方阱流体气液相平衡性质和临界非对称性的计算机模拟研究
|
摘要
本文通过巨正则系综下的Monte Carlo模拟研究了具有方阱势能的流体的相平衡性质和临界非对称性。通过完整标度下的Q参数方法结合Histogram reweighting技术以及有限尺寸标度分析预测了阱宽为=1.5,链长分别为2,4,8,16的方阱链的临界温度值和临界密度值,临界温度比不完整标度理论下得到的结果要低。并根据Flory-Huggins理论进行外推获得了无限长的方阱链的临界温度。
采用完整标度下Q参数方法重新模拟了阱宽分别为λ=1.25,1.75,2.0的方阱单体的临界温度和临界密度,并采用近临界标度算法获得了在近临界区域的气液相平衡曲线,分析了不同阱宽方阱流体的临界非对称性质,结果表明,阱宽越小,系统的临界非对称性越强。通过对共存曲线直径拟合发现,阱宽越小,|t|2β项与|t|1-α项的系数比越大。说明相互作用范围越小,|t|2β项的贡献越重要,与已有分析一致。
本文还采用该标度算法还预测了阱宽为=1.5的方阱二聚体和链长为4的方阱链的近临界相平衡性质以及临界非对称性。通过考察共存曲线直径的临界奇异性发现,方阱二聚体的共存曲线直径|t|2β项的作用比方阱单体更明显,说明分子体积越大,|t|2β项越占主导地位。但是链长为4的方阱链的共存曲线直径中|t|2β项的作用比方阱二聚体要弱,而是|t|1-α项占主导地位。可能的原因是链长为4的方阱链分子团在一起,缩小了分子体积,而不是以伸展的形式存在。因此,我们认为除了分子相互作用范围和分子体积之外,链状分子的分子构型也会对系统的临界非对称性产生影响。我们还利用Hyper parallel tempering MC模拟获得了方阱二聚体远离临界区域的相平衡曲线,其中共存密度由密度概率分布双峰等面积准则来确定。获得的共存曲线与已有模拟结果相吻合。最终给出了方阱二聚体完整的气液相平衡曲线。
The vapor-liquid phase equilibrium properties and critical asymmetry of fluids with Square-Well potential were investigated by grand-canonical ensemble Monte Carlo simulation based on complete scaling theory. With the help of histogram reweighting technique and Finite-Size Scaling theory, we obtained the critical temperatures and critical densities of Square-Well chain molecules with λ=1.5and2,4,8,16segments. The values of critical temperatures are lower than that presented before based on incompelete scaling theory. And the critical temperature for an infinitely long Square-Well chain was estimated.
The critical properties of Square-Well fluids with λ=1.25,1.75,2.0were reexamined using the Q-parameter method. The vapor-liquid coexistence curve in near-critical region for Square-Well monomers with λ=1.25,1.75,2.0were obtained by a scaling algorithms for precise simulation of fluid coexistence close to criticality. The results implied that the system with a smaller value of λ showed stronger critical asymmetry. Analyzing the coexistence diameter by fitting to a scaling relation made us concluded that the radio of coefficients in terms|t|2β and|t|1-α in Square-Well fluid with1=1.25was the largest, which means the smaller of inaction range, the more important in|t|2β term to coexistence diameter. This fact is in agreement with the conclusion in other papers.
The vapor-liquid phase equilibrium properties and critical asymmetry of Square-Well dimer and tetramer with λ=1.5were studied by the same scaling algorithms. It showed that the term of|t|2β contributed more to coexistence diameter for Square-Well dimer than that for Square-Well monomer. That means fluids with a bigger molecule size had a much more dominating effect to the singular of coexistence diameter. While analyzing the results for Square-Well tetramer, we found that the domination of|t|2β term to the coexistence diameter was smaller for Square-Well tetramer fluid than that for Square-Well dimer fluid, and|t|1-α term dominate the singular behavior of coexistence diameter for Square-Well tetramer. The reason may be that the Square-Well tetramer molecule existed not in the form of a linear chain but in the form of a curly chain. Therefore, except the interacting range and molecule size, the molecule configuration of chain fluids was expected to impact the critical asymmetry. We also performed hyper parallel tempering Monte Carlo simulations for Square-Well dimer to predict coexistence properties far from critical point. The coexistence vapor and liquid densities were located by equal-area criterion for the double-peak of density probability distribution. The results are in good agreement with previous ones. Finally, the complete vapor-liquid coexistence curve of Square-Well dimer was showed.
采用完整标度下Q参数方法重新模拟了阱宽分别为λ=1.25,1.75,2.0的方阱单体的临界温度和临界密度,并采用近临界标度算法获得了在近临界区域的气液相平衡曲线,分析了不同阱宽方阱流体的临界非对称性质,结果表明,阱宽越小,系统的临界非对称性越强。通过对共存曲线直径拟合发现,阱宽越小,|t|2β项与|t|1-α项的系数比越大。说明相互作用范围越小,|t|2β项的贡献越重要,与已有分析一致。
本文还采用该标度算法还预测了阱宽为=1.5的方阱二聚体和链长为4的方阱链的近临界相平衡性质以及临界非对称性。通过考察共存曲线直径的临界奇异性发现,方阱二聚体的共存曲线直径|t|2β项的作用比方阱单体更明显,说明分子体积越大,|t|2β项越占主导地位。但是链长为4的方阱链的共存曲线直径中|t|2β项的作用比方阱二聚体要弱,而是|t|1-α项占主导地位。可能的原因是链长为4的方阱链分子团在一起,缩小了分子体积,而不是以伸展的形式存在。因此,我们认为除了分子相互作用范围和分子体积之外,链状分子的分子构型也会对系统的临界非对称性产生影响。我们还利用Hyper parallel tempering MC模拟获得了方阱二聚体远离临界区域的相平衡曲线,其中共存密度由密度概率分布双峰等面积准则来确定。获得的共存曲线与已有模拟结果相吻合。最终给出了方阱二聚体完整的气液相平衡曲线。
The vapor-liquid phase equilibrium properties and critical asymmetry of fluids with Square-Well potential were investigated by grand-canonical ensemble Monte Carlo simulation based on complete scaling theory. With the help of histogram reweighting technique and Finite-Size Scaling theory, we obtained the critical temperatures and critical densities of Square-Well chain molecules with λ=1.5and2,4,8,16segments. The values of critical temperatures are lower than that presented before based on incompelete scaling theory. And the critical temperature for an infinitely long Square-Well chain was estimated.
The critical properties of Square-Well fluids with λ=1.25,1.75,2.0were reexamined using the Q-parameter method. The vapor-liquid coexistence curve in near-critical region for Square-Well monomers with λ=1.25,1.75,2.0were obtained by a scaling algorithms for precise simulation of fluid coexistence close to criticality. The results implied that the system with a smaller value of λ showed stronger critical asymmetry. Analyzing the coexistence diameter by fitting to a scaling relation made us concluded that the radio of coefficients in terms|t|2β and|t|1-α in Square-Well fluid with1=1.25was the largest, which means the smaller of inaction range, the more important in|t|2β term to coexistence diameter. This fact is in agreement with the conclusion in other papers.
The vapor-liquid phase equilibrium properties and critical asymmetry of Square-Well dimer and tetramer with λ=1.5were studied by the same scaling algorithms. It showed that the term of|t|2β contributed more to coexistence diameter for Square-Well dimer than that for Square-Well monomer. That means fluids with a bigger molecule size had a much more dominating effect to the singular of coexistence diameter. While analyzing the results for Square-Well tetramer, we found that the domination of|t|2β term to the coexistence diameter was smaller for Square-Well tetramer fluid than that for Square-Well dimer fluid, and|t|1-α term dominate the singular behavior of coexistence diameter for Square-Well tetramer. The reason may be that the Square-Well tetramer molecule existed not in the form of a linear chain but in the form of a curly chain. Therefore, except the interacting range and molecule size, the molecule configuration of chain fluids was expected to impact the critical asymmetry. We also performed hyper parallel tempering Monte Carlo simulations for Square-Well dimer to predict coexistence properties far from critical point. The coexistence vapor and liquid densities were located by equal-area criterion for the double-peak of density probability distribution. The results are in good agreement with previous ones. Finally, the complete vapor-liquid coexistence curve of Square-Well dimer was showed.
引文
[1]于渌,郝柏林,陈晓松,边缘奇迹——相变和临界现象,科学出版社,2005.
[2]S. J. Blundell, M. K. Blundell. Concepts in Thermal Physics. Oxford University Press, 2008.
[3]D. Chandler, Introduction to Modern Statistical Mechanics. Oxford University Press, 1987.
[4]林宗涵,热力学与统计物理学,北京大学出版社,2007.
[5]B. Hayes. The World in a Spin. American Scientist,2000,88(5):384-388.
[6]张志东,伊辛模型的研究进展简介,自然杂志,2008,30(2)：94-101.
[7]S. G Brush. History of the Lenz-Ising Model. Rev. Mod. Phys.1967,39(4):883-893.
[8]R. K. Pathria, Statistical Mechanics,2nd Edtoan(英文影印版),世界图书出版公司,2001. [9] K. Christensen, N. R. Moloney, Complexity and Criticality(英文影印版),复旦大学出版社,2006.
