# Thermodiffusion of Chained Molecules: From Oligomers to the High Polymer Limit

## TL;DR

This paper studies how temperature differences affect the movement of chained molecules, showing how their length and solvent influence their behavior.

## Contribution

The paper generalizes a theoretical approach to calculate thermodiffusion coefficients for polymer molecules from oligomers to high polymers.

## Key findings

- The thermodiffusion coefficient D_T of polystyrene in toluene and ethylbenzene matches experimental data across chain lengths.
- Alkane molecules show negative D_T values and migrate to hotter regions in all solvents studied.
- Predictions for alkanes in cyclohexane deviate more from experimental data, similar to earlier findings in molecular mixtures.

## Abstract

Thermodiffusion of entangled molecules in an inhomogeneous
temperature
field is determined by their length. With increasing length, the thermophoretic
velocity increases in magnitude and sometimes changes its direction,
depending on the nature of the polymer and the solvent. Thus, the
theoretical description of thermodiffusion, already a multifactorial
phenomenon, is complicated by the appearance of another important
property. Here, we generalize to chained molecules an approach recently
proposed for molecular systems and calculate the thermodiffusion coefficients
of polymer molecules, starting from oligomers up to the high polymer
limit. The calculations were performed for two types of chained moleculespolystyrene
(PS) and alkanesdissolved in one of three nonpolar solventstoluene,
ethylbenzene, or cyclohexane. For both types of chain molecules, the
thermodiffusion coefficient D

T
saturates with length, but with different scaling exponents.
The predicted values of D

T
of PS in toluene and ethylbenzene are in excellent agreement with
experimental data over the entire range of chain lengths from monomer
to high polymer. In particular, the plateau value of the product ηD

T
(where η is a solvent
viscosity) proves to be close to the experimentally observed universal
value ≈ 6 · 10–15 N/K. The theoretical
dependencies for D

T
of
alkanes in the same solvents also agree well with the data, although
they slightly overestimate it. More significant deviations of the
predictions from the measurements occur when cyclohexane is used as
a solvent. This behavior is similar to that found earlier for molecular
mixtures. In all solvents studied, alkane molecules manifest the negative
values of the thermodiffusion coefficients and migrate to the hotter
layers.