  The effect of chain topology on the statics and dynamics of chain at the
interface of two immiscible fluids is studied by means of molecular dynamics
simulations. For three topologically different chains, namely, linear, ring,
and trefoil-knot of same molecular weight the effect of varying both
polymer--fluid and fluid--fluid interaction nature on the width of the fluid
interface, chain conformation, shape, and chain dynamics. For sharp-interface
binary-fluid system, the interface width is insensitive to both topology and
polymer-fluid interaction nature, while a weak non-monotonic variation is seen
for weak-interface system. Chain extension normal to the interface plane is
significantly affected by the topology with trefoil-knot chain, due to the
additional constraint, has the largest value compared to both linear and ring
polymers. Instantaneous shapes are also quantified through shape parameters.
Furthermore, it is observed that the qualitative behavior of center of mass
mean-square displacement (MSD) is independent of topology, i.e., all the chain
types show same diffusion exponent $\alpha~(\approx 1)$. However, the
self-diffusion constant depends on the topology and it is largest for
trefoil-knot chain. An interesting observation pertaining the early time
behavior of monomeric-MSD is that, within the sub-diffusive regime, the values
of $\alpha$ for different parameters (independent of topology) are grouped into
two distinct ranges (0.52--0.59 and 0.62--0.67) which is related to the
different chain conformation for polymer-fluid interaction range below and
above a threshold value equal to that of the self-interaction of the pure fluid
phase.