[10]H. E. Stanley. Scaling, University, and Renormalization:Three pillars of Modern Critical Phenomena. Rev. Mod. Phys.1999,71(2):S358-S366.
[11]L. P. Kadanoff, W. Gotze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, J. Swift, Static Phenomena Near Critical Points:Theory and Experiment. Rev. Mod. Phys.1967,39(2):395-430.
[12]M. E. Fisher, The Theory of Equilibrium Critical Phenomena. Rep. Prog. Phys.1967, 30(2):615-730.
[13]A. Pelissetto, E. Vicari, Critical Phenomena and Renormalization-Group Theory. Phys. Rep.,2002,368(6):549-727.
[14]K. G Wilson, Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture. Phys. Rev. B,1971,4(9):3174-3183
[15]K. G Wilson, Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior. Phys. Rev. B,1971,4(9):3184-3205.
[16]T. D. Lee, C. N. Yang, Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model. Phys. Rev.1952,87(3):410-419.
[17]Simon Reif-Acherman. The History of the Rectilinear Diameter Law. Quim. Nova.2010, 33(9):2003-2010.
[18]N. D. Mermin, J. J. Rehr, Generality of the Singular Diameter of the Liquid-Vapor Coexistence Curve. Phys. Rev. Lett.,1971,26(19):1155-1156.
[19]J. J. Rehr, N. D. Mermin, Revised Scaling Equation of State at Liquid-Vapor Critical Point. Phys. Rev. A,1973,8(1):472-480.
[20]Y. C. Kim, M. E. Fisher, G. Orkoulas, Asymmetric Fluid Criticality. I. Scaling with Pressure Mixing. Phys. Rev. E,2003,67(06):061506.
[21]J. Weiner, K. H. Langley, N. C. Ford, Experimental Evidence for a Departure from the Law of the Rectilinear Diameter. Phys. Rev. Lett.1974,32(16):879-881.
[22]C. N. Yang, C. P. Yang. Critical Point in Liquid-Gas Translations. Phys. Rev. Lett.1964, 13(9):303-305.
[23]G. Orkoulas, M. E. Fisher, C. Ustun, The Yang-Yang Relation and the Specific Heats of Propane and Carbon Dioxide. J. Chem. Phys.2000,113(12):7530-7545.
[24]G. Orkoulas, M. E. Fisher, A. Z. Panagiotopoulos, Precise Simulation of Criticality in Asymmetric Fluids. Phys. Rev. E,2001,63(05):051507.
[25]F. J. egner, Corrections to Scaling Law. Phys. Rev. B,1972,5(11):4529-4536.
[26]M. E. Fisher, G Orkoulas, The Yang-Yang Anomaly in Fluid Criticality:Experiment and Scaling Theory. Phys. Rev. Lett.,2000,85(4):696-699.
[27]M. A. Anisimov, J. T. Wang, Nature of Asymmetry in Fluid Criticality. Phys. Rev. Lett. 2006,97(02):025703.
[28]J. T. Wang, M. A. Anisimov, Nature of Vapor-Liquid Asymmetry in Fluid Criticality. 2007,75(05):051107.
[29]C. E. Bertrand, M. A. Anisimov, Complete Scaling for Inhomogeneous Fluids. Phys. Rev. Lett.2010,104(20):205702.
[30]M. A. Anisimov, Phys. Rev. Lett. Divergence of Tolman's Length for a Droplet Near the Critical Point.2007,98(3):035702.
[31]C. E. Bertrand, J. V. Sengers, M. A. Anisimov, Critical Behavior of the Dielectric Constant in Asymmetric Fluids. J. Phys. Chem. B,2011,115(48):14000-14007.
[32]P. L. Perez, G P. Sanchez, C. A. Cerdeirina, J. Thoen, Dielectric Constant of Fluids and Fluid Mixtures at Criticality. Phys. Rev. E,2010,81(4):041121.
[33]I. M. Abdulagatov, N. G Polikhronidi, T. J. Bruno, R. G. Batyrova, G V. Sepanov. Measurements of the Isochoric Heat Capacity, the Critical Point (Tc, pc) and Vapor-Liquid Coexistence Curve (Ts, ps) of High-Purity Toluene Near the Critical Point. Fluid Phase Equilibria.2008,263(1):71-84.
[34]L. M. Radzhabova, G. V. Stepanov, I. M. Abdulagatov, K. A. Shakhbanov. Experimental Study of the Isochoric Heat Capacity and Coexistence-Curve Singular Diameter of sec-Butanol Near the Critical Point and Yang-Yang Anomaly Strength. Phys. Chem. Liq.2013, 51(1):75-101.
[35]M. A. Anisimov, F. Zhong, M. Barmatz. Resolving the Yang-Yang Dilemma in 3He Near the Critical Point. J. Low Temp.2004,137(1-2):69-88.
[36]C. A. Cerdeirina, M. A. Anisimov, J. V. Sengers. The Nature of Singular Coexistence-Curve Diameters of Liquid-Liquid Equilibria. Chem. Phys. Lett.2006,424(4-6): 414-419.
[37]J. T. Wang, C. A. Cerdeirina, M. A. Anisimov, J. V. Sengers, Principle of Isomorphism and Complete Scaling for Binary-Fluid Criticality. Phys. Rev. E,2008,77(03):031127.
[38]G. P. Sanchez, P. L. Perez, C. A. Cerdeirina, J. V. Sengers, M. A. Anisimov. Asymmetric Criticality in Weakly Compressible Liquid Mixtures. J. Chem. Phys.2010,132(15):154502.
[39]J. Leys, P. L. Perez, G Cordoyiannis, C. A. Cerdeirina, C. Glorieux, J. Thoen. Temperature, Concentration, and Frequency Dependence of the Dielectric Constant Near the Critical Point of the Binary Liquid Mixture Nitrobenzene-Tetradecane. J. Chem. Phys.2010, 132(10):104508.
[40]P. L. Perez, C. S. P. Tripathi, J. Leys, C. A. Cerdeirina, C. Glorieux, J. Thoen. The Yang-Yang Anomaly in Liquid-Liquid Criticality:Experimental Evidence from Adiabatic Scanning Calorimetry. Chem. Phys. Lett.2012,523:69-73.
[41]T. X. Yin, S. X. Liu, J. J. Xie, W. G. Shen. Asymmetric Criticality of the Osmotic Compressibility in Binary Mixtures. J. Chem. Phys.2013,138(2):024504.
[42]C. E. Bertrand, J. F. Nicoll, M. A. Anisimov, Comparison of Complete Scaling and a Field-Theoretic Treatment of Asymmetric Fluid Criticality. Phys. Rev. E,2012,85(3): 031131.
[43]M. A. Anisimov, Universality versus Nonuniversality in Asymmetric Fluid Criticality. Cond. Matt. Phys.,2013,16(2):23603:1-10.
[44]V. K. Kulinskii, N. P. Malomuzh, The Nature of the Rectilinear Diameter Singularity. Phys. A,2007,388(5):621-627.
[45]K. Binder. Finite Size Effects on Phase Transitions. Ferroelectrics,1987,73(1):43-67.
[46]M. E Fisher, A. E. Ferdinand, Interfacial, Boundary, and Size Effects at Critical Points. Phys. Rev. Lett.1967,19(4):169-172.
[47]M. E. Fisher, Critical Phenomena. Academic Press,1971.
[48]V. Privman, Finite Size Scaling and the Numerical Simulation of Statiscal Systems. World Scientific, Singapore,1990.
[49]M. E. Fisher, M. N. Barber. Scaling Theory for Finite-Size Effects in the Critical Region. Phys. Rev. Lett.1972,28(3):1516-1519.
[50]V. Privman, M. E. Fisher. Convergence of Finite-Size Scaling Renormalization. J. Phys. A:Math. Gen.1983,16(9):L295-L301.
[51]J. G. Brankov, D. M. Danchev, N. S. Tonchev. Theory of Critical Phenomena in Finite-Size System:Scaling and Quantum Effects. World Scientific, Singapore,2000.
[52]D. P. Landau, K. Binder. A Guide to Monte Carlo Simulations in Statistical Physics,3rd. Cambridge University Press, Cambridge,2009.
[53]K. Binder. Computer Simulations of Critical Phenomena and Phase Behavior of Fluids. Mol. Phys,2010,108(14):1797-1815.
[54]K. Binder. Finite Size Scaling Analysis of Ising Model Block Distribution Functions. Z. Phys. B:Condens. Matter,1981,43(2):119-140.
[55]K. Binder, Computational Methods in Field Theory, Springer, Berlin,1992.
[56]L. Vega, E. de Miguel, L. F. Rull. Phase Equilibria and Critical Behavior of Square-Well Fluids of Variable Width by Gibbs Ensemble Monte Carlo Simulation. J. Chem. Phys.1992, 96(3):2296-2305.
[57]F. A. Escobedo, J. J. de Pablo. Simulation and Prediction of Vapour-Liquid Equilibria for Chain Molecules. Mol. Phys.1996,87(2):347-366.
[58]J. R. Elliott, L. Hu. Vapor-Liquid Equilibria of Square-Well Spheres. J. Chem. Phys. 1999,110(6):3043-3048.
