## Experimental Observations Of Nonequilibrium Concentration Fluctuations In A Polymer Solution

Light-scattering experiments in solutions of polystyrene with mass-averaged molecular weight M w = 96,400 dissolved in toluene have been performed in our laboratory. The polystyrene solution was contained in a horizontal layer located between an upper and lower plate. The optical arrangement was similar to the one used earlier for measuring nonequilibrium fluctuations in liquid mixtures of toluene and n-hexane [9]. Because of the dependence of the nonequilibrium enhancement of the fluctuations on k-4, the experiments have to be done with small values of the scattering angle. Temperature gradients were applied by raising the temperature of the upper plate and lowering the temperature of the lower plate symmetrically so that the average temperature of the solution remained always at 25°C.

Details concerning the experimental apparatus and the experimental procedure will be presented elsewhere [ 18] The polystyrene solutions used in the experiment were taken from the same batches as those used by Zhang et al. [22] for measuring the mass-diffusion coefficient and the Soret coefficient of these polymer solutions.

Figure 1. Normalized experimental light-scattering correlation functions, obtained at k = 1030 cm-1 for a solution of polystyrene (Mw = 96,400, w = 2.50%) in toluene subjected to various temperature gradients Vr[18], t (s)

Figure 1. Normalized experimental light-scattering correlation functions, obtained at k = 1030 cm-1 for a solution of polystyrene (Mw = 96,400, w = 2.50%) in toluene subjected to various temperature gradients Vr[18],

Figure 1 shows the experimental time-dependent correlation functions obtained at k = 1030 cm-1 for various values of the temperature gradient VT in a solution of polystyrene in toluene with a polymer concentration of w = 2.50%. The data are relative to the intensity of the stray light that serves as a local oscillator in the heterodyne scattering experiments. The correlation functions obtained for all values of VT can be represented by a single exponential oc e'Dk2t with a diffusion coefficient D independent of VT [18]. Hence, the scattering does arise from concentration fluctuations at all values of VT. By comparing the experimental correlation functions obtained at finite VT with the one obtained at VT = 0, we can deduce from the light-scattering measurements an experimental value for the enhancement Ac (VT, k) in Eq. (2).

Experimental data were obtained for solutions with polymer concentrations varying from w = 0.50% to w = 4.00% or, equivalently, from c = 0.00431 to c = 0.0348 g cm-3, to be compared with the estimated overlap concentration c* = 0.0274 g cm-3 [22]. Hence, the experimental results correspond to polystyrene-toluene solutions in the dilute and semidilute solution regime.

Figure 2 Nonequilibrium enhancement A, of the concentration fluctuations in a dilute (open symbols: c = 0.00431 g cm-3 and a semidilute (filled symbols: c = 0.00348 g cm-3 polystyrene-toluene solutions as a function of (VT2/k4. The lines represent linear fits to the experimental data [23].

Figure 2 Nonequilibrium enhancement A, of the concentration fluctuations in a dilute (open symbols: c = 0.00431 g cm-3 and a semidilute (filled symbols: c = 0.00348 g cm-3 polystyrene-toluene solutions as a function of (VT2/k4. The lines represent linear fits to the experimental data [23].

In Figure2 we have plotted the nonequilibrium enhancement Ac of the concentration fluctuations in a dilute and a semidilute polystyrene-toluene solution as a function of ( V T2/k4 [23]. It is seen that the nonequilibrium enhancement Ac indeed is proportional to ( V T)2 and inversely proportional to k4 in accordance with Eq. (3). Linear fits to these data yield experimental values for the coefficient A*C in Eq. (3).

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