Statistical rate theory of interfacial transport. I. Theoretical development

Abstract

After assuming that the transport of molecules between phases at thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between phases is developed by using a first order perturbation analysis of the Schrooinger equation and the Boltzmann definition of entropy. This leads to an Einstein-type relation with the constant of proportionality being the average rate of exchange between microscopic states of different molecular distributions. A hypothesis is introduced which leads to the conclusion that this exchange rate is unchanged as the system moves through the molecular distributions leading to equilibrium, and to it being equal to the molecular rate of exchange between phases in the final equilibrium state. This allows a complete expression for the rate of molecular transport between phases to be developed. The validity of the hypothesis can be examined by comparing the predictions that follow from the derived rate expressions with the available experimental data. This comparison is reported in subsequent parts of this work.

Adsorption–desorption kinetics and chemical potential of adsorbed and gas-phase particles

“…͑Ward may argue that according to his theory the desorption rate is not always inversely proportional to gas-phase pressure because the ''exchange'' constant K might depend on pressure. The latter however disagrees with his definition of this constant.͒ Taking into account comments ͑1͒-͑4͒, we conclude that the formalism proposed and used by Ward et al 8,9 is physically incorrect and accordingly cannot be employed as a basis for simulations of adsorption and desorption kinetics. In particular, the attempts 10 to generalize this formalism to the case of heterogeneous surfaces are not correct either.…”

“…An alternative approach for the use of the chemical potential of adsorbed and gas-phase particles for describing the adsorption-desorption kinetics was proposed and actively employed by Ward et al 8,9 For nondissociative adsorption on the uniform surface, for example, they write…”

“…͑9͒, it is instructive to scrutinize its derivation given by Ward, Findlay, and Rizk 8 ͑WFR͒ ͓note that the formalism 8 was reproduced with minor modifications in Refs. 9͑b͒ and 9͑e͔͒.…”

Methodology of non-equilibrium thermodynamics for kinetics research of CO2 capture by ionic liquids

“…In the CO 2 dissolution kinetics investigations in brines by Ji et al [111], the concentration of CO 2 (aq) at the vapor-liquid interface was considered as the instantaneous equilibrium concentration. However, the investigations of Ward et al showed that the usual assumption of the instantaneous equilibrium at the liquid-gas interface may lead to the illogical consequence [112], and they developed the statistical rate theory (SRT) to describe the molecular transport rate at the vapor-liquid and solid-liquid interfaces based on a first-order perturbation analysis of the Schrödinger equation and the Boltzmann definition of entropy [113][114][115]. In this paper, SRT is used to describe the molecular transport rate at the vapor-liquid interface, and the rate expression is composed of the following three parts [114] as shown in eq.…”

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

“…IKL was recently extended to include lateral interactions according to regular solution theory and the Kiselev association model as well as energetic heterogeneity (mRSK and LF-mRSK models) (Marczewski 2011). This model was also compared to the classic SRT model, corresponding to the same equilibrium isotherms but developed in opposition to the classic Langmuir kinetics (Ward and Findlay 1982;Zhdanov 2001;Rudzinski and Panczyk 2002a, b;Panczyk 2006;Plazinski et al 2009). Moreover, a new ''fractal-like'' ''approach'' to MOE, IKL and SRT models provided other possible extensions to those equations (Haerifar and Azizian 2012).…”