We present a thermodynamic model of adsorption-induced deformation of microporous carbons. The model represents the carbon structure as a macroscopically isotropic disordered three-dimensional medium composed of stacks of slit-shaped pores of different sizes embedded in an incompressible amorphous matrix. Adsorption stress in pores is calculated by means of Monte Carlo simulations. The proposed model reproduces qualitatively the experimental nonmonotonic dilatometric deformation curve for argon adsorption on carbide-derived activated carbon at 243 K and pressure up to 1.2 MPa. The elastic deformation (contraction at low pressures and swelling at higher pressures) results from the adsorption stress that depends strongly on the pore size. The pore size distribution determines the shape of the deformation curve, whereas the bulk modulus controls the extent of the sample deformation.

A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered (O) and disordered (D) forms of water are treated as two components, and we assume that the density of the D component is larger. The density of the sample is determined by the fraction of cells occupied by the O and D forms of water. Due to the larger density of the D state, the strength of the van der Waals (vdW) interactions increases in the direction O-O

We show that amphiphilic and colloidal systems with competing interactions can be described by the same Landau-Brazovskii functional. The functional is obtained by a systematic coarse-graining procedure applied to systems with isotropic interaction potentials. Microscopic expressions for the coefficients in the functional are derived. We propose simple criteria to distinguish the effective interparticle potentials that can lead to macro-or microsegregation. Our considerations concern also charged globular proteins in aqueous solutions and other system with effective short-range attraction long-range repulsion interactions.

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A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced.We assume attraction J 1 between the first neighbors and repulsion J 2 between the third neighbors.The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J 2 /J 1 < 1/3. In addition to the homogeneous phases, the third phase with periodically distributed clusters appears for J 2 /J 1 > 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J 2 /J 1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J 2 /J 1 . Based on the exact results, for J 2 /J 1 > 1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9 < J 2 /J 1 < 1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T = 0, local spatial inhomogeneities appear for finite T . Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density ρ that we associate with formation of living clusters, and if the repulsion is strong, another maximum for ρ = 1/2.

Systems composed of spherical charged particles in solvents containing counterions and inducing effective short-range attraction are studied in the framework of mesoscopic field-theory. We limit ourselves to meanfield approximation (MF) and to weak ordering. We discuss properties of potentials consisting of strong shortrange attraction and weak long-range repulsion (SALR) in the context of formation of nonuniform distribution of particles on a mesoscopic length scale instead of macroscopic phase separation. In earlier work it was found that spherical, cylindrical and slab-like clusters of particles are formed, and for low enough temperatures the clusters form ordered, periodic bcc, hexagonal and lamellar phases. In addition, a gyroid phase was predicted in which two interwoven regular network-like clusters branching in triple junctions are formed. At properly rescaled density and temperature, the coexistence lines between different ordered phases were found to be universal in MF, with the exception of the gyroid phase. Here the phase diagram is determined for two choices of the SALR potential, one corresponding to a large range of the attractive part of the potential, and the other one to a very small range of attraction. We find that the region of stability of the gyroid phase very weakly depends on the form of the SALR potential within the approximate theory.

The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced by Pȩkalski, Ciach, and Almarza [J. Chem. Phys. 140, 114701 (2014)] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases-the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our results concern spontaneous pattern formation on solid surfaces, fluid interfaces or membranes that is driven by competing interactions between adsorbing particles or molecules.

Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions for the correlation functions and for the grand potential are obtained for weak ordering on mesoscopic length scales. Stability analysis of the disordered phase is performed in mean-field approximation (MF) and beyond. MF shows existence of either a spinodal or a λ-surface on the volume-fractions -temperature phase diagram. Separation into homogeneous phases or formation of inhomogeneous distribution of particles occurs on the low-temperature side of the former or the latter surface respectively, depending on both the interaction potentials and the size ratios between particles of different species. Beyond MF the spinodal surface is shifted, and the instability at the λ-surface is suppressed by fluctuations. We interpret the λ-surface as a borderline between homogeneous and inhomogeneous (containing clusters or other aggregates) structure of the disordered phase. For two-component systems explicit expressions for the MF spinodal and λ-surfaces are derived. Examples of interaction potentials of simple form are analyzed in some detail, in order to identify conditions leading to inhomogeneous structures.