Vanishing linear term in chemical potential difference in volume term of work of critical nucleus formation for phase transition without volume change

Abstract

A question is given on the form n({\mu}_{\beta}-{\mu}_{\alpha}) for the volume term of work of formation of critical nucleus. Here, n is the number of molecule undergone the phase transition, {\mu} denotes the chemical potential, {\alpha} and {\beta} represent the parent and nucleating phases, respectively. In this paper we concentrate phase transition without volume change. We have calculated the volume term in terms of the chemical potential difference {\mu}_{re}-{\mu}_{eq}$ for this case. Here, {\mu}_{re} is the chemical potential of the reservoir and {\mu}_{eq} that at the phase transition. We have W_{vol} = -[({\kappa}_{\beta}-{\kappa}_{\alpha})/(2v_{eq}^2)] ({\mu}_{re}-{\mu}_{eq})^2 V_{\beta} with {\kappa} denoting the isothermal compressibility, v_{eq} being the molecular volume at the phase transition, V_{\beta} the volume of the nucleus.