Coexistence and spinodal curves in directionally bonded liquids using the four-cluster approximation

Bodegom, Erik; Meijer, Paul H. E.

doi:10.1063/1.446861

Cited by 11 publications

(4 citation statements)

References 23 publications

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“…This statement seems to be rather unfounded and is contradicted by the work of Barker and Fock and by most of the other studies mentioned earlier. The curves obtained by Barker and Fock were somewhat narrower than the experimentally determined phase diagrams, and more recently Bodegom and Meijer [20] have obtained better agreement for the B_arker and Fock model using a higher-order approximation. Downloaded by [Tulane University] at 21:38 04 January 2015 A more rigourous approach to the statistical mechanics of lattice models involves their reduction to the equivalent spin~ Ising model of ferromagnets by the 'decoration' transformation [21].…”

Section: Introductionmentioning

confidence: 83%

“…In summary, (21)-(23) for g~(a), FAB and KAa are used in (20) to determine AAB, and the fraction of sites not bonded, XA and Xa, are obtained by solving (19) and (18), respectively. Expression (15) is then used together with XA, Xa and their derivatives with respect to the number density to calculate the contribution due to bonding Z b~ Finally, the hard-sphere repulsive term (13), the mean-field attractive term (14), and the association term (15) are combined to give the mixture's total compressibility factor (4).…”

Section: Associating Bandary Mk~tures Of Equal Sizesmentioning

confidence: 99%

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Theory of closed-loop liquid-liquid immiscibility in mixtures of molecules with directional attractive forces

Jackson¹

1991

Molecular Physics

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The phase equilibria of a binary mixture of equal-sized hard spheres (diameters or1 = a2) with mean-field attractive forces between like species (all = a22) and non between unlike species (a~2 = 0) are determined using an 'augmented' van der Waals equation of state. This system is found to have a symmetrical phase diagram exhibiting a large extent of liquid-liquid immiscibility and a tricritical point. Directional attractive forces between the unlike species and then introduced in the form of off-centre, square-well bonding sites, and a perturbation term representing the contribution due to bonding is added to the equation of state. The phase behaviour of systems with varying degrees of association is investigated. As the strength of the site-site bonding interaction is increased relative to that of the mean-field attractions, closed-loop liquid-liquid immiscibility is found with the corresponding lower and upper critical solution points. The region of liquid-liquid coexistence decreases with increasing bonding strength until it disappears completely due to extensive association between the unlike species of the mixture. The fraction of bonded molecules is determined to provide an explanation of the phase behaviour; closed-loop immiscibility is a direct consequence of the dramatic increase in bonding as the temperature is decreased. Existing calculations for lattice models exhibiting closed-loop coexistence are discussed in the context of the results of this continuum approach, a first of its kind. Advantages of the approach in describing the properties of real systems exhibiting closed-loop immiscibility are pointed out.

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Section: Introductionmentioning

confidence: 83%

Section: Associating Bandary Mk~tures Of Equal Sizesmentioning

confidence: 99%

Theory of closed-loop liquid-liquid immiscibility in mixtures of molecules with directional attractive forces

Jackson¹

1991

Molecular Physics

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“…) exp(vJkT)These satisfy eq20 if the v^'s are replaced with u^' s. The distribution of contacts can be calculated by replacing the Vot/s's with Mo^'s in eq19. Obviously, the values of monomerweighting factors also change.…”

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confidence: 99%

Statistical Thermodynamics of Molecules with Orientation-Dependent Interactions in Homogeneous and Inhomogeneous Systems

Besseling¹,

Scheutjens²

1994

J. Phys. Chem.

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A lattice theory is presented for homogeneous and heterogeneous systems containing molecules with orientationdependent interactions. Correlations due to interactions are accounted for in first-order (quasi-chemical) approximation by allowing variations of the distribution of intermolecular contacts. To model heterogeneous systems, parallel lattice layers are allowed to be differently occupied. A partition function, written as a sum over distributions of molecules over orientations and locations and of intermolecular contacts, is derived for an arbitrary collection of monomeric species. Using a maximum term argument, self-consistent field equations are derived for the equilibrium distributions. These equations are solved numerically. Allowing lattice sites to be vacant, free-volume effects can be accounted for. Expressions are obtained for energy, entropy, chemical potentials, pressure, and surface tension. The capabilities of the method are illustrated by applying it to a number of specific systems, one of which exhibits a closed-loop coexistence curve. Another model in which one component is energetically anisotropic has an asymetric coexistence curve. Properties of coexisting phases and of the interface between them are investigated. With these models, it is found that orientational interactions may lead to a pronounced ordering in the interface and a negative interfacial entropy.

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“…As a final introductory point, we note the applications of quasi-chemical approximations in treating lattice models of water [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Those efforts may have received less attention than they deserve because of their lack of conventional molecular realism.…”

Section: Introductionmentioning

confidence: 99%

Quasi-chemical theories of associated liquids

LAVIOL¹

1998

Molecular Physics

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It is shown how traditional development of theories of fluids based upon the concept of physical clustering can be adapted to an alternative local clustering definition. The alternative clustering definition can preserve a detailed valence description of the interactions between a solution species and its nearneighbors, i.e., cooperativity and saturation of coordination for strong association. These clusters remain finite even for condensed phases. The simplest theory to which these developments lead is analogous to quasi-chemical theories of cooperative phenomena. The present quasi-chemical theories require additional consideration of packing issues because they don't impose lattice discretizations on the continuous problem. These quasi-chemical theories do not require pair decomposable interaction potential energy models. Since calculations may be required only for moderately sized clusters, we suggest that these quasi-chemical theories could be implemented with computational tools of current molecular electronic structure theory. This can avoid an intermediate step of approximate force field generation.

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Coexistence and spinodal curves in directionally bonded liquids using the four-cluster approximation

Abstract: Coexistence curve of acetonitrile and cyclohexane liquid system J. Chem. Phys. 84, 3999 (1986); 10.1063/1.450110Critical behavior of the diameters of liquid-liquid coexistence curves

Cited by 11 publications

References 23 publications

Theory of closed-loop liquid-liquid immiscibility in mixtures of molecules with directional attractive forces

Theory of closed-loop liquid-liquid immiscibility in mixtures of molecules with directional attractive forces

Statistical Thermodynamics of Molecules with Orientation-Dependent Interactions in Homogeneous and Inhomogeneous Systems

Quasi-chemical theories of associated liquids

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