J. Phys. Chem. 1989, 93, 7547-7549 as of 02,from water in a nonsacrificial system, are in progress in our laboratory.
Acknowledgment. This work was supported by the US-Israel Binational Science Foundation, by the E. Berman Foundation,
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by the Wolfson Foundation, and by the Materials Division of the US.Army Office for Research and Development. We thank Dr. J. Rabani for valuable discussions and for the generous donation of the Ir complex. We are grateful to Prof. G. Czapski for the use of the HP diode-array spectrophotometer.
Unusual Thermal Diffusion of Ionic Surfactants near the Critical Mlcelle Concentration Derek G. Leaist* and Lu Hui Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7 (Received: June 19, 1989)
Thermal diffusion of aqueous sodium dodecyl sulfate (NaDS) has been determined conductometrically at 25 'C and molalities from 0.002 to 0.4 mol kg-I. The measured Soret coefficientsjump by about a factor of 4 as the concentration is raised through the critical micelle concentration at 0.008 mol kg-'. The formation of micelles sharply reduces the electrolyte's isothermal diffusion coefficient. The thermally induced composition gradient is therefore large because the rate of ordinary diffusion opposing its formation is so low. The molar enthalpy of transport of completely dissociated submicellar NaDS is about 1 order of magnitude larger than the corresponding quantity for the micellar form of the electrolyte.
Introduction The flow of heat through a nonisothermal solution causes the solute to diffuse relative to the Eventually the thermally driven flow of solute is balanced by ordinary diffusion back down the induced concentration gradient. The steady state that is reached can be described by the Soret coefficient u = -d In mldT which gives the fractional change in molality per degree. In favorable cases thermal diffusion can produce useful separations. The interpretation of enthalpies of transport derived from measured Soret coefficients provides a sensitive test of microscopic theories of solutions. The present work is a study of the thermal diffusion of micelle-forming electrolyte^.^^^ These materials resemble simple strong electrolytes at low concentrations. But as the concentration is raised, large ionic aggregates suddenly form at a critical micelle concentration (cmc). Haase69' and Thomaes8 have investigated the related problem of thermal diffusion near critical solution points where homogeneous solutions separate into two distinct phases. The chemical potential gradients driving ordinary diffusion vanish at these points. The critical values of u are therefore infinitely large because thermal diffusion can proceed unchecked. Micellar aggregation is not a true phase separation. Nevertheless, isothermal diffusion coefficients plummet at the cmc,9-11which might lead to very large Soret effects. Soret coefficients are reported here for aqueous solutions of sodium dodecyl sulfate (NaDS). This system's cmc (0.008 M at 25 0C)12914is high enough for u to be determined both above (1) Tyrrell, H. J. V. Dvfusion and Heat Flow in Liquids; Butterworths:
London, 1961. (2) Agar, J. N. In The Structure of Electrolytic Solutions; Hamer, W. J., Ed.; Wilev: New York. 1959; Chaoter 13. (3) Agar,-J. N. In Advances in Ehctrochemistry and Electrochemical Engineering; Delahay, P., Tobias, C. W., Eds.; Interscience: New York, 1963; Chapter 2. (4) Wennerstrom, H.; Lindman, B. Phys. Rep. 1979, 52, 1. (5) Winsor, P. A. Chem. Rev. 1968, 68, 1. (6) Haase, R.; Sky, M. Z . 2.Phys. Chem. (Munich) 1968, 57, 56. (7) Haase, R. Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 256. (8) Thomaes, G. J. J . Chem. Phys. 1956, 25, 32. (9) Weinheimer, R. M.; Evans, D. F.; Cussler, E. L. J. Colloid Interface Sci. 1981, 80, 357. (10) Evans, D. F.; Mukherjee, S.; Mitchell, D. J.; Ninham, B. W. J . Colloid Interface Sci. 1983, 93, 184. (1 1) Leaist, D. G. J. Colloid Interface Sci. 1986, 1 1 1 , 230. (12) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986.
