Polymer thermophoresis in solvents and solvent mixtures

The thermophoresis of homopolymer chains dissolved in a pure non-electrolyte solvent or solvent mixture is theoretically examined. Thermophoresis is related to the temperature-dependent pressure gradient in the solvent layer surrounding the monomer units (mers). The gradient is produced by small changes in the solvent or solvent mixture density due to the mer-solvent interaction. The London-van der Waals interaction was considered as the main reason of the excess pressure around mers. The resulting expression for the thermophoretic mobility (TM) contains the Hamaker constant for mer-solvent interaction, as well as solvent thermodynamic parameters, including the cubic thermal expansion coefficients of the solvents and the temperature coefficient of the solvent partition factor (for the solvent mixture). This expression is used to calculate the interaction constants for polystyrene and poly(methyl methacrylate) in several organic solvents and binary solvent mixtures using thermophoretic data obtained from thermal field-flow fractionation. The calculated constants are compared with values in the literature and found to follow the same order among the different solvents and to be of the same order of value although several times larger. Furthermore, the model explains weak polymer thermophoresis in water compared with less polar solvents, which correlates also with monomer size. The concentration dependence of polystyrene TM in solvent mixtures also provides a satisfactory explanation by the proposed theory using a concept of secondary diffusiophoresis due to secondary temperature-induced solvent concentration gradient. The method for the evaluation of the diffusiophoresis contribution is proposed.