We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy delta E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for delta E as a function of the ratio of the mean plate distance H, to the corrugation length lambda: For lambda<>H.

The interaction of a long flexible polymer chain with mesoscopic particles of spherical or elongated cylindrical shape is investigated by field-theoretic methods using the polymer-magnet analogy. In the case that these particles are immersed in a dilute polymer solution and exhibit purely repulsive surfaces we study density profiles for monomers and chain ends near such a particle, the change of configurational entropy by immersing a particle into the solution, and the depletion interaction between a particle and a distant planar wall. Both ideal chains and chains with an excluded-volume interaction are considered. We also analyze particle surfaces with a short-ranged attraction and the adsorption-desorption transition for an ideal polymer chain. Properties such as the number of surface contacts are evaluated both in the adsorbed limit, in which the thickness of the adsorbed layer is much smaller than the unperturbed polymer size so that ground-state dominance applies, and at the adsorption threshold. ͓S1063-651X͑96͒02308-2͔ PACS number͑s͒: 05.70.Jk, 68.35.Rh, 61.25.Hq, 82.70.Dd ͩ ‫ץ‬ ‫ץ‬L Ϫ⌬ D ͪ Z L ͑ r,rЈ͒ϭ0 ͑1.2a͒ with the ''initial condition''

The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres, quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modeling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.

The Casimir force between macroscopic bodies depends strongly on their shape and orientation.To study this geometry dependence in the case of two deformed metal plates, we use a path integral quantization of the electromagnetic field which properly treats the many-body nature of the interaction, going beyond the commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary deformations we provide an analytical result for the deformation induced change in Casimir energy, which is exact to second order in the deformation amplitude. For the specific case of sinusoidally corrugated plates, we calculate both the normal and the lateral Casimir forces. The deformation induced change in the Casimir interaction of a flat and a corrugated plate shows an interesting crossover as a function of the ratio of the mean plate distance H to the corrugation length λ: For λ ≪ H we find a slower decay ∼ H −4 , compared to the H −5 behavior predicted by PWS which we show to be valid only for λ ≫ H. The amplitude of the lateral force between two corrugated plates which are out of registry is shown to have a maximum at an optimal wavelength of λ ≈ 2.5 H. With increasing H/λ 0.3 the PWS approach becomes a progressively worse description of the lateral force due to many-body effects. These results may be of relevance for the design and operation of novel microelectromechanical systems (MEMS) and other nanoscale devices.

Long-ranged correlations in a fluid close to its critical point T c cause distinct forces between immersed colloidal particles and the container walls. We calculate such a force and its temperature dependence for the generic case of a spherical particle located at a distance D from a planar wall and find that the force attains a maximum at a temperature T max ͑D͒ above T c , which facilitates quantitative experimental tests. The corresponding effective pair interaction between the colloidal particles themselves, potentially leading to aggregation, is also discussed. [S0031-9007(98)06900-2] PACS numbers: 64.60. Fr, 64.75. + g, 68.35.Rh, 82.70.Dd In 1948 Casimir [1] predicted that the confinement of quantum mechanical vacuum fluctuations of the electromagnetic field causes long-ranged forces between two conducting uncharged plates. Only recently, this so-called Casimir effect was tested experimentally [2] with high accuracy for the force on a conducting sphere near a conducting planar surface.Thirty years later Fisher and de Gennes [3] pointed out that an analogous effect should occur in a thin film of a binary liquid mixture near the critical demixing point T c of the bulk mixture. In this case the confinement of critical fluctuations of an order parameter field induces long-ranged forces between the surfaces of the film [4]. In recent years the so-called "critical Casimir effect" has attracted increasing theoretical interest [5,6]. In spite of these efforts-and in contrast to the quantum mechanical Casimir effect-the critical Casimir effect lacks so far an unambiguous experimental verification. This unsatisfactory state of affairs persists mainly due to a combination of two reasons. First, so far most theoretical studies have been restricted to the special case T T c . In this case the bulk correlation length j 6 j 6 0 jtj 2n , where t ͑T 2 T c ͒͞T c _ 0 and n is a standard bulk critical exponent, is infinitely large which cannot be realized experimentally. In practice the divergence of j is limited, e.g., by a finite temperature resolution, spatial inhomogeneities of T , and external fields such as gravity. In addition, the knowledge of the temperature dependence of the critical Casimir force is indispensable for experimental tests in order to be able to subtract the regular background contributions due to the omnipresent dispersion forces. Second, most theoretical studies deal with the parallel plate geometry which happens to be unsuitable for actual measurements because, surprisingly, it turns out that it is too demanding to keep the plates sufficiently parallel. The preferential geometry consists of a sphere located near a planar wall [2] rather than of two parallel plates.We consider the generic case of a spherical particle with mesoscopic radius R immersed in a binary liquid mixture at a distance D of closest approach surface-to-surface from a planar boundary wall. The particle may be regarded as a freely moving colloidal particle, but it can also model a sphere attached to the tip of an atomic force mic...