0022-365418912093-7547$01.50/0
TABLE I: Measured Soret Coefficients and Enthalpies of Transport for Aqueous Sodium Dodecyl Sulfate at 25 OC %/mol kg-l o / ~ O - K-I ~ 1 + (d In -yJd In m) H*/kJ mol-! 0.002
0.004 0.006 0.010 0.020 0.050 0.100 0.200 0.300 0.400
7.8 8.0 8.2 32.0
0.98" 0.97" 0.96" 0.05b O.OSb 0.09b 0.1 6b
21.0 14.0 7.8 6.1 5.3 4.9
"From In y+ = -1.17m1l2/(1
11.3 11.5 11.6 2.2
1.5 1.8 1.9
+ m 1 / 2 ) .bReference 16.
and below the critical micelle region. The enthalpies of transport of the dissociated and micellar forms of the electrolyte can therefore be measured and compared. Conveniently, the change in enthalpy due to the formation of NaDS micelles is almost zero at 25 0C,12914 which means the cmc can be treated as a constant along a thermal diffusion column operated near room temperature. Premicellar association is negligible for this s y ~ t e m . ' ~ - ~Iso' thermal diffusion of aqueous NaDS has already been studied.lOJ1
Experimental Section The Soret coefficient of aqueous NaDS (BDH, specially pure grade) was determined according to the conductometric procedure of Agar and Turner,l* with only minor modifications.19 The Soret cell contained a cylindrical solution channel (diameter 0.60 cm, height 1.219 cm) in the center of a Lucite disk (diameter 5 cm), which wasclamped between upper and lower copper thermostat blocks held at 30 and 20 OC, respectively. Electrolyte transport was followed by using a Jones bridge to monitor changes in electrical resistance across pairs of small platinum electrodes (13) Flockhart, B. D. J. Colloid Sci. 1957, 12, 557. (14) Flockhart, B. D. J . Colloid Sci. 1961, 16, 484. (15) Smith, A. L.; Parfitt, G. D. J . Phys. Chem. 1962, 66, 942. (16) Cutler, S. G.; Meares, P.; Hall, D. G. J. Chem. Soc., Faraday Trans. I 1978, 74, 1758. (17) Kale, K.; Cussler, E. L.; Evans, D. F. J. Phys. Chem. 1980, 84, 593. (18) Agar, J. N.; Turner, J. C. R. J. Phys. Chem. 1960, 64, 1000. (19) Leaist, D. G. J . Solution Chem., in press.
0 1989 American Chemical Society
1548
Letters
The Journal of Physical Chemistry, Vol. 93, No. 22, 1989
located at 1/6 and 5/6 of the height of the solution column. u was evaluated by the initial slope method.20 The conductance data required to calculate u from the measured resistances were obtained from ref 15 (C < 0.045 M) and from measurements made using an auxiliary conductance cell (C > 0.045 M). Published densities2' were used to convert from molar (C) to molal concentrations ( m ) .
