在此研究中，我們利用近年所提出的卜瓦松－比克曼(Poisson-Bikerman) 分子熱力學模型推導電解質於混合溶劑中的德拜－休克爾活性係數公式。特別地，此模型探討離子與水的尺寸同時考慮粒子間的空隙，以及水的極化效應和離子-離子、離子-水在水溶液中的相關效應。在考慮水-甲醇混合溶劑的情況下，數值計算的成果分為兩部分。第一部分應用推導出的公式擬合三種1:1 電解質(NaF、NaCl、NaBr) 在不同混合溶劑濃度與固定溫度與壓力的條件下的平均活性係數，其結果很好的擬合實驗數據但在數據較少時對應的調整參數αmix1、αmix2、αmix3 會出現極值；第二部分預測了電解質在混合溶劑中的平均活性係數，我們透過計算兩種溶劑濃度下的調整參數αmix1、αmix2、αmix3 來預測在其他濃度時的活性係數。另外也透過該計算方式推導出一個彈性調整參數Δαi，使其在僅需擬合電解質在純溶劑中的實驗數據便能夠預測在混合溶劑中的平均活性係數。因此，與在水溶液中需要3 個調整參數的情況相比，我們在這最多僅需增加一個參數便可得到混合溶劑中的活性係數。

We derive a generalized Debye-Hückel equation of electrolytes in mixed solvent system by applying Poisson-Bikerman molecular thermodynamic model proposed recently. Especially, the model accounts for the size effect of ion and water molecules of any volume and shape with interstitial voids, the polarization effect of water, and ion-ion and ion-water correlation effects in multicomponent aqueous electrolytes. In the case of water-methanol mixed solvent, the results of numerical simulation could be organized into two parts. First part: We apply the formula to fit the mean activity coefficients of NaF, NaCl, and NaBr in different composition proportion of water-methanol mixed solvent at fixed temperature 298.15 K and pressure 1.01 bar, and the results are in good agreement with the experimental data but might occur extreme value on adjustable parameters (αmix1 , αmix2 , and αmix3 ) in insufficient data or only low concentration. Second part: We predict activity coefficients by combing adjustable parameters of two groups of experimental data. Moreover, we design a flexible, adjustable parameter Δαi to predict activity coefficients of mixture from fitting experimental data of electrolyte in pure solvent. Consequently, compared with aqueous system, we obtain the ion activity in mixed solvent by adding at most one more parameter.

Acknowledgements ------------------------------------------------- i
摘要 ------------------------------------------------------------- ii
Abstract --------------------------------------------------------- iii
Contents --------------------------------------------------------- iv
1 Introduction --------------------------------------------------- 1
2 Thermodynamic model with the Poisson-Bikerman theory ----------- 3
2.1 Fourth-order Poisson–Bikerman theory for mixed solvent ------- 3
2.2 Linear fourth-order Poisson–Bikerman equation ---------------- 4
2.3 Activity Coefficient Formula with Linear 4PBik equation ------ 11
2.3.1 General solutions of linear 4PBik equation ----------------- 11
2.3.2 Unique solution of linear 4PBik equation ------------------- 12
2.3.3 General Debye-Hückel equation ------------------------------ 14
3 Numerical Simulations ------------------------------------------ 16
3.1 Parameter Design and Unit Transformation --------------------- 16
3.1.1 Dielectric constant ---------------------------------------- 16
3.1.2 Born radius and Born energy -------------------------------- 17
3.1.3 Conversion of concentration units -------------------------- 18
3.1.4 Solvent density and density gradient ----------------------- 18
3.2 The Fitting Result of 1:1 Electrolytes ----------------------- 20
3.3 The Prediction Result of 1:1 Electrolytes -------------------- 23
3.3.1 The first type formula ------------------------------------- 23
3.3.2 The second type formula ------------------------------------ 25
4 Conclusions ---------------------------------------------------- 31
References ------------------------------------------------------- 32
Appendix --------------------------------------------------------- 34

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