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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 Non-random two-liquid model ： ウィキペディア英語版 Non-random two-liquid model The non-random two-liquid model〔Renon H., Prausnitz J. M., "Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures", AIChE J., 14(1), S.135–144, 1968〕 (short NRTL equation) is an activity coefficient model that correlates the activity coefficients $\backslash gamma\_i$ of a compound i with its mole fractions $x\_i$ in the liquid phase concerned. It is frequently applied in the field of chemical engineering to calculate phase equilibria. The concept of NRTL is based on the hypothesis of Wilson that the local concentration around a molecule is different from the bulk concentration. This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind $U\_$ and that with the molecules of the other kind $U\_$. The energy difference also introduces a non-randomness at the local molecular level. The NRTL model belongs to the so-called local-composition models. Other models of this type are the Wilson model, the UNIQUAC model, and the group contribution model UNIFAC. These local-composition models are not thermodynamically consistent due to the assumption that the local composition around molecule i is independent of the local composition around molecule j. This assumption is not true, as was shown by Flemmer in 1976.〔McDermott (Fluid Phase Equilibrium 1(1977)33) and Flemr (Coll. Czech. Chem.Comm., 41 (1976) 3347)〕 ==Equations for a binary mixture== For a binary mixture the following equations〔Reid R. C., Prausnitz J. M., Poling B. E., ''The Properties of Gases & Liquids'', 4th Edition, McGraw-Hill, 1988〕 are used: $$ \left\\left(\frac\left(\frac}\right)^2 +\frac} \right ) \\ \\ \ln\ \gamma_2=x^2_1\left(gas constant and T the absolute temperature, and Uij is the energy between molecular surface i and j. Uii is the energy of evaporation. Here Uij has to be equal to Uji, but $\backslash Delta\; g\_$ is not necessary equal to $\backslash Delta\; g\_$. The parameters $\backslash alpha\_$ and $\backslash alpha\_$ are the so-called non-randomness parameter, for which usually $\backslash alpha\_$ is set equal to $\backslash alpha\_$. For a liquid, in which the local distribution is random around the center molecule, the parameter $\backslash alpha\_=0$. In that case the equations reduce to the one-parameter Margules activity model: $$ \left\" TITLE="\tau_">+\tau_ \right )=Ax^2_2 \\ \ln\ \gamma_2=x^2_1\left(\right )=Ax^2_1 \end\right. In practice, $\backslash alpha\_$ is set to 0.2, 0.3 or 0.48. The latter value is frequently used for aqueous systems. The high value reflects the ordered structure caused by hydrogen bonds. However in the description of liquid-liquid equilibria the non-randomness parameter is set to 0.2 to avoid wrong liquid-liquid description. In some cases a better phase equilibria description is obtained by setting $\backslash alpha\_=-1$.〔Effective Local Compositions in Phase Equilibrium Correlations, J. M. Marina, D. P. Tassios Ind. Eng. Chem. Process Des. Dev., 1973, 12 (1), pp 67–71〕 However this mathematical solution is impossible from a physical point of view, since no system can be more random than random ($\backslash alpha\_$ =0). In general NRTL offers more flexibility in the description of phase equilibria than other activity models due to the extra non-randomness parameters. However in practice this flexibility is reduced in order to avoid wrong equilibrium description outside the range of regressed data. The limiting activity coefficients, aka the activity coefficients at infinite dilution, are calculated by: $$ \left\" TITLE="\tau_">+\tau_ \exp)} \right ) \\ \ln\ \gamma_2^\infty=\left(+\tau_\exp)}\right ) \end\right. The expressions show that at $\backslash alpha\_=0$ the limiting activity coefficients are equal. This situation that occurs for molecules of equal size, but of different polarities. It also shows, since three parameters are available, that multiple sets of solutions are possible. 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「Non-random two-liquid model」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.