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

TL;DR

This study investigates how fixed and adaptive confinement boundaries influence colloidal self-assembly, revealing differences in cluster formation, pressure behavior, and bistability mechanisms through an exactly solved one-dimensional lattice model.

Contribution

It provides a detailed comparison of fixed versus elastic boundary effects on colloidal self-assembly using an exact lattice model in the GCE, highlighting novel bistability phenomena.

Findings

Pressure dependence varies with boundary conditions.

Bistability occurs with elastic boundaries.

Cluster number and size depend on confinement type.

Abstract

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 [J. P\k{e}kalski 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.