i separately, but only their products. The introduction of the product of two constants as a symbol for the diffusivity of the adsorbed phase may appear to be a purely formal step, and will have no effect on the interpretation of experimental results below. However, as has been mentioned, the concept can be useful in explaining the dependence of the apparent diffusivity on crystal size if local equilibrium is not rapidly established.Substituting eqn (lo), (11) and (13) into eqn (12) and gathering the terms,2426 DIFFUSION MODEL FOR ZEOLITE CRYSTALS The relation between chemical potential gradient and concentration gradient will now be treated. On the basis of eqn (1)-(4) we readily derive ae. 1 -' = -(i - Oa)Oi ap RT so that e! 1 ei RT 2 = -(i-O&'. Calculating on the basis of the total amount adsorbed, or, referring again to eqn (l), fl' a' _ - m - N , C i(i-Oa)Oi RT i = 1 From eqn (15) and (17) P' J ~ , ~ - . = -N=D;,~- lpieioj- - RT The fluxes at the individual occupation levels have now been related to the common chemical potential gradient, so they may be summed to give the total flux Introducing eqn (19) ni m C i ( k O a ) 8 i i = l For evaluation of the adsorption uptake experiments Fick's law is usually applied in the form where D, is the effective or overall diffusion coefficient.J, = -D,a' (23) Comparing eqn (22) and (23) m m C i(i-0a)6i i = 1 Owing to the equilibrium restriction, eqn (1 3), not all intrinsic diffusivities in eqn (24) may be chosen independently. Combining eqn (24) and (13) m m i - 1K . FIEDLER AND D . GELBlN 2427 Eqn (25) is the working equation of our model, permitting interpretation of experi- mental effective diffusivities at different adsorption concentrations on a sound thermodynamic basis. The intrinsic diffusivities in eqn (25) are all independent. The first sum in the numerator includes all diffusivities between cavities at occupation levels differing by only one, i.e.where the right- and left-hand sides of the reaction equation are identical. This is eqn (9) for j = i. Exchange of molecules between these cavities does not affect occupation level distribution and the diffusivities are not restricted by eqn (13). The second sum in the numerator of eqn (25) includes the diffusivities between cavities at occupation levels differing by more than one. Exchange of molecules between these cavities influences occupation level distribution, but since eqn (13) has been applied, the diffusivities within the summation limits are independent. The numerator requires the summation over all cavities of the intrinsic diffusivities of the mobile phase, multiplied by p i , the probability that a molecule is mobile, multiplied by 8i8j-l, the probability that a cavity occupied by i molecules will have a neighbour occupied by j - 1 molecules.The denominator of eqn (25) is the reciprocal of the chemical potential gradient with respect to total amount adsorbed, eqn (19). Before analysing experimental results with eqn (25), the compatibility of this expression with the commonly used Darken equation Ci + qi- 1 + 4i- 1 + Ci will be investigated. D* is generally termed the self-diffusivity. It is necessary to make rather restrictive assumptions to derive eqn (26) from (25). We do not necessarily consider the following assumptions to be either likely or plausible. On the contrary, we are pointing out that, accepting the validity of our derivation, authors using the Darken equation for zeolitic systems involving multiple occupation levels are themselves tacitly making these assumptions.(1) The Di, i-lpi term will be assumed proportional to the occupation level, Di,i-Ipi = i Dx.x-1Px (27) where Dx,x-l and p x are constants. specific function of Dx,x-lpx, Eqn (28) is appropriate in the sense that it leads to the desired result, since eqn (14) and (28) yield (2) The remaining intrinsic diffusion coefficients will be expressed as an appropriate Di,j-IPi = ~ D x , x - i P x ( i + j K j , i - I , i , j - i ) * (28) which is useful in simplifying the numerator of eqn (25). Introducing eqn (1 S ) , (27) and (29) into eqn (25), rearranging, and gathering terms, Since the summation over i equals 8, and that over j equals2428 DIFFUSION MODEL FOR ZEOLITE CRYSTALS (3) The application of eqn (31) will be restricted to concentration ranges where 8, < 1.One might also assume that cavities apparently saturated with m molecules within the experimental range of temperatures and pressures still permit passage of one additional mobile molecule, so that all cavities contribute to the total flux. Then, the limits for j in eqn (30) become 1 < j < m+ 1, and which is equivalent to Darken’s law, eqn (26), with Eqn (33) relates Darken’s self-diffusivity to our intrinsic diffusivity, if eqn (27) and Considering the nature of the restrictions involved, it appears unlikely that Darken’s equation should be applied to zeolitic systems with multiple occupation levels.Another simplified, but not necessarily more plausible, equation is derived if, instead of eqn (27) and (28), it is assumed that the Di, i-lpi terms are independent of occupation level, lI* = Dx,x-lpx* (33) (28) apply. and Introducing eqn (18), (34) and (35) into eqn (25) Since only one diffusivity is needed for the simplified eqn (31) and (36), they may be useful for curve-fitting the concentration dependence of the measured effective diffusivity where computer routines are not available, or where insufficient data do not warrant detailed analysis. COMPARISON WITH PUBLISHED DATA Recently Ruthven and Doetsch published thermodynamic and kinetic data for four hydrocarbons in 13X zeolite crystals at four different temperatures. Of particular interest are the diffusivities of n-heptane which go through a minimum with increasing sorbate concentration.This behaviour cannot be explained satis- factorily by the Darken equation. Below we demonstrate the ability of our model to analyse data read from photographic enlargements of the figures in ref. (7). TABLE 1 .-THERMODYNAMIC CONSTANTS N ~ l p i si Ei 0.49 1 -56.8 -53 600 2 -77.0 -63 000 3 -91.6 -66300 The thermodynamic constants obtained by fitting the equilibrium isotherms between 409 and 488 K to eqn (1)-(6) are listed in table 1. Both the entropy and the adsorption energy increase negatively with loading. The number of effective cavities per unit weight NJp is only0.82 of the theoreticalvalue given in ref. (7) ; the saturationK . FIEDLER A N D D. GELBIN 2429 occupation level is m = 3.With these constants and eqn (1)-(6) the Bi values have been calculated for all experimental conditions; an example is given in fig. 2 at 458 K. Cavity loading varies from zero to three molecules, and over the entire concentration range different occupation levels exist side by side, as was also observed in ref. (5). 1 0 eCd-1 FIG. 2.-Distribution of cavity occupation densities against total amount adsorbed ; n-heptane and zeolite 13X at 458 K.7 In fitting eqn (25) to the rate data in ref. (7) it was not possible to determine the intrinsic diffusivities between cavities at occupation levels differing by more than one to any satisfactory degree of statistical significance. Average values were either close to zero or negative; the standard deviation was extremely large.The accuracy of the remaining diffusivities also suffered from the error in the faulty coefficients. TABLE 2.-DATA FOR COMBINATIONS OF CAVITY OCCUPATION LEVELS, T = 437 K occupation levels r i, j - 1 10 20 30 21 31 32 average .elative - weight Fj 0.234 0.175 0.01 8 0.195 0.040 0.338 equilibrium constant e i e j - , p j e i - , 1 1.37 0.092 1 0.067 1 It appears that major contributions to flow are derived only from molecules jumping between cavities differing by one in occupation level. This fact may be partly explained by an examination of the factors Fj,j-l = Fi,j-l/( Fi,j-l), S J where F;, j - 1 are the relative weights of the intrinsic diffusivities according to eqn (25). The average values F ; , j - 1 over the entire concentration range at 437 K are listed in table 2.Since the relative weight of D30p3 is only 0.018 and that of D31p3 only2430 DIFFUSION MODEL FOR ZEOLITE CRYSTALS 0.040, that is, < 5 % of the total contribution, it is not surprising that these diffusivities cannot be determined by curve-fitting to any degree of accuracy. However, the relative weight of DZ0pZ is 17.5 % of the total. The equilibrium constants have also been calculated according to eqn (3), (6) and (14) and the data in table 1, and are given in the last column of table 2. Whereas the ratio 8380/8182 is only 0.092 and 0301/8~ is only 0.067, the equilibrium ratio 6,8,/8? is determined to be 1.37. The values at the other temperatures are related to each other in a similar manner. The extremely low diffusivity DZ0p2 determined by curve-fitting the kinetic data is a result of the high relative weighting factor.There is a discrepancy between the thermo- dynamic results, indicating a high probability that cavities occupied by two molecules have empty neighbours, and the kinetic results, indicating that jumps from cavities holding two molecules into empty cavities are not contributing appreciably to total flow. In eqn (12) we have assumed that a cavity holding i molecules will have a number of neighbours holding j - 1 molecules proportional to 6,-1. Fowler-Guggenheim statistics * however would lead to a higher probability that empty cavities have neighbours holding one molecule than those holding two, without necessarily changing appreciably the total cavity distribution as determined by eqn (1)-(6).The possibility of applying Fowler-Guggenheim statistics to our kinetic model warrants further study. Neglecting the second sum in the numerator of eqn (25) and limiting curve fitting to determination of the Di,i-Ipi values, the accuracy of the individual diffusivities is very good, see table 3. TABLE 3.-INTRINSIC DIFFUSION COEFFICIENTS (lo-' Cm2 S-I) T 409K 438K 458K 488K DlOPl 0.65 1.02 1.51 2.14 f 0.11 0.04 0.04 0.05 D21P2 0.71 1.14 1.53 1.99 - + 0.07 0.04 0.07 0.08 D32P3 0.68 0.85 1.14 1.71 0.01 0.01 0.03 0.08 CT curve 0.03 0.02 0.04 0.04 The overall dependence of D, on sorbate concentration calculated with the constants given in tables 1 and 3 for the four temperatures studied is shown as solid lines in fig. 3 and compared with the experimental points.The standard deviation of the entire curve is listed in the last row of table 3. Agreement is highly satisfactory, except for slight deviations near 8, = 1 at 458 K. The three intrinsic diffusion coefficients in table 3 are about equal at the lowest temperature, but there is a clear tendency for D3,p3 to drop behind the other values as the temperature increases. This may mean that at 488 K the vibration of sorbate molecules within the cavity has increased to a point where passage through the cavity at high occupation level is impeded. Neglecting differences in the Di, i-lpi, the minimum in the effective diffusion coefficient with increasing concentration is caused by the nature of the total weighting factor m i= 1K . FIEDLER AND D.GELBIN 243 1 This is the total probability that a cavity will have a neighbour occupied by one less molecule than itself, multiplied by the statistical thermodynamic expression for the rate of change of chemical potential with respect to cavity loading. Darken's law cannot give a good description of the results, since the intrinsic diffusivities of the adsorbed phase do not increase proportionally to occupation level, 1.2- 7.0- ~ 0.8- I, 3 I 2 6 0.6- 0.4 - 0.2- as required by eqn (27), but The average activation 0.4 kcal mol-1 in agreement actually decrease slightly. energy of the intrinsic diffusion coefficients is 6.0+ with the activation energy of D, given in ref. (7). 0 -pe49J a I c o- 2.b 3.0 42[-1 FIG, 3.-Experimental diffusion coefficient against total amount adsorbed ; n-heptane and zeolite 13X at 0,488 ; a, 458 ; 0,438 and A, 409 K.' CONCLUSIONS (1) A model has been presented and equations derived which interpret adsorption rate data on the basis of a statistical thermodynamic approach, taking into account2432 DIFFUSION MODEL FOR ZEOLITE CRYSTALS the discrete cavity structure of zeolites. In contrast to previous kinetic models, the diffusion coefficients may vary with local cavity occupation level.(2) The validity of the Darken equation in zeolitic systems involving multiple occupation levels is dependent on restrictive assumptions compared with the general model. (3) In one system reported in the literature, contribution to flow appears to come mainly from molecular jumps between pairs of cavities differing in occupation level by just one. At elevated temperatures intrinsic diffusivity decreases if occupation level is high, indicating blockage of passage by previously adsorbed molecules.Nevertheless, the effective overall diffusion coefficient goes through a minimum with increasing concentration and then rises at higher zeolite loading. This behaviour is determined by the total probability that a cavity will have a neighbour occupied by one less molecule than itself, multiplied by the rate of change of chemical potential with respect to zeolite loading. T. L. Hill, Thermodynamics ojSmall Systems (N.Y.-Amsterdam, 1964), part 11. V. A. Bakaev, Doklady Acad. Nauk S.S.S.R., 1967,167,369. D. M. Ruthven, Nature, Phys. Sci., 1971,232, 70. (Liblice/CSSR, 1975), p. 194-223. P. Brauer, A. Lopatkin and G. Stepanez, Adv. Chem., 1971, 102,97. D. M. Ruthven and R. I. Derrah, J.C.S. Faraday Z, 1972, 68, 2332. R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, New York, 1939). 4K. Fiedler, H. Stach and W. Schirmer, Proc. 2nd Czechoslovak Con5 Physical Adsorption ' D. M. Ruthven and I. H. Doetsch, Amer. Znst.Chem.Eng. J., 1976, 22, 882. (PAPER 7/609) NOMENCLATURE a Ci D" Di, j - 1 &,x- 1 D Z E F i J K AI rn Nc p g a s Q Pi 4i total amount adsorbed, eqn (1) concentration of cavities holding i molecules, one of which is mobile self diffusivity in the Darken equation (26) intrinsic diffusivity of molecules moving from cavity with i mole- cules to one with j - 1 molecules intrinsic diffusivity between all pairs of cavities differing in occupa- tion level by one, assumed constant effective overall diffusivity measured in adsorption uptake experi- ment energy of adsorption relative weighting factor, eqn (37) number of molecules in cavity, also called occupation level flux adsorption equilibrium const ant distance between cavities saturation number of molecules per cavity total number of cavities gas pressure probability that one of i molecules in cavity will be mobile standard canonic partition function concentration of cavities holding i molecules, all of which are adsorbed rnol ~ m - ~ rnol CM-~ cm2 s-l cm2 s-l cm2 s-l cm2 s-l J mo1-1 I mol cm-2 s-l cm rnol CM-~ Pa - - - - rnol ~ m - ~K. FIEDLER AND D. GELBIN R gas constant r radial coordinate S standard entropy T temperature 8i a standard chemical activity P standard chemical potential P fraction of cavities holding i molecules, eqn (1 1) specific gravity of zeolite crystal 2433 J K-' mo1-I cm J K-' mol-I K - - J mol-' g C M - ~

