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Lee LL. A theory on the liquid structures of molecular dimers based on the BBGKY hierarchy: the direct correlation function. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2077257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Lloyd L. Lee
- Department of Chemical & Materials Engineering, California State Polytechnic University, Pomona, CA, USA
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Ploetz EA, Smith PE. Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for liquid mixtures. J Chem Phys 2015; 142:094504. [PMID: 25747091 PMCID: PMC4352168 DOI: 10.1063/1.4913514] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 02/12/2015] [Indexed: 11/15/2022] Open
Abstract
Kirkwood-Buff or Fluctuation Solution Theory can be used to provide experimental pair fluctuations, and/or integrals over the pair distribution functions, from experimental thermodynamic data on liquid mixtures. Here, this type of approach is used to provide triplet and quadruplet fluctuations, and the corresponding integrals over the triplet and quadruplet distribution functions, in a purely thermodynamic manner that avoids the use of structure factors. The approach is then applied to binary mixtures of water + methanol and benzene + methanol over the full composition range under ambient conditions. The observed correlations between the different species vary significantly with composition. The magnitude of the fluctuations and integrals appears to increase as the number of the most polar molecule involved in the fluctuation or integral also increases. A simple physical picture of the fluctuations is provided to help rationalize some of these variations.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
| | - Paul E Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
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Ploetz EA, Karunaweera S, Smith PE. Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids. J Chem Phys 2015; 142:044502. [PMID: 25637990 PMCID: PMC4312347 DOI: 10.1063/1.4905562] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Accepted: 12/22/2014] [Indexed: 11/14/2022] Open
Abstract
Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.
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Affiliation(s)
- Elizabeth A Ploetz
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
| | - Sadish Karunaweera
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
| | - Paul E Smith
- Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, USA
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Gögelein C, Romano F, Sciortino F, Giacometti A. Fluid-fluid and fluid-solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory. J Chem Phys 2012; 136:094512. [DOI: 10.1063/1.3689308] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Chandler D, Weeks JD, Andersen HC. Van der waals picture of liquids, solids, and phase transformations. Science 2010; 220:787-94. [PMID: 17834156 DOI: 10.1126/science.220.4599.787] [Citation(s) in RCA: 425] [Impact Index Per Article: 30.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.
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Affiliation(s)
- K.E. Gubbins
- a School of Chemical Engineering, Olin Hall, Cornell University , Ithaca , New York , 14853 , U.S.A
| | - C.G. Gray
- b Physics Department , University of Guelph , Guelph , Ontario , Canada
| | - P.A. Egelstaff
- b Physics Department , University of Guelph , Guelph , Ontario , Canada
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Hamad EZ, Mansoori GA, Ely JF. Conformality in the Kirkwood–Buff solution theory of statistical mechanics. J Chem Phys 1987. [DOI: 10.1063/1.452743] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Kato T, Fujiyama T, Nomura H. Estimation of Parameters,G11,G22, andG12in the Kirkwood-Buff Solution Theory on the Basis of the Concentration Fluctuation Data Obtained from Rayleigh Scattering. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 1982. [DOI: 10.1246/bcsj.55.3368] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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The structure of binary liquids. The Kirkwood-Buff theory of liquid mixtures, illustrated on the basis of the systems water/methanol, water/ethanol, and cyclohexane/2,3-dimethylbutane, as a link between thermodynamic data and x-ray and neutron scattering results. J SOLUTION CHEM 1979. [DOI: 10.1007/bf00650747] [Citation(s) in RCA: 55] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Gray CG, Gubbins KE, Twu CH. Perturbation theory for molecular fluids: Third-order term in the Pople expansion. J Chem Phys 1978. [DOI: 10.1063/1.436383] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lee LL. Correlation functions of classical fluids. V. The perturbation theory for soft spheres. J Chem Phys 1977. [DOI: 10.1063/1.433730] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lovett R, DeHaven PW, Vieceli JJ, Buff FP. Generalized van der Waals theories for surface tension and interfacial width. J Chem Phys 1973. [DOI: 10.1063/1.1679447] [Citation(s) in RCA: 105] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang S, Egelstaff P, Gubbins K. Monte Carlo study of perturbation theory for the radial distribution function. Mol Phys 1973. [DOI: 10.1080/00268977300100401] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Smith WR. Perturbation theory and one-fluid corresponding states theories for fluid mixtures. CAN J CHEM ENG 1972. [DOI: 10.1002/cjce.5450500223] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Good RJ, Hope CJ. Test of Combining Rules for Intermolecular Distances. Potential Function Constants from Second Virial Coefficients. J Chem Phys 1971. [DOI: 10.1063/1.1675495] [Citation(s) in RCA: 64] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Henderson D, Barker JA. Perturbation Theory and the Equation of State of Mixtures of Hard Spheres. J Chem Phys 1968. [DOI: 10.1063/1.1670610] [Citation(s) in RCA: 30] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Throop GJ, Bearman RJ. Excess Thermodynamic Functions for Binary Mixtures as Calculated from the Percus—Yevick Equation for the Lennard‐Jones Potential. J Chem Phys 1967. [DOI: 10.1063/1.1712330] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Salsburg ZW. Theory of Multicomponent Fluid Mixtures. III. A Pseudo Pair Potential. J Chem Phys 1962. [DOI: 10.1063/1.1732813] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Buff FP, Brout R. Some Tests of the Superposition Approximation in the Liquid Phase. J Chem Phys 1960. [DOI: 10.1063/1.1731421] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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