The calculation of correlation functions in fluids by a weighted density concept

Kasch, M.; Chen, X.S.; Forstmann, F.

doi:10.1080/00268979200100321

Cited by 10 publications

(2 citation statements)

References 26 publications

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“…Going a step further, the inhomogeneous direct correlation functions can be locally approximated by correlation functions of the homogeneous fluid evaluated at appropriate weighted densities [12,[50][51][52]. For our complex model electrolyte we have achieved very good results using the approximation (13).…”

Section: The Electrolyte At the Electrodementioning

confidence: 99%

Integral equation theory for the electrode-electrolyte interface with the central force water model. Results for an aqueous solution of sodium chloride

Vossen

Forstmann

1995

Molecular Physics

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The structure of an aqueous solution of sodium chloride at a planar elec- at the uncharged and charged electrode. The rather rigid ice-like water structure found previously at the neutral surface strongly repels the ions. Steric interactions between the differently sized ions and the ice-like water structure dominates the ionic distribution near the electrode. This model electrolyte also responds differently to opposite charges on the electrode. We found the asymmetry in the differential capacitance curve entirely determined by the response of the interfacial water structure.

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Section: The Electrolyte At the Electrodementioning

confidence: 99%

Integral equation theory for the electrode-electrolyte interface with the central force water model. Results for an aqueous solution of sodium chloride

Vossen

Forstmann

1995

Molecular Physics

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“…where c(2) b (q = 0) is the Fourier transform of the two-body direct correlation function in the zero wavevector limit. The second equality gives the well-known integral giving the excess (over ideal) pressure in the compressibility route, P c exc , see Reference [42]. Term B: This term does not require further manipulation and it can be given a clear physical interpretation.…”

Section: E Compressibility Contact Theoremmentioning

confidence: 99%

Force density functional theory in- and out-of-equilibrium

Tschopp,

Sammüller,

Hermann

et al. 2022

Preprint

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When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in-and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. For both approaches we explicitly prove the hard-wall contact theorem that connects the value of the density profile at the hard-wall with the bulk pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

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An orientational instability in the vapour and the liquid‐vapour interface of a dipolar hard sphere fluid

Kasch

Forstmann

1994

Ber Bunsenges Phys Chem

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the wave vector q, one finds with short-chain amphiphiles Z(q) to drop monotonically. Upon increasing ( i , j ) , one observes a gradual evolution of a correlation peak (Fig. 19 in [I]), followed by a q -4 decay for large q (Porod's law). As Teubner and Strey [I21 have shown, the curves can be fitted rather well bywith a < 0, and b > 0. With increasing (i, j ) , the position of the peak moves gradually towards lower q, with the q -4 decay becoming increasingly wider. The evolution of the peak indicates a gradual evolution of a characteristic periodicity d in the mixture that increases with increasing ( i , j ) , while the fact that Porod's is increasingly better obeyed indicates that the scattering length density gradient at the interfaces becomes increasingly steeper. If d is interpreted as mean distance between the centers of the dispersed domains, a simple calculation [I31 shows that the position of the peak is solely determined by the mass balance, irrespective of the model used for describing the mixtures.I am indebted to all of my coworkers for their assistance with the experiments, and their contributions to the discussions.The hard sphere dipole fluid shows an instability towards formation of oriented clusters in the vapour before condensation. The coexistence interface profile is derived from a WDA approximation of the direct correlation function. Integration of the equation for V p yields also the orientation of the dipoles near the interface.

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The calculation of correlation functions in fluids by a weighted density concept

Cited by 10 publications

References 26 publications

Integral equation theory for the electrode-electrolyte interface with the central force water model. Results for an aqueous solution of sodium chloride

Integral equation theory for the electrode-electrolyte interface with the central force water model. Results for an aqueous solution of sodium chloride

Force density functional theory in- and out-of-equilibrium

An orientational instability in the vapour and the liquid‐vapour interface of a dipolar hard sphere fluid

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