On the virial coefficients of confined fluids: Analytic expressions for the thermodynamic properties of hard particles with attractions in slit and cylindrical pores to second order

On the virial expansion of model adsorptive systems

We investigate the thermodynamic properties of various super-critical model adsorptive systems with different fluid-solid attractive strengths using the confined-density virial expansion, with coefficients calculated using the Mayer-sampling Monte Carlo method up to fifth order. We find that the virial expansion converges for adsorptive systems over a density range corresponding approximately to the film-formation regime. Beyond this regime, higher order effects become increasingly important. The virial expansion of the density profile is also investigated. It is determined that this expansion gives insight into the structure associated with adsorption. We also find that weakly attractive systems have a more negative second virial coefficient than strongly attractive systems. This runs counter to the usual interpretation of bulk fluid virial coefficients. This is due to the infinite-dilution limit being very different for adsorbed fluids compared to bulk fluids.

Compressing Θ-Chain in Slit Geometry

When compressed in a slit of width D, a Θ-chain that displays the scaling of size R₀ (diameter) with respect to the number of monomers N, R₀ ∼ aN^1/2, expands in the lateral direction as R_|| ∼ aN^ν(a/D)^2ν-1. Provided that the Θ condition is strictly maintained throughout the compression, the well-known scaling exponent of Θ-chain in two dimensions, ν = 4/7, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from R₀/D < 1 to R₀/D ≫ 1, ν gradually deviates from ν = 1/2 and plateaus at ν = 3/4, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the Θ condition under confinement because of two major effects. First, as the dimension is reduced from three to two dimensions, the contributions of higher order virial terms, which can be ignored in three dimensions at large N, become significant, making the perturbative expansion used in Flory-type approach inherently problematic. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the second virial coefficient (B₂) changes from B₂ = 0 (Θ condition) in free space to B₂ > 0 (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.