Elementary transition state theory of the Soret and Dufour effects

Abstract

The elementary transition state approach has been used to obtain a simple model theory for the Soret effect (thermal diffusion) and the Dufour effect. The flow of heat in the Dufour effect is identified as the transport of the enthalpy change of activation as molecules diffuse. The theory as now formulated applies only to thermodynamically ideal mixtures of substances with molecules of nearly equal size. The results of the theory conform to the Onsager reciprocal relationship. When the results were fit to data on thermal diffusion for two liquid systems, a close fit was obtained and yielded reasonable values of between 2 and 3 kcal mol-I for enthalpy changes of activation and differences between the entropy changes of activation for the two components of between 0 and 1 cal K-1 mol'-.Assume that midway between site a and site b there is a position of high potential energy through which a molecule must pass in jumping from site a to site b or vice versa. The temperature at this position is denoted by Tm, and we can write Xm -Xa = Xb -Xm = X/2.[2]In the elementary transition state theory of isothermal diffusion, the probability per unit time that a molecule of component i makes a transition from one equilibrium site to the next is given by kBT pi= y( -jr exp(-AGi/RT) (i = 1, 2) [3] The Soret effect (thermal diffusion) is the occurrence of a diffusion flux due to a temperature gradient. The Dufour effect is the reciprocal phenomenon, the occurrence of a heat flux due to a chemical potential gradient. Both effects have been extensively studied in gases, and the Soret effect has been studied both theoretically and experimentally in liquids. However, partly because of the smallness of the effect, accurate measurements of the Dufour effect in liquids have only recently been carried out (1). There does not seem to be a model theory of the liquid-state Dufour effect in the literature. This paper presents a simple model theory for both effects in liquids, based on elementary transition state theory. The liquid is represented by a somewhat disordered quasi-lattice model in which a molecule can move from one equilibrium position to another, passing through a transition state of high potential energy. This beginning point has been used in previous theories of the Soret effect (2, 3). The Soret effect Consider a liquid two-component mixture that is uniform in the y and z directions but has a temperature and composition that depend on x and t, the time. Denote two adjacent equilibrium molecular positions by a and b, and assume that the two components are similar enough that these positions can be occupied by molecules of component 1 or component 2. Let xa be the value of the x coordinate at site a and Xb (presumed larger than Xa) be the value of x at site b. Let the jump distance, X, be given by X = Xb -Xa [1] and assume that this distance is equal for all pairs of adjacent sites. The temperature at xa is denoted by Ta, and the concentration of component 1 at xa is denoted by cla, with similar definitions for Tb, C2a, ...

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