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We consider a statistical mechanical model of a generic flexible polyelectrolyte, comprised of identically charged monomers with long range electrostatic interactions, and short-range interactions quantified by a disorder field along the polymer contour sequence, which is randomly quenched. The free energy and the monomer density profile of the system for no electrolyte screening are calculated in the case of a system composed of two infinite planar bounding surfaces with an intervening oppositely charged polyelectrolyte chain. We show that the effect of the contour sequence disorder, mediated by short-range interactions, leads to an enhanced localization of the polyelectrolyte chain and a first order phase transition at a critical value of the inter-surface spacing. This phase transition results in an abrupt change of the pressure from negative to positive values, effectively eliminating polyelectrolyte mediated bridging attraction.

We present a derivation of generalized Poisson-Boltzmann equations starting {from} classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by (Bazant et al., 2011), whereby the structuring near the surface is determined by bulk coefficients., Comment: 6 pages

We explore the implications of the conservation law(s) and the corresponding "continuity equation(s)", resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and can not be reduced to one another, but neither are they disjoint alternatives. We analyze the relation between them and elucidate the fundamental role that the chain backfolding plays in the determination of their relative strength and importance. Finally, we show that the correct penalty potential in the effective free energy, implementing these conservation laws, should actually connect both the tensorial and the vectorial constraints. We show that the consequences of the polymer chains connectivity for their consistent mesoscopic description are thus not only highly non-trivial but that its proper implementation is absolutely crucial for a consistent coarse grained description of the main-chain polymer nematics., Comment: 9 pages, 1 figure

The exact solution, via transfer matrix, of the simple one dimensional lattice Coulomb gas (1d LCG) model can reproduce peculiar features of ionic liquid capacitors, such as overscreening, layering, and camel- and bell-shaped capacitance curves. Using the same transfer matrix method, we now compute the bulk properties of the 1d LCG in the constant voltage ensemble. We unveil a phase diagram with rich structure exhibiting a low density disordered and high density ordered phases, separated by a first order phase transition at low temperature; the solid state at full packing can be ordered or not, depending on the temperature. This phase diagram, which is strikingly similar to its three dimensional counterpart, also sheds light on the behaviour of the confined system., Comment: 6 pages, 6 figures

Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nano-structured devices. In the past decade, many new materials have become available, which has stimulated the need of understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights in related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed matter physics, high energy physics, chemistry and biology. In this review, we summarize major breakthroughs and emphasize the common origin of van der Waals and Casimir interactions. We examine progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications., Comment: 54 pages, 18 figures, 400+ references. Review article

We study the thermal fluctuation induced interactions between two surfaces containing Brownian charges which are held at different temperatures. Using a dynamical form of Debye-H\"uckel theory implemented within the stochastic equation for the density of mobile Brownian charges, we derive expressions for the average force between the two surfaces as well as its variance. The latter is found both for the normal, of finite mean, as well as the lateral force, of zero mean, between the surfaces., Comment: 6 pages, 3 figures, EPL style

We study the Poisson-Boltzmann equation in the context of dense charged fluids where steric effects become important. We generalise the lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other approximations, valid for more realistic equations of state, such as the Carnahan-Starling approximation and find strong differences in the shapes of the free energy functions. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation., Comment: 9 pages, 6 figures

We study the problem of charge regulation and its effects on electrostatic interactions between dissociable charge groups immersed in a univalent electrolyte, within a family of one dimensional exactly solvable models. We consider the case of both charge regulated plates, but also the interaction of pairs of finite size dielectric "particles". Using the transfer matrix formalism we are able to determine the disjoining pressure as well as the correlations between the charge and the dipole moments of the objects as a function of their separation and electrolyte concentration, Comment: 6 pages, 3 figures

We consider how membrane fluctuations can modify the miscibility of lipid mixtures, that is to say how the phase diagram of a boundary-constrained membrane is modified when the membrane is allowed to fluctuate freely in the case of zero surface tension. In order for fluctuations to have an effect, the different lipid types must have differing Gaussian rigidities. We show, somewhat paradoxically, that fluctuation-induced interactions can be treated approximately in a mean-field type theory. Our calculations predict that, depending on the difference in bending and Gaussian rigidity of the lipids, membrane fluctuations can either favor or disfavor mixing., Comment: 25 pages Latex IOP Style, 2 figures

