  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.
