A. Ciach

Adsorption-Induced Deformation of Microporous Carbons: Pore Size Distribution Effect

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.

Universal sequence of ordered structures obtained from mesoscopic description of self-assembly

Abstract Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived from the microscopic theory by a systematic coarse-graining procedure. Grandthermodynamic potential functional for hard spherical particles that interact with (solvent mediated) spherically-symmetric potentials of arbitrary form is a sum of two terms. In the first term microscopic length-scale fluctuations are included, and the second term is the contribution associated with mesoscopic length-scale fluctuations. In the approximate theory the first term has the form of the density functional in the local density approximation, whereas the second term has the form known from the field theory and depends on the pair correlation function for which a pair of equations similar to the Ornstein-Zernicke equation with a particular closure is obtained. For weak ordering the theory can be reduced to the Brazovskii field theory with the effective Hamiltonian having the form of the grand-potential functional in the local density approximation. Within the framework of this theory we obtain and discuss the λ-line and the universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. The sequence of phases agrees with experimental observations and with simulations of many self-assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential we find the bicontinuous gyroid phase (Ia3d symmetry) that may be related to a network forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.

Microscopic model for microemulsions. I. Ground state properties

The ground state of several variants of a new microemulsion model is examined in detail. We find oil–microemulsion–water and oil–surfactant–water equilibria, and coexistence between microemulsions of different geometrical structures (lamellar, tubular, and ‘‘brick’’). We find vanishing or low surface tension between bulk oil and water at the three‐phase coexistence in different versions of the model. Our results suggest that the model is capable of reproducing many of the striking features of real microemulsions and deserves a detailed study at nonzero temperatures.

Effect of competition between Coulomb and dispersion forces on phase transitions in ionic systems

A restricted primitive model (RPM) for ionic systems in which the Coulomb and hard-core interactions are supplemented with short-range (SR) interactions between all the components, including solvent particles, is introduced and studied within a mean-field approximation. Continuum-space as well as simple-cubic lattice systems are considered. A continuous and a first-order phase transition, separated by a tricritical point (tcp), are found between uniform and charge-ordered phases in all the systems considered. The position of the tcp as well as the slope of the line of the continuous transition depend on both the model and the SR interactions. For weak or vanishing SR interactions, at temperatures lower than the transition temperature, two oppositely charged sublattices are found on the simple-cubic lattice, whereas in the continuum case a lamellar structure consisting of charged layers of alternating sign occurs. For strong SR interactions the structure becomes incommensurate with the lattice in the latti...

Microscopic model for microemulsions. II. Behavior at low temperatures and critical point

Low temperature properties and critical behavior for the more simple versions of the microemulsion model introduced in Ref. 1 are investigated. For the lattice case with nearest‐neighbor interactions an analytic asymptotic expression for the surface tension at the oil–microemulsions–water coexistence is found for low T. For both lattice and continuum cases the critical point is determined, and we show how an oscillating phase (microemulsion) may be formed below the critical temperature.

Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation

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.

Field-theoretic approach to ionic systems: Criticality and tricriticality

Abstract A Landau-Ginzburg functional of two order parameters (charge-density φ and mass-density deviation η) is developed in order to yield a field theory relevant to ionic lattice gases as well as a family of off-lattice models of ionic fluids that go beyond the restricted primitive model (RPM). In a mean-field (MF) approximation an instability of a uniform phase with respect to charge fluctuations with a wave-number k ≠ 0 is found. This second-order transition to a charge-ordered phase terminates at a tricritical point (tcp). Beyond MF, a singularity of a mass correlation function for k → 0 occurs at ion concentration lower than that of the MF tcp. An effective functional depending only on η is constructed. For low ion concentration the usual Landau form of the simple-fluid (Ising) functional is obtained; hence in this theory the critical point is in the Ising universality class.

Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

Capillary condensation of periodic phases in self-assembling systems

Self-assembling systems confined in slit-like pores of a width L are studied. We focus on phase transitions between uniform and ordered periodic phases. As shown by previous experimental and theoretical studies, the periodic phases respond elastically to the applied stress when the size λ of the unit cell is much larger than the size of molecules. For such phases a simple modification of the Kelvin equation for the phase coexistence in a slit is derived. The shift of the phase transition in confinement is given by two terms. The first term is the standard Kelvin equation, and the second one depends on the elastic modulus of the periodic phase. The modified Kelvin equation (MKE) is verified by explicit calculations in a lattice model for oil–water–surfactant mixtures. We show that the two terms can be comparable even for L∼10λ. While for L>5λ the MKE is obeyed very well in our model, for narrow slits we find significant deviations between actual transitions and the MKE, associated with an inelastic behavio...

Bicontinuous phase in a lattice model for surfactant mixtures

A lattice counterpart of a bicontinuous phase is found in a three‐dimensional lattice model of ternary surfactant mixtures. The structure of this phase is determined and discussed. The region of stability of the new phase in the parameter space is found at zero temperature. Also determined are the boundary of stability of the disordered phase, the water–water structure factor in this phase, and the disorder line.