Fluctuations of the thermal or classical component of the van der Waals force between two dielectric slabs, modelled as an ensemble of polarizable dipoles which interact via the usual electrostatic dipole-dipole interaction, are evaluated. In the model the instantaneous force is a deterministic function of the dipole configurations in the slabs and its fluctuations are purely due to dipole fluctuations (no background thermal fluctuations of the electromagnetic field are considered). The average of the force and its variance are computed. The fluctuations of the force exhibit normal thermodynamic scaling in that they are proportional to the area of the two plates, and even more importantly, do not depend on any microscopic cut-off in the theory. The average and the variance of the thermal van der Waals forces give a unique fingerprint of these fluctuation interactions., Comment: 5 pages Revtex

Dielectric spectroscopy is used to investigate fundamental length scales describing the structure of hyaluronic acid sodium salt (Na-HA) semidilute aqueous solutions. In salt-free regime, the length scale of the relaxation mode detected in MHz range scales with HA concentration as $c_\mathrm{HA}^{-0.5}$ and corresponds to the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution. The same scaling was observed for the case of long, genomic DNA. Conversely, the length scale of the mode detected in kHz range also varies with HA concentration as $c_\mathrm{HA}^{-0.5}$ which differs from the case of DNA ($c_\mathrm{DNA}^{-0.25}$). The observed behavior suggests that the relaxation in the kHz range reveals the de Gennes-Dobrynin renormalized Debye screening length, and not the average size of the chain, as the pertinent length scale. Similarly, with increasing added salt the electrostatic contribution to the HA persistence length is observed to scale as the Debye length, contrary to scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. We argue that the observed features of the kHz range relaxation are due to much weaker electrostatic interactions that lead to the absence of Manning condensation as well as a rather high flexibility of HA as compared to DNA., Comment: 11 pages, 8 figures, submitted to PRE

We derive the complete form of the van der Waals dispersion interaction between two infinitely long anisotropic semiconducting/insulating thin cylinders at all separations. The derivation is based on the general theory of dispersion interactions between anisotropic media as formulated in [J. N. Munday, D. Iannuzzi, Yu. S. Barash and F. Capasso, {\sl Phys. Rev. A} {\bf 71}, 042102 (2005)]. This formulation is then used to calculate the dispersion interactions between a pair of single walled carbon nanotubes at all separations and all angles. Non-retarded and retarded forms of the interactions are developed separately. The possibility of repulsive dispersion interactions and non-monotonic dispersion interactions is discussed within the framework of the new formulation.

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the inter-surface space upon increasing the solvent/membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer., Comment: 4 pages, 3 figures

We compare weak and strong coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte-Carlo simulations. Analytical results in both weak and strong coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak and the strong coupling limits., Comment: 15 pages, 8 figures

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 figures

We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self averaging and is given by a description in terms of effective dielectric functions. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric function proximal to each other across the dielectrically homogeneous slab., Comment: 4 pages RevTex, 1 pdf figure

We study the interaction of two cylinders with helical charge distribution mediated by neutralizing counterions, by analyzing the separation as well as the azimuthal angle dependence of the interaction force in the weak and strong coupling limit. While the azimuthal dependence of the interaction in the weak coupling limit is overall small and mostly negligible, the strong coupling limit leads to qualitatively new features of the interaction, among others also to an orientationally dependent optimal configuration that is driven by angular dependence of the correlation attraction. We investigate the properties of this azimuthal ordering in detail and compare it to existing results., Comment: 11 pages, 12 figures

Dielectric spectroscopy is used to investigate fundamental length scales of 146 bp short-fragment (nucleosomal) dilute Na-DNA solutions. Two relaxation modes are detected: the high- and the low-frequency mode. Dependence of the corresponding length scales on the DNA and on the (uni-valent) salt concentration is studied in detail, being different from the case of long, genomic DNA, investigated before. In low added salt regime, the length scale of the high-frequency mode scales as the average separation between DNAs, though it is smaller in absolute magnitude, whereas the length scale of the low-frequency mode is equal to the contour length of DNA. These fundamental length scales in low added salt regime do not depend on whether DNA is in a double stranded or single stranded form. On the other hand, with increasing added salt, the characteristic length scale of low-frequency mode diminishes at low DNA concentrations probably due to dynamical formation of denaturation bubbles and/or fraying in the vicinity of DNA denaturation threshold., Comment: Accepted for publication in Europhysics Letters. 5 pages, 4 figures

