标题： 临界核形成功的体积项相对于平衡化学势的差异 显示英文标题

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

摘要： 临界核形成的功有时写作 \[ W=n \, \text\{{\Delta }{\mu }\} + \text\{{\gamma }\} \, A. \] 第一项 \( W_\{\text\{{卷积}\}\} = n \text\{{\Delta }{\mu } \} \) 称为体积项，第二项 \( \text\{{\gamma }\} A \) 称为表面项，其中{\gamma }是界面张力，\( A \) 是核的面积。 Nishioka 和 Kusaka [J. 化学物理] [96 (1992) 5370] 推导出 W_{卷积}=n{\Delta }{\mu } ，其中 n=V_{\beta }/v_{\beta }， {\Delta }{\mu } ={\mu }_{\beta }(T,p_{\alpha })-{\mu }_{\alpha }(T,p_{\alpha }) 通过重写 W_{卷积}=-(p_{\beta }-p_{\alpha })V_{\beta }，通过对不可压缩的{\beta }相的等温 Gibbs-Duhem 关系积分得到，其中 {\alpha }和{\beta }表示母相和成核相， V_{\beta }是核的体积， v_{\beta }是常数，表示{\beta }相的分子体积，{\mu }、 T 和 p 分别表示化学势、温度和压力。 我们注意到， {\Delta }{\mu } ={\mu }_{\beta }(T, p_{\alpha }) -{\mu }_{\alpha }(T, p_{\alpha }) 通常不是一个可以直接测量的量。 本文中，我们将 W_{卷积}=-(p_{\beta }-p_{\alpha })V_{\beta }重写为 {\mu }_{再}-{\mu }_{等于}的形式，其中 {\mu }_{重新} 和 {\mu }_{等于} 分别为储层的化学势（等于真实系统的化学势，为{\alpha }相和{\beta }相所共有）以及平衡时的化学势。 这里，量 {\mu }_{重新}-{\mu }_{等于} 是可以直接测量的过饱和度。 所得到的形式与 W_{卷积}=n{\Delta }{\mu } 相似，但略有不同。 显示英文摘要

摘要： 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}.