Screened Coulomb interactions of general macroions with nonzero particle volume

Abstract

A semianalytical approach is developed to calculate the effective pair potential of rigid arbitrarily shaped macroions with a nonvanishing particle volume, valid within linear screening theory and the mean-field approximation. The essential ingredient for this framework is a mapping of the particle to a singular charge distribution with adjustable effective charge and shape parameters determined by the particle surface electrostatic potential. For charged spheres, this method reproduces the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Further exemplary benchmarks of the method for more complicated cases, like tori, triaxial ellipsoids, and additive torus-sphere mixtures, leads to accurate closed-form integral expressions for all particle separations and orientations. The findings are relevant for determining the phase behavior of macroions with experiments and simulations for various particle shapes.

Nemato-elasticity of hybrid molecular-colloidal liquid crystals

“…For instance, the balance between surface anchoring and intercolloidal forces is likely to be quite different for short rods for which surface anchoring contributions play a more prominent role. Also, the bendsplay elastic anisotropy for conventional nematic order is expected to be different in view of the intricate electrostatic interactions between finite-aspect-ratio colloidal particles [101,102]. We reiterate that all predictions presented here are subject to the condition that the rods be strongly aligned along their director m.…”

Anisotropic electrostatic screening of charged colloids in nematic solvents

“…To determine the anisotropic electrostatic potential, we first derive an analytical expression by mapping the charged particle to an ionpenetrable spherical shell with radius R and surface charge density e S , followed by a multipole expansion. The approach is more extensively explained in Materials and Methods, the Supplementary Materials, and (46).…”

“…Using the LSA, which entails that the two-body electrostatic potential is given by the sum of the single-particle electrostatic potentials of the two particles, gives the DLVO expression (Eq. 2) if one uses the stress-tensor method (46). However, applying the LSA directly to Eq.…”

“…This method resembles how the electrostatic part of the DLVO expression can be obtained by solving the auxiliary problem of a spherical shell or a point charge, accounting properly for ion-hard core exclusions, although still using the free energy route. The point/shell charge value together with the ions contained within r < a equals the charge on the particle [see, for a more detailed discussion, the appendix in (28) for the shell calculation and (46) for the point-charge method]. Unfortunately, a similar method to determine  S does not apply here since (r) is inhomogeneous for r < a when the particle is dispersed in an anisotropic dielectric medium, which therefore requires a numerical fit.…”