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak coupling level the image charge effects are generally small, making their mark only in the second order fluctuation term. However, in the strong coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long range image potentials., Comment: 21 pages, 8 figures

We report on a detailed characterization of complex dielectric response of Na-DNA aqueous solutions by means of low-frequency dielectric spectroscopy (40 Hz - 110 MHz). Results reveal two broad relaxation modes of strength 20<\Delta\epsilon_LF<100 and 5<\Delta\epsilon_HF<20, centered at 0.5 kHz<\nu_LF<70 kHz and 0.1 MHz<\nu_HF<15 MHz. The characteristic length scale of the LF process, 50

We investigate the electrostatic contribution to the persistence length of a semiflexible polymer chain whose segments interact via a screened Debye-H\" uckel dipolar interaction potential. We derive the expressions for the renormalized persistence length on the level of a 1/D-expansion method already successfully used in other contexts of polyelectrolye physics. We investigate different limiting forms of the renormalized persistence length of the dipolar chain and show that in general it depends less strongly on the screening length than in the context of a monopolar chain. We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. This can be understood solely on the basis of a swifter decay of the dipolar interactions with separation compared to the monopolar electrostatic interactions. We comment also on the general contribution of higher multipoles on the electrostatic renormalization of the bending rigidity., Comment: 19 pages, 3 figures

We investigate the orientational order of transverse polarization vectors of long columns of nucleosomal core particles and their coupling to positional order in high density mesophases discovered recently. Inhomogeneous polar ordering of these columns precipitates crystalization of the 2D sections with different orientations of the transverse polarization vector on each column in the unit cell. We propose possible scenarios for going from the 2D hexagonal phase into distorted lamellar and related phases observed experimentally., Comment: 4 pages and 2 figures

Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic layers. We then compare our result with an approximation based on an anisotropic-continuum representation of the stratified medium. Satisfactory agreement between discrete-layer and continuum models is reached only for thicknesses of ten or more layers., Comment: 9 pages and 4 figures

We investigate interactions between an elastic membrane and a substrate characterized by quenched positional disorder in the height function. We show that the positional disorder transforms the standard secondary DLVO minimum into two separate states: the hovering state characterized by a planar membrane at a finite separation from the interface and a pinned state where the membrane follows closely the asperities of the substrate and is as a consequence quite corrugated. The transition between the two states is continuous and depends on the parameters of the underlying DLVO potential as well as the parameters describing the quenched height-height correlation function of the substrate., Comment: 7 pages, incl. 1 figure

Optical experiments on calf thymus DNA films subjected to different buffer environments are reported. The optical conductivity is that of a disordered or lightly doped semiconductor with a well-defined band-gap for charge excitations and low frequency transport determined by a small number of strongly localized electron states., Comment: 5 pages, 3 figures submitted to PRL

We investigate the orientational order of transverse polarization vectors of long, stiff polymer molecules and their coupling to bond orientational and positional order in high density mesophases. Homogeneous ordering of transverse polarization vector promotes distortions in the hexatic phase, whereas inhomogeneous ordering precipitates crystalization of the 2D sections with different orientations of the transverse polarization vector on each molecule in the unit cell. We propose possible scenarios for going from the hexatic phase, through the distorted hexatic phase to the crystalline phase with an orthorhombic unit cell observed experimentally for the case of DNA., Comment: 4 pages, 2 figures

We investigate the pseudo-Casimir force acting between two charged surfaces confining a single polyelectrolyte chain with opposite charge. We expand the exact free energy to the second order in the local electrostatic field as well as the replicated polymer density field around the mean-field (saddle-point) solution. The quadratic terms lead to a fluctuation interaction that is partly due to the (thermal) Casimir effect for the confined electrostatic field and partly due to the pseudo-Casimir effect due to the confined replicated polymer density field. We study the intersurface separation dependence of both effects and show that the pseudo-Casimir effect leads to a long range attraction between the surfaces that decays with an anomalous algebraic exponent of $\sim 1.7$, smaller than the standard exponent of 2 in the case of Casimir interactions., Comment: 18 pages, 4 figures

