Wertheim's thermodynamic perturbation theory with double-bond association and its application to colloid-linker mixtures

TL;DR

This paper extends Wertheim's thermodynamic perturbation theory to account for double bonds in multicomponent mixtures, specifically applied to colloid-linker systems, revealing how linker flexibility influences loop formation and assembly.

Contribution

The authors develop a generalized theory for double-bond associations in multicomponent mixtures, enabling analysis of complex colloid-linker interactions with flexible linkers.

Findings

Double bonds can form between any pair of bonding sites, generalizing previous theories.

Loop formation in linkers depends on end-to-end distance and site spacing.

Looping can be mitigated by adjusting linker flexibility to improve colloidal assembly.

Abstract

We extend Wertheim's thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules' arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles ("colloids") and flexible chain molecules ("linkers"). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. Due to their flexibility, a significant fraction of linkers can "loop" with both ends bonding to sites on the same colloid instead of bridging sites on different colloids. We use the theory to show that the fraction of linkers in loops depends sensitively on the linker end-to-end distance relative to the colloid bonding-site distance, which suggests strategies for mitigating the loop formation that may otherwise hinder linker-mediated colloidal assembly.