Friday, May 3, 2013

1305.0332 (Atsushi Mori)

Volume term of work of critical nucleus formation in terms of chemical
potential difference relative to equilibrium one

Atsushi Mori
The work of formation of a critical nucleus is sometimes written as W=n{\Delta}{\mu}+{\gamma}A. The first term W_{vol}=n{\Delta}{\mu} is called the volume term and the second term {\gamma}A the surface term with {\gamma} being the interfacial tension and A the area of the nucleus. Nishioka and Kusaka [J. Chem. Phys. 96 (1992) 5370] derived W_{vol}=n{\Delta}{\mu} with n=V_{\beta}/v_{\beta} and {\Delta}{\mu}={\mu}_{\beta}(T,p_{\alpha})-{\mu}_{\alpha}(T,p_{\alpha}) by rewriting W_{vol}=-(p_{\beta}-p_{\alpha})V_{\beta} by integrating the isothermal Gibbs-Duhem relation for an incompressible {\beta} phase, where {\alpha} and {\beta} represent the parent and nucleating phases, V_{\beta} is the volume of the nucleus, v_{\beta}, which is constant, the molecular volume of the {\beta} phase, {\mu}, T, and p denote the chemical potential, the temperature, and the pressure, respectively. We note here that {\Delta}{\mu}={\mu}_{\beta}(T,p_{\alpha})-{\mu}_{\alpha}(T,p_{\alpha}) is, in general, not a directly measurable quantity. In this paper, we have rewritten W_{vol}=-(p_{\beta}-p_{\alpha})V_{\beta} in terms of {\mu}_{re}-{\mu}_{eq}, where {\mu}_{re} and {\mu}_{eq} are the chemical potential of the reservoir (equaling that of the real system, common to the {\alpha} and {\beta} phases) and that at equilibrium. Here, the quantity {\mu}_{re}-{\mu}_{eq} is the directly measurable supersaturation. The obtained form is similar to but slightly different from W_{vol}=n{\Delta}{\mu}.
View original:

No comments:

Post a Comment