Activity and Steady-State Kinetics of One-Dimensional Kinetic Ising Model

TL;DR

This paper investigates the kinetics of a one-dimensional Ising model under quasi-chemical approximation, introducing instantaneous activities to better understand steady-state kinetics and chevron plot behaviors.

Contribution

It introduces the concept of instantaneous activities and activity coefficients, providing a new perspective on the kinetics and chevron plot analysis of the 1D Ising model.

Findings

QCA best describes the equilibrium of 1DIS with constant NNI

Instantaneous activities simplify the kinetic equations

New insights into chevron plot rollover phenomena

Abstract

In this work we focused on the kinetics of a one-dimensional Ising system (1DIS) with constant nearest-neighbor interaction (NNI). The exact solution of both thermodynamics and kinetics of this system under quasi-chemical approximation (QCA) had been shown in the literature, and the equilibrium solution was exact. In this work, it was discussed why QCA applied the best in the case of 1DIS with constant NNI. Furthermore, extension had been made to discuss that due to this special reason, perhaps the kinetics of the system under QCA is the correct steady-state kinetics. Inspired by this observation, the activity and activity coefficients of the system was studied closely to re-examine the form of the equation of motion under QCA. A novel concept---the instantaneous activities and the corresponding instantaneous activity coefficients---was introduced, and in terms of these quantities the kinetics seemed to be much simpler and physically more meaningful. The chevron plot of this system was also discussed and new way of looking at the \emph{rollover} of chevron plots was presented.