Multiscale approach to nematic liquid crystals via statistical field theory.

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients A, B, C, L_{1}, and L_{2} of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of Monte Carlo simulation.

Modulation of Elasticity and Interactions in Charged Lipid Multibilayers: Monovalent Salt Solutions.

We have studied the electrostatic screening effect of NaCl solutions on the interactions between anionic lipid bilayers in the fluid lamellar phase using a Poisson-Boltzmann-based mean-field approach with constant charge and constant potential limiting charge regulation boundary conditions. The full DLVO potential, including the electrostatic, hydration and van der Waals interactions, was coupled to thermal bending fluctuations of the membranes via a variational Gaussian Ansatz. This allowed us to analyze the coupling between the osmotic pressure and the fluctuation amplitudes and compare them both simultaneously with their measured dependence on the bilayer separation, determined by the small-angle X-ray scattering experiments. High-structural resolution analysis of the scattering data revealed no significant changes of membrane structure as a function of salt concentration. Parsimonious description of our results is consistent with the constant charge limit of the general charge regulation phenomenology, with fully dissociated lipid charge groups, together with a 6-fold reduction of the membranes' bending rigidity upon increasing NaCl concentration.

Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

van der Waals torque and force between dielectrically anisotropic layered media.

We analyse van der Waals interactions between a pair of dielectrically anisotropic plane-layered media interacting across a dielectrically isotropic solvent medium. We develop a general formalism based on transfer matrices to investigate the van der Waals torque and force in the limit of weak birefringence and dielectric matching between the ordinary axes of the anisotropic layers and the solvent. We apply this formalism to study the following systems: (i) a pair of single anisotropic layers, (ii) a single anisotropic layer interacting with a multilayered slab consisting of alternating anisotropic and isotropic layers, and (iii) a pair of multilayered slabs each consisting of alternating anisotropic and isotropic layers, looking at the cases where the optic axes lie parallel and/or perpendicular to the plane of the layers. For the first case, the optic axes of the oppositely facing anisotropic layers of the two interacting slabs generally possess an angular mismatch, and within each multilayered slab the optic axes may either be the same or undergo constant angular increments across the anisotropic layers. In particular, we examine how the behaviors of the van der Waals torque and force can be "tuned" by adjusting the layer thicknesses, the relative angular increment within each slab, and the angular mismatch between the slabs.

Nonequilibrium Tuning of the Thermal Casimir Effect.

In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Casimir forces between two plates containing Brownian charges can be modulated by decorrelating the system through the application of an electric field, which generates a nonequilibrium steady state with a constant current in one or both plates, reducing the ensuing fluctuation-generated normal force while at the same time generating a lateral drag force. This hypothesis is confirmed by detailed numerical simulations as well as an analytical approach based on stochastic density functional theory.

Pseudo-Casimir stresses and elasticity of a confined elastomer film.

Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links. Herein, we consider an incompressible and flat elastomer film of an axisymmetric shape confined between two large hard co-planar substrates, with the axis of the film perpendicular to the substrates. We address the impact that thermal fluctuations of the cross-links have on the free energy of elastic deformation of the system, subject to the requirement that the fluctuating elastomer cannot detach from the substrates. We examine the behavior of the deformation free energy for one case where a rigid pinning boundary condition is applied to a class of elastic fluctuations at the confining surfaces, and another case where the same elastic fluctuations are subjected to soft "gluing" potentials. We find that there can be significant departures (both quantitative and qualitative) from the prediction of classical rubber elasticity theory when elastic fluctuations are included. Finally, we compare the character of the attractive part of the elastic fluctuation-induced, or pseudo-Casimir, stress with the standard thermal Casimir stress in confined but non-elastomeric systems, finding the same power law decay behavior when a rigid pinning boundary condition is applied; for the case of the gluing potential, we find that the leading order correction to the attractive part of the fluctuation stress decays inversely with the inter-substrate separation.

Hydrodynamic fluctuation-induced forces in confined fluids.

