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

TL;DR

This paper derives the volume term of the work of critical nucleus formation during phase transitions without volume change, revealing a quadratic dependence on the chemical potential difference.

Contribution

It provides a new calculation of the volume term in terms of chemical potential difference for phase transitions without volume change, highlighting the vanishing linear term.

Findings

Derived the volume term as proportional to the square of chemical potential difference.

Showed the absence of a linear term in the chemical potential difference in this specific phase transition.

Presented an explicit formula involving compressibility and molecular volume.

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.