Lateral ordering during self-organization of statistical multiblock copolymers

Abstract

The self-organization of statistical multiblock and Bernoulli AB copolymers is studied. The initial ensemble is generated via the polymer-analogous reaction A→B that proceeds with the accelerating effect of neighboring B units. In a two-dimensional model, the reaction is performed in a rectangle composed of stretched chains. Then, the rectangle is closed into a cylinder, so that ring chains are located on its side surface. The self-organization of the ensemble is simulated via the successive rotation of each upper ring over the lower ring until arrangement with the maximum (in modulus) energy of attraction between chains is attained. Self-organization by energy is accompanied by lateral ordering: the sizes of clusters—accumulations of the one-type units—and mean heights HA (HB) of stems—columns consisting of A or B units perpendicular to chains—increase. The ratio between the values of HA, as well as HB, for ordered and initial ensembles is independent of the average composition of the system and as a rule increases as the length of blocks increases and the length of chains decreases. Features of generation of the ensemble of short chains and their ordering are revealed. It is shown that, during ordering of multiblock copolymers, the probabilistic properties (the stochastic behavior) of the ensemble are disturbed. The self-organization of statistical multiblock copolymers in a three-dimensional model is investigated via rotation of rings in the torus of the rectangular cross-section. The effects of various factors on self-organization by energy and local ordering in 2D and 3D models are similar; however, the efficiency of ordering in the three-dimensional system is always lower because, in this case, arrangements with the maximum energy of attraction simultaneously to two neighboring chains, rather than to one, are implemented for the majority of chains.