Effect of polymer-graft modification on the order formation in particle assembly structures.

The propensity of particle brush materials to form long-ranged ordered assembly structures is shown to sensitively depend on the brush architecture (i.e., the particle radius as well as molecular weight and grafting density of surface-bound chains). In the limit of stretched chain conformations of surface-grafted chains the formation of regular particle array structures is observed and interpreted as a consequence of hard-sphere-type interactions between polymer-grafted particles. As the degree of polymerization of surface-grafted chains increases beyond a threshold value, a reduction of the structural regularity is observed that is rationalized with the increased volume occupied by relaxed polymer segments. The capacity of polymer grafts to increase or decrease order in particle brush assembly structures is interpreted on the basis of a mean-field scaling model, and "design criteria" are developed to help guide the future synthesis of colloidal systems that are capable of forming mechanically robust yet ordered assembly structures.