J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1909-1911 Very Large Thermal Separations for Polyelectrolytes in Salt Solutions Derek G. Leaist" and Ling Hao Department of Chemistry, University of Western Ontario , London, Ontario , Canada N6A 5B7 A conductivity method is used to measure the Soret coefficient and heat of transport of aqueous sodium poly(styrenesu1fonate) (Na,PSSA). The data are used to calculate thermal separation factors for Na,PSSA dis-solved in aqueous sodium chloride solutions. The calculations show that large steady-state concentration gra- dients in the polyelectrolyte will be established when a temperature gradient is applied to mixed Na,PSSA-NaCI solutions, ranging up to 80% change in concentration per degree as the polyelectrolyte concentration approaches zero.The Soret coefficient and heat of transport of aqueous sodium benzenesulfonate are mea- sured and compared with the corresponding values for Na,PSSA. The distribution of components in a mixture changes when a temperature gradient is applied.' In many non-isothermal salt solutions, for example, solvent migrates to the warmer regions and salt migrates to the cooler regions.2 Though thermal diffusion measurements provide fundamental infor- mation about molecular interactions, the steady-state separa- tions that can be achieved (typically 0.1-1?4 change in concentration per degree) are usually too small to be useful in practice. The purpose of the present work is to show that thermal separations for polyelectrolytes dissolved in salt solu- tions can be much larger: 10-100% change in concentration per degree.It has been known for some time that large thermal separa- tions can be achieved for high polymers dissolved in solvents of low molecular eight.',^,^ To see if polyelectrolytes show similar behaviour, thermal diffusion measurements are reported here for aqueous sodium poly(styrenesu1fonate) (Na,PSSA, n = 340) of average molecular weight 70000 g mol-'. The size of the poly(styrenesu1fonate) ion should give Na,PSSA a much larger heat of tran~port~.~ than that of a simple salt. Since the heat of transport measures the tendency of a substance to migrate in a temperature gradient, large thermal separations might be observed for aqueous Na,PSSA.In fact, the measured separations were disappointing, ca. 0.4% change in concentration of Na,PSSA per degree. (Similar results were reported in an earlier study of poly- electrolyte thermal diff~sion.~)In binary Na,PSSA-water solutions, however, the sodium and poly(styrenesu1fonate) ions must diffuse together to prevent charge separation. Even if the poly(styrenesu1fonate) ions were drawn strongly to the cold plate, they would be held back electrostatically by the sodium counterions which have much smaller heats of trans- port. By adding a supporting electrolyte, such as NaCl, it might be possible to unleash the polyions from their counterions and thereby achieve much larger thermal separations. This idea prompted us to use thermal diffusion data for Na,PSSA-water and NaC1-water to calculate thermal separations for Na,PSSA-NaC1-water solutions.Experimental The Soret coefficient,"2 defined by 0 = -(l/mKdrn/dT)steaciy state (1) is a convenient measure of thermal diffusion. It gives the frac- tional change in solute molality, rn, per degree under steady- state conditions. The Soret coefficients of aqueous Na,PSSA solutions reported here were measured with a conductivity cell' which held a 1.219 cm column of solution sandwiched between nickel-plated copper cylinders controlled at 30.0 "C (top) and 20.0"C (bottom). Thermal diffusion was followed by measuring electrical resistances Rdt) and RL(t)across upper (U) and lower (L) pairs of platinum electrodes located at and 2 of the cell height h.The quantity Y(t)= [Rdt)-R,(t)]/[Rdt) + RL(t)]decays exponentially to the steady-state value Y,: Y(t)= Y, + Y, exp(-t/8). The