Results Soret coefficients were measured at mean NaDS molalities m from 0.002 to 0.4 mol kg-l. The results are given in Table I. Below the cmc (0.008 mol kg-I), u for the fully dissociated electrolyte is about 0.008 K-l. In the neighborhood of the cmc u jumps by at least a factor of 4 and then gradually decreases at higher concentrations. u for the fully micellized electrolyte ( m 5 0.1 mol kg-I) drops to about 0.005 K-I for the most concentrated solution that was used. The measured values of u were usually reproducible within f0.0003 K-I. At 0.010mol kg-I, where u is extremely sensitive to composition, the reproducibility was poorer, f0.002 K-I. As anticipated in the Introduction, u is indeed large near the cmc. At 0,010 mol kg-I, for example, the measured value 0.032 K-I implies that a 10 K temperature difference would produce a steady-state molality difference of about 30%of e. The value of u at the cmc is probably even larger. Unfortunately, the present technique could not be used to determine the critical value of u because the Soret coefficient, diffusion coefficient, and molar conductance would be essentially discontinuous along the thermal diffusion column, whereas all of these quantities are treated as constants in the equationsI8Smused to evaluate u from the measured resistances. The molar enthalpies of transport of aqueous NaDS given in Table I were calculated from the measured Soret coefficients as follows:'-3 H* = 2 R P [ l
+ (d In y+/d
In m)r]o
Below the cmc the stoichiometric mean ionic activity coefficient y+ was estimated from the semiempirical relationz2 In y+ = -1.17
+
TABLE II: Soret Coefficients of Aqwous sodium Dodecyl Sulfate at 25 @Cfrom the Chemical Equilibrium Model 1 + (d In -ill d In m)b
m/mol kg-'
y+'
0.0075 0.0078
1.000 0.999 0.993 0.978 0.952 0.905 0.821 0.556 0.421
0.0080 0.0082 0.0085 0.0090 0.0100 0.0150 0.0200
0.998 0.908 0.560 0.303 0.165 0.096
0.058 0.034 0.034
ttc
1.000 0.986 0.902 0.752 0.561 0.373 0.208 0.039
0.008
H*/kJ mol-l 11.5
u / ~ O - ~K-'
11.4 10.6 9.1 7.3
5.5 3.9 2.3
2.0
8 8 13 20 30 39 46 45 39
@ y += ( m + m - ) 1 / 2 / m bEquation . 6. CEquation 7.
The chemical equilibrium model, which has been used to interpret the unusual isothermal diffusion behavior of ionic surfactant~,~-"will now be used to analyze the remarkable "lambda-shaped" concentration dependence of the Soret coefficient of aqueous NaDS. It is of particular interest to estimate the maximum value of u attained in the critical micelle region where experiments are not practicable. n and q will stand for the average number of surfactant ions and bound counterions per micelle: nDS-
+ qNa+ = (NaqDSn)4-"
(2)
The molalities of the free surfactant ions (m-),free counterions (m+),and micelles (m,) are related by the conditions of chemical equilibrium and electroneutrality as follows. K = c,/c-"c+q
c+ = c-
+ ( n - q)c,
(3) (4)
K is the equilibrium constant for reaction 2. Reasonable values"' of n, q, and K for aqueous NaDS a t 25 OC are respectively 60, 50, and (5600)*q (mol kg-l)'-V. Given the total NaDS molality m m = m- + nm, (5)
m 1 / 2 /1( m'I2). Above the cmc, y+ was evaluated from specific-ion electrode data.16 Micellar aggregation sharply reduces the number of free ions per mole of electrolyte, which in turn sharply reduces y+ above the cmc (see Table I). In this region the value of the thermodynamic factor 1 d In y+/d In m is obtained as the difference between two numbers of similar magnitude, which gives the derived H* values large uncertainties (10-20%).
eq 3-5 can be solved for m-, m+, and m,. Neglecting ion-ion interactions, the activity of the NaDS comjonent ( a = Yi2m2) is given by m+m-, and hence yi = (m';m-)'/2/m.Differentiating eq 3-5 provides the following expression for the thermodynamic factor.
Discussion It is noteworthy that the enthalpy of transport of completely dissociated NaDS is about 1 order of magnitude larger than the corresponding quantity for the micellar form of the electrolyte. This result is qualitatively consistent with the hydrophobic hyd r a t i ~ n of ~ ~the- ~alkyl ~ chains of the free DS- ions. The ordering and enhanced hydrogen bonding of the water molecules near the alkyl groups would reduce the entropy density in front of an approaching DS- ion and increase it behind the ion. The resulting evolution of heat ahead of the ion and the absorption of heat astern would contribute to a positive enthalpy of This contribution would be absent for micellar NaDS because the alkyl groups are confined to the core of the micelles, isolated from the solvent. The formation of ion pairs on the micelle surface and the consequent reduction in hydration would further reduce H*.
