Ring and linear copolymer blends under confinement

The behavior of dense mixtures of two topologically different diblock-copolymer (CP) chains, viz., linear(L)-CP and ring(R)-CP of same molecular weight which forms lamellae is studied under confinement by two non-selective substrates. The effect of varying interaction strength between L-CP and R-CP, from purely repulsive ({\it demixed state}) to weakly attractive ({\it mixed state}), on the morphology, domain size, chain conformations and distribution of chains in the film are investigated. In the demixed state, collective structure factor $S(q)$ shows a split of the predominant peak indicating the presence of two dominant length scales. While there is only one predominant peak in the mixed state, and hence a lamellar structure with single domain size. We show that the peak position $q*$ of $S(q)$ can be varied with the L/R interaction strength and thus allow one to control domain size by tuning L/R interaction strength without altering the chain size. We further characterize the chain size and illustrate that this domain size variation is a consequence of the variation in the size of L-CPs. Furthermore, results on the average instantaneous shape of R/L-CP reveal that their shapes are very different both in bulk and near the substrate, and R-CP assumes an oblate shape near the substrate. This shape/size difference leads to the segregation of R-CPs near the polymer-substrate interface and hence a relatively higher density of R-CPs at the interface.