用于强水化和缔合相互作用电解质溶液的化学反应热力学模型的开发及应用
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摘要
多元复杂氯化物电解质溶液体系如CuH_2_2–MH_2n–H_2O（M=Li，Na，K，Mg，Ca），由于存在强水化，强缔合，以及强水化和缔合作用竞争，溶液结构与性质复杂，用以往的电解质热力学模型如Pitzer模型等计算时不仅描述能力差、预测困难，且无法解释溶液结构与性质之间的联系。
为了解决这一难题，我们在Stokes–Robinson逐级水化模型基础上，引入离子缔合，充分考虑水化、缔合作用竞争影响，建立了以系列水化离子，水化离子对物种为基础，综合考虑了离子间的长程静电作用以及水化、缔合短程作用，并以化学反应为基本特征的化学反应模型。化学反应模型不仅数学形式简单，高度对称，有坚实的理论基础；而且通过推理证明它严格遵守Gibbs–Duhem方程。当电解质溶液达到热力学平衡时，体系的自由能处于最低状态。利用这一原理化学反应模型通过自由能最优化可求得各个物种在化学或相平衡下的浓度分布，进而计算电解质溶液的系列热力学性质。由于直接参数拟合过程具有计算复杂，规模大，变量数众多，结果可靠性低等困难。我们采用嵌套二步优化构架设计，引入分区粒子群最优化算法进行参数拟合，突破了上述困难，模拟测试表明该算法寻优成功率，计算结果的可靠性明显高于原来的算法。
作为应用实例，我们用化学反应模型计算了氯化物LiH_2，NaH_2，KH_2，MgH_2_2，CaH_2_2，CuH_22的六种二元体系以及15种三元体系的热力学性质。计算表明化学反应不仅可以准确描述二元体系的热力学性质，而且补充少量的三元体系参数也可以准确地描述三元体系的热力学性质。若不生成盐盐缔合物种，化学反应模型仅用相应二元体系模型参数就可以直接预测三元体系的热力学性质，例如所预测的LiH_2–CaH_2_2–H2O，LiH_2–MgH_22–H2O三元体系aw，计算值的平均偏差分别为0.0027和0.0029，最大偏差分别为0.0065和0.0081；所预测的LiH_2–CaH_2_2–H_2O，LiH_2–MgH_2_2–H2O三元体系溶解度等温线也与实验数据高度接近。特别地，化学反应模型所预测的痕量CuH_2_2在LiH_2–H_2O体系中含Cu物种浓度分布曲线与Brugger紫外光谱解析结果保持高度一致，所预测的痕量CuH_2_2在NaH_2–H_2O体系中含Cu物种浓度分布曲线与Haung用热力学模型计算的结果也非常相近。
通过大量的计算发现，化学反应模型实际充当了桥梁作用，沟通溶液的微观结构与宏观热力学性质之间的联系。通过它，可以帮助我们理解电解质微观结构对溶液热力学性质影响机制。
水化作用，缔合作用以及水化缔合作用竞争在溶液中扮演着重要角色。它不仅在二元体系中决定着水的活度曲线走向和电解质在水溶液中的溶解度；而且在三元体系中，对水的活度，溶解度等温线，以及物种浓度分布曲线造成关键性的影响。例如，在三元体系中，痕量CuH_2_2在MH_2n–H2O（M=Li, Na, K, Ca）体系中的含Cu物种的浓度分布受阴离子与水分子竞争配位作用的影响，这种部分配位作用也是水化缔合作用竞争的一种形式。由于不同氯化物MH_2n供氯离子不同，其阴离子和H_2O分子在Cu–H_2缔合物上的竞争配位作用也存在差别，使痕量CuH_2_2在MH_2n–H_2O（M=Li, Na, K, Ca）体系中的含Cu物种的浓度分布曲线呈有规律的变化。当盐盐缔合作用很强时，三元体系中可能生成盐盐缔合物种，此时，三元体系的热力学性质不能简单地用二元体系的模型参数直接预测，而必须用三元体系溶解度等温数据来拟合盐盐缔合物种的参数，才能较好地描述三元体系溶解度等温线。用水化缔合作用竞争可以很好解释为什么缔合物的形成使得固相溶解度在共晶点附近比预测结果偏大的原因。无论是阴离子与H2O分子竞争配位，还是生成盐盐缔合物种，水化缔合作用竞争都会使得三元体系等水活度线呈不同程度的弯曲。
本工作开发的化学反应模型能很好地解释由于上述水化，缔合作用，水化缔合作用竞争的影响所引起的一系列现象，表现出强大的分析能力。
Strong hydration, association and competition between hydration and association in themultiple metal chlorides aqueous solution of CuH_22–MH_2n–H2O (M=Li, Na, K, Mg, Ca) leadto complexity of solution structure and properties inlcuding component asctivities, solubility.Developed thermodynamic models up to now for electrolyte solution, such as the Pitzermodel, cannot describe or predict their thermodynamic properties, and cannot explain therelation of the solution structure and properties either.
To overcome this difficult, based on the Stokes–Robinson stepwise hydration model, weintroduced ion–association interaction into the stepwise hydration model, develop a newthermodynamic model is called reaction model (RM). The reaction model consists of thelong–range electrostatic interaction and short interaction of hydration and association. It is notonly simple in mathematical, high symmetrical, but also built on solid theoretical foundationand strictly abides Gibbs–Duhem regulation. There is a minimum value of free Gibbs energyof the electrolyte solution to reach a thermodynamic equilibrium. By this principle, reactionmodel obtains the various species concentration under chemical or phase equilibriumcondition by energy optimization, then further calculate series thermodynamic properties withthem. Because of the large number of variables, complicated, large scale computation and lowreliability of results, many difficults were encountered in direct parameter fitting. To solvethis problem, a framework design of the nested two–step optimization was adopt in this work.An algorithm named Partitioning Quantum–behaver Particle Swarm Optimization (PQPSO) isapplied in parameters evauation. The simulation tests show that the success rate and thereliability of the optimization results have improved significantly than primary method.
As examples of application, we use the reaction model to calculate the thermodynamicproperties of six binary aqueous systems and15ternary aqueous systems of metal chloridesLiH_2, NaH_2, KH_2, MgH_22,CaH_22and CuH_22. Calculations results show that the reaction modelcan accurately describe the thermodynamic properties of not only the binary system, but alsothe ternary system if adding small number of the ternary parameters. The reaction model canpredict the thermodynamic properties of the ternary system only with the correspondingbinary parameters, such as the predicted awvalue of LiH_2–CaH_22–H2O and LiH_2–MgH_22–H2Osystem, the corresponding calculated average deviations are0.0027and0.0029, the maximumdeviation are0.0065and0.0081, respectively. The predicted isotherm of LiH_2–CaH_22–H2Oand LiH_2–MgH_22–H2O system are highly consist with the experimental data. In particular, ourpredicted Cu-containing species concentration distribution curve of trace CuH_22in LiH_2–H2Osystem is highly consistent with Brugger’s analytical results of UV spectra; at the same time, the predicted same result in the NaH_2–H2O system is very similar to thermodynamic modelcalculation results by Haung.
By a large amount of computing, it is found that the reaction model can act as a bridge,which connects the microscopic structure and the thermodynamics properties. It helps usunderstand the mechanism how the microscopic structure characteristic of electrolytesolutions affect their thermodynamics properties.
In some electrolyte aqueous solutions, hydration, association and the competition betweenhydration and association play important role to the thermodynamics properties. Theseinteraction not only seriously impact the binary water activities, determine the electrolytesolubility with the different structural characteristics in aqueous solution; but also cause astrong effect on water activities, solubility isotherms in the ternary system, as well as on thespecies concentration distribution curve. For example, the Cu–containing speciesconcentration distribution curve of the trace CuH_22in MH_2n–H2O(M=Li, Na, K, Ca) systemsis affected by the coordination competition between anions and water molecules which is alsoa form of competition of hydration and association. Different H_2–donation ability of metalchloride MH_2nleads to that the competition coordination of the anions and H2O molecules toCu–H_2complex is also differences, so the concentration distribution curves of Cu–containingspecies of trace CuH_22in MH_2n–H2O (M=Li Na, K, Ca) systems present variation regularly.When a salt–salt association species will generate in the ternary system due to the strongsalt–salt association, thermodynamic properties of the ternary system can not be directlypredicted simply with the binary parameters. One must evalue the parameters of salt–saltassociation species with fitting solubility isotherm data to better describe ternary solubilityisotherms.
With the competition between hydration and association, it can also well explain why theformation of salt–salt association complex makes the solubility of solid phase larger than thepredicted results near the eutectic points. Either the competition coordination of the anion andthe H2O molecule, or the formation of salt–salt association species, the competition ofhydration and association will make iso awlines in the ternary system bending in differentdegrees.
The reaction model developed in this work can well explain above described seriesphenomena caused by the impaction of hydration, association and the competition ofhydration and association, exhibits a powerful analytical ability.
为了解决这一难题，我们在Stokes–Robinson逐级水化模型基础上，引入离子缔合，充分考虑水化、缔合作用竞争影响，建立了以系列水化离子，水化离子对物种为基础，综合考虑了离子间的长程静电作用以及水化、缔合短程作用，并以化学反应为基本特征的化学反应模型。化学反应模型不仅数学形式简单，高度对称，有坚实的理论基础；而且通过推理证明它严格遵守Gibbs–Duhem方程。当电解质溶液达到热力学平衡时，体系的自由能处于最低状态。利用这一原理化学反应模型通过自由能最优化可求得各个物种在化学或相平衡下的浓度分布，进而计算电解质溶液的系列热力学性质。由于直接参数拟合过程具有计算复杂，规模大，变量数众多，结果可靠性低等困难。我们采用嵌套二步优化构架设计，引入分区粒子群最优化算法进行参数拟合，突破了上述困难，模拟测试表明该算法寻优成功率，计算结果的可靠性明显高于原来的算法。
作为应用实例，我们用化学反应模型计算了氯化物LiH_2，NaH_2，KH_2，MgH_2_2，CaH_2_2，CuH_22的六种二元体系以及15种三元体系的热力学性质。计算表明化学反应不仅可以准确描述二元体系的热力学性质，而且补充少量的三元体系参数也可以准确地描述三元体系的热力学性质。若不生成盐盐缔合物种，化学反应模型仅用相应二元体系模型参数就可以直接预测三元体系的热力学性质，例如所预测的LiH_2–CaH_2_2–H2O，LiH_2–MgH_22–H2O三元体系aw，计算值的平均偏差分别为0.0027和0.0029，最大偏差分别为0.0065和0.0081；所预测的LiH_2–CaH_2_2–H_2O，LiH_2–MgH_2_2–H2O三元体系溶解度等温线也与实验数据高度接近。特别地，化学反应模型所预测的痕量CuH_2_2在LiH_2–H_2O体系中含Cu物种浓度分布曲线与Brugger紫外光谱解析结果保持高度一致，所预测的痕量CuH_2_2在NaH_2–H_2O体系中含Cu物种浓度分布曲线与Haung用热力学模型计算的结果也非常相近。
通过大量的计算发现，化学反应模型实际充当了桥梁作用，沟通溶液的微观结构与宏观热力学性质之间的联系。通过它，可以帮助我们理解电解质微观结构对溶液热力学性质影响机制。
水化作用，缔合作用以及水化缔合作用竞争在溶液中扮演着重要角色。它不仅在二元体系中决定着水的活度曲线走向和电解质在水溶液中的溶解度；而且在三元体系中，对水的活度，溶解度等温线，以及物种浓度分布曲线造成关键性的影响。例如，在三元体系中，痕量CuH_2_2在MH_2n–H2O（M=Li, Na, K, Ca）体系中的含Cu物种的浓度分布受阴离子与水分子竞争配位作用的影响，这种部分配位作用也是水化缔合作用竞争的一种形式。由于不同氯化物MH_2n供氯离子不同，其阴离子和H_2O分子在Cu–H_2缔合物上的竞争配位作用也存在差别，使痕量CuH_2_2在MH_2n–H_2O（M=Li, Na, K, Ca）体系中的含Cu物种的浓度分布曲线呈有规律的变化。当盐盐缔合作用很强时，三元体系中可能生成盐盐缔合物种，此时，三元体系的热力学性质不能简单地用二元体系的模型参数直接预测，而必须用三元体系溶解度等温数据来拟合盐盐缔合物种的参数，才能较好地描述三元体系溶解度等温线。用水化缔合作用竞争可以很好解释为什么缔合物的形成使得固相溶解度在共晶点附近比预测结果偏大的原因。无论是阴离子与H2O分子竞争配位，还是生成盐盐缔合物种，水化缔合作用竞争都会使得三元体系等水活度线呈不同程度的弯曲。
本工作开发的化学反应模型能很好地解释由于上述水化，缔合作用，水化缔合作用竞争的影响所引起的一系列现象，表现出强大的分析能力。
Strong hydration, association and competition between hydration and association in themultiple metal chlorides aqueous solution of CuH_22–MH_2n–H2O (M=Li, Na, K, Mg, Ca) leadto complexity of solution structure and properties inlcuding component asctivities, solubility.Developed thermodynamic models up to now for electrolyte solution, such as the Pitzermodel, cannot describe or predict their thermodynamic properties, and cannot explain therelation of the solution structure and properties either.
To overcome this difficult, based on the Stokes–Robinson stepwise hydration model, weintroduced ion–association interaction into the stepwise hydration model, develop a newthermodynamic model is called reaction model (RM). The reaction model consists of thelong–range electrostatic interaction and short interaction of hydration and association. It is notonly simple in mathematical, high symmetrical, but also built on solid theoretical foundationand strictly abides Gibbs–Duhem regulation. There is a minimum value of free Gibbs energyof the electrolyte solution to reach a thermodynamic equilibrium. By this principle, reactionmodel obtains the various species concentration under chemical or phase equilibriumcondition by energy optimization, then further calculate series thermodynamic properties withthem. Because of the large number of variables, complicated, large scale computation and lowreliability of results, many difficults were encountered in direct parameter fitting. To solvethis problem, a framework design of the nested two–step optimization was adopt in this work.An algorithm named Partitioning Quantum–behaver Particle Swarm Optimization (PQPSO) isapplied in parameters evauation. The simulation tests show that the success rate and thereliability of the optimization results have improved significantly than primary method.
As examples of application, we use the reaction model to calculate the thermodynamicproperties of six binary aqueous systems and15ternary aqueous systems of metal chloridesLiH_2, NaH_2, KH_2, MgH_22,CaH_22and CuH_22. Calculations results show that the reaction modelcan accurately describe the thermodynamic properties of not only the binary system, but alsothe ternary system if adding small number of the ternary parameters. The reaction model canpredict the thermodynamic properties of the ternary system only with the correspondingbinary parameters, such as the predicted awvalue of LiH_2–CaH_22–H2O and LiH_2–MgH_22–H2Osystem, the corresponding calculated average deviations are0.0027and0.0029, the maximumdeviation are0.0065and0.0081, respectively. The predicted isotherm of LiH_2–CaH_22–H2Oand LiH_2–MgH_22–H2O system are highly consist with the experimental data. In particular, ourpredicted Cu-containing species concentration distribution curve of trace CuH_22in LiH_2–H2Osystem is highly consistent with Brugger’s analytical results of UV spectra; at the same time, the predicted same result in the NaH_2–H2O system is very similar to thermodynamic modelcalculation results by Haung.
By a large amount of computing, it is found that the reaction model can act as a bridge,which connects the microscopic structure and the thermodynamics properties. It helps usunderstand the mechanism how the microscopic structure characteristic of electrolytesolutions affect their thermodynamics properties.
In some electrolyte aqueous solutions, hydration, association and the competition betweenhydration and association play important role to the thermodynamics properties. Theseinteraction not only seriously impact the binary water activities, determine the electrolytesolubility with the different structural characteristics in aqueous solution; but also cause astrong effect on water activities, solubility isotherms in the ternary system, as well as on thespecies concentration distribution curve. For example, the Cu–containing speciesconcentration distribution curve of the trace CuH_22in MH_2n–H2O(M=Li, Na, K, Ca) systemsis affected by the coordination competition between anions and water molecules which is alsoa form of competition of hydration and association. Different H_2–donation ability of metalchloride MH_2nleads to that the competition coordination of the anions and H2O molecules toCu–H_2complex is also differences, so the concentration distribution curves of Cu–containingspecies of trace CuH_22in MH_2n–H2O (M=Li Na, K, Ca) systems present variation regularly.When a salt–salt association species will generate in the ternary system due to the strongsalt–salt association, thermodynamic properties of the ternary system can not be directlypredicted simply with the binary parameters. One must evalue the parameters of salt–saltassociation species with fitting solubility isotherm data to better describe ternary solubilityisotherms.
With the competition between hydration and association, it can also well explain why theformation of salt–salt association complex makes the solubility of solid phase larger than thepredicted results near the eutectic points. Either the competition coordination of the anion andthe H2O molecule, or the formation of salt–salt association species, the competition ofhydration and association will make iso awlines in the ternary system bending in differentdegrees.
The reaction model developed in this work can well explain above described seriesphenomena caused by the impaction of hydration, association and the competition ofhydration and association, exhibits a powerful analytical ability.
引文
[1]彭时利.海相深层富钾硼卤水析盐规律及钾的分离途径研究:[成都理工大学硕士学位论文].成都:成都理工大学,2009,22–45
[2]周永全,房艳,房春辉.硼酸盐水溶液结构及研究方法.盐湖研究,2010,18(2):65–72
[3]张爱芸，姚燕.硼酸盐水溶液中硼物种的存在形式及影响因素.盐湖研究,2007,15(2):50–56
[4]夏树屏,高世扬,李军,等.硼酸盐的红外光谱.盐湖研究,1995,3(3):49–53
[5]王奖,朱黎霞,夏树屏,等.水合铵硼氧酸盐及其饱和溶液的FTIR和Raman光谱研究.高等学校化学学报,2004,25(7):1213–1217
[6]张林进,叶旭初.水溶液中硼氧配阴离子的存在形式及影响因素.无机盐工业,2008,40(2):4–8
[7]高世扬,贾永忠,夏树屏,等.盐卤硼酸盐化学XXX.含硼水溶液中硼氧配阴离子存在形式及其相互作用.陕西师范大学学报,2000,28(3):70–78
[8]贾永忠,高世扬,夏树屏,等.过饱和硼酸盐水溶液的Raman光谱.高等学校化学学报,2001,22(1):99–103
[9]尹国寅.含锂、硼水盐体系Li2B4O7–H2O, LiCl–Li2B4O7–H2O热力学性质的量热研究.[青海中科院盐湖研究所博士学位论文].青海:青海中科院盐湖研究所,2005,41–106
[10]张爱芸.含锂、硼水盐体系Li2B4O7–H2O, Li2B4O7–MgCl2–H2O298.15K下热力学性质的等压法和电动势法研究及离子相互作用模型的表述.[青海中科院盐湖研究所博士学位论文].青海:青海中科院盐湖研究所,2004,21–38
[11]程波波,周红艳,曾德文.富锂卤水高温蒸发结晶分离镁和锂的方法.无机盐工业,2008,40(8):38–55
[12]王文磊,曾德文,杜勇,等.重金属湿法冶金过程中钙镁结晶的工业现状及相关相图研究进展.中国科学.化学辑,2010,40(9):1226–1242
[13] Wu X, He W, Guan B, et al. Solubility of Calcium Sulfate Dihydrate in Ca–Mg–KChloride Salt Solution in The Range of (348.15to371.15) K. J. Chem. Eng. Data,2010,55(6):2100–2107
[14] Li Z, Demopoulos P G. Development of an Improved Chemical Model for TheEstimation of CaSO4Solubilities in The HCl–CaCl2–H2O System up to100°C. Ind.Eng. Chem. Res.,2006,45(9):2915–2921
[15]方度.氯碱工艺学.北京:化学工业出版社,1990,112–284
[16]化学工业部科学技术情报研究所编,氯碱工业手册,大连:化学工业部科学技术情报研究所,1978,94–182
[17] Skripkin M Yu, Chernykh L V. Solubility in the Systems CuCl2–MCl–H2O (M=Li,Na, K, Cs, NH4) at25and50oC. Zhurnal Neorganiccheskoi Khimii.1994,39(10):1747–1751
[18] Brugger J, Mcphail D C, Black J, et al. Complexation of Metal Ions in Brines:Application of Electronic Spectroscopy in The Study of The Cu(II)–LiCl–H2O SystemBetween25°C and90°C. Geochim.Cosmochim. Acta,2001,65(16):2691–2708
[19]曾德文,林大泽.熔盐水化物相变储能材料的应用及理论预测方法.中国工程科学,2005,17(Supp):301–305
[20]夏熙,刘洪涛.一种正在迅速发展的贮能装置──超级电容器[A].中国上海:电动车及新型电池学术交流会议论文集[C],2003,136–147
[21]夏熙,刘洪涛.一种正在迅速发展的贮能装置—超级电容器(2).电池工业,2004,9(4):181–188
[22]翟楠松,张东来,徐殿国,等.超级电容国内外研究及应用现状[A].中国合肥:中国仪器仪表学会第九届青年学术会议论文集[C],2007,1–4
[23] Jalilehvand F, Sp ngberg D, Lindqvist–Reis P, et al. Hydration of the Calcium Ion. AnEXAFS, Large–Angle X–ray Scattering, and Molecular Dynamics Simulation Study. J.Am. Chem. Soc.,2001,123(3):431–441
[24] Tongraar A, Liedl K R, Rode B M. Solvation of Ca2+in Water Studied byBorn–Oppenheimer ab Initio QM/MM Dynamics. J. Phys. Chem. A,1997,101(35),6299–6309
[25]周崇松,兰昌云,范必威等.金属离子在生命过程中的作用机制.广州化学,2005,30(1):58–64
[26]杨频,高飞.生物无机化学原理[M].北京:科学出版社,2002,35–324
[27] Zeng D, Voigt W, Phase Diagram Calculation of Molten Salt Hydrates Using TheModified BET Equation, Computer Coupling of Phase Diagrams and Thermochemistry,2003,27:243–251
[28] Debye P, Hückel E. The Theory of Electrolytes. Physikalishce Zeitschrift,1923,24:185–206
[29] Bromley L A. J. Chem. Approximate Individual Ion Values of β(or B) in ExtendedDebye–Hückel Theory for Univalent Aqueous Solutions at298.15K. J. Chem.Thermodyn.,1972,4:669–673
[30] Bromley L A. Thermodynamic Properties of Strong Electrolytes in Aqueous Solutions.AICHE. J.,1973,19(2):313–320
[31] Fowler R H, Guggenheim E A. Statistical Thermodynamics. Cambridge UniversityPress,1956.
[32] Pitzer K S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equation.Journal of physical chemistry,1973,77(2):268–277
[33] Pitzer K S. Mayorga G. Thermodynamics of Electrolytes. II. Activity and OsmoticCoefficients for Strong Electrolytes with One or Both Ions Univalent. Journal ofPhysical Chemistry,1973,77(79):2300–2308
[34] Pitzer K S, Mayorga G. Thermodynamics of Electrolytes. III. Activity and OsmoticCoefficients for2–2Electrolytes. J. Solution. Chem.,1974,3(7):539–546
[35] Pitzer K S, Kim J J. Thermodynamics of Electrolytes. IV. Activity and OsmoticCoefficients for Mixed Electrolytes. J. Am. Chem. Soc.,1974,96(18):5701–5707
[36] Pitzer K S, Simonson J M. Thermodynamics of Multicomponent, Miscible, IonicSystems: Thoery and Equation. J. Phys. Chem.,1986,90(13):3005–3009
[37] Clegg S L, Pitzer K S, Thermodynamics of Multicomponent, Miscible, Ionic Solutions:Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem.,1992,96(8):3513–3520
[38] Percus J K, Yevick G. Hard–Core Insertion in the Many–Body Problem. Phys. Rev.,1964,136: B290–B296
[39] Lebowitz J L, Percus J K. Mean Spherical Model for Lattice Gases with Extended HardCores and Continuum Fluids. Phys. Rev.,1966,144:251–258
[40] Waisman E, Lebowitz J L. Mean Spherical Model Integral Equation for Charged HardSpheres I. Method of Solution. J. Chem. Phys.,1972,56:3086–3093
[41] Renon H, Prausnitz J M. Local Compositions in Thermodynamic Excess Functions forLiquid Mixture. AICHE. J.,1968,14(1):135–144
[42] Renon H, Prausnitz J M. Estimation of Parameters for the NRTL Equation for ExcessGibbs Energy of Strongly Nonideal Liquid Mixture. Ind. Eng. Chem. Process Des.Dev.,1969,8(3):413–419
[43] Abrams D S, Prausnitz J M. Statistical Thermodynamics of Liquid Mixtures: A NewExpression for The Excess Gibbs Energy of Partly or Completely Miscible Systems.AICHE. J.,1975.21(1):116–128
[44] Wilson G M. Vapor–Liquid Equilibrium. XI. A New Expression for the Excess FreeEnergy of Mixing. Ibid.,1964,86:127–130
[45] Fredenslund Aa, Jones R L, Praunitz J M. Group–contribution Estimation of ActivityCoefficients in Nonideal Liquid Mixtures. AICHE. J.,1975,21(6):1086–1099
[46] Sander B, Fredenslund Aa, Rasmussen P. Calculation of Vapour–Liquid Equilibria inMixed Solvent/salt Systems Using an Extended UNIQUAC Equation. Chem. Eng. Sci.,1986,41(5):1171–1183
[47] Stokes R H, Robinson R A. Ionic Hydration and Activity in Electrolyte Solutions. J.Am. Chem. Soc.,1948,70(5):1870–1878
[48] Rboinson R A, Stokes R H. Electrolyte Solutions.2nd ed. London: Butterworth.1959,254–271
[49] Stokes R H, Robinson R A. Solvation Equilibria in Very Concentrated ElectrolyteSolutions. Journal of Solution Chemistry,1973,2(2–3):173–191
[50] Voigt W. Calculation of Salt Activities in Molten Salt Hydrates Applying the ModifiedBET Equation. I: Binary Systems. Monatshefte für Chemie,1993,124:839–848
[51] Abraham M. L'activiti D'un Sel a Hautes Concentrations Dans L'eau Pure. J. Chem.Phys.,1981,78:57–59
[52] Braunstein J, Ally M R. On the Abraham Equation for Salt Activities in ConcentratedSolutions. Monatshefte für Chemie,1996,127,269–273
[53] Ally M R, Braunstein J. Statistical Mechanics of Multilayer Adsorption: Electrolyteand Water Activities in Concentrated Solutions. J. Chem. Thermodynamics,1998,30,49–58
[54] Phutela R C, Pitzer K S. Thermodynamics of Aqueous Calcium Chloride. Journal ofSolution Chemistry,1983,12(3):201–207
[55] Rard J A, Clegg S L. Critical Evaluation of the Thermodynamic Properties of AqueousCalcium Chloride.1. Osmotic and Activity Coefficients of0–10.77mol·kg–1AqueousCalcium Chloride Solution at298.15K and Correlation with Extended PitzerIon–Interaction Models. J. Chem. Eng. Data,1997,42:819–849
[56] Larentzos J P, Criscenti L J. A Molecular Dynamics Study of Alkaline Earth MetalChloride Complexation in Aqueous Solution. J. Phys. Chem. B,2008,112(45):14243–14250
[57] Sherman D M. Collings M D. Ion asSociation in Concentrated NaCl Brines fromAmbient to Supercritical Conditions: Results from Classical Molecular DynamicsSimulations. Geochem. Trans.,2002,3(11):102–107
[58] Xia F F, Yi H B, Zeng D. Hydrates of Copper Dichloride in Aqueous Solution: ADensity Functional Theory and Polarized Continuum Model Investigation. J. Phys.Chem. A.2009,113(51):14029–14038
[59] Xia F F, Yi H B, Zeng D, Hydrates of Cu2+and CuCl+in Dilute Aqueous Solution: ADensity Functional Theory and Polarized Continuum Model Investigation. J. Phys.Chem. A,2010,114(32):8406–8416
[60] Yi H B, Xia F F, Zhou Q.[CuCl3] and [CuCl4]2Hydrates in Concentrated AqueousSolution:A Density Functional Theory and ab Initio Study. J. Phys. Chem. A.2011,115(17):4416–4426
[61] Rudolph W, Brooker M H, Pye C C. Hydration of Lithium Ion in Aqueous Solutions. J.Phys. Chem.,1995,99(11):3793–3797
[62] Rudolph W W, Irmerb G, Hefter G T. Raman Spectroscopic Investigation of Speciationin MgSO4(aq). Phys. Chem. Chem. Phys.,2003,5:5253–5261
[63] Buchner R, Chen T, Hefter G. Complexity in “Simple” Electrolyte Solutions: IonPairing in MgSO4(aq). J. Phys. Chem. B,2004,108(7):2365–2375
[64] Stokes R H, Robinson R A. The application of Volume Fraction Statistics to TheCalculation of Activities of Hydrated Electrolytes. Trans. Faraday Soc.,1957,53:301–304
[65] Clegg S L, Pitzer K S. Brimblecombe. Thermodynamics of Multicomponent, Miscible,Ionic Solutions.2. Mixtures Including Unsymmetrical Electrolytes. J. Phys. Chem.,1992,96:9470–9479
[66] Born M. Volume and hydration of Ions. Z. Phys.,1920,1(1):45–47
[67] Stokes R H, Levien B J. The Osmotic and Activity Coefficients of Zinc Nitrate, ZincPerchlo Rate, Transference Numbers of Zinc Perchlorate Solutions. J. Am. Chem. Soc.,1946,68(2):333–330
[68] Pitzer K S, Silvester L F. Thermodynamics of Electrolytes. VI. Weak Electrolytesincluding H3PO4. Journal of Solution Chemistry,1976,5(4):269–278
[69] ftp://plato.la.asu.edu/pub/donlp2/, or ftp.mathematik.tu-darmstadt.de/pub/department/software/opti/DONLP2/donlp2.html
[70] Sun J, Feng B, Xu W. Particle Swam Optimization with Particles Having QuantumBehavior. Portland (USA):2004IEEE Congress on Evolutionary Computation,2004,1:325–331
[71] Zhang Z G., Duan Z H. Lithium Chloride Ionic Association in Dilute Aqueous Solution:A Constrained Molecular Dynamics Study. Chemical Physics,2004,297:221–233
[72] Huang Z. Introduction to The Theory of Electrolyte Solution. China, Beijing: SciencePress,1983,70–71
[73] Lobo V M M, Quaresma J L. Handbook of Electrolyte Solutions, Part A; Elservier.University of Coimbra,3000, press,1989
[74] Tanaka Y, Ogita N, Tamura Y, A Molecular Dynamics Study of the Structure of anLiCl·3H2O Solution. Z. Naturforsch,1987,42a:29–34
[75] Goldberg R N. Evaluated Activity and Osmotic Coefficients for Aqueous Solutions:Bi–univalent Compounds of Lead, Copper, Manganese, and Uranium. J. Phys. Chem.Ref. Data,1979,8(4):1005–1050
[76] Rard J A, Miller D G.. Isopiestic Determination of the Osmotic and ActivityCoefficients of Aqueous MgCl2Solutions at25oC. J. Chem. Eng. Data,1981,26(1):38–43
[77] Gibbard H F, Scatchard G. Liquid–vapor Equilibrium of Aqueous Lithium Chloride,from25to100deg and From1.0to18.5Molal, and Related Properties. J. Chem. Eng.Data,1973,18(3):293–298
[78] Hamer W J, Wu Y. Osmotic Coefficients and Mean Activity Coefficients ofUni–univalent Electrolytes in Water at25°C. J. Phys. Chem. Ref. Data,1972,1(4):1047–1100
[79] Ichikawa K, Kameda Y, Matsumoto T, Misawa W. Indirect and Direct CorrelationsBetween Unlike Ions in Incompletely Hydrated Solution. J. Phys. C: Solid State Phys.,1984,17: L725–L729
[80] Howell I, Neilson G W. Li+hydration in Concentrated Aqueous Solution. Journal ofPhysics: Condensed Matter,1996,8:4455–4463
[81] Newsome J R, Neilson G W, Enderby J E. Lithium Ions in Aqueous Solution. J. Phys.C: Soli. St. Phys.,1980,13: L923–L926
[82] Yan F, Chunhui F, Shiyang G.. X–ray Difraction Study on The Structure of AqueousLi2S04Solution at Different Concentrations. Journal of Salt Lake Research,2003,11(2):41–45
[83] Lyubartsev A P, Laasonen K, Laaksonen A. Hydration of Li+ion. An ab InitioMolecular Dynamics Simulation. J. Chem. Phy.,2001,114(7):3121–3126
[84] Kameda Y, Ebata H, Uemura O. Raman Spectroscopic Study of Concentrated AqueousLiBr Solutions. Bulletin of the Chemical Society of Japan,1994,67(4):929–935
[85] Scholz B, Luedemann H D, Franck E U. Spectra of Cu(Ⅱ)–Complexes in AqueousSolution at High Temperature and Pressures. Ber. Bunsen–Ges.,1972,76:406–409
[86] Stace A J, Walker N R, Firth S.[Cu(H2O)n]2+Clusters: The First Evidence of AqueousCu(II) in The Gas Phase. J. Am. Chem. Soc.,1997,119:10239–10240
[87] Walker N R, Firth S, Stace A J. Stable Cu(II) Coordination Complexes in The GasPhase. Chemical Physics Letters.1998,292:125–132
[88] Duncombe B J, Duale K, Buchanan–Smith A, et al. The Solvation of Cu2+withGas–Phase Clusters of Water and Ammonia. J. Phys. Chem. A,2007,111:5158–5165
[89] Marini G W, Liedl K R, Rode B M，Investigation of Cu2+Hydration and theJahn–Teller Effect in Solution by QM/MM MonteCarlo Simulations. J. Phys. Chem. A,1999,103(51):11387–11393
[90] Todorova T, Hünenberger P H, Hutter J. Car–Parrinello Molecular Dynamics Simula–tions of CaCl2Aqueous Solutions. J. Chem. Theory Comput.,2008,4(5):779–789
[91] Pye C C, Rudolph W W. An ab Initio and Raman Investigation of Magnesium(II)Hydration. J. Phys. Chem. A,1998,102(48):9933–9943
[92] Pitzer K S, Wang P, Rard J A, et al. Thermodynamics of Electrolytes.13. IonicStrength Dependence of Higher–Order Terms; Equations for CaCl2and MgCl2. Journalof Solution Chemistry,1999,28(4):265–282
[93] Fulton J L, Chen Y, Heald S M, Balasubramanian M. Hydration and Contact IonPairing of Ca2+with Cl in Supercritical Aqueous Solution. Jounal of Chemical Physics,2006,125(9):094507–1
[94] Schwenk C F, Loeffler H H, Rode B M. Molecular Dynamics Simulations of Ca2+inWater: Comparison of a Classical Simulation Including Three–body Corrections andBorn–Oppenheimer ab Initio and Density Functional Theory Quantum Mechanical/molecular Mechanics Simulations. J. Chem. Phys.,2001,115(23):10809–1
[95] Lei X L, Pan B C. Structures Stability, Vibration Entropy and IR Spectra of HydratedCalcium Ion Clusters [Ca(H2O)n]2+(n=120,27): A Systematic Investigation byDensity Functional Theory. J. Phys. Chem. A,2010,114:7595–7603
[96] Li R, Jiang Z, S Shi, et al. Raman Spectra and17O NMR Study Effects of CaCl2andMgCl2on Water Structure. Journal of Molecular Structure,2003,645:69–75
[97] Fulton J L, Heald S M, Badyal Y S, et al. Understanding the Effects of Concentrationon The Solvation Structure of Ca2+in Aqueous Solution. I: The perspective on LocalStructure from EXAFS and XANES. J. Phys. Chem. A,2003,107:4688–4696
[98] Tongraar A, Rode B M. Structural Arrangement and Dynamics of The Hydrated Mg2+:An ab Initio QM/MM Molecular Dynamics Simulation. Chemical Physics Letters,2005,409(4–6):304–309
[99] Tongraar A, Role B M. The Role of Non–additive Contributions on The HydrationShell Structure of Mg2+Studied by Born–Oppenheimer ab Initio Quantum MechanicalMolecular Dynamics Simulation. Chemical Pysics Letters,2001,346(5–6):485–491
[100] Callahan K M, Casillas–Ituarte N N, Roeselova M, et al. Solvation of MagnesiumDication: Molecular Dynamics Simulation and Vibrational Spectroscopic Study ofMagnesium Chloride in Aqueous Solutions. J. Phys. Chem. A,2010,114:5141–5148
[101] Moran H E. System Lithium Chloride–Water. J. Phys. Chem.,1956,60(12):1666–1667
[102] Pinho S P, Macedo E A, Solubility of NaCl, NaBr, and KCl in Water, Methanol,Ethanol, and Their Mixed Solvents. J. Chem. Eng. Data,2005,50(1):29–32
[103] Guendouzi M E, Errougui A, Solubility in the Ternary Aqueous Systems Containing M,Cl, NO3, and SO42with M=NH4+, Li+, or Mg2+at T=298.15K. J. Chem. Eng. Data,2009,54:376–381
[104]丁秀萍,毕玉敬,时历杰.三元体系NaCl–CaCl2–H2O25oC相关系研究.盐湖研究,2009,17(3):40–43
[105] Rard J A. Isopiestic Investigation of Water Activities of Aqueous Nickel(2+) Chlorideand Copper(2+) Chloride Solutions and The Thermodynamic Solubility Product ofNickel Dichloride Hexahydrate at298.15K. J. Chem. Eng. Data,1992,37(4):433–442
[106] Filippov V K, Charykov N A. Fedorov Yu A. Sodium Chloride–nickle Dichloride(Copper Dichloride)–Water System at25oC. Zhurnal Neorganiccheskoi Khimii,1986,31(7):1861–1868
[107] Yanatieva O K. Polythermal Solubilities in The Systems CaCl2–MgCl2–H2O andCaC12–NaCI–H2O. Zhur. Prikl. Khim.,1946,19:709–722
[108] Lee W B, Egerton A C. LXXXIII. Heterogeneous Equilibria Between the Chlorides ofCalcium, Magnesium, Potassium, and Their Aqueous Solutions. Part I. J. Chem. Soc.Trans.,1923,123:706–716
[109] Linke W F, Seidell A. Solubility of Inorganic and Metal Organic Compounds.American Chemical Society, Washington:1965.
[110] Farelo F, Fernandes C, Avelino A. Solubilities for Six Ternary Systems: NaCl+NH4Cl+H2O, KCl+NH4Cl+H2O, NaCl+LiCl+H2O, KCl+LiCl+H2O, NaCl+AlCl3+H2O, and KCl+AlCl3+H2O at T)(298to333) K. J. Chem. Eng. Data,2005,50(4),1470–1477
[111] Campbell A N, Kartzmark E M. The System LiCl–KCl–H2O at25oC. Can. J. Chem.,1956,34:672–678
[112] Texler N R, Holdway S, Neilson G W, Monte Carlo Simulations and NeutronDiffraction Studies of The Peptide Forming System0.5mol/kg CuCl2–5mol/kgNaCl–H2O at293and353K. J. Chem. Soc. Faraday Trans.,1998,94(1):59–65
[113] Haung H. Estimation of Pitzer’s Ion Interaction Parameters For Electrolytes Involvedin Complex Formation Using a Chemical Equilibrium Model. Journal of SolutionChemistry,1989,18(11):1069–1084
[114] Kurlyandskaya I I, Solomonik I G, Glazunova E D, et al. New Trends in theDevelopment of Methods for Catalyst Preparation for The Processes of OrganochlorineSynthesis. Kinetics and Catalysis,2001,42(3):381–389
[115] Hynes J E, Garrett B B, Moulton W G. Magnetic Resonance of KCuC13. The Journalof Chemical Physics,1970,52(5):2672–2678
[116] Sakurai T, Taketani A, Kimura S, et al. ESR Measurements of KCuCl3under MultiExtreme Conditions. Orlando, Florida (USA): AIP conference proceedings.2006,850:1057–1058
[117]何配华.微量铜在复杂氯化物多元体系溶液中的络合行为研究.[湖南大学硕士学位论文],湖南:湖南大学化学化工学院,2010,32–45
[118] Balarev Ch, Spassov D. Formation Double Salts of Divalent Metal Chlorides. ZhurnalNeorganiccheskoi Khimii,1980,25:2814
[119] Guangming L, Yan Y, Fengqin W, et al. Isopiestic Determination of ActivityCoeficients of LiCl and CaCl2in LiCl CaCl2H2O System at298.15K. Acta PhysicoChimica Sinica,1999,15(10):956960
[120] Filippov A, Mihelbson K N. Thermodynamic Study on The System LiCl–CaCl2–H2Oat25°C and35°C Zh. Neorg. Khim.,1977,22:1689–1694
[121] Yan Y, Bai S, Peng–Sheng S, et al. Isopiestic Determination of Osmotic and ActivityCoeficients in LiCI MgCl2H2O25oC. Acta Chimica Sinica,1999,50:809–848
[122] Voskressenskaja N K, Janatieva O K. Solubility Equilibrium of The SystemLiCl–MgCl2–H2O. Izv. Akad. Nauk. SSSR. Ser. Khim.,1937,97–121
[123] Dinane A, Mounir A. Water Activities, Osmotic and Activity Coefficients in AqueousMixtures of Sodium and Magnesium Chlorides at298.15K by The HygrometricMethod. Fluid Phase Equilibria,2003,206:13–25
[124] Yan Y D, Zhang M L, et al, Electrochemical Study of The Codeposition of Mg–Li–AlAlloys from LiCl–KCl–MgCl2–AlCl3Melts. J. Appl. Electrochem,2009,39:455–461
[125] Hatttori T, Igarashi K, Mochinaga J, Enthalpies of Fusion of Intermediate Com pounds,KMgCl3, K2MgCl4, K2BaCl4, KCaCl3, K2SrCl4, K2LaCl4, K3PrCl6, K2NdCl6,K2Gd3Cl10and KDy3Cl10, Bull. Chem. Soc. Jpn.,1981,54:1883–1884
[126] Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization of the LiCl–NaCl–KCl–RbCl–CsCl–MgCl2–CaCl2System Using the Modified Quasi–chemicalModel. Metallurgical and Materials Transaction A,2001,32a:1361–1383
[127] Stokes R H, Robinson R A. Interactions in Aqueous Nonelectrolyte Solutions. I.Solute–Solvent Equilibria. J. Phys. Chem.,1966,70(7):2126–2131
[128] Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization of the LiCl–NaCl–KCl–RbCl–CsCl–MgCl2–CaCl2System Using the Modified Quasi–chemicalModel. Metallurgical and Materials Transactions A,2001,32A:1361–1383
[129] Brynestad J, Yakel H L, Smith G P. Temperature Dependence of the AbsorptionSpectrum of Nickel(II)–Doped KMgCl3and the Crystal Structure of KMgCl3. TheJournal of Chemical Physics,1996,45(12):4653–4664
[130] Robelin C, Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization ofthe (NaCl+KCl+MgCl2+CaCl2+MnCl2+FeCl2+CoCl2+NiCl2) System. J. Chem.Thermodynamics,2004,36:809–828
[131] Kennedy J. Eberhart R. Particle Swarm Optimization. Washington (USA): IEEE int.Conf. Neural Network,1995,1942–1948
[132] Sun J, Xu W B, Feng B, A Global Search Strategy of Quantum–behaved ParticleSwarm Optimization, Wuxi (China): IEEE Conference on Cybernetics and IntelligentSystems,2004,111–116
[133] Lu Y, Liao Z, Chen W F. An Automatic Registration Framework using QuantumParticle Swarm Optimization for Remote Sensing Images. Beijing (China):International Conference on Wavelet Analysis and Pattern Recognition,2007,2:484–488
[134] Sun J, Fang W, Xu W B. A Quantum–Behaved Particle Swarm Optimization WithDiversity–Guided Mutation for the Design of Two–Dimensional IIR Digital Filters,IEEE Trans. Circuits Syst. II,2010,57(2):141–145
[135] Huang Z, Wang Y J, Yang C Y, et al. A New Improved Quantum–behaved ParticleSwarm Optimization Model. Xi’an (China): IEEE Conference on Industrial Electronicsand Applications,2009,1560–1564
[136] Liu J, Xu W, Sun J. Quantum–behaved Particle Swarm Optimization with MutationOperator. Washington (USA):17th IEEE International Conference on Tools withArtificial Intelligence,2005,237–240
[137] Liu J, Sun J, Xu W B. Quantum–behaved Particle Swarm Optimization With ImmuneMemory and Vaccination. Atlanta (USA): IEEE International Conference on GranularComputing,2006,453–456
[138] Su D B, Xu W B, Sun J. Quantum–Behaved Particle Swarm Optimization WithCrossover Operator. Shanghai (China): International Conference on Wireless Networksand Information Systems,2009,399–402
[139] Gill S S, Chandel R, Chandel A. Swarm Intelligence Based Circuit Partitioning.Shanghai (China):2010Asia Pacific Conference on Postgraduate Research inMicroelectronics&Electronics.2010,41–44
[140] Chamberlain B L, University of Washington; Graph Partitioning Algorithms forDistributing Workloads of Parallel Computations. Technical Report UW–CSE–98–10
[141] Radha H, Vetterli M, Leonardi R. Image Compression Using Binary Space PartitioningTrees. Evanston (USA): IEEE Transaction on Image Processing,1996,5:1610–1624
[142] Pal N R, Bezdek J C. Complexity Reduction for “Large Image” Hanover (USA):Processing. IEEE Transaction on Systems, Man, And, Cybernetics─Part B: Cybernetics,2002,32:598–611
[143] Kashtiban A M, Ahandani M A. Various Strategies for Partitioning of Memeplexes inShuffled Frog Leaping Algorithm. Tehran (Iran): Proceedings of the14th InternationalCSI Computer Conference.2009:576–581
[144] Shi Y, Eberhart R C. Empirical study of Particle Swarm Optimization, Columbia(Canada): IEEE Congress on Evolutionary Computation,1999,3:101–106
[145] Clerc M, Kennedy J, The Particle Swarm Explosion, Stability, and Convergence in aMultidimensional Complex Space. IEEE Transactions on Evolutionary Computation,2002,6(1):58–73
[146] Liu Y, Liang F. An adaptive Hybrid Particle Swarm Optimization. Changsha (Hunan):Second International Symposium on Computational Intelligence and Design,2009,1:87–90
[147] Cao L, Wang S, Liu X, et al. Research on Improved QPSO Algorithm Based onCooperative Evolution with Two Populations. Wuxi (China): International conferenceon Life System Modeling and Intelligent Computing,2010,93–100
[148] Lu K, Fang K, Xie G. A Hybrid Quantum–Behaved Particle Swarm OptimizationAlgorithm for Clustering Analysis. Jinan (China):15th IEEE International Conferenceon Fuzzy Systems and Knowledge Discovery,2008,1:21–25
[149] Riget J, Vesterstr m J S. A Diversity–guided Particle Swarm Optimizer–the ARPSO.Technical Report, EVAlife,2002–02, Department of Computer Science, University ofAarhus,2002:3294–3299
[150] Fawcett W B, Tikanen A C. Role of Solvent Permittivity in Estimation of ElectrolyteActivity Coefficients on the Basis of the Mean Spherical Approximation. J. Phys.Chem.,1996,100(10):4251–4255
[151] Colie C H, Ritson D M, Hasted J B. Dielectric Properties of Aqueous Ionic Solutions.Parts I and II. J. Chem. Phys.,1948,16:1–21
[152] Radia I, Jean–Charles de H, Walterb F. The Simultaneous Representation of DielectricConstant, Volume and Activity Coefficients Using an Electrolyte Equation of State.Fluid Phase Equilibria,2008,271:19–27
[153] Simonin J, Bernard O, Blum L. Ionic Solutions in the Binding Mean SphericalApproximation: Thermodynamic Properties of Mixtures of Associating Electrolytes. J.Phys. Chem. B,1999,103(4):699–704
[154] Wang P, Anderko A, Computation of Dielectric Constants of Solvent Mixtures andElectrolyte Solutions. Fluid Phase Equilibria,2001,186:103–122
[155] Sunner J, Kebarle P. Unimolecular Dissociation of Ions. Effect on Mass–SpectrometricMeasurements of Ion–Molecule Association Equilibria. J. Phys. Chem.,1981,85(4):327–335
[156] Frank H S, Evans M W. Free Volume and Entropy in Condensed Systems III. Entropyin Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure andThermodynamics in Aqueous Electrolytes. J. Chern. Phys.,1945,13:507–532
[157] Ulich H. Ionic Entropy and Solvation. Z. Elektrochem,1930,36:497–564
[158] Zavitsas A A. Aqueous Solutions of Calcium Ions: Hydration Numbers and The Effectof Temperature. J. Phys. Chem. B,2005,109(43),20636–20640
[159]吕秉玲,林志祥.纯碱生产相图分析.北京:化学工业出版社,1991,45–50
[160]大连制碱工业研究所编,纯碱工业知识.大连:大连制碱工业研究所,1975,56–87
[161] Christov C. Thermodynamic Study of The CuCl2–MCl2–H2O Systems (M=Mg, Co) at298.15K. Collect. Czech. Chem. Commun,1996,61:507–512
[162] Zdanovskii A B. Functional Relation of The Properties of The Mixed and IndividualSolutions. Tr. Solyanoi Lab. Vses. Inst. Galurgii Akad. Nauk SSSR,1936,2:70–75
[163] Zdanovskii A B. Regularities in the Property Variations of Mixed Solutions. Tr.Solyanoi Lab. Akad. Nauk SSSR,1936,6(5):70–73
[164] Glueckauf E. The Influence of Ionic Hydration on Activity Coefficients inConcentrated Electrolyte Solutions. Trans. Faraday. Soc.,1955,51:1235–1244
[165] Hewish N A, Neilson G W, Enderby J E. Enviroment of Ca2+ions in aqueous solvent.Nature,1982,297(13):138–139
[166] Mcmillan W G, Mayer J E. The Statistical Thermodynamics of MulticomponentSystems. J. Chem. Phys,1945,13(7):276-305.
