Excluded volume effects in macromolecular forces and ion-interface interactions

Interactions between zwitterionic membranes in complex electrolytes

We investigate the electrostatic interactions of zwitterionic membranes immersed in mixed electrolytes composed of mono- and multivalent ions. We show that the presence of monovalent salt is a necessary condition for the existence of a finite electrostatic force on the membrane. As a result, the mean-field membrane pressure originating from the surface dipoles exhibits a nonuniform salt dependence, characterized by an enhancement for dilute salt conditions and a decrease at intermediate salt concentrations. On addition of multivalent cations to the submolar salt solution, the separate interactions of these cations with the opposite charges of the surface dipoles makes the intermembrane pressure more repulsive at low membrane separation distances and strongly attractive at intermediate distances, resulting in a discontinuous like-charge binding transition followed by the membrane binding transition. By extending our formalism to account for correlation corrections associated with large salt concentrations, we show that membranes of high surface dipole density immersed in molar salt solutions may undergo a membrane binding transition even without the multivalent cations. Hence, the tuning of the surface polarization forces by membrane engineering can be an efficient way to adjust the equilibrium configuration of dipolar membranes in concentrated salt solutions.

Debye-Hückel theory of weakly curved macroions: Implementing ion specificity through a composite Coulomb-Yukawa interaction potential

The free energy of a weakly curved, isolated macroion embedded in a symmetric 1:1 electrolyte solution is calculated on the basis of linear Debye-Hückel theory, thereby accounting for nonelectrostatic Yukawa pair interactions between the mobile ions and of the mobile ions with the macroion surface, present in addition to the electrostatic Coulomb potential. The Yukawa interactions between anion-anion, cation-cation, and anion-cation pairs are independent from each other and serve as a model for solvent-mediated ion-specific effects. We derive expressions for the free energy of a planar surface, the spontaneous curvature, the bending stiffness, and the Gaussian modulus. It is shown that a perturbation expansion, valid if the Yukawa interactions make a small contribution to the overall free energy, yields simple analytic results that exhibit good agreement with the general free energy over the range of experimentally relevant interaction parameters.

Surface tension of a Yukawa fluid according to mean-field theory

Yukawa fluids consist of particles that interact through a repulsive or attractive Yukawa potential. A surface tension arises at the walls of the container that encloses the fluid or at the interface between two coexisting phases. We calculate that surface tension on the level of mean-field theory, thereby either ignoring the particle size (ideal Yukawa fluid) or accounting for a non-vanishing particle size through a nonideal contribution to the free energy, exemplified either on the level of a lattice gas (lattice Yukawa fluid) or based on the Carnahan-Starling equation of state (Carnahan-Starling Yukawa fluid). Our mean-field results, which do not rely on assuming small gradients of the particle concentrations, become exact in the limit of large temperature and large screening length. They are calculated numerically in the general case and analytically in the two limits of small particle concentration and close to the critical point for a phase-separating system. For a sufficiently small particle concentration, our predicted surface tension is accurate whereas for a phase boundary, we expect good agreement with exact calculations in the limit of a large screening length and if the mean-field model employs the Carnahan-Starling equation of state.

Microscopic formulation of nonlocal electrostatics in polar liquids embedding polarizable ions

Nonlocal electrostatic interactions associated with finite solvent size and ion polarizability are investigated within the mean-field linear response theory. To this end, we introduce a field-theoretic model of a polar liquid composed of linear multipole solvent molecules and embedding polarizable ions modeled as Drude oscillators. Unlike previous dipolar Poisson-Boltzmann formulations treating the solvent molecules as point dipoles, our model is able to qualitatively reproduce the non-local dielectric response behavior of polar liquids observed in molecular dynamics simulations and atomic force microscope experiments for water solvent at charged interfaces. The present theory explains the formation of the associated interfacial hydration layers in terms of a cooperative dipolar response mechanism driven by the reaction of the solvent molecules to their own polarization field. We also incorporate into the theory the relative multipole moments of water molecules obtained from quantum mechanical calculations and show that the multipolar contributions to the dielectric permittivity are largely dominated by the dipolar one. We find that this stems from the mutual cancellation of the first two interfacial hydration layers of opposite net charge for multipolar liquids. Within the same nonlocal dielectric response theory, we show that the induced ion polarizability reverses the interfacial ion density trends predicted by the Poisson-Boltzmann theory, resulting in a surface affinity of coions and exclusion of counterions. The results indicate that the consideration of the discrete charge composition of solvent molecules and ions is the key step towards a microscopic understanding of nonlocal electrostatic effects in polar solvents.