Not macro, not micro, but meso: Three coarse-grained methods for thermodynamic properties of partially structured fluids

Macroscopic thermodynamics (e.g., classical equations of state) cannot provide an adequate description of the equilibrium properties of complex fluids or of simple fluids under near-microscopic constraints; such fluids have partial structure. Microscopic thermodynamics, through atomistic-level theory or simulations, can give such a description in principle, but the required calculations are often excessive and the required detailed atomic information may not be available. Mesothermodynamics provides an intermediate method by describing fluids on a scale that reflects the fluidʹs significant (but not detailed) properties as determined by whatever is responsible for partial structure. Mesothermodynamics is not new but has made remarkable progress. To introduce its achievements to a wide audience, three examples are presented: phase transitions in a diblock copolymer; liquid–liquid equilibria in a binary mixture confined within a narrow pore; and pattern recognition by adsorption of a statistically-characterized heteropolymer on a statistically-characterized surface. Each example uses a somewhat different method: Landau expansion, density-functional theory and field theory. All three examples show that mesothermodynamics can yield analytic results for the phase behavior of partially-structured fluids. Mesothermodynamics provides a powerful tool for development of new materials and for calculating thermodynamic properties of fluids under geometric constraints such as interfaces.