Statistical Mechanical Theory of Ionic Solutions Based on the Interaction Site Model: Dielectric Properties and Pair Correlation Functions

The exact expression of the dielectric constant for polar polyatomic molecular fluids is obtained in terms of the site-site direct correlation function. This equation is closely related to the formula of the dielectric constant in terms of the molecular direct correlation function (the Ramshaw equation, Ramshaw, 1972, J. chem. Phys., 57, 2684. We discuss why RISM-l theory gives a trivial expression for the dielectric constant using equations obtained here, and show that RISM-2 theory leads to a non-trivial result for the dielectric constant of molecular liquids. IntroductionSince the proposal of the RISM integral equation by Chandler and Andersen [1], the theory based on the interaction site formalism has played an important role in the study of structure and thermodynamic properties of molecular liquids [2, 3]. The RISM-! type theory has been applied to many systems including polar liquids and ionic solutions [4][5][6][7][8][9][10][11][12][13]. It is well known that RISM-1 theory is successful in describing the short range structure and thermodynamic properties of these systems.However, the RISM-1 theory is obtained by direct application of the PY or HNC approximations for simple liquids to the theory of the molecular liquids without any theoretical justification. The theory has some essential theoretical inconsistencies. The most important is the fact that the asymptotic forms of the site-site direct correlation functions obtained from the RISM-1 approximations at large separations are different from those of the exact functions [14][15][16][17]. Because of this inconsistency, all the RISM-1 theory lead to the same trivial result for the dielectric constant of polar fluids [18].In order to overcome this difficulty, two types of theories have been proposed within the framework of the interaction site formalism. One is the theory based on the interaction site cluster expansion, that is, the proper integral equation theory by Chandler et al. [19] and Rossky and Chiles [20] and the optimized cluster expansion theory by Lupkowsky and Monson [21]. The other is the RISM-2 theory based on the method of functional Taylor expansions [22,23]. Recently, one of the authors and Arakawa indicated that the RISM-2 theory is free from any theoretical inconsistencies similar to those of the RISM-1 theory [14]. This suggests that the RISM-2 theory will give a non-trivial result for the dielectric constant of polar fluids. One of the purposes of this work is to obtain the expression for the dielectric constant of polar fluids, using the site-site direct correlation function of RISM-2 (SSDCF-2), and

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“…The static dielectric function e(k) of fluids composed of polar polyatomic molecules can be expressed as [25] 1 4nil tr Z~, (4) e(k---)-1 -k2…”

Section: The Dielectric Constant In Terms Of the Ssdcf-2mentioning

confidence: 99%

The dielectric constant and the site-site direct correlation function of the RISM-2 theory for polar polyatomic molecular fluids

Ohba

Nomura

1992

Molecular Physics

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“…For the present purposes, we can compare the structural predictions of the extended RISM equation at the extremes, comparing the physical charges (table 1) to those obtained with effective charges chosen so that the asymptotic amplitude of c(r) is reduced by the factor of A given by (14). (y is given by the physical model charges.)…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Although it provides us with a stringent sensitivity test, under normal fluid conditions one does not anticipate the extreme limiting behaviour given by (14), which would in fact signal a ferroelectrie transition. Instead, the behaviour of a that can be reasonably expected [21] for rigid dipolar particles as y increases from zero suggests a smooth increase in A from 2/3 toward 1, with a fairly rapid rise of A from 2/3 to a value that is already quite near 1 when y=2.…”

Section: Expected Beha¥iour Of Amentioning

confidence: 99%

“…Recently, there has been a growing effort aimed at the structural description of molecular liquids composed of polar molecules interacting through reasonably realistic pair potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. These potentials are most frequently expressed as so-called interaction site models (ISMs).…”

Section: Introductionmentioning

confidence: 99%

“…That is, the intermolecular potential is expressed as a sum of spherically symmetric pairwise additive terms each depending on the distance between one of several point sites located in one molecule and one such site in a second molecule. This form is prevalent for the analytical expression of potentials used both in computer simulation [1][2][3][4] as well as more analytical approaches [5][6][7][8][9][10][11][12][13][14][15]. However, for m. any important systems, simulation is presently infeasible, and this provides a special motivation for exploring more analytical approaches, such as integral equation formulations.…”

Section: Introductionmentioning

confidence: 99%

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The coupling of long and short range correlations in ISM liquids

1983

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A simple modification of the HNC-like closure within the extended RISM equation formalism is considered which assures that the asymptotic form of the site-site direct correlation functions is consistent with the dielectric constant. The short ranged structural results obtained with the modification are compared to those following from the original closure for three strongly polar diatomic models, with the result that only very small differences are found. These results demonstrate both that the short ranged results are only weakly coupled to the asymptotic amplitudes, and that the latter can potentially be corrected in a relatively straightforward manner.

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Recent Progress in the Statistical Mechanical Mechanics of Interaction Site Fluids

Monson

Morriss

1990

Advances in Chemical Physics

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Statistical Mechanical Theory of Ionic Solutions Based on the Interaction Site Model: Dielectric Properties and Pair Correlation Functions

Cited by 18 publications

References 31 publications

The dielectric constant and the site-site direct correlation function of the RISM-2 theory for polar polyatomic molecular fluids

The dielectric constant and the site-site direct correlation function of the RISM-2 theory for polar polyatomic molecular fluids

The coupling of long and short range correlations in ISM liquids

Recent Progress in the Statistical Mechanical Mechanics of Interaction Site Fluids

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