Mechanism of Polymer Thermophoresis in Nonaqueous Solvents

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The thermophoresis of homopolymer chains dissolved in a pure nonelectrolyte solvent is theoretically examined. Using a similar approach to that used for suspended particles, thermophoresis is related to the temperature-dependent osmotic pressure gradient in the solvent layer surrounding the monomer units (mers). The gradient is produced by small changes in the concentration of solvent molecules (i.e., solvent density) as a result of the mer−solvent interaction energy. The resulting expression contains the interaction energy as well as solvent thermodynamic parameters, including the cubic coefficient of thermal expansion, the isothermal compressibility and its temperature coefficient. Using the general dependence of dipole−dipole potentials on the distance between interacting objects, an expression for thermophoretic mobility that contains a characteristic Hamaker constant is obtained. The resulting expression is used to calculate interaction constants for polystyrene and poly(methyl methacrylate) in several organic solvents using thermophoresis data obtained from thermal field-flow fractionation. The calculated constants are compared to values in the literature and found to follow the same order among the different solvents. Furthermore, the model is consistent with laboratory measurements of polymer thermophoresis, which is weak in water compared to less polar solvents, and which correlates with monomer size. In nonelectrolyte solvents, London dispersion forces must play a major role since other dipole−dipole interactions are insufficient to produce the required interaction energies. Finally, the model predicts that to have a measurable thermophoretic mobility in a given solvent, the polymer should have a Hamaker constant that is greater than 10−15 kT, as calculated by simple but commonly used theoretical models.