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

Abstract

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. C 2015 AIP Publishing LLC. [http://dx

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

“…More detailed descriptions of the model and the transfer matrix method used for finding the exact solutions of the model in the GCE can be found in [19].…”

“…In order to study the effects of confinement on the self-assembled structures, we changed the boundary conditions of the model from periodic to rigid or elastic in Ref. [19]. In the current study we continue the investigation of the confined system with particles interacting via the pair potential given by Eq.…”

“…[19], we assume that the confinement can be either rigid or elastic. For rigid boundary conditions the distance L between the confining walls is fixed, while in the case of elastic walls we assume that it may oscillate around L 0 , which is the equilibrium width of an empty system.…”

“…We observed a different bistability in Ref. [19], where we studied particles interacting with the SALR potential and confined by boundaries, whose separation could be varied at the cost of elastic energy. When the average number of particles is too small or too large for given L for formation of the optimal bulk structure, some compromise must occur between the excess of the free energy associated with the structural deformations, and the elastic energy cost due to adjusting the size of the compartment to the optimal structure of the confined fluid.…”

“…In this work we consider the simple generic model of the system with competing short-range attraction and longer-range repulsion (SALR) that can be solved exactly [16]. The model was solved exactly and systematically analyzed in the bulk [16][17][18] and in confinement [19] in the grand canonical ensemble (GCE). Recently a procedure to extract full Canonical information from Grand-Canonical results has been proposed in Ref.…”