William Kung

Thermodynamics of ternary electrolytes: Enhanced adsorption of macroions as minority component to liquid interfaces

We study the equilibrium thermodynamics between two ternary ionic systems in immiscible solvents characterized by different dielectric constants. We consider system geometries wherein the two phases of immiscible solvents occupy, respectively, semi-infinite regions of space separated by neutral and charged planar interfaces. Specifically we analyze the case where the ternary system is composed of a pair of symmetric ions plus a minority charged component of high valence. We describe the system by means of a nonlinear mean-field theory. We first obtain exact analytical solutions for the electrostatic potentials, as well as density profiles for a symmetric binary system, and then extend these results to the ternary case using the perturbation theory. We show that the corresponding adsorption and depletion of multivalent macroions at the interface are highly enhanced when compared with the monovalent case.

Nanoparticles in aqueous media: crystallization and solvation charge asymmetry

We examine the issue of whether dispersion forces can lead to crystallization in a system of charged nanoparticles in aqueous solution with NaCl salt. To this end, we determine the effective pair potential (EPP) among the nanoparticles starting from a model system that explicitly includes the salt ions and the water molecules, using the well-tested simple point charge extended (SPC/E) model for the latter. The two-particle correlations among the components of this model system are determined using the reference interaction site model (RISM) equation complemented with the hypernetted-chain (HNC) closure. The EPP at infinite nanoparticle dilution is obtained from these correlations after contracting the salt ions and water molecules following the method presented in P. Gonzalez-Mozuelos, J. Phys. Chem. B, 2006, 110, 22702. The dressed-interaction-site theory (DIST) discussed in that work shows that the corresponding EPP has a short-range contribution plus a screened electrostatic (Yukawa) potential with renormalized charges and dielectric constant. A polynomial-fitting scheme is devised to quantify the dependence of the effective electrostatic paramenters on the underlying salt concentration. As such, we derive the phase diagram for our system, using a mean field approach based upon the computed EPP, for a range of (finite) nanoparticle densities and salt concentrations and demonstrate crystallization. Findings from our model also suggest the possibility of crystallization occurring preferentially among nanoparticles with negative charges than those with positive charges of the same magnitude and thus exhibiting charge asymmetry due to solvation effects.

Hydrodynamics of polar liquid crystals.

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C infinity v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D infinity h) in that it contains terms violating the n --> -n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

A minimal model of nanoparticle crystallization in polar solvents via steric effects

Motivated by recent experimental findings, we present here a minimal analytical model illustrating that the steric interactions among the ionic components can provide a simple, generic mechanism for like-charge crystallization in prototypical nanoparticle systems with counterions in polar solvents. In particular, the underlying steric interactions among these ionic components arise from the structural organization of the polar solvent molecules surrounding these ions as molecular dipole moments that may cooperatively enhance or counteract existing entropic depletion and electrostatic forces. Phenomenologically capturing these steric effects, we assume only the existence of a short-range pairwise Gaussian interaction, which has already been employed usefully for nanoparticles with hydrophillic surfaces or grafted-polymer coatings, among these ionic components (nanoparticles and counterions). The corresponding Gaussian interaction parameters characterize tunable interaction strengths. Making use of an analytically obtained effective pairwise potential between two nanoparticles, upon the contraction of counterions, we derive phase diagrams for nanoparticle systems of varying charge- and size-ratios as a function of particle densities, and observe crystallization for a range of parameters. We further demonstrate that our minimal model is compatible with the phenomenon of charge asymmetry.

Mediation of long-range attraction selectively between negatively charged colloids on surfaces by solvation

We propose a mean-field analytical model to account for the observed asymmetry in the ability to form long-range attraction by the negatively charged colloidal particles and not their equivalently charged positive counterpart. We conjecture that this asymmetry is due to solvation effects, and we phenomenologically capture its physics by considering the relative strength of this water-induced short-range repulsion between the different charge species. We then apply our model to the colloidal system of negatively charged disks that are neutralized by a sea of counterions and strongly absorbed to an interface in a compressible binary system. We demonstrate the resulting coexistence between a dilute isotropic ionic phase and a condensed hexagonal lattice phase as a function of density and interaction strength.

Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem

We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models that consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol’d tongues in the regime of low AC-driving amplitude or high AC-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro’s argument that holds in the perturbative regime of large driving amplitudes or low driving frequency where the effect of pinning is weak.

Poisson-bracket approach to the dynamics of bent-core molecules

We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial C infinity v symmetry to biaxial systems exhibiting local C2v symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar-body axis (n) as well as a polar axis (p) along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the p-->-p symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.

Adsorption Profiles and Solvation of Ions at Liquid-Liquid Interfaces and Membranes

William Kung1, Francisco J. Solis2 and Monica Olvera de la Cruz3 1Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208-3108 2Division of Mathematical and Natural Sciences, Arizona State University, Glendale, AZ 85306 3Department of Materials Science and Engineering, Department of Chemistry, Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208-3108 USA