Info

Figure 3. Mass diffusion coefficient D of the polystyrene-toluene solutions as a function of the polymer concentration. The open symbols indicate data obtained with an optical beam-bending technique [22] and the filled symbols data obtained from light scattering. The dashed line represents Eq. (5) and the solid curve represents Eq.(7).

A comparison of the values of the diffusion coefficients deduced from the light-scattering measurements and those measured with the optical beam-bending method is shown in Fig. 3. Zhang et al. [22] found that the concentration dependence of the diffusion coefficient is well represented by a commonly used truncated virial expansion [27]:

with Do = 4.71 x 10-7 cm2 s-i and kD = 22 cm3 g-1. This linear concentration dependence corresponds to the dashed line in Fig. 3. For concentrations c/c* > 0 (1) in the semidilute regime, the diffusion coefficient is expected to vary as

independent of the molecular mass of the polymer [28]. In Eq. (6) v = 10/17 = 0.588 is the exponent that characterizes the scaling of the radius of gyration with the mass of the polymer [29]. To combine Eqs. (5) and (6) Nystrom and Roots [30] have proposed a scaling approximation of the form

with XD= rD(kDc) as a scaling variable and where AD=A +rD. In Eq. (7) A = (1 - v)/ (3v - 1) = 0.539 and B = (2 - 3 v)/(3 v - 1) = 0.309, while rD is an adjustable constant. The solid curve in Fig. 3 represents Eq. (7) with rD = 0.48 as determined by us from the measurements of Zhang et al. [22] for the polystyrene solution with Mw = 96,400. In the concentration range of the light-scattering measurements any deviations from a linear relation are negligibly small.

Figure4. The inverse Soretcoefficient S T ofthepolystyrene-toluene solutions as a function ofthe polymer concentration. The symbols indicate data obtained with an optical beam-bending technique [22]. The dashed line represents Eq.(9)andthesolidcurverepresents Eq.(10).

Figure4. The inverse Soretcoefficient S T ofthepolystyrene-toluene solutions as a function ofthe polymer concentration. The symbols indicate data obtained with an optical beam-bending technique [22]. The dashed line represents Eq.(9)andthesolidcurverepresents Eq.(10).

The values of the Soret coefficient ST obtained by Zhang et al. [22] for the same polymer solutions in the concentration range corresponding to the light-scattering measurements are shown in Fig.4. The thermal-diffusion coefficient D th is defined as the product of D and ST [19,20]

The values of D th deduced from the experimental data for D and ST are shown in Fig. 5. The thermal-diffusion coefficient D th turns out to be rather insensitive to the concentration c, the variation being no more than 5%. Hence, at low concentrations we expect St _ to vary as

with S t,0 = 0.240 K-1 and ks = 24 cm3 g-1 found by Zhang et al. [22]. This linear concentration dependence is represented by the dashed line in Fig. 4. To extend the representation of St1 beyond the linear regime we assume in analogy to Eq. (7)

with XS = rs(ksc) and As = A + r-is, where r-is is again an adjustable constant. The solid curve in Fig. 4 represents Eq. (10) with rs = 1.16 as determined by Li et al. [18]. The curve in Fig. 5 represents the thermal-diffusion coefficient calculated as the product of D and ST as given by Eqs. (7) and (10).

0 0

Post a comment