Ordering of anisotropic polarizable polymer chains on the full many-body level

We study the effect of dielectric anisotropy of polymers on their equilibrium ordering within mean-field theory but with a formalism that takes into account the full n-body nature of van der Waals forces. Dielectric anisotropy within polymers is to be expected as the electronic properties of the polymer will typically be different along the polymer than across its cross section. It is therefore physically intuitive that larger charge fluctuations can be induced along the chain than perpendicular to it. We show that this dielectric anisotropy leads to n-body interactions which can induce an isotropic--nematic transition. The two body and three body components of the full van der Waals interaction are extracted and it is shown how the two body term behaves like the phenomenological self-aligning-pairwise nematic interaction. At the three body interaction level we see that the nematic phase that is energetically favorable is discotic, however on the full n-body interaction level we find that the normal axial nematic phase is always the stable ordered phase. The n-body nature of our approach also shows that the key parameter driving the nematic-isotropic transition is the bare persistence length of the polymer chain.Comment: 12 pages Revtex, 4 figure

Continuous Crystallization in Hexagonally-Ordered Materials

We demonstrate that the phase transition from columnar-hexagonal liquid crystal to hexagonal-crystalline solid falls into an unusual universality class, which in three-dimensional allows for both discontinuous transitions as well as continuous transitions, characterized by a single set of exponents. We show by a renormalization group calculation (to first order in $\epsilon = 4-d$) that the critical exponents of the continuous transition are precisely those of the XY model, which gives rise to a continuous evolution of elastic moduli. Although the fixed points of the present model are found to be identical to the XY model, the elastic compliance to deformations in the plane of hexagonal order, $\mu$, is nonetheless shown to critically influence the crystallization transition, with the continuous transition being driven to first order by fluctuations as the in plane response grows weaker, $\mu \to 0$.Comment: 4 pages, 2 figures (revised version

Thermodynamics of nano-spheres encapsulated in virus capsids

We investigate the thermodynamics of complexation of functionalized charged nano-spheres with viral proteins. The physics of this problem is governed by electrostatic interaction between the proteins and the nano-sphere cores (screened by salt ions), but also by configurational degrees of freedom of the charged protein N-tails. We approach the problem by constructing an appropriate complexation free energy functional. On the basis of both numerical and analytical studies of this functional we construct the phase diagram for the assembly which contains the information on the assembled structures that appear in the thermodynamical equilibrium, depending on the size and surface charge density of the nano-sphere cores. We show that both the nano-sphere core charge as well as its radius determine the size of the capsid that forms around the core.Comment: Submitte

Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

Overscreening in 1D lattice Coulomb gas model of ionic liquids

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble one dimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean field level of approximation, without any additional interactions.Comment: 4 pages 5 .eps figure

Role of Multipoles in Counterion-Mediated Interactions between Charged Surfaces: Strong and Weak Coupling

We present general arguments for the importance, or lack thereof, of the structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean-field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.Comment: 12 pages, 3 figure

Counterion-Mediated Weak and Strong Coupling Electrostatic Interaction between Like-Charged Cylindrical Dielectrics

We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). The results are compared with extensive Monte-Carlo simulations exhibiting good agreement with the limiting weak and strong coupling results in their respective regime of validity.Comment: 19 pages, 10 figure