[2]周永全,房艳,房春辉.硼酸盐水溶液结构及研究方法.盐湖研究,2010,18(2):65–72
[3]张爱芸，姚燕.硼酸盐水溶液中硼物种的存在形式及影响因素.盐湖研究,2007,15(2):50–56
[4]夏树屏,高世扬,李军,等.硼酸盐的红外光谱.盐湖研究,1995,3(3):49–53
[5]王奖,朱黎霞,夏树屏,等.水合铵硼氧酸盐及其饱和溶液的FTIR和Raman光谱研究.高等学校化学学报,2004,25(7):1213–1217
[6]张林进,叶旭初.水溶液中硼氧配阴离子的存在形式及影响因素.无机盐工业,2008,40(2):4–8
[7]高世扬,贾永忠,夏树屏,等.盐卤硼酸盐化学XXX.含硼水溶液中硼氧配阴离子存在形式及其相互作用.陕西师范大学学报,2000,28(3):70–78
[8]贾永忠,高世扬,夏树屏,等.过饱和硼酸盐水溶液的Raman光谱.高等学校化学学报,2001,22(1):99–103
[9]尹国寅.含锂、硼水盐体系Li2B4O7–H2O, LiCl–Li2B4O7–H2O热力学性质的量热研究.[青海中科院盐湖研究所博士学位论文].青海:青海中科院盐湖研究所,2005,41–106
[10]张爱芸.含锂、硼水盐体系Li2B4O7–H2O, Li2B4O7–MgCl2–H2O298.15K下热力学性质的等压法和电动势法研究及离子相互作用模型的表述.[青海中科院盐湖研究所博士学位论文].青海:青海中科院盐湖研究所,2004,21–38
[11]程波波,周红艳,曾德文.富锂卤水高温蒸发结晶分离镁和锂的方法.无机盐工业,2008,40(8):38–55
[12]王文磊,曾德文,杜勇,等.重金属湿法冶金过程中钙镁结晶的工业现状及相关相图研究进展.中国科学.化学辑,2010,40(9):1226–1242
[13] Wu X, He W, Guan B, et al. Solubility of Calcium Sulfate Dihydrate in Ca–Mg–KChloride Salt Solution in The Range of (348.15to371.15) K. J. Chem. Eng. Data,2010,55(6):2100–2107
[14] Li Z, Demopoulos P G. Development of an Improved Chemical Model for TheEstimation of CaSO4Solubilities in The HCl–CaCl2–H2O System up to100°C. Ind.Eng. Chem. Res.,2006,45(9):2915–2921
[15]方度.氯碱工艺学.北京:化学工业出版社,1990,112–284
[16]化学工业部科学技术情报研究所编,氯碱工业手册,大连:化学工业部科学技术情报研究所,1978,94–182
[17] Skripkin M Yu, Chernykh L V. Solubility in the Systems CuCl2–MCl–H2O (M=Li,Na, K, Cs, NH4) at25and50oC. Zhurnal Neorganiccheskoi Khimii.1994,39(10):1747–1751
[18] Brugger J, Mcphail D C, Black J, et al. Complexation of Metal Ions in Brines:Application of Electronic Spectroscopy in The Study of The Cu(II)–LiCl–H2O SystemBetween25°C and90°C. Geochim.Cosmochim. Acta,2001,65(16):2691–2708
[19]曾德文,林大泽.熔盐水化物相变储能材料的应用及理论预测方法.中国工程科学,2005,17(Supp):301–305
[20]夏熙,刘洪涛.一种正在迅速发展的贮能装置──超级电容器[A].中国上海:电动车及新型电池学术交流会议论文集[C],2003,136–147
[21]夏熙,刘洪涛.一种正在迅速发展的贮能装置—超级电容器(2).电池工业,2004,9(4):181–188
[22]翟楠松,张东来,徐殿国,等.超级电容国内外研究及应用现状[A].中国合肥:中国仪器仪表学会第九届青年学术会议论文集[C],2007,1–4
[23] Jalilehvand F, Sp ngberg D, Lindqvist–Reis P, et al. Hydration of the Calcium Ion. AnEXAFS, Large–Angle X–ray Scattering, and Molecular Dynamics Simulation Study. J.Am. Chem. Soc.,2001,123(3):431–441
[24] Tongraar A, Liedl K R, Rode B M. Solvation of Ca2+in Water Studied byBorn–Oppenheimer ab Initio QM/MM Dynamics. J. Phys. Chem. A,1997,101(35),6299–6309
[25]周崇松,兰昌云,范必威等.金属离子在生命过程中的作用机制.广州化学,2005,30(1):58–64
[26]杨频,高飞.生物无机化学原理[M].北京:科学出版社,2002,35–324
[27] Zeng D, Voigt W, Phase Diagram Calculation of Molten Salt Hydrates Using TheModified BET Equation, Computer Coupling of Phase Diagrams and Thermochemistry,2003,27:243–251
[28] Debye P, Hückel E. The Theory of Electrolytes. Physikalishce Zeitschrift,1923,24:185–206
[29] Bromley L A. J. Chem. Approximate Individual Ion Values of β(or B) in ExtendedDebye–Hückel Theory for Univalent Aqueous Solutions at298.15K. J. Chem.Thermodyn.,1972,4:669–673
[30] Bromley L A. Thermodynamic Properties of Strong Electrolytes in Aqueous Solutions.AICHE. J.,1973,19(2):313–320
[31] Fowler R H, Guggenheim E A. Statistical Thermodynamics. Cambridge UniversityPress,1956.
[32] Pitzer K S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equation.Journal of physical chemistry,1973,77(2):268–277
[33] Pitzer K S. Mayorga G. Thermodynamics of Electrolytes. II. Activity and OsmoticCoefficients for Strong Electrolytes with One or Both Ions Univalent. Journal ofPhysical Chemistry,1973,77(79):2300–2308
[34] Pitzer K S, Mayorga G. Thermodynamics of Electrolytes. III. Activity and OsmoticCoefficients for2–2Electrolytes. J. Solution. Chem.,1974,3(7):539–546
[35] Pitzer K S, Kim J J. Thermodynamics of Electrolytes. IV. Activity and OsmoticCoefficients for Mixed Electrolytes. J. Am. Chem. Soc.,1974,96(18):5701–5707
[36] Pitzer K S, Simonson J M. Thermodynamics of Multicomponent, Miscible, IonicSystems: Thoery and Equation. J. Phys. Chem.,1986,90(13):3005–3009
[37] Clegg S L, Pitzer K S, Thermodynamics of Multicomponent, Miscible, Ionic Solutions:Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem.,1992,96(8):3513–3520
[38] Percus J K, Yevick G. Hard–Core Insertion in the Many–Body Problem. Phys. Rev.,1964,136: B290–B296
[39] Lebowitz J L, Percus J K. Mean Spherical Model for Lattice Gases with Extended HardCores and Continuum Fluids. Phys. Rev.,1966,144:251–258
[40] Waisman E, Lebowitz J L. Mean Spherical Model Integral Equation for Charged HardSpheres I. Method of Solution. J. Chem. Phys.,1972,56:3086–3093
[41] Renon H, Prausnitz J M. Local Compositions in Thermodynamic Excess Functions forLiquid Mixture. AICHE. J.,1968,14(1):135–144
[42] Renon H, Prausnitz J M. Estimation of Parameters for the NRTL Equation for ExcessGibbs Energy of Strongly Nonideal Liquid Mixture. Ind. Eng. Chem. Process Des.Dev.,1969,8(3):413–419
[43] Abrams D S, Prausnitz J M. Statistical Thermodynamics of Liquid Mixtures: A NewExpression for The Excess Gibbs Energy of Partly or Completely Miscible Systems.AICHE. J.,1975.21(1):116–128
[44] Wilson G M. Vapor–Liquid Equilibrium. XI. A New Expression for the Excess FreeEnergy of Mixing. Ibid.,1964,86:127–130
[45] Fredenslund Aa, Jones R L, Praunitz J M. Group–contribution Estimation of ActivityCoefficients in Nonideal Liquid Mixtures. AICHE. J.,1975,21(6):1086–1099
[46] Sander B, Fredenslund Aa, Rasmussen P. Calculation of Vapour–Liquid Equilibria inMixed Solvent/salt Systems Using an Extended UNIQUAC Equation. Chem. Eng. Sci.,1986,41(5):1171–1183
[47] Stokes R H, Robinson R A. Ionic Hydration and Activity in Electrolyte Solutions. J.Am. Chem. Soc.,1948,70(5):1870–1878
[48] Rboinson R A, Stokes R H. Electrolyte Solutions.2nd ed. London: Butterworth.1959,254–271
[49] Stokes R H, Robinson R A. Solvation Equilibria in Very Concentrated ElectrolyteSolutions. Journal of Solution Chemistry,1973,2(2–3):173–191
[50] Voigt W. Calculation of Salt Activities in Molten Salt Hydrates Applying the ModifiedBET Equation. I: Binary Systems. Monatshefte für Chemie,1993,124:839–848
[51] Abraham M. L'activiti D'un Sel a Hautes Concentrations Dans L'eau Pure. J. Chem.Phys.,1981,78:57–59
[52] Braunstein J, Ally M R. On the Abraham Equation for Salt Activities in ConcentratedSolutions. Monatshefte für Chemie,1996,127,269–273
[53] Ally M R, Braunstein J. Statistical Mechanics of Multilayer Adsorption: Electrolyteand Water Activities in Concentrated Solutions. J. Chem. Thermodynamics,1998,30,49–58
[54] Phutela R C, Pitzer K S. Thermodynamics of Aqueous Calcium Chloride. Journal ofSolution Chemistry,1983,12(3):201–207
[55] Rard J A, Clegg S L. Critical Evaluation of the Thermodynamic Properties of AqueousCalcium Chloride.1. Osmotic and Activity Coefficients of0–10.77mol·kg–1AqueousCalcium Chloride Solution at298.15K and Correlation with Extended PitzerIon–Interaction Models. J. Chem. Eng. Data,1997,42:819–849
[56] Larentzos J P, Criscenti L J. A Molecular Dynamics Study of Alkaline Earth MetalChloride Complexation in Aqueous Solution. J. Phys. Chem. B,2008,112(45):14243–14250
[57] Sherman D M. Collings M D. Ion asSociation in Concentrated NaCl Brines fromAmbient to Supercritical Conditions: Results from Classical Molecular DynamicsSimulations. Geochem. Trans.,2002,3(11):102–107
[58] Xia F F, Yi H B, Zeng D. Hydrates of Copper Dichloride in Aqueous Solution: ADensity Functional Theory and Polarized Continuum Model Investigation. J. Phys.Chem. A.2009,113(51):14029–14038
[59] Xia F F, Yi H B, Zeng D, Hydrates of Cu2+and CuCl+in Dilute Aqueous Solution: ADensity Functional Theory and Polarized Continuum Model Investigation. J. Phys.Chem. A,2010,114(32):8406–8416
[60] Yi H B, Xia F F, Zhou Q.[CuCl3] and [CuCl4]2Hydrates in Concentrated AqueousSolution:A Density Functional Theory and ab Initio Study. J. Phys. Chem. A.2011,115(17):4416–4426
[61] Rudolph W, Brooker M H, Pye C C. Hydration of Lithium Ion in Aqueous Solutions. J.Phys. Chem.,1995,99(11):3793–3797