ISSN:0300-9599    

DOI:10.1039/F19787402423

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

pH Calibration of Tetroxalate, Tartrate and Phthalate Buffer Solutions at above 100°C BY GARY D. MANNING* Department of Metallurgy, Imperial College, London S.W.7 Received 17th June, 1977 The pHs of three standard buffer solutions has been measured using a hydrogen electrode against a silver-silver chloride electrode in a cell nominally without a liquid-liquid junction. The measure- ments have been carried out at 95-120°C in 0.05 mol kg-' potassium tetroxalate, 100-160°C in saturated (25°C) potassium hydrogen tartrate and 100-200°C in 0.05 mol kg-' potassium hydrogen phthalate solution. It has been shown that the method cannot be used to calibrate phosphate or borate buffers at >1WC because of excessive reduction of silver chloride by hydrogen, although such solutions remain useful buffers at elevated temperatures.Ever since the glass electrode became commercially available, pH has become a major measurable parameter in many studies of aqueous solutions at below the boiling point. To avoid difficulties concerning the precise thermodynamic definition of pH all practical pH measurements are normally made with respect to a series of seven standard buffer solutions which have been calibrated on a conventional scale. between 0 and 95"C, by Bates and his co-workers [ref. (2) and references therein]. Recent advances in the fields of nuclear technology, hydrometallurgy and geo- chemistry have promoted much interest in the properties of aqueous solutions at temperatures above 100°C and there now exists a real need for practical pH measure- ment under these conditions.The present study has sought to test the suitability of the standard buffer solutions at elevated temperatures and to calibrate them if possible. The method of measurement and assignment of pH to the solutions was similar to that used by Bates. The e.m.f., E, of the cell was measured as a function of temperature. Assuming conventional standard states, the acidity function, P(aHYcl), is given by Pt, Pd or Ir(H,) I buffer, KCl(m) f Ag-AgCI, Pt in WhichfH, is the fugacity of hydrogen. and extrapolated (at constant temperature) to m = 0, to give For each buffer, p(aHycl)m was measured at three different chloride concentrations P(~,Yc,)" = lim p(a,ycJm* m-rO The pHs of the buffer solution is given by ??HS = P(aHyCl>o +log YE1 2434G.D. MANNING 2435 where y& is the activity coefficient of the chloride ion in the buffer solution at infinitely dilute chloride concentration and is defined conventionally by in which A , is the temperature dependent Debye-Hiickel parameter. The value of the ionic strength, I, of the buffer solution in the absence of KCl may be calculated with sufficient accuracy (& 10 %) from the p(aHycI)" data. EXPERIMENTAL APPARATUS A schematic cross-section of the autoclave is shown in fig. 1. The autoclave body was constructed of 316 S16 stainless steel and had two adjacent pots 3 in (7.62 cm) in diameter and 3 in deep both containing close-fitting polytetrafluoroethylene (PTFE) liners 0.125 in (0.3175 cm) thick. The autoclave head, which was also constructed of stainless steel, was equipped with seven standard pressure unions (Autoclave Engineers) above each pot and the pressure seal with the main body was achieved using two Viton-rubber O-rings concentric with the pots.Measurements were made only on the solution in one of the pots while the solution in the other was used to presaturate the hydrogen with water vapour at room temperature. 14 FIG. 1 .-Schematic cross-section of the autoclave assembly. (1) Hydrogen from cylinder. (2) Catalytic deoxygenator. (3) Carbon dioxide trap. (4) PTFE tube. (5) Glass sinter. (6) PTFE liners. (7) PTFE tube. (8) Silver-silver chloride electrode in protective sheath (only one shown). (9) Thermowell inside sheath. (10) Hydrogen electrode (only one shown). (11) Silicone fiuid. (12) Pressure gauge.(13) " Through-electrodes " (only two shown). (14) To exhaust. (15) O-ring. The autoclave was surrounded by a substantial aluminium heat sink which was heated from beneath and on two opposite sides by three planar heating elements. Hollow cooling plates were bolted onto the two remaining sides. The temperature of the heat sink was controlled to +O.l"C but this was smoothed to +O.O2"C inside the autoclave. The temperature of the solution was measured with an iron-constantan thermocouple inserted down a stainless-steel thermowell which dipped into the solution, but was protected2436 pH OF BUFFER SOLUTIONS ABOVE Ioooc from it by a Pyrex glass or PTFE sheath, the latter being used at higher temperatures. The thermocouple was calibrated at the steam point and at the melting points of spectroscopically pure indium and tin every few experimental rum4 The cold junction was kept at the ice point throughout.In this manner the temperature of the solution could be measured to better than & 0.05"C. The pressure was measured with a 300 x 2 lbf in-2 * bourdon tube gauge filled with a silicone fluid and calibrated against a dead-weight tester. The atmospheric pressure was read from a mercury barometer. FIG. 2.-Cross-section of a " through-electrode ". (1) Co-axial socket. (2) Space filled with Araldite. (3) Copper collar. (4) Stainless steel tube. (5) Alumina sheath. (6) Platinum wire. (7) Gland nut. (8) Pressure union. The " through-electrodes " which connected the external potential measuring circuit to the hydrogen and silver-silver chloride eIectrodes inside the autoclave were each based on a co-axial socket bonded with the high temperature epoxy resin Araldite AT 1 to a Iength of stainless steel tube equipped with a copper collar at one end.Through this tube passed a length of platinum wire inside an alumina sheath (fig. 2). These " through-electrodes" have several advantages. The external pressure seal with the autoclave is a standard union and may be broken and remade many times without leakage difficulties. The electrical circuit may be easily broken at the co-axial socket and the platinum wire is effectively screened by the stainless steel tube which is connected both to the co-axial screening and the autoclave body but is isolated from the solution by the PFTE liner.Araldite AT 1 (the * Atm and lbf in-2 are used as pressure units throughout. 1 atm = 14.6960 lbf in-2 = 101.325 kPa.G. D. MANNING 2437 internal pressure seal) is quite resistant to chemical attack and will withstand temperatures in excess of 240°C although with some loss of mechanical strength. However, there is a considerable temperature gradient along each " through-electrode " and when the autoclave was at 200°C the co-axial socket was at less than 50"C, there was therefore no danger of failure. The e.m.f. of the cell was measured using a six digit digital voltmeter as the ultimate potential standard, in conjunction with a Vibron electrometer and a simple potentiometer. A potentiometric recorder was also included so that the change in e.m.f. with time could be monitored.The electrometer was effectively used as a very high impedance (>lOl5 SZ) amplifier which minimised the possibility of electrode polarisation and also enabled measure- ments to be taken when the internal resistance of the cell had been greatly increased by the use of a porous PTFE disc (see below). The whole circuit was calibrated against the digital voltmeter and accurate to kO.02 mV. ELECTRODES Two pairs of hydrogen and silver-silver chloride electrodes were used in each experi- mental run. Each hydrogen electrode consisted of a 3 x 0.5 cm strip of platinum foil, spot welded to a platinum wire which could be simply hooked onto a loop formed from the platinum wire of a " through-electrode ". It was arranged that the electrodes cut the solution-gas interface, although with at least half of the foil submerged, so that equilibrium would be quickly established.The electrodes were not platinised in the normal way because lead in the platinum black, derived from the lead acetate invariably added to the plating solution to ensure good deposit^,^ might be leached by buffer solutions at elevated temperatures with unknown results. Also platinum black is known to catalyse the hydrogenation of phthalates to cyclohexane carboxylic acids.6 Instead the electrodes were plated with palladium black which has been recommended as a rather less active catalyst which does not cataIyse the hydrogenation of phthaIates.6 Plating each electrode for 1 min at 100 mA cm-2 in a solution of 0.5 mol kg-' H2PdCI4 and 0.1 mol kg-l in HCI gave tenacious, brown-black deposits of palladium black. In the absence of a catalyst, potassium hydrogen phthalate solution was found to be completely stable under hydrogen up to 200°C.However, palladium black did catalyse hydrogenation at temperatures above 120°C. Smooth iridium hydrogen electrodes were therefore used in this solution.7* These were not totally inert but the rate of hydrogenation was very slow and the final pH values of the experimental phthalate solutions were rarely >0.03 units higher than the initial values. Electroplating iridium from aqueous solution is not easy although there are various recommended procedure^.^-^^ That recommended by Tyrell l6 was used and gave smooth, dark-grey deposits of iridium metal which could only be removed by abrasion.Thermal type silver-silver chloride electrodes l7 were used and prepared as recommended by Ives and Janz.18 The electrodes were supported on a spiral of platinum wire which could be hooked onto the wires of the " through-electrodes " in a similar manner to the hydrogen electrodes. Initially batches of electrodes were prepared and immersed in 0.05 mol kg-l KCl solution overnight and their bias potentials measured, but because these were usually within 0.05 mV of the mean, subsequent electrodes were taken straight from the oven and stored dry, in the dark, until required, at which time an arbitrary pair was chosen. Because the silver chloride in the electrodes tended to be both leached by the solutions and reduced by hydrogen to silver at elevated temperatures, only in a minority of cases could an electrode be re-used and normally a new pair of electrodes was employed for each experimental run. To minimise the leaching of silver chloride each electrode was surrounded by a Pyrex glass sheath containing a sintered glass disc or in the case of the phthalate solutions at above 14O"C, a similar PTFE sheath containing a porous PTFE sintered disc.These were supported by tantalum wires from the autoclave head and in this way each electrode wits only in immediate contact with about 5 cm3 of solution.2438 pw OF BUFFER SOLUTIONS ABOVE 100°C The PTFE sheaths were employed because those of glass tended to crack at the higher temperatures, however, the PTFE had several disadvantages. Firstly, because PTFE is hydrophobic, the porous discs were difficult to wet and this could only be achieved by submerging them in the solution, evacuating to remove air and then releasing the vacuum.The small amount of solution in each porous disc increased the internal resistance of the cell to such an extent that the electrometer required a significant time to reach its final reading. Hydrogen bubbles which formed as the solution was heated clung tenaciously to the PTFE and if occasionally one formed around a porous disc it effectively caused an infinite resistance making further measurements impossible. Heat transfer across the water- PTFE-water boundaries seemed particularly poor and the solution inside the sheaths took a long time to come to thermal equilibrium with the bulk of the solution causing the cell's e.m.f.to lag badly behind the temperature. This last effect was so bad at <14O"C as to make the use of PTFE sheaths impractical under these conditions and therefore glass ones were used up to this temperature. Initially a small quantity of solid silver chloride was added to each sheath to ensure that the solution inside was saturated. This was satisfactory for the measurements on the tetroxalate solutions at low pH and low temperature but at the higher pH and high tempera- tures used for the other buffers extensive reduction of AgCl occurred causing, in the case of the phthalate buffer solutions, the pH to be significantly lowered. No solid AgCl was added therefore to the sheaths in the tartrate or phthalate solutions and although some reduction still took place, as indicated by a brown stain of metallic Ag on the inside of the sheaths at the solution-gas interface, this was not sufficient to affect the pH value.MATERIALS AgC103 was prepared from AnalaR AgN03 and GPR NaClO, by the method already described,lg but was recrystallised thee times. GPR Ag20 was leached with hot water in a Soxhlet appaxatus for several hours to remove any entrained electrolytes, as recommended by Bates.'' AgCl was prepared by the addition of dilute A.R. hydrochloric acid to a solution of AgN03, and purified by recrystallisation from concentrated ammonia solution as described by Zimmerman. Commerical high purity H2 (>99.99 %) was used. Because 0, is a particularly objection- able impurity, being reduced at a hydrogen electrode and causing a bias potential, the H2 was passed through a catalytic deoxygenator then through a CO, trap before entering the autoclave.AnalaR potassium tetroxalate [KH3(C204)2 2H20) has an uncertain water content and titration against standard NaOH solution showed it to have a purity of 98.49 %. Because the solid may not be dried at above 60°C without some decompositionz2 a sample was repreatedly crushed, dried at 50°C and analysed until constant purity was obtained (99.60 %). The necessary adjustment for this value was made when preparing the solutions. AnalaR potassium hydrogen phthalate was dried at 120°C for 3 h before use and AnalaR potassium hydrogen tartrate (KHC4H406) was used without treatment, from the bottle. AnalaR KCl was dried at 150°C for 6 h.The sample used contained (0.0033 mol % Br and therefore no attempt at further purification was made.23 Good quality distilled water (conductivity < 1.5 x 0-l when freshly boiled) was used and the solutions were prepared by weight, the necessary adjustment for the buoyancy of air being made.24 The saturated tartrate solutions were prepared by keeping an excess of the solid in contact with the solution for at least 2 h, with occasional shaking, at 25+ 0.2"C. The required amount of KCl was then dissolved in this solution. METHOD About 130 g of the bufferlchloride solution were placed in each pot. The hydrogen and silver-silver chloride electrodes were washed with the solution and hung on their respective " through-electrodes ". The sheaths around the silver-silver chloride electrodes were filled with solution and, in the case of the tetroxalate solutions, a small amount of solid AgCl added.After the autoclave had been sealed and all the pressure and electrical connectionsG . D. MANNING 2439 had been made, Hz was bubbled through the system for 2h during which time the bias potential between the two hydrogen electrodes usually dropped to 0.1 mV. No significant evaporation of the solution occurred during this period. The outlet was then sealed and the internal pressure allowed to rise to 3040lbfir1-~, the Hz was then shut off and the measurement cell isolated from all parts of the system apart from the gauge. The apparatus was left overnight in this condition and the power to the heaters turned on in the early morning.When the thermocouple and the recorder indicated that thermal equilibrium had been attained, the pressure, temperature and e.m.f. of the two pairs of electrodes were read. The temperature was then raised and a new set of readings taken. Measurements were taken only during ascending temperatures. On cooling to room temperature the pH of the measurement and saturation solutions were compared with that of the original buffer solution, with a glass electrode. CALCULATIONS HYDROGEN FUGACITY The hydrogen fugacity at each temperature was calculated by subtracting the saturated vapour pressure of water 2 5 from the total pressure. However, three second order effects, which become more important at higher temperatures, were also considered. (i) If the osmotic coefficient of the solution is significantly less than unity, due to the solutes, the vapour pressure becomes significantly lower than that of pure water.The most concentrated solution presently used (0.05 mol kg-1 KH phthalate, 0.02 mol kg-l KCl) has an ionic strength of about 0.072 mol kg-’. In the absence of any specific data, the solution was assumed to act like that of a simple 1 : 1 electrolyte, and Greeley’s value 26 of the osmotic coefficient of a solution of HCl of similar strength at 200°C indicates that the vapour pressure would be at most 0.5 lbf in-, lower than that of pure water, equivalent to an error of 0.002pH units at this temperature. However, in the absence of any real data and since this was the worst possible case and the correction becomes negligible at lower temperatures and ionic strengths, the effect was ignored.(ii) The presence of a second, inert gas above a liquid generally increases the liquid’s vapour pressure.27 Ignoring fugacity coefficients, in which P is the total pressure, P, is the vapour pressure of the solution alone and P,’ is the vapour pressure of the solution in the presence of the second gas. vi is the partial molal volume of water in the solution but was assumed equal to that of pure water. With the H2 pressures used, the effect was only significant (0.001-0.003 pH units) between 1 60-2OO0C, but was incorporated for completeness. (iii) The empirical equation of state according to Shaw and Wones 28 gives a fugacity coefficient for pure H2 at 4 atm pressure of 1.002 between 100 and 200°C.Greeley et aZ.29 have calculated a value of 1.026 for H2 at a partial pressure of 1.6 atm in the presence of saturated water vapour at 200°C. However, this latter value seems too high, since a strongly polar molecule such as H,O would be expected to decrease rather than increase the fugacity coefficient. An independent calculation was made therefore using the method of Needes 30 to calculate the fugacity of H, in gaseous mixtures of H2 and H20 at elevated temperatures. The system is effectively solved for fugacities, pressures and mole fractions simultaneously using the virial equation of state terminated after two terms. The virial constants for H, and H,O were calculated from the Lennard-Jones potential and the interaction constant from2440 pH OF BUFFER SOLUTIONS ABOVE 100°C the Stockmeyer potential.l A representative calculation on a mixture containing 0.2 mole % H, and 0.8 mole % H20 in the presence of liquid water at 200°C yielded a value for the total pressure of 19.5614 atm. The partial pressures of H20 and H2 in the mixture were 15.3833 and 4.1660 atm and their respective fugacity coefficients 0.9266 and 1.0016. This last value is not sufficiently different from unity to effect the present work and therefore a fugacity coefficient of one is assumed throughout. MOLALITY OF SOLUTIONS A calculation based on the density of saturated water vapour and the volume of the gas space in the autoclave pot at 200°C showed that the molalities of the buffer and KCI at this temperature would be 0.6 % higher than those at room temperature due to the evaporation of water into the gas phase.Such a change would have a negligible effect on the hydrogen ion activity because of buffer action, but the change in chloride concentration is equivalent to 0.003 units inp(aHycl). This is not totally insignificant but is considerably smaller than the uncertainty in the chloride molality introduced by the solubility of AgCl. The effect was therefore ignored and mcl taken as equal to the initial molality of KCI. E ~ ~ / A ~ c I AND PHYSICAL CONSTANTS Greeley et aZ.29 have measured EXgIAgC1 between 25 and 275°C. Their values are in good agreement with those obtained by Bates and Bower 32 between 0 and 95°C from the most extensive investigation carried out on this electrode, and also with those of Izaki and Arai 3 3 up to 175"C, obtained from a much less sophisticated investigation.Greeley's data between 25 and 225°C were therefore smoothed with respect to temperature to give, E&/AgC1 = 0.235 75-4.427 22 x t-4.002 32 x f 2 + 1.056 56 x (t"C; 0 = 0.10 mV) and all values were then calculated from this function. The Debye-Huckel constants, A , and B,, were calculated between 100 and 200°C using the density of water from ref. (25) and the dielectric constant of water from Akerlof and O ~ h r y . ~ ~ The fundamental constants were taken from Taylor et uZ.,~' thus making (RIP) In 10 = 0.000 198 416 deg-l. t3-2.301 03 x 10-l1 t 4 STATISTICAL TREATMENT OF DATA For each buffer solution and chloride concentration several values of p(aHyCl),,, were generally obtained at each set temperature.However, despite these temperatures being nominally the same from one experimental run to the next, the actual tempera- tures of the solutions at which measurements were made usually differed slightly and by more than the likely error in the temperature measurement. It was, therefore, not possible simply to average the respective values of p(aHycl), for one specific buffer solution and chloride concentration at each set temperature to obtain a mean. Therefore, all the p(aHycl)m data for solutions of the same composition were weighted equally and smoothed with respect to temperature by fitting the product, Tp(aHycl), on to best fitting polynomials in T, (34 (3b) Tp(a,yC,)(T), = A+BT+ CT2 + DT3 + . . .. p(aHycl)(T), = A/T+ B+ CT+ DT2 + .. .. which could then be rearranged to give,G. D. MANNING 2441 This was performed using a standard computer program which also calculated the F ratios for successive pairs of polynomials enabling the statistical F-test to be applied.36 The series were terminated when additional terms failed to give a signifi- cantly better fit of the data at approximately the 95 % confidence level. For each buffer, p(aHyCJm was extrapolated linearly as a function of m (at constant temperature) to obtain p(aHyCI)O at m = 0. This was the general procedure of Bates and his co-workers and the accuracy of the present data could not justify any more sophisticated method. The extrapolation was performed at all tempera- tures simultaneously by operating on the smoothing functions to give p(aHyC1)" directly as a similar function of temperature.Thus defines p(aHycl)(T)" as the intercept at m = 0 of the best (least squares) straight line of gradient a(T) obtained by plotting p(aHycl)(T), against m at each temperature. The standard error, go, of the intercept, p(aHycl)", is calculated 36 from the standard error of the three values of p(a,y,,) about the best straight line at each temperature. P(aHYCl)(T)m = a(T) +P(aHYCI)(T)" RESULTS AND DISCUSSIONS 0.05 mol kg-l KH3(0x), SOLUTION Comparison of the final pH values of solutions which had been heated under H2 (with no electrodes present) or under air with their initial pH, indicated that extensive TABLE EXPERIMENTAL VALUES OF THE ACIDITY FUNCTION IN 0.05 moI kg-I KH3(Ox)2, rn KCl SOLUTIONS set P(aHYCl)m p@Wcl)m temperature/"C z/"C m = 0.015 t/"C m = 0'010 r/"C 90 100 110 120 92.76 92.76 93.09 93.1 1 102.66 102.68 102.74 102.75 112.66 112.66 112.85 112.85 122.60 122.64 123.27 123.23 1.902 1.897 1.908 1.908 1.942 1.933 1.934 1.933 1.957 1.948 1.964 1.965 1.993 1.988 2.008 2.001 92.43 92.45 92.85 92.85 102.81 102.79 102.38 102.42 112.87 112.87 112.40 112.40 123.1 1 122.10 122.15 - 1.899 1.900 1.884 1.885 1.924 1.923 1.936 1.922 1.951 1.949 1.961 1.950 2.000 1.997 1.978 - 92.93 92.93 - - 102.79 102.79 - - 112.85 112.85 - - 121.85 121.87 - - TABLE 2.-sMOOTHED VALUES OF THE ACIDITY FUNCTION AND DERIVED DATA FOR 0.05 mol kg-I KH,(OX)~ SOLUTION ~ ( a ~ d t % r/"c m = 0.015 rn = 0.010 rn = 0.005 a(T) p(UHyCl)(T)' U0 I 95 1.910 1.900 1.900 1.04 1.893 0.006 0.0719 100 1.924 1.91 5 1.913 1.09 1.906 0.004 0.0713 105 1.938 1.930 1.926 1.18 1.920 0.003 0.0708 110 1.953 1.947 1.940 1.29 1.934 0.001 0.0702 115 1.969 1.964 1.955 1.44 1.948 0.003 0.0697 120 1.986 1.982 1.970 1.62 1.963 0.005 0.0691 P(aHYC1)m m = 0.005 1.895 1.896 - - 1.920 1.920 - - 1.949 1.949 - - 1.979 1.979 - - PHS 1.779 1.792 1.804 1.817 1.830 1.8432442 PH OF BUFFER SOLUTIONS ABOVE 100°C thermal decomposition occurred at temperatures > 130°C.No e.m.f. measurements were made, therefore, at temperatures above 125°C. KC1 molalities of 0.005, 0.010, and 0.015 were employed and the experimental values of the acidity function in these solutions, calculated from eqn (l), are given in table 1. Smoothing functions with three terms were found adequate to fit the data and the smoothed values of p ( a ~ r y ~ , ) ~ and derived data are given in table 2.TABLE 3.-EXPERIMENTAL VALUES OF THE ACIDITY FUNCTION IN SATURATED (25°C) KH TARTRATE, m KCI SOLUTIONS set temperaturel'c t/"C 95 110 120 130 140 150 160 97.59 97.59 97.58 97.58 - - 113.03 113.03 112.00 112.00 121.95 121.86 122.23 122.25 132.73 132.73 131.41 131.46 142.49 142.49 141.69 141.69 151.85 151.85 150.94 150.98 161.66 161.69 161.55 161.59 I p(arrycl)m rn = 0.015 3.743 3.744 3.754 3.756 - - 3.805 3.805 3.807 3.809 3.841 3.844 3.852 3.852 3.901 3.889 3.898 3.895 3.961 3.954 3.947 3.953 3.997 3.994 4.003 4.004 4.052 4.045 4.045 4.049 - t/"C 97.54 97.56 97.74 97.74 97.74 97.74 112.68 112.70 - - 123.00 123.00 122.68 122.70 132.31 - - - 142.31 141.96 141.87 141.96 142.01 151.71 - - - 161.39 161.89 161.34 161.37 p(aHyc1)m rn = 0.0 10 3.748 3.746 3.760 3.763 3.753 3.758 3.801 3.802 - - 3.841 3.837 3.854 3.845 3.892 - - - 3.924 3.927 3.937 3.927 3.929 3.973 - - 4.000 4.006 4.009 4.009 t/"C 97.91 97.91 - - - - 1 12.18 112.20 - - 122.56 122.58 - - 132.21 132.22 I I 142.34 142.34 - - - 151.61 151.63 - 161.00 161.00 - - p(aHycl)m m = 0.0053 3.757 3.763 - - - 3.803 3.806 - 3.850 3.848 - - 3.890 3.883 I - 3.906 3.918 - - - 3.946 3.943 I - 3.961 3.946 - - Extrapolation to 95-120°C of Pinching's and Bates' values 37 of the second dissociation constant of oxalic acid between 0 and 50°C showed that the concentration of oxalate ion in the solution was still negligible at the higher temperatures and therefore that the method of Bower et could be used to calculate the ionic strength. Thus, I = 0.05+m, (4)G.D. MANNING and it is assumed that 2443 and therefore At each temperature, by initially letting mH = (aHycl)" and substituting into eqn (4), a first value for I was obtained, which on substitution into eqn (5), together with p(aHyCl)O gave a better value for mH. Three or four reiterations gave a constant value for the ionic strength. The value of ao, nominally an effective ionic radius, was not very critical. Values of 2, 4 and 6 A were tried but these led to a difference of only 4.5 % between the smallest and largest values of I obtained at each temperature, corresponding to a difference of 0.002 units in log y& calculated from eqn (2). a. was therefore taken as 4A and the values of I obtained substituted into eqn (2) to give the final values of pH, quoted in table 2.These are compared with the experimental values of pH, for the same solution of Bates derived by Bower et al. 38 and Bower and Bates 39 in fig. 3. 1 I I I I I I 1.82 1*86 t 1.78 c % L 1.74 .1; 1.66 0 0 0 L O 0 A 0 L A I I 1 1 I I 1 0 20 40 60 80 100 120 t/"C FIG. 3.-pHs plotted against temperature for 0.05 mol kg-1 potassium tetroxalate solution. 0 and A from Bates derived from Bower et aZ.39 and Bower and Bates,39 respectively ; 0, present work. SATURATED (25°C) KH TARTRATE SOLUTION (0.0341 mol kg-l) Comparison of initial and find pH values of solutions which had been heated showed that thermal decomposition occurred at 170-1 80°C. However, the solution was stable up to 162°C.Experimental values of the acidity function in solutions containing 0.005, 0.010 and 0.015 mol kg-l KCl are given in table 3. A four term smoothing function was required and the resultant smoothed values of p(aHycJm and derived data are given in table 4. The ionic strength was calculated by a reiterative method described by Bates 40 similar to that used for oxalate. The required first2444 pH OF BUFFER SOLUTIONS ABOVE 100°C and second dissociation constants of tartaric acid were obtained by extrapolating the values for temperatures between 0 and 50°C of Bates and Canha111.~~ The ionic strength was found to be very insensitive to the value of ao, so that substitution of 2, 4 or 6 A for this parameter led to values of log y& identical to three decimal places.The final values of pH, are given in table 4 and are compared with the experimental values of Bates,2 derived from the data of Bates et aL40 and Bower and Bates 39 in fig. 4. TABLE 4.-sMOOTHED VALUES OF THE ACIDITY FUNCTION AND DERIVED DATA FOR SATURATED (25°C) KH TARTRATE SOLUTION 2l"C 100 105 110 115 120 125 130 135 140 145 150 155 1 60 3.757 3.774 3.793 3.815 3.838 3.863 3.888 3.914 3.940 3.966 3.992 4.017 4.041 3.760 3.775 3.792 3.81 I 3.832 3.854 3.876 3.899 3.921 3.943 3.964 3.983 4.001 3.765 3.781 3.799 3.817 3.837 3.857 3.876 3.984 3.910 3.925 3.938 3.947 3.953 - 0.83 - 0.71 -0.52 - 0.25 0.12 0.62 1.25 2.04 2.99 4.12 5.45 6.98 8.73 3.769 3.784 3.800 3.817 3.835 3.852 3.868 3.882 3.894 3.904 3.910 3.913 3.911 I 0.001 0.0399 0.003 0.005 0.006 0.007 0.0397 0.008 0.008 0.006 0.005 0.0395 0.003 0.001 0.002 0.005 0.0393 3.82ii1111_1 3.70 3.58 '" t .B 3.54 c.A A 0 0 0 0 0 a 0 A PHS 3.676 3.690 3.705 3.721 3.738 3.753 3.768 3.781 3.791 3.800 3.804 3.806 3.802 I I 1 1 I I I ' I I 20 40 60 80 100 120 140 160 tf"C FIG. 4.-pHs plotted against temperature for saturated (25°C) potassium hydrogen tartate solution. 0 and A from Bates derived from Bates et aL40 and Bower and Bates,39 respectively ; 0, present work.G. D. MANNING 2445 4.60 4.50- 4.40- $ 4.30- 4.20- 4.10- 4 .WLQ 0.05 rnol kg-l KH PHTHALATE SOLUTION This solution was found to be stable under air to 200°C and is expected to remain so to considerably higher temperatures, since although solid phthalic acid decomposes at 200-230°C to the very stable anhydride, this reaction would not occur in aqueous solution.As previously noted, the solution is also stable under H2 in the absence of a hydrogenation catalyst. Reproducible results could not be obtained from solutions containing only 0.005 rnol kg-l KCl because of excessive reduction of AgCl by H2. KC1 molarities of 0.010, 0.015 and 0.020 were therefore used. However, even in these reduction was sometimes significant at the highest temperature, although the effect (as measured by the final pH of the solution) varied from run to run for similar solutions. Several experimental runs were required to obtain even reasonable agreement between results at above 180°C and no value ofp(aHyC1)0.015 was obtained above 191°C and therefore a value at 200°C had to be estimated by extrapolation of the respective smoothing function.The experimental acidity functions are given in table 5 and the smoothed data, calculated from the five term smoothing functions, are given in table 6. The ionic strength of this buffer solution was found by Hamer et ~ 1 . ~ ~ to be only very slightly dependent on temperature, and changes by only 0.000 08 mol kg-l between 50 and 60°C. Linear extrapolation on this basis gives values for the ionic strength of 0.052 89 and 0.052 09 mol kg-l at 100 and 200°C respectively, therefore a mean value of 0.052 50 mol kg-l was used across this temperature range. The values of pH, are given in table 6 and are compared with the experimental values of Bates derived from Hamer and Acree 43 and Bower and Bates 39 in fig.5. - 4.70 j I t I I 1 I I I I 0 0 0 0 0 0 0 0 0 A 0 A A b t/"C FIG. 5.-pHs plotted against temperature for 0.05 mol kg-' potassium hydrogen phthalate solution 0 and A from Bates respectively; 0, present work. derived from Hamer and Acree 43 and Bower and2446 set temperaturePC 95 1 00 110 120 130 140 pH OF BUFFER SOLUTIONS ABOVE 100°C TABLE 5.-EXPERIMENTAL VALUES OF THE ACIDITY FUNCTION IN 0.05 mol kg-l KH PHTHALATE, rn KCl SOLUTIONS t/"C 97.47 97.47 97.81 97.8 1 - - - - - - - - 112.35 112.35 112.56 112.56 - - - - 122.18 122.18 123.01 123.03 - - - - 132.03 132.38 132.40 - - - - - - - 141.25 141.63 141.65 142.12 142.10 141.87 141.87 141.27 141.28 P(aHYdm m = 0.020 4.329 4.326 4.339 4.335 - - - - - - - - - 4.429 4.426 4.416 4.420 - - - - 4.484 4.478 4.476 4.486 - - - 4.524 4.533 4.551 - - - - - - I 4.569 4.586 4.594 4.575 4.568 4.589 4.569 4.557 4.566 t/"C 93.00 * 93.00 * 97.63 97.64 97.66 97.66 97.88 97.57 97.77 97.77 101.65 102.64 102.68 1 12.30 112.74 112.37 112.39 112.59 112.59 112.72 1 12.73 122.76 122.78 122.35 122.35 122.38 122.40 - - 132.02 132.05 132.03 132.02 132.02 132.02 131.92 131.92 132.54 132.52 142.28 142.30 142.22 142.23 141.96 141.96 141.68 I - p(aHYCl)m m = 0.015 4.294 4.288 4.321 4.298 4.312 4.314 4.330 4.337 4.320 4.300 4.335 4.346 4.346 4.428 4.430 4.426 4.41 6 4.406 4.410 4.424 4.422 4.503 4.505 4.512 4.506 4.500 4.496 - - 4.543 4.543 4.578 4.575 4.597 4.604 4.536 4.536 4.532 4.529 4.63 1 4.627 4.621 4.625 4.592 4.599 4.590 I - t/"C 97.34 97.36 97.41 97.19 97.19 - - - - - 103.00 103.00 - 113.24 113.10 112.18 112.66 112.66 - - - 123.75 123.64 122.23 122.25 122.75 122.75 122.59 122.57 132.03 132.28 132.30 132.14 132.14 - - - - - 141.92 141.92 141.97 141.97 141.41 141.4 1 - - p(u€Iycl)m 4.355 4.351 4.326 4.334 4.331 m = 0.010 - - - - - 4.361 4.353 - 4.444 4.445 4.454 4.435 4.428 - I - 4.505 4.505 4.476 4.476 4.442 4.462 4.481 4.479 4.553 4.516 4.509 4.537 4.525 - - - - - 4.562 4.566 4.593 4.565 4.577 4.571 - -set ternperaturel'c 150 160 170 180 190 200 t/"C - - - - I - - 161.22 161.22 161.26 161.26 160.87 160.87 - - - 180.78 1 80.80 180.87 180.87 179.79 - - - 200.68 200.73 200.57 200.59 200.30 200.32 p(arryci)m rn = 0.020 - - - - - - - - 4.680 4.675 4.696 4.678 4.668 4.675 - - - 4.804 4.793 4.825 4.805 4.806 - I - 4.924 4.919 4.948 4.917 4.905 4.945 G .D. MANNING TABLE 5.-contd. tpc 152.18 152.14 151.98 151.98 151.37 151.37 152.21 152.25 161.63 161.64 160.99 161.19 - - 170.65 171.44 171.44 180.83 180.62 - - - 190.01 190.31 190.31 - - - - - - P(aHYC1)m rn = 0.015 4.668 4.668 4.694 4.690 4.679 4.676 4.642 4.648 4.730 4.723 4.705 4.705 - - 4.783 4.758 4.753 4.832 4.807 - - - 4.872 4.861 4.859 - - - - - I tl"C 150.94 150.94 150.97 150.97 - - - I 164.07 * 164.03 * 160.67 - - - 170.68 - 180.34 180.34 180.34 180.36 179.31 - - 199.61 199.54 196.78 * 196.92 * 198.63 * 199.65 2447 P(aHYCl)m m = 0.010 4.647 4.645 4.641 4.605 - - - - 4.685 4.690 4.666 - - 1 4.729 - - 4.780 4.775 4.790 4.772 4.780 1 - - 4.833 4.841 4.858 4.837 4.854 4.852 * Slightly different set temperatures were used. KH2P04 + Na2HP04 SOL UTI o NS The two phosphate standard buffer solutions contain 0.025 mol kg-l KH2P04, 0.025 mol kg-l Na2HP04 and 0.008 695 mol kg-l KH2P04, 0.030 43 mol kg-1 Na,HPO, and have pHs values, at 25"C, of 6.865 and 7.41 3, respectively. The former solution was completely stable at 200°C and is expected to remain so to higher temperatures.The latter qualitatively identical solution is expected to behave similarly, although because it was originally chosen primarily for use in biological studies it has been calibrated to only 50°C by Bates. An attempt to calibrate the former solution at >lOO"C was made using sheathed silver-silver chloride electrodes against palladium black hydrogen electrodes. However catastrophic reduction of AgCl took place at >12O"C making further measurements by this method impossible.2448 t/"C 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195 200 pH OF BUFFER SOLUTIONS ABOVE 100°C TABLE 6.-sMvIOOTHED VALUES OF THE ACIDITY FUNCTION AND DERIVED DATA FOR 0.05 mol kg-l KH PHTHALATE SOLUTION m = 0.020 4.349 4.383 4.414 4.442 4.468 4.493 4.517 4.541 4.566 4.592 4.619 4.647 4.676 4.706 4.736 4.768 4.800 4.832 4.864 4.894 4.924 p(apycl)(T)m rn = 0.015 4.333 4.369 4.405 4.441 4.477 4.511 4.544 4.575 4.605 4.63 3 4.660 4.686 4.710 4.735 4.759 4.783 4.809 4.836 4.865 4.897 4.933 m = 0.010 4.356 4.389 4.41 8 4.444 4.4 69 4.494 4.518 4.542 4.567 4.592 4.619 4.645 4.673 4.700 4.727 4.753 4.778 4.801 4.821 4.837 4.848 4 T ) - 0.73 - 0.55 - 0.40 - 0.27 -0.18 -0.12 - 0.08 - 0.07 - 0.05 - 0.03 0.02 0.12 0.29 0.55 0.94 1.47 2.18 3.1 1 4.29 5.75 7.53 ?'(aHWd(T)' 4.357 4.388 4.41 8 4.447 4.474 4.501 4.527 4.554 4.580 4.606 4.632 4.657 4.682 4.705 4.727 4.746 4.763 4.176 4.785 4.790 4.789 a' 0.03 5 0.03 1 0.020 0.004 0.01 5 0.031 0.048 0.060 (4.069 0.074 0.074 0.072 0.064 0.057 0.049 0.040 0.036 0.035 0.040 0.057 LO84 PHS 4.254 4.284 4.313 4.340 4.366 4.394.4.41 6 4.441 4.465 4.490 4.514 4.537 4.560 4.582 4.602 4.619 4.633 4.645 4.65 1 4.654 4.651 Ionic strength, I , taken as 0.052 50 at all temperatures. 0.01 mol kg-l Na2B407 SOLUTION It was evident from the attempt to calibrate the phosphate buffer that no measure- ments at >lOO"C would be possible in this solution due to reduction of AgCl at the high pH [pH, (95°C) = 8.81. Mesmer et aZ.44 have studied boric acid-borate equilibria to 292"C, the buffer solution itself was therefore expected to be totally thermally stable.This was confirmed by keeping a sample (under N2) at 200°C for 4 h. On cooling, no significant change of pH had occurred. (If heated under air, the final pH was always 0.04 units lower than its initial value, presumably due to C02 absorption). SATURATED (25°C) Ca(OH), SOLUTION (0.0203 mol kg-I) For completeness it is recorded that this high pH standard of Bates may not be calibrated at above 60°C because the solubility of Ca(OH), has an inverse temperature dependence. The pHs data shown in fig. 3-5 were smoothed by fitting to eqn (3). The co- efficients of the resulting polynomials are given in table 7. The values of pHs predicted from these functions at below 80 "C are all within 0.003 units of the 'recommended' values of Bates.ERRORS The largest errors derive from the silver-silver chloride electrodes. Pairs of hydrogen electrodes invariably agreed to 0.2 mV but the bias potential between two silver-silver chloride electrodes often exceeded 2 mV at high temperatures, high pHG. D. MANNING 2449 and low KCl concentrations. Solid AgCl is thermodynamically unstable with respect to reduction by H2 under all conditions presently employed. In several cases at the highest temperatures in phthalate solutions, the potential of a silver-silver chloride electrode came to within 0.5 mV of that of the hydrogen electrodes due, it is believed, to finely divided metallic silver derived from AgCl reduction acting as a hydrogen e l e c t r ~ d e .~ ~ Such reduction would also increase the chloride ion con- centration inside the sheath. The solubility of AgCl at elevated temperatures introduces two systematic errors. Firstly, the resulting difference in composition between the solutions on each side of the sintered discs will lead to a liquid-liquid junction potential. This is expected to be small since the transport numbers of all ions tend to 0.5 with increasing ternperat~re.~~ Secondly, if the dissolved AgCl is assumed totally dissociated (as was done by Greeley et the chloride ion molality will be increased. However, the formation of complexes, AgClr-l)-(n = 1 to 4), suggests that dissociation will not be complete. In a solution containing KCl (or HCl) and AgCl of molarities rn and s respectively the actual chloride ion molality, mcl, is given by, m&+m& 3s-m+- +m& -(2s-m)+- + [ 3 [:: k2 k41 where k, are molarity formation constants related to the thermodynamic constants, Kn, by = k, YAg% -(n = 1 to 4).YAgCl, Values of s and m were interpolated from Raridon 47 (who has measured the solubility of AgCl in 0.01-3.06 mol kg-l HCl up to 200°C) and K, taken from H e l g e ~ o n . ~ ~ Activity coefficients were introduced into one calculation by letting yAgCIO = 1 1 - A?I+ =- = 2 t o 4 ) 1 +4B,IJn and I = 0.0525 + m (cf. phthalate). The results are given in table 8 in which 6 = log mc,/rn is the error introduced into p(aHycl)m assuming AgCl to be totally dissociated, 6’ is the error assuming silver-chloro species to be formed and 6’* is the error if activity coefficients are included.It is clear that in dilute solutions of KCl saturated with AgCl the free chloride ion molality is actually less than if no AgCl were present (i.e. 6’ is negative), moreover it is a better approximation to ignore the presence of AgCl than to assume it to be totally dissociated. The inclusion of activity coefficients does not alter these conclusions.2450 pH OF BUFFER SOLUTIONS ABOVE 100°C No directly comparable measurements on these buffer solutions at > 100°C have been made. The pH values obtained by Le Peintre 49 and by Kryukov et aL5' in the oxalate, tartrate and phthalate buffers agree within experimental errors with those presented here, although since both sets of workers employed cell involving liquid-liquid junctions direct comparison is not justified.Agreement with Bates and his co-workers seems to be good although Bates' pH, data appear to move towards higher values at > 100°C (particularly in oxalate and tartrate) than those presently described. The reason for this remains unclear. TABLE 7.-vALUES OF COEFFICIENTS IN EQN (3b) REQUIRED TO GIVE PHs solution tetroxalate tartrate phthalate temperature range/"C 0-120 25- 160 0-200 10-3 A 1.210 663 0.065 191 8.004 45 1 10-1 B -0.897 95 1.890 62 - 11.159 96 10' c 0.297 541 - 1.323 969 6.820 578 lo4 D -0.255 99 3.674 88 -20.570 56 107 E - - 3.304 31 31.497 20 109 F - - - 1.925 43 Q 0.005 0.006 0.003 TABLE ERRORS INTRODUCED INTO P(aHyc1)m BY THE PRESENCE OF SILVER CHLORIDE tl"C m = 0.005 rn = 0.010 m = 0.015 rn = 0.020 100 6 6' 150 6 6' 175 6 6' 200 6 6' 6'* 0.003 0.000 0.020 0.000 0.035 0.001 0.086 O.OO0 0.01 1 0.002 0.000 0.010 - 0.002 0.020 - 0.004 0.047 - 0.01 2 - 0.008 0.001 - 0.001 0.007 - 0.003 0.01 5 - 0.005 0.034 - 0.014 - 0.01 3 0.001 0.000 0.006 - 0.003 0.012 - 0.006 0.028 - 0.014 - 0.01 5 The simple hydrogen electrode will remain the best pH electrode under ideal conditions over a very wide range of temperatures and pressures but its reducing properties make it unsuitable in many practical situations.Although the glass electrode is rapidly corroded by aqueous solutions at elevated temperatures other pH responsive electrode systems, e.g. metal-metal oxides, may well prove more resistant to attack. Many natural and synthetic minerals also respond to pH.It is probable, therefore, that a pH electrode with a realistic life at elevated temperatures will be developed and that known buffers will be required for its routine calibration. The author is grateful for advice given to him by Dr. A. R. Burkin, and also for a bursary from the Rio Tinto Zinc Co. throughout the course of this work. R. G. Bates, Determination ofpH; Theory and Practice (John Wiley and Sons, 2nd edn, 1973). R. G. Bates, J. Res. Nut. Bur. Stand. A, 1962, 66, 179. R. G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1960-1961,1,163. Cornit6 International des Poids et Mesures, Metrol., 1969,5, 34. A. M. Feltham and M. Spiro, Chem. Rev., 1971, 71, 177. W. J. Hamer and S. F. Acree, J. Res. Nut. Bur. Stand., 1944,33, 87. ' A.E. Lorch and L. P. Hammett, J. Amer. Chem. SOC., 1933, 55, 70; A. E. Lorch, Analyt. Chem., 1934,6,164.245 1 G . D. MANNING G. N. Lewis and T. B. Broughton, J. Amer. Chem. Soc., 1917,39,2245. F. H. Reid, Metallurgical Rev., 1963,8, 167. lo A. Perley and J. B. Godshalk, British Patent 567,722/1942 ; U.S. Patent 2,416,949. l 1 E. L. MacNamara, U.S. Patent 3,207,680/1965. l2 G. A. Conn, Plating, 1965,52,1258. l3 R. M. Skomoraski and N. J. Paterson, US. Patent 3,639,219/1972. l4 P. J. Ovendon, Nature, 1957, 179, 39. l5 N. V. Ignatova and B. J. Vasserman, U.S.S.R. Patent 136,056/1960; Chem. Abs., 1961, 55, l6 18396e. C. J. Tyrell, Trans. Inst. Metal. Finishing, 1965,43,161 ; British Patent 1.022,451/1964. l8 D. J. D. Ives and G. J. Jam, Reference Electrodes (Academic Press, London and N.Y., 1961).l9 W. C. Fernelius, Inorg. Synth., 1946, 2,4. 2o R. G. Bates, Electrometric pH Determinations (John Wiley and Sons, 1954). 21 W. Zimmerman, J. Amer. Chem. Soc., 1952, 74, 852. 22 R. G. Bates, G. D. Pinching and E. R. Smith, J. Res. Nut. Bur. Stand., 1950, 45,418. 23 G. D. Pinching and R. G. Bates, J. Res. Nut. Bur. Stand., 1946, 37, 311. 24 A. I. Vogel, Quantitative Inorganic Analysis (Longmans, London, 1962). 2 5 U.K. Committee on the Properties of Steam, U.K. Steam Tables in S.I. Units (Edward Arnold, 26 R. S. Greeley, W. T. Smith, M. H. Lietzke and R. W. Stoughton, J. Phys. Chem., 1960,64,1445. 27 K . Denbigh, The Principles of Chemical Equilibrium (Cambridge Univ. Press, 1971). 28 H. R. Shaw and D. R. Wones, Amer. J. Sci., 1964,262,918. 29 R. S. Greeley, W. T. Smith, R. W. Stoughton and M. H. Lietzke, J. Phys. Chem., 1960,64,652. 30 C. R. S. Needes, Ph.D. Thesis (University of London, 1969). 31 J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (John 32 R. G. Bates and V. E. Bower, J. Res. Nut. Bur. Stand., 1954, 53, 283. 33 T. Izaki and K. Arai, Suiyokai-Shi, 1968, 16, 367. 34 G. C. Akerlof and H. I. Oshry, J. Amer. Chem. Soc., 1950,72,2844. 35 B. N. Taylor, W. H. Parker and D. N. Langenberg, Rev. Mod. Phys., 1969,41, 375. 36 C. Chatfield, Statistics for Technology (Penguin, 1970). 37 G. D. Pinching and R. G. Bates, J. Res. Nut. Bur. Stand., 1948, 40,405. 38 V. E. Bower, R. G. Bates and E. R. Smith, J. Res. Nat. Bur. Stand., 1953, 51, 189. 39 V. Bower and R. G. Bates, J. Res. Nut. Bur. Stand., 1957, 59, 261. 40 R. G. Bates, V. E. Bower, R. G. Miller and E. R. Smith, J. Res. Nat. Bur. Stand., 1951,47,433. 41 R. G. Bates and R. G. Canham, J. Res. Nut. Bur. Stand., 1951, 47, 343. 42 W. J. Hamer, G. D. Pinching and S. F. Acree, J. Res. Nat. Bur. Stand., 1946,36, 47. 43 W. J. Hamer and S. F. Acree, J. Res. Nut. Bur. Stand., 1944,32,215. 44 R. E. Mesmer, C. F. Baes and F. H. Sweeton, Inorg. Chem., 1972, 11, 537. 45 N. J. Anderson, PhD. Thesis (University of Chicago, 1945). 46 H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, 47 R. J. Raridon, Ph.D. Thesis (Vanderbilt University, Tennessee, 1959). 48 H. C. Helgeson, Amer. J. Sci., 1969, 267, 729. 49 M. M. Le Peintre, SOC. Franc. Elect. Bull., 1960, 1, 584. C. K. Rule and V. K. La Mer, J. Amer. Chem. Soc., 1936,58,2339. 1 970). Wiley and Sons, 1954). N.Y., 3rd edn, 1958). P. A. Kryukov, V. D. Perkovets, L. I. Starostina and B. S. Smolyakov, Izvest. sibirsk. Otdel. Akad. Nauk S.S.S.R., ser. khim. Nauk, 1966,7,29. (PAPER 7/1046)