The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entropic part of the free energy enhances the effective repulsive interactions between the chains. This configurational contribution goes as the fourth root of the direct interactions. Enhancement originates from the coupling between bending fluctuations and the compressibility of the nematic array normal to the average director. In the second part of the paper we use osmotic stress to measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl solutions. These measurements cover 5 orders of magnitude in DNA osmotic pressure. At high osmotic pressures the equation of state, dominated by exponentially decaying hydration repulsion, is independent of the ionic strength. At lower pressures the equation of state is dominated by fluctuation enhanced electrostatic double layer repulsion. The measured equation of state for DNA fits well with our theory for all salt concentrations. We are able to extract the strength of the direct electrostatic double layer repulsion. This is a new and alternative way of measuring effective charge densities along semiflexible polyelectrolytes., Comment: text + 5 figures. Submitted to PRE

We formulate low-frequency charge-fluctuation forces between charged cylinders - parallel or skewed - in salt solution: forces from dipolar van der Waals fluctuations and those from the correlated monopolar fluctuations of mobile ions. At high salt concentrations forces are exponentially screened. In low-salt solutions dipolar energies go as $R^{-5}$ or $R^{-4}$; monopolar energies vary as $R^{-1}$ or $\ln{R}$, where $R$ is the minimal separation between cylinders. However, pairwise summability of rod-rod forces is easily violated in low-salt conditions. Perhaps the most important result is not the derivation of pair potentials but rather the demonstration that some of these expressions may not be used for the very problems that originally motivated their derivation., Comment: 8 pages and 1 fig in ps format

We analyse the elastic energy of an intercalated smectic where orientationally ordered polymers with an average orientation varying from layer to layer are intercalated between smectic planes. The lowest order terms in the coupling between polymer director and smectic layer curvature are added to the smectic elastic energy. Integration over the smectic degrees of freedom leaves an effective polymer twist energy that has to be included into the total polymer elastic energy leading to a fluctuational renormalization of the intercalated polymer twist modulus. If the polymers are chiral this in its turn leads to a renormalization of the cholesteric pitch., Comment: 8 pages, 1 fig in ps available from rudi@helix.nih.gov Replaced version also contains title and abstract in the main text

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid crystalline phase digram: a higher-density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction; and a lower-density cholesteric region with fluid-like positional order. X-rays scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a six-fold azimuthal modulation of the first order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order that had been expected from the change in optical birefringence patterns and that is consistent with a rapid onset of molecular positional disorder. This change in motion was previously inferred from intermolecular force measurements and is now confirmed by $\rm ^{31}P$ NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between $\sim 120$ mg/ml to $\sim 600$ mg/ml, allows measurement of the free energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states., Comment: 14 pages, 3 figures in gif format available at http://abulafia.mgsl.dcrt.nih.gov/pics.html E-mail: rudi@helix.nih.gov

Arguments are presented to the effect that embedding semi-flexible (wormlike) ideal polymers into a fluctuating, flexible surface leads to an effective attractive orientational interaction between polymer segments that precipitates an orientational ordering transition of the polymer chains on the surface even in the case of otherwise ideal (non-interacting) chains. The orientational interaction is analogous to the (zero order) Casimir force and is due to the energy change in surface conformational fluctuations in the presence of embedded semi-flexible chains., Comment: LaTeX, 11 pages

A microscopic model of a surface polymer network - membrane system is introduced, with contact polymer surface interactions that can be either repulsive or attractive and sliplinks of functionality four randomly distributed over the supporting membrane surface anchoring the polymers to it. For the supporting surface perturbed from a planar configuration and a small relative number of surface sliplinks, we investigate an expansion of the free energy in terms of the local curvatures of the surface and the surface density of sliplinks, obtained through the application of the Balian - Bloch - Duplantier multiple surface scattering method. As a result, the dependence of the curvature elastic modulus, the Gaussian modulus as well as of the spontaneous curvature of the "dressed" membrane, ~{\sl i.e.} polymer network plus membrane matrix, is obtained on the mean polymer bulk end to end separation and the surface density of sliplinks., Comment: 15 pages with one included compressed uuencoded figure.

The issue of different parameterizations of the axisymmetric vesicle shape addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E {\bf 47} (1993) 461 ] is reassesed, especially as it transpires through the corresponding Euler - Lagrange equations of the associated elastic energy functional. It is argued that for regular, smooth contours of vesicles with spherical topology, different parameterizations of the surface are equivalent and that the corresponding Euler - Lagrange equations are in essence the same. If, however, one allows for discontinuous (higher) derivatives of the contour line at the pole, the differently parameterized Euler - Lagrange equations cease to be equivalent and describe different physical problems. It nevertheless appears to be true that the elastic energy corresponding to smooth contours remains a global minimum., Comment: 10 pages, latex, one figure included