[59]J. J. de Pablo, J. M. Prausnitz, H. J. Strauch, P. T. Cummings, Molecular Simulation of Water along the Liquid-Vapor Coexistence Curve from 25℃ to the Critical Point. J. Chem. Phys.1990,93(10):7355-7359.
[60]D. G Green, G Jackson, E. de Miguel, L. F. Rull. Vapor-Liquid and Liquid-Liquid Phase Equilibria of Mixtures Containing Square-Well Molecules by Gibbs Ensemble Monte Carlo Simulation. J. Chem. Phys.1994,101(4):3190-3204.
[61]N. B. Wilding, A. D. Bruce. Density Fluctuations and Field Mixing in the Critical Fluid. J. Phys. Condens. Matter.1992,4(12):3087-3108.
[62]A. D. Bruce, N. B. Wilding, Scaling Fields and Universality of the Liquid-Gas Critical Point. Phys. Rev. Lett.1992,68(2):193-196.
[63]N. B. Wilding, M. Muller, Liquid-Vapor Asymmetry in Pure Fluids:A Monte Carlo Study. J. Chem. Phys.1995,102(6):2562-2573.
[64]N. B. Wilding. Critical-Point and Coexistence-Curve Properties of the Lennard-Jones Fluid:A Finite-Size Scaling Study. Phys. Rev. E,1995,52(1):602-611.
[65]Q. L. Yan, J. J. de Pablo, Phase Equilibria of Size-Asymmetric Primitive Model Electrolytes. Phys. Lett.2001,86(10):2054-2057.
[66]J. P. Pellitero, P. Ungerer, G. Orkoulas, A. D. Mackie, Critical Point Estimation of the Lennard-Jones Pure Fluid and Binary Mixtures. J. Chem. Phys.2006,125(5):054515.
[67]A. Z. Panagiotopoulos, Critical Parameters of the Restricted Primitive Model. J. Chem. Phys.2002,116(7):3007-3011.
[68]P. J. Camp, G. N. Patey, Coexistence and Criticality of Liquids with Long-Range Potentials. J. Chem. Phys.2001,114(1):399-408.
[69]J. M. Caillol, D. Levesque, J. J. Weis, Critical Behavior of the Restricted Primitive Model Revisted. J. Chem. Phys.2002,116(24):10794-10800.
[70]S. Moghaddam, A. Z. Panagiotopoulos, Lattice Discretization Effects on the Critical Parameters of Model Nonpolar and Polar Fluids. J. Chem. Phys.2003,118(16):7556-7561.
[71]Y. C. Kim, M. E. Fisher. Fluid Critical Points from Simulations:The Bruce-Wilding Method and Yang-Yang Anomalies. J. Phys. Chem. B,2004,108(21):6750-6759.
[72]E. Luijten, M. E. fisher, A. Z. Panagiotopoulos. Universality Class of Criticality in the Restricted Primitive Model Electrolyte. Phys. Rev. Lett.2002,88(18):185701.
[73]Y. C. Kim, M. E. Fisher, Asymmetric Fluid Criticality. Ⅱ. Finite-size Scaling for Simulation. Phys. Rev. E,2003,68(4):041506.
[74]Y. C. Kim, M. E. Fisher, E. Luijten, Precise Simulation of Near-Critical Fluid Coexistence. Phys. Rev. Lett.,2003,91(6):065701.
[75]Y. C. Kim, M. E. Fisher, Fluid Coexistence Close to Criticality:Scaling Algorithms for Precise Simulation. Comput. Phys. Commun.2005,169:295-300.
[76]Y. C. Kim, Yang-Yang Anomalies and Coexistence Diameters:Simulation of Asymmetric Fluids. Phys. Rev. E,2005,71(5):051501.
[77]Y. C. Kim, M. E. Fisher. Singular Coexistence-Curve Diameters:Experiments and Simulations. Chem. Phys. Lett.2005,414(1-3):185-192.
[78]R. L. C. Vink, H. H. Wensink. Coexistence Diameter in Two-Dimensional Colloid-Polymer Mixtures. Phys. Rev. E,2006,74(1):010102(R).
[79]R. L. C. Vink, Critical Behavior of a Colloid-Polymer Mixture Confined between Walls, Phys. Rev. E,2006,73(5):056118.
[80]R. L. C. Vink, A. D. Virgiliis, J. Forbach, K. Binder, Phase Diagram and Structure of Colloid-Polymer Mixtures Confined between Walls. Phys. Rev. E,2006,74(3):031601.
[81]F. L. Verso, R. L. C. Vink, D. Pini, L. Reatto, Critical Behavior in Colloid-Polymer Mixtures:Theory and Simulations. Phys. Rev. E,2006,73(6):061407.
[82]R. L. C. Vink, T. Neuhaus, H. Lowen. Fluid Phase Separation inside a Static Periodic Field:An Effectively Two-Dimensional Critical Phenomenon. J. Chem. Phys.2011,134(20): 204907.
[83]R. L. C. Vink. Critical Behavior of the Widom-Rowlinson Mixture:Coexostence Diameter and Order Paremeter. J. Chem. Phys.2006,124(09):094502.
[84]R. C. Ren, C. J. O'Keeffe, G. Orkoulas. Scaling Fields of Pressure Mixing in the Widom-Rowlinson Model. J. Chem. Phys.2006,125(14):144505.
[85]Y. C. Kim, M. E. Fisher, A. Z. Panagiotopoulos. Universality of Ionic Criticality:Size-and Charge-Asymmetric Electrolytes. Phys. Rev. Lett.2005,95(19):195703.
[86]J. P. Pellitero, P. Ungerer, A. D. Mackie. Near Critical Coexistence for an AUA Model of Thiophenes. Rev. IFP.2008,63(3):277-282.
[87]M. Nayhouse, A. M. Amlani, G. Orkoulas. Precise Simulation of the Freezing Transition of Supercritical Lennard-Jones. J. Chem. Phys.2011,135(15):154103.
[88]M. Nayhouse, A. M. Amlani, V. R. Heng, G. Orkoulas. Simulation of Fluid-Solid Coexistence via Thermodynamic Intrgration Using a Modified Cell Model. J. Phys:Condens. Matter,2012,24(15):155101.
[89]J. M. Prausnitz, R. N. Lichtenthaler, E. G de Azevedo. Molecular Thermodynamics of Fluid-Phase Equilibria,3rd ed. Prentice-Hall, Upper Saddle River, NJ,1999.
[90]G Orkoulas, A. Z. Panagiotopoulos. Phase Behavior of the Restricted Primitive Model and Square-Well Fluids from Monte Carlo Simulations in the Grand Canonical Ensemble. J. chem. Phys.1999,110(3):1581-1590.
[91]D. L. Pagan, J. D. Gunton. Phase Behavior of Short-Range Square-Well Model. J. Chem. Phys.2005,122(18):184515.
[92]E. de Miguel. Critical Behavior of the Square-Well Fluid with X=2:A Finite-Size Study. Phys. Rev. E,1997,55(2):1347-1354.
[93]L.A. Davies, A. G Villegas, G. Jackson. Phase Equilibria of a Square-Well Monomer-Dimer Mixture:Gibbs Ensemble Computer Simulation and Statistical Associating Fluid Theory for Potentials of Variable Range. Phys. Rev. E,1998,57(2):2035-2044.
[94]J. Y. Cui, J. R. Elliott. Phase Envelopes for Variable Width Square-Well Chain Fluids. J. Chem. Phys.2001,114(16):7283-7290.
[95]S. B. Kiselev, J. f. Ely, J. R. Eliott. Molecular Dynamic Simulations and Global Equation of State of Square-Well Fluids with the Well-Widths from λ=1.1 to 2.1. Mol. Phys.104(15): 2545-2559.
[96]E. S. Paschinger, A. L. Benavides, R. Castanedapriego. Vapor-Liquid Equilibrium and Critical Behavior of the Square-Well Fluid of Variable Range:A Theoretical Study. J. Chem. Phys.2005,123(23):234513.
[97]A. G. Villegas, A. Galindo, P. J. Whitehead, S. J. Mills. G Jackson, A. N. Burgess. Statistical Associating Fluid Theory for Chain Molecules with Attractive Potentials of Variable Range. J. Chem. Phys.1997,106(10):4168-4186.
[98]J. W. Jiang, J. M. Prausnitz, Equation of State for Thermodynamic Properties of Chain Fluids Near-to and Far-from the Vapor-Liquid Critical Region. J. Chem. Phys.1999,111(13): 5964-5974.
[99]A. Galindo, L. A. Davies, A. Gil-Villegas, G. Jackson. The Thermodynamics of Mixtures and the Corresponding Mixing Rules in the SAFT-VR Approach for Potentials of Variable Range. Mol. Phys.1998,93(2):241-252.
[100]J. L. Li, H. H. He, C. J. Peng, H. L. Liu, Y. Hu. A New Development of Equation of State for Square-Well Chain-Like Molecules with Variable Width 1.1 [101]J. A. White. Global Renormalization Calculations Compared with Simulations for Square-Well Fluids:Widths 3.0 and 1.5. J. Chem. Phys.2000,113(4):1580-1586.
[102]E. Forte, F. Llovell, L. F. Vega, J. P. M. Trusler, A. Galindo, Application of a Renormalization-Group Treatment to the Statistical Associating Fluid Theory for Potentials of Variable Range(SAFT-VR). J. Chem. Phys.2011,134(15):154102.