ISSN:0300-9599    

DOI:10.1039/F19787402434

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Solid State Reactions of Radiosulphur in Ag+ Doped Potassium Chloride MASOUD KASRAI," BASHIR NABARDI~ AND RAZIEH M. RAIE Institute of Nuclear Science and Technology, University of Tehran, P.O. Box 2989, Tehran, Iran Received 24th November, 1977 The chemical state of 35S produced by the 35Cl(n,p)35S reaction has been studied in both pure and Ag+ doped KCI. The results indicate that in doped crystals the 35S2- proportion is greatly reduced while the 35SO:- and 35S02- fractions have not been affected. Isochronal thermal annealing of both doped and pure crystals has been studied and the results have been compared with thermo- luminescence and thermal bleaching of induced silver centres. A good agreement is found between the temperature region of the reduction process of 35S, in the course of isochronal thermal annealing, and thermoluminescence data. A mechanism is proposed which explains the various oxidation and reduction processes in relation to thermoluminescence findings and thermal bleaching of different defect centres.The behaviour of 35S produced by the (n, p ) reaction in alkali chlorides has been investigated in several laboratories recently.1-4 The analytical problems involved in the measurement of different forms of radiosulphur have also been ta~kled.~. These investigations led to the identification of four independent precursors for 5S in the lattice. It is generally accepted that radiosulphide in solution originates from (35S2-+ 35S-) and CN3%- from radioactive neutral sulphur in the lattice. The exact nature of the precursors of 35SOz- and 3 5 S 0 2 - in the lattice is not known.However, there is some evidence to show that these entities originate from the interaction of trapped hole centres with the radio~ulphur.~~ * Impurities such as OH-, CN- and Ca2+ play an important role in determining the state of 35S as well as 32P in the alkali chloride lattices. A small amount of OH- impurity is sufficient to enhance the formation of high valence states of both 35S and 32P,99 lo while the presence of either CN- or Ca2+ stabilizes 35S in its low valence states.'# * A large body of spectroscopic information is now available regarding the behaviour of Ag+-doped alkali chloride crystals towards ionising radiati0ns.l It is interest- ing to try to correlate this information with the chemical states of 35S produced in the doped matrix, in order to have a better picture of the types of solid state reactions involved in the latter case.EXPERIMENTAL MATERIALS AnalaR grade potassium chloride was recrystallized twice from doubly distilled water. Potassium chloride, even in the " pure " form, contains substantial amounts of hydroxide ions which can affect the chemical form of 35S and 32P.9-10 Therefore, the hydroxide content of potassium chloride was reduced prior to doping by fusing the sample under t Present address : Nuclear Research Centre, Atomic Energy Centre, Atomic Energy Organization of Iran, Tehran. 2452M. KASRAI, B . NABARDI AND R . M. RAIE 2453 hydrogen chloride gas, as described before. * Silver chloride was precipitated from AnalaR grade silver nitrate and hydrochloric acid.The precipitate was thoroughly washed with doubly distilled water to neutral reaction and dried in an over at 105°C to a constant weight. All the preparations were performed in darkness to avoid the exposure of silver chloride to light. PREPARATION OF DOPED SAMPLES Weighed amounts of silver chloride and potassium chloride were mixed, degassed at 250°C under vacuum and sealed in a silica tube. The mixture was fused in a furnace at 780°C for 10min and then slowly cooled to room temperature. At this stage, the silver content of the doped sample was determined by neutron activation analysis using the 658 and 884 K eV gamma peaks of llomAg. After analysis more dilute samples were prepared by mixing a weighed amount of the solid solution with additional potassium chloride.The samples thus prepared weighed about 5 g and were transparent and clear although not single crystals. They were crushed to give crystals of 2-3 mm in diameter ; smaller pieces were excluded. Three such crystals were analysed in each batch for silver content. The values obtained were reasonably close to each other, showing that the samples were fairly uniformly doped with silver. Attempts were made to prepare uniformly doped samples with 1 mol % of silver. This was not very successful owing to the segregation of AgCl. NEUTRON AND GAMMA IRRADIATIONS Samples were heat-sealed in polythene vials, wrapped in aluminium foil and neutron irradiated in the Tehran University Research Reactor at a flux of 6 x lo1" neutron cm-2 s-l for 30 min.Post gamma irradiation was carried out using a 5000 Ci 6oCo source at room temperature. ANNEALING Isochronal thermal annealing of pure and doped samples was carried out in a thermo- statically controlled air oven for 30 min at the required temperature. Doped samples which are colourless before irradiation become brown. After thermal annealing at 450°C for 30min the colour changed to light brown. During annealing, the samples were covered with aluminium foil. Photoannealing was performed by placing the samples 25 cm from a medium pressure U.V. lamp. RADIOCHEMICAL ANALYSIS All samples were stored for at least 2 weeks prior to radiochemical analysis so that the 42K and 38Cl activities reached a sufficiently low level. The activity due to the long-lived llomAg isotope in doped samples was found to be negligible.Separation of 35S species into sulphide, thiocyanate, sulphite and sulphate in the presence of carriers and cyanide ion was carried out by the procedure described previou~ly.~ In the present system, there was a possibility that silver sulphide might be formed which would interfere with the analytical methods used. However, silver sulphide is soluble in alkali cyanide solutions forming a silver complex and sulphide ions.18 This was verified by the deliberate addition of macroscopic amounts of Ag2S into the system. RESULTS AND DISCUSSION Ag+ EFFECTS All samples were kept in darkness before and during the dissolution. The data presented are the mean values of at least three independent analyses. The reproduc- ibility was found to be within & 1.5 %.For comparison, all samples were neutron irradiated under the same conditions and for the same time. The effects of Ag+ concentration on the distribution of 35S among the valence states are presented in fig. 1. As the concentration of Ag+ is increased in the lattice,2454 RADIOSULPHUR I N Ag+ DOPED KCI the proportion of 35S0 is increased at the expense of 35S2-, while the proportion of (3sSO$- + 35S02-) remains virtually constant. The maximum effect is observed at 0.05 mol % of Ag+. mole % Ag+ FIG. 1.-Distribution of 35S as a function of concentration of Ag+ in KCl. 0, 35S2- ; 0, CNJ5S-; n , 35S0g- + 35S0:-. When Ag+ doped alkali chlorides are exposed to ionising radiation at 77 I< the prominent absorption bands are due to the neutral silver (Ago) and a trapped hole centre.No F band has been observed at this temperature.12 The electrons released on irradiation are preferentially trapped by silver ions rather than anion sites. However, if the irradiation is performed at room temperature, in addition to the F band, several new absorption bands are observed,'l the principal ones being B, E and D which are believed to be due to the Ag-, Ago and trapped hole centres, respectively.l'* l6 Increasing the concentration of Ag+ in the lattice has led to suppression of the F band and enhancement of the other bands.ll The above observations clearly indicate that electrons would be less available for 35S due to the competition with silver ions in the doped crystals. This is consistent with our data.One interesting feature of these data is that the fraction of 3 5 S 0 3 - and 3 s S 0 2 - has not changed during doping. This is in agreement with the previous suggestion that the precursors of the oxidised species result from the interaction of V type centres with radiosulphur.'. 7 9 * Although the identity of the trapped hole centres in silver doped alkali chlorides is not well known, it should not be significantly different in nature from the pure crystal l2 and therefore there should not be any major change in the yields of 35S032- and 35SOi-. It has been shown that if the nature of the trapped hole centres is altered due to the incorporation of CN- ions, it has a marked effect on the ( 3 5 S 0 $ - + "'SSo2-) yields.* THERMAL ANNEALING Isochronal thermal annealing of silver doped samples containing various propor- tions of silver are presented in fig.2, along with those of a pure sample. The thermal annealing pattern of 35S in doped samples is significantly different from the pure samples above 300°C. In the pure sample an initial reduction process takes place at the expense of neutral sulphur at - 150-200°C which is followed at 250°C onwardsM. KASRAI, B . NABARDI AND R . M. RAIE 2455 by an oxidation process at the expense of both neutral sulphur and the sulphide fraction. The fraction of neutral sulphur approaches zero as the temperature reaches 450°C. Since the boiling point of sulphur is 445°C and it has been shown that 35S moves towards the surface around this temperature,2 no attempt was made to go beyond 450°C in these experiments.100 2 0 0 3 0 0 4 0 0 I I I I I 100 200 3 0 0 4 0 0 temperature/"(= FIG. 2.-Annealing isochronal patterns for (a) pure KCI, (b) 0.005 mole % Ag+ ; (c) 0.05 mole % As+; (4 0.1 mole % Ag+. 0, 35S2-; 0, CN3?3-; A, 35S02-+35S02-. Thermoluminescence studies of gamma irradiated alkali chloride crystals have revealed interesting results which bear some resemblance to the above observa- ti0ns.l 9-22 Ausin and Alvarez Rivas, while investigating the thermoluminescence behaviour of irradiated alkali chloride crystals as a result of isochronal thermal annealing, in the range of 0-400°C, found several luminescence peaks which varied in intensity and peak position as the concentration of F centres increased in the initial sample.They also found a linear relationship between the total numbers of photons emitted during the thermoluminescence experiment and the concentration of F centres before heating. From these observations and photo-annealing experi- ments, Ausin and Alvarez Rivas concluded that the luminescence glow is partly due to the reaction of the F centres and trapped interstitial chlorine atoms and partly due to the formation of F centre aggregates or retrapping of electrons by anion vacancies.22 For a moderate irradiation, with F centre concentrations of -5 x 10l6 ~ m - ~ , the main thermoluminescence peak lies at 150-180°C and all thermo- luminescence glow virtually vanishes beyond 300°C for KCl crystals.20 Although no direct estimate of the F centre concentration is available in our case, it is not unreasonable to suggest that the concentration of the F centres in our sample is in the order of 10-l6 ~ m - ~ ; as this is within the " fast stage " of coloration in the alkali chloride,23 and our samples were exposed to a concomitant gamma dose of 1-782456 RADIOSULPHUR IN Ag+ DOPED KCl -1 Mrad.Having assumed that, we can reasonably compare the thermolumines- cence data with our observations regarding the behaviour of 5S. In fig. 2(a) the onset of the reduction process coincides with the thermolumines- cence peak at 15O-18O0C, which is due to the release of electrons in the lattice. Electrons are captured by the zero-valence sulphur and sulphide ions are formed. The fact that the (35SO$- + 35SO$-) fraction remains unchanged in this region is consistent with the nature of the precursors of these species being " SCl " compounds in the lattice 7* * and thermoluminescence findings.21 The " SCl " species are, apparently, unable to trap electrons.In their studies, Ausin and Alvarez Rivas have recorded the V band intensities during isochronal thermal annealing. Although the intensity of the band begins to decrease at around 150°C, major destruction of the centres occurs at about 200°C and is followed by total destruction at 300°C. We observed a similar pattern in the behaviour of the (35SO$- + 35SO$-) fraction, which parallels the annihilation of the V centres. In the range 200 to 300°C both F centres and V centres are mobile and therefore there is a competition between 35S reacting with these entities.As a result, an oxidation reaction is observed which tails off at around 350°C when all the defect centres are virtually destroyed in the pure crystal.21 In this range perhaps radiosulphur is also mobile which would facilitate the reaction, particularly the oxidation reactions involving chlorine atoms. Indeed in the case of chlorine implanted crystals the oxidation process is greatly enhanced when the crystal is heated above 200°C.' The pattern of isochromal thermal annealing in the Ag+ doped KC1 [fig. 2(b), (c) and (d)] is similar to that in the pure crystal [fig. 2(a)] up to 200°C. The maximum in the 35S2- fraction in the doped samples has been slightly shifted towards a higher temperature (250°C). This may be because there is more than one kind of electron trap in these samples which are thermally more stable than F centres.I4 The main difference arises above 300°C.Here the sulphide fraction begins to rise again at the expense of neutral sulphur. This becomes more prominent as the concentration of Ag+ is increased in the lattice [see fig. 2(6)-(d)]. This behaviour can be explained if we consider the nature of the trapped electron centres in the Ag+ doped matrix and follow their thermal stabilities. As outlined above, apart from F centres, E and B centres are also present in the doped alkali chloride crystals.11* 14* l6 Recent investigation of the isochronal thermal annealing of Ag+ doped potassium chloride indicates that the B centre starts to decay slowly from -340°C and is totally destroyed at about 550°C.The major decay occurs at around 400°C. l7 The concentration of Ag+ in the above investigation was 0.2 mol %, which is close enough to our sample of 0.1 % [see fig. 2(d)] for direct comparison. It is interesting to note that the commencement of the second maximum in the 35S2- fraction in doped crystals coincides with the thermal decay of the B centre. The decay products of this centre are Ag+, Ago and e l e c t r o n ~ . ~ ~ These electrons are available to be trapped at neutral sulphur sites to form the S2- ions. The oxidation process observed in the pure crystal at high temperatures is also seen here with lower intensity. Indeed the oxidation is reversed around 400°C owing to the availability of electrons released from the B centres. The neutral sulphur fraction seems to be more stable in doped crystals in the range 150-350°C.This is due to the fact that when F centres are annealed in this range, electrons are partially trapped at Ag+ sites and therefore 35S0 can survive until silver centres begin to decay at higher temperatures.M. KASRAI, B. NABARDI A N D R. M. RAIE 2457 POST-GAMMA IRRADIATION A neutron irradiated pure potassium chloride sample was gamma-irradiated (3 Mrad) at room temperature prior to isochronal thermal annealing. The results of these experiments are presented in fig. 3 along with those for the untreated sample. It can be seen that the principal effect of gamma irradiation on the initial distribution of 3sS is primarily the conversion of the S2- fraction to neutral sulphur, with little or no effect on the (35SO$-+35SOf-) proportion; this is in agreement with recent work.lo When crystals were free from OH- impurities, post-gamma irradiation had very little effect as far as the oxidation process was concerned.80 - 70 - 6 0 - x 3 5 0 - ..-( w f 4 0 - s % VJ 30- n 20- '< -- -- - -3"- I f temperature/"C FIG. 3.-Post-ganima irradiation effects, dashed line : annealing isochronal curve for the post- irradiated pure sample ; full line : untreated sampIe. O,., 35S2- ; 0 , W , CN3'S-; A,A, 35SO$-+ 35S0z-. I00 200 3 00 4 00 When thermal annealing of the post irradiated sample is compared with that of the untreated sample, as the former approaches 200°C the curves join together and there- after follow the same pattern. The data indicate that the main role of gamma irradiation, apart from producing V and F centres, has been the ionisation of the radiosulphide precursor to neutral sulphur. It is possible that the sulphite and sulphate precursor might have suffered further oxidation, but this cannot be detected in our method of analysis, since all oxidized forms of sulphur end up as either 35SO$- or 35SOi- in water. Perhaps a higher proportion of the oxidized form of 35S should be found above 200°C in the post-irradiated sample according to the mechanism outlined above. But if we bear in mind that on irradiation equal numbers of F and V centres are formed and that at high doses the system approaches ~aturation,~~ the observed annealing pattern may be justified.In view of the present findings and spectroscopic studies of sulphur impurities in alkali chlorides, it is reasonable to suggest that 3sS- ion should play an important2458 RADIOSULPHUR I N Ag+ DOPED KCl role in the thermal annealing process, although it cannot be distinguished from 35S2- in our analytical measurements.* The identity of the S- ion is now well established in alkali 2 5 If the band corresponding to the S2- in an alkali chloride is bleached by U.V.excitation, an S- ion and an F centre are formed and the process is rever~ible.~~ Therefore we suggest that the ionisation observed as a result of gamma- irradiation may well be due partly to the loss of one electron by the 35S- ion, as double ionisation of 35S2- is less likely to occur. This electron is regained when the crystal is heated from ambient temperature to around 200°C.PHOTO-ANNEALING EFFECTS The results of U.V. bleaching of Ag+ doped samples are shown in fig. 4. Ultra- violet irradiation has led to an increase in the fraction of radiosulphide, mostly at the expence of the neutral sulphur and (35S0g-+35S02-) portions. The process is virtually complete in 1 h. 2ot 1 60 I20 100 2 4 0 timelmin FIG. 4.-Photoannealing of Ag+ doped KCI (0.01 mole %). 0, "S2- ; 0, CN3'S- ; A, 35S03-+ 35so:-. The data suggest that once the F centres adjacent to 35S0 sites are bleached, subsequent irradiation has no effect. There is more chance that electrons released from F centres will be trapped at Ag+ sites. It is interesting to note that, although very small, a significant proportion of 35SO$- and 35SOi- precursors have been bleached.This indicates that these precursors behave like V centres. The authors thank the Atomic Organisation of Iran for radiation facilities and Dr. A. Owlya for the laboratory facilities and his support. We are also grateful to Dr. A. G. Maddock for his comments and interest throughout this work. A. G. Maddock and R. I. Mirsky, Proc. 2nd I.A.E.A. Conf. Chemical Eflects of Nuclear Transformations, Vienna, 1964 (Vienna, 1965), vol. 11, p. 41. C. Chioton, M. Szabo, I. Zamfir and T. Costea, J. Inorg. NucZear Chem., 1968, 30, 1377. J. Cifka and V. BraCokovA, J. Inorg. Nuclear Chem., 1966,28,2483. R. C. Milham, A. Adams and J. E. Willard, ref. (l), p. 31. M. Kasrai and A. G. Maddock, J. Chem. SOC. A , 1970,1105. ti J. P. Meyer and J. P. Adloff, Radiochim.Acta, 1966, 6, 217. ' M. Kasrai, A. G. Maddock and J. H. Freeman, Trans. Fuvahy SOC., 1971, 67, 2108.M. KASRAI, B . NABARDI A N D R . M. RAIE 2459 * A. G. Maddock, I. S. Suh, M. Kasrai and M. Raie, J.C.S. Faraday 11, 1976, 72, 257. lo J. L. Baptista and N. S. S. Marques, J. Inorg. Nuclear Chem., 1974,36,1683. J. L. Baptista, G. W. A. Newton and V. J. Robinson, Trans. Faraday SOC., 1968, 64,456. H. W. Etzel and J. H. Schulman, J. Chern. Phys., 1954,22,1549. C. I. Delbecq, W. Hayes, M. C. M. O'Brien and P. H. Yuster, Proc. Roy. SOC. A, 1963,271,243. l 3 N. I. Mel'nikov, R. A. Zhitnokov and P. G. Baranov, Fiz. Tverd. Tela, 1972, 14, 884 (Sov. Phys.-Solid State, 1972, 14, 753). l4 W. Kleeman, 2. Phys., 1968, 214,285. N . I. Mel'nikov, P. G. Baranov, R. A. Zhitnikov and N. G. Romanov, Fiz. Tuerd. Tela, 1971, 13, 2276 (Sov. Phys.-Solid State, 1972, 13, 1909). l6 P. D. Alekseev, B. D. Lobanov and I. A. Parlianovich, Fiz. Tverd. Tela, 1975, 17, 679 (Sou. Phys.-Solid State, 1975, 17,439). A. Altymyshov and B. Arapov, Fiz. Tuerd. Tela, 1975, 17, 1969 (Sou. Phys.-Solid State, 1975, 17, 1027). '' J. W. Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry (Longmans, London, 1923), vol. 3, p. 445. l 9 S. C. Jain and P. C. Mehendru, Phys. Rev., 1965, 140, A975. 2o V. Aush and J. L. Alvarez Rivas, J. Phys. C, 1971,5, 82 ; Phys. Rev., 1972, B6,4828. 21 V. Aush and J. L. Alvarez Rivas, J. Phys. C, 1974, 7,2255. 22 V. Aush and J. L. Alvarez Rivas, J. Phys. C, 1977,10,1089. 23 P. V. Mitchell, D. A. Wiegand and R. Smoluchowski, Phys. Rev., 1961, 121,484. 24 J. Prakash and F. Fischer, Phys. Stat. Sol., 1977, 3%, 499; F. Fischer and G. Grundig, 25 M. Baba, T. Ikeda and S . Yoshida, Japan J. Appl. Phys., 1976, 15, 231 ; 1975, 14, 1273. 2. Phys., 1965, 184,299. (PAPER 7/2071)

ISSN:0300-9599    

DOI:10.1039/F19787402452

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Effect of Polyelectrolytes upon the Kinetics of Ionic Reactions Part 6.-Some General Aspects BY ROBERTO FERNANDEZ-PRINI* Departamento de Quimica de Reactores, Comisi6n Nacional de Energia Atbmica, Avda. Libertador 8250, 1429-Buenos Aires, Argentina Received 2 1st December, 1977 The rate constant changes of ionic reactions due to the electrostatic polyelectrolyte effect can be described in some detail. For second-order reactions between ions of equal charge sign, it is shown that the inhomogeneous distribution of reactive ions is equivalent to a primary salt effect ; the primary salt effect cannot explain the results at high macroion concentration. An expression is derived for this case taking into account the probability of site occupancy by both reactive partners. For first-order reactions, the overall change in rate constant with polymer concentration may be explained in terms of the theories of polyelectrolyte solutions, even when the electrostatic effect may be coupled with more specific interactions. The study of the effect of macroions on the kinetics of reactions is an active area in polyelectrolyte physical chemistry.l.When the substrate is an ion, the inhomo- geneity introduced by the macroions on the ionic distribution may couple with more specific substrate-macroion interactions, e.g. dipolar attraction, hydrogen bonding, hydrophobic interactions, etc., to produce important modifications in the rate of reaction of the ionic substrate. Furthermore, when the substrate ions are drawn to the vicinity of an oppositely charged macromolecule by the large polyionic electric field, the reaction between the substrate and any reactive group forming part of the macroion, will be strongly favoured.Interactions in polyelectrolyte solutions may produce remarkable effects on the kinetics of ionic reactiom2 Morawetz and Vogel reported that the rate of aquation of Co(NH3)5C12+ induced by Hg2+ ions is enhanced 176 000 times when poly-(vinylsulphonic acid) is present in a concentration of 5 x equivalent ~ l m - ~ . In the case of macromolecules having no significant electrostatic interactions with the substrate, synergetic effects can also be observed. Klotz et aL4 found that the hydrolysis of phenolic esters could be increased by factors similar to those found for enzymes, when the solution contained poly(ethy1eneimine) (PEI) modified by the inclusion of reactive groups and non-polar chains into the macroion.In this case hydrophobic interactions between the substrate and the non-polar groups in the macromolecule draw the substrate close to the polyion which subsequently is attacked by the specifically reactive groups of substituted PEI producing a large overall kinetic effect. In spite of the variety of detailed mechanisms responsible for the observed modifica- tions in the rates of reaction of ionic substrates in polyionic solutions, it is possible to visualize some general trends which may be accounted for by electrostatic interactions. Even when the direct electrostatic contribution to the observed changes in reaction rates is quantitatively small, in many instances it is the causative factor of the overall rate modification^,^-^ i.e.when the (electrostatic) polyelectrolyte effect is suppressed 2460R . FERNANDEZ-PRINI 246 1 by salt addition or by neutralization of the polyionic charge, in the case of weak polyelectrolytes, no modification in the rate constants is observed. Mita et aL9 have recently analysed the influence of the polyelectrolyte effect upon various types of reactions. They successfully interpreted the results in terms of a type of primary salt effect using polyelectrolyte theories ; they used this interpretation to oppose the view that the effects arise from an increased concentration of reactant ions in the vicinity of the polyionic chain. In this work the features of the electrostatic interactions for first and second order reactions are discussed and the general behaviour to be expected is described, thus allowing rationalization of the observations in different systems.It is demonstrated that the primary salt effect approach is identical to that considering local distribution of ions. SECOND ORDER REACTIONS In general the rates of reactions involving oppositely charged mobile ions are inhibited by macroions,lO* l1 while the rate of reaction between two ions of equal charge is increased by polyelectrolytes having charge opposite to that of the reactant It has been proposed lo that the experimental results can be explained in terms of the modified local concentration of reactant ions due to the large electrostatic potential near the macroionic chain.If k2 and k; denote the second-order rate constants in the presence and absence of polyelectrolyte respectively, the argument above leads to the following expression for the rate of reaction u2, ions.3, 12-14 v2 = k,(m,) . (mB) = k,”(m,. m,). (1) The angular brackets indicate averages taken over the polyionic domains into which the solution volume is divided.2 Hence (mi) = mp, the stoichiometric concentration of ion i. The local concentration of species i is related to the reduced electrostatic potential, A@, by the Boltzmann relation A@ being the difference in reduced electrostatic potential referred to the domain boundary, hence at the boundary A@ = 0 and mi = m:. Eqn (2) may be replaced in eqn (l), and the rate constant ratio becomes, mi = rn; .exp (- ziA@) (2) If z, and Z, have the same sign, k2/ka will be larger than unity. If they have opposite signs the rate constant ratio will be smaller than unity. Eqn (3) is then capable of explaining qualitatively the experimental observations. When both reactant partners are concentrated in the same element of volume near the polyion, the rate of collision increases and the reaction will proceed at a higher rate than in the absence of polyion. In contrast, when the reactants have opposite charge they will be separated by the macroion which attracts ions of opposite charge to the chain and repels the reactants having the same charge sign. Using new experimental evidence, Morawetz et aL3* l2 suggested that eqn (3) was not adequate to represent the results. The medium near the chain may be different from that in the bulk of the solution and consequently it would not be adequate to identify ki with the rate constant in polyelectrolyte solution by eqn (3).Furthermore the electrostatic interaction may not be the only contributing factor in fixing the local2462 POLYELECTROLYTES I N IONIC REACTIONS distribution of ions. An outstanding example of this is the reaction between the cationic species of crystal violet with OH- ions;15 when polyanions are added the reaction is inhibited but when polycations are present the rate of reaction of both ions is increased. This is attributed to strong non-electrostatic interactions between the crystal violet cation and the positive macroion. In principle, A@ in eqn (2) may be replaced by Ajii/kT, where Ajii denotes the change in electrochemical potential of species i when it approaches the polyion.In this way non-electrostatic interactions can be included as well. In spite of the fact that specific interactions are responsible for the observed differences in the accelerating power of polyelectrolytes for different reactive ions of equal charge, for many ionic reactions in polyelectrolyte solutions which have no added salt, Aili, will be dominated by electrostatic interactions. These have been shown 5 9 7-9 to be in many cases the causative factor in the observed changes in reaction rate in polyelectrolyte solutions. A simple verification of this fact being the almost complete suppression of rate enhancement when sufficient salt is added to the polyelectrolyte solution.An apparently different way of explaining the polyelectrolyte effect on reaction rates is currently employed by Ise and coworkers using an approach analogous to that of Bronsted for ionic reactions in electrolyte solutions (primary-salt effect). They assume that, where yi is the activity coefficient of reactant i in the polyelectrolyte solution and the superscript # denotes the activated complex. Ise and Okubo l1 employed eqn (4) to explain quantitatively the observed inhibition in urea synthesis by polyelectrolytes. The activity coefficients of reactants in eqn (4) are experimental quantities and y z was assumed to be unity for the cyanate-ammonium reaction because the activated complex is in this case electrically neutral. They were able to account for the experimental kinetic results and also for the change in inhibition produced when polyanion salts with different monovalent counterions were employed.The activity coefficients may also be expressed in terms of polyelectrolyte theory, thus obtaining expressions for k2/kz which enable the theoretical prediction of the rate constant ratio. Mita et aL9 have used these expressions to explain experimental results. Eqn (3) and (4) have been considered to correspond to different models of reactant ion-polyelectrolyte interactions, it may be shown however that they are completely equivalent. This stems from the fact that the activity coefficients of mobile ions in polyelectrolyte solutions are related to the electrostatic potential in the polyionic domain.Marcus l6 derived a simplified expression for yi from the ratio of the concentration in the domain boundary, where the electrostatic force vanishes, to the average concentration in the solution. Thus, yi = m*/rn: and taking domain averages in eqn (2), m.4 = m.*{exp (-z,A@)>. Hence, y i = 1 /(exp ( - ziA<D)). (7)R. FERNANDEZ-PRINI If eqn (7) is now replaced in eqn (2), we have 2463 (8) which demonstrates the equivalence of eqn (3) and (4). If the yi terms in eqn (4) are expressed in terms of electrostatic interactions as described by the theory of polyelectrolyte solutions, eqn (8) is strictly valid. On the other hand, if the experimental activity coefficient data are employed to obtain the yi terms, existing non-electrostatic effects will contribute to yi and the factor ziA@ should be replaced by Ajii to maintain the validity of eqn (8).log (mm) FIG. 1 .-Effect of polyelectrolyte concentration on the rate constant of reactions involving two reactive counterions. The effect of the presence of polyelectrolytes on the value of the rate constant ratio for reactions between two mobile counterions increases with the polyelectrolyte Concentration, m, (expressed in monomoles dm-3) whenever m, is small compared with the concentrations of reactive counterions. This is illustrated in fig. 1. However k,/kz” is observed to pass through a maximum at m, = (mm)max, and then to decrease with m, because when there are too many inacroions the reacting counterions will be conceiitrated in different polyionic domains.for the quotient yA.yB/yA#B. They dealt with the situation corresponding to nz, smaller than mA or m B , i.e. to the ascending limb of the curve in fig. 1. For zA = zB their expression leads to negative values of k,/kz when m, > (2mm)max and the maximum of the ratio of rate constants is an artifact of their assumption that reaction only proceeds between condensed ions of one species and uncondensed ions of the other. Eqn (4) is basically unable to explain the descending limb of the experimental curve of k,/kz against m,; this will be discussed below. According to eqn (3), kJk; would be expected to increase with m, as the fraction of condensed l7 reactant counterions increases. When the polyelectrolyte becomes saturated with counterions, i.e. m, = (mm)max, a further addition of macroions would not be expected to affect the value of k,/k$ because it does not essentially alter the counterion distribution.Consequently the situation as described by eqn (3), as was the case for eqn (4), corresponds to an increasing value of k,/kz at low m,, with a plateau then being attained at m, > (m,),,,, as observed for first order reactions (see next section). Mita et aL9 have derived expressions based on Manning’s theory2464 POLYELECTROLYTES I N IONIC REACTIONS In order that eqn (3) may account for the experimental situation depicted in fig. 1, it is assumed that (kZ)max occurs when the degree of condensation of both reactants is a maximum on the same polyionic site (these polyionic sites will consist in general of more than one monomeric unit).Hence in eqn (1) the averages indicated should not be considered domain averages over all the solution, but rather the excess concentration of reactant averaged over those domains corresponding to sites occupied by both reactant ions. When an excess of macroion relative to the concentration of reactive partners A and B exists, the reaction of these in the vicinity of the chain will be constant, however there is a probability (increasing with m,) that some counterions A condense onto different polyionic sites from counterions B, producing a decrease in the rate of reaction compared with k2/k20 at (mm)max. In other words, if the polyelectrolyte concentration is increased above (mm)max, the fraction of sites containing only one reactive partner, either A or B, will increase. Under these conditions k2/ki will decrease as m, increases.According to this picture, the polyelectrolyte effect of rate enhancement is fundamentally due to those reactant counterions A and B condensed onto the same polyionic site. This implies that the averaged concentrations appearing in eqii (1) should be taken on occupied polyionic sites ; that is, that they will equal theydomain average over all the solution multiplied by the probability that a site be occupied by both reactant ions. Let us assume that the polyelectrolyte is first saturated by condensed B counterions and as rn, increases further, reactant A reaches saturation. This situation arises whenever lzAl < lzBl and mA > m,, or when 1 . ~ ~ 1 > lzBl and mA % inB.* Under these circumstances the number of polyionic sites per unit volume will be given by, mm rnL = - K (9) where K is the number of monomers per site.If m, increases, a situation is attained where all B and a fraction of A are condensed onto macroionic sites. When m, increases more, a point is reached where all A is condensed (if lzAl >, Izcounterionl, if not a constant maximum fraction of A).17 At this point (k2/k5) is maximum, and this is taken as the reference state to describe the polyelectrolyte effect on the rate of reaction. A further addition of polyelectrolyte will increase the fraction of sites having condensed B and no condensed A, thus leading to no enhancement of the rate of reaction. If the probability that A occupies a site already occupied by B is denoted by PA, eqn (3) may be transformed into Pi will be given by, P:= I, Pf: = m i .Kim,, for mA > mL for mA < mL eqn (10) becomes for mA < mL, log (k2lk3 = log (h/G)rnax-log (mrnlmi K) = log (kdk3max-log (RIK) (1 1) * Many experimental results were obtained for IZA~ > [zBl and mA & mg. In this case the relevant reactant concentration variable is mA, because as soon as all A becomes condensed a further addition of polyelectrolyte (considered in the log mm scale) will suffice to produce maximum condensation of B counterions.R . FERNANDEZ-PRINI 2465 where R = m,/m, is the concentration ratio between polyelectrolyte (expressed as monomer units) and added mobile ions (either inert salt or reactant ions), in the present case ms = mA ; (k2/k9max is the value corresponding to m A = mL. Eqn (1 1) reflects the fact that for high polymer concentrations, log (k2/k;) decreases linearly with log m, and the slope is (- l), a fact previously noted by Morawetz and VogeL3 According to eqn (l), at (m,),,,, R,,, = K and the size of the site may be calculated from the experimental data.Eqn (1 1) explains in a simple fashion that different values of (mm)max will be found for a given macroion whenever different initial concentrations of reactants are employed, because the maximum really depends on the ratio mm/mA and consequently there is no need to find other causes l 3 to explain the change in (mdrna. TABLE EFFECT OF POLYELECTROLYTES ON THE RATE OF REACTIONS INVOLVING TWO REACTIVE COUNTERIONS POlY- electrolyte PVS PP PSS PVS PMES PVS PMES PVS ref.reactant A 14 Co(Phen)$+ 3 Hgz+ 12 Fez+ Cophen): + 1.9 x 10-3 2 x 10-4 2 x 10-5 1 . 9 ~ 10-3 4 0 - 3 Co(NH 3) sCP+ 5x10-5 5x10-6 1.2~10-4 2.1 x 10-4 Co(NH3) gCP+ LOX 10-4 c~~-CO(NH~)~(N~): 5 x 10-5 5 x 10-6 3.8 x 10-4 trans-Co(NH3)4(N3); 5.9 x 10-4 9 x 10-4 4 x 10-4 s x 10-4 Ru(NHs):+ V" X = 2-aminopyridine, coO\lH3)5x+' 3-carboxylate (z = 3) X = p-dimethylamino- benzoate (z = 3) X = o-methylbenzoate X = p-sulphobenzoate X = o-sulphobenzoate (2 = 2) > 10-4 (2 = 1) (2 = 1) < 10-4 3.2 x 10-2 2.3 x 10-2 5.3 x 10-3 <6x 10-5 5 . 3 ~ 10-3 5.5 x 10-3 4 0 - 3 < 10-3 1.3 x 10-3 2 x 10-5 -- 4x 10-5 2 . 6 ~ 10-3 4.8 x 10-3 descending K 9.5 9.5 - 2.4 4.2 2.0 7.6 12 35.5 57 10.6 10.6 11 - - - - - slope -1.0 -0.8 -1.2 -0.8 - 1.0 -1.0 -0.93 - 1.3 - - -0.6 - 0.7 -0.6 -0.6 -0.7 -0.9 -0.9 -0.8 Since eqn (4) is a relation between thermodynamic quantities it is not possible to introduce into it the probability of simultaneous site occupancy.According to polyelectrolyte theory, 6, the activity coefficient of mobile ions depends very little on m,, consequently eqn (1 1) can only predict a monotonous increase in k2/k; with polyelectrolyte concentration until a maximum value is attained, thereon remaining constant. Table 1 summarizes the available data on bimolecular reactions in polyelectrolyte solutions. These data had to be interpolated from the reported graphs and this procedure will thus introduce some uncertainty into the analysis. On the other hand, very few studies have been undertaken to define the details of the log (k2/k2) against log (m,) curves.The results in table 1 show that the predictions of eqn (1 1) are largely confirmed. Except for the results in ref. (13), the descending limbs of the curves have slopes close to (- 1.0) as predicted. With regard to the calculated number of monomers per site, K, it is between 2 and 12 for lzAl > 1 ; for lzAl = 1, the values of K are 35.5 and 57.2466 POLYELECTROLYTES IN IONIC REACTIONS It must be remembered that all the polyelectrolytes in table 1 have the same value for the distance between two adjacent ionogenic groups, 0.255nm, which is the distance corresponding to monomers in poly-(vinylic) and poly-(phosphate) macroions. The observed range of K values suggests that specific interactions between counterions of equal charge play an important role in determining the value of (mm)max, i.e.the counterion-polyion interaction. FIRST ORDER PROCESSES For ionic substrates which undergo reaction by a unimolecular mechanism, the electrostatic polyelectrolyte effect would not be expected to influence the rate of reaction. The unimolecular hydrolysis of doubly charged phenyl phosphates however, is accelerated by polycation~,~~ 8 * l9 the rate constant ratio k/k" becoming >20. We shall describe some general features which characterize phenomenologically the observed effect of the polyelectrolytes on this type of reactions. The value of k/k" in polyelectrolyte solutions is found to depend on the concentra- tion ratio, R = (mm/m,), which is the fundamental concentration variable in poly- electrolyte theories.In general m, denotes the concentration of added mobile ions, but for solutions without added salts, m, = concentration of ionic substrate. The rate constant ratio increases with R until a maximum acceleration is observed for R = R,,,; from then on k/k" becomes independent of R. The rate enhancement by macroions is completely inhibited if enough electrolyte is added to the solution; this is strong evidence that the effect depends on the existence of an electrostatic field around the polymer chains. Moreover, the fact that k/k" depends on R rather than on mm,5 is a typical feature of phenomena governed by the polyelectrolyte effect, as described by the domain models of polyelectrolyte solutions.16* l7 The maximum value of k/k" increases as the polyelectrolyte-substrate interaction becomes more intense, 8 $ R,,, is the concentration ratio corresponding to the maximum interaction between polyion and reactant ions.Consequently the value of R,,, should depend on the charge density of the polymer and on the charge of the substrate. For weak polyions the charge density of the chain also depends on the degree of neutralization of the macroion i. The same dependence of k/k" on R will be found for bimolecular reactions involving other ions and species having a constant concentration in the polymer domain. This is the case when the other reactive partner is H,Q, a reactive group attached to the polymeric chain, or, at constant pH, OH- and H3Q+ ions. We shall define the polyelectrolyte interaction parameter, %A, by the expression, where Y is some intensive property of the solution for a given value of R and the subindices s and p denote its value in the electrolyte solution (no polyelectrolyte present, R = 0), and in polyelectrolyte solutions having no added salt (R = a), respectively.The kinetic %A is obtained if Yis made equal to the rate constant. Fig. 2 is a plot of the kinetic %A against R for a number of reactions in solutions of two polycations. Fig. 2 contains the kinetic data corresponding to the uni- molecular hydrolysis of p-nitro- and 2,4-dinitro-phenyl phosphates in poly-(vinyl- benzyltrimethylammonium chloride) (PVBA-Cl) solutions,5* a non-reactive strong polycation. Also in fig. 2, the kinetic interaction parameter is plotted for the same substrates reacting with the amino groups in PEI of various degrees of neutralization, as well as that for the reaction of acetylsalicylic acid with PEL7 The predictions ofR.FERNANDEZ-PRINI 2467 the electrostatic model are fully supported in all these systems. For bivalent substrate anions R,,, - 8 in PVBA-Cl solutions and ill,,, - 10 in PEI solutions; for univalent acetylsalicylate ion in PEI, iR,,, - 28. 0-0-i- 150 R : NPP/PVBA-Cl. (b) A : NPP/PEI (i = 0.47). (c) + : DNPP/PEI (i = 0.39). (d) 0 : FIG. 2.-% A (kinetic) against R for the following reacting systems : (a) 8 : DNPP/PVBA-CI, NPP/PEI (i = 0.25), 0 : DNPP/PEI (i = 0.24). (e) A: AAS/PEI (i = 0.39). (NPP: p-nitro- phenyl phosphate, DNPP : 2,4-dinitrophenyl phosphate, AAS : acetylsalicylic acid).The electrostatic nature of the kinetic %A is even more clear if the curves illustrated in fig. 2 are compared to those in fig. 3, where the osmotic interaction parameter, corresponding to poly-(methacrylic acid) of various degrees of neutralization with added NaBr,20 is plotted against R = mm/mNaBr for different values of the degree of neutralization. The curves of fig. 3 correspond approximately to iR,,, - 30. According to Manning’s theory of counterion condensation, the local distribu- tion of mobile ions depends on the charge parameter, 5, defined by, (13) e2 5 = itst = i- EkTb where b is the distance between two adjacent ionogenic groups and cst is the charge parameter when all the ionogenic groups are ionized. When 5 exceeds a critical value (tcrit), Manning’s theory assumes that the counterions condense onto the polymer chain to such an extent that the charge parameter is maintained equal to tcrit.It is interesting to try applying Manning’s model of counterion condensation to explain the kinetic effects for two reasons. First, it is a simple model having a clear physical meaning and secondly because it has proved quite successful in reproducing thermodynamic and transport propei-ties of polyelectrolyte solutions.2* l7 According to Manning’s theory, for monovalent ionogenic groups, tcrit = 1 /z, where z is the counterion charge number. A consequence of this model is that polyvalent counterions condense preferentially to monovalent ones. Thus the case of bivalent substrate ions appears particularly amenable to description by this model.As iR increases, complete condensation of bivalent counterions occurs when the substrate concentration nzs is sufficiently small compared to im,. This condition is expressed by im, l n s = --(l--a) = Z2468 POLYELECTROLYTES I N IONIC REACTIONS where a is the fraction of uncondensed counterions. That is, This expression agrees with the observation that X,,, depends only on the charge density and the substrate ion charge number. For PVBA-Cl and PEI solutions, iR,,, is predicted to be 2.4 and 2.7, respectively. These values are some 3.5 times smaller than observed. 0 1 I I 50 100 150 R (b) 0 : i = 0.5, (c) + : i = 0.3. FIG. 3.-% A (osmotic) against R for poly-(methacrylic acid) with added NaBr.20 (a) V : i = 0.8, This discrepancy between observed and calculated values of iR,,, may be attributed to the simplifications inherent in Manning’s model.The model is success- fully applied to the calculation of those properties which depend mainly on the free- counterions (e. g., counterion activity coefficient, counterion diffusion coefficient, osmotic coefficient, etc.). On the other hand, the observed effect of polyelectrolytes on the rate of reaction is governed mainly by the condensed counterions, and the hypothesis of counterion condensation similar to a phase transition, does not adequately represent the detailed phenomenon. This is probably also the reason why Holtzer and Manning 21 found that the condensation model did not explain correctly the titration of weak polyions, which is also strongly dependent on the state of the condensed counterions. CONCLUSIONS (1) The inhibition of the rate of reaction produced by macroions on ionic reactions between mobile ions with charges of opposite sign, and the enhancement of the rates of reaction between two ions having the same charge sign caused by oppositely charged macroions (for low R values), can be explained either by the primary salt effect, as applied to polyelectrolyte solutions, or by the local distribution of ionic reactant.Both approaches are shown to be identical in these cases. (2) The primary salt effect is basically unable to explain the decrease in kJk; for large rn, values. If the probability of simultaneous occupancy of macroionic sites by both reactant partners is taken into account, an expression based on local distribu- tion of ions can be derived which agrees with experiment yielding a descending slope of (- 1 .O) and allowing calculation of the number of monomers per site.R.FERNANDEZ-PRINI 2469 (3) For first order reactions, the electrostatic effect explains qualitatively the k/k" curve which is similar to that for %A for the osmotic coefficients. (4) The observation that R,,, is only a function of polyion charge density and substrate charge is demonstrated theoretically. The theory of counter-ion condensa- tion is, however, inadequate to predict quantitatively the value of R,,,. This is attributed to the fact that processes dealing with the condensed counterions, like the polyelectrolyte effect on the rates of reaction and the titration of weak polyions, cannot be dealt with by the simple model of counterion condensation. H. Morawetz, Accounts Chem. Res., 1970, 3, 354 ; Pure Appl. Chem., 1974, 38, 267. E. Baumgartner and R. Fernhndez-Prini, Polyelectrolytes, ed. K. C . Frisch, D. Klempner and A. V. Patris (Technomic Publ., 1976). H. Morawetz and B. Vogel, J. Amer. Chem. SOC., 1969, 91, 563. I. Klotz, G. Roger and I. Scarpa, Proc. Natl. Acad. Sci. U.S.A., 1971, 68, 263 ; H. Klefer, W. Congdon, I. Scarpa and I. Klotz, Proc. Natl. Acad. Sci. U.S.A., 1972, 69, 2155. R. Ferntindez-Prini and D. Turyn, J.C.S. Faraday I, 1973,69, 1326. D. Turyn, E. Baumgartner and R. FernAndez-Prini, Biophys. Chem., 1974, 2,269. R. Fernhndez-Prini, E. Baumgartner and D. Turyn, J.C.S. Farachy I, 1978, 74, 1196. K. Mita, S. Kunugi, T. Okubo and N. he, J.C.S. Faraday I, 1975,71,936 ; K. Mita, T. Okubo and N. Ise, J.C.S. Faraday I, 1976, 72, 1033. ' R. Fernhndez-Prini and E. Baumgartner, J. Amer. Chem. SOC., 1974,96,4489. lo H. Morawetz and J. A. Shafer, J. Phys. Chem., 1963,67, 1293. l 1 T. Okubo and N. Ise, Proc. Roy. SOC. A , 1972,327,413. l2 H. Morawetz and G. Gordimer, J. Amer. Chem. SOC., 1970,92, 7532. l3 R. C. Patel, G. Atkinson and E. Baumgartner, Bioinorg. Chem., 1973, 3, 1. l4 S. Bruckner, V. Crescenzi and F. Quadrifoglio, J. Chem. SOC. A, 1970, 1168. l5 T. Okubo and N. Ise, J. Amer. Chem. SOC., 1973,95,2293. l6 R. A. Marcus, J. Chem. Phys., 1955, 23, 1058; A. Katchalsky, Pure and Appl. Chem., 1971, 26, 327. G. S. Manning, J. Chem. Phys., 1969, 51, 934; Ann. Rev. Phys. Chem., 1972, 23, 117. l 8 E. S. Gould, J. Amer. Chem. SOC., 1970, 92,6797. l9 T. Ueda, S. Harada and N. Ise, Polymer J., 1972, 3,476. 2o Z. Alexandrowicz, J. Polymer Sci., 1960, 43, 337. G. S. Manning and A. Holtzer, J. Chem. Phys., 1973,77,2206. (PAPER 7/2247)

