Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical, and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension γ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to γ(R) and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed.

Controlled self-assembly of biomolecular rods on structured substrates

We report on the evaporative self-assembly and orientational ordering of semi-flexible spherocylindrical M13 phages on asymmetric stranded webs of thin amorphous carbon films. Although the phages were dispersed with a low concentration in the isotropic phase, the substrate edges induced nematic ordering and bending of the phages. As revealed by transmission electron microscopy, phages were aligned parallel to the curved substrate edges. This two-dimensional self-assembly on structured substrates opens a new route to the design of structures of orientationally ordered semi-flexible biomacromolecules.

Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

Recently, new insights into the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work, I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle α, for 0 < α < 2π, which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for 0 < α < 2π and by adopting different reference regions.