[103]W. Zhao, L. Wu, L. Wang, L. Y. Li, J. Cai. Critical Asymmetry in Renormalization Group Theory for Fluids. J. Chem. Phys.2013,138(23):234502.
[104]L. Wang, W. Zhao. L. Wu, L. Y. Li, J. Cai. Improved Renormalization Group Theory for Critical Asymmetry of Fluids. J. Chem. Phys.2013,139(12):124103.
[105]A. Z. Panagiotopoulos. Monte Carlo Methods for Phase Equilibria of Fluids. J. Phys.: Condens. Matter.2000,12(3):R25-R52.
[106]N. Metropolis. The Beginning of the Monte Carlo Method. Los Alamos Science.1987, 12(Special Issue):125-130.
[107]N. Metropolis, A. Rosenbluth, M. Rosenbluth, Equation of State Calculations by Fast Computing Machines. J. Chem. Phys.1953,21(6):1087-1092.
[108]A. Z. Panagiotopoulos. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Mol. Phys.1987,61(4):813-826.
[109]B. Smit, S. Karaborni, J. L. Siepmann. Computer Simulations of Vapor-Liquid Phase Equilibria of n-Alkanes. J. Chem. Phys.1995,102(5):2126-2140.
[110]Y. Guissani, B. Guillot. A Computer Simulation Study of the Liquid-Vapor Coexistence Curve of Water. J. Chem. Phys.1993,98(10):8221-8235.
[111]J. M. Caillol. A Monte Carlo Study of the Liquid-Vapor Coexistence of Charged Hard Spheres. J. Chem. Phys.1994,100(3):2161-2169.
[112]V. Padmanabhan, S. K. Kumar, A. Yethiraj. Phase Behavior of Semiflexible Polymer Chains. J. Chem. Phys.2008,128(12):124908.
[113]A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar. Monte Carlo Simulations of Phase Equilibria for a Lattice Homopolymer Model. J. Chem. Phys.1995,102(2):1014-1024.
[114]J. J. de Pablo, J. M. Prausnitz. Phase Equilibria for Fluid Mixtures from Monte-Carlo Simulation. Fluid Phase Equilibria.1989,53:177-189.
[115]R. Khare, A. K. Sum, S. K. Nath, J. J. de Pablo. Simulation of Vapor-Liquid Phase Equilibria of Primary Alcohols and Alcohol-Alkane Mixtures. J. Phys. Chem. B 2004, 108(28):10071-10076.
[116]J. Vorholz, V. I. Harismiadis, B. Rumpf, A. Z. Panagiotopoulos, G. Maurer. Vapor+Liquid Equilibrium of Water, Carbon Dioxide, and the Binary System, Water+Carbon Dioxide, from Molecular Simulation. Fluid Phase Equilibria.2000,170(2):203-234.
[117]刘蓓,张现仁.MCM-41中混合势模型及简单流体吸附的巨正则Monte Carlo模拟. 计算机与应用化学,2004,21(5)：685-689.
[118]B. Smit. Grand Canonical Monte Carlo Simulations of Chain Molecules:Adsorption Isotherms of Alkanes in Zeolites. Mol. Phys.1995,85(1):153-172.
[119]曾余瑶,张秉坚.金属-有机骨架材料MOF-5的改进与吸附甲烷的巨正则蒙特卡罗模拟.物理化学学报,2008,24(8)：1493-1497.
[120]R. L. C. Vink, J. Horbach. Grand Canonical Monte Carlo Simulation of a Model Colloid-Polymer Mixture:Coexistence Line, Critical Behavior, and Interfacial Tension. J. Chem. Phys.121(7):3253-3258.
[121]P. J. Lenart, A. Z. Panagiotopoulos. Tracing the Critical Loci of Binary Fluid Mixtures Using Molecular Simulations. J. Phys. Chem. B 2006,110(34):17200-17206.
[122]J. J. Potoff, A. Z. Panagiotopoulos. Surface Tension of the Three-Dimensional Lennard-Jones Fluid from Histogram-Reweighting Monte Carlo Simulations. J. Chem. Phys. 112(14):6411-6415.
[123]D. J. Ashton, N. B. Wilding. Grand Canonical Simulation of Phase Behavior in Highly Size-Asymmetrical Binary Fluids.2011,109(7-10):999-1007.
[124]O. M. Suleimenov, A. Z. Panagiotopoulos, T. M. Seward. Grand Canonical Monte Carlo Simulations of Phase Equilibria of Pure Silicon Tetrachloride and Its Binary Mixture with Carbon Dioxide. Mol. Phys.2003,101(21):3213-3221.
[125]A. M. Ferrenberg, R. H. Swendsen. New Monte Carlo Technique for Studying Phase Transitions. Phys. Rev. Lett.1988,61(23):2635-2638.
[126]A. M. Ferrenberg, R. H. Swendsen. Optimized Monte Carlo Data Analysis. Phys. Rev. Lett.1989,63(12):1195-1198.
[127]F. A. Escobedo, J. J. de Pablo. Expanded Grand Canonical and Gibbs Ensemble Monte Carlo Simulation of Polymers. J. Chem. Phys.1996,105(10):4391-4394.
[128]M. Fitzgerald, R. R. Picard, R. N. Silver. Canonical Transition Probabilities for Adaptive Metropolis Simulation. Europhys. Lett.1999,46(3):282-287.
[129]M. Fitzgerald, R. R. Picard, R. N. Silver. Monte Carlo Transition Dynamics and Variance Reduction. J. Stat. Phys.2000,98(1/2):321-345.
[130]J. R. Errington. Direct Calculation of Liquid-Vapor Phase Equilibria from Transition Matrix Monte Carlo Simulation. J. Chem. Phys.2003,118(22):9915-9925.
[131]J. K. Singh, J. R. Errington. Calculation of Phase Coexistence Properties and Surface Tensions of n-Alkanes with Grand-Canonical Transition-Matrix Monte Carlo Simulation and Finite-Size Scaling. J. Phys. Chem. B,2006,110(3):1369-1376.
[132]E. M. Grzelak, J. R. Errington. Computation of Interfacial Properties via Grand Canonical Transition Matrix Monte Carlo Simulation. J. Chem. Phys.128(1):014710.
[133]V. K. Shen, J. R. Errington. Determination of Fluid Phase Behavior Using Transition-Matrix Monte Carlo:Binary Lennard-Jones Mixtures. J. Chem. Phys.2005,122(6): 064508.
[134]F. del Rio, E. Avalos, R. Espindola, L. F. Rull, G. Jackson, S. Lago. Vapour-Liquid Equilibrium of the Square-Well Fluid of Variable Range via a Hybrid Simulation Approach. Mol. Phys.2002,100(15):2531-2546.
[135]D. A. de Lonngi, F. del Rio, Square-Well Perturbation Theory for the Structure of Simple Fluids. Mol. Phys.1985,56(3):691-700.
[136]M. G Noro, D. Frenkel, Extended Corresponding-States Behavior for Particles with Variable Range Attractions. J. Chem. Phys.2000,113(8):2941-2944.
[137]N. Asherie, A. Lomakin, G B.Benedek. Phase Diagram of Colloidal Solutions. Phys. Rev. Lett.1996,77(23):4832-4835.
[138]A. L. Benavides, A. Gil-Villegas. The Thermodynamics of Molecules with Discrete Potentials. Mol. Phys.2001,97(12):1225-1232.
[139]M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, New York:1989.
[140]Frenkel&Smith著,汪文川等译,分子模拟—从算法到应用.化学工业出版社,北京：2002.
[141]I. R. McDonald, K. Singer, Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures. J. Chem. Phys.1967,47(11):4766-4772.
[142]W. W. Wood. Monte Carlo Calculations for Hard Disks in the Isothermal-Isobaric Ensemble. J. Chem. Phys.1968,48(1):415-434.
[143]D. N. Card, J. P. Valleau, Monte Carlo Study of the Thermodynamics of Electrolyte Solutions, J. Chem. Phys.1970,52(12):6232-6240.
[144]Z. W. Salsburg, J. D. Jackson, W. Fickett, W. W. Wood. Application of the Monte Carlo Method to the Lattice-Gas Model. I. Two-Dimensional Triangular Lattice. J. Chem. Phys. 1959,30(1):65-72.
[145]G. Bhanot, S. Black, P. Carter, R. Salvador, A New Method for the Partition Function of Discrete Systems with Application to the 3D Ising Model. Phys. Lett. B,1987,183(3-4): 331-336.
[146]G. Bhanot, K. M. Bitar, S. Black, P. Carter, R. Salvador, The Partition Function of Z(2) and Z(8) Lattice Gauge Theory in Four Dimensions, a Novel Approach to Simulations of Lattice Systems. Phys. Lett. B,1987,187(3-4):381-386.
[147]G. Bhanot, K. M. Bitar, R. Salvador, On Solving Four-Demensional SU(2) Gauge by Numerically Finding Its Partition Function. Phys. Lett. B,1987,188(2):246-252.
[148]A. M. Ferrenberg, D. P. Landau, Critical Behavior of the Three-Dimensional Ising Model:A High-Resolution Monte Carlo Study. Phys. Rev. B,1991,44(10):5081-5091.
