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

Abstract

In the present work a theoretical model based on linear non-equilibrium thermodynamics and the concept of Eyring's activation energy of viscous flow is developed to estimate the Soret coefficient in dilute polymer solutions. The model is capable of predicting a sign change in the Soret coefficient, when the polymer molecular weight changes. The key part of the model is the way that the net heat of transport of the polymer molecules is simulated. Employing the Mark-Houwink equation, which correlates the polymer solution intrinsic viscosity with its molecular weight, the net heat of transport of the polymer is correlated with the activation energy of viscous flow of the polymer's monomer in the liquid state, the Mark-Houwink solution parameter, and the polymer molecular weight. The model is evaluated against the experimental data, where qualitative and in some cases quantitative agreement is found.

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

“…Once the segregation process is triggered and molecules attain a maximum drift velocity, the thermal forces are counteracted by the drag and other forces, such as the Brownian forces. A concentration is established gradually with time, leading to a concentration-induced diffusion flow opposite to the thermodiffusion-induced flow, and this causes a decrease in the overall drift velocity and drag forces (Eslamian and Saghir, 2010d). Villain-Guillot and Würger (2011) argued that the Soret motion in binary liquids arises to a large extent from rectified velocity fluctuations around molecules.…”

“…One successful approach is the linear nonequilibrium thermodynamics, Eq. (2), if the net heat of transport in polymer mixtures can be modeled adequately (Eslamian and Saghir, 2010d). In their approach, it was assumed that the net heat of transport of the solvent molecules equals the activation energy of viscous flow of the solvent in the pure state, i.e.…”

Modeling of DNA thermophoresis in dilute solutions using the non-equilibrium thermodynamics approach

“…In the absence of a concentration gradient at the earlier stages of the process, both species are forced to move in the direction of the heat flow, due to the influence of the thermal forces that work on all molecules in the opposite direction of the temperature gradient which is the same as the direction of the heat flow. A concentration gradient is gradually established in the mixture, due to the interaction of thermal, concentration, and other forces; the thermophobic component (DNA or solvent molecule) is pushed toward the cold side, whereas the other molecule has to move to the hot side [9].…”

“…[9][10][11][12][13]) to DNA solutions as well. Among the existing thermodiffusion models on polymer solutions, our modeling approach [9], which is based on non-equilibrium thermodynamics [11] and Eyring's activation energy of viscous flow, presents a practicable expression for the estimation of Soret coefficients in dilute polymer solutions. The formula works well on both long-chain and short-chain polymer solutions and predicts a sign change when the polymer molecular weight changes.…”

“…Nevertheless, a sign change has been observed in DNA solutions when temperature changes [6]. Owing to the importance of DNA manipulation for biological applications, in this work we attempted to modify an existing nonequilibrium thermodynamics model expression [9] to make it suitable for DNA molecules, as well.…”