Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusion

TL;DR

This paper theoretically investigates colloids with key-lock interactions, revealing regimes of exponential relaxation, aging phenomena, and anomalous diffusion, with implications for experimental systems like DNA-grafted particles and antibody-coated colloids.

Contribution

It introduces a theoretical framework predicting distinct dynamical regimes in key-lock colloids, including aging and subdiffusive behavior, based on coverage and interaction parameters.

Findings

Localized regime with exponential departure times

Transition to diffusive regime with longer bound states

Potential for anomalous, subdiffusive transport

Abstract

The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles grafted with antibodies to cell-membrane proteins. Depending on the coverage of the functional groups, we predict two distinct regimes. In the low coverage localized regime, there is an exponential distribution of departure times. As the coverage is increased the system enters a diffusive regime resulting from the interplay of particle desorption and diffusion. This interplay leads to much longer bound state lifetimes, a phenomenon qualitatively similar to aging in glassy systems. The diffusion behavior is analogous to dispersive transport in disordered semiconductors: depending on the interaction parameters it may range from a finite renormalization of the diffusion coefficient to anomalous, subdiffusive behavior. We make connections to recent experiments and discuss the implications for future studies.