[149]B. A. Berg, T. Neuhaus, Multicanonical Ensemble:A New Approach to Simulate First-Order Phase Transitions. Phys. Rev. Lett.1992,68(1):9-12.
[150]J. J. Potoff, A. Z. Panagiotopoulos, Critical Point and Phase Behavior of the Pure Fluid and a Lennard-Jones Mixture. J. Chem. Phys.1998,109(24):10914-10920.
[151]G C. Boulougouris, L. D. Persteras, I. G Economou, D. N. Theodorou, Predicting Fluid Phase Equilibrium via Histogram Reweighting with Gibbs Ensemble Monte Carlo Simulations. J. Supercritical Fluids,2010,55(2):503-509.
[152]N. B. Wilding, P. Sollich, Grand Canonical Ensemble Simulation Studies of Polydisperse Fluids. J. Chem. Phys.2002,116(16):7116-7126.
[153]P. B. Conrad, J. J. de Pablo, Comparison of Histogram Reweighting Techniques for a Flexible Water Model. Fluid Phase Equilibria,1998,150-151:51-61.
[154]J. J. de Pablo, Q. L. Yan, F. A. Escobedo, Simulation of Phase Transitions in Fluids. Annu. Rev. Phys. Chem.1999,50:377-411.
[155]N. B. Wilding. Computer Simulation of Fluid Phase Transition. Am. J. Phys.2001, 69(11):1147-1157.
[156]J. J. de Pablo, M. Laso, U. W. Suter, Simulation of Polyethylene Above and Below the Melting Point. J. Chem. Phys.1992,96(3):2395-2403.
[157]J. J. de Pablo, M. Laso, U. W. Suter, Estimation of the Chemical Potential of Chain Molecules by Simulation. J. Chem. Phys.1992,96(8):6157-6162.
[158]D. Frenkel, G C. A. M. Mooij, B. Smit, Novel Scheme to Study Structural and Thermal Properties of Continuously Deformable Molecules. J. Phys. Condens. Matt.1992,4(12): 3053-3076.
[159]Q. L. Yan, J. J. de Pablo, Hyper Parallel Tempering Monte Carlo:Application to the Lennard-Jones Fluid and the Restricted Primitive Model. J. Chem. Phys.1999,111(21): 9509-9516.
[160]Q. L. Yan, J. J. de Pablo, Hyper Parallel Tempering Monte Carlo Simulation of Polymeric Systems. J. Chem. Phys.2000,113(3):1276-1282.
[161]M. S. Wertheim, Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics. J. Stat. Phys.1984,35(1-2):19-34.
[162]M. S. Wertheim, Thermodynamic Perturbation Theory of Polymerization. J. Chem. Phys.1987,87(12):7323-7331.
[163]A. G. Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, A. N. Burgess, Statistical Associating Fluid Theory for Chain Molecules with Attractive Potentials of Variable Range. J. Chem. Phys.1997,106(10):4168-4186.
[164]M. J. Lee, C. McCabe, P. T. Cummings, Square-Well Chain Molecules:a Semi-Empirical Equation of State and Monte Carlo Simulation Data. Fluid Phase Equilibria. 2004,221 (1-2):63-72.
[165]A. Yethiraj, C. K. Hall. Sauare-well Diatomics:Bulk Equation of State, Density Profiles Near Walls, Virial Coefficients and Coexistence Properties. Mol. Phys,1991,72(3): 619-641.
[166]F. A. Escobedo, J. J. De Pablo, Simulation of Chain Molecules for Prediction of Thermodynamic Properties. Fluid Phase Equilibria.1996,116(1-2):312-319.
[167]J. J. de Pablo, Simulation of Phase Equilibria for Chain Molecules. Fluid Phase Equilibria.1995,104:195-206.
[168]J. K. Singh, D. A. Kofke, J. R. Errington. Surface Tension and Vapor-Liquid Phase Coexistence of the Square-Well Fluid. J. Chem. Phys.2003,119(6):3405-3412.
[169]M. M. Tsypin, H. W. J. Blote, Probability Distribution of the Order Parameter for the Three-Dimensional Ising-model Universality Class:A High-Precision Monte Carlo Study. Phys. Rev. E,2000,62(1):73-76.
[2]S. J. Blundell, M. K. Blundell. Concepts in Thermal Physics. Oxford University Press, 2008.
[3]D. Chandler, Introduction to Modern Statistical Mechanics. Oxford University Press, 1987.
[4]林宗涵,热力学与统计物理学,北京大学出版社,2007.
[5]B. Hayes. The World in a Spin. American Scientist,2000,88(5):384-388.
[6]张志东,伊辛模型的研究进展简介,自然杂志,2008,30(2)：94-101.
[7]S. G Brush. History of the Lenz-Ising Model. Rev. Mod. Phys.1967,39(4):883-893.
[8]R. K. Pathria, Statistical Mechanics,2nd Edtoan(英文影印版),世界图书出版公司,2001. [9] K. Christensen, N. R. Moloney, Complexity and Criticality(英文影印版),复旦大学出版社,2006.
[10]H. E. Stanley. Scaling, University, and Renormalization:Three pillars of Modern Critical Phenomena. Rev. Mod. Phys.1999,71(2):S358-S366.
[11]L. P. Kadanoff, W. Gotze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, J. Swift, Static Phenomena Near Critical Points:Theory and Experiment. Rev. Mod. Phys.1967,39(2):395-430.
[12]M. E. Fisher, The Theory of Equilibrium Critical Phenomena. Rep. Prog. Phys.1967, 30(2):615-730.
[13]A. Pelissetto, E. Vicari, Critical Phenomena and Renormalization-Group Theory. Phys. Rep.,2002,368(6):549-727.
[14]K. G Wilson, Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture. Phys. Rev. B,1971,4(9):3174-3183
[15]K. G Wilson, Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior. Phys. Rev. B,1971,4(9):3184-3205.
[16]T. D. Lee, C. N. Yang, Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model. Phys. Rev.1952,87(3):410-419.
[17]Simon Reif-Acherman. The History of the Rectilinear Diameter Law. Quim. Nova.2010, 33(9):2003-2010.
[18]N. D. Mermin, J. J. Rehr, Generality of the Singular Diameter of the Liquid-Vapor Coexistence Curve. Phys. Rev. Lett.,1971,26(19):1155-1156.
[19]J. J. Rehr, N. D. Mermin, Revised Scaling Equation of State at Liquid-Vapor Critical Point. Phys. Rev. A,1973,8(1):472-480.
[20]Y. C. Kim, M. E. Fisher, G. Orkoulas, Asymmetric Fluid Criticality. I. Scaling with Pressure Mixing. Phys. Rev. E,2003,67(06):061506.
[21]J. Weiner, K. H. Langley, N. C. Ford, Experimental Evidence for a Departure from the Law of the Rectilinear Diameter. Phys. Rev. Lett.1974,32(16):879-881.
[22]C. N. Yang, C. P. Yang. Critical Point in Liquid-Gas Translations. Phys. Rev. Lett.1964, 13(9):303-305.
[23]G. Orkoulas, M. E. Fisher, C. Ustun, The Yang-Yang Relation and the Specific Heats of Propane and Carbon Dioxide. J. Chem. Phys.2000,113(12):7530-7545.
[24]G. Orkoulas, M. E. Fisher, A. Z. Panagiotopoulos, Precise Simulation of Criticality in Asymmetric Fluids. Phys. Rev. E,2001,63(05):051507.
[25]F. J. egner, Corrections to Scaling Law. Phys. Rev. B,1972,5(11):4529-4536.
[26]M. E. Fisher, G Orkoulas, The Yang-Yang Anomaly in Fluid Criticality:Experiment and Scaling Theory. Phys. Rev. Lett.,2000,85(4):696-699.
[27]M. A. Anisimov, J. T. Wang, Nature of Asymmetry in Fluid Criticality. Phys. Rev. Lett. 2006,97(02):025703.
[28]J. T. Wang, M. A. Anisimov, Nature of Vapor-Liquid Asymmetry in Fluid Criticality. 2007,75(05):051107.
[29]C. E. Bertrand, M. A. Anisimov, Complete Scaling for Inhomogeneous Fluids. Phys. Rev. Lett.2010,104(20):205702.
[30]M. A. Anisimov, Phys. Rev. Lett. Divergence of Tolman's Length for a Droplet Near the Critical Point.2007,98(3):035702.
[31]C. E. Bertrand, J. V. Sengers, M. A. Anisimov, Critical Behavior of the Dielectric Constant in Asymmetric Fluids. J. Phys. Chem. B,2011,115(48):14000-14007.
[32]P. L. Perez, G P. Sanchez, C. A. Cerdeirina, J. Thoen, Dielectric Constant of Fluids and Fluid Mixtures at Criticality. Phys. Rev. E,2010,81(4):041121.
[33]I. M. Abdulagatov, N. G Polikhronidi, T. J. Bruno, R. G. Batyrova, G V. Sepanov. Measurements of the Isochoric Heat Capacity, the Critical Point (Tc, pc) and Vapor-Liquid Coexistence Curve (Ts, ps) of High-Purity Toluene Near the Critical Point. Fluid Phase Equilibria.2008,263(1):71-84.
