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

• Volume term of nucleation work of the form of nΔμnΔμ has been mathematically considered.
• For this form incompressibility in a sense was regarded to be required so for.
• Without incompressibility approximation we have this form relying on the mean value theorem.
• In this form ΔμΔμ is the reservoir's chemical with respect to the equilibrium one.

The work of formation of a critical nucleus is sometimes written as W=nΔμ+γAW=nΔμ+γA. The first term Wvol=nΔμWvol=nΔμ is called the volume term and the second term γAγA the surface term with γγ being the interfacial tension and A   the area of the nucleus. Nishioka and Kusaka [J. Chem. Phys. 96 (1992) 5370] derived Wvol=nΔμWvol=nΔμ with n=Vβ/vβn=Vβ/vβ and Δμ=μβ(T,pα)−μα(T,pα)Δμ=μβ(T,pα)−μα(T,pα) by rewriting Wvol=−(pβ−pα)VβWvol=−(pβ−pα)Vβ by integrating the isothermal Gibbs–Duhem relation for an incompressible ββ phase, where αα and ββ represent the parent and nucleating phases, VβVβ is the volume of the nucleus, vβvβ, which is constant, the molecular volume of the ββ phase, μμ, T, and p   denote the chemical potential, the temperature, and the pressure, respectively. We note here that Δμ=μβ(T,pα)−μα(T,pα)Δμ=μβ(T,pα)−μα(T,pα) is, in general, not a directly measurable quantity. In this paper, we have rewritten Wvol=−(pβ−pα)VβWvol=−(pβ−pα)Vβ in terms of μre−μeqμre−μeq, where μreμre and μeqμeq are the chemical potential of the reservoir (equaling that of the real system, common to the αα and ββ phases) and that at equilibrium. Here, the quantity μre−μeqμre−μeq is the directly measurable supersaturation. The obtained form is similar to but slightly different from Wvol=nΔμWvol=nΔμ.