[62] Rudolph W W, Irmerb G, Hefter G T. Raman Spectroscopic Investigation of Speciationin MgSO4(aq). Phys. Chem. Chem. Phys.,2003,5:5253–5261
[63] Buchner R, Chen T, Hefter G. Complexity in “Simple” Electrolyte Solutions: IonPairing in MgSO4(aq). J. Phys. Chem. B,2004,108(7):2365–2375
[64] Stokes R H, Robinson R A. The application of Volume Fraction Statistics to TheCalculation of Activities of Hydrated Electrolytes. Trans. Faraday Soc.,1957,53:301–304
[65] Clegg S L, Pitzer K S. Brimblecombe. Thermodynamics of Multicomponent, Miscible,Ionic Solutions.2. Mixtures Including Unsymmetrical Electrolytes. J. Phys. Chem.,1992,96:9470–9479
[66] Born M. Volume and hydration of Ions. Z. Phys.,1920,1(1):45–47
[67] Stokes R H, Levien B J. The Osmotic and Activity Coefficients of Zinc Nitrate, ZincPerchlo Rate, Transference Numbers of Zinc Perchlorate Solutions. J. Am. Chem. Soc.,1946,68(2):333–330
[68] Pitzer K S, Silvester L F. Thermodynamics of Electrolytes. VI. Weak Electrolytesincluding H3PO4. Journal of Solution Chemistry,1976,5(4):269–278
[69] ftp://plato.la.asu.edu/pub/donlp2/, or ftp.mathematik.tu-darmstadt.de/pub/department/software/opti/DONLP2/donlp2.html
[70] Sun J, Feng B, Xu W. Particle Swam Optimization with Particles Having QuantumBehavior. Portland (USA):2004IEEE Congress on Evolutionary Computation,2004,1:325–331
[71] Zhang Z G., Duan Z H. Lithium Chloride Ionic Association in Dilute Aqueous Solution:A Constrained Molecular Dynamics Study. Chemical Physics,2004,297:221–233
[72] Huang Z. Introduction to The Theory of Electrolyte Solution. China, Beijing: SciencePress,1983,70–71
[73] Lobo V M M, Quaresma J L. Handbook of Electrolyte Solutions, Part A; Elservier.University of Coimbra,3000, press,1989
[74] Tanaka Y, Ogita N, Tamura Y, A Molecular Dynamics Study of the Structure of anLiCl·3H2O Solution. Z. Naturforsch,1987,42a:29–34
[75] Goldberg R N. Evaluated Activity and Osmotic Coefficients for Aqueous Solutions:Bi–univalent Compounds of Lead, Copper, Manganese, and Uranium. J. Phys. Chem.Ref. Data,1979,8(4):1005–1050
[76] Rard J A, Miller D G.. Isopiestic Determination of the Osmotic and ActivityCoefficients of Aqueous MgCl2Solutions at25oC. J. Chem. Eng. Data,1981,26(1):38–43
[77] Gibbard H F, Scatchard G. Liquid–vapor Equilibrium of Aqueous Lithium Chloride,from25to100deg and From1.0to18.5Molal, and Related Properties. J. Chem. Eng.Data,1973,18(3):293–298
[78] Hamer W J, Wu Y. Osmotic Coefficients and Mean Activity Coefficients ofUni–univalent Electrolytes in Water at25°C. J. Phys. Chem. Ref. Data,1972,1(4):1047–1100
[79] Ichikawa K, Kameda Y, Matsumoto T, Misawa W. Indirect and Direct CorrelationsBetween Unlike Ions in Incompletely Hydrated Solution. J. Phys. C: Solid State Phys.,1984,17: L725–L729
[80] Howell I, Neilson G W. Li+hydration in Concentrated Aqueous Solution. Journal ofPhysics: Condensed Matter,1996,8:4455–4463
[81] Newsome J R, Neilson G W, Enderby J E. Lithium Ions in Aqueous Solution. J. Phys.C: Soli. St. Phys.,1980,13: L923–L926
[82] Yan F, Chunhui F, Shiyang G.. X–ray Difraction Study on The Structure of AqueousLi2S04Solution at Different Concentrations. Journal of Salt Lake Research,2003,11(2):41–45
[83] Lyubartsev A P, Laasonen K, Laaksonen A. Hydration of Li+ion. An ab InitioMolecular Dynamics Simulation. J. Chem. Phy.,2001,114(7):3121–3126
[84] Kameda Y, Ebata H, Uemura O. Raman Spectroscopic Study of Concentrated AqueousLiBr Solutions. Bulletin of the Chemical Society of Japan,1994,67(4):929–935
[85] Scholz B, Luedemann H D, Franck E U. Spectra of Cu(Ⅱ)–Complexes in AqueousSolution at High Temperature and Pressures. Ber. Bunsen–Ges.,1972,76:406–409
[86] Stace A J, Walker N R, Firth S.[Cu(H2O)n]2+Clusters: The First Evidence of AqueousCu(II) in The Gas Phase. J. Am. Chem. Soc.,1997,119:10239–10240
[87] Walker N R, Firth S, Stace A J. Stable Cu(II) Coordination Complexes in The GasPhase. Chemical Physics Letters.1998,292:125–132
[88] Duncombe B J, Duale K, Buchanan–Smith A, et al. The Solvation of Cu2+withGas–Phase Clusters of Water and Ammonia. J. Phys. Chem. A,2007,111:5158–5165
[89] Marini G W, Liedl K R, Rode B M，Investigation of Cu2+Hydration and theJahn–Teller Effect in Solution by QM/MM MonteCarlo Simulations. J. Phys. Chem. A,1999,103(51):11387–11393
[90] Todorova T, Hünenberger P H, Hutter J. Car–Parrinello Molecular Dynamics Simula–tions of CaCl2Aqueous Solutions. J. Chem. Theory Comput.,2008,4(5):779–789
[91] Pye C C, Rudolph W W. An ab Initio and Raman Investigation of Magnesium(II)Hydration. J. Phys. Chem. A,1998,102(48):9933–9943
[92] Pitzer K S, Wang P, Rard J A, et al. Thermodynamics of Electrolytes.13. IonicStrength Dependence of Higher–Order Terms; Equations for CaCl2and MgCl2. Journalof Solution Chemistry,1999,28(4):265–282
[93] Fulton J L, Chen Y, Heald S M, Balasubramanian M. Hydration and Contact IonPairing of Ca2+with Cl in Supercritical Aqueous Solution. Jounal of Chemical Physics,2006,125(9):094507–1
[94] Schwenk C F, Loeffler H H, Rode B M. Molecular Dynamics Simulations of Ca2+inWater: Comparison of a Classical Simulation Including Three–body Corrections andBorn–Oppenheimer ab Initio and Density Functional Theory Quantum Mechanical/molecular Mechanics Simulations. J. Chem. Phys.,2001,115(23):10809–1
[95] Lei X L, Pan B C. Structures Stability, Vibration Entropy and IR Spectra of HydratedCalcium Ion Clusters [Ca(H2O)n]2+(n=120,27): A Systematic Investigation byDensity Functional Theory. J. Phys. Chem. A,2010,114:7595–7603
[96] Li R, Jiang Z, S Shi, et al. Raman Spectra and17O NMR Study Effects of CaCl2andMgCl2on Water Structure. Journal of Molecular Structure,2003,645:69–75
[97] Fulton J L, Heald S M, Badyal Y S, et al. Understanding the Effects of Concentrationon The Solvation Structure of Ca2+in Aqueous Solution. I: The perspective on LocalStructure from EXAFS and XANES. J. Phys. Chem. A,2003,107:4688–4696
[98] Tongraar A, Rode B M. Structural Arrangement and Dynamics of The Hydrated Mg2+:An ab Initio QM/MM Molecular Dynamics Simulation. Chemical Physics Letters,2005,409(4–6):304–309
[99] Tongraar A, Role B M. The Role of Non–additive Contributions on The HydrationShell Structure of Mg2+Studied by Born–Oppenheimer ab Initio Quantum MechanicalMolecular Dynamics Simulation. Chemical Pysics Letters,2001,346(5–6):485–491
[100] Callahan K M, Casillas–Ituarte N N, Roeselova M, et al. Solvation of MagnesiumDication: Molecular Dynamics Simulation and Vibrational Spectroscopic Study ofMagnesium Chloride in Aqueous Solutions. J. Phys. Chem. A,2010,114:5141–5148
[101] Moran H E. System Lithium Chloride–Water. J. Phys. Chem.,1956,60(12):1666–1667
[102] Pinho S P, Macedo E A, Solubility of NaCl, NaBr, and KCl in Water, Methanol,Ethanol, and Their Mixed Solvents. J. Chem. Eng. Data,2005,50(1):29–32
[103] Guendouzi M E, Errougui A, Solubility in the Ternary Aqueous Systems Containing M,Cl, NO3, and SO42with M=NH4+, Li+, or Mg2+at T=298.15K. J. Chem. Eng. Data,2009,54:376–381
[104]丁秀萍,毕玉敬,时历杰.三元体系NaCl–CaCl2–H2O25oC相关系研究.盐湖研究,2009,17(3):40–43
[105] Rard J A. Isopiestic Investigation of Water Activities of Aqueous Nickel(2+) Chlorideand Copper(2+) Chloride Solutions and The Thermodynamic Solubility Product ofNickel Dichloride Hexahydrate at298.15K. J. Chem. Eng. Data,1992,37(4):433–442
[106] Filippov V K, Charykov N A. Fedorov Yu A. Sodium Chloride–nickle Dichloride(Copper Dichloride)–Water System at25oC. Zhurnal Neorganiccheskoi Khimii,1986,31(7):1861–1868
[107] Yanatieva O K. Polythermal Solubilities in The Systems CaCl2–MgCl2–H2O andCaC12–NaCI–H2O. Zhur. Prikl. Khim.,1946,19:709–722
[108] Lee W B, Egerton A C. LXXXIII. Heterogeneous Equilibria Between the Chlorides ofCalcium, Magnesium, Potassium, and Their Aqueous Solutions. Part I. J. Chem. Soc.Trans.,1923,123:706–716
[109] Linke W F, Seidell A. Solubility of Inorganic and Metal Organic Compounds.American Chemical Society, Washington:1965.
