No abstract

The material transport equations derived by non-equilibrium thermodynamics are used to describe the material transport in binary non-isothermal molecular systems. The chemical potentials of the components used in the equations are calculated using statistical mechanics. As the material transport equations contain chemical potentials at constant pressure, the local pressure distribution necessary in calculations is obtained using the condition of the local thermodynamic equilibrium around the selected molecular particle. The Laplace contribution to the local pressure distribution within the layer of the liquid around the particle is accounted. The calculations yield the results equivalent to previous approaches and add new terms to the Soret coefficient, which are related to the difference in the translational and rotational thermal motion between the molecules. The kinetic contribution to thermodiffusion explains the isotope thermodiffusion effect, the role of the molecular symmetry, and the sign change in thermodiffusion observed in binary systems. The proposed theory describes thermodiffusion in binary molecular systems with a limited miscibility.

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

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.

An approach to the transport of material in a temperature gradient is outlined using nonequilibrium thermodynamics theory. The model is applicable to the thermophoresis of colloids and nanoparticles in systems with limited miscibility. Component chemical potentials in binary systems are calculated using statistical mechanics. The local pressure distribution is obtained using the condition of local thermodynamic equilibrium around the suspended particle. The Laplace contribution of the local pressure distribution within the layer of liquid surrounding the particle leads to a size dependence that is consistent with empirical data. The contribution of Keezom interaction to the thermodiffusion coefficient is calculated using empirical values of the thermodiffusion coefficient for silica particles in water and acetonitrile. The resulting interaction energies are consistent with those found in the literature.