ISSN:0300-9599    

DOI:10.1039/F19787402460

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Stability of Metal Uncharged Ligand Complexes in Ion Exchangers Part 3.-Complex Ion Selectivity and Stepwise Stability Constants BY ANDRB MAES AND ADRIEN CREMERS" Centrum voor Oppervlaktescheikunde en Colloidale Scheikunde, Katholieke Universiteit de Leuven, de Croylaan 42, B-3030 Heverlee, Belgium Received 3rd January, 1978 A new method is presented for obtaining the stepwise stability constants of ion-exchanged metal- uncharged ligand complexes : it is based upon the measurement of the effect of increasing ligand concentration on complex-ion selectivity and provides a more sensitive means of characterizing adsorbed complexes than the usual method, relying on the measurement of ligand numbers in the exchanger. In special cases where a more favourable coordination of the fist ligand in the ion exchanger (as compared with the bulk solution) is accompanied by a less favourable coordination of the second ligand, a maximum occurs in the complex ion selectivity coefficient.This maximum occurs at a critical ligand concentration which equals the reciprocal of the average stability constant (2/K,K2) of the complex in solution. The maximum selectivity coefficient of the complex ion depends mainly on the ratio of stepwise stability constants in solution, Kl/K2, and its upper limit equals the ratio of stepwise constants, ~ l / K l in the exchanger and the solution. The method is illustrated by the case of the silver-thiourea coniplex in a macroreticular sulphonic acid resin in which the stability constant for the onecomplex exceeds the value in solution by more than four orders of magnitude.The study of the effect of ion exchange adsorption on the stability of metal- uncharged ligand complexes, which was initiated by Walton, 1-3 has received renewed interest recently. The stability constant of transition metal ions with ligands such as ethyleiiediamine or bipyridyl is increased in sulphonic acid resins,4* the effect being about one order of magnitude. Occasionally, such stabilization effects have been reported for monodentate ligands such as pyridine 6 * or thiourea.* The usual approach in determining the thermodynamic stability of such ion- exchanged complexes is based on a comparison of the ligand numbers of the metal ion in the bulk solution and the ion exchanger, as obtained from phase distribution data of metal and ligand.However, in assigning the correct amount of ligand to the coordinating metal ion in the exchanger, a significant amount of ligand may be present as exchangeable cation or physisorbed species. These corrections, which have to be estimated indirectly, must be subtracted from the overall ligand content of the exchanger and may be quite large, particularly so when dealing with unstable complexes and strongly basic ligands such as amines. An important aspect which has been overlooked in the past is the quantitative relation between the higher stability constants in the ion exchanger and the effect of complex formation on selectivity enhan~ement.~ A recent paper lo from this laboratory presented a new method for obtaining the overall stability constant of the coordinatively saturated complex in the ion exchanger.The results of this method, based upon a comparison of the ion exchange selectivity of the complex and the 2470A. MAES AND A . CREMERS 247 I aqueous cation, were shown to be in excellent agreement with the results obtained from complex formation analysis. Admittedly, the quantitative relation between excess overall stability constant and selectivity enhancement has also been stated by others but was not tested experimentally. Furthermore, it became apparent that stabilization phenomena in montmorillonite clay were more pronounced than in resins, the effect reaching up to three orders of magnitude for silver-thiourea and copper-ethylene diamine complexes. This paper presents an additional method, based upon the measurement of the effect of ligand concentration on ion exchange selectivity, for obtaining the stepwise stability constants of the intermediate complexes in the exchanger.The measurement of the selectivity enhancement will be shown to provide a much more sensitive criterion for complex stabilization and to obviate the necessity of measuring the ligand number of the intermediate complexes. The method is illustrated for the silver-thiourea complex in a sulphonic acid resin. This example is a particularly useful one in that it shows a case in which the measurement of ligand number is inadequate for the characterization of the complex but has to be combined with selectivity measurements. Additional cases will be treated in subsequent papers.THEORETICAL As shown in Part 1,l0 the ratio of the overall complex stability constants in the ion exchanger and the bulk solution P,/Pn, is identical to the thermodynamic equilibrium constant for the exchange of the aqueous metal ion M and the coordina- tively saturated complex ML,. This equilibrium constant is simply obtained as the ratio of equilibrium constants relating to the exchange of both species and an isovalent, non-complex forming reference cation Baq. In essence, this approach relies upon identical choices for the standard states of the uncharged ligand L in both phases (the hypothetical unimolal solution with the properties of the infinite dilution) and a concentration-independent unit partition coefficient (i.e. ideal behaviour of L in both phases).The same reasoning applies to the stability of some intermediate complex MLi (omitting valence signs for simplicity), i.e. in which K&,M refers to the equilibrium constant of the aqueous metal ion and the complex. However, unless the ratio of stepwise stability constants is unusually large, a separate study of the selectivity of intermediate complexes is generally not possible. In practice, at any intermediate ligand concentration, one is dealing with a mixture of species M . . . MLi . . . ML,, ranging from the aqueous metal ion to the saturated complex, and the distribution of the metal ion among the range of species is deter- mined by the cumulative stability constants pi and pi. We therefore define the overall selectivity coefficient Kc(L) at some arbitrary ligand concentration, a directly measurable property of the system as in which 2 refers to the respective equivalent fractions of exchangeable (complex) ions and m to their molalities in the equilibrium solution.Eqn (2) may be expressed in terms of cumulative stability constants Bi and pi2472 STABILITY OF METAL LIGAND COMPLEXES in which fM, fML . . . fMLn are the activity coefficients (defined in Part 1) in the multi- component system and L, the free ligand concentration, taken as identical in both phases. For the liquid phase, molality ratios have been identified with activity ratios, a reasonable assumption for isovalent species at low ionic strength. The activity coefficientsf,,f,,, . . .fMLn, which may be a function of both overall loading and the relative composition of the exchanger Z,, ZML .. . ZMLn seem hardly accessible to experimental evaluation. Eqn (3) is therefore of limited use, unless approximations are made with regard to the thermodynamic behaviour of the various species. Confining our attention to the case of a given overall loading and dis- regarding the effect of shifting composition onfM/fMLi (taken as unity) eqn (3) takes the simple form i = n i = 1 K,yn, in analogy with the notation used in Part 1 refers to coefficients at some arbitrary ligand concentration and in the the ratio of selectivity absence of L. Several interesting possibilities may be considered with regard to the dependence of K&n on free ligand concentration, as exemplified in eqn (4), but we propose to limit the discussion to two general cases which are most often found in practice.case 1 : xi > K,, i.e. the stepwise stability constants of all intermediate complexes are higher in the ion exchanger than in the bulk soliition. In such a case, K&n increases up to the characteristic limit for the coordinatively saturated complex pn/Pn, either continuously or in more-or-less pronounced steps depending on the relative values of K i and IC,. case 2 : Kl > Kl ; z2 < K2 . . . K,, < K,,, i.e. the coordination of the first ligand is favoured in the ion exchanger, whereas the opposite is true for the coordination of subsequent ligands. In such a case, K& attains a maximum value for a critical ligand concentration L,,,. This maximum may extend over a broad range of ligand concentrations or may be quite pronounced, depending on the relative values of the stepwise stability constants and the extent of ion exchanger stabilization of the first complex.In view of the practical importance in optimizing separation conditions in the presence of complexing agents, we explore this aspect in greater detail. Without loss of generality, we may particularize the analysis for the case of a two-complex ML2 for which Kl > K1 and K2 < K2. In that case, eqn (4) takes the simple form : l+81L+B,L2 1 +p1L+p,L2' Kiyn = - The value of the free ligand concentration L,,,, leading to a maximum in K&, is of course found by differentiation of eqn (5) : in which p2/P2 = r . L:axP2(B1-~P1)-2~ma~P2(r-1)-(~1 - P I ) = 0 (6) Three cases should be considered : (a) r = 1 ; i.e.identical overall stabilities of the complex ML2 in both phases. K',,,attains a maximum when the degree of formation of the complex in the bulk Solution is 0.5 (iisoln = 1) i.e. Lmm = l/JE- (7)A. MAES AND A. CREMERS 2473 This maximum value of K& is given by The upper limit of this maximum is given by Bl/pl which will usually not be attained unless Kl % K2. This is clearly illustrated in fig. 1 which shows the effect of the Kl/K2 ratio on the symmetrical Klyn-L relationship for a constant value of Kl/K1 = 10. The upper limit of Kiyn (max) is approached when Kl exceeds K2 by some three orders of magnitude. When K1 < K,, as is often the case with silver-amine complexes, KlYn (max) remains well below Kl/Kl. -log L FIG. l.-KLyn dependence on free ligand concentration for the case p2 = p2(= 10') and ,& = lop1 ; values of are, from top to bottom lo5, lo4, 1 0 3 e 5 and lo3. (b) r 2 1 ; overall stabilization of ML, in the ion exchanger.In such a case The second term under the square root sign is significantly larger than the first one : putting p1 = p p l and since p > r > 1, Consequently, p2 ( r - Q2 < PI. (p- l)@-r). (10) -- If we further take JB1 -Pl/2/j1 - rpi 1: 1, an approximation which is partly com- pensated by dropping the relatively small P2(r- 1) term, it may be anticipated that2474 STABILITY OF METAL LIGAND COMPLEXES eqn (7) will give a good estimate of L,,,. This is confirmed by the calculations in table 1, which shows a coniparison of L,,,, calculated from eqn (9), and the approxi- mate solution eqn (7), for the case of Kl > K2 and Kl < K2.For both cases, the maximum in Kiyn occurs at ligand concentrations which are only slightly higher than those estimated from eqn (7), especially so for the case Kl > K2. Moreover, similarly to case (a), the upper limit of K , / K , for KLYn (max) is not reached for small Kl /K2 ratios. TABLE 1 .-CRITICAL LIGAND CONCENTRATION Lmag CORRESPONDING TO K,',,(max), AS CAL- CULATED FROM EQN (9) FOR VARIOUS K,, Kz, K1, Kz COMBINATIONS r = p 2 / P 2 -log L S X log Filly2 log i32/K2 log r Ieqn (911 log K&(rnax) O.S. :a p2 > p2 = 10' lOgK1 = 4 ; 1OgKZ = 3 1.5 -1 0.5 3.474 1.305 2.0 -1 1 3.466 1 .so2 3 .O -1 2 3.463 2.801 4.0 -1 3 3.463 3.801 1 -0.5 0.5 3.098 0.552 1.5 -1 0.5 3.384 0.795 2 -1 1 3.350 1.298 3 -1 2 3.337 2.274 4 -1 3 3.335 3.274 5 -1 4 3.335 4.274 log K1 = 3 ; log 1 .2 = 4 O.D.,& p2 < p 2 = 10" 102 MI = 6 ; log KZ = 5 1 -2 -1 5.536 0.802 1 -3 -2 5.536 0.801 2 -3 -1 5.503 1.789 3 -4 -1 5.500 0.787 1 -2 -1 5.469 0.279 1 -3 -2 5.664 0.274 2 -3 -1 5.515 1.150 3 -4 -1 5.501 2.137 log K1 = 5 ; log K 2 = 6 log Ksyn (L = 1 / 4 / 8 2 ) 1.305 1.802 2.801 3.800 0.500 0.786 1.265 2.256 3.255 4.255 0.802 0.801 1.789 2.787 0.265 0.256 1.150 2.137 a O.S. is the overall stabilization ; b O.D. is the overall destabilization. (c) r < 1, i.e. overall destabilization of ML2 in the ion exchanger. In view of the arguments, presented above, L,,, may also be approximated by eqn (7). This is confirmed by the calculations, shown in table 1.In contrast to the case r > 1, the L,,, value estimated from eqn (7) is slightly below that predicted from eqn (9). Fig. 2 shows a graphical illustration of the effect of ligand concentration on K&n, as calculated from eqn (5) for the case p2 > pz and f12 < p2. The calculations shown in table 1 and fig. 1 and 2 necessitate various comments. First of all, it appears that KLyn is insensitive to small variations of L near L = 1 i.e. KLyn Omax) N K&(L = l/,/Z). Therefore, one may be confident that, from the standpoint of separation chemistry, optimal conditions prevail at L = 1/,/j2 (of course when Kl > Kl and E2 < K2). Secondly, it is possible to make a rapid estimate of Kl and E2 from two experimental measurements : KSyn for the coordina-A .MAES AND A . CREMERS 2475 - log L - log L FIG. 2.--K& dependence on free ligand concentration, as calculated from eqn (5) at various combination - of stability constants in the bulk solution and in the ion exchanger for the case of - 8 2 > 82 (left) - and 2 < p2, The l/l/Evalues are indicated by arrows. Left - : p1 = lo4, p2 = lo7 : b31 =lo7, PZ = lo'* (d). Right: p1 = lo_", p2 = l o l l : p1 = lo8, F2 = 1010 (a); ,!?I = lo9, -- p1 = lo7, p2 - = lo9 (a); p1 = 108, p2 = 1010 (6); p1 = 103, - p2 = 107 : p1 = 106, j2 109 ( c ) ; fl2 = iolo (b) ; pl = lo5, p2 = loi1 : pl = 107, rS, = 1010 ; p' = 108, p2 = 1010 (d). tively saturated complex, yielding p2/p2 and secondly KSyn for L = l / d & yielding PI from eqn (5). The third comment is of a more general nature and relates to the sensitivity of the two methods for measuring the stability of adsorbed complexes.K&n is much more sensitive to small variations of L, as compared with the ligand number of the adsorbed ions. This is readily seen by comparing the first derivatives 6Kiyn/6L and Gn/SL. For example in the case of a one-complex, or a two-complex at low ligand concentration (12) l+P,L s y n N ____ ?,tr (l+P,L) - The method of characterizing the stability of adsorbed complexes from selectivity changes offers an additional advantage from a purely experimental point of view: Klyn is directly related to the measured experimental property (i.e. the overall metal concentration in the solution) whereas the ligand number of adsorbed ions has to be obtained from generally small variations in overall ligand content of the bulk solution and subsequently to be corrected for ion exchange contributions.Never- theless, in attempting to characterize adsorbed complexes, it seems preferable to combine both methods to make sure that no unusual coordinations occur in the ion exchanger which, of course, could not be detected from selectivity nieasurements alone.2476 STABILITY OF METAL LIGAND COMPLEXES EXPERIMENTAL The ion exchanger used in this study is the strong acid macroporous sodium Lewatite (SP 1080; Merck, Analytical grade, 100-200 mesh) used in Part 2 of this series. The sodium-silver reference equilibria were carried out at constant total concentration (0.01 mol dm-3) relying on methods described in Part 2 and measuring the distribution of both ions, using radioactive 22Na and llornAg.The effect of thiourea (TU) on the exchange of silver ions was investigated in three sets of equilibrium measurements at the same total concentration (Ag+Na) : the first set was carried out at an overall molar ratio TU/Ag of 10 and a pH of 5.6-5.8 ; the second and third sets were carried out in the presence of 0.1 rnol dm--3 TU at pH values of 5.6-5.8 and 2.1, respectively. After sampling the batches of set 3, constant amounts of HN03 were added and the systems were re-equilibrated (pH = 0.87-0.89) and the equilibrium solutions analysed for Na and Ag. Some additional tests were carried out at low TU concentration (TU/Ag molar ratio of 5 ) by equilibrating batches of resin at p H values of 5, 2, and 1 respectively adjusting the overall amount of silver added to 50 % of the resin ion capacity (half loading). Only in the first set were TU phase distributions measured, using 14C labelled TU.RESULTS AND DISCUSSION The ion exchange isotherms for silver-sodium in the absence and presence of thiourea are summarized in fig. 3, which shows the equivalent fraction of (complex) 1 ' , I I I 1 6 5 4 3 2 -log mAg FIG. 3.-Sodium silver ion exchange isotherm in macroreticular sulphonic acid resin in the absence (0) and presence of TU: (0) -0.01 mol dm-3 TU, pH = 5.6-5.8 (set 1); (0) 0.1 mol dm-3 TU, pH = 5.6-5.8 (set 2) ; (A) 0.1 mol dm-3 TU, pH = 2 (set 3) ; (A) 0.1 mol dm-3 TU, pH = 0.88. Numbers in parenthesis indicate sodium ion loading.Inset: ligand numbers of adsor?d silver ions ; dashed curve corresponds to the bulk solution complex l2 and full line to values log K2 = 2.32 - a d log K3 = 1.77. silver ions in the resin phase against the logarithm of molar silver concentration in the equilibrium solution. The addition of TU has a significant effect on the ion exchange behaviour of silver: the first set (pH N 5.7, TU/Ag = 10) leads to a downward shift of the exchange isotherm by some three orders of magnitude. The ligand numbers of the silver in the ion exchanger, as shown in the inset of fig. 3, vary in theA . MAES AND A . CREMERS 2477 range 1.8-2.4 and are well below the corresponding values in the bulk solution, as calculated from the stability constants, reported by Berthon and Luca.12 Adding 0.1 rnol dm-3 TU (set 2), and keeping the pH constant, leads to a shift of silver ions back into the bulk solution.In both sets, 1 and 2, the Na+Ag ion occupancy equals the resin exchange capacity. Lowering the pH to ~ 2 , keeping the overall TU concentration at 0.1 mol dm-3, leads to an additional, though minor shift of silver into the liquid phase: however, a significant fraction of the resin exchange complex is now being neutralized by hydrogen, as evidenced from the observed shift of Na ions into the bulk solution. Lowering the pH down to 21 1, leads to an increase in the silver concentration in the bulk solution by nearly a factor of 10, whereas the sodium ions are almost totally displaced from the resin phase, their occupancy being < 3 %. The quantitative effect of complex formation on the exchange behaviour of silver ions can be expressed with reference to the sodium ion, using in which 2 and m are the overall equivalent fraction and molalities in the resin and the equilibrium solution.The results of these calculations are summarized in fig. 4, showing the resin-composition dependence of In K,(L). Graphical integration of the areas below these curves yields the values of In K, the overall equilibrium constants, given in table 2, along with the corresponding free ligand concentration at which the isotherms were carried out. These ligand concentrations were calculated from the known stability constants of silver, liquid phase composition and pH using 0.2 at 0.6 0.8 2, FIG. 4.411 Kc values, defined in eqn (13) as a function of silver loading in the absence (lower curve) and presence of TU. Symbols explained in fig.3.2478 STABILITY OF METAL LIGAND COMPLEXES for the stability of the protonated thiourea ion.ll It is apparent that lower ligand concentrations, which may be changed by pH variations, lead to enhanced selectivities of the complex. This is confirmed by the selectivity coefficients at half loading and very low ligand concentration, also shown in table 2. The data at pH = 1, shown in fig. 3, confirm the same trend but have not been included in the calculations due to the fairly large errors on K,, on account of the very low sodium occupancies. TABLE 2.-EFFECT OF TU MOLARITY ON SODIUM-SILVER SELECTIVITY : In K VALUES AS OBTAINED FROM GRAPHICAL INTEGRATION OF THE DATA IN FIG.4 (LEFT PART) AND InK, VALUES AT Z A ~ = 0.5 AT VERY LOW LIGAND CONCENTRATION In K mTu In Kc(& = 0.5) mTu Na-Ag 1.55 I 1.45 - Na-AgTU 8.55 10-2*4-10-1*6 8.65 8.35 x 10-3 7.35 5 x 9.94 1.75 x 10-3 7.15 9 . 5 ~ 9.97 5 . 6 0 ~ 30-4 The selectivity data can be understood in terms of a very large increase in the first formation constant and a decrease in the stepwise constants x2, & and K4. A first estimate of R2 and R, can be made on the basis of the ligand numbers, shown in fig. 3 : the result is that log K 2 = 2.32 and log z3 = 1.77. The stability constant K, can then be calculated from the In K values, which are reported in table 2, using the equation I + K ~ L + K ~ R ~ L ~ 1+K2L+K2K,L2+K2K3K4L3 -- and assuming a negligible contribution of the four-complex in the resin.The resulting value is log K1 /Kl = 4.3 4 0.1. A final test is shown in fig. 5 in which the experimental K& values at 50 % loading have been fitted in terms of eqn (4). This equation gives a good description of the 4 3 2 1 - log L log 2 3 = 1.45 (log K1 = 7.04 ; FIG. 5.-Effect of TU concentration on KLyn at Z A ~ = 0.5. Full line corresponds to eqn (4) using log K1 = 11.34. log Kz = 3.57; log K3 = 2.23 ; - lOgKz = 2.65 ; log K4 = 0.78)."A . MAES A N D A . CREMERS 2479 experimental data : the best fit stepwise stability constants are log Kl = 11.34; log K4 = 0.78).12 Perhaps it is worth mentioning that the maximum value of K&,, is reached at L N l / , / r K 2 , as predicted in the theoretical section. The stability pattern of the silver-thiourea complex in this resin is similar to that found in montmorillonite :9 a very large stability enhancement on the one- complex (one order of magnitude higher in the resin) which is partly offset in the less favourable coordination of additional ligands, the overall effect being about lo3 in p3 for both cases. At present, the reason for this extreme case of stabilization, which has never before been reported in the literature, is only speculative.In view of the similar behaviour in aluminosilicates, 9* l3 hydrophobic contributions to the stabilization cannot be invoked. Such a hypothesis seems particularly unattractive, considering that the excess free energy loss pertaining to the coordination of the first ligand is identical to the free energy of transfer of n-butane from aqueous solution to liquid hydrocarbon.14 An alternative and perhaps more plausible hypothesis is the formation of polynuclear complexes or polymer chains in the ion exchanger, as proposed for silver-ethylenediamine complexes. In solution, no such evidence is available for the silver-thiourea case, all complexes being identified as mononuclear species in which both nitrogen and sulphur may be involved as donor groups.9 However, in crystalline solids, polymeric forms are quite common in which sulphur bridging occurs between coordinating silver ions, such as the tris-thiourea-silver- per~hlorate,~' the bis-thiourea-silver chloride and the mono-thiosemicarbazide- silver ch1oride.l The special arrangement of negative charges in the ion exchanger may very well promote the formation of such chain-like structures in which the bridging ligand, corresponding perhaps to the one-complex, is very strongly bound.Whatever the nature of the stabilization phenomenon may be, this effect may be put to practical use in the development of extremely selective methods for metal removal. The present case is a particularly interesting one in that it makes possible the extremely efficient removal of silver ions, irrespective of the salinity or acidity of the aqueous phase.20 log R2 = 2.65 ; log R3 = 1.45 (log K1 = 7.04 ; log K2 = 3.57 ; log KS = 2.23 ; 9 We thank the Belgian Government (Programmatie van het Wetenschapsbeleid), the Katholieke Universiteit Leuven (Fonds derde cyclys) and the " Fonds voor Kollektief Fundamenteel Onderzoek " for financial support. R. H. Stokes and H. F. Walton, J. Amer. Chem. Soc., 1954, 76, 3327. L. Cockerel1 and H. F. Walton, J. Phys. Chem., 1962, 66, 75. M. C. Suryaraman and H. F. Walton, J. Phys. Chem., 1962, 66,75. 0. R. Skorokhod and A. A. Kalinina, Rum. J. Phys. Chem., 1975,49,187. A. Maes, P. Peigneur and A. Cremers, J.C.S. Faruduy I, 1978,74, 182. Chem., 1976,49,227. 0. R. Skorokhod and A. A. Kalinina, Russ. J. Phys. Chem., 1974,48,1663. 0. R. Skorokhod and A. G. Varavva, Russ. J. Phys. Chem., 1972,46,986. J. Pleysier and A. Cremers, J.C.S. Faruduy I, 1975, 71, 256. ti M. Kh. Akhmetov, L. A. Sapozhnikova, E. A. Savel'ev and G. N. Al'tshuler, Russ. J. Phys. l o A. Maes, P. Marynen and A. Cremers, J.C.S. Furuday I, 1977,73,1297. l 1 C. L. Sill& and A. E. Martell, Stability Constants of Metal Ion Complexes (The Chemical Society, London, 1964, 1971). l2 G. Berthon and C. Luca, Bull. SOC. chim. France, 1969,432. J. Pleysier and A. Cremers, Proc. 3rd In?. Conf. Mol. Sieves (Leuven University Press, Leuven, 1973), p. 206.2480 STABILITY OF METAL LIGAND COMPLEXES l4 C. McAulifFe, J. Phys. Chem., 1966,70,1267. l5 0. Erca and G. Berthon, Thermochim. Acta, 1973, 6,47. l6 A.'Belloms, D. De Marco and A. De Robertis, TaZanta, 1973,20, 1225. l7 M. R. Udupa and B. Krebs, Inorg. Chim. A m , 1973,7, 271. l8 E. A. Vizzini and E. L. Amma, J. Amer. Chem. SOC., 1966, 88,2872. l9 M. Nardelli, G. F. Gaspari, G. G. Battistini and A. Musatti, Chem. Comm., 1965, 187. 2o A. Cremers, J. Pleysier and A. Maes, U.S. Patent 4,051,026 ; U.K. Patent 1,462,599. (PAPER 8/006)