[110] Farelo F, Fernandes C, Avelino A. Solubilities for Six Ternary Systems: NaCl+NH4Cl+H2O, KCl+NH4Cl+H2O, NaCl+LiCl+H2O, KCl+LiCl+H2O, NaCl+AlCl3+H2O, and KCl+AlCl3+H2O at T)(298to333) K. J. Chem. Eng. Data,2005,50(4),1470–1477
[111] Campbell A N, Kartzmark E M. The System LiCl–KCl–H2O at25oC. Can. J. Chem.,1956,34:672–678
[112] Texler N R, Holdway S, Neilson G W, Monte Carlo Simulations and NeutronDiffraction Studies of The Peptide Forming System0.5mol/kg CuCl2–5mol/kgNaCl–H2O at293and353K. J. Chem. Soc. Faraday Trans.,1998,94(1):59–65
[113] Haung H. Estimation of Pitzer’s Ion Interaction Parameters For Electrolytes Involvedin Complex Formation Using a Chemical Equilibrium Model. Journal of SolutionChemistry,1989,18(11):1069–1084
[114] Kurlyandskaya I I, Solomonik I G, Glazunova E D, et al. New Trends in theDevelopment of Methods for Catalyst Preparation for The Processes of OrganochlorineSynthesis. Kinetics and Catalysis,2001,42(3):381–389
[115] Hynes J E, Garrett B B, Moulton W G. Magnetic Resonance of KCuC13. The Journalof Chemical Physics,1970,52(5):2672–2678
[116] Sakurai T, Taketani A, Kimura S, et al. ESR Measurements of KCuCl3under MultiExtreme Conditions. Orlando, Florida (USA): AIP conference proceedings.2006,850:1057–1058
[117]何配华.微量铜在复杂氯化物多元体系溶液中的络合行为研究.[湖南大学硕士学位论文],湖南:湖南大学化学化工学院,2010,32–45
[118] Balarev Ch, Spassov D. Formation Double Salts of Divalent Metal Chlorides. ZhurnalNeorganiccheskoi Khimii,1980,25:2814
[119] Guangming L, Yan Y, Fengqin W, et al. Isopiestic Determination of ActivityCoeficients of LiCl and CaCl2in LiCl CaCl2H2O System at298.15K. Acta PhysicoChimica Sinica,1999,15(10):956960
[120] Filippov A, Mihelbson K N. Thermodynamic Study on The System LiCl–CaCl2–H2Oat25°C and35°C Zh. Neorg. Khim.,1977,22:1689–1694
[121] Yan Y, Bai S, Peng–Sheng S, et al. Isopiestic Determination of Osmotic and ActivityCoeficients in LiCI MgCl2H2O25oC. Acta Chimica Sinica,1999,50:809–848
[122] Voskressenskaja N K, Janatieva O K. Solubility Equilibrium of The SystemLiCl–MgCl2–H2O. Izv. Akad. Nauk. SSSR. Ser. Khim.,1937,97–121
[123] Dinane A, Mounir A. Water Activities, Osmotic and Activity Coefficients in AqueousMixtures of Sodium and Magnesium Chlorides at298.15K by The HygrometricMethod. Fluid Phase Equilibria,2003,206:13–25
[124] Yan Y D, Zhang M L, et al, Electrochemical Study of The Codeposition of Mg–Li–AlAlloys from LiCl–KCl–MgCl2–AlCl3Melts. J. Appl. Electrochem,2009,39:455–461
[125] Hatttori T, Igarashi K, Mochinaga J, Enthalpies of Fusion of Intermediate Com pounds,KMgCl3, K2MgCl4, K2BaCl4, KCaCl3, K2SrCl4, K2LaCl4, K3PrCl6, K2NdCl6,K2Gd3Cl10and KDy3Cl10, Bull. Chem. Soc. Jpn.,1981,54:1883–1884
[126] Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization of the LiCl–NaCl–KCl–RbCl–CsCl–MgCl2–CaCl2System Using the Modified Quasi–chemicalModel. Metallurgical and Materials Transaction A,2001,32a:1361–1383
[127] Stokes R H, Robinson R A. Interactions in Aqueous Nonelectrolyte Solutions. I.Solute–Solvent Equilibria. J. Phys. Chem.,1966,70(7):2126–2131
[128] Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization of the LiCl–NaCl–KCl–RbCl–CsCl–MgCl2–CaCl2System Using the Modified Quasi–chemicalModel. Metallurgical and Materials Transactions A,2001,32A:1361–1383
[129] Brynestad J, Yakel H L, Smith G P. Temperature Dependence of the AbsorptionSpectrum of Nickel(II)–Doped KMgCl3and the Crystal Structure of KMgCl3. TheJournal of Chemical Physics,1996,45(12):4653–4664
[130] Robelin C, Chartrand P, Pelton A D. Thermodynamic Evaluation and Optimization ofthe (NaCl+KCl+MgCl2+CaCl2+MnCl2+FeCl2+CoCl2+NiCl2) System. J. Chem.Thermodynamics,2004,36:809–828
[131] Kennedy J. Eberhart R. Particle Swarm Optimization. Washington (USA): IEEE int.Conf. Neural Network,1995,1942–1948
[132] Sun J, Xu W B, Feng B, A Global Search Strategy of Quantum–behaved ParticleSwarm Optimization, Wuxi (China): IEEE Conference on Cybernetics and IntelligentSystems,2004,111–116
[133] Lu Y, Liao Z, Chen W F. An Automatic Registration Framework using QuantumParticle Swarm Optimization for Remote Sensing Images. Beijing (China):International Conference on Wavelet Analysis and Pattern Recognition,2007,2:484–488
[134] Sun J, Fang W, Xu W B. A Quantum–Behaved Particle Swarm Optimization WithDiversity–Guided Mutation for the Design of Two–Dimensional IIR Digital Filters,IEEE Trans. Circuits Syst. II,2010,57(2):141–145
[135] Huang Z, Wang Y J, Yang C Y, et al. A New Improved Quantum–behaved ParticleSwarm Optimization Model. Xi’an (China): IEEE Conference on Industrial Electronicsand Applications,2009,1560–1564
[136] Liu J, Xu W, Sun J. Quantum–behaved Particle Swarm Optimization with MutationOperator. Washington (USA):17th IEEE International Conference on Tools withArtificial Intelligence,2005,237–240
[137] Liu J, Sun J, Xu W B. Quantum–behaved Particle Swarm Optimization With ImmuneMemory and Vaccination. Atlanta (USA): IEEE International Conference on GranularComputing,2006,453–456
[138] Su D B, Xu W B, Sun J. Quantum–Behaved Particle Swarm Optimization WithCrossover Operator. Shanghai (China): International Conference on Wireless Networksand Information Systems,2009,399–402
[139] Gill S S, Chandel R, Chandel A. Swarm Intelligence Based Circuit Partitioning.Shanghai (China):2010Asia Pacific Conference on Postgraduate Research inMicroelectronics&Electronics.2010,41–44
[140] Chamberlain B L, University of Washington; Graph Partitioning Algorithms forDistributing Workloads of Parallel Computations. Technical Report UW–CSE–98–10
[141] Radha H, Vetterli M, Leonardi R. Image Compression Using Binary Space PartitioningTrees. Evanston (USA): IEEE Transaction on Image Processing,1996,5:1610–1624
[142] Pal N R, Bezdek J C. Complexity Reduction for “Large Image” Hanover (USA):Processing. IEEE Transaction on Systems, Man, And, Cybernetics─Part B: Cybernetics,2002,32:598–611
[143] Kashtiban A M, Ahandani M A. Various Strategies for Partitioning of Memeplexes inShuffled Frog Leaping Algorithm. Tehran (Iran): Proceedings of the14th InternationalCSI Computer Conference.2009:576–581
[144] Shi Y, Eberhart R C. Empirical study of Particle Swarm Optimization, Columbia(Canada): IEEE Congress on Evolutionary Computation,1999,3:101–106
[145] Clerc M, Kennedy J, The Particle Swarm Explosion, Stability, and Convergence in aMultidimensional Complex Space. IEEE Transactions on Evolutionary Computation,2002,6(1):58–73
[146] Liu Y, Liang F. An adaptive Hybrid Particle Swarm Optimization. Changsha (Hunan):Second International Symposium on Computational Intelligence and Design,2009,1:87–90
[147] Cao L, Wang S, Liu X, et al. Research on Improved QPSO Algorithm Based onCooperative Evolution with Two Populations. Wuxi (China): International conferenceon Life System Modeling and Intelligent Computing,2010,93–100
[148] Lu K, Fang K, Xie G. A Hybrid Quantum–Behaved Particle Swarm OptimizationAlgorithm for Clustering Analysis. Jinan (China):15th IEEE International Conferenceon Fuzzy Systems and Knowledge Discovery,2008,1:21–25
[149] Riget J, Vesterstr m J S. A Diversity–guided Particle Swarm Optimizer–the ARPSO.Technical Report, EVAlife,2002–02, Department of Computer Science, University ofAarhus,2002:3294–3299
[150] Fawcett W B, Tikanen A C. Role of Solvent Permittivity in Estimation of ElectrolyteActivity Coefficients on the Basis of the Mean Spherical Approximation. J. Phys.Chem.,1996,100(10):4251–4255
[151] Colie C H, Ritson D M, Hasted J B. Dielectric Properties of Aqueous Ionic Solutions.Parts I and II. J. Chem. Phys.,1948,16:1–21
[152] Radia I, Jean–Charles de H, Walterb F. The Simultaneous Representation of DielectricConstant, Volume and Activity Coefficients Using an Electrolyte Equation of State.Fluid Phase Equilibria,2008,271:19–27
[153] Simonin J, Bernard O, Blum L. Ionic Solutions in the Binding Mean SphericalApproximation: Thermodynamic Properties of Mixtures of Associating Electrolytes. J.Phys. Chem. B,1999,103(4):699–704
[154] Wang P, Anderko A, Computation of Dielectric Constants of Solvent Mixtures andElectrolyte Solutions. Fluid Phase Equilibria,2001,186:103–122
[155] Sunner J, Kebarle P. Unimolecular Dissociation of Ions. Effect on Mass–SpectrometricMeasurements of Ion–Molecule Association Equilibria. J. Phys. Chem.,1981,85(4):327–335
[156] Frank H S, Evans M W. Free Volume and Entropy in Condensed Systems III. Entropyin Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure andThermodynamics in Aqueous Electrolytes. J. Chern. Phys.,1945,13:507–532
[157] Ulich H. Ionic Entropy and Solvation. Z. Elektrochem,1930,36:497–564
[158] Zavitsas A A. Aqueous Solutions of Calcium Ions: Hydration Numbers and The Effectof Temperature. J. Phys. Chem. B,2005,109(43),20636–20640
[159]吕秉玲,林志祥.纯碱生产相图分析.北京:化学工业出版社,1991,45–50
[160]大连制碱工业研究所编,纯碱工业知识.大连:大连制碱工业研究所,1975,56–87
[161] Christov C. Thermodynamic Study of The CuCl2–MCl2–H2O Systems (M=Mg, Co) at298.15K. Collect. Czech. Chem. Commun,1996,61:507–512
[162] Zdanovskii A B. Functional Relation of The Properties of The Mixed and IndividualSolutions. Tr. Solyanoi Lab. Vses. Inst. Galurgii Akad. Nauk SSSR,1936,2:70–75
[163] Zdanovskii A B. Regularities in the Property Variations of Mixed Solutions. Tr.Solyanoi Lab. Akad. Nauk SSSR,1936,6(5):70–73
[164] Glueckauf E. The Influence of Ionic Hydration on Activity Coefficients inConcentrated Electrolyte Solutions. Trans. Faraday. Soc.,1955,51:1235–1244
[165] Hewish N A, Neilson G W, Enderby J E. Enviroment of Ca2+ions in aqueous solvent.Nature,1982,297(13):138–139
[166] Mcmillan W G, Mayer J E. The Statistical Thermodynamics of MulticomponentSystems. J. Chem. Phys,1945,13(7):276-305.
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