Semen N. Semenov

Mechanism of particle thermophoresis in pure solvents

The thermophoresis of particles suspended in a pure solvent is theoretically examined. Thermophoresis is related to the temperature-induced pressure gradient in the solvent surrounding the particle and the resulting relative motion of the particle and the surrounding liquid. The excess pressure is produced by the particle-solvent interaction. As the interaction potential, London-van der Waals forces are considered. Using the known dependence of the interaction potential on the distance between the particle and the solvent molecule, an expression for the thermophoretic mobility (TM) (the particle velocity in a unit temperature gradient) is obtained. The resulting expressions are used to calculate the TM values for silica particles in several organic solvents and water. The calculated TM values for silica particles are of the same order as those reported in the literature. The model is consistent with laboratory measurements of particle thermophoresis, which is weak in water compared with organic solvents. This can be explained by the very low cubic thermal expansion coefficient for water. The calculated retention values for silica particles in thermal field-flow fractionation experiments performed in three organic solvents also follow the order known from literature.

Statistical Thermodynamics of Material Transport in Nonisothermal Suspensions

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.

Theory of Soret Coefficients in Binary Organic Solvents

Thermodiffusion in binary molecular liquids is examined using the nonequilibrium thermodynamic model, where the thermodynamic parameters are calculated using equations based on statistical mechanics. In this approach, thermodiffusion is quantified through the variation in binary chemical potential and its temperature and concentration dependence. The model is applied to solutions of organic solvents, in order to compare our theoretical results to experimental results from the literature. A measurable contribution of the orientation-dependent Keezom interaction is shown, where the possible orientations are averaged using the Boltzmann weighting factor. Calculations of enthalpies of evaporation from the model yield good agreement with experimental values from the literature. However, calculations of the associated energetic parameters were several times larger than those reported in the literature from numeric simulations of material transport.

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.

Comment on "Soret motion in non-ionic binary molecular mixtures" [J. Chem. Phys. 135, 054102 (2011)].

The material transport equations derived in the article by Leroyer and Würger [J. Chem. Phys. 135, 054102 (2011)] do not adequately provide a description of material transport in liquid binary systems. An alternate approach based on non-equilibrium thermodynamics is presented.

Unified Hydrodynamic Model of Thermodiffusion and Cross-Diffusion in Liquids

Abstract Over the last six years, we have published a series of papers developing a hydrodynamic model of thermodiffusion in liquids and liquid mixtures. Initial work focused on the movement of polymers dissolved in nonpolar solvents arising from the pressure gradient induced by asymmetry in polymer–solvent interactions as a result of the temperature-induced concentration gradient in the solvent. As that model was refined, we examined secondary effects of a macroscopic pressure gradient in the solvent, and finally extended our hydrodynamic approach to cross-diffusion and thermodiffusion in solvent mixtures. Application of the model is currently limited to non-ionic liquids, where molecular interaction energies can be estimated by Hamaker constants or similar parameters. In this paper we present the body of work as a whole, in order to ensure a consistent nomenclature and unify the model for application to liquid mixtures in general. To test the model, values of Soret coefficients for mixtures of toluene and n-hexane have been calculated using parameters in the literature.

Comment on ‘‘Role of the Velocity Frame of Reference in Thermodiffusion in Liquid Mixtures’’ by M. Eslamian, C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.

Rejoinder to the reply to a comment by S.N. Semenov and M.E. Schimpf on ‘Role of the velocity frame of reference in thermodiffusion in liquid mixtures’, Philosophical Magazine vol. 92, 705 (2012), by M. Eslamian, C.G. Jian and M.Z. Saghir

Rejoinder to the reply to a comment by S.N. Semenov and M.E. Schimpf on ‘Role of the velocity frame of reference in thermodiffusion in liquid mixtures’, Philosophical Magazine vol. 92, 705 (2012), by M. Eslamian, C.G. Jian and M.Z. Saghir Semen N. Semenov a & Martin E. Schimpf b a Institute of Biochemical Physics RAS, 117977 Moscow, Kosygin Street 4, Russia b Department of Chemistry, Boise State University, Boise, ID, USA

Statistical Thermodynamics of Material Transport in Non-Isothermal Mixtures

This chapter outlines a theoretical framework for the microscopic approach to material transport in liquid mixtures, and applies that framework to binary one-phase systems. The material transport in this approach includes no hydrodynamic processes related to the macroscopic transfer of momenta. In analyzing the current state of thermodynamic theory, we indicate critically important refinements necessary to use non-equilibrium thermodynamics and statistical mechanics in the application to material transport in nonisothermal mixtures.