Modeling the role of supramolecular clustering in multivalent assembly

In self-assembled systems, a combination of multiple weak supramolecular interactions is often utilized to enable strong yet reversible binding. When modeling the behavior of these multivalent interfaces, it is commonly assumed that binding pairs are independent, i.e., the probability of a pair being bound is unaffected by the bound state of neighboring pairs. Inspired by recent experimental work, we report that for a variety of systems this assumption may not hold, leading to the formation of clusters at the binding interface. Through a series of analytical and numerical models of end-functionalized brushes, we reveal the role of cluster size on binding thermodynamics, detail how entropic contributions from polymer chains provide tunable control of cluster size, and provide predictions for cluster size as a function of system architecture. Investigation of these models yields surprising results: within the melting window, the enthalpy of binding of multivalent interfaces is predicted to depend only on cluster size and not on the overall valency of the multivalent system. Moreover, clustering is predicted to be significant even in systems with only weak dipole and dispersion interactions between neighboring groups. Combined, this work brings to light the potential impacts of clustering on multivalent self-assembly, providing theoretical justification for previous experimental observations and paving the way for future work in this area.