ISSN:0300-9599    

DOI:10.1039/F19787402470

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Kinetic Electron Spin Resonance Spectroscopy Part 6 .-Formation and Termination Reactions of Aliphatic Radicals by Reductive Dissociation of Halogeno-compounds BY PETER B. AYSCOUGH" AND GRAHAM LAMBERT Department of Physical Chemistry, University of Leeds, Leeds LS2 9JT Received 23rd January, 1978 The reactions of hydroxy-alkyl radicals with a variety of aliphatic halogeno-compounds RX have been studied. By examining the effects of varying concentrations of RX on the concentration and lifetime of the hydroxy-alkyl radicals it is shown that these are replaced by radicals Re produced by electron transfer to RX and subsequent loss of X-. Peak intensity anomalies are satisfactorily explained in terms of a hyperfine energy induced E-A polarization plus a contribution from an initial (emissive) polarization.Self-termination rate constants for nine aliphatic radicals have been determined. These rate constants are in the range 3 x 10' to 5 x lo9 dm3 mo1-' s-l in propan-2-01 at 300 K and have an inverse correlation with molecular mass. The problems associated with measurements of rate constants for the electron transfer step are discussed. For the reaction of Me,dOH with trichloroacetic acid the value (6.1 k 1.9) x lo6 dm3 mol-' s-' was obtained in propan-2-01 at 293 K. A number of radicals with oxygen attached directly to the radical centre have been shown to behave as one-electron reducing agents. For example, radicals R'R2eORy3 derived from alcohols and ethers 2-4 or cyclic ether^,^ reduce nitro compounds,2 carbonyl compounds and organic halogeno-compounds. Similarly k0; and dOOH have been shown by e.s.r.methods to reduce various halogeno- compounds RX where X = C1, Br, I to the radical Re by electron-transfer followed by the loss of X-.6 Phosphorus-centred radicals $03-, HP0: and H$O; also act as one-electron reducing agents though it has been suggested7 that the process involves halogen atom transfer. Beckwith and Norman studied the reactions of k0; and dOOH with a number of different halogeno-compounds in an aqueous rapid flow system using e.s.r. to detect the radicals formed. Since only one radical was observed in each case it was suggested that the method may have general applicability in the e.s.r. studies of specific radicals. The order of ease of reductive cleavage of RX was X = I > Br > C1, the same as for the reaction of hydrated electrons.8 Thus bromo- and chloro- compounds were reduced only if they contained substituents capable of stabilising the resulting radical.The reducing properties of the radical Me2bOH towards a number of halogeno-compounds were also investigated : the radical was found to be a less powerful reducing agent than 60; or dOOH. Other workers have also used radicals of the type R1R2e0H to generate a variety of different radicals for e.s.r. studies. 9-15 The only kinetic studies of the rate of electron transfer between ketyl radicals and halogeno-compounds are those of Gilbert, Norman and Sealy l4 who measured 24812482 KINETIC E . S . R . STUDIES OF ALIPHATIC RADICALS rate constants for the rate of electron transfer from 6H20H to ICH2CH2COOH and ICH,COOH.EXPERIMENTAL The e.s.r. and pulse photolysis system employed in this work has been described earlier. The system can be employed to record either changes in peak heights with time, using a C.A.T. (computer for averaging transients), or to record the spectrum of radicals present at any time during or after the light pulse using a gated integrator. Applications of kinetic e.s.r. spectroscopy to the study of ketyl radicals have been described in previous papers in this series.l* A method for correcting kinetic data for the effects of chemically induced dynamic electron polarization (CIDEP) has been described recently and has been employed in these studies. Chemicals used were of the highest purity available commercially and were used without further purification.Solutions were flowed through the sample cavity at a rate of a few cm3 per minute to avoid depletion and overheating. Rigorous degassing of the solvent (propan- 2-01) was necessary in order to avoid loss of radicals by reaction with dissolved oxygen when faster flow rates were needed. t FIG. 1.-C.A.T. traces for the high field q = 3 line of the e.s.r. spectrum of Me2k0H for various concentrations of trichloroacetic acid (a) none, (b) 4 x 1O-q (c) 8 x (d) 1.6 x mol dm-3. Upward pointing arrows indicate the light-on position, downward pointing arrows indicate the light-off position.P . B . AYSCOUGH A N D G . LAMBERT 2453 RESULTS Preliminary observations using a 5 % volume solution of acetone in propan-2-01 showed that the addition of as little as mol dm-3 of trichloracetic acid caused a significant diminution of the size of the seven-line spectrum associated with Me,eOH radicals, and a reduction in the lifetime of these radicals as observed from the C.A.T.traces. The effect of increasing the concentration of trichloracetic acid is shown clearly in fig. 1 : with a concentration of 1.6 x mol dm-3 the decay of the Me2d0H radical signal is less than the fall-time of the light pulse (x 100 ps). Measurements of the time-averaged e.s.r. signal from mixtures of 5 % volume acetone in propan-2-01 with increasing concentrations of trichloracetic acid showed that the spectrum of Me,kOH was being progressively replaced by another seven-line spectrum (hyperfine splitting = 0.29 mT) attributed to the radical eCl,COOH, as is shown in fig.2. Similar behaviour was observed when the radicals kH,OH, MekHOH or (CH,),bOH (produced by the photolysis of di-t-butyl peroxide in the appropriate alcohol) were used as reducing agents or when acetone was photolysed in the presence of methanol, ethanol or cyclohexanol (which results in the formation of the solvent radical R1R2kOH as well as Me,kOH radicals). These results may be interpreted in terms of a reaction sequence R ~ R ~ ~ O H + RX -+ R~R~COH+ +x- + R. R1R2CO+HX+R*. Since the relative concentrations of radicals R1R2kOH and Re can be varied over a very wide range simply by changing the concentration of RX, measurements of the rate of the electron transfer reactions are in principle possible. KINETIC SCHEME In most of this work the radical Me,kOH has been used as electron donor: generally it has been produced by the photolysis of acetone in propan-2-01 since this results in a higher steady state concentration than that resulting from photolysis of, for example, di-t-butyl peroxide in the same solvent.The reaction scheme given below may be appropriately modified for other ketyl radicals used as electron donors. (The superscripts s and t refer to the first excited singlet and triplet states of the molecules respectively) h v Me2C0 + (Me,CO)' (Me,CO)' + (Me,CO)' kisc (Me,CO)' 3 Me,CO k d (Me,CO)'+ Me,CHOH -+ 2Me2d0H ka Me,eOH+RX R-+Me,CO+HX k, 2Me,dOH 4 molecular products kl Ra+Me,COH 3 molecular products k2 2R- -+ molecular products k3 .2484 KINETIC E .S . R . STUDIES OF ALIPHATIC RADICALS In the absence of RX and in the dark period following a pulse the rate of dis- appearance of Me2dOH is given by eqn (1) . a = 2k,[Me2COH12 d[Me,COH] - dt and the second-order termination rate constant k, is readily evaluated. Similarly, when sufficient RX is added that only the radical Ra is seen in the steady state, it can be assumed that the only reaction occurring during the dark period is the combination or disproportionation of R- radicals and --- dCR*l - 2k3[R.12. dt Thus values of the second-order termination rate constant k3 may be obtained for any radicals which can be observed under these conditions. For intermediate situations in which both radicals R. and Me,doH are observed, the steady state concentrations of these radicals may be used, according to eqn (3), to permit the evaluation of k, if k2 and k3 are known.(3) P I - keCRXI [Me,dOH] k,[Me,tOH] + 2k3[R*]’ It is generally assumed on statistical grounds that k2 = 2(k1k,)3 and this assumption has been shown to be justified in the case of the radicals CH20H, MedHOH and Me2COH using direct e.s.r. measurements of radical decays.2o Others have reached the same conclusions and we have used this simplifying assumption in our analyses. In principle, therefore, k, may be determined by using direct measurements of kl and k3 in separate experiments, and measuring [Re] and [Me,dOH] in the steady state for a range of values of [RX]. However, in practice, serious difficulties resulted from the various spin polarization effects referred to in an earlier paper and it is necessary to take these into account before establishing the most appropriate conditions for the kinetic measurements. SPIN POLARIZATION EFFECTS The spectra shown in fig.2 are typical of the spectra obtained during the light pulse and from which [Re] and [Me,dOH] are to be measured. In fig. 2(a), the spectrum of the Me,kOH radicals obtained from acetone + propan-2-01 solution containing x mol dm-3 trichloracetic acid (TCA), intensity anomalies indicative of the operation of a hyperfine energy induced radical pair mechanism (E-A polariza- tion) are present. However, in the spectrum shown in fig. 2(b), with mol dm-3 TCA, the intensity anomalies are greater (all low field lines are in emission), despite the lower concentration and shorter lifetime of Me,eOH radicals.This is contrary to the well-established relationship between V4, the enhancement factor defined as [&(q) - &(q)]/[&(q) + &(q)], and concentration. [SH(q) and &(q) are peak heights for the high field and low field lines characterized by a given total nuclear spin state 41. It is also opposite in direction to the effect of S-To mixing induced by a g-factor difference between the encountering radicals. (The radical-pair theory predicts that for g1 > g2 the e.s.r. spectrum of radical 1 will show a totally emissive component while radical 2 will show enhanced absorption. For the radicals C12eC0,H (1)P. B. AYSCOUGH AND G . LAMBERT 2485 FIG. 2.-E.s.r. spectrum obtained by photolysis of 5 % volume acetone in propan-2-01 containing (a) !O-4, (b) mol dm-3 trichloroacetic acid.The central septet (1 : 2 : 3 : 4 : 3 : 2 : 1) is attributed to CClzCOzH radicals, the outer septet (1 : 6 : 15 : 20 : 15 : 6 : 1) is attributed to MezCOH radicals. I I I I 2 4 6 8 0' apparent radical concentration (c) FIG. 3.-Dependence of log( Vz/c) on apparent radical concentration (c) for the radical MezCOH in propan-2-01 in the presence of the radicals C12dC02H and (?H(CHzCO2H)CO2H. 0, Trichloro- acetic acid ; 0, bromosuccinic acid.2486 KINETIC E . S . R . STUDIES OF ALIPHATIC RADICALS and Me,eOH (2) Ag = f0.0050, so the Me,dOH radicals should show enhanced absorption, whereas we observe overall emission).22 We therefore conclude that the observed emissive component is the result of initial polarization of the Me,kOH radicals derived from triplet acetone and is independent of the radical-pair mechanism.To confirm this hypothesis we examined the dependence of the enhancement factor for the q = 2 lines of the e.s.r. spectrum of Me2dOH radicals on varing con- centrations of RX, where RX = CC13C0,H and CHBr(CH,CO,H)CO,H. Fig. 3 shows plots of log ( V2/c) against c, where c is the apparent concentrations of Me,COH radicals, i.e. after correcting for E-A polarization (by summing the heights of the high-field and low-field lines with q = 2). If E-A polarization were the only polarization effect present, Vq/c would be constant (as shown by dashed line in fig. 3) : in fact it increases markedly as c decreases and is virtually independent of the counter- radical. [Cl,dCO,H and 6H(CH,C02H)C02H, which are derived from TCA and bromosuccinic acid respectively, have quite different hyperfine parameters.] Con- versely, the initial polarization effect satisfactorily explains the observed increase in the emissive component with decreasing Me,kOH concentration.As is seen in fig. I the average lifetime of Me,eOH decreases with increasing RX concentration. A shorter lifetime means that fewer of the initially einissively polarized radicals have time to relax to thermal equilibrium; thus the contribution to the overall signal intensity from thermalised radicals is reduced and the emissive component is more readily observable. TABLE 1 .-RADICALS FORMED BY REDUCTIVE ELIMINATION FROM HALOGENO-COMPOUNDS IN halopeno-compound ally1 bromide iodoacetic acid dichloracetic acid trichloracetic acid bromosuccinic acid dibromosuccinic acid 2-bromopropionic acid 2-bromoisobutyric acid 2-bromo-n-butyric acid hexachloroacetone PROPAN-2-OL AT 300 K hyperfine splittings radical aa -H/mT US -rr/mT aci/rnT - H 1.395 H2C-C-CH2 0'425 1.477 CHClC02H 2.012 - 0.335 - 0.290 *CC12C02H - CH(CH2C02H)C02H 2.075 2.36 * CH(CHBrC02H)C02H 0.775 2.027 - CWMeC02H 2.04 2.465 - *CMe,C02H - 2.150 - *CH(CH2Me)C02H 2.01 2.305 - *ccl~coccl~ - CH2C62H 2.112 - - - 0.305 (k0.006) (k0.006) (f0.006) * = 0.090 k 0.006 mT We should note that the closely parallel observations of Zeldes and Livingston 9* 23 on the electron transfer from Me,dOH to oxalic acid may be explained in the same way, though this was not understood at the time.The initial polarization of the Me,dOH radicals may be transferred to the radical R- during the transfer step if this reaction occurs during the spin-lattice relaxation time of Me,dOH (ts is probably of the order of tens of microseconds in the systems under investigation). Such an occurrence must therefore be taken into account in measurements of [Re] taken < 100 ps after the end of the light pulse.P . B . AYSCOUGH AND G . LAMBERT 2487 4 - 3 - 2- 1 - MEASUREMENT OF TERMINATION RATE CONSTANTS Table 1 lists the radicals generated by photolysis of acetone in propan-2-01 at 300 K containing a halogeno-compound RX. Where the radicals have been char- acterised earlier by e.s.r. spectroscopy, the hyperfine coupling constants are in good agreement with those already reported.6 1 ms P 0.5 1.0 1.5 20 2.5 timelms FIG.4 . 4 4 Typical C.A.T. decay curve for the radical kC12C02H in propan-2-01 at 300 K. (6) Second-order analysis of data taken from the curve shown in (a). Radicals with large hyperfine splittings (> 1 .O mT) show intensity anomalies characteristic of E-A polarizations. In measurements of second order termination rate constants k, from the decay curves obtained from the C.A.T. traces, these anomalies were eliminated either by using the central peak where possible or by summing the traces for low- and high-field peaks with the same q index. The effects of initial polarization, where present, were eliminated by using peak heights obtained after 200ps from the end of the light pulse ( c , ~ ~ ) and plotting cZOO/ct against t (see fig.4) : the slope is then czoO k,. cZoO is estimated in the usual way, i.e. by calibrating the C.A.T. trace by comparison of doubly integrated spectra for standard solutions of DPPH in propan-2-01. 1-792488 KINETIC E . S . R . STUDIES OF ALIPHATIC RADICALS 0 Ten separate determinations of k, for Me,COH radicals in propan-2-01 were made, five using acetone as initiator and five using di-tert-butyl peroxide, giving a mean value 2k, = 1.40 x lo9 dm3 mol-1 s-I with a standard deviation of 0.09 x lo9 dm3 mol-1 s-l. FOP other radicals at least three separate determinations of k4 were made. The main error is however in the measurement of absolute values of concentration : previous studies of this kind suggest that errors of +20 % are typical.TABLE 2.-TERMINATION RATE CONSTANTS (kj) FOR VARIOUS RADICALS (Re) IN PROPAN-2-OL AT 300 K molecular 10qR I/ 10-8 k3/ radical R* mass/g mol dm-3 (f20 %) dm3 mol-1 s-1 CM2kHCH2 41 CHMeC02H 73 CH(CH2Me)C02H 87 .CMe2CO2H 87 CHCICOpH 93.5 CH(CH2C02H)COZH 117 CC12C02H 128 *CH(CHBrCO2H)CO2H 196 CCI 2cocc13 229.5 0.42 1.16 1.89 3 .OO 3.02 2.33 3.90 1.93 6.58 28.0If: 6.5 1 1.6+ 2.8 5.5& 1.2 5.6f 1.2 4.2f 0.9 3.9+ 0.9 2.3k0.5 1.6f 0.4 1.5f 0.4 The self termination rate constants (2k3) cover the range 3 x lo8 to 5 x lo9 dm3 mol-' s-l. There is a good correlation with molecular mass which has been noted earlier by other workers for both gas phase 24 and liquid phase reaction^.^^'^* The explanation advanced by Watts and Ingold 25 is based on the breakdown of the assumption that for diffusion controlled reactions the diffusion radius can be identified with the reaction radius (half the collision diameter) in order to obtain the relationship kdiff = 8 RT/3000q between the reaction rate and the coefficient of viscosity.For reactions between radicals in which the unpaired spin is strongly localised, so that there is an orientation requirement for reaction to occur, k, is likely to be less than kdiff by an amount which increases with increasing molecular size (and hence molecular mass). ESTIMATION OF RATE CONSTANT FOR ELECTRON EXCHANGE ke We noted earlier that in order to estimate k, we need values of k l , k3 and absolute values of [R.] and [Me2dOH] for various concentrations of RX, using eqn (3). The two rate constants required are readily obtained, as has been shown, but there are considerable difficulties in obtaining an adequate range of values of [R-] and [Me2dOH] in many of the systems examined.When the pseudo-first order rate constant ke[RX] is large, so that [R.]/[Me,dOH] is also large, the lifetime of Me,eOH is so reduced that the effects of initial polariza- tion become acute. Conversely, when [RX] is low (z mol dm-3) the ratio [R-]/[Me2dOH] is strongly flow-dependent and it is evident that depletion of RX is occurring during the residence time of the solution in the cavity. We were restricted to flow rates < 1 cm3 s-l and generally used rather smaller flow rates once it had been established that the ratio [R.]/[Me,eOH] was not affected by increasing the flow rate further.The absolute concentration of Me,eOH radicals in the presence of initial polariza- tion was obtained using the peak difference method described ear1ier.l This requires characterisation of the E-A polarization under conditions in which there isP . B . AYSCOUGH AND G . LAMBERT 2489 little or no initial polarization. The pair of q = 2 peaks were chosen (relative intensity 6 in the 1 : 6 : 15 : 20 : 15 : 6 : 1 septet), since these were the largest peaks not overlapped by the peaks from the radical R.. A further problem which may be serious when [We] = [Me,kOH] is the transfer of polarization from Me,bOH to Re during encounters. This means that characterisation of the E-A polarization of Me2610H radicals alone may lead to erroneous " corrections " when applied to systems in which encounters between Me,kOH and Re are a significant proportion of the total.Accordingly the most reliable measurements are those in which [Re] < [Me2bOH], which is unfortunately the situation in which depletion of RX during the photolysis is most likely to be serious. Despite these difficulties it was possible to carry out the analysis for the reaction Me,kOH + CC1,CO2H -+ Me,CO + HCl+ dC12C02H since conditions were particularly favourable in this case.28 A value of (6.1 & 1.9) x lo6 dm3 mol-l s-l at 293 K was obtained. This value is within the range of values quoted by Gilbert et aZ.14 for the similar reactions of CH20H with iodo-compounds. It is clearly possible in principle to measure rates of many similar electron transfer reactions which generate free radicals, though the errors associated with spin polarization effects on the one hand, and rapid depletion of RX on the other, may not be easily avoided.We are grateful to the S.R.C. for the award of a research studentship to one of us, and to Dr. A. J. Elliot for helpful discussions. Part 5. P. B. Ayscough, G. Lambert and A. J. Elliot, J.C.S. Farday Z, 1976, 72, 1770. M. McMillan and R. 0. C. Norman, J. Chem. Soc. B, 1968,590. N. H. Anderson, A. J. Dobbs, D. J. Edge, R. 0. C. Norman and P. R. West, J. Chem. Soc. B, 1971, 1004. A. L. Buley and R. 0. C. Norman, Proc. Chem. Sac., 1964,225. A. L. J. Beckwith and P. K. Tindal, Austral. J. Chem., 1971, 24,2099. A. L. J. Beckwith and R. 0. C. Norman, J. Chem. SOC. B, 1969,400. A. L. J. Beckwith, Austral. J. Chem., 1972, 25, 1887. A. Szutka, J. K. Thomas, S. Gordon and E. J. Hart, J. Phys. Chem., 1965, 69,289. H. Zeldes and R. Livingston, J. Phys. Chem., 1970,74,3336. lo H. Zeldes and R. Livingston, J. Phys. Chem., 1972,76, 3348. l 1 H. Zeldes and R. Livingston, J. Phys. Chem., 1973,77,2076. l3 R. 0. C. Norman and R. J. Pritchett, J. Chem. Soc. B, 1967,378. l4 B. C. Gilbert, R. 0. C. Norman and R. C. Sealy, J.C.S. Perkin ZZ, 1974, 1435. l 5 P. B. Ayscough, T. H. English and D. A. Tong, J. Phys. E, 1976,9, 31. P. B. Ayscough and M. C. Brice, J. Chem. SOC. By 1971,491. l7 P. B. Ayscough and R. C. Sealy, J.C.S. Perkin ZZ, 1973, 543. P. B. Ayscough and R. C. Sealy, J.C.S. Perkin ZI, 1973, 1620. P. B. Ayscough and R. C. Sealy, J.C.S. Perkin ZI, 1974, 1402. 'O R. Duck, MSc. Thesis (Leeds University, 1978). 21 B. C. Gilbert, R. 0. C. Norman and R. C. Sealy, J.C.S. Perkin ZZ, 1975, 303. 22 F. J. Adrian, J. Chem. Phys., 1971,54, 3918. 23 R. Livingston and H. Zeldes, J. Magnetic Resonance, 1973,9, 331. 24 L. Bertrand, G. R. de Mark, G. Huybrechts, J. Albreyts and M. Toth, Chem. Phys. Letters, 2 5 G. B. Watts and K. U. Ingold, J. Amer. Chem. SOC., 1972,94,491. 26 U. Borgwardt, W. Schnabel and A. Henglein, Macromol. Chenz., 1969, 127, 176. 27 K. Horie and I. Mita, PoZymer J., 1977, 9, 201. J. K. Dohrmann, R. Livingston and H. Zeldes, J. Amer. Chem. Soc., 1971,93, 3343. 1970,5, 183. G. Lambert, Ph.D. Thesis (Leeds University, 1977). (PAPER 8/113)

