# Interaction and self-assembly of membrane-binding and membrane-excluding colloids embedded in lamellar phases

## TL;DR

This paper develops an analytical model for the interactions of colloids embedded in lamellar phases, considering membrane adhesion, impenetrability, and fluctuations, and validates predictions with Monte Carlo simulations and experimental data.

## Contribution

It introduces a comprehensive analytical framework for membrane-mediated colloid interactions in lamellar phases, including fluctuation effects and finite-size considerations.

## Key findings

- Analytical expressions for colloid interactions in lamellar phases.
- Monte Carlo simulations match experimental data semi-quantitatively.
- Prediction of finite-size, densely packed colloid aggregates.

## Abstract

Within the framework of a discrete Gaussian model, we present analytical results for the interaction induced by a lamellar phase between small embedded colloids. We consider the two limits of particles strongly adherent to the adjacent membranes and of particles impenetrable to the membranes. Our approach takes into account the finite size of the colloids, the discrete nature of the layers, and includes the Casimir-like effect of fluctuations, which is very important for dilute phases. Monte Carlo simulations of the statistical behavior of the membrane-interacting colloids account semi-quantitatively, without any adjustable parameters, for the experimental data measured on silica nanospheres inserted within lyotropic smectics. We predict the existence of finite-size and densely packed particle aggregates originating from the competition between attractive interactions between colloids in the same layer and repulsion between colloids one layer apart.