Statistical Mechanics of DNA-Mediated Colloidal Aggregation

TL;DR

This paper develops a statistical mechanical model for DNA-mediated colloidal aggregation, linking DNA thermodynamics to aggregation behavior, and validates it with experimental data.

Contribution

It introduces a universal framework connecting DNA hybridization free energy with colloidal aggregation, accounting for slow DNA dynamics and partial ergodicity.

Findings

Model accurately predicts aggregation fractions across different particle sizes.

The theory quantitatively matches experimental melting curves.

Introduces concept of angular localization of DNA linkers.

Abstract

We present a statistical mechanical model of aggregation in colloidal systems with DNA mediated interactions. We obtain a general result for the two-particle binding energy in terms of the hybridization free energy $\Delta G$ of DNA and two model dependent properties: the average number of available DNA bridges $\left< N\right>$ and the effective DNA conccentration $c_{eff}$. We calculate these parameters for a particular DNA bridging scheme. The fraction of all the $n$-mers, including the infinite aggregate, are shown to be universal functions of a single parameter directly related to the two-particle binding energy. We explicitly take into account the partial ergodicity of the problem resulting from the slow DNA binding-unbinding dynamics, and introduce the concept of angular localization of DNA linkers. In this way, we obtain a direct link between DNA thermodynamics and the global aggregation and melting properties in DNA-colloidal systems. The results of the theory are shown to be in quantitative agreement with two recent experiments with particles of micron and nanometer size. PACS numbers: 81.16.Dn, 82.20.Db, 68.65.-k, 87.14.Gg