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

Abstract

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.

Colloidal particles in liquid crystal films and at interfaces

“…The quadrupolar tail of d −6 was also found experimentally for colloidal particles with the tangential boundary conditions [49,66]. Theoretically, the quadrupolequadrupole asymptotic behavior was studied in detail using molecular theory, which accounts for the anisotropy of molecular interactions [67].…”

Wall–colloid interaction in nematic solvents: external field effects

“…Nematic colloids are an important class of materials that are of current interest both for the fundamental questions they pose and because of potential applications [1][2][3]. A good deal of effort has focused on understanding colloidal interactions and ordering in bulk systems [4][5][6][7][8][9][10]. The interactions in bulk systems are now reasonably well understood from both phenomenological [4][5][6] and molecular [8,9] viewpoints.…”

“…A good deal of effort has focused on understanding colloidal interactions and ordering in bulk systems [4][5][6][7][8][9][10]. The interactions in bulk systems are now reasonably well understood from both phenomenological [4][5][6] and molecular [8,9] viewpoints. A discussion and comparison of both approaches is given in [9].…”

“…The interactions in bulk systems are now reasonably well understood from both phenomenological [4][5][6] and molecular [8,9] viewpoints. A discussion and comparison of both approaches is given in [9].…”

Effect of substrate geometry on liquid-crystal-mediated nanocylinder-substrate interactions

“…(IET), which has also been recently applied to spherical nanoparticles in LCs [35][36][37] , studying the colloid induced structure and interactions between them. However, IET does not produce spontaneously ordered phases, so these calculations were performed using (arbitrarily) weak aligning fields.…”