ISSN:0300-9599    

DOI:10.1039/F19787402481

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Relation between Prspylene Oxidation Performance of Copper- based Bimetallic Catalysts and the Redox Behaviour of their Surfaces @Y TOMOYUKI INUI,* TAKASHI UEDA, IVhSATOSHI SUEHlRO AND HARUO SHINGU Department of Hydrocarbon Chemistry, Faculty of Engineering, Kyoto University, Yoshida, Sakyo-ku, Kyoto, 606 Japan Received 13th February, 1978 Propylene oxidation and surface oxidation-reduction rate processes on supported bimetallic catalysts which consist of Cu as substrate with small amounts of adherent Ag, Au or Rh have been studied and the relation between them discussed The adhering components enhanced the rates of both the reduction of a preoxidized surface and of propylene oxidation in the order Rh 9 Au > Ag, but exerted no effect on the oxidation rate of a prereduced surface.The reduction processes were kinetically divided into three stages as follows : (1) the accelerating reduction rate psriod (ARP ; fraction reduced x = 0-0.3), (2) the maximal reduction rate period (MRP ; x = 0.3-0.Q (3) the decelerating reduction rate period (DRP ; x = 0.65-0.95). For all the catalysts, Arrhenius parameters of each reduction rate coefficient in the period MRP and DRP, and the rate of propylene oxidation showed compensation effects : log A = E/(2.3 RT,)+log C, and indicated the same isokinetic temperature Ts, (615 & 9 K). E for the initial reduction rate (&) was correlated with that of the rate of propylene oxidation (Eo) for each catalyst by the expression Ek = Eo f (8.5 L- 0.9) kcal m01-l. The accelerating eEects of the adhering coinponents were observed during the incubation period in the early stages of ARP.This indicates that small amounts of a metal which is more difficult to oxidize than Cu, having a dispersed structure on the surface of Cu substrate exhibit a spillover of the reductant gas, and perform the role of initiation nuclei for reaction with the surface oxygen. Recently, Schmidt and Luss found that the chemical composition of the active surface of an alloy catalyst in the working state differs to a marked degree from the bulk composition : they studied as model reaction the oxidation of ammonia and HCN synthesis over 90 % platinum-10 % rhodium gauze catalysts. Sinfelt ct aL2 and Ponec et aL3 reported independently that a second metal component added to a substrate metallic catalyst exerted markedly different effects on some hydrogenation and dehydrogenation reactions.These fundamental discoveries have already made a profound impact on catalytic refinii~g.~ Thus, when considering the surface structure of bimetallic catalysts, Sinfelt proposed the “ bimetallic cluster coccept ” on the understanding that the composition at the external surface of i? metallic catalyst differs from that in the interior, noting that catalyst performance varies markedly with the form of fine clusters of metallic elements which may be highly dispersed on the support. This eases interpretation in terms of the “electronic factor ”,6~ ’ as compared with models in which the bimetallic catalyst is considered as a uniform alloy. Since then, numerous studies of the correlation between the structural character- istics of bimetallic catalysts and their performance have been cond~cted.~~ *-I2 This finding was rapidly explored by Sinfelt, Ponec and others.2490T . INUI, T. UEDA, M. SUEHIRO AND H. SHINGU 249 1 However, the role of the second metal component which has such marked effects on the catalytic performance even when added in small amounts, and the relations between the kind of metals added or the structure of the clusters and these effects, are not yet quantitatively understood ; we are still at the state of accumulating infor- rnati~n.~. 8* l1 In our earlier work,13 it was observed that by the addition of small amounts of silver to a supported copper catalyst, both the oxidation activities of propylene or isobutene and their selectivity to form acrylaldehyde or methacrylaldehyde increased ; a favourable eEect on catalytic stability was also noted.This paper reports comparative studies on propylene oxidation and oxidation- reduction rate characteristics on the surface of Cu catalysts to which small amounts of Ag, Au or Rh adhere; we also consider the role of additives and the correlation between them. EXPERIMENTAL CATALYSTS Seven catalysts, of composition shown in table 1, were used. A porous SiO2-AI2O3 support pretreated at high temperature, 28 % porosity, 20-30 mesh, was impregnated with a solution of the ammonium complex of cupric nitrate. After drying and decomposition by heating, it was reduced completely in flowing hydrogen while the temperature was raised at a constant rate from 20 to 400°C for 2 h, and then treated at 800°C for a period of 30min in the same gas flow.The content of reduced copper was 10.0 wt %. The second metallic component was added, as less than 5 wt %, by the following ion-exchange method. The reduced copper catalyst was dipped into a 2 % aqueous solution of the precious metal salt containing the appropriate amount of the metallic ion to be exchanged, with shaking and cooling in an ice-water bath for enough time to complete the ion exchange reaction. A nitrogen blanket was used throughout the operation to prevent the oxidation of the copper surface as much as possible. Chemical research grade silver acetate, rhodium chloride and hydrogen tetrachloroaurate were used as the reagents. Afier washing the catalyst with distilled water and drying, reduction in hydrogen flow and heat treatment at 800-910°C for 30 min were repeated.The surface area of the support was measured as 1.6 m2 6-l (B.E.T.), and from measure- ment of the CO adsorption capacity l4 the copper area was estimated to be 17.4 m2 8-l of copper. The mean particle diameter of copper on the support, assuming it to be spherical, was calculated to be 40 nm. APPARATUS AND PROCEDURE A conventional fixed-bed flow reactor system was used for the catalytic oxidation of propylene. 5.0 cm3 of the catalyst was packed in a U-shaped Pyrex-glass reactor 9.5 nim in diameter. The catalyst bed was 9.0 cm in length, and contained a 3.5 mm O.D. thermo- couple well inserted into the longitudinal axis. The temperature profile of the bed was measured by shifting a thermocouple inside the well.Temperature control was provided by immersing the reactor in an electrically heated salt bath with stirring. The gas composition was established as : C3H6, 25 ; 02, 5 ; H20, 50 ; N2, 20 in mol %, so as to maintain a stable stationary state ; oxygen content of the catalyst during the reactions at 300-350°C was varied over 43-18 atomic % on the basis of complete oxidation to C u O as 100 %.13 With a constant space velocity of mixed. gas, 3600 h-l, the bath temperature was varied within the range of 30-75 % O2 conversion and 4--1OoC average temperature difference (A&,) between the catalyst bed and bath. The products were analysed both by gas chromatography and by chemical analysis.Oxidation and reduction rate processes on the catalyst surface were measured with a Shimadzu micro-thermogravimetric analyser TG-20 (tolerance 1 pg) with a gas flow control and gas purification system.2492 REDUCTION RATES OF BIMETALLIC CATALYSTS A 15 mg portion of the catalyst sample was placed in the sample pan which was suspended in the centre of a transparent quartz tube (13 mm diam.). After the sample was preoxidized or prereduced completely at 400°C, reduction of the former by 6 % Hz or oxidation of the latter by 6 % O2 diluted with He, was investigated at a constant temperature within the range 200-4OO0C, and with a constant flow rate, 50 cm3 min-l. Reproducible results were obtained without any hysteresis by the repeated use of such redox cycles under these conditions.RESULTS PERFORMANCE OF PROPYLENE OXIDATION Reaction values at 30 and 50 % O2 conversion and Arrhenius parameters for the space-time conversion of 0, (0, STC) on each catalyst are shown in table 1. Compared with the Performance of the copper catalyst (C-1) as standard, yield and selectivity for acrylaldehyde increased with the Cu-Ag catalyst (C-2) whereas for the Cu-Au catalyst (C-5) additional combustion activity was obvious and decrease of yield and selectivity for acrylaldehyde were noticeable at higher temperature ; however for the Cu-Au-Ag catalyst (C-7) the combusion activity associated with Au TABLE 1 .-CONSTITUENTS OF CATALYST SAMPLES AND THEIR PERFORMANCE IN C3 H6 OXIDATION performance of C3H 6 oxidation 30 % conversion of 0 2 50 % conversion of 0 2 catalyst STYAI STYA/ number metal contentlwt % a TC/OC SA/ % mol dm-3 h-1 T,/"C SA/ % mol dm-3 h-1 c-1 10.0 c u 296 79.0 1.34 326 78.2 2.03 C-2 9.7 CU-0.3 Ag 296 82.0 1.35 326 78.8 2.08 C-3 10.0 cU-0.05 Rh 203 38.0 0.32 286 27.1 0.37 C-4 9.7 CU-0.3 Rh 249 47.5 0.38 300 43.7 0.66 C-5 9.5 CU-0.5 AU 289 80.0 1.18 321 69.8 1.55 C-6 9.5 CU-0.5 Au-0.05 Rh 263 47.0 0.33 312 57.0 1.11 C-7 9.2 CU-0.5 Au-0.3 Ag 292 82.0 1.36 324 78.5 2.03 Arrhenius parameters of 0 2 STC catalyst number metal content/wt % E/kcal mol-1 A/mol dm-3 h-I c-1 10.0 c u 11.9 9.1 104 C-2 9.7 CU-0.3 Ag 11.9 9.1 104 C-5 9.5 CU-0.5 AU 10.7 3.4 104 C-6 9.5 CU-0.5 Au-0.05 Rh 8.3 5.0 103 C-7 9.2 CU-0.5 Au-0.3 Ag 11.1 4.7 104 C-3 10.0 CU-0.05 Rh 4.5 2.4 lo2 C-4 9.7 CU-0.3 Rh 6.0 7.9 lo2 a All catalysts are supported on silica-alumina.Average catalyst-bed temperature. C Selectivity of acrylaldehyde. d Space-time yield of acrylaldehyde. was moderated. For the 9.7 % Cu-0.3 % Rh catalyst (C-4) marked combustion activity was noted, and 30 % 0, conversion was attained at about 50°C below that of C-1. For the catalyst C-3 whose Rh content was reduced to one-sixth compared with C-4, further combusion activity was observed. For the catalyst C-6 to which Au together with Rh the effect of Rh mentioned above was inhibited. By-products other than acrylaldehyde were complete combustion products, C02 and H,O, with small amounts of acetaldehyde and acetic acid. For example, at an average catalyst-bed temperature of 326°C for the catalyst C-2, selectivities of COz,T .INUI, T . UEDA, M. SUEHIRO A N D H. SHINGU 2493 CH3CH0 and CH,COOH were 15.9, 4.4 and 0.9 %, respectively, on the basis or converted propylene. The do,, values corresponding to 30 and 50 % O2 conversion were 4.0 0.5 and 6.7 & 0.5"C, respectively, essentially independent of bath tempera- ture. A 0.5 % Au catalyst was almost inactive for propylene oxidation at <350°C. Popylene was oxidized by a 0.3 % Ag catalyst to the extent of one-tenth, in comparison with the 9.7 % Cu-O.3 % Ag catalyst (C-2), but the products were only those of complete combustion. O2 STC values at 250°C by catalysts, 3.7 % Rh, 0.5 % Rh, 0.05 % Rh, 9.7 % Cu-0.3 % Rh (C-4) and 10 % Cu-0.05 % Rh (C-3) were 4.81,0.65, 0.12, 2.48 and 3.10 mol dm-3 h-l, respectively. temperature/"C 350 300 250 0.8 0.7 n r( --.!+ rn I '0 E 0.6 - z 9 k r/l 0.5 nl M - 0.4 0 . 3 I I I I I I i 1.6 1.7 1.8 1.9 103 KIT FIG. 1.-Arrhenius plots for the oxidation rates of propylene of various catalysts. Catalyst number for each curve is : 0, C-1 ; 0, C-2; A, C-7 ; El, c-5 ; D, (2-6; 0, c-4; c-3. Thus, each single-component additive was different from the bimetallic catalysts with respect to both oxidation activity and product selectivity. Accordingly, rate enhancement of the bimetallic catalyst reaction could be a synergistic effect between the copper substrate and the additives dispersed near the surface. The straight Arrhenius plots for O2 STC of each catalyst converged to T, = 623 K, as shown in fig. 1, and showed a compensation effect expressed by eqn (1) : log A = E/(2.3 RT,) +log C, (1) where C, is the value of O2 STC at T,, namely 6.2 mol dm-3 h-l.The value of E, as shown in table 1, ranged from 4.5 kcal mol-l for C-3 to 11.9 kcal mol-i for C-1, while the oxidation rate decreased in the following order (expressed as catalyst numbers) : C-3 > C-4 > C-6 > C-5 > C-7 > C-2 = C-I.2494 REDUCTION RATES OF BIMETALLIC CATALYSTS Further, at T, = 350°C or more, the temperature difference (A@ within about 1 cm of catalyst-bed length from the inlet exceeded 20°C or so, and the reaction developed a tendency to concentrate at the inlet end and to be runaway, therefore, the stationary state was not attained at that temperature. REDUCTION RATE CHARACTERISTICS OF PREOXIDIZED SURFACE VARIATION OF REDUCTION RATE COURSE WITH TEMPERATURE Variation of fraction reduced (x) with time ( t ) in the case of the catalyst C-1 as an example is shown in fig.2. The (x, t ) curve, as is typically shown in the middle temperature range, 230”C, presented an S-shape similar to that found with auto- oxidation : x increased rapidly during the initial stages, maintained a maximal increasing rate in the range x + 0.3-0.8, and then increased more slowly. At higher temperature the steady rate began at an earlier stage and increased in magnitude, and the range of x over which this rate was maintained was extended. These tendencies were similarly shown for other catalysts. I .O 0.8 0.6 ’ 0.4 0.2 0 0 5 10 15 20 t/min FIG. 2.-Effect of temperature on the variation of fraction reduced with time. The copper catalyst C-1 was used.Temperatures (“C) for each curve are : (a) 400 ; (b) 350 ; (c) 300 ; (d) 270 ; (e) 250 ; ( f ) 230; (d 200. KINETIC DIVISION OF THE REDUCTION RATE PROCESS As shown in fig. 3, linearity was established in log x against log t plots from the initial time of the reduction up to x + 0.3, which corresponds to the inflection point of the (x, t ) curve in fig. 2. This period should be called the accelerating reduction rate period (ARP) (Voge and Atkins)15 since the reduction rate accelerates. The slopes of all the straight lines in fig. 3 are 1.6kO.l regardless of temperature. Moreover, this value agreed for all the catalysts listed in table 1. However, the intercepts of the abscissa ( x = 0.01) for those parallel straight lines, i.e., the incubation periods (ti) in which the initiation of reduction occurs are clearly differentiated.The order of t , is expressed with catalyst number and time (min) as follows : C-3(0.14) < C-4(0.17) < C-6(0.29) < C-5(0.39) < C-7(0.40) < C-2(0.60) < C-l(0.71) and summarized with components as follows, Cu-Rh < CU-AU < Cu-Ag < CU.T . INUI, T. UEDA, M . SUEHIRO AND H. SHINGU 2495 O2 uptake by the single element catalysts Rh, Au or Ag on the same support, having the same weight percent as the bimetallic catalysts, was not observed by TG measurement with 6 % O2 up to 500°C. From the inflection point of the x against t curve in fig. 2 at about 0.8 of x, it was shown as in fig. 4 that linearity was established in x against log t Elovich plots.This period was devoted as the maximal reduction rate period (MRP). The straight lines in fig. 4 may be expressed by eqn (2), which is the approximate solution of the integral from of eqn (3) : x = (2.3/a) log t + (2.314 log ak dx/dt = k exp (-ak) where k represents initial rate, and a the coefficient of rate decrease. a is obtained from the slope of the straight line, 2.3/a, and k from the intercept of the straight line at x = 0, i.e., the induction period to = (ak)-l. to decreased exponentially, while Y 0.1 0.5 1 5 1 0 50 100 t/min FIG. 3.-Logarithmic plots for the variations of fraction reduced with time at various temperatures. Data shown in fig. 2 were used. 0.1 0.5 1 5 10 50 100 tlrnin FIG. 4.-Sen1i-logarithmic plots for the variations of fraction reduced with time at various tempera- tures.Data shown in fig. 2 were used.2496 REDUCTION RATES OF BIMETALLIC CATALYSTS decrease of a was slight ; consequently changes of k mainly depend on changes of to. These values are discussed later. Above the idection point of the (x, t ) curve, except for x > 0.95, i.e., in the region in which the reduction rate decreased gradually (x >0.65), linearity was obtained in (dxldt, log t ) plots as in fig. 5. This range is called the decelerating 0.1 0.5 1 5 10 50 100 r/min FIG. 5.-Semi-logarithmic plots for the variations of the rate of fraction reduced with time at various temperatures. Data shown in fig. 2 were used. temperature /" C 400 350 300 270250 230 200 a 4 b 1 3 s- 0.5 0 . 1 0.05 1 . 4 1.6 1.8' 2.0 2.2 tlmin foreachcurveis: 0,C-1; (B,C-2; A,C-7; U,C-5; II,C-6; O,C-4; O,C-5. FIG.6.-Arrhenius plots for the initial reduction rate (k) of various catalysts. Catalyst numberT. INUI, T . UEDA, M. SUEHIRO AND H . SHINGU 2497 reduction rate period (DRP). The maximal rate obtained from the maximum point of the curve in fig. 5 was represented as I?,,,, and the mass transfer coefficient obtained from the slope of the straight line JA(dx/dt)/A log tl was represented as p. These values are discussed later. COMPENSATION EFFECT ON REDUCTION RATE Straight Arrhenius plots for the coefficients k, to, p and R,,, converged to constant T,, 61 5 + 9 K, for each coefficient as exemplified for k in fig. 6 ; the compensation effect is indicated similarly as in the case of O2 STC of propylene oxidation mentioned above.At higher temperatures, above 300°C, the straight lines turned downward and converged to another T,. This was attributed to an increase in the consumption rate of H2 on the surface of the catalyst sample, and the influence of the H2 supply in the TG apparatus on the reduction-rate-determining step. Therefore, the T, which was obtained by extrapolation of the straight lines in the lower temperature region was employed. The order of to, whose temperature dependence is negative, was reversed as compared with the other coefficients. T, and C, values for each coefficient are shown in table 2. TABLE 2.-PARAMETER OF COMPENSATION EFFECT FOR THE SEVEN CATALYSTS OF THE RATE OF HYDROGEN REDUCTION AND THE RATE OF PROPYLENE OXTDATION k,/min-l 11 623 (t&/min 0.11 610 u G l - l a x M ~ i ~ - 3.4 613 PJmin-l 8.3 606 (02 STC),/mol dm-3 h-l 6.2 623 The order for these coefficients was as follows : C-3 > C-4 > C-6 > C-5 > C-7 > C-2 > C-1.This agrees with the order of both ti and O2 STC. It was noted that the correlation between the reduction rate constant (k) and propylene oxidation rate (0, STC) regarding activation energy for each catalyst could be expressed as eqn (4) Ek = E0+(8.5+0.9) kcal mol-l. (4) OXIDATION RATE CHARACTERISTICS OF PREREDUCED SURFACES As shown in fig. 7, fast O2 uptake took place for about 1 min initially, without an induction period, then its rate decreased abruptly and it continued for a long time at a slow rate. This course coincided, within experimental error for each catalyst and temperature.In the Elovich plots for fraction oxidized (y), as shown in fig. 8, the rate of O2 uptake slowed down above y = 0.5 (35OoC)-0.2 (200°C). From the approximate straight line in the stage of fast O2 uptake, the initial rate, kox/min-l, was obtained for each catalyst in the same way as k. Temperature dependence on k,, obtained from its Arrhenius plots may be expressed as in eqn ( 5 ) : kox = 94 exp (-4.1 x 103/RT). (5)2498 REDUCTION RATES OF BIMETALLIC CATALYSTS 1.0 I - a I I I O O 5 10 1s 20 tlmin FIG. 7.-Effect of temperature on the variation of fraction oxidized with time. These curves coincided for all the catalysts listed in table 1 at each temperature. Oxidation temperature ("C) for each curve is : (a) 350 ; (b) 300 ; (c) 250 ; (4 200.0.8 0.6 0.4 A 0.2 0 - - I I I I I I l l l I I 1 I I 1 1 1 1 I 1 1 t L 0.1 0.5 1 5 10 50 t/min FIG. 8.-Semi-logarithmic plots for the variations of fraction oxidized with time at various tempera- tures. Data shown in fig. 7 were used. DISCUSSION Adherling components exert common accelerating effects on the rates of both reduction of a preoxidized surface and propylene oxidation in the order Rh % Au > Ag, but do not have any effect on the oxidation rate of a prereduced surface. Close examination of the characteristics shown in the reduction process is therefore essential. In the period ARP, the increase of x up to 0.3 was directly proportional to t1*6 independent of catalyst composition and temperature, indicating that the reduction develops by the same reaction process regardless of conditions from initiation to the stage at which the reduced surface corresponding to x = 0.3 is formed.It may be considered that during this process the reduced metallic part which originated on the oxidized surface as the nuclei of initiating reduction itself develops autocatalytically over the surface. Voge and Atkins l5 observed that the increase of x depends on the second power of t, and proposed a disc-like spread of metallic copper on the outer surface of anT. INUI, T. UEDA, M . SUEHIRO AND H. SHINGU 2499 oxide particle of copper, the increase of radius being proportional to time. 111 this work, however, x increased as tlg6, so some retardation factor such as the delay of desorption of water produced l6 may exist.The existence of different incubation times indicates that adhering metallic clusters were dispersed on the oxidized surface of the catalyst as nuclei on to which hydrogen was adsorbed preferentially and then migrated to the surrounding cupric oxide, which is a hydrogen acceptor. This phenomena may be regarded as so-called hydrogeii spill-0ver.l' The period MRP commenced from the stage at which the second order growth of the reduced metallic part on the surface attained saturation, and in which the reduction progresses inward from the oxide layer to a depth of 70 A (30 atomic layers of copper). Since the reduction rate obeyed an Elovich equation in this period, it was considered that the process including hydrogen adsorption and diffusion to the reaction phase was the rate-determining step. The linear relationship shown in (dxldt against log t ) plots in the period DRP has been analysed by the authors,18 with the finding that the slope /? conforms to the variation of mass transfer rate decrease with time in media in which the resistance to reactant diffusion increases with time.In this case, the increase in the resistance may correspond to the increase in thickness of metallic copper layer with the progress of the reduction. The boundaries of the region 0.65 < x < 0.95 are equivalent to Cu thicknesses of 50 and 90 A, respectively. Appearance of the accelerating effect not only in ti but also in k and /3 due to the additives shows that the hydrogen spillover effect continued in both period MRP and DRP. The compensation effects for k and /3 indicate that the accelerating effect of additives was displayed more markedly compared with the copper catalyst at lower temperature.At T,, however, the effect of difference of surface structure on the reduction rate vanished completely, suggesting that, at T,, the formation rate of nuclei from the cupric oxide by hydrogen reduction becomes so fast that its action is not differentiated from the role of nuclei composed of the second metallic component which has existed from the beginning. Next, despite the lower oxygen affinity of the additives compared with Cu, effects such as lowering of the oxidation rate of the surface were not observed. This was attributed to the added metal being dispersed in islands on the copper surface, with the substrate matrix Cu adequately exposed. Comparison of the oxidation-rate courses as shown in fig.8 with those of reduction shown in fig. 4 indicates that the initial rate in the range of y = 0.5(350°C)-0.2(2000C) is much faster than that of reduction. Finally, correlation between the performance of propylene oxidation and oxida- tion-reduction-rate characteristics of the surface must be discussed. The oxygen content during yropylene oxidation under the same gas composition as in this paper, at 300-350°C, was measured in our previous study l3 as 0.43-0.18, respectively, (expressed as y ) . On the other hand, the stationary concentration of adsorbed propylene during its oxidation is very much lower than that of oxygen. Therefore, the steady state of propylene oxidation can be regarded as being maintained by microscopic reaction cycles in which the reduction of the oxidized surface by adsorbed propylene occurs at the start as the rate-determining step; then a more reduced catalytic surface is produced by desorption of products and oxygen in the gas phase is rapidly supplied to the reduced surface exposed thereby.We may conclude that this similarity between the hydrogen reduction of the2500 REDUCTION RATES OF BIMETALLIC CATALYSTS oxidized surface and propylene reduction of the partially oxidized surface during stationary catalytic oxidation explains the similarity of effects, such as the similar compensation effects of the additives. Furthermore, the order of the propylene oxidation rates with varying catalysts, shown in the compensation effect, may also be understood from another view- point,16* '' i.e., that with increasing amount of products such as acrylaldehyde whose adsorption strengths are stronger than that of further oxidized products such as carbon dioxide or acetaldehyde, large magnitudes of the frequency factor and activa- tion energy for the oxidation rate are to be expected.As in the case of rhodium addition, if the hydrogen spillover effect on the first step of propylene oxidation, (i.e., hydrogen transfer from the methyl group of propylene),20 is too strong, an unfavourable effect on the selectivity of acrylaldehyde formation results. However, with the addition of silver, whose spillover effect is fairly moderate, the silver would instead act as follows.The added silver prevents the accumulation of surface intermediates by the accelerating effect of the silver on combustion of these materials, thereby preventing inhibition of the reaction by the intermediates, and maintains the stability of the stationary state. It was concluded that these effects reinforce one another, and that the added silver gives a favourable effect on catalytic performance. L. D. Schmidt and D. Luss, J. Catalysis, 1971, 22,269. J . H. Sinfelt, J. L. Carter and D. J. C. Yates, J. Catalysis, 1972, 24, 283. V. Ponec and W. M. H. Sachtler, J. Catalysis, 1972, 24, 250. M. Boudart, Award Symposium on Catalysis by Metals, Division of Petroleum Chemistry, Inc. h e r . Chem. SOC., Preprints, 1976, No. 2, 330. J. H. Sinfelt, J. Catalysis, 1973, 29, 308. D. A. Dowden, J. Chem. Soc., 1950,242. J . H. Sinfelt, Award Symposium on Catalysis by Metals, Division of Petroleum Chemistry, Inc. Amer. Chem. SOC., Preprints, 1976, No. 2, p. 350. J. R. Schrieffer, Award Symposium on Catalysis by Metals, Division of Petroleum Chemistry, Inc. Amer. Chem. SOC., Preprints, 1976, p. 331. lo F. W. Lytle, G. H. Via and J. H. Sinfelt, Award Symposium on Catalysis by Metals, Division of Petroleum Chemistry, Inc. Amer. Chem. SOC., Preprints, 1976, p. 366. l1 W. M. H. Sachtler, Award Symposium on Catalysis by Metals, Division of Petroleum Chemistry, Inc. Amer. Chem. SOC., Preprints, 1976, p. 353. l2 J. K. A. Clarke, Chem. Rev., 1975,75,291. l3 H. Shingu, T. Okazaki and T. Inui, Shokubai (Catalyst), 1964, 6, 32. l4 J. J. F. Scholten and A. V. Montefoort, J. Catalysis, 1962, 1, 85. l5 H. H. Voge and L. T. Atkins, J. Catalysis, 1962, 1, 171. l6 T. Inui, T. Ueda and M. Suehiro, Nippon Kagaku Kaishi, 1977, 934. l7 P. A. Sermon and G. C. Bond, Catalysis Rev., 1973, 8, 211. T. Inui, M. Murasawa and H. Shingu, Shokubai, 1975, 17, 109P. l9 C. Kemball, Proc. Roy. Soc. A, 1953, 217, 376. *O C. R. Adams and T. J. Jennings, J. Catalysis, 1964, 3, 549. ti G. M. Schwab, Disc. Faraday SOC., 1950, 82, 166. (PAPER 8 /253)

ISSN:0300-9599    

DOI:10.1039/F19787402490

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Surface Tension Minimum in Ionic Surfact ant Systems BY JOSEPH A. BEUNEN, D. JOHN MITCHELL AND LEE R. WHITE* Department of Applied Mathematics, Institute of Advanced Studies, Research School of Physical Sciences, Australian National University, Canberra, A.C.T. 2600, Australia Received 27th February, 1978 A theory is developed to explain the minimum in the surface tension of solutions of sparingly soluble ionic surfactants and its dependence on surfactant and electrolyte concentrations. The fundamental assumption is that at low pH, an acidic surfactant will be mostly undissolved and that this precipitate acts as a reservoir of surfactant molecules which enter the solution in the dissociated form as the pH is increased. This increase in solution concentration results in increased adsorption at the interface with a consequent lowering of the surface tension.At the so-called solubility edge, the surfactant becomes completely soluble and the solution concentration of surfactant becomes constant. Thus there is no further tendency for y to decrease as pH is increased. Indeed the conversion of neutral to charged surfactant species causes the monolayer to charge up. Thus, for pH values greater than the solubility edge the increasing electrostatic repulsion of negative surfactant from the interface causes y to increase. A minimum in y exists, therefore, at the solubility edge. In this model there is no necessity to postulate complexes of the surfactant species with peculiar surface activity to explain the observed y(pH) behaviour as has been suggested by other authors.Quantitative comparison of the theory and experiment for the oleic acid system is presented. 1. INTRODUCTION The surface tension of dilute aqueous solutions of certain surfactants has been found to exhibit a minimum as the pH of the solution is varied. The phenomenon occurs for both acidic and basic surfactants and depends sensitively on the ionic strength of the solution and the surfactant concentration. Fig. 1 illustrates some results for oleic acid obtained by Kulkarni and S0masundaran.l There is a significant variation in surface tension over the pH range, the minimum being more pronounced under conditions of high ionic strength. Apart from its intrinsic interest as a hitherto unexplained aspect of surface behaviour, this phenomenon has generated considerable discussion by virtue of its relation to mineral fl0tation.l. For a given surfactant, the flotation rate is observed to go through a maximum in the same pH range in which the surface tension minimum would occur. Clearly flotation is a non-equilibrium phenomenon and is probably influenced more by processes occurring at the mineral-solution and mineral-air interfaces than by those taking place at the solution-air interface.Nevertheless there must be some common underlying factor responsible for the correlation between flotation rate and surface tension. In determining the surface tension variation with pH, surfactant solution chemistry plays a major role. As will be discussed more fully later, there exists a certain pH below which an acid surfactant exists largely in the neutral form and a precipitate is present if the total concentration of surfactant is sufficiently high.In this pH range the concentration of neutral surfactant is, therefore, fixed. At higher pH the precipitate is no longer present and the concentration of neutral species 25012502 SURFACE TENSION MINIMUM 60.0 45.0 ?J 30 0 f-' 4:O 6.0 8:O 10.0 PH FIG. 1.-Surface tension of 3 x and 1.6 x mol dm-3 oleic acid in the presence of 0.2 mol dm-3 K+ (+) mol dm-3 K+ (x). Results of Kulkarni and Somasundaran.' decreases as more and more are hydrolysed to form ions. For a basic surfactant the situation is reversed. Finch and Smith consider the case of dodecylamine. They attribute the decrease in surface tension at low pH to the formation of increasing numbers of neutral surfactant molecules, the ions being dismissed as less surface active.The increase in surface tension at high pH is then difficult to reconcile with the constant con- centration of neutral species in this regime. These authors, therefore, postulate the formation at intermediate pH of an ion-neutral complex whose high surface activity is largely responsible for the low surface tension. The increase in surface tension at high pH is then a consequence of the breakdown of this complex. There are, however, several problems with the explanation, some of which indeed are discussed by the authors themselves. In addition it is difficult to see why the complex should have a greater surface activity than the separate molecules of which it is composed.Kulkarni and Somasundaran similarly invoke the existence of an ion-neutral complex, though in the case of oleic acid there is more independent evidence for its exi~tence.~ Neither paper, however, appears to treat adequately the effect of the single ions. Likewise, the intrinsic contribution of the surface potential to the surface tension does not seem to be recognised. In this paper we aim to show that it is not necessary to assume the existence of complexes in order to explain the surface tension results. If proper account is taken of the surface activity of the ionised form of the surfactant and of the contri- bution of the surface potential, then both the direction and magnitude of the observed variation can be adequately explained. This is not to say that the complexes do not exist.Rather, we maintain that they are not of prime importance in determining the surface tension variation. The gross features of this variation can be obtained without assuming the formation of complexes. Their effect is then to modify the results of a crude theory to bring them into better agreement with experiment. In the following section Thus in what follows we assume complexes do not form.J . A . BEUNEN, D . J . MITCHELL AND L . R. WHITE 2503 we formulate the problem froiii a rigorous thermodynamic standpoint. To carry through the calculation of the surface tension a model is required for the adsorption of surfactant molecules at an interface; this is developed in section 3. In the final section results are presented and discussed.The theory will be developed for the case of an acid surfactant, but that for a base is entirely analogous. 2. THEORETICAL MODEL We consider the following experiment ; C moles of weak acid surfactant RH is dissolved in one litre of aqueous solution of alkali MOH of known concentration. A known amount of the salt MX is added to adjust the ionic strength. The pH of the system is then varied by addition of the strong acid HX. We wish to derive the equations which will predict the variation in the surface tension y (or surface pressure) with pH. The solution species assumed present in this zero’th-order model are H+, OH-, RH, R-, M+, X- and we denote the activity of species by a. Thus, in the solution, we have where and aH+aQH- = K , (2.1) a,,+ = 1 0 - p ~ (2.2) (2.3) where K, is the dissociation constant for the weak acid surfactant.At high pH, the surfactant species is predominantly the R- form and at low pH, the dominant species is the undissociated RH form. The ionic species R- is stabilized in solution by Born energies and hydration, whereas the neutral species shows a distinct tendency for aggregation to minimize the hydrocarbon tail interaction with water. At low concentrations of RH (i.e., at high pH), this attraction of the hydrocarbon tails is dominated by the entropic contribution to the total free energy, when the RH species exists in solution as individual molecules. As the concentration of the RH species is increased (by lowering the pH), the entropic contribution to the free energy becomes less important, until a critical concentration is reached at which the tendency for aggregation will dominate.Further lowering of the pH will not change the solution concentration of the RH species, and the RH species so formed will precipitate out of solution. The pW at which this critical concentration of RH is reached, the so called “ solubility edge”, is simply calculated as follows: in the presence of precipitated RH, the chemical potential of the RH species is a constant (equal to the chemical potential of solid surfactant). Thus, we have where K, is the solubility product of the surfactant. At the solubility edge, a surfactant mass balance yields where we ignore the differences between activity and concentration in view of the low concentrations involved (C - From eqn (2.3) and (2.4): we have that a,,+a,- = K , (2.4) a,-+a,, = C (2.5) mol dm-3).a h = KJKa (2.6)2504 SURFACE TENSION MINIMUM is the activity (concentration) of RH in solution in the presence of the precipitate. Using eqn (2.4), (2.5) and (2.6) we obtain i.e., the solubility edge occurs at P H ~ = PKs+log,, [C-(KsIKa)I* (2.8) To calculate the surface tension of a system such as this, we must differentiate between the regimes pH < pHs where a precipitate is present and pH > pH, where no undissolved solid RH exists. The surface tension can in general be computed from the Gibbs adsorption isotherm (2.9) dy = -C T i dpi I where the sum is over all species in the system, where T i is the adsorption excess of the ith species and pi is its chemical potential.kT We have dpi = - dai ai kT - dCi N - Ci (2.10) where Ci is the concentration of the ith species in mol dm-3. Eqn (2.10) is exact if the activity coefficient of the species is constant across the pH range of the experiment. This will be so for the supporting ions M+ and X- since their concentrations change little over the pH range. Eqn (2.10) is a good approximation when the concentration is small even if it is changing considerably across the pH range. This situation adequately describes the other species Hf, OH-, R-, RH in the system. 1 I I > 0 B X FIG. 2.-“ Zero’th-order ” Stern layer model of Healy and White.lJ . A . BEUNEN, D . J . MITCHELL AND L. R. WHITE 2505 At the air-water interface a monolayer of RH and R- molecules exists.The relative amounts of each species in the monolayer is determined by the solution pH. The numbers of R- and RH molecules in the monolayer per unit surface area are denoted Yi- and rkH, respectively. The corresponding surface charge density is go = -qr:.-. (2.11) To determine the adsorption excesses of the ionic species, we must supply a model of the double layer which extends from the layer of head group ions at x = 0 to the bulk solution at x = co. We have chosen the “ zero’th-order ” Stern model of Healy and White illustrated schematically in fig. 2. In this model, there is assumed to exist an inner layer 0 < x < p of dielectric constant in which the density of electrolyte ions is zero due to finite ion size. Thus, the electrostatic potential (given by v21j9=o O < X < P ) 1s where $,, and lj9B are the potentials at the plane of head-group charge x = 0 and at x = p, respectively.At x = 0, we require 4 R = - - G o dx 0 & I so that $0 = h?+(oolm (2.12) where KI = E I / ~ z ~ (2.13) is the inner layer capacitance. We do not take lateral ion size into account in this model. Thus, in the region x 2 p , where the medium has the bulk solution dielectric constant E, the classical Gouy-Chapman theory is assumed to be valid. The concentration of the ith ion type (valency zi, bulk concentration Ci) is taken to be (2.14) The potential $(x) is therefore determined by the Poisson-Boltzmann equation Ci(4 = Ci exp [-wlj9(x)lkTl* where N is Avogadro’s number. The boundary conditions on @(x) are 444 -b 0 $(PI = @B X+Q) In our system all species are monovalent and we may write (2.15)2506 where SURFACE TENSION MINIMUM (2.16) and (2.17) is the total concentration of positive or negative ions in the bulk solution.If ao(ra-) is given, eqn (2.12) and (2.15) can be solved for @o and ~p (provided a value is assigned to the inner layer capacitance KJ. All cationic species have a positive adsorption excess due to their attraction to the negative monolayer, rl = cir+ (2.18) where [from eqn (2.14)], r+ = (exp [- q$(x)/kT] - 1) dx P > O (2.19) and all anionic species have a negative adsorption excess due to their repulsion from the monolayer, where ri = c i r (2.20) a3 = [ (exp [q$(x)/kT] - 11 dx < 0. (2.21) The adsorption excess of the R- species has two components, the adsorption in the monolayer and the adsorption in the double layer whereas the adsorption excess of the neutral species has only the monolayer component r R H = r&.(2.23) For our monovalent electrolyte system we have r R - = Ti- + c R - r - (2.22) ri- CO r++r- = -- tanh q1,b~/4kT (2.24) where we have used eqn (2.11), (2.15) and (2.16). This result is easily derived by making the change of variables (2.25) in the integrals (2.19) and (2.21) which define r+ and r- and using the first integral of the Poisson-Boltzmann equation 32nkTNC0 * - d$ = -[ ] sinh (q#/2kT). dx E x 103 (2.26)J . A . BEUNEN, D . J . MITCHELL A N D L . R . WHITE 2507 Since the quantity I?:- determines the charge density of the monolayer and hence the double-layer potential, all ionic excess quantities can be calculated if I-& is known.The monolayer adsorption excesses I?;- and must be calculated by a separate theory of monolayer adsorption which is developed in section 3. The exact details of that part of the theory are not important for the discussion of the qualitative features of the phenomenon of surface tension minima which follows below. We can now proceed to calculate the surface tension of the system from the Gibbs adsorption isotherm (2.9). We have, from eqn (2.9) dCH + dC0I-I- - r H + -- r o H - -- dY dCR- dCRH - = -rR- --rRH - kT CR - CRH CH+ COH- dCx- dCM+ CX- CMf rx- - - r M + - * Using the surface excess eqn (2.18), (2.20), (2.22) and (2.23) (2.27) (2.28) From charge neutrality in the bulk solution d(CH+ +CMi) = d(CoH-+Cx-+CR-).(2.29) Also, in the experiment described at the start of this section, the pH is changed by adding HX to the system, so that the metal ion concentration remains constant dCM+ = 0. Eqn (2.28) becomes (2.30) Differentiating eqn (2.3) we have dCH+ dCR- dCRH cHi cR' CRH +- = -* Eliminating dCR- from eqn (2.31), with the aid of eqn (2.32) we obtain (2.32) (2.33) This equation can be used to show the form of the y@H) curve without numerical computation. First let us consider the pH regime where there is undissolved RH surfactant in the system, i.e., pH < pH,. In this regime, the solution concentration of RH molecules is constant and given by eqn (2.6). Thus, for pH < pH, dCR, = 0 (2.34) and (2.35)2508 SURFACE TENSION MINIMUM The charge neutrality of the interfacial double layer system requires rM++rH+-roH--rx--rR- = o r;, = CO(T+ --I--) so that where we have used eqn (2.17), (2.18), (2.20) and (2.22).Thus r:--(r+ +r-)CH+ = (Co-CH+)r+-(CO+CH+)r- > O since r+ > o r- .C o from their definitions. Now dCH+ = d In uH+ = -2.303 dpH. CH+ Therefore, in the presence of the precipitate -- dy - 2.303 m[r;- -(r+ +r-)cH+] dPH (2.36) (2.37) (2.38) (2.39) < 0. (2.40) As the pH is increased, the surface tension of the system will decrease if there is undissolved surfactant present. In the regime pH > pHs when all the surfactant is in solution, we have CR- +CRH = C the total concentration of surfactant in this system. Thus, for pH > pH,, we have dCRH = -dCR-. (2.41) Coupling this result with the general result in eqn (2.32), we can eliminate dC,- to yield (2.42) Substituting this result in the general expression (2.33), we obtain Using a result from section 3, eqn (3.20), (2.44)J .A . BEUNEN, D . J . MITCHELL AND L . R . WHITE 2509 since $o is negative. From eqn (2.24) we see that (r++r-) is positive since Il/p is negative. Therefore Thus, for pH > pH, dr > 0. dPH When the system contains no precipitated increase with increasing pH. This analysis is (2.45) (2.46) surfactant, the surface tension will therefore capable of explaining the observed surface tension minimum (surface pressure maximum) without the necessity of postulating the formation of surfactant complexes with peculiar surface activities. Note that this simple analysis would predict a sharp cusp in the y(pH) graph.The smooth minimum observed experimentally can be explained by the fact that prior to precipitation a series of surfactant complexes, dimers, trimers and micelle-like species, must form as precursors to a macroscopic insoluble precipitate. This gradual onset of aggregation (over a pH range of -0.5 say) will lead to a smooth transition to the insoluble phase and imply a rounding of the sharp cusp predicted here. The theory outlined above predicts the qualitative features of the surface tension minimum. To compare theory and experiment quantitatively, we must first derive adsorption isotherms for the RH and R- species. 3. ADSORPTION ISOTHERMS In this section we derive the monolayer adsorption excess of a weak acid surfactant in terms of bulk system properties.The monolayer is comprised of two species R- and RH whose chemical potentials we denote by p- and po, respectively. The monolayer can be regarded as an open thermodynamic system able to exchange particles and energy with the bulk solution which acts as a reservoir wherein the chemical potentials of RH and R- can be varied. Consequently the thermodynamic properties of the monolayer system can most readily be calculated in the grand canonical ensemble.6- Consider, therefore, a unit area of the surface in equilibrium with the underlying solution. Let No and N- be the number of RH and R- species respectively on this area. The adsorption excesses are then just the thermodynamic averages of No and N- rSRH = <No) (3.1) rk- = ( N J . (3.2) The grand partition function for the monolayer is where Q(No, N-, T ) is the canonical partition function for a monolayer with given composition (No, N-).The average quantities ( N o ) and ( N - ) are evaluated by appealing to the maximum term approximation 6* i.e., (No) and (N-> are the values of No and N- corresponding to the maximum term in the summation (3.3). The evaluation of the partition function Q(No, N-, T ) is dependent on the model assumed for the monolayer and the particular approximations used. Since it is not2510 SURFACE TENSION MINIMUM the purpose of this work to develop a general model for monolayers, we choose one of the simplest models with some degree of physical reality, viz., the two-dimensional van der Waals gas. We assume that the monolayer molecules can be modelled by vertically orientated rods which possess lateral size so that a.is the area occupied by a molecule when the monolayer is close packed. We allow the molecules to interact with each other in a meanJieZd sense only, via dispersion forces and an exclusion potential which prevents overlap of the molecules. Since the observed spreading pressures are for most of the pH range equal to or greater than the equilibrium spreading pressure, the monolayer will be densely packed. Thus the above assump- tions will have a reasonable validity. The partition function can be related to the Helmholtz free energy in the usual way One component of the free energy is the electrostatic work done in charging up the interface Q(No, N-, T) = exp [-F(No, N-, T)/kT].(3.4) F,,(N-) = [ t,ho(a’) do’ (3.5) 0 where t,ho(a’) is the electrostatic potential at a charged head group when the total surface charge is a’. To determine I,!I~(~’) we assume the electrostatic model sum- marized by eqn (2.1 l), (2.12) and (2.15) to be valid. Thus, we may write where Fo is the free energy of the monolayer when the electrostatic interactions between the charged head groups is “ switched off ”. This free energy takes account of the kinetic energy of the molecules and the non-coulombic interaction of each molecule with its environment. It can be evaluated by calculating the corresponding partition function 6 * FWO, N-, T> = FO(N0, N-, T ) +Fe,(N-) (3.6) A-2(No+N-) [exp (- U/kT) dNor dN-r (3.7) 1 QdNo, N-, T) = ~ N o ! N - ! where U is the potential energy of a given configuration of the (No + N-) molecules and A is the thermal wavelength.6* U = co if any two molecules overlap In our model U has the form = U(No, N-) otherwise.The van der Waals approximation to the partition function is then [l -(N,+N-)a,](No+”-)exp [ - U(N,, N-)/kT]. (3.8) QdNo, N-, T ) = The interaction energy U(No, N-) is calculated by assuming that the head group and tail of each molecule contribute separately. The head group contribution to U(No, N-) is where upad and uh_ead are assumed to be independent of packing fraction. To compute the tail contribution, we assume all tails are identical, and that any two tails interact via a potential +(r). The energy of interaction of any one tail with the rest of the tails is A - 2(No+ N - ) No!N- ! N Uhead +N-u~_““~ J 4(r) P ( 9 2nrdrJ .A . BEUNEN, D . J . MITCHELL AND L. R. WHITE 251 1 where p(r) is the density of tails at distance r from the given tail. In the mean field theory adopted here, we assume and that the integral 14(r) 2nrdr is independent of packing fraction. Thus we write P(r) = (No+N-) for the energy of interaction of a tail u = (No+N-)utai'ao (3.9) where dail is the interaction energy of a tail with the rest of the environment when the monolayer is close packed (i.e., No + N- = a; l). The contribution of the tails to U(No, N-) is then and we may write +(No + NJ2 utai1a0 U(No, N - ) = No~~ead+N-~h_"ad++(NO+ N - ) 2 utai1a0. (3.10) The above expressions enable us to find the maximum term in eqn (3.3). Differ- entiating the logarithm of the summand of eqn (3.3) with respect to No and N- and equating the resultant expressions to zero yields two equations to be solved for the adsorption excesses, uiz.(3.11) (3.12) The chemical potentials p o and p- of the two monolayer species must equal the chemical potentials of the corresponding species in bulk solution, i.e., (3.13) (3.14) where CRH and CR- are the bulk concentrations of RH and R- in mo1drne3 of solution and M is the number of moles of solution per dm3 of solution (-55.5). Using these equations, we may write eqn (3.11) and (3.12) in the form CRH po = pg+kTln - M CR- p- =pO_+k~In- M2512 SURFACE TENSION MINIMUM where K = exp (upad+ uiail+ kT In A2+ kT In a,' -pg)/kT. (3.17) The constant K plays the role of the dissociation constant for the reaction solution vacant - adsorbed species +surface site - species (3.18) andkTln Kcan be seen to be the free energy change in transferring a neutral surfactant molecule from bulk solution to the close-packed monolayer.The first term on the right hand side of eqn (3.15) and (3.16) is the usual product of concentrations occurring in the mass-action equation corresponding to the reaction (3.18). All the other terms on the right hand side represent the activity coefficient terms which appear in the mass-action equation when the species involved interact with each other. The same constant Kappears in both eqn (3.15) and (3.16) since we have used the approximation (3.19) which implies that the non-coulombic free energy change on transferring a head group from bulk solution to the surface is independent of the state of charge of the head group.The validity of this approximation is of little importance since the free energy change on transfer of the tail is the dominant contribution to K. The approximation also serves to limit the number of adjustable parameters. Uhead- 0 po" = uh_'"--p_ 0 Subtracting eqn (3.15) from (3.16) we obtain (3.20) a result which we made use of in the last section. This equation expresses the fact that because the negative R- species in the monolayer interact repulsively with one another, the R- species are less readily adsorbed than the neutral RH species under identical solution conditions. Provided the density riH+ri- does not become too low, the isotherms (3.15) and (3.16) should provide a good description of the adsorption process, Only three parameters ao, utail and K are introduced, all having a well defined physical meaning.As we shall demonstrate below, these parameters may be obtained from separate experimental (n, a) data on the neutral surfactant species. At low pH, the surfactant will be present entirely as the neutral form in solution and in the monolayer. In this region, the monolayer is uncharged and all ionic surface excesses are zero and eqn (2.9) reduces to dy = -riHdPRH (3.21) The adsorption isotherm (3.15) becomes, for low pH, from which it follows that (3.23)J . A . BEUNEN, D. J . MITCHELL AND L. R . WHITE 2513 The surface pressure at low pH is then (3.24) where yo is the surface tension of the electrolyte solution with no monolayer present (rS = 0).Using eqn (3.21) and (3.22) Writing where a is the area per molecule in the monolayer, eqn (3.25) becomes rkH = a - l ( n-- a::"') a-a,) = kT. (3.25) (3.26) Eqn (3.26) is the two dimensional analogue of the van der Waals equation of state. While such a result is hardly surprising, it has been included since its derivation from the Gibb's adsorption isotherm does not seem to have appeared in the monolayer literature before. By fitting experimental (n, a) data to the theoretical eqn (3.26), the parameters a. and dai* can be determined for a given surfactant, for our present purposes oleic acid. 30.01 20.0 n 10.0 + + + 36.0 46.0 ~ 50.0-- a FIG. 3.-Van der Waals isotherm corresponding to the parameter values used in the calculation.The crosses are data taken from fig. 3 of Feher et al.* The required experimental data for oleic acid are not plentiful. None could be found for the temperature (25°C) of the y(pH) measurements of concern to us here. The data adopted are taken from Feher et aL8 and correspond to T = 21°C. Com- parison of theoretical calculations for one temperature with experimental results for another are admittedly uncertain. However, in view of the small temperature2514 SURFACE TENSION MINIMUM difference, it was considered more important to determine parameter values from an independent set of data so that the validity of the theory might be more realistically tested. Fig. 3 shows a fit of eqn (3.26) to the data. The curve is not a least-squares fit but has been chosen to match the experimental results more closely at high pressures, i.e., in that part of the isotherm which is important for the subsequent surface tension calculation.Clearly a two-dimensional van der Waals gas does not model the monolayer well at low pressures. In this region the monolayer has a lower surface pressure than the model predicts, i.e., it apparently exhibits a greater degree of cohesion. This could arise because, at large areas per molecule, the increased flexibility of the hydrocarbon chains allows a greater attractive interaction between neighbouring molecules than would be expected on the basis of the average headgroup separation. Such behaviour is not taken into account by the model. Modifications to this van der Waals model have not been attempted since the predic- tion of a (n, a) isotherm is ancillary to the main purposes of this paper and since the model, in spite of its crudeness, fits the data quite well in the regime of interest.The parameter values corresponding to the curve of fig. 3 are a, = 21.3 A2 and -3.7 kT. An additional indication of the molecular cross-section a. is provided by X-ray diffraction of solid oleic acid.g In the solid state sleic acid consists of layers, the molecules in each layer having their long axes parallel to each other and normal to the plane. The dimensions of the unit cell suggest a closest- packed area of 22.6 A2 per molecule. Thus a value of 21.3 A2 for an effective cross- sectional area does not seem unreasonable. To determine the constant K, we use the fact that in the y(pH) measurements low pdl corresponds to the presence of undissolved oleic acid.Thus the surface tension at low pH should be y,-.rr,, where y o is the surface tension of the electrolyte solution in the absence of surfactant and neq (= 30.5 dyn cm-I at 21OC) is the equilibrium spreading pressure of oleic acid. The value of a corresponding to n = 7teq is taken directly from the fitted (n, a) curve (3.26). Thus the adsorption excess of undissociated oleic acid at low pH is known and K can be determined by substituting into the isotherm (3.22). We obtain K = 10-11-3 corresponding to a free energy of transfer from bulk solution to the monolayer of - 26.1 kT per inolecule. It should be noted, however, that these parameter values are subject to another source of uncertainty arising from error in the measured areas per molecule.In typical monolayer experiments these are calculated on the assumption that all the surfactant remains on the surface. Initially the supporting solution contains no surfactant, but as the monolayer is compressed an increasing amount of surfactant desorbs so that chemical equilibrium between the monolayer and solution is main- tained. Thus the experimental values for the areas per molecule are too small. From the area per molecule at the equilibrium spreading pressure and the corres- ponding surfactant concentration in the underlying solution, i.e., the saturation concentration of oleic acid, the magnitude of the error can be estimated. For a Langmuir trough 1 cm in depth it is about 5 % at the high pressure end of the isotherm and of course less at lower pressures.An error of this order has some effect on the parameter values but the resulting error in the final results is likely to be minor compared with those introduced by the crudeness of the calculation. Uiail = 4. RESULTS Having determined all the adsorption isotherm parameters, we return to the calculation of theoretical y(pH) curves for oleic acid. We need one other model parameter uiz., the inner layer capacitance KI of section 2. Following Healy andJ . A . BEUNEN, D. J . MITCHELL AND L . R. WHITE 2515 White ' and in keeping with the simplicity of the model developed in this paper, has been taken as equal to the bulk dielectric constant E equal to 80. The Stern layer thickness has been assigned a value of 3 A, which seems consistent with known values for ionic radii (e.g., 2.3A in the case of a fully hydrated potassium ion)'' when some allowance is made for the fact that the centre of charge on the head groups is some distance above the lower surface of the monolayer.and are : K, = and K, = With the exception of the temperature the remaining parameters have been chosen to match the conditions of the surface tension experi- ments. Thus total oleate concentration C has been taken as 3 x lo-$ mol dm-3. For the case of high salt concentration C,+ is taken as 0.2 mol dm-3. For the other case, that of zero added electrolyte, CM+ is not of course zero since some alkali has been added to bring the solution to a starting pH of 1 1.2. Thus this case corresponds to a CM+ of 1.6 x The solution parameters for oleic acid are taken from Jung 60.0 - 35.0 - 3e.0 r I 10.0 4.0 6.0 8.0 PH FIG.4.-Calculated variation of surface tension with pH; upper curve corresponds to 1 . 6 ~ mol dm-3 M+ ions, the lower curve to 0.2 mol dm-3 M+. The points are those of fig. 1. Numerically, we proceed by starting at low pH, where y is known (42.1 erg cm-2) from the equilibrium spreading pressure of oleic acid. A small increment in pH is made and the concentrations of all ionic species determined at this new pH together with the solution concentrations of surfactant via eqn (2.1), (2.3) and (2.17). Then eqn (2.12), (2.15), (3.15) and (3.20) are solved simultaneously for the values of ri-? r&, @p and @'. The ionic adsorption excesses r+ and can now be deter- mined [eqn (2.24)].Eqn (2.40) can then be used to compute the increment dy in y corresponding to the increment dpH. By successively increasing pH in small steps and incrementing y by the above procedure, we calculate y(pH) up to the solubility edge. At this pH we continue the procedure with the exception that the eqn (2.40) for dy is replaced by the pH > pH, form, eqn (2.43). The calculated surface tension variation is presented in fig. 4 together with the experimental points of fig. 1 for comparison. The semi-quantitative agreement2516 SURFACE TENSION MINIMUM between the two must be regarded as satisfactory in view of the crudeness of the theory and the fact that it uses essentially no fitted parameters. The discrepancies that are in evidence in fig.4 are the result of the approximations made, rather than any fundamental error in the calculation. For example, the minimum takes the form of an unphysical cusp because the transition between the two pH regimes is taken to be infinitely sharp. At low pH, where there is precipitate, the activity of the RH species, aKH, is assumed to be constant since the activity of RH molecules in the interior of a crystal of precipitate is not affected by changes in the solution. At the solubility edge the precipitate disappears and the activity aRH now begins to vary with pH in accordance with eqn (2.5). Close to the solubility edge, however, the amount of precipitate is vanishingly small and cannot maintain a constant activity for the RH molecules.Hence aRH will actually begin to vary even before the solubility edge is reached, and the variation of all activities with pH will change continuously from that characteristic of low pH to that appropriate to high pH. It follows that the minimum will now be smooth since, as explained in section 2, the different variation of the surface tension in the two regimes is essentially a consequence of the different behaviour of the surfactant activities. 0.8 0.7 n iY k, B + 0.6 m d 0.5 - I- 4.0 6.0 8:O 10.0 PH FIG. 5.-Calculated variation with pH of ao(I'k- +rh), the normalised surface density of surfactant ; the upper curve is for 0.2 mol dm-3 M+, the lower for 1.6 x mol dm-j M+. The replacement of activities by concentrations is also a possible source of error. In particular this approximation underestimates the stability of ions in solution and hence overestimates the adsorption excess of surfactant ions. While this error is in the right direction it is probably too small an effect to account for the discrepancy at low pH.Likewise the temperature difference between calculated and experimental results (about 1 %) is also too small. Possibly this discrepancy is due to an incorrect estimation of the equilibrium pressure from the data of Feher et aL8 since this determines the limiting value of the surface tension at low pH. Theory predicts that the pH at which the minimum occurs, i.e., the solubility edge, should depend on the concentration of added surfactant but not on the ionicJ . A . BEUNEN, D . J . MITCHELL AND L . R .WHITE 2517 strength. The experimental results, on the other hand, suggest that the minimum is shifted to higher pH under low salt conditions. A possible cause for this dis- agreement lies in the value used for the dissociation constant K,. If this is determined in high salt conditions then the value appropriate for low salt is smaller, since the dissolved ions would lack the stabilising influence afforded by a large concentration of inert electrolyte. A lower value for K, would cause the solubility edge to be shifted to higher pH. Some insight into the physical factors leading to a surface tension minimum is provided by fig. 5. This is a plot of the total adsorption excess of surfactant iiormalised to a value of unity for a close-packed monolayer, i.e., ao(17~H+r~-). From this graph it is apparent that the surface tension minimum corresponds to a maximum in the number of adsorbed molecules.The physical processes causing the maximum may be envisaged as follows. At high pH there is no precipitate so the total amount of surfactant is fixed. As the pH is lowered the adsorption excess increases partly because, as Finch and Smith point out, the proportion of neutral surfactant in solution increases. However, at the same time the ionisation of the monolayer also decreases. Hence the surface potential falls and so an increasing proportion of the ions are also able to adsorb on to the surface. When the solubility edge is reached, however, a precipitate begins to form ; thenceforth the concentration of neutral species remains fixed while that of the ions decreases as these are neutralised and precipitate out. Although the surface potential continues to decrease, the concentration of ions decreases sufficiently rapidly to bring about a reduction in the number of adsorbed molecules. Thus, when all relevant physical factors are taken into account, the desired variation in surface tension can be obtained without invoking the existence of any ion-neutral complexes. The effect of such complexes, if present, would be twofold. First, since they are an additional soluble species, the solubility edge would be shifted to lower pH. Secondly, the depth of the minimum would be raised or lowered according as the complex was less or more surface active than its constituents. In any case their effect would be confined to intermediate pH and would not alter the gross features of the curve. The authors thank Dr. Somasundaran for bringing the problem to our attention and Prof. T. W. Healy for suggesting the explanation developed above. R. D. Kulkarni and P. Somasundaran, Amer. Inst. Chem. Eng. Symp. Ser., 1975,71,124. J. A. Finch and G. W. Smith, J. CoIIoid Interface Sci., 1973, 45, 81. R. F. Jung, MSc. Thesis (University of Melbourne, 1975). T. W. Healy and L. R. White, Adu. CoIIoid Sci., 1978, to appear. E. J. W. Verwey and J. Th. G. Overbeek, The Theory of the StabiIity of Lyophobic Colloids. (Elsevier, New York, 1948). D. A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976). T. L. Hill, An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, 1960). A. I. Feher, F. D. Collins and T. W. Healy, Austral. J. Chem., 1977, 30, 511. S. Abrahamsson and I. Ryderstedt-Nahringbauer, Acta Cryst., 1962, 15, 1261- lo F. A. Cotton and G. Wilkinson, Aduancedhorganic Chemistry (Interscience, NeM York, 1972) (PAPER 8/358)

