Designed self-assembly of programmable colloidal atom-electron equivalents

TL;DR

This paper develops a statistical mechanical model for programmable colloidal atom-electron equivalents, revealing how valency influences interactions and providing design principles for targeted self-assembly.

Contribution

It introduces a theoretical framework for PAE-EE interactions, highlighting the impact of valency and identifying optimal conditions for self-assembly.

Findings

Interaction strength converges at high valency.

Optimal valency maximizes selective binding.

Model agrees with explicit simulations.

Abstract

To unlock the potential for assembling complex colloidal "molecules", we investigate a minimal binary system of programmable colloidal atom-electron equivalents (PAE-EE), where electron equivalents (EEs) are multivalent linkers with two distinct types of single-stranded DNA (ssDNA) ends complementary to those ssDNAs on binary programmable atom equivalents (PAEs). We derive a statistical mechanical framework for calculating the effective interaction between PAEs mediated by EEs with arbitrary valency, which quantitatively agrees with simulations that explicitly include EEs. Our analysis reveals an anomalous dependence of PAE-PAE interactions on the EE valency, showing that EE-mediated interactions converge at the large valency limit. Moreover, we identify an optimal EE valency that maximizes the interaction difference between targeted and non-targeted binding pairs of PAEs. These findings offer design principles for targeted self-assembly in PAE-EE systems.