Heterogeneous morphology and dynamics of polyelectrolyte brush condensates in trivalent counterion solution

Recent experiments have shown that trivalent ion, spermidine$^{3+}$, can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of trivalent ions to polyelectrolyte charge. A further increase of trivalent ion concentration conducive to a charge inversion elicits modest reswelling and homogenizes the morphology of brush condensate. Our study provides a new insight into the origin of the diversity in DNA organization in cell nuclei as well as the ion-dependent morphological variation in polyelectrolyte brush layer of biological membranes.