We study thermal, fluctuation-induced hydrodynamic interaction forces in a classical, compressible, viscous fluid confined between two rigid, planar walls with no-slip boundary conditions. We calculate hydrodynamic fluctuations using the linearized, stochastic Navier-Stokes formalism of Landau and Lifshitz. The mean fluctuation-induced force acting on the fluid boundaries vanishes in this system, so we evaluate the two-point, time-dependent force correlations. The equal-time correlation function of the forces acting on a single wall gives the force variance, which we show to be finite and independent of the plate separation at large inter-plate distances. The equal-time, cross-plate force correlation, on the other hand, decays with the inverse inter-plate distance and is independent of the fluid viscosity at large distances; it turns out to be negative over the whole range of plate separations, indicating that the two bounding plates are subjected to counter-phase correlations. We show that the time-dependent force correlations exhibit damped temporal oscillations for small plate separations and a more irregular oscillatory behavior at large separations. The long-range hydrodynamic correlations reported here represent a "secondary Casimir effect", because the mean fluctuation-induced force, which represents the primary Casimir effect, is absent.

Effective interactions between fluid membranes.

A self-consistent theory is proposed for the general problem of interacting undulating fluid membranes subject to the constraint that they do not interpenetrate. We implement the steric constraint via an exact functional integral representation and, through the use of a saddle-point approximation, transform it into a novel effective steric potential. The steric potential is found to consist of two contributions: one generated by zero-mode fluctuations of the membranes and the other by thermal bending fluctuations. For membranes of cross-sectional area S, we find that the bending fluctuation part scales with the intermembrane separation d as d-2 for d≪√S but crosses over to d-4 scaling for d≫√S, whereas the zero-mode part of the steric potential always scales as d-2. For membranes interacting exclusively via the steric potential, we obtain closed-form expressions for the effective interaction potential and for the rms undulation amplitude σ, which becomes small at low temperatures T and/or large bending stiffnesses κ. Moreover, σ scales as d for d≪√S but saturates at √kBTS/κ for d≫√S. In addition, using variational Gaussian theory, we apply our self-consistent treatment to study intermembrane interactions subject to different types of potentials: (i) the Moreira-Netz potential for a pair of strongly charged membranes with an intervening solution of multivalent counterions, (ii) an attractive square well, (iii) the Morse potential, and (iv) a combination of hydration and van der Waals interactions.

Molecular recognition by van der Waals interaction between polymers with sequence-specific polarizabilities.

We analyze van der Waals interactions between two rigid polymers with sequence-specific, anisotropic polarizabilities along the polymer backbones, so that the dipole moments fluctuate parallel to the polymer backbones. Assuming that each polymer has a quenched-in polarizability sequence which reflects, for example, the polynucleotide sequence of a double-stranded DNA molecule, we study the van der Waals interaction energy between a pair of such polymers with rod-like structure for the cases where their respective polarizability sequences are (i) distinct and (ii) identical, with both zero and non-zero correlation length of the polarizability correlator along the polymer backbones in the latter case. For identical polymers, we find a novel r(-5) scaling behavior of the van der Waals interaction energy for small inter-polymer separation r, in contradistinction to the r(-4) scaling behavior of distinct polymers, with furthermore a pronounced angular dependence favoring attraction between sufficiently aligned identical polymers. Such behavior can assist the molecular recognition between polymers.

Correlation potential of a test ion near a strongly charged plate.

We analytically calculate the correlation potential of a test ion near a strongly charged plate inside a dilute m:-n electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate Δz is much larger than a Gouy-Chapman length, the plate surface will behave effectively as an infinitely charged surface, and the dielectric constant of the plate effectively plays no role. (2) If Δz is larger than a Gouy-Chapman length but shorter than a Debye length, the correlation potential can be interpreted in terms of an image charge that is three times larger than the source charge. This behavior is independent of the valences of the ions. (3) The Green's function vanishes inside the plate if the surface charge density is infinitely large; hence the electrostatic potential is constant there. In this respect, a strongly charged plate behaves like a conductor plate. (4) If Δz is smaller than a Gouy-Chapman length, the correlation potential is dominated by the conventional image charge due to the dielectric discontinuity at the interface. (5) If Δz is larger than a Debye length, the leading order behavior of the correlation potential will depend on the valences of the ions in the electrolyte. Furthermore, inside an asymmetric electrolyte, the correlation potential is singly screened, i.e., it undergoes exponential decay with a decay width equal to the Debye length.

Phenomenological theory of isotropic-genesis nematic elastomers.

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment.