Adsorption of triblock copolymers confined between two plates: An analytical approach

Abstract

We present an approximate analytical approach to the adsorption problem of ABA triblock copolymers confined between two parallel plates in a θ solvent and give the expression of the propagator q(x, t) as a piece-wise function by solving the modified diffusion equation. In this way, the role of separation between the two plates, adsorption energy and block lengths on segment concentration profile, chain conformations, and interaction potential is then investigated, which agrees well with the numerical results. It is demonstrated that there are parallels between lengthening adsorbing A blocks and increasing surface affinity: strong adsorption and long adsorbing blocks favor the formation of loops and bridges, whereas more tails and free chains exist in the case of weak adsorption and short A blocks at large separations. For moderate and strong adsorptions, the bridging fraction begins to plummet at a separation larger than the end-to-end distance of non-adsorbing B block RB and becomes negligible at above 2RB owing to the entropy effect. The depth of the potential well in the interaction potential profile depends on the adsorption energy and A block length, while the location of the potential minimum corresponds to the onset of the sharp decrease in bridges.