Lattice model results for lamellar phases in slits

Effects of rigid or adaptive confinement on colloidal self-assembly. Fixed vs. fluctuating number of confined particles

The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the grand canonical ensemble (GCE) in Pȩkalski et al. [J. Chem. Phys. 142, 014903 (2015)]. The model considers a pair interaction defined by a short-range attraction plus a longer-range repulsion. We consider thermodynamic states corresponding to self-assembly into clusters. Both fixed and adaptive boundaries are studied. For fixed boundaries, there are particular states in which, for equal average densities, the number of clusters in the GCE is larger than in the canonical ensemble. The dependence of pressure on density has a different form when the system size changes with fixed number of particles and when the number of particles changes with fixed size of the system. In the former case, the pressure has a nonmonotonic dependence on the system size. The anomalous increase of pressure for expanding system is accompanied by formation of a larger number of smaller clusters. In the case of elastic confining surfaces, we observe a bistability, i.e., two significantly different system sizes occur with almost the same probability. The mechanism of the bistability in the closed system is different to that of the case of permeable walls, where the two equilibrium system sizes correspond to a different number of particles.

Bistability in a self-assembling system confined by elastic walls: exact results in a one-dimensional lattice model

The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pȩkalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.

Swollen lamellar phases confined in capillarylike pores

Structure and mechanical properties of swollen lamellar phases confined in square-base pipes are studied in a mesoscopic lattice model for oil-water-surfactant mixtures. Structure depends crucially on a thermodynamic state and is quite different far and close to the coexistence with a uniform phase. Lamellar domains with different orientations of lamellas are formed in most cases, and the mechanics is determined mainly by domain-wall energies. Shift of phase equilibria in square-base pipes compared to the bulk is just opposite to the shift in slits. We find capillary delamellarization for short-period and for swollen phases, for hydrophilic and for neutral external surfaces.

Lamellar phases confined in quasicylindrical pores: lattice model results

A two-dimensional (2D) vector lattice model of microemulsions is applied to study the structure of lamellar phases confined in long rectangular pores. One-point distribution functions are calculated within mean field approximation. The effects of pore geometry and surface fields are considered. A 2D analog of an onion phase is favored by a pore with strongly hydrophilic walls. For neutral walls, far from the phase boundaries, the lamellar phase is stable inside the pore. By contrast, close to the lamellar-tubular phase boundary a pore with neutral walls favors a 2D tubular phase. This is the analog of capillary condensation. In all cases the excess pressure is calculated as a function of the pore geometry.