relaxation time is 8 = h2/n2D,where D is the mutual diffusion coefficient evaluated at the mean cell tem- perature. The method of linear least-squares was used to evaluate Y, from plots of Y(t)US. exp(-t/O). Soret coefficients were calculated from values of the initial slope', Y,, accord-ing to the relation cr = -n2Y1/2,/(3)BAT.The factor B = -(a In R/a In m)T was evaluated from plots of the log of the mean cell resistance us. the log of the mean cell molality. Mutual diffusion coefficients were measured at 25°C by the Taylor dispersion method.' Solutions were prepared by weight with distilled, deionised water and Na,PSSA (PolySciences) of average molecular weight 70000 g mol-' (n = 340). Thermal diffusion of aqueous sodium benzenesulfonate (Aldrich), which is chemi- cally and structurally analogous to the sodium styrenesulfon- ate monomer, was also measured.Results and Discussion Na,PSSA(m ,)-Water The Soret coefficient of aqueous Na,PSSA was measured at sodium ion molalities (nrnl)from 0.001 to 0.010 mol kg-'. The values of c1 at each composition were reproducible within &O.OOOl to k0.0002 K-'. Table 1 summarises the results. Despite a molecular weight of 70000 g mol-', the Table 1 Soret coefficient of aqueous Na,PSSA(rn,) at 25 "C nrnJmol kg - ~/io-~m2s-' B OlK' O.Oo0 - - 0.0052" 0.00 1 1.08 0.97 0.0045, 0.002 1.06 0.98 0.0043, 0.003 1.05 0.98 0.00418 0.005 1.04 0.98 0.0039, 0.010 1.00 0.99 0.0037, " Obtained by extrapolation of u1us.(nrn,)'". Soret coefficient of Na,PSSA is not large, only ca. 0.004 K-'. Soret coefficients of simple salts, such as aqueous NaC1, are similar in magnitude.6 To understand this result, it is helpful to use the thermody- namic identity :2*10 which relates the Soret coefficient of Na,PSSA to its chemical potential p1 and its heat of transport QT. When Na,PSSA diffuses out of an element of solution, the heat QT per mole of Na,PSSA is absorbed in order to maintain constant tem-perature. The activity of aqueous Na,PSSA is akaapSSA= (nml)nmly>+ll,and hence p1= py + RT ln[(nml)nmly>+l'] (3) where ykl is the stoichiometric mean ionic activity coefi- cient.Differentiation gives QT = (n + 1)RT201[1+ (d In yk '/d In ml)T] (4) The activity coefficient term vanishes in the limit of infinite dilution : Qfo = (n + 1)RT20y= nQi: + Qg', (5) Extrapolation of the Soret coefficient values in Table 1 gives 07 = 0.0052 (+0.0002) K-', and hence QTo = 1300 (+50) kJ mol-' for the limiting heat of transport of Na,PSSA (n = 340). Adopting the recommended value6*" Q;t;,"= 1.33 kJ mol-' leads to Qgs, = 850 f50 kJ mol-' for the limiting heat of transport of the poly(styrenesu1fonate) ion. Eqn. (5) shows that the limiting Soret coefficient of Na,PSSA is proportional to the number-weighted average of the heats of transport of n mol of sodium ions plus 1 mol of poly(styrenesu1fonate) ions: RT2ay = QTo/(n + 1) = (nQ6:+ Q$!,)/(n + 1).Consequently, thermal separations for Na,PSSA are relatively small despite its large molar heat of transport. The data for aqueous sodium benzenesulfonate in Table 2 illustrate this point nicely. The limiting heat of transport of this 1 :1 salt is Q* = 2RT200= 7.8 (k0.3) kJ mol-', about 170 (ca. 42) times smaller than that of Na,PSSA, yet the Soret coefficient sodium benzenesulfonate is nearly identical to that of Na,PSSA. The prospects for large thermal separa- tions in binary polyelectrolyte solutions are not bright. Na,PSSA(rn,)-NaCl(rn,)-Water The chemical potentials and heats of transport2," of Na,PSSA and NaCl in ternary Na,PSSA(m,)-Table 2 Soret coefficient of aqueous sodium benzenesulfonate at 25 "C m/mol kg- ' D/w9 m2 s-' B a/K - O.OO0 - - 0.0053" 0.001 1.06 0.98 0.0045, 0.002 1.05 0.97 0.0043, 0.003 1.05 0.96 0.0042 0.005 1.05 0.96 0.0040, 0.010 1.04 0.95 0.0038, " Obtained by extrapolation of D us.m"'. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 NaCl(m,)-water solutions are given by p1= p: + RT ln[(nm, + m2)"mly",+,'] (6) P2 = + RT lnC(nm1 + m2b2 7: 21 (7) QT = TuI(~PI/~In m1)T + To2(dpc,/aIn m2)T (8) Q: = Toi(d~2/8 In mi)T + To2(8~2/8In m2)T (9) Proceeding as before, the exact limiting expressions nm2 QTO/RT~ = [i + n2m1 0; (10)nm, + m2 ]rT:+ nm, + m, Q:O/RT~ = nm1 m2 nm,+ m2 oy + 11 + nm,+ m2If39 (11) are obtained.The limiting Soret coefficients of Na,PSSA(m,)-NaCl(m,) solutions are functions of the heats of transport and the ratio of the solute molalities. Limiting ionic heats of transport are strictly additive. The values QT" = 1300 kJ mol-' and Q:' = 3.99 kJ mol-' obtained for binary Na,PSSA-water and NaC1-water l1 solu-tions can therefore be used in eqn. (10) and (11) to calculate accurate limiting Soret coefficients for ternary Na,PSSA-NaC1-water solutions. Fig. 1 shows the Soret coefficient of Na,PSSA dissolved in aqueous NaCl solutions calculated according to eqn. (10) and (11). As the ratio m1/m2 drops to zero, the Soret coefficient of Na,PSSA reaches an astonishingly large value : oy(m1/m2 +0) = [Q:' -(nQzo/2)]/RT2 = 0.84 K-', imply-ing an 84% change in Na,PSSA concentration per degree.The Soret coefficient values shown in Fig. 1 are accurate only at infinite dilution where activity Coefficients, ion associ- ation and other complicating factors are unimportant. In view of the rather weak concentration dependence of ol, the calculated limiting values should nevertheless provide a rea- sonable qualitative guide to the thermal diffusion behaviour of dilute Na,PSSA-NaCl solutions. For example, the Soret coefficient for trace amounts of Na,PSSA( 1) dissolved in dilute NaCl solutions should be ca. 0.8 K-'. The thermodynamic analysis presented here shows that thermal separations for polyelectrolyte M,P dissolved in sup- porting salt solutions can be of the order of n times larger than the separations for a binary solution of the poly-electrolyte.Unfortunately, the experimental technique used in 0.9 I I I 0.8 0.7 0.6 -0.5 I Y,0-b 0.4 0.3 0.2 0.1 0.0 0.00 0.05 0.10 0.15 0.20 nm,/(nm, +m2)Fig. 1 Limiting Soret coefficient of Na,PSSA in aqueous Na,PSSA(m,)-NaCl(m,) solutions plotted against the fraction of the sodium ion molality contributed by Na,PSSA J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 191 1 the present study is not well suited to the measurement of this effect because the conductivity changes caused by thermal diffusion of the supporting electrolyte would tend to overwhelm those caused by the polyelectrolyte. Also, because polyelectrolytes diffuse very slowly in supporting salt solu- 2 3 4 J.N. Agar, in The Structure of Electrolytic Solutions, ed. W. J. Hamer, Wiley, New York, 1959, ch. 13. A. H. Emery and H. G. Drickamer, J. Chem. Phys., 1956, 26, 620. M. Schimpf and C. Giddings, J. Polym. Sci. Part B, 1989, 27, 1317. tions, polyelectrolyte gradients develop at long times where the solution columns are prone to convection. For these reasons the thermal separations calculated according to the additivity rule may be more reliable than those obtained by direct measurement, at least for dilute solutions. 5 6 7 H. J. V. Tyrrell, Chem. Commun., 1967, 456. J. L. Lin in Measurement of the Transport Properties of Fluids, ed. W. A. Wakeham, A. Nagashima and J. V. Sengers, Blackwell, Oxford, 1991, ch. 10. J. N. Agar and V. M. M. Lobo, Electrochimica Acta, 1975, 20, 319. The authors thank the Natural Sciences and Engineering 8 9 D.G. Leaist and L. Hui, J. Phys. Chem., 1990,94, 447. D. G. Leaist and L. Hao, J. Solution Chem., 1992, 21, 345. Research Council for financial support of this research. 10 K. G. Denbigh, The Thermodynamics of the Steady State, Methuen, London, 1951, p. 20. References 11 N. Takeyama and K. Nakashima, J. Solution Chem., 1988, 17, 305. 1 H. J. V. Tyrrell, Diffusion and Heat Flow in Liquids, Butter-worths, London, 1961. Paper 4/01266F; Received 18th March, 1994