Thermophoresis of Dissolved Molecules and Polymers: Consideration of the Temperature-Induced Macroscopic Pressure Gradient

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The movement of molecules and homopolymer chains dissolved in a nonelectrolyte solvent in response to a temperature gradient is considered a consequence of temperature-induced pressure gradients in the solvent layer surrounding the solute molecules. Local pressure gradients are produced by nonuniform London–van der Waals interactions, established by gradients in the concentration (density) of solvent molecules. The density gradient is produced by variations in solvent thermal expansion within the nonuniform temperature field. The resulting expression for the velocity of the solute contains the Hamaker constants for solute-solvent and solute-solute interactions, the radius of the solute molecule, and the viscosity and cubic coefficient of thermal expansion of the solvent. In this paper we consider an additional force that arises from directional asymmetry in the interaction between solvent molecules. In a closed cell, the resulting macroscopic pressure gradient gives rise to a volume force that affects the motion of dissolved solutes. An expression for this macroscopic pressure gradient is derived and the resulting force is incorporated into the expression for the solute velocity. The expression is used to calculate thermodiffusion coefficients for polystyrene in several organic solvents. When these values are compared to those measured in the laboratory, the consistency is better than that found in previous reports, which did not consider the macroscopic pressure gradient that arises in a closed thermodiffusion cell. The model also allows for the movement of solute in either direction, depending on the relative values of the solvent and solute Hamaker constants.