Generalized van der Waals theory. IV. Variational determination of the hard-sphere diameter

Hooper, M. A.; Nordholm, Sture

doi:10.1071/ch9811809

Cited by 17 publications

(7 citation statements)

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“…There are several options for improvement of the IL-DFT. These include the introduction of other weight function alternatives for the coarse-grained densities, , a variationally determined “Coulomb hole”, and an improved estimate of how excluded volume influences the interactions. At least some of these options will be explored in future work, where we also will consider the introduction of chain stiffness into the model.…”

Section: Resultsmentioning

confidence: 99%

A Classical Density Functional Theory of Ionic Liquids

2011

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Classical Density Functional Theory of Ionic Liquids 3 Other approachesILs are fascinating from a theoretical standpoint. In order to treat ILs, a theory must account for both electrostatic and steric correlations. Attempts to develop such a theory have appeared in the literature. These include the lattice based model by Kornyshev and co-workers (Fedorov et al. , 2008;Kornyshev , 2007). In another lattice approach by Lauw and coworkers (Lauw et al. , 2009), both cations and anions were modelled by a star-like architecture, with each monomer subject to an independently specified dielectric response. Under certain circumstances, these models were able to qualitatively reproduce the so-called "camel-shaped" differential capacitance, C D , profile observed in imidazolium ILs at carbon electrodes (Islam et al. , 2009;Lockett et al. , 2008a). This behaviour is an indication of subtle structuring effects at charged surfaces and is a stern test for theory. Although camel-shaped C D profiles are predicted, qualitative discrepancy against experimental results remains. This is not surprising since these crude theories lack a proper description of electrostatic correlations despite accounting for steric contributions. Charge-charge correlations have been shown to be important in interfacial phenomena of highly coupled electrostatic fluids. As with dispersion forces, ionic correlations are always attractive and lower the total energy. Thus, we expect that they will also play a role in establishing the camel shape of the C D . That this is the case, is seen from both simulations (Lamperski & Zydor , 2007;Vatamanu et al. , 2010) (Fedorov et al. , 2010;Trulsson et al. , 2010), play an important role in determining their properties. In this work, we will use a model for ILs wherein the molecular ions interact via dispersion, as well as electrostatic, forces and the cation has an oligomeric structure consistent with imidazolium ions. This model has also been adopted by us in previous recent publications (Forsman et al. , 2011;Trulsson et al. , 2010), and employs the methods of polymer free energy density functional theory (DFT) (Woodward , 1991). The result will be a simple, albeit approximate DFT for ILs. We have already introduced the salient features of the theory in a previous publication (Forsman et al. , 2011). Here, we will present a much more thorough treatment, emphasizing the relation to theories of simpler fluids. We will also extend the scope of the study with some emphasis on temperature dependence and the effects of ion-specific adsorption. The IL-DFT that we will discuss here is an off-lattice theory, whose accuracy can be straightforwardly tested against computer simulations of the same molecular model. We will begin with a discussion of relevant earlier work, in order to introduce the essential mechanistic components that will be combined in our density functional theory for ionic liquids. Classical density functional theory (DFT) of simple fluidsThe ideal gas law is known and used by most physicists and chemist...

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Section: Resultsmentioning

confidence: 99%

A Classical Density Functional Theory of Ionic Liquids

2011

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“…This difference is, of course, due to the inclusion of the entropy in U,,f~(r). Mathematically the relation between the two series becomes obvious, when one notes that Uoff(r)= 1/fl ~ dB' UK(r, /3'), (19) 0 whence the substitution of the right hand side of (18) into (19) immediately gives (17) for larger r. Equation (19) is more easily recognized as a free energy charging procedure when the ' charging variable' A =/3'//3 is introduced.…”

Section: En E Rgy ([3"-1)mentioning

confidence: 99%

“…Values of the coefficients V~,, are given in Appendix A where the extension of the series to higher values of fim2r -3 is also outlined. From (19) and (20) …”

Section: En E Rgy ([3"-1)mentioning

confidence: 99%

“…The GvdW theory was developed as an alternative to the predominant integral equation and numerical simulation approaches to liquid theory. It is a free energy density functional theory and has been discussed at length in previous articles [16][17][18][19]. Wishing to maintain computational simplicity we will not fully exploit the theory.…”

Section: Ueff(r)mentioning

confidence: 99%

“…The validity of this representation of dipolar interactions is therefore not limited by perturbation approximation to small m 2 values. The thermodynamic properties are estimated by use of the generalized van der Waals (GvdW) theory recently developed [16][17][18][19]. The simplicity of this theory makes it well suited to exploratory calculations of the properties of the model system interacting by U~ff(r) truncated at a hard sphere diameter a.…”

Section: Introductionmentioning

confidence: 99%

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An effective pair potential for dipolar fluids

Woodward

Nordholm

1984

Molecular Physics

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The possibility of representing the orientational correlations in a dipolar fluid by an effective pair potential, Ueff(r), depending only on the separation r, is considered. Uetf(r) is obtained from the two-particle orientational partition function by series expansion and direct numerical integration methods for a wide range of interaction strengths. Free energies are obtained for the dipolar hard sphere fluid by use of the GvdW theory of simple fluids and compared with Monte Carlo simulation results. The coexistence curve is also obtained and compared with Monte Carlo, Pad6 and MSA results. The critical temperature is overestimated by about 30 per cent but the critical volume agrees well with the simulation estimate.

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