Adsorption of block copolymers on solid surfaces: A Monte Carlo study

Abstract

Using hyper-parallel tempering Monte Carlo simulation, multiple histogram reweighting method, and finite size scaling, we investigate the adsorption of fully flexible and rod-coil chains on the square lattice. We find that the phase behaviour changes with the chain length and flexibility. For homonuclear rod-coil chains, the phase diagram consists of only gas-disorder liquid critical point. Weakening of the interaction energy between the segments belonging to two different subunits gives rise to an order-disorder transition. The topology of the resulting phase diagram depends on the chain length and flexibility. For short chains, both fully flexible and rod-coil diblock copolymers form lamellar ordered phase with fully stretched chains, and the order-disorder transition is of the first order. The phase diagrams are similar for both chain architectures and consist of two binodals meeting in the triple point. When the chain length increases the order-disorder transition becomes second-order and the difference in the phase behaviour between the fully flexible and the rod-coil diblock copolymers becomes more pronounced. While for the former chain architecture the topology of the phase diagram involves a λ-line which meets the gas-disordered liquid binodal in the critical end-point, in the latter case the λ-line meets the gas-disordered liquid critical point and forms the tricritical point. We trace back these changes to the change in the morphology of the ordered phase. The mechanism of the order-disorder transition involves the formation of domains resembling those observed during the spinodal decomposition process. The domains subsequently merge and arrange into lamellae. These observations are supported by integral geometry analysis.

Structure and phase behaviour of diblock copolymer monolayers investigated by means of Monte Carlo simulation

“…The most important parameter is the interaction energy between the unlike segments and its relation to the interaction energies between the segments of the same type. If u AB is weaker relative to u AA and u BB , the microphase separation is promoted [48]. The resulting sequence of the phase diagrams with a continuous order-disorder transition and a critical end point, or a tricritical point bears some resemblance to the phase behaviour reported for other models.…”

“…We are now in a position to make more general comments regarding the relation of the results obtained for the model used in this and our previous [48] work with other models considered in the literature. In our model the chain stiffness and interaction energies model the difference in chemistry of the polymeric molecules.…”

“…Hence the question of the estimation of the global phase diagram for such systems takes on increased importance. Very recently we have determined the global phase diagrams of monolayers of diblock copolymers [48]. Similar to the vast majority of theoretical studies we have assumed that the interactions between the dissimilar segments are weakened.…”

Density functional theory for polymeric systems in 2D

“…Already for heteronuclear dimers the corresponding phase diagrams may involve a λ-line, two critical points or a tricritical point [8,9]. Longer, fully flexible or rod-coil lattice models of diblock copolymers were investigated by means of Monte Carlo simulation very recently [10,11]. All these studies show an intimate and complex connection between the shape of a polyatomic molecule and its phase behaviour within the adsorbed monolayer.…”

Evidence of a first-order smectic-hexatic transition and its proximity to a tricritical point in smectic films

“…Recently, there has been an increased interest in fascinating material properties of the systems in the vicinity of the tricritical point (TCP), where the phase transition behavior changes from first to second order. This was mainly followed by the discovery of fluctuation induced TCP in skyrmionic magnetic lattices [6][7][8] (although obvious connection exists with many other physical systems ranging from colloidal crystals [9] or block-copolymers [10][11][12] to helimagnets [13]). Understanding of phase transition physics close to TCP is important in such systems as liquid water [14] or ice [15].…”