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

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 <i>D</i>_<i>T</i> saturates with length, but with different scaling exponents. The predicted values of <i>D</i>_<i>T</i> 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 η<i>D</i>_<i>T</i> (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 <i>D</i>_<i>T</i> 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.