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

The work of formation of a critical nucleus is sometimes written as W=nΔμ+γA. The first term W_{vol}=nΔμ is called the volume term and the second term γA the surface term with γ being the interfacial tension and A the area of the nucleus. Nishioka and Kusaka [J. Chem. Phys. 96 (1992) 5370] derived W_{vol}=nΔμ with n=V_β/v_β and Δμ=μ_β(T,p_α)-μ_α(T,p_α) by rewriting W_{vol}=-(p_β-p_α)V_β by integrating the isothermal Gibbs-Duhem relation for an incompressible β phase, where α and β represent the parent and nucleating phases, V_β is the volume of the nucleus, v_β, which is constant, the molecular volume of the β phase, μ, T, and p denote the chemical potential, the temperature, and the pressure, respectively. We note here that Δμ=μ_β(T,p_α)-μ_α(T,p_α) is, in general, not a directly measurable quantity. In this paper, we have rewritten W_{vol}=-(p_β-p_α)V_β in terms of μ_{re}-μ_{eq}, where μ_{re} and μ_{eq} are the chemical potential of the reservoir (equaling that of the real system, common to the α and β phases) and that at equilibrium. Here, the quantity μ_{re}-μ_{eq} is the directly measurable supersaturation. The obtained form is similar to but slightly different from W_{vol}=nΔμ.