Van der Waals interactions across stratified media

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 figure

Recursion relations for generalized Fresnel coefficients: Casimir force in a planar cavity

We emphasize and demonstrate that, besides using the usual recursion relations involving successive layers, generalized Fresnel coefficients of a multilayer can equivalently be calculated using the recursion relations involving stacks of layers, as introduced some time ago [M. S. Tomas, Phys. Rev. A 51, 2545 (1995)]. Moreover, since the definition of the generalized Fresnel coefficients employed does not imply properties of the stacks, these nonstandard recursion relations can be used to calculate Fresnel coefficients not only for local systems but also for a general multilayer consisting of various types (local, nonlocal, inhomogeneous etc.) of layers. Their utility is illustrated by deriving a few simple algorithms for calculating the reflectivity of a Bragg mirror and extending the formula for the Casimir force in a planar cavity to arbitrary media.Comment: 5 pages, 2 figures, slightly expande

Three-body Casimir effects and non-monotonic forces

Casimir interactions are not pair-wise additive. This property leads to collective effects that we study for a pair of objects near a conducting wall. We employ a scattering approach to compute the interaction in terms of fluctuating multipoles. The wall can lead to a non-monotonic force between the objects. For two atoms with anisotropic electric and magnetic dipole polarizabilities we demonstrate that this non-monotonic effect results from a competition between two- and three body interactions. By including higher order multipoles we obtain the force between two macroscopic metallic spheres for a wide range of sphere separations and distances to the wall.Comment: 4 pages, 4 figure

Osmotic properties of polyethyleneglycols: quantitative features of brush and bulk scaling laws

From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander - de Gennes theory of polymer brushes successfully describes the intermembrane distance vs. applied osmotic stress data of Kenworthy et al. for PEG-grafted multilamellar liposomes [Biophys. J. (1995) 68:1921]. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semi-dilute regime of bulk polymer solutions). The condition that attached polymers behave as semi-dilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander - de Gennes brush scaling laws yield effective monomer lengths of 3.3 to 3.5 AA, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal content of PEG-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.Comment: 26 pages with figure

Charge Fluctuation Forces Between Stiff Polyelectrolytes in Salt Solution: Pairwise Summability Re-examined

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 forma