Nematic-fluid structure in wall-field geometry. II. The direct correlation function

Sokolovska, T. G.; Sokolovskii, R. O.; Patey, G. N.

doi:10.1063/1.2213250

Cited by 3 publications

(15 citation statements)

References 22 publications

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“…In our previous studies we suggested that a general solution of the Ornstein-Zernike equation for a nematic fluid in the presence of a wall, arbitrarily oriented with respect to the nematic director, can be very useful for the investigation of dilute nematic colloids. In fact, we suggested using the wall-nematogen direct correlation function, obtained explicitly in [11], as an ansatz for the direct correlation function in nematic colloids. This ansatz permits explicit microscopic calculations of the density and orientational profiles, as well as potentials of mean force for large colloidal particles, such as those used in numerous experiments.…”

Section: Discussionmentioning

confidence: 99%

“…The factor 5/4 is not accidental. Formally we can take the limit of zero field (ξ → ∞) for the case of the tilted wall (from equation (17) of [11]). In this case the asymptote of the wall-nematogen total correlation function tends to a constant value at large distances from the wall,…”

Section: Corrected Ansatz For Small or Zero Fieldsmentioning

confidence: 99%

“…It is important that the solution was obtained subject to well defined boundary conditions at infinity: the director parallel to the field. This ansatz is very convenient because within the MSA the wall-nematic direct correlation function can be obtained in explicit form [11]. This permits explicit microscopic calculations of the density and orientational profiles [12], as well as effective interactions (potentials of mean force) between pairs of colloidal particles [13].…”

Section: Introduction To Molecular Modelling and Correlations In Nemamentioning

confidence: 99%

“…We investigated the reliability of the ansatz in [11]. The test calculations were based on verification of an exact consequence of the impenetrability of hard cores, namely h CN (R 12 ,ω 2 ) = −1 if R 12 < Σ+σ 2 .…”

Section: Introduction To Molecular Modelling and Correlations In Nemamentioning

confidence: 99%

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Improved ansatz for the direct correlation function in dilute nematic colloids

Sokolovska¹,

Sokolovskii²,

Patey³

2007

Condens. Matter Phys.

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We present an improved analytical ansatz for the colloid-nematic direct correlation function. This ansatz is more accurate than our earlier version, and yields numerical results that are very close to the true mean spherical approximation for dilute nematic colloids. Furthermore, the improved ansatz is valid for external fields of any strength. We examine the zero-field behavior of the colloid-colloid potential of mean force in light of the improved ansatz, and show that at zero field and large separations this function decays as R −5 and grows as Σ 6 , where Σ is the colloidal diameter. These dependencies are consistent with our earlier conclusions based on a less accurate version of the ansatz. As with the original ansatz, the improved version remains analytical and can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries, e.g. in droplets.

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Section: Discussionmentioning

confidence: 99%

Section: Corrected Ansatz For Small or Zero Fieldsmentioning

confidence: 99%

Section: Introduction To Molecular Modelling and Correlations In Nemamentioning

confidence: 99%

Section: Introduction To Molecular Modelling and Correlations In Nemamentioning

confidence: 99%

See 2 more Smart Citations

Improved ansatz for the direct correlation function in dilute nematic colloids

Sokolovska¹,

Sokolovskii²,

Patey³

2007

Condens. Matter Phys.

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“…At long distances, this description leads to a repulsive force between a colloidal 'multipole' and its mirror image in the surface plane, closely akin to the repulsive interaction between an electrostatic multipole and an inert (nonpolarizable) wall. In the present paper, we consider wall-colloid interactions at the molecular level, applying the statistical mechanical approach used in our earlier work [8,9,[16][17][18][19][20]. We identify a different, field-dependent, wall-colloid interaction which can be attractive or repulsive depending on the particular type of anchoring at the wall and colloidal surfaces.…”

mentioning

confidence: 99%

Wall–colloid interaction in nematic solvents: external field effects

Sokolovska¹,

Patey²

2009

J. Phys.: Condens. Matter

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We propose a molecular theory of colloid-wall interactions in nematic media that predicts a new effective force acting on colloidal particles in the presence of an external field. In contrast to the so-called 'image' interaction that is always repulsive at long distances, the force identified here can be attractive or repulsive, depending on the type of anchoring at the wall and colloidal surfaces. The effective force on a colloidal particle decreases with distance s from the wall as exp(-s/ξ), where ξ is a magnetic (electric) coherence length. At weak fields the force is proportional to (Σ/ξ)(3) for 'quadrupolar' colloids and to (Σ/ξ)(2) for 'dipoles', where Σ is the colloidal diameter. A brief discussion of recent experiments in the light of our findings is presented.

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Bridging the gap between phenomenology and microscopic theory: Asymptotes in nematic colloids

2008

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The Ornstein-Zernike equation is applied to nematic colloids with up-down symmetry to determine how the electrostatic analogy and other phenomenological results appear in molecular theory. In contrast to phenomenological approaches, the molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For our molecular parameters the resulting anchoring appears to be realistic, neither rigid nor infinitely weak. For this case, the effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. We show that a simple van der Waals approximation gives a potential of mean force that in some important aspects is similar to the phenomenological results obtained in the limit of weak anchoring; at large separations the potential varies as Sigma8, where Sigma is the colloidal diameter. In contrast, the more sophisticated mean spherical approximation yields a Sigma6 dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation (or magnetic coherence) length xi inherent in the nematic sample is essential in an analysis of the Sigma dependence. At infinite xi the leading Sigma dependence is Sigma6, but this shifts to Sigma8 when xi is finite. The correlation length also influences the orientational behavior of the effective interaction. The so-called quadrupole interaction that determines the long-range behavior at infinite xi transforms into a superposition of screened "multipoles" when xi is finite. The basic approach employed in this paper can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets.

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Nematic-fluid structure in wall-field geometry. II. The direct correlation function

Cited by 3 publications

References 22 publications

Improved ansatz for the direct correlation function in dilute nematic colloids

Improved ansatz for the direct correlation function in dilute nematic colloids

Wall–colloid interaction in nematic solvents: external field effects

Bridging the gap between phenomenology and microscopic theory: Asymptotes in nematic colloids

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