The free ions and the micelles equilibrate rapidly2' enough to maintain local chemical equilibrium along the diffusion path. In order to interpret the measured enthalpy of transport per mole of total NaDS, it is helpful to know the fractions of the electrolyte transported as free ions or micelles: t+ = j-/(j- + nj,) and t , = nj,/(jnj,), respectively. The molar flux density of each species, ji,is given approximately by28-(ciDi/RT)Viii,where Di and Vpi are the diffusion coefficient and electrochemical potential gradient for species i ( i = +, -, m). The conditions of local chemical equilibrium (nVp- + qVp+ = p,) and zero electrical ( n - q)jm) together with the flux density current (j+= j equations lead to the following approximate expression for t*.
+
(20) Agar, J. N.; Turner, J. C. R.Proc. R. Soc. London 1960, A255,307. (21) De Lisi, R.;Genova, C.; Testa, R.;Liveri, V. T. J. Solution Chem. 1984, 13, 121. (22) Guggenheim, E. A.; Turgeon, J. C. Trans. Faraday Soc. 1955, 51, 747. (23) Franks, F.; Ives, D. J. J. Chem. Soc. 1960, 741. (24) De Visser, C.; Somsen, G. J. Phys. Chem. 1974, 78, 1719. (25) Fuchs, R.;Hagan, C. P. J. Phys. Chem. 1973, 77, 1797. (26) Cifra, P.; Romanov, A. J. Solution Chem. 1984, 13, 431.
I + - d= -In y* d In m
m m+ + m- + (n - q)2m, 2 m+m- + n2m+m, + q2m-mm
(6)
+
+
ti =
mD-[m+D+- q ( n - q)mmDmI m+mD+D- + n2m+m,D+D, + q2m-m,DD,
(7)
The respective v a l u e ~ ~ 0.72 -~l X 1.34 X and 0.10 X m2 s-I for D-, D+, and D, may be used to estimate t+. The fraction of total NaDS transported in micellar form can be evaluated from the identity t+ + t , = 1. (27) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.;Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J . Phys. Chem. 1976, 80, 905. (28) Leaist, D. G. J. Chem. Soc., Faraday Trans. I 1982, 78, 3069.
,
J. Phys. Chem. 1989,93, 7549-7552
soiwl
01 0.0
0;ol
I
m /mol kg" 0;' 9.2
op2
I
0.2
I
0.14
I
I
04 m'/'/ (mol kg-'
I
0.6
Figure 1. Soret coefficient for aqueous solutions of sodium dodecyl sulfate at 25 OC: (a) measured values; (-) predicted values from the chemical equilibrium model using eq 1 and 6-8.
The thermodynamic theory of thermal diffusion with associat i ~ provides n ~ ~ the following relation between the measured molar enthalpy of transport of NaDS and the intrinsic molar enthalpies of transport of the dissociated and micellar forms of the electrolyte. H* = tiHi* tmHm* HI* (8)
+
+
The term H,* is a reactive contributionB from the enthalpy change (29) Agar, J . N.; Lin, J. J . Solution Chem. 1987, 16, 973.