ISSN:0300-9599    

DOI:10.1039/F19787402501

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Low Temperature Infrared Spectroscopic Study of the Solvation of Ions in Water t BY IMANTS M. STRAUSS AND MARTYN C. R. SYMONS* Department of Chemistry, The University, Leicester LE 1 7RH Received 13th March, 1978 In general, when aqueous electrolyte solutions are frozen, the infrared spectrum in the 0-H stretching region reveals narrow bands assignable to ice and to salt hydrates. Using as solvent dilute solutions of HOD in DzO, we have detected several novel hydrate bands using this procedure. However, in some cases, glassification occurred, and in others it could be achieved using certain dilute additives, such as t-butyl alcohol. These glasses gave bands which were appreciably narrower than those for the solutions at O'C, and consequently, two or more features could sometimes be resolved.This has enabled us to assign bands to HOD molecules hydrogen bonded to the halide ions and to various oxyions. These bands were all on the high frequency side of the main water band and were generally narrower than this band. The shift is discussed in terms of the number of primary and secondary solvent molecules associated with the anions, and the narrowing in terms of the precision of anion hydrogen bonding. In contrast, most cations simply induce a small shift in the broad water band, which may be to high or low frequencies. This shows that the spectral properties of water molecules bound to the cations are dominated by the other water molecules to which each is hydrogen bonded. At high concentrations of salt, new bands were obtained, shifted from the position of the anion solvate band by the cations.These are assigned to solvent shared ion-pairs, Interactions between water molecules and ions have been studied by infrared or Raman spectroscopy using the 0-H stretching modes of water (or of HOD, or the 0-D stretch of D20 or HOD) under three different conditions. In the first, an almost completely inert medium such as carbon tetrachloride is used, in conjunction with tetra-alkylarnmonium salts. By this means hydrogen bonding between anions and monomeric water molecules is studied. In the second method, an aprotic, basic solvent such as methyl cyanide is employed.2 This opens up the possibility of using alkali-metal salts, but the situation is more complicated because on the one hand the basic solvent coordinates to the cations, added water entering into cmpetitive equilibria, and on the other, the water forms hydrogen bonds to the basic solvent molecules, and anions have to compete with this bonding.Thus weakly solvated ions such as perchlorate may not be appreciably aquated. Nevertheless, the infrared bands are quite narrow, and Kuntz and Chang have shown that a considerable range of solvates can be nicely studied under these conditions. For water, another difference of importance is that the units studied are no longer just the ions bonded to monomeric water, but rather, the species B B H" H' / and A----H-0 / \ M-I--,-O 9 H B j- Taken as Solvation Spectra, Part 59. 2518I . M. STRAUSS A N D M. C . R . SYMONS 2519 where B is a basic solvent molecule.These solvent interactions have a major effect on the band positions and on equilibrium constants. The third system that has been widely studied is, of course, solutions of electrolytes in ~ a t e r . ~ ’ ~ Unfortunately, results are far less informative, mainly because of the extreme widths of the corresponding bands. Except for salts containing C104, BFZ, PF; and related anions, no clearly defined new bands are obtained in the fundamental 0-H stretching region, and all that can be done is to study the small shifts that represent the overall effect of a range of superimposed broad bands. Salts containing large anions such as C104 give new, high frequency bands in the 3560-3600 cm-l region which have variously been assigned to (OH)free groups and to 0-H groups weakly hydrogen bonded to the bulky anions.7* This controversy is discussed below.Whatever may be the correct assignment, one can argue that the anion effect is entirely located in this high frequency band, and hence that residual shifts of the bulk-water band caused by such salts must stem from the effect of the cations. Hence an order of shifts for the cations has been adduced.g In the fundamental 0-H stretch region infrared intensities are biased towards strongly hydrogen bonded groups, and oscillators make only a minor contribution. However, in the overtone regions, such as 2vOH, selection rules are such that the (O-H)free and weakly bound (OH) groups have a greater intensity than the strongly bound groups. Thus in the 2vOH region for HOD in D,O a well defined, asymmetric band appears with a maximum at ~7120cm-I.Hence this spectral region has been widely used to study the effect of electrolytes on the concen- tration of (OH),,, groups in water,10-12 but not to study the ion-solvates directly. We have recently shown that for methanolic solutions of electrolytes, resolved features assignable to anion solvates can often be obtained by working at low tempera- tures, either just above, or below the glass-point of the s01ution.l~ The aim of the present study was to explore the possible advantages of a similar study of aqueous solutions at low temperatures. If direct information about liquid-phase solutions is sought, it is imperative to avoid extensive phase-separation, and this is especially difficult for aqueous solutions because of the powerful tendency for ice crystals to grow on cooling.However, when this can be avoided, we maintain that the rigid glasses closely resemble their fluid solutions and hence that infrared spectral features can be directly related to those present, but not resolved, in the fluid solution spectra. EXPERIMENTAL MATERIALS [‘HI water was used as supplied. The [HOD] therein was always <5 % and was controlled by suitable additions of purified H20. Salts were all analytical grade, and were dried in VQCUU for ~ 2 4 h at elevated temperatures directly prior to use. Solutions were prepared by weight. Infrared spectra were measured using a Unicam SP 100 double-beam spectrometer using a prismlgrating combination. A SPECAC variable temperature cell was used which enabled the sample to be examined down to 93 K with a stability of & 1 K.Details of the e l l are given in Part 54.13 Cell windows were Irtran-2 (SPECAC) separated by suitable Teflon spacers. TESTS FOR PHASE-SEPARATION A variety of factors have helped us to distinguish between glassy and crystalline phases. These include : (i) A marked increase in light-scattering on phase-separation, resulting in a shift in the base-line on solidification. No such shift occurred when the solutions glassified. This 1-802520 SOLVATION OF IONS IN WATER criterion is unambiguous when it occurs, but unfortunately under some circumstances no clear base-line shifts occurred despite other strong indications of at least partial phase- separation. (ii) The appearance of a narrow band at 328Ocm-l (for solutions of HOD in D20 at 173 K ; A v ~ = 50 crn-l), which is assigned to 0-H oscillators of pure ice cry~ta1s.l~ (iii) The appearance of very narrow features attributable to salt hydrates.In some cases these corresponded to published results for specific hydrates, but in others they appear to belong to novel hydrates not previously studied by infrared spectroscopy. Generally, these narrow features were accompanied by a narrow '' ice " band at 3280 cm-I. Typical results are shown in fig. 1. (iv) Where there was still some doubt, we used paramagnetic probes such as di-t-butyl nitroxide or Mn2f cations : if well defined e.s.r. hyperfine features were obtained on cooling, then glassification was extensive, but if single broad lines were obtained then phase-separation was diagnosed.In selected cases, in attempts to avoid phase-separation, low concentrations of organic co-solvents (methanol, t-butyl alcohol, glycerol or dimethylsulphoxide) were added. In other cases, very rapid cooling was sufficient to avoid phase-separation, 60 - 50- 40 - I I I 1 3200 3300 3400 3500 3600 wavenumber Icm-' FIG. 1 .-Infrared absorption spectra of HOD in DzO in the 0-H stretching region containing ; (top line) sodium fluoride (1 mol kg-') at 133 K and (lower line) potassium fluoride (3.6 mol kg-') at 133 K. RESULTS AND DISCUSSION Results are summarised in the table 1 and in fig. 1-7. Before outlining the detailed behaviour of specific salts it may be helpful if the general trends are outlined. These trends, and the conclusions drawn therefrom, closely resemble the more complete study reported for methanolic solutions.I .M. STRAUSS AND M. C. R. SYMONS 252 1 GENERALISATIONS Before considering specific electrolytes, we draw attention to certain general features and offer explanations thereof. In many cases, resolved bands were obtained, between the limiting values of the ice band at 3280 cm-I and the " (OH) ''free band in the 3600 cm-1 region (see, for example, fig. 2 and the table 1). There are two reasons why these bands are only resolved at low temperatures. One is that cooling narrows all the bands, and the other is that the bulk-water band shifts to low frequencies more rapidly than those assigned to ion solvates. TABLE BA BAND MAXIMA (cm-l) FOR THE 0-H STRETCHING MODES OF HOD MOLECULES HYDROGEN BONDED TO ANIONS anion F- C1- Br' I- NOT SO$- CIOT Clog bandmaxima 3320 3370 3400 3425 3410 3465 3480 3530 at 173K In all cases when resolved high-frequency bands were obtained, we assign them to anion-hydrates rather than to cation-hydrates.These assignments rest heavily upon the results for tetra-alkylamrnonium salts for which no cation bands were expected and also upon the observation that these bands were initially independent of the nature of the cations but clearly dependent on the nature of the anions. Finally, well-defined trends for the anions were obtained so that the results are self consistent, and agree well with the results for the corresponding anion solvates obtained from methanolic solutions, (fig. 3). All the anions gave high frequency shifts from the bulk 1 I I I I 3200 3300 3400 3500 3600 wavenumber/crn-' FIO.2.-Typical spectrum for 9 mol dm-3 (Me4N+Cl-), (a) at 300 K, (b) at 133 K.2522 SOLVATION OF IONS I N WATER water band, increasing, in general, with increase in anion radius and with cooling. Since a shift to high frequencies indicates the presence of weaker hydrogen bonds, it appears that the anions form weaker bonds to water than water-water bonds at low temperatures. \ a 1 I I 3300 . 3100 3500 wavenumberlcm- ' FIG. 3.-Comparison of the band maxima (cm-') assigned to various anion solvates in water (I) and methanol (11) at E 173 K, with data for the mono solvates of Bu4N+ salts in carbon tetrachloride (corrected to % 173 K, the average estimated shift being FZ 10 cm-l).(a) C10; ; (b) NO; ; (c) I- ; (d) Br- ; (e) C1-. The 45" line separates regions of positive and negative shift. All the resolved anion-hydrate bands were relatively narrow, and temperature insensitive. However, cation-solvate bands were not resolved from the bulk water bands except possibly for Mg2+ and A13+. From the shifts observed for the bulk water band we infer that the alkali-metal cations induce small high-frequency shifts, the shift increasing with cation size. The divalent cations induce small low-frequency shifts. Even in concentrated solutions, the widths were comparable with, or greater than, those for the bulk water band in glassy solutions. Since, in general, cooling produced no sign of resolution we conclude that the temperature coefficients (dv/dT) for the cation solvates are close to that for bulk water.These generalisations are explained satisfactorily in terms of the following model. The hydrogen bonds formed by anions such as C1- are weaker than those for bulk water because each chloride forms x6 such bonds,15* l6 whereas each water molecule forms only two?' However, the powerful negative fields of the anions constrain the 6-ve oxygen atoms away from the anions, and this, together with the repulsions between the closely packed, coordinated molecules force the hydrogen bonds formed by the anion to remain linear and equivalent. This explains the smaller widths and also the relative temperature insensitivity, provided the solvation number does not change. Indeed we argue that this insensitivity is good evidence in favour of temperature independent solvation numbers.In contrast, the hydrogen bonds for the cations are made to secondary solvent molecules that are themselves part of the bulk solvent " structure ". Hence variations in the strength of the cation-water bonds has only a secondary effect upon the 0-H1 . M . STRAUSS AND M . C . R. SYMONS 2523 stretching frequencies. Indeed, the span of available frequencies on the high frequency side of the bulk water band is clearly far smaller than that available for the anions, since even if the metal-oxygen bond were infinitely weak the 0-H protons should remain bound to neighbouring water molecules, albeit by weaker bonds than those in bulk water. Probably a value about half-way between those for bulk water and OHfree groups (= 3400 cm-l) represents the extreme upper limit of shift for the cations. This explains the smaller shifts observed for cations.It also explains the absence of band narrowing and the fact that the temperature sensitivity remains close to that for bulk water. These properties arise because the 0-H protons are directly bound to bulk water and are subject to the same influences such as hydrogen bond stretching and bending and indeed, breaking. Steric crowding now makes it difficult for all secondary solvent molecules to form good hydrogen bonds, so we would predict even greater band-widths than that for bulk water. Our results seem to confirm this, but it is difficult to obtain any quantitative data since separate bands are not resolved.We stress that these conclusions do not mean that cations have little effect on the 0-H stretching frequency for water. It means that their effect is large, but fortuitously straddles the effect of water itself and hence for solutions in bulk water the shifts are not apparent. COMPARISON WITH SOLUTIONS I N INERT MEDIA In our related study of ions in methanol l 3 we compared the OH frequencies for monomeric methanol bound to anions in inert media with those for primary methanol molecules solvating these anions in bulk methanol. The relative shifts, which were positive or negative depending on the anion, were discussed in terms of primary and secondary solvation. Thus on going from X- - - HOMe to MeOH - - - X- - - - HOMe, a positive shift (weaker bonding) was postulated, whilst on going to X- - - - HO - - - HOMe, a negative shift (stronger bonding) was envisaged for the primary solvent molecules.Results for water in inert media are compared with our present data, and with the methanol data, in fig. 3. In trying to understand these trends we note that there is an added complication of bound and free OH groups. We compare the unit X- - - - HOH, having one bound and one free OH group, with the full hydrated anion in which each primary water molecule is probably bound to three others. Thus we consider the following changes : Me I H2O X - - - - HOH -+ HOH - - - X-- - - HOH (1) H H HOH H20 /’ + X-- - - HO / X- - - - HO HOH HOH H (3)2524 SOLVATION OF IONS I N WATER The overall changes on going from an inert solvent to bulk water, shown in fig.3, are similar to those for methanol, but are more positive. This difference arises, in our view, because of step (3) which has no counterpart in methanol. Thus step (1) should give an increase in v (weaker bonding), step (2) should give a decrease in v (stronger bonding), step (3) should follow (2) and cause v to increase (weaker bonding) whilst step (4) should cause a decrease in v. Tertiary water molecules will also play a significant role, but the major shifts should be accommodated by reaction (1)-(4). ION-PAIR FORMATION In our studies of frozen methanolic solutions we often obtained two narrow anion solvate bands, the high-frequency band being favoured by high concentrations of salt. These were assigned to solvent-shared ion pair units such as (I).R Indeed, because these bands were narrow, the influence of the cations was more accurately measured for these units than for bulk methan01.l~ In the present study, the solvate bands were too broad to show separate ion-pair features, but cation shifts were obtainable both for the room temperature and low temperature spectra. In many cases the tendency towards phase separation made it impossible to study low temperature spectra of dilute solutions of many electrolytes, and hence it has not always been possible to avoid ion-pairing effects. COMPARISON WITH ROOM TEMPERATURE SHIFTS Although electrolyte solutions have been widely studied at room much of this work related to H20 rather than MOD, or to HOD in H20 rather than HOD in D20. We therefore studied the room temperature spectra for the present systems. Apart from the Clog, BFT and PF; salts, only single broad bands were obtained. Walrafen has analysed such bands into several components, but in our view if there is no direct evidence for two or more bands in the form of inflections or shoulders, such a procedure is, at best, arbitrary.We prefer to infer band positions from shifts, using the results for perchlorate salts to give a measure of the separate cation shifts.9 The very small shifts detected for Me,N+ cations by this method means that for other salts of this cation the shifts will be dominated by the anions, and cation effects on the anion solvates at high concentrations will be small. Hence limiting shifts can be, to a first approximation, assigned to the anion solvates.The results are included in fig. 4 and can be compared with the low temperature data given in table 1. It is worth noting that the limiting shifts obtained from corres- ponding lithium salts were all M 15 cm-l greater. This extra shift is assigned to the influence of Li+ in Li+ - - - 0-H - - - X- units.I . M. STRAUSS AND M. C. R. SYMONS 2525 COMPARISON OF ANION SHIFTS In our study of the OH proton resonance shifts induced by anions in water and methanol,’ we drew attention to the good correlation between anion basicities and n.m.r. shifts, strong bases causing a large downfield shift, and weak bases causing a large up-field shift from the pure water or methanol values. As can be seen in fig. 4, the present infrared results give a far less satisfactory correlation.Only for C1-, Br- and I- is the expected dependency clear. Fluoride gives a smaller shift than might be expected if our assignments are correct (3370 cm-l), but a far larger shift if Walrafen’s results are correct (3140 cm-l). Also our tentative results for F- in low-temperature methanol l3 (3100 cm-l) is clearly out of line with the present results. d -i wavenumber /cm-’ FIG. 4.-Comparison of band maxima assigned to anion hydrates with pKa values for the conjugate acids. 0 Room temperature (HtO), 0 173 K (H20), @ 173 K (MeOH). Results for the oxyions CIOZ, C10; and SOj- fail to correlate with the halide ion results, with nitrate falling between the two correlating curves. It is curious that these large differences occur when the n.m.r.correlation was so good.I8 We tentatively suggest that the difference arises primarily because the n.m.r. shift depends both on the actual resonance shift for the hydroxyl protons of the primary solvation sphere and on the number of such protons, being a weighted mean shift. In contrast the infrared frequency shifts are a measure of the relative strengths of the hydrogen bonds and are not dependent in this sense on solvation numbers. For the oxyanions, there are more available points of attachment than for the halide ions, but the negative charge is dilutely spread onto each oxide ligand. Thus each water proton experiences a reduced charge and hence forms a weaker bond. To a first approximation, for C104 the maximum charge per oxygen is a, rising to 3 for C103 and 3 for Sot-.This correlates reasonably with the experimental shifts. Nitrate occupies a special place because of its asymmetric so1vation.20 Thus if, for example, two oxide ligands form hydrogen bonds because of the high polarisability2526 SOLVATION OF IONS IN WATER of the anion, the maximum charge increases from -3 to -$. If only one oxygen is hydrogen bonded the effective charge is - 1. Hence the differences between the monatomic anions and oxy-anions can be qualitatively understood. It remains curious, however, that bringing in the extra factor of the solvation number should lead to a relatively good correlation with the pK, values of the conjugate acids (used as a measure of basicity).l* TETRA-ALKYLAMMONIUM HALIDES Because of the interesting report of the detection of a novel low-frequency Raman band for 0-H or 0-D oscillators associated with Bu4N+ ions, we have searched for such a band in the room temperature and low temperature infrared spectra of a variety of tetra-alkylammonium salts. However, we have been unable to detect such a band, and conclude that water associated with the R,N+ ions cannot be distinguished from bulk water by infrared spectroscopy, even under conditions that greatly favour clathrate formation. SOME DETAILS FLUORIDES We had difficulty in preventing the formation of defined hydrates (fig.I). Although concentrated potassium fluoride appears to give glassy solids, nevertheless relatively sharp hydrate bands seemed to be unavoidable. Concentrated solutions of CsF gave reasonable glasses, but the F- solvate band was not separated from the bulk solvent band, only a broad single band centred at 3340 cm-l being detected.At the high concentrations used, solvent shared ion-pairs must predominate and hence the I I I I 3300 3400 3500 3600 wavenumber 1crn-l FIG. 5.-Infrared spectra of HOD in D20 in the 0-H stretching region containing sodium iodide : (a) 5.4 mol kg-I and (b) 10.8 mol kg-' at 173 K : in both cases the samples were polycrystalline.I . M . STRAUSS A N D M . C. R . SYMONS MgC12.12H20 2527 I t FIG. 6.-Location of band maxima for the 0-H stretching mode of HOD in various hydrates. The novel hydrates of unknown composition are indicated as xHzO. Broad bands are shown with arrow heads. LiN03. rH2O I I I 3300 3400 3500 3600 wavenwnber/crn-' FIG.7.-0-H stretching region of the infrared spectra of HOD in D20 containing (a) NaCI04 (7.2 mol dm-3), (6) NaC104+CH30D (0.018 mole fraction) and (c) NaC104+ Me2S0 (0.015 mole fraction), at 133 K.2528 SOLVATION OF IONS I N WATER F- solvate band would be shifted to high frequencies by the Cs+ ions. If we take the Cs+ shift to be 20-30 cm-l, this gives a peak for the unperturbed F- solvate at ~ 3 3 1 5 cm-l, in reasonable agreement with expectation. This value is close to those for the low frequency bands for the KF and NaF hydrates (fig. 6). SALTS WITH LARGE ANIONS Overtone infrared results for aqueous Na+BPh; confirm that only the cations are solvated in the normal manner.I2 By bonding to lone-pair " groups " of water molecules, they liberate an excess of (OH)f,,, groups whose spectra can be molritored in the overtone region.In the fundamental region, HOD molecules show a resolved band in the 3580 cm-l region which we again assign to (OH)free groups in water. [We stress that this frequency is well removed from that for monomeric HOD molecules in inert media primarily because there remain three reasonably strong hydrogen bonds which cause a small low frequency shift for the free 0-H oscillators. The oscillator is clearly unique and has all the chemical properties expected for free (OH) groups.] Unfortunately the solubility of Na+BPliZ is low, and we have been unable to obtain well defined spectra from glassy solutions. When organic solutes such as methanol or dimethylsulphoxide were added to give glasses, the (OH)fre, band was so greatly diminished that again no good data could be obtained.This arises, in our view, because such solutes provide an excess of lone-pair groups that scavenge the (OH),,, groups efficiently. Perchlorates are more soluble, but, except for the magnesium salt, phase separation normally occurred. The resulting spectra (fig. 7) for the lithium and sodium salts are remarkably well defined, and correspond to no known hydrates. Indeed, for NaClO,, the known hydrate spectrum grew in at high concentrations. On adding methanol the hydrate features were lost, being replaced by a broader, cation independent band at ~ 3 5 4 0 cm-l comparable with that for the magnesium salt at 3530 cm-l. We therefore postulate that these bands are due to hydrated perchlorate ions.We would not expect such hydrate water to be scavenged by methanol, despite the weakness of the actual hydrogen bonds, because of the strong, super- imposed, coulombic forces. CRYSTAL HYDRATES Since the detection of hydrates was not our primary concern in this work, we do no more than report our new data and show some typical spectra (fig. 5 and 6). We stress that we have, incidentally, discovered a variety of novel spectra for hydrates which have not been previously reported. It would be of interest to attempt to define the composition of these complexes, but this was outside the scope of the present study. We thank the S.R.C. for a research grant to I. M. S . S. C. Mohr, W. D. Wilk and G. M. Barrow, J. Amer. Chem. SOC., 1965, 87, 3048. I. D. Kuntz and C. J. Cheng, J. Arner. Chem. Soc., 1975,97,4852. G. E. Walrafen, J. Chem. Phys., 1971, 55, 768. T. T. Wall and D. F. Hornig, J. Chem. Phys., 1965,43, 2079. K. A. Hartmann, J. Phys. Chem., 1966,70,270. G. E. Walrafen, J. Chem. Phys., 1970,52,4176. ' G. Brink and M. Falk, Canud. J. Chem., 1970,48,2096. * D. M. Adams, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. F u r d y Soc., 1971,67,611; L. J. Bellamy, M. J. Blandamer, M. C. R. Symons and D. Waddington, Trans. Furaday Soc., 1971, 67, 3435.I. M. STRAUSS AND M. C. R. SYMONS 2529 M. C. R. Symons and D. Waddington, Chem. Phys. Letters, 1975,32, 133. lo W. A. P. Luck and W. Ditter, J. Mol. Struct., 1967, 1, 339. l 1 J. Paquette and C. Jolicoeur, J. Solution Chem., 1977, 6, 403. I2 S. E. Jackson and M. C. R. Symons, Chem. Phys. Letters, 1976,37,551. l3 I. M. Strauss and M. C. R. Symons, J.C.S. Faraduy I, 1977, 73, 1796. l4 I. S. Ginns and M. C. R. Symons, J.C.S. Dalton, 1972, 143. l5 A. K. Soper, G. W. Neilson, J. E. Enderby and R. A. Howe, J. Phys. C, 1977,10,1793. l6 G. Licheri, G. Piccaluga and G. Pinna, J. Chem. Phys., 1976, 64,2437. S. E. Jackson, I. M. Strauss and M. C. R. Symons, J.C.S. Chem. Comm., 1977, 174. J. Davies, S. Ormondroyd and M. C. R. Symons, J.C.S. Faraday ZZ, 1972,68,686. l9 R. N. Butler and M. C. R. Symons, Trans. Faraday SOC., 1969, 65,2559. 2o T. J. V. Findlay and M. C. R. Symons, J.C.S. Faraday ZI, 1976, 72, 820. (PAPER 8/461)

