Molecular-Weight Dependent Thermal Diffusion in Dilute Polymer Solutions

Thermal diffusion of high polymers in a continuous medium is independent of the molecular weight $M_w$. Accounting for the solvent molecular structure and the Brownian motion of the solute, we derive an additional contribution of opposite sign which is significant for short chains but vanishes as $M_w\to \infty$. Our findings explain the dependence on $M_w$ observed recently for polystyrene, and its inverse Soret effect at very small $M_w$. Moreover, they bridge the gap between the macroscopic hydrodynamics description for large solutes and the enthalpy-of-transport picture for small molecules.

Figure 1

Schematic view of a random move $\widehat{x}(t)$ of a solute molecule (+), accompanied by an opposite solvent flow (#). The coherent current of both solute and solvent correspond to the volume of a single bead. In a uniform system, the left and right states occur with equal probability. A temperature gradient gives rise to thermal forces that favor one of the positions, thus resulting in a net solute velocity $u_2$.

Figure 2

Reduced thermophoretic mobility as a function of the chain length $n$. The points are calculated from Eq. (15) with $\nu =0.6$. The dashed lines indicate the maximum and minimum values $D_T^{(\max )}=\beta {\epsilon }_p/(6\pi \eta a)$ and $D_T^{(\min )}$. The latter is given by Eq. (15) for $n=1$; it may be positive or negative, depending on the relative magnitude of the two terms.