Hard-Sphere Model of Binary Liquid Mixtures

Snider, Neil; Herrington, Thelma M.

doi:10.1063/1.1703300

Cited by 87 publications

(17 citation statements)

References 21 publications

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“…HS theory provides expressions for g 0 ij for every (i, j) in terms of the diameters d i and mole fractions x i of all of the species and the packing fraction ξ (the volume fraction filled by the hard spheres) (12,13). From this one can then determine the excess entropy of the fluid with respect to an ideal gas, S ex (12)(13)(14). S ex , which is negative in sign, accurately describes the reduction in entropy due to the mutual avoidance of overlaps between all of the component spheres.…”

Section: Theorymentioning

confidence: 99%

“…The theory of HS fluid mixtures is well established and rigorous (10)(11)(12)(13)(14). Before applying it quantitatively to crowding, it is useful to describe qualitatively what it says about the processes depicted in Fig.…”

Section: Theorymentioning

confidence: 99%

“…1-5 used here, with two distinctions. First, the coefficients were not explicitly factored into separate solvent packing and composition terms in the manner of Snider and Herrington (14). So the effects of crowder size and solvent packing were not separately analyzed, as they are here.…”

Section: Theorymentioning

confidence: 99%

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Analysis of the size dependence of macromolecular crowding shows that smaller is better

Sharp

2015

Proc. Natl. Acad. Sci. U.S.A.

139

129

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The aqueous milieu inside cells contains as much as 30-40% dissolved protein and RNA by volume. This large concentration of macromolecules is expected to cause significant deviations from solution ideality. In vivo biochemical reaction rates and equilibria might differ significantly from those measured in the majority of in vitro experiments that are performed at much lower macromolecule concentrations. Consequently crowding, a nonspecific phenomenon believed to arise from the large excluded volume of these macromolecules, has been studied extensively by experimental and theoretical methods. However, the relevant theory has not been applied consistently. When the steric effects of macromolecular crowders and small molecules like water and ions are treated on an equal footing, the effect of the macromolecules is opposite to that commonly believed. Large molecules are less effective at crowding than water and ions. There is also a surprisingly weak dependence on crowder size. Molecules of medium size, ∼5 Å radius, have the same effect as much larger macromolecules like proteins and RNA. These results require a reassessment of observed high-concentration effects and of strategies to mimic in vivo conditions with in vitro experiments. T he milieu inside cells contains a large amount of solutes that include small ions, metabolites, and macromolecules. Typical protein/RNA concentrations range from 300 mg/mL to 400 mg/mL or about 30-40% by weight. These are 10-fold or more higher than the macromolecular concentrations usually encountered in in vitro measurements and could lead to significant nonideality in solution behavior. The possibility that in vivo biochemical reaction rates and equilibria might be quite different from measured values due to this nonideality has stimulated considerable research. Macromolecular crowding in particular has stimulated a large number of studies, which have been extensively reviewed (1-5). Crowding has been variously described as physical occupation of volume by the macromolecules, which is then unavailable to other molecules, as an excluded volume effect, as a nonspecific effect due to steric repulsion, and as eliminating positions at which the protein can be placed (2, 5, 6). The other contribution to nonideality is from interactions between various solution components, either attractive or repulsive-repulsive interactions distinct from the van der Waals core repulsion or steric factor underlying crowding. We know very little about the contribution of intersolute interactions to nonideality in vivo. Crowding has been more extensively studied because the steric or excluded volume of a macromolecule is a welldefined property, it is always present, and its qualitative effect on biochemical reactions seems obvious (2). However, as I demonstrate in this paper, the effect of crowding macromolecules on a biochemical reaction is not obvious, the relevant theory has not been consistently applied, and indeed the effect is opposite to that commonly believed.Analyses of the effect of crowding mac...

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

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Analysis of the size dependence of macromolecular crowding shows that smaller is better

Sharp

2015

Proc. Natl. Acad. Sci. U.S.A.

139

129

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“…temperature and volume. In this work we discuss a semi-theoretical For zHS we use the theoretical expression of treatment of simple mixtures which extends the Pe'cu~ and Yevick as by Carnahan and work of Snider and Herrington (7). Unlike most Since eq.…”

Section: Equation Of State and Chemical Potentialmentioning

confidence: 99%

A Semi-theoretical van der Waals Equation for Calculation of Vapor-Liquid Equilibria at High Pressures

Vera¹,

Prausnitz²

1971

Can. J. Chem.

