Polymers attached to the surface, e.g. polymer brushes, represent a unique way how to functionalize the surface. Its morphology is controlled by brush parameters such as grafting density, composition, chemical nature etc. and determine the response of the surface to external environment. Mixed binary brushes contain two different homopolymer branches attached to single point on the surface and exhibit a wide range of morphologies ranging from aggregates to ripple structure. Compositional fluctuations during the grafting process that hampers formation of morphology can be controlled by using Y-shaped initiators where each deposition point accepts different type of polymer. Phase behavior of Y-shaped brushes is described in theory and by simulation studies mainly for monodisperse cases. Nevertheless, real polymers are always polydisperse and using highly polydisperse polymer brings new options to control the formation of surface morphology.

Here, we employ Dissipative Particle Dynamics (DPD) to study the influence of polydispersity on self-assembly of Y-shaped polymer brushes. We vary brush grafting density, composition of the branches and their incompatibility to describe complex behavior of brushes at good solvent conditions. Moreover, we introduce the polydispersity by varying chain length of one branch and keeping other branch of the brush monodisperse. We consider low and high polydispersity and restrict our investigations to polydispersity indexes (PDI) that are used in experiments. We model the polydispersity by Schultz-Zimm distribution.

We show that our results for monodisperse systems agree with previous experimental and theoretical works and that ripple structure and aggregates are observed. Furthermore, the scaling of the brush height in our model agrees with theoretical predictions and with previous modeling results. In polydisperse systems, only disordered structures or aggregates are assembled by brushes with PDI < 1.5 sparsely grafted onto the surface with grafting density lower that 0.1 chains/nm². Moreover, increasing the grafting density above 0.5 chains/nm² triggers formation of perforated layer (PL) that is not observed in monodisperse systems. PL phase window widens with increasing the PDI up to 2 and the grafting density up to 1.0 chains/nm². At high grafting densities and PDIs the PL phase is stable over wide range of phase diagram.

Finally, we show that increasing PDI lead to asymmetry of phase diagrams. High content of polydisperse chains prefer formation of aggregates over the ripple structure and increase the order-disorder transition while high content of monodisperse chains favours ripple structure and lowers the order-disorder transition.