  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.