ISSN:0300-9599    

DOI:10.1039/F19787402518

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Nuclear Magnetic Resonance Technique to Distinguish between Micelle Size Changes and Secondary Aggregation in Anionic and Nonionic Surfactant Solutions BY EDWIN J. STAPLES AND GORDON J. T. TIDDY* Unilever Research Port Sunlight Laboratory, Port Sunlight, Wirral, Merseyside L62 4XN Received 17ih March, 1978 The presence of surfactants in large micelles gives rise to broad n.ni.r. resonances because of the long correlation time for diffusion around the micelle. This has been used to investigate the structure of surfactant aggregates in systems where other evidence indicates that large micelles occur. For polyethylene oxide surfactants at the cloud point, the surfactant micelles are small and the large units are formed by secondary aggregation of small micelles. For sodium dodecylsulphate with added salt, octanol or other surfactants, large micelles are formed.The changes in micelle size indicated by changes in n.m.r. linewidths are in agreement with changes measured by the quasi- elastic light scattering technique. The shape and size of surfactant micelles have been a subject of widespread interest to surface and colloid chemists. Recently, Tanford has drawn attention to the fact that in dilute solution, measured micelle aggregation numbers are often incompatible with a spherical ~hape.l-~ Theoretical considerations 1-3 lead to the suggestion that small micelles are oblate (disc-shaped) spheroids rather than prolate (rod-shaped) spheroids at high ionic strength. At high concentrations, in the presence of salt or semi-polar solubilisates, micellar solutions exhibit streaming birefringence, high viscosity and/or viscoelasticity.'-lo In addition, surfactant mobility becomes reduced, as evidenced by the broad n.m.r. This behaviour is attributed to the formation of large micelles, usually assumed to be long rods. An alternative explanation, not usually considered, is that the large micelles are in fact aggregates of small mice1les.l In this paper we demonstrate how 1i.m.r. can be used to distinguish between these two possibilities in several different systems. Nonionic polyethylene oxide surfactants exhibit a cloud point, and the size of surfactant aggregates increases rapidly as the temperature is raised towards this point.l1-lS Most authors have interpreted this observation to indicate that the micelle aggregation number increases, but Tanford and co-workers have reinforced earlier suggestions 3* l4 that the process is in fact micellar aggregation.The structure of non-ionic micelles at the cloud point is the first system we have chosen to study. The other systems chosen all contain sodium dodecyl sulphate (SDS) as the surfactant. A number of authors have suggested that SDS forms large rod-shaped micelles in the presence of salt,16 additives such as octano1,17 or other surfactants.1° Tanford has proposed that these may also be aggregates of small mice1les.l We have used n.m.r. to investigate these possibilities, choosing systems for study where other measurements are available for comparison. N.m.r. spectra of micellar solutions are an average of contributions from monomer and micellar surfactant, because of the fast exchange between the two. In the 2530E .J . STAPLES AND G . J . T . TIDDY 253 1 present study, concentrations were chosen so that the contribution of the micellar surfactant is dominant. The basis of the n.m.r. method is that the formation of large micelles will increase the time taken for a surfactant molecule to diffuse around the micelle surface. This will lead to the presence of a long correlation time in the distribution of surfactant motions, having a large effect on n.m.r. linewidths. The linewidths will be larger than those normally observed for liquids, and a smaller increase will be observed in the spin-lattice relaxation rate. In the next section of the paper we describe the n.m.r.theory and subsequently demonstrate its application to the various micellar systems. THEORETICAL For protons, the rate of spin-lattice or spin-spin relaxation is usually determined by the modulation of the dipolar interaction between the particular nucleus and its neighbours, due to molecular motion. The theory for the case of isotropic motion is well known,I8 and in recent years the effects of anisotropic motions have received considerable attention. Surfactant molecules at the surfactant /water interface of a micelle are oriented at an angle to the surface, with head groups in the water and alkyl chains away from the water. The result is a strong anisotropy in the molecular motion. A convenient description of the effect on relaxation rates for nuclei relaxing uia the quadrupole mechanism has been given by Henriksson et aZ.,19 based on the earlier paper of Wennerstrom and co-workers.20 For dipolar relaxation, a similar treatment can be developed. Following Henriksson et aZ.,19 for a pair of like spin-4 nuclei at a distance r apart, the spin-lattice relaxation rate (l/Tl) and the spin-spin relaxation rate (1 IT2) can be written :l 1 - 9 y4A2 - - - .+%f(O) + $J"(o,) + 1(2coo)] 7'' 8 r where coo is the nuclear resonance frequency, y is the nuclear gyromagnetic ratio, and J(0) are spectral densities.We assume that the surfactant mobility can be split up into two contributions.20 One is a fast motion due to local translations, rotation and conformational changes, described by an effective correlation time z, and the second is a slow motion due to the orientation of the surfactant at the prfactant /water interface with correlation time 7:.The spectral density functions J(m) can be split into " fast " and " slow " contributions [JF(co), JS(co)] as indicated in eqn (3). The order parameter, S, describes the orientation of the vector joining the pair of protons concerned, and is given by the time average S = +(3 cos2 ODM- l), where ODM is the angle between the H-H vector and the normal to the micelle surface. The resulting expressions for relaxation rates are given in eqn (4)-(7). 1 9 y4h2 - - - - ,_[s2f(.:) + (1 - S2)52Z] TI 8 r (4) 1 9 y4h2 -- - - -[s2g(.:) + (1 - s2)52:] T2 8 r6 ( 5 )2532 N.M.R. OF MICELLES where r is the distance between the nuclei concerned. If more than two protons are involved, the relaxation rates must be summed over all the proton pairs.The process that determines 7: is the reorientation of the surfactant molecule with respect to the waterlsurfactant interface. This is determined either by diffusion around the micelle surface, or by exchange of surfactant monomers between micelles. The latter process occurs at a rate 21* 22 of < lo4 s-l, while the time for diffusion around the micelle depends on micelle size, but is in the range 10-9-10-5 s. Thus measurement of relaxation rates should enable a micelle size to be estimated if a diffusion coefficient is assumed. Changes in size should be more directly available. It should be possible to distinguish between large aggregates of small micelles (7: N s) and large micelles (7; 2: s).1000 6 .:Is FIG. 1.40) Linewidths (Ava) and ( x ) spin-lattice relaxation rate (T;l) calculated from eqn (6)-(9) as indicated in the text. (Assuming S = 0.3, and n.m.r. frequency of 60.0 MHz). For a surfactant of chain length n, each proton can interact with 2n+ 1 other protons. In principle each of these pair interactions has a unique value of rz, T:, r and S. In addition, we have to include contributions from interactions between protons on neighbouring molecules. This leads to a rather large number of variables, and limits the use of the equations to obtain information on micelles, unless further simplifications can be made. In the application of eqn (6)-(9) we note that S is expected to be -0.3, from values determined for liquid crystal^.^^-^^ Studies on long chain hydrocarbons show that the maximum value of 7';' is -50 s-l (at 20 M H z ) .~ ~ The motions of the hydro- carbon alkyl chains are expected to be similar to the chain motions of surfactantsE . J . STAPLES AND G . J . T . TIDDY 2533 in micelles, except for the effect of anchoring the surfactant head group at the water/ surfactant interface. Thus we can use the Ti' value from the hydrocarbons to estimate the constant factor y4h2/r6 in eqn (4) and (5). This procedure does not take full account of intermolecular effects, but these are likely to be small. Calculations of Ti' and linewidth (Av+ = nT;') have been carried out using eqn (4)-(7), while making allowance for the difference in measurement frequency between this study and that of Cutnell and Stejskal,26 and assuming a value of 0.3 for the order parameter, S.These are given in fig. 1, as a function of 7;. The maximum contribution to T i ' is - 1.6 s-l, while the changes in linewidth are orders of magnitude larger. Thus we expect broad n.m.r. resonances for large micelles, with only a small change in T '. Note that the largest change in Ti' occurs when there is only a minor change in Av+. Towards the end of this study, an improved description of the n.m.r. theory was reported, which enabled calculation of the completed line shape to be made.27 The assumptions involved are similar to those in the present work, but the requisite spectra of liquid crystalline phases are not available in our case. EXPERIMENTAL MATERIALS Hexaethyleneglycoldodecyl ether (C12E6) was obtained from Nikko Chemicals, Tokyo ; sodium dodecyl sulphate (SDS) was obtained from B.D.H.(spec. pure) as was octanol; deuterium oxide (>99.8 %) was obtained from Hopkin and Williams. All were used without further purification. Dodecyldimethylammoniopropane sulphonate (C12DPS) was prepared in this laboratory using the method of Clunie et aZ;28 the material was >99 % pure by elemental analysis and exhibited no minimum in the surface tension against log (concentration) plot. MEASUREMENTS Spin-lattice relaxation rates were obtained using a Bruker 32243 spin echo spectrometer operating at 60.0 MHz using a n-t-n/2 pulse sequence, (n/2 pulse length N 2 ps). Because all the protons in the sample contribute to the signal, the longitudinal decay will be a sum of the individual c w e s for each group of protons. However the Tl value obtained from the fmt part of the decay (T1 observed) will be given by eqn (8) where nj, is the fraction of protons in group i with relaxation time Tli.If there is a large distribution of Tl values then a non-exponential relaxation process occurs. This was observed in all the cases studied here, with deviations from exponential behaviour being observed after - 60 % magnetisation recovery for C12E6 and SDS solutions, and after 90 % recovery for SDS+C12DPS mixtures. In each case it was possible to measure the initial slope given by eqn (8). The values of (1/Ti)obsend are mainly determined by the contributions of alkyl chain relaxation. Values were reproducible to better than &5 %.Linewidths were measured from spectra obtained using a Bruker WH-90 spectrometer operating at 90 MHz. The main surfactant CH2 resonance was clearly observable in all spectra where measurements were made, as was the 0-CH2CH2-0 resonance of C12Es. However, for the OCH2 group of octanol and SDS, and terminal methyl groups, measure- ments of linewidths were complicated by the observation of multiplets due to indirect scalar coupling (J) from neighbouring CH2 groups. For narrow lines (Av+ < 6 Hz) the linewidth was measured from the central line of the 1 : 2 : 1 triplets. For very broad lines (Av+ > 2OHz) no multiplet structure was apparent, and the J contribution to the linewidth was eliminated from the observed linewidth by subtracting the value of the separation of the multiplet components in spectra with narrow lines.For multiplets between these two2534 N . M . R . OF MICELLES extremes it is difficult to obtain an accurate measure of linewidth without simulation of spectra, although the qualitative effects of increased line broadening are obvious. For these spectra we have attempted to allow for the J contribution to Av+ by estimating the degree of collapse of the multiplet structure. The error in the A v ~ values determined in this way is large, =+30 %. When the resonance became very broad, it was difficult to measure an accurate A v ~ value because of the need to estimate a base line, and low intensity peak maxima. Overlap of resonances also limited the number of signals that could be used for measurements. For these reasons, only Av+ values of the main alkyl resonance have been used to estimate 7: values.RESULTS AND DISCUSSION In the previous section we have explained that Ti' values are an average for all protons in the molecule, and except for C12E6, are dominated by the contribution of the alkyl CH, groups. For Av& values we have indicated the difficulties in taking account of J coupling. The measured linewidth of any resonance line is the sum of contributions from magnetic field inhomogeneities, chemical shift distributions, J coupling and relaxation effects. In the present systems, a limit of ~ 0 . 5 Hz can be put on the magnetic field inhomogeneity contribution, since the linewidth of residual protons in the 2H20 was always less than this value.No chemical shift distribution is expected for separate single-group resonances (e.g., OCH2 in SDS), and the estimation of the J contribution has been discussed above. For the main alkyl chain resonances, a contribution from CH, group chemical shift variation along the chain, and inter-CH, group J coupling will be present. The magnitude of these contributions is not expected to be dependent on micelle size. The linewidth of the SDS (CH,) resonance in solutions known to contain small micelles is ~ 5 . 5 Hz and this is taken as the maximum contribution from these sources. C12E6 MICELLES The values of A V ~ for the (OCH,CH2)6 and (CH,), peaks, together with TY1 values, are shown as a function of temperature in fig. 2 for 44.4 mmol dm-3 CI2E6 in D20 containing 0.1 mol dm-3 NaCl.This composition was chosen to lie within the range chosen for study by Tanford and co-worker~,~~ and had a cloud point of 320 K. This value agrees well with the value reported previously for C12E6 + H 2 0 (320- 1 K) in the absence of salt. The main alkyl chain resonance generally decreases in width as the temperature is increased, while a slight increase is observed for the ethylene oxide resonance. The logarithm of the spin-lattice relaxation rate is linearly dependent on inverse temperature with an activation energy of 20 kJ mol-'. No increase in Ti' is observed at the cloud point. There are small changes in the Av+ values at the cloud point, none of which are likely to be caused by changes in the spin-spin relaxation rates, since they have opposing dependences on temperature. The observed effects are probably due to small changes in the chemical shifts of the nearly equivalent groups of protons.Certainly the values of Av+ are far less than those observed for the other surfactant system in this study. The results are in agreement with the previous study by Clemett,29 who was unable to observe any effect of the cloud point on relaxation rates in C10E5 solutions. In their study of C12E6 micelles by light-scattering, Balmbra and co-workers estimate that if the nonionic micelles are large rods, then the rod length is -40 nm at 318 K, just below the cloud point.ll In our case we have 0.1 mol dm-3 NaCl present, but since the cloud points are similar, the micelle size would be expected to be of the same order of magnitude.Using a self-diffusion coefficient of - 5 x 10-10 m2 s-l , a value higher than that measured for surfactants in liquid crystals,30E. J . STAPLES AND G . J . T . TIDDY 2535 the time for diffusion around the micelle is calculated to be s ( t = Z2/4D). This would result in a line-width of > lo3 Hz (from fig. 1) and is incompatible with the present results. (The 7: value estimated for rotational diffusion of the whole micelle is an order of magnitude larger, and this process can be neglected.) It is likely that the order parameter (S) is lower in nonionic surfactant systems since the temp]K 333 323 313 303 1 I cloud point in I '"1 I 3!4 1 310 311 3.12 313 K/Tx lo3 FIG. 2.-Linewidths and spin-lattice relaxation rate of C1& (44.4 mmol dm-3 plus 0.1 mol dm-3 sodium chloride in deuterium oxide) as a function of temperature.0, (CH& ; x , (OCH2CH2)6 ; D, Ti1. n.m.r. resonances are narrower than those in ionic Even with an order parameter of 0.1, a broadening of N 100 Hz would be expected for large micelles just below the cloud point. At this temperature the maximum contribution from this mechanism to Ti' and Av+ are < 1.65 s-l and <2 Hz respectively. With a reduced order parameter (S = 0.1) this gave a 7: value of < 5 x lo-* s which is of the correct magnitude for diffusion around a normal small micelle. Thus the n.m.r. measurements provide strong evidence that a secondary association of small micelles occurs as the cloud point is approached, in agreement with Tanford l5 and other have suggested that this secondary process involves association of polyoxyethylene chains between different micelles.This seems to be rather unlikely, in view of the fact that the presence of polyoxyethylene chains at an interface is thought to provide a repulsive force to stabilise colloidal particles against aggregation. Also, when the cloud phase first separates it contains about 3 % surfactant.ll Assuming a hydrocarbon core radius of 1.25 nm for the micelle, and a water content for the micelle aggregates similar to that of the initially separated nonionic phase, then the average distance between micelles is about 9.5 nm for a closed packed structure. This is too large for association between polyoxyethylene chains on adjacent micelles, which requires a surfactant content of about 30 %.An alternative explanation can be derived by considering the forces, present in l4 Tanford and co-workers2536 N . M . R . OF MICELLES lamellar liquid crystal phases containing uncharged lipids. Le Neveu and co- workers have suggested 32 that the forces in the lecithin + water lamellar phase system can be understood in terms of a " hydration " force and van der Waals forces. The hydration force derives from the attraction between head groups and water, and gives a repulsive force between lipid aggregates, while van der Waals forces cause an attraction between lipid aggregates. When the liquid crystal phase is in equilibrium with water (containing extremely small concentration of lipid monomer) these forces are balanced. Nonionic surfactants are dehydrated as the temperature is increased.This implies that the hydration-repulsion force between nonionic micelles will also decrease with increasing temperature. As the cloud point is approached a balance between this force and the van der Waals force occurs resulting in secondary aggrega- tion. Similar results should be observed for all pure nonionic surfactants in water, just below the cloud point. This explanation is consistent with the shape of the phase boundaries of surfactant and water mixtures above the cloud point, which show 11* 31 that the surfactant phase still contains -97 % water. It is consistent also with the known decrease of cloud point with increasing surfactant alkyl chain length, and the increase with increasing surfactant ethylene oxide content.If it is postulated that the hydrated surfactant 8oi C I I 1 I I 1 0.2 0.4 0.6 0.8 1.0 1.2 added NaCl/mol dm-3 FIG. 3.-Linewidths and spin-lattice relaxation rate of SDS (6.9 x mol dm-3 in deuterium oxide) as a function of sodium chloride concentration at 300 I(. Open circIes are values calculated from Q.E.L.S. data l6 as indicated in the text. Circles, (CH2), ; x , -0CH2 ; El, ql.E . J. STAPLES AND G . J . T. TIDDY 2537 phase of C8E3 has a similar structure to that of a normal nonionic surfactant above the cloud point, then the fact that heats of solution 33 of C8E3 and C,E6 are similar 33 is also consistent with the explanation given. As a final comment, it should be noted that the observation of two aqueous phases in mixtures of cationiclanionic surfactants and in anionic surfactantlsalt systems can be explained in an analogous way, with an electrostatic repulsion force replacing the hydration force.34 103 KIT 20 0: I 0.2 mole ratio octanol : SDS FIG. 4.-(a) Alkyl chain linewidths for SDS (0.69 x mol dxr3) as a function of temperature at two levels of added salt. Upper line, 1.1 mol dm-3 NaCl ; lower line, 0.6 mol dm-3 NaCl. (b) Effect of added octanol on alkyl chain linewidth of SDS (5 x rnol dm-3) in 0.3 mol dm-3 sodium chloride. Open circles are values calculated using Q.E.L.S. data 36 as described in the text.2538 N . M . R . OF MICELLES S D S ~ S A L T AND OCTANOL Linewidths and relaxation times are shown in fig. 3 for SDS as a function of sodium chloride content. The concentration of SDS selected (0.69 x mol dm-3 was that chosen by Mazer, Benedek and Carey16 for an investigation of SDS micelles using quasi-electric light scattering (Q.E.L.S.) spectroscopy. The surfactant monomer concentration is reduced by the addition of salt, which causes a small initial increase in linewidths and spin-lattice relaxation rate.A sharp increase in Av+ is observed at salt levels above -0.4 mol dm-3, while no further change is observed in the spin-lattice relaxation rate. Although not shown in fig. 3, the line- width of the terminal CH3 resonance followed the same pattern of behaviour as the (OCH,) and (CH,), peaks, but its final value was lower (21 8 Hz). The dependence of alkyl chain linewidths on temperature is shown at two salt concentrations in fig.4. The changes in linewidths observed here correlate very well with changes in micelle size obtained from Q.E.L.S. measurements. Maser et al. concluded I 6 that SDS miceiles occur as large rods when the added sodium chloride level is >0.4 mol dm-3 and that the rod length decreases as the temperature is increased. Because of the large number of possible variables, including the additional complication of flexible rod-shaped micelles, it is difficult to compare micelle sizes estimated from n.m.r. and Q.E.L.S. measurements directly. If 27 > lo-* s, and assuming that T: is determined by diffusion around the micelle, then the equations for Av, can be simplified to : where A and B are constants, and Im is the largest dimension of the micelle. The contribution to Av+, obs from mechanisms other than those due to the slow correlation time is given by Avi, and is assumed to equal 5.5 Hz.We expect that Im determined from n.m.r. should be related to the mean hydrodynamic radius (E) of the micelle measured I 6 using Q.E.L.S. For a first approximation we assume that Im is proportional to a, and have calculated the open circles in fig. 3 using the data points for 0.6 mol dm-3 salt to obtain the scaling factor. Although the spread in the values is small, the two sets of data are consistent. Calculations using Perrin's relationship 3 5 for prolate ellipsoids did not improve the fit. It is not possible to compare results at different temperatures because the activation energy for surfactant diffusion within the micelle is not known.Also, the linewidth contribution from other sources decreases with increasing temperature, giving an additional variable. However, the results are in qualitative agreement. For the very broad lines observed in - 1 .O mol dm-3 salt, the relative values of Av, for the OCH2, (CH,),, and CH3 peaks are N 1 : - 1 : -0.1. This is in agreement with the dependence of Av+ on the square of the order parameter as predicted by eqn (5), and published values of S for liquid crystal^.^^-^^ The absence of any dependence of Ti' on salt concentration is not in agreement with the theory. A possible reason for this is that a distribution of micelle sizes occurs. This would reduce the T i ' contribution, because at any composition only a fraction of micelles would have the size corresponding to the maximum increase.The effect of octanol on SDS linewidths was investigated for the range of concentrations examined by Clarke and Hall using a viscometric technique. l7 Results are given in fig. 4(b) and show that the linewidths increase as octanol is added. Again, the changes in A V ~ correlate with results obtained by Q.E.L.S.,36 with a linear dependence of Im on w.Open circles refer to linewidths calculated using the Q.E.L.S. data and fitted for the values at an octanol/SDS mol ratio of 0.175 : 1 as above.E. J . STAPLES AND G . J . T. TIDDY 2539 The proportionality constant is of similar magnitude to that calculated for SDS in salt only, indicating that the same type of aggregates are present in both systems. Calculations of Av+ using the axial ratios reported by Clarke and Hall l7 gave changes in the correct direction, but the agreement was poor.This is not surprising in view of the many assumptions involved,17 and the discrepancy found in similar calculations with Q.E.L.S. data. Again, the ratios of Av3 values for different lines were in agreement with observed order parameter^.^^'^^ The OCH2 lines of SDS and octanol could be observed separately, and the Av3 values were the same within experimental error. This indicates that they have similar rates of diffusion within the surfactant /water interface, and that there is no preferential solubilisation of octanol in large or small micelles. SDS + C, ,DPS Previous studies on the related system SDS + C1 6DPS have shown that broad n.m.r. resonances occur when viscoelastic solutions are obtained.9 9 lo Linewidths and 7';' measurements for equimolar mixtures of SDS and C12DPS (0.347 mol kg-l) are given in fig. 5, and care was taken to avoid the time dependent phenomena reported 5001 SDSl!O C18 Oy6 d.4 0:2 0.2 0.4 0.6 0.8 1.0 ClzDPS FIG. 5.-Linewidths (at 300 K) and spin-lattice relaxation rates (at 295 K) for mixtures of equirnoIar (0.347molkg-') SDS and C12 DPS. The values for NMe2 peaks refer to those of C12 DPS, while the CH3 and (CH2), peaks are averages of the overlapping peaks from both surfactants. 0, (CH2), ; x, NMez ; 0, CH3 ; El, Ti1. previously.1° The broad n.m.r. resonances do occur for solutions that are visco- elastic, and linewidths are in the ratio expected from order parameters. Little change is observed in T;' for the SDS rich solution, but the increase of - 1 s-l observed for addition of SDS to ClzDPS micelles is in reasonable agreement with the2540 N.M.R.OF MICELLES calculations given in fig. 1. The maximum broadening is far larger than was observed for the other systems. This indicates that the micelles are much larger in this system than in the other systems. The difference in Av+ values between head group resonances for SDS and C12DPS was difficult to estimate quantitatively because of overlap of the spectra. However, those of C12DPS (except for the NMe, resonance) did appear to be broader in the region 0.5-0.7 SDS. Diffusion coefficients are not expected to differ by more than -20 % within large and small micelles. This is insufficient to account for the observations, which may indicate a difference in micelle compositions between large and small micelles.The absence of a Ti' increase in this region is in agreement with the existence of a distribution of micelle sizes. CONCLUSION Independent of the details involved in the dependence of n.m.r. linewidth on micelle size for rods or discs, the Av+ values of SDS solutions containing sodium chloride, octanol and added C12DPS are incompatible with the idea of aggregated small spherical micelles. Aggregated small micelles do occur in nonionic surfactant solutions at and above the cloud point. Obviously, the difference in behaviour is due to the different forces acting in the systems. In nonionic surfactants, the forces are weak, while in SDS micelles even in salt solutions, the electrostatic forces are sufficiently large to play a dominant role in determining micelle shape and size.We would like to thank Prof. G. B. Benedek and Dr. A. L. Smith for useful discussions, and Mrs. E. Howarth for technical assistance. C. Tanford, J. Phys. Chem., 1974,78,2469. C. Tanford, J. Phys. Chem., 1972,76,3020. C. Tanford, Proc. Nut. Acad. Sci. U.S.A., 1974, 71, 1811. H. V. Tartar, J. Phys. Chem., 1955,59,1195. R. M. Bain and A. J. Hyde, Symp. Farahy SOC., 1971,5,141. H. Janeschitz-Kriegl and J. J. P. Papenhuijzen, Rheol. Acta, 1971, 10,461. D. Sad, G. J. T. Tiddy, B. A. Wheeler, P. A. Wheeler and E. Willis, J.C.S. Furuday I, 1974, 70,163. lo G. J. T. Tiddy and P. A. Wheeler, J. Phys. (Paris) Colioq., 1975, 36, C1-167.R. R. Balmbra, J. S. Clunie, J. M. Corkill and J. F. Goodman, Trans. Faraday Soc., 1962, 58,1661. l2 R. R. Balmbra, J. S. Clunie, J. M. Corkill and J. F. Goodman, Trans. Faraday Soc., 1964, 60,979. l 3 P. H. Elworthy and C. B. Macfarlane, J. Chem. Soc., 1963, 907. 14D. Atwood, J. Phys. Chem., 1968,72,339. Is C. Tanford, Y . Nozaki and M. F. Rohde, J. Phys. Chem., 1977,81,1555. l6 N. A. Mazer, G. B. Benedek and M. C. Carey, J. Phys. Chem., 1976,80,1075. l7 D. E. Clarke and D. G. Hall, CoZZuid Polymer Sci., 1974,252, 153. l 8 A. Abragam, The Principles of Nuclear Mugnetism (Oxford University Press, Oxford, 1961). l9 U. Henriksson, L. Odberg, J. C. Eriksson and L. Westman, J. Phys. Chem., 1977,81,76. 2o H. Wamerstrom, G. Lindblom and B. Lindman, Chem. Scriptu, 1974,6,97. J. Rassing, P. J. Sams and E. Wyn-Jones, J.C.S. Faraday IZ, 1974,70, 1247. 22 E. A. G. Aniansson, S. N. Wall, M. Algren, H. Hoffman, I. Keilmann, W. Ulbricht, R. Zana, J. Lang and C. Tondre, J. Phys. Chem., 1976,80,905. 23 B. Mely, J. Charvolin and P. Keller, Chem. Phys. Lipids, 1975,15,161. 24 W. Neiderburger and J. Seelig, Ber. Bumenges. phys. Chem., 1974, 78,947. 25 L. W. Reeves and A. S. Tracey, J. Amer. Chem. SOC., 1975,97,5729 ; I?. Fujiwara, L. W. Reeves, A. S. Tracey and L. A. Wilson, J. Amer. Chem. SOC., 1974, 96, 5249. 26 J. D. Cutnell and E. 0. Stejskal, J. Chem. Phys., 1972,56,6219. ' P. A. Winsor, Solvent Properties of AmphiphiZic Cornpour& (Butterworth, London, 1954). * J. C. Eriksson and G. Gillberg, Acta Chem. Scand., 1966,20, 2019.E. J . STAPLES AND G . J . T . TIDDY 2541 27 J. Ulmius and H. Wennerstrom, J. Magnetic Resonance, 1977, 28, 309 ; H. Wennerstrom and 28 J. S. Clunie, J. M. Corkill, J. F. Goodman and C. P. Ogden, Trans. Furuduy SOC., 1967,63,505. 29 C. J. Clemett, J. Chem. Soc. A , 1970, 2251. 30 S. B. W. Roeder, E. E. Burnell, An-Li Kuo and C. G. Wade, J. Chem. Phys., 1976, 64, 1848 ; 31 G. J. T. Tiddy, unpublished results. 32 D. M. Le Neveu, R. P. Rand, V. A. Parsegian and D. Gingell, Biophys. J., 1977,18,209. 33 D. E. Clarke and D. G. Hall, KolloidZ., 1972,250,961. 34 D. G. Hall and G. J. T. Tiddy, Anionic Surfactants, ed. A. Lucassen-Reynders (Marcel-Decker, 35 C. Tanford, Physical Chemistry of Macromolecules (John Wiley, New York, 1961), p. 327. 36 A. Lips and E. J. Staples, unpublished results. J. UImius, J. Magnetic Resonance, 1976, 23, 431. G. Lindblom and H. Wennerstrom, Biophys. Chem., 1977, 6, 167. N.Y.), to be published. (PAPER 8/SOl)

ISSN:0300-9599    

DOI:10.1039/F19787402530

出版商:RSC    

年代:1978

数据来源: RSC