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An equation of the van der Waals type is derived and applied to the calculation of vapor-liquid equilibria at elevated pressures. For the hard-sphere part of the equation the theoretical relation of Carnahan-Starling is used. The effect of intermolecular forces is represented by the usual van der Waals term but the "constant a" is permitted to vary with temperature and density as dictated by the experimental PVT data for argon; this variation of the "constant a" is generalized for other simple fluids through corresponding states. While this treatment is of little interest for representing the configurational properties of pure fluids, it is useful for calculating the properties of simple fluid mixtures. Illustrative vapor-liquid equilibrium calculations are performed for binary and ternary mixtures of nitrogen, argon, and oxygen at 6 and 18 atm.On d6duit une equation de type van der Waals qu'on applique au calcul des Cquilibres liquide-vapeur aux pressions Blevees. Pour la partie sphere rigide de I'equation, on utilise la relation theorique de Carnahan-Starling. L'effet des forces intermolCculaires est represente par le parametre habitue1 de van der Waals, mais la "constante a" est ajustable en fonction de la temperature et de la densit6 comme I'exigent les donnees PVT experimentales pour I'argon; par les Btats correspondants on gknbralise aux autres fluides simples cette variation de la "constante a". Le present traitement prksente peu d1int6r6t pour la representation des propridtks configuratiomelles des fluides purs, par contre il est utile pour le calcul des proprietes des melanges de fluides simples. shown that the structure of a real fluid is similar ~h , compressibility factor of a pure fluid is to that of a hard-sphere fluid ; that is, the distribu-given by an expression of the van der waals type tion of molecules in space is determined primarily by the molecule's repulsive forces while the at-C11 Pv z = -= a ZHS --tractive forces may be considered to produce a R T R T V uniform potential field which holds themolecules together. This view is remarkably similar to that where zHS is the compressibility factor of a hardproposed by van der Waals years ago and sphere fluid at temperature Tand molar volume v. therefore several modern theories of fluids and The van der Waals a is a in the fluid mixtures are called "augmented" or zeroth approximation (8); it depends on both "modified" van der Waals theories. temperature and volume. In this work we discuss a semi-theoretical For zHS we use the theoretical expression of treatment of simple mixtures which extends the Pe'cu~ and Yevick as by Carnahan and work of Snider and Herrington (7). Unlike most (' 1 previous work, our treatment is not limited to [2] ZHS = 1 + 5 + 5 2 -k 3 liquids at low pressures but is applicable also to analytical form which is useful for implementation on an electronic computer. and b = (2/3)xNAo3, where NA is Avogadro's number and o is the molecular diameter.

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“…Reiss et al [3] came to similar results using the scaled-particle theory. The hard-sphere model of binary liquid mixtures was proposed by Snider and Herrington [6] and they used it to calculate the excess thermodynamic functions. Mulero et al [7] reviewed the accuracy of twenty two equations of state for hard spheres in order to perform their applications.…”

Section: Introductionmentioning

confidence: 99%

Thermal Expansivity of Ternary Liquid Mixtures: Application of Hard-Sphere Models and Flory's Statistical Theory

Tripathi

Awasthi

2010

Acta Phys. Pol. A

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Seven hard-sphere models and Flory's statistical mechanical theory have been applied to evaluate thermal expansion coefficient of ternary liquid systems involving dimethyl sulfoxide with phenol/o-cresol in carbon tetrachloride at 293.15, 303.15 and 313.15 K. The results thus obtained are compared with the experimental values of thermal expansivity. The relative applicability of all these approaches to the present investigation has been checked and discussed. The excess values of thermal expansivity have also been calculated and utilized to study the presence and strength of intermolecular interactions in the ternary liquid systems under investigation.

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Hard-Sphere Model of Binary Liquid Mixtures

Cited by 87 publications

References 21 publications

Analysis of the size dependence of macromolecular crowding shows that smaller is better

Analysis of the size dependence of macromolecular crowding shows that smaller is better

A Semi-theoretical van der Waals Equation for Calculation of Vapor-Liquid Equilibria at High Pressures

Thermal Expansivity of Ternary Liquid Mixtures: Application of Hard-Sphere Models and Flory's Statistical Theory

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