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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Excess chemical potential ： ウィキペディア英語版 Excess chemical potential The excess chemical potential is defined as the difference between the chemical potential of a given species and that of an ideal gas under the same conditions (in particular, at the same pressure, temperature, and composition). Chemical potential of a pure fluid can be estimated by the Widom insertion method. For a system of diameter $L$ and volume $V$, at constant temperature :$T$, the classical partition function $Q(N,V,T)=\backslash fracN!\}\backslash int\_^\backslash ldots\backslash int\_^ds^\backslash exp(U(s^;L))$ s is a scaled coordinate. :$F(N,V,T)=\; -k\_T\backslash ln\; Q=-k\_T\backslash ln\backslash left(\backslash fracN!\}\backslash right)-k\_T\; \backslash ln;L)\; )\}=$ ::$\backslash ;=F\_(N,V,T)+F\_(N,V,T)$ combining the above equation with the definition of chemical potential, $\backslash mu\_=\; \backslash left(\backslash frac$, we get the chemical potential of a sufficiently large system from :$\backslash mu=\; -k\_T\backslash ln(Q\_/Q\_)=-k\_T\backslash ln\backslash left(\backslash frac\backslash right)\; -\; k\_T\; \backslash ln)\; )\})\; )\}\}=\backslash mu\_(\backslash rho)\; +\; \backslash mu\_$ wherein the chemical potential of an ideal gas can be evaluated analytically. Now let's focus on $\backslash mu\_$, since the potential energy of an N+1 particle system can be separated into the potential energy of an N particle system and the potential of the excess particle interacting with the N particle system, that is, :$\backslash Delta\; U\backslash equiv\; U(s^)\; -\; U(s^)$ and :$\backslash mu\_=\; -k\_T\; \backslash ln\; \backslash int\; ds\_\; \backslash langle\; \backslash exp(-\backslash beta\backslash Delta\; U)\backslash rangle\_$. Thus far we converted the excess chemical potential into an ensemble average, and the integral in the above equation can be sampled by the brute force Monte Carlo method. The calculating of excess chemical potential is not limited to homogeneous systems, but has also been extended to inhomogeneous systems by the Widom insertion method, or other ensembles such as NPT and NVE. ==See also== Apparent molar property 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Excess chemical potential」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.