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due to the formation of micelles which arises because the dissociated and the micellar forms of the electrolyte diffuse at different rates, which tends to perturb the concentrations of the species from their equilibrium values. The reaction that takes place to adjust the concentrations of the species of their local equilibrium values contributes to the overall enthalpy of transport. For the system under discussion, however, the enthalpy change of micellization is so small14 that HI*may be neglected. The chemical equilibrium model was used to calculate the values of yt, 1 + d In yi/d In m, and ti given in Table 11. In order to estimate u in the critical micelle region, the constant values 11.5 and 1.9 kJ mol-' were assumed for Hi*and Hm*,respectively, and then u was calculated via eq 1 and 8. The values of u estimated by this procedure are plotted in Figure 1. The maximum value of u, 0.048 K-I, is predicted at 0.012 mol kg-'. Although the agreement with the measured u values is only qualitative, the comparison suggests that the chemical equilibrium model can account for the main features of thermal diffusion in the critical micelle region. Better agreement could no doubt be obtained by elaborating the model to include polydispersity of the micelles and ion-ion interactions. In conclusion, the present work shows that the large Soret effect observed for aqueous NaDS solutions does not result from an unusually strong coupling between the flows of heat and matter. Instead, the micellar aggregation reduces the rate of diffusion opposing the thermal generation of composition differences. Other micelle-forming electrolytes and other kinds of aggregating solutes should also demonstrate unusually large Soret effects.
Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council.
Low-Temperature (144 K) '*@XeNMR of Amorphous Materials: Effects of Pore Size Distribution on Chemical Shift T. T. P. Cheung Phillips Research Center, Phillips Petroleum Company, Bartlesville, Oklahoma 74004 (Received: June 26, 1989; In Final Form: September 4, 1989)
Iz9Xenuclear magnetic resonance (NMR) spectra of xenon adsorbed on amorphous silica, alumina, and silicaalumina have been measured as a function of the xenon loading at 144 K. At low xenon loadings, the IBXe chemical shift shows a nonlinear dependence on the xenon loading. In the amorphous alumina and silica-alumina, a parabolic-like curvature in the chemical shift similar to that observed in Y zeolites with (+2) cations is observed even though the xenon adsorption sites in the amorphous materials are much weaker. The nonlinear dependence of the Iz9Xechemical shift on the xenon loading can be explained by the presence of a broad distribution in the micropore size and the fact that the chemical shift is an inverse function of the micropore size.
A number of papers have recently appeared on the application of "Xe nuclear magnetic resonance (NMR) to the study of porous materials. Several conclusions emerge from the investigation of materials with uniform pore such as Y zeolites: (1) At
low loadings of xenon, if the xenon adsorption sites in the pores are weak, the lz9Xechemical shift, u, increases linearly with the xenon loading and thus with the xenon density p within the pores. That is u
Ito, T.; Fraissard, J. P. In Proceedings of the 5th International Conference on Zeolites, Naples; Heyden: London, 1980; pp 510-515. (2) Ito, T.; Fraissard, J. P. J. Chem. Phys. 1982, 76, 5225; J . Chem. Soc., (1)
Faraday Trans. 1 1981,83,451.
(3) de Menorval, L. C.; Fraissard, J. P.; Ito, T. J . Chem. Soc., Faraday Trans. 1 1982, 78,403. (4) Ito, T.; de Menorval, L. C.; Guerrier, E.; Fraissard, J. P. Chem. Phys. Lett. 1984, 111, 271. ( 5 ) Springuel-Huet, M. A.; Ito, T.; Fraissard, J. P. In Proceedings of the Congress on Structure and Rcacrivity of Modified Zeolites, Prague; Elsevier: Amsterdam. 1984.
= uo
+ cp
(1) where c is the proportionality coefficient. (2) The chemical shift (6) Scharpf, E. W.; Crecely, R. W.; Gates, B. C.; Dybowski, C. R. J. Phys. Chem. 1986, 90, 9. (7) Cheung, T. T. P.; Fu, C. M.; Wharry, S.J . Phys. Chem. 1988, 92, 5 170.
( 8 ) Demarquay, J.; Fraissard, J. Chem. Phys. Lett. 1987, 136, 314. (9) Fraissard, J.; Ito, T.; Springuel-Huet, M.; Demarquay, J. In Proceedings of the 7th International Zeolite Conference, Tokyo; Elsevier: Amsterdam, 1986; pp 393-400.
0022-3654/89/2093-7549$01.50/00 1989 American Chemical Society
