Diblock copolymer–selective nanoparticle mixtures in the lamellar phase confined between two parallel walls: a mean field model

We present a mean field model for a mixture of AB diblock-copolymers and A-block selective nanoparticles confined between two identical non-selective walls. A horizontally symmetric lamellar structure of the nanocomposite is considered where nanoparticles are allowed to segregate between the polymer–wall interfaces. For a fixed value of wall separation, we study changes in the free energy as a function of the number of lamellar layers and the amount of nanoparticle uptake in the A-phase denoted by y = ϕx with 0 ≤ x ≤ 1 for a given value of ϕ, where ϕ is the overall nanoparticle volume fraction. The absorption isotherm for nanoparticle uptake in the A-phase as a function of ϕ shows saturation beyond a threshold value ϕs, and the optimal value of uptake y increases with increasing strength of monomer–nanoparticle attractive interaction. Increasing ϕ above ϕs produces a decrease in the optimal number of lamellar layers which is related to a jump-like transition of the chain extension. The effect of varying film thickness is also studied. By considering A-block selective walls we also investigated a wetting transition of the copolymer film and found the transition to be discontinuous. A corresponding phase diagram is constructed.