[34]L. M. Radzhabova, G. V. Stepanov, I. M. Abdulagatov, K. A. Shakhbanov. Experimental Study of the Isochoric Heat Capacity and Coexistence-Curve Singular Diameter of sec-Butanol Near the Critical Point and Yang-Yang Anomaly Strength. Phys. Chem. Liq.2013, 51(1):75-101.
[35]M. A. Anisimov, F. Zhong, M. Barmatz. Resolving the Yang-Yang Dilemma in 3He Near the Critical Point. J. Low Temp.2004,137(1-2):69-88.
[36]C. A. Cerdeirina, M. A. Anisimov, J. V. Sengers. The Nature of Singular Coexistence-Curve Diameters of Liquid-Liquid Equilibria. Chem. Phys. Lett.2006,424(4-6): 414-419.
[37]J. T. Wang, C. A. Cerdeirina, M. A. Anisimov, J. V. Sengers, Principle of Isomorphism and Complete Scaling for Binary-Fluid Criticality. Phys. Rev. E,2008,77(03):031127.
[38]G. P. Sanchez, P. L. Perez, C. A. Cerdeirina, J. V. Sengers, M. A. Anisimov. Asymmetric Criticality in Weakly Compressible Liquid Mixtures. J. Chem. Phys.2010,132(15):154502.
[39]J. Leys, P. L. Perez, G Cordoyiannis, C. A. Cerdeirina, C. Glorieux, J. Thoen. Temperature, Concentration, and Frequency Dependence of the Dielectric Constant Near the Critical Point of the Binary Liquid Mixture Nitrobenzene-Tetradecane. J. Chem. Phys.2010, 132(10):104508.
[40]P. L. Perez, C. S. P. Tripathi, J. Leys, C. A. Cerdeirina, C. Glorieux, J. Thoen. The Yang-Yang Anomaly in Liquid-Liquid Criticality:Experimental Evidence from Adiabatic Scanning Calorimetry. Chem. Phys. Lett.2012,523:69-73.
[41]T. X. Yin, S. X. Liu, J. J. Xie, W. G. Shen. Asymmetric Criticality of the Osmotic Compressibility in Binary Mixtures. J. Chem. Phys.2013,138(2):024504.
[42]C. E. Bertrand, J. F. Nicoll, M. A. Anisimov, Comparison of Complete Scaling and a Field-Theoretic Treatment of Asymmetric Fluid Criticality. Phys. Rev. E,2012,85(3): 031131.
[43]M. A. Anisimov, Universality versus Nonuniversality in Asymmetric Fluid Criticality. Cond. Matt. Phys.,2013,16(2):23603:1-10.
[44]V. K. Kulinskii, N. P. Malomuzh, The Nature of the Rectilinear Diameter Singularity. Phys. A,2007,388(5):621-627.
[45]K. Binder. Finite Size Effects on Phase Transitions. Ferroelectrics,1987,73(1):43-67.
[46]M. E Fisher, A. E. Ferdinand, Interfacial, Boundary, and Size Effects at Critical Points. Phys. Rev. Lett.1967,19(4):169-172.
[47]M. E. Fisher, Critical Phenomena. Academic Press,1971.
[48]V. Privman, Finite Size Scaling and the Numerical Simulation of Statiscal Systems. World Scientific, Singapore,1990.
[49]M. E. Fisher, M. N. Barber. Scaling Theory for Finite-Size Effects in the Critical Region. Phys. Rev. Lett.1972,28(3):1516-1519.
[50]V. Privman, M. E. Fisher. Convergence of Finite-Size Scaling Renormalization. J. Phys. A:Math. Gen.1983,16(9):L295-L301.
[51]J. G. Brankov, D. M. Danchev, N. S. Tonchev. Theory of Critical Phenomena in Finite-Size System:Scaling and Quantum Effects. World Scientific, Singapore,2000.
[52]D. P. Landau, K. Binder. A Guide to Monte Carlo Simulations in Statistical Physics,3rd. Cambridge University Press, Cambridge,2009.
[53]K. Binder. Computer Simulations of Critical Phenomena and Phase Behavior of Fluids. Mol. Phys,2010,108(14):1797-1815.
[54]K. Binder. Finite Size Scaling Analysis of Ising Model Block Distribution Functions. Z. Phys. B:Condens. Matter,1981,43(2):119-140.
[55]K. Binder, Computational Methods in Field Theory, Springer, Berlin,1992.
[56]L. Vega, E. de Miguel, L. F. Rull. Phase Equilibria and Critical Behavior of Square-Well Fluids of Variable Width by Gibbs Ensemble Monte Carlo Simulation. J. Chem. Phys.1992, 96(3):2296-2305.
[57]F. A. Escobedo, J. J. de Pablo. Simulation and Prediction of Vapour-Liquid Equilibria for Chain Molecules. Mol. Phys.1996,87(2):347-366.
[58]J. R. Elliott, L. Hu. Vapor-Liquid Equilibria of Square-Well Spheres. J. Chem. Phys. 1999,110(6):3043-3048.
[59]J. J. de Pablo, J. M. Prausnitz, H. J. Strauch, P. T. Cummings, Molecular Simulation of Water along the Liquid-Vapor Coexistence Curve from 25℃ to the Critical Point. J. Chem. Phys.1990,93(10):7355-7359.
[60]D. G Green, G Jackson, E. de Miguel, L. F. Rull. Vapor-Liquid and Liquid-Liquid Phase Equilibria of Mixtures Containing Square-Well Molecules by Gibbs Ensemble Monte Carlo Simulation. J. Chem. Phys.1994,101(4):3190-3204.
[61]N. B. Wilding, A. D. Bruce. Density Fluctuations and Field Mixing in the Critical Fluid. J. Phys. Condens. Matter.1992,4(12):3087-3108.
[62]A. D. Bruce, N. B. Wilding, Scaling Fields and Universality of the Liquid-Gas Critical Point. Phys. Rev. Lett.1992,68(2):193-196.
[63]N. B. Wilding, M. Muller, Liquid-Vapor Asymmetry in Pure Fluids:A Monte Carlo Study. J. Chem. Phys.1995,102(6):2562-2573.
[64]N. B. Wilding. Critical-Point and Coexistence-Curve Properties of the Lennard-Jones Fluid:A Finite-Size Scaling Study. Phys. Rev. E,1995,52(1):602-611.
[65]Q. L. Yan, J. J. de Pablo, Phase Equilibria of Size-Asymmetric Primitive Model Electrolytes. Phys. Lett.2001,86(10):2054-2057.
[66]J. P. Pellitero, P. Ungerer, G. Orkoulas, A. D. Mackie, Critical Point Estimation of the Lennard-Jones Pure Fluid and Binary Mixtures. J. Chem. Phys.2006,125(5):054515.
[67]A. Z. Panagiotopoulos, Critical Parameters of the Restricted Primitive Model. J. Chem. Phys.2002,116(7):3007-3011.
[68]P. J. Camp, G. N. Patey, Coexistence and Criticality of Liquids with Long-Range Potentials. J. Chem. Phys.2001,114(1):399-408.
[69]J. M. Caillol, D. Levesque, J. J. Weis, Critical Behavior of the Restricted Primitive Model Revisted. J. Chem. Phys.2002,116(24):10794-10800.
[70]S. Moghaddam, A. Z. Panagiotopoulos, Lattice Discretization Effects on the Critical Parameters of Model Nonpolar and Polar Fluids. J. Chem. Phys.2003,118(16):7556-7561.
[71]Y. C. Kim, M. E. Fisher. Fluid Critical Points from Simulations:The Bruce-Wilding Method and Yang-Yang Anomalies. J. Phys. Chem. B,2004,108(21):6750-6759.
[72]E. Luijten, M. E. fisher, A. Z. Panagiotopoulos. Universality Class of Criticality in the Restricted Primitive Model Electrolyte. Phys. Rev. Lett.2002,88(18):185701.
[73]Y. C. Kim, M. E. Fisher, Asymmetric Fluid Criticality. Ⅱ. Finite-size Scaling for Simulation. Phys. Rev. E,2003,68(4):041506.
[74]Y. C. Kim, M. E. Fisher, E. Luijten, Precise Simulation of Near-Critical Fluid Coexistence. Phys. Rev. Lett.,2003,91(6):065701.
[75]Y. C. Kim, M. E. Fisher, Fluid Coexistence Close to Criticality:Scaling Algorithms for Precise Simulation. Comput. Phys. Commun.2005,169:295-300.
[76]Y. C. Kim, Yang-Yang Anomalies and Coexistence Diameters:Simulation of Asymmetric Fluids. Phys. Rev. E,2005,71(5):051501.
[77]Y. C. Kim, M. E. Fisher. Singular Coexistence-Curve Diameters:Experiments and Simulations. Chem. Phys. Lett.2005,414(1-3):185-192.
[78]R. L. C. Vink, H. H. Wensink. Coexistence Diameter in Two-Dimensional Colloid-Polymer Mixtures. Phys. Rev. E,2006,74(1):010102(R).
[79]R. L. C. Vink, Critical Behavior of a Colloid-Polymer Mixture Confined between Walls, Phys. Rev. E,2006,73(5):056118.
[80]R. L. C. Vink, A. D. Virgiliis, J. Forbach, K. Binder, Phase Diagram and Structure of Colloid-Polymer Mixtures Confined between Walls. Phys. Rev. E,2006,74(3):031601.
