Thermophoresis of dissolved molecules and polymers: Consideration of the temperature-induced macroscopic pressure gradient

Abstract

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.

Thermal diffusion by Brownian-motion-induced fluid stress

“…Piazza and Guarino use this model to qualitatively predict the role of electrostatics in the thermal diffusion of charged micelles [8]. In general, these studies use the hydrodynamic equations to calculate a pressure gradient and/or volume force acting locally on the particles that is induced by a non-uniform distribution of solvent molecules or temperature dependent solvent-particle interaction [8,13,14,15,16,17]. Others also include a macroscopic pressure gradient due to the response of the solvent alone to the temperature gradient and this model nearly quantitatively reproduces the mobility of polymers as measured in experiments [14].…”

“…In general, these studies use the hydrodynamic equations to calculate a pressure gradient and/or volume force acting locally on the particles that is induced by a non-uniform distribution of solvent molecules or temperature dependent solvent-particle interaction [8,13,14,15,16,17]. Others also include a macroscopic pressure gradient due to the response of the solvent alone to the temperature gradient and this model nearly quantitatively reproduces the mobility of polymers as measured in experiments [14]. Another approach begins with the kinetic theory of diffusion in a nonuniform temperature field to derive expressions for the Soret coefficient which allow for both positive and negative values of S T [18].…”

Non-equilibrium Thermodynamic Model for the Estimation of the Soret Coefficient in Dilute Polymer Solutions

“…As mentioned in Sect. 1, several workers have developed hydrodynamic/Brownian motion thermodiffusion models, e.g., [9][10][11]. These models, as discussed by Hartung et al [8], are, in general, successful in predicting the experimental data, but usually contain matching parameters that are not easily determined or even well understood.…”

“…However, later it was shown that Khazanovich model predictions show fair agreement with experimental data [7,8], but the model apparently predicts unphysical correlation between the effective segment size and the chain stiffness [8]. Hartung et al [8] also tested the Semenov-Schimpf hydrodynamic model [9], using a reverse fitting method, and found fair qualitative agreement against the experimental data, with a proper choice of the radius of the polymer monomer. They also tested the Brenner hydrodynamic/ Brownian motion model [10] in a similar way and obtained rather good agreement with the experimental data, provided that the matching parameter of the Brenner model (λ) is chosen to be 3.70.…”

Advances in Thermodiffusion and Thermophoresis (Soret Effect) in Liquid Mixtures

“…His model can potentially predict a sign change as the two effects have opposing signs. Runyon and Williams (2011) clarified and further developed the thermal flow-field fractionation method (ThFFF) applied to polyacrylates and compared their experimental results with the theories of Semenov and Schimpf (2004) and Mes (2003). They had to estimate the undetermined input parameters in those theories.…”