Bonding interactions between ligand-decorated colloidal particles

ABSTRACT

We study the interactions between particles that form reversible bonds. Theoretically, we find that the mean association constant between a pair of such particles can be well approximated by a double exponential function of the individual bond free energy when at least one of the following conditions holds: (i) when the individual bond strength is sufficiently weak and (ii) when the bond-forming ligands are randomly (Poisson) distributed among the particles in the system. In experiments with ligand-grafted colloidal particles, randomness in both the number of the ligands per colloid and the spatial distribution on the colloid is inherent to common fabrication techniques. We theoretically investigate the effect of quenched disordered ligand positions on interaction heterogeneity. Furthermore, we perform Monte Carlo simulations of colloidal particles decorated with mobile, quenched disordered, or uniformly distributed ligands to investigate the extent to which the mean association constant is a good approximation for the magnitude of the effective interactions in such systems, and to define the limits of applicability of the double exponential expression. We find that for large enough particles (100 nm–1 µm in diameter) at usual experimental parameters, the simple analytical expression provides a good description of the inter-particle interactions. The theory is finally extended beyond dimeric bonds to general multimeric complexes.

GRAPHICAL ABSTRACT

Keywords:

• Bonding interactions
• ligand-coated particles
• colloidal interactions
• multivalent binding

Acknowledgments

The authors acknowledge fruitful discussion with Daan Frenkel, Stefano Angioletti-Uberti, Bortolo M. Mogneti and James D. Farrell, as well as the anonymous referee for useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Herchel Smith scholarship (T.C.), the CAS PIFI fellowship (T.C.) and by the European Union's Horizon 2020 programme under ETN grant 674979-NANOTRANS (J.D.).