[81]F. L. Verso, R. L. C. Vink, D. Pini, L. Reatto, Critical Behavior in Colloid-Polymer Mixtures:Theory and Simulations. Phys. Rev. E,2006,73(6):061407.
[82]R. L. C. Vink, T. Neuhaus, H. Lowen. Fluid Phase Separation inside a Static Periodic Field:An Effectively Two-Dimensional Critical Phenomenon. J. Chem. Phys.2011,134(20): 204907.
[83]R. L. C. Vink. Critical Behavior of the Widom-Rowlinson Mixture:Coexostence Diameter and Order Paremeter. J. Chem. Phys.2006,124(09):094502.
[84]R. C. Ren, C. J. O'Keeffe, G. Orkoulas. Scaling Fields of Pressure Mixing in the Widom-Rowlinson Model. J. Chem. Phys.2006,125(14):144505.
[85]Y. C. Kim, M. E. Fisher, A. Z. Panagiotopoulos. Universality of Ionic Criticality:Size-and Charge-Asymmetric Electrolytes. Phys. Rev. Lett.2005,95(19):195703.
[86]J. P. Pellitero, P. Ungerer, A. D. Mackie. Near Critical Coexistence for an AUA Model of Thiophenes. Rev. IFP.2008,63(3):277-282.
[87]M. Nayhouse, A. M. Amlani, G. Orkoulas. Precise Simulation of the Freezing Transition of Supercritical Lennard-Jones. J. Chem. Phys.2011,135(15):154103.
[88]M. Nayhouse, A. M. Amlani, V. R. Heng, G. Orkoulas. Simulation of Fluid-Solid Coexistence via Thermodynamic Intrgration Using a Modified Cell Model. J. Phys:Condens. Matter,2012,24(15):155101.
[89]J. M. Prausnitz, R. N. Lichtenthaler, E. G de Azevedo. Molecular Thermodynamics of Fluid-Phase Equilibria,3rd ed. Prentice-Hall, Upper Saddle River, NJ,1999.
[90]G Orkoulas, A. Z. Panagiotopoulos. Phase Behavior of the Restricted Primitive Model and Square-Well Fluids from Monte Carlo Simulations in the Grand Canonical Ensemble. J. chem. Phys.1999,110(3):1581-1590.
[91]D. L. Pagan, J. D. Gunton. Phase Behavior of Short-Range Square-Well Model. J. Chem. Phys.2005,122(18):184515.
[92]E. de Miguel. Critical Behavior of the Square-Well Fluid with X=2:A Finite-Size Study. Phys. Rev. E,1997,55(2):1347-1354.
[93]L.A. Davies, A. G Villegas, G. Jackson. Phase Equilibria of a Square-Well Monomer-Dimer Mixture:Gibbs Ensemble Computer Simulation and Statistical Associating Fluid Theory for Potentials of Variable Range. Phys. Rev. E,1998,57(2):2035-2044.
[94]J. Y. Cui, J. R. Elliott. Phase Envelopes for Variable Width Square-Well Chain Fluids. J. Chem. Phys.2001,114(16):7283-7290.
[95]S. B. Kiselev, J. f. Ely, J. R. Eliott. Molecular Dynamic Simulations and Global Equation of State of Square-Well Fluids with the Well-Widths from λ=1.1 to 2.1. Mol. Phys.104(15): 2545-2559.
[96]E. S. Paschinger, A. L. Benavides, R. Castanedapriego. Vapor-Liquid Equilibrium and Critical Behavior of the Square-Well Fluid of Variable Range:A Theoretical Study. J. Chem. Phys.2005,123(23):234513.
[97]A. G. Villegas, A. Galindo, P. J. Whitehead, S. J. Mills. G Jackson, A. N. Burgess. Statistical Associating Fluid Theory for Chain Molecules with Attractive Potentials of Variable Range. J. Chem. Phys.1997,106(10):4168-4186.
[98]J. W. Jiang, J. M. Prausnitz, Equation of State for Thermodynamic Properties of Chain Fluids Near-to and Far-from the Vapor-Liquid Critical Region. J. Chem. Phys.1999,111(13): 5964-5974.
[99]A. Galindo, L. A. Davies, A. Gil-Villegas, G. Jackson. The Thermodynamics of Mixtures and the Corresponding Mixing Rules in the SAFT-VR Approach for Potentials of Variable Range. Mol. Phys.1998,93(2):241-252.
[100]J. L. Li, H. H. He, C. J. Peng, H. L. Liu, Y. Hu. A New Development of Equation of State for Square-Well Chain-Like Molecules with Variable Width 1.1
[102]E. Forte, F. Llovell, L. F. Vega, J. P. M. Trusler, A. Galindo, Application of a Renormalization-Group Treatment to the Statistical Associating Fluid Theory for Potentials of Variable Range(SAFT-VR). J. Chem. Phys.2011,134(15):154102.
[103]W. Zhao, L. Wu, L. Wang, L. Y. Li, J. Cai. Critical Asymmetry in Renormalization Group Theory for Fluids. J. Chem. Phys.2013,138(23):234502.
[104]L. Wang, W. Zhao. L. Wu, L. Y. Li, J. Cai. Improved Renormalization Group Theory for Critical Asymmetry of Fluids. J. Chem. Phys.2013,139(12):124103.
[105]A. Z. Panagiotopoulos. Monte Carlo Methods for Phase Equilibria of Fluids. J. Phys.: Condens. Matter.2000,12(3):R25-R52.
[106]N. Metropolis. The Beginning of the Monte Carlo Method. Los Alamos Science.1987, 12(Special Issue):125-130.
[107]N. Metropolis, A. Rosenbluth, M. Rosenbluth, Equation of State Calculations by Fast Computing Machines. J. Chem. Phys.1953,21(6):1087-1092.
[108]A. Z. Panagiotopoulos. Direct Determination of Phase Coexistence Properties of Fluids by Monte Carlo Simulation in a New Ensemble. Mol. Phys.1987,61(4):813-826.
[109]B. Smit, S. Karaborni, J. L. Siepmann. Computer Simulations of Vapor-Liquid Phase Equilibria of n-Alkanes. J. Chem. Phys.1995,102(5):2126-2140.
[110]Y. Guissani, B. Guillot. A Computer Simulation Study of the Liquid-Vapor Coexistence Curve of Water. J. Chem. Phys.1993,98(10):8221-8235.
[111]J. M. Caillol. A Monte Carlo Study of the Liquid-Vapor Coexistence of Charged Hard Spheres. J. Chem. Phys.1994,100(3):2161-2169.
[112]V. Padmanabhan, S. K. Kumar, A. Yethiraj. Phase Behavior of Semiflexible Polymer Chains. J. Chem. Phys.2008,128(12):124908.
[113]A. D. Mackie, A. Z. Panagiotopoulos, S. K. Kumar. Monte Carlo Simulations of Phase Equilibria for a Lattice Homopolymer Model. J. Chem. Phys.1995,102(2):1014-1024.
[114]J. J. de Pablo, J. M. Prausnitz. Phase Equilibria for Fluid Mixtures from Monte-Carlo Simulation. Fluid Phase Equilibria.1989,53:177-189.
[115]R. Khare, A. K. Sum, S. K. Nath, J. J. de Pablo. Simulation of Vapor-Liquid Phase Equilibria of Primary Alcohols and Alcohol-Alkane Mixtures. J. Phys. Chem. B 2004, 108(28):10071-10076.
[116]J. Vorholz, V. I. Harismiadis, B. Rumpf, A. Z. Panagiotopoulos, G. Maurer. Vapor+Liquid Equilibrium of Water, Carbon Dioxide, and the Binary System, Water+Carbon Dioxide, from Molecular Simulation. Fluid Phase Equilibria.2000,170(2):203-234.
[117]刘蓓,张现仁.MCM-41中混合势模型及简单流体吸附的巨正则Monte Carlo模拟. 计算机与应用化学,2004,21(5)：685-689.
[118]B. Smit. Grand Canonical Monte Carlo Simulations of Chain Molecules:Adsorption Isotherms of Alkanes in Zeolites. Mol. Phys.1995,85(1):153-172.
[119]曾余瑶,张秉坚.金属-有机骨架材料MOF-5的改进与吸附甲烷的巨正则蒙特卡罗模拟.物理化学学报,2008,24(8)：1493-1497.
[120]R. L. C. Vink, J. Horbach. Grand Canonical Monte Carlo Simulation of a Model Colloid-Polymer Mixture:Coexistence Line, Critical Behavior, and Interfacial Tension. J. Chem. Phys.121(7):3253-3258.
[121]P. J. Lenart, A. Z. Panagiotopoulos. Tracing the Critical Loci of Binary Fluid Mixtures Using Molecular Simulations. J. Phys. Chem. B 2006,110(34):17200-17206.
[122]J. J. Potoff, A. Z. Panagiotopoulos. Surface Tension of the Three-Dimensional Lennard-Jones Fluid from Histogram-Reweighting Monte Carlo Simulations. J. Chem. Phys. 112(14):6411-6415.
[123]D. J. Ashton, N. B. Wilding. Grand Canonical Simulation of Phase Behavior in Highly Size-Asymmetrical Binary Fluids.2011,109(7-10):999-1007.
[124]O. M. Suleimenov, A. Z. Panagiotopoulos, T. M. Seward. Grand Canonical Monte Carlo Simulations of Phase Equilibria of Pure Silicon Tetrachloride and Its Binary Mixture with Carbon Dioxide. Mol. Phys.2003,101(21):3213-3221.
[125]A. M. Ferrenberg, R. H. Swendsen. New Monte Carlo Technique for Studying Phase Transitions. Phys. Rev. Lett.1988,61(23):2635-2638.
[126]A. M. Ferrenberg, R. H. Swendsen. Optimized Monte Carlo Data Analysis. Phys. Rev. Lett.1989,63(12):1195-1198.
[127]F. A. Escobedo, J. J. de Pablo. Expanded Grand Canonical and Gibbs Ensemble Monte Carlo Simulation of Polymers. J. Chem. Phys.1996,105(10):4391-4394.
[128]M. Fitzgerald, R. R. Picard, R. N. Silver. Canonical Transition Probabilities for Adaptive Metropolis Simulation. Europhys. Lett.1999,46(3):282-287.
[129]M. Fitzgerald, R. R. Picard, R. N. Silver. Monte Carlo Transition Dynamics and Variance Reduction. J. Stat. Phys.2000,98(1/2):321-345.
[130]J. R. Errington. Direct Calculation of Liquid-Vapor Phase Equilibria from Transition Matrix Monte Carlo Simulation. J. Chem. Phys.2003,118(22):9915-9925.
[131]J. K. Singh, J. R. Errington. Calculation of Phase Coexistence Properties and Surface Tensions of n-Alkanes with Grand-Canonical Transition-Matrix Monte Carlo Simulation and Finite-Size Scaling. J. Phys. Chem. B,2006,110(3):1369-1376.
[132]E. M. Grzelak, J. R. Errington. Computation of Interfacial Properties via Grand Canonical Transition Matrix Monte Carlo Simulation. J. Chem. Phys.128(1):014710.
[133]V. K. Shen, J. R. Errington. Determination of Fluid Phase Behavior Using Transition-Matrix Monte Carlo:Binary Lennard-Jones Mixtures. J. Chem. Phys.2005,122(6): 064508.
[134]F. del Rio, E. Avalos, R. Espindola, L. F. Rull, G. Jackson, S. Lago. Vapour-Liquid Equilibrium of the Square-Well Fluid of Variable Range via a Hybrid Simulation Approach. Mol. Phys.2002,100(15):2531-2546.
[135]D. A. de Lonngi, F. del Rio, Square-Well Perturbation Theory for the Structure of Simple Fluids. Mol. Phys.1985,56(3):691-700.
[136]M. G Noro, D. Frenkel, Extended Corresponding-States Behavior for Particles with Variable Range Attractions. J. Chem. Phys.2000,113(8):2941-2944.
[137]N. Asherie, A. Lomakin, G B.Benedek. Phase Diagram of Colloidal Solutions. Phys. Rev. Lett.1996,77(23):4832-4835.
[138]A. L. Benavides, A. Gil-Villegas. The Thermodynamics of Molecules with Discrete Potentials. Mol. Phys.2001,97(12):1225-1232.
[139]M. P. Allen, D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, New York:1989.
[140]Frenkel&Smith著,汪文川等译,分子模拟—从算法到应用.化学工业出版社,北京：2002.
[141]I. R. McDonald, K. Singer, Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures. J. Chem. Phys.1967,47(11):4766-4772.
[142]W. W. Wood. Monte Carlo Calculations for Hard Disks in the Isothermal-Isobaric Ensemble. J. Chem. Phys.1968,48(1):415-434.
[143]D. N. Card, J. P. Valleau, Monte Carlo Study of the Thermodynamics of Electrolyte Solutions, J. Chem. Phys.1970,52(12):6232-6240.
[144]Z. W. Salsburg, J. D. Jackson, W. Fickett, W. W. Wood. Application of the Monte Carlo Method to the Lattice-Gas Model. I. Two-Dimensional Triangular Lattice. J. Chem. Phys. 1959,30(1):65-72.
[145]G. Bhanot, S. Black, P. Carter, R. Salvador, A New Method for the Partition Function of Discrete Systems with Application to the 3D Ising Model. Phys. Lett. B,1987,183(3-4): 331-336.
[146]G. Bhanot, K. M. Bitar, S. Black, P. Carter, R. Salvador, The Partition Function of Z(2) and Z(8) Lattice Gauge Theory in Four Dimensions, a Novel Approach to Simulations of Lattice Systems. Phys. Lett. B,1987,187(3-4):381-386.
[147]G. Bhanot, K. M. Bitar, R. Salvador, On Solving Four-Demensional SU(2) Gauge by Numerically Finding Its Partition Function. Phys. Lett. B,1987,188(2):246-252.
[148]A. M. Ferrenberg, D. P. Landau, Critical Behavior of the Three-Dimensional Ising Model:A High-Resolution Monte Carlo Study. Phys. Rev. B,1991,44(10):5081-5091.
[149]B. A. Berg, T. Neuhaus, Multicanonical Ensemble:A New Approach to Simulate First-Order Phase Transitions. Phys. Rev. Lett.1992,68(1):9-12.
[150]J. J. Potoff, A. Z. Panagiotopoulos, Critical Point and Phase Behavior of the Pure Fluid and a Lennard-Jones Mixture. J. Chem. Phys.1998,109(24):10914-10920.
[151]G C. Boulougouris, L. D. Persteras, I. G Economou, D. N. Theodorou, Predicting Fluid Phase Equilibrium via Histogram Reweighting with Gibbs Ensemble Monte Carlo Simulations. J. Supercritical Fluids,2010,55(2):503-509.
[152]N. B. Wilding, P. Sollich, Grand Canonical Ensemble Simulation Studies of Polydisperse Fluids. J. Chem. Phys.2002,116(16):7116-7126.
[153]P. B. Conrad, J. J. de Pablo, Comparison of Histogram Reweighting Techniques for a Flexible Water Model. Fluid Phase Equilibria,1998,150-151:51-61.
[154]J. J. de Pablo, Q. L. Yan, F. A. Escobedo, Simulation of Phase Transitions in Fluids. Annu. Rev. Phys. Chem.1999,50:377-411.
[155]N. B. Wilding. Computer Simulation of Fluid Phase Transition. Am. J. Phys.2001, 69(11):1147-1157.
[156]J. J. de Pablo, M. Laso, U. W. Suter, Simulation of Polyethylene Above and Below the Melting Point. J. Chem. Phys.1992,96(3):2395-2403.
[157]J. J. de Pablo, M. Laso, U. W. Suter, Estimation of the Chemical Potential of Chain Molecules by Simulation. J. Chem. Phys.1992,96(8):6157-6162.
[158]D. Frenkel, G C. A. M. Mooij, B. Smit, Novel Scheme to Study Structural and Thermal Properties of Continuously Deformable Molecules. J. Phys. Condens. Matt.1992,4(12): 3053-3076.
[159]Q. L. Yan, J. J. de Pablo, Hyper Parallel Tempering Monte Carlo:Application to the Lennard-Jones Fluid and the Restricted Primitive Model. J. Chem. Phys.1999,111(21): 9509-9516.
[160]Q. L. Yan, J. J. de Pablo, Hyper Parallel Tempering Monte Carlo Simulation of Polymeric Systems. J. Chem. Phys.2000,113(3):1276-1282.
[161]M. S. Wertheim, Fluids with Highly Directional Attractive Forces. I. Statistical Thermodynamics. J. Stat. Phys.1984,35(1-2):19-34.
[162]M. S. Wertheim, Thermodynamic Perturbation Theory of Polymerization. J. Chem. Phys.1987,87(12):7323-7331.
[163]A. G. Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, A. N. Burgess, Statistical Associating Fluid Theory for Chain Molecules with Attractive Potentials of Variable Range. J. Chem. Phys.1997,106(10):4168-4186.
[164]M. J. Lee, C. McCabe, P. T. Cummings, Square-Well Chain Molecules:a Semi-Empirical Equation of State and Monte Carlo Simulation Data. Fluid Phase Equilibria. 2004,221 (1-2):63-72.
[165]A. Yethiraj, C. K. Hall. Sauare-well Diatomics:Bulk Equation of State, Density Profiles Near Walls, Virial Coefficients and Coexistence Properties. Mol. Phys,1991,72(3): 619-641.
[166]F. A. Escobedo, J. J. De Pablo, Simulation of Chain Molecules for Prediction of Thermodynamic Properties. Fluid Phase Equilibria.1996,116(1-2):312-319.
[167]J. J. de Pablo, Simulation of Phase Equilibria for Chain Molecules. Fluid Phase Equilibria.1995,104:195-206.
[168]J. K. Singh, D. A. Kofke, J. R. Errington. Surface Tension and Vapor-Liquid Phase Coexistence of the Square-Well Fluid. J. Chem. Phys.2003,119(6):3405-3412.
[169]M. M. Tsypin, H. W. J. Blote, Probability Distribution of the Order Parameter for the Three-Dimensional Ising-model Universality Class:A High-Precision Monte Carlo Study. Phys. Rev. E,2000,62(1):73-76.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |