We use Langevin dynamics
simulations to study the knotting properties
of copolyelectrolyte rings carrying neutral segments. We show that
by solely tuning the relative length of the neutral and charged blocks,
one can achieve different combinations of knot contour position and
size. Strikingly, the latter is shown to vary nonmonotonically with
the length of the neutral segment; at the same time, the knot switches
from being pinned at the block’s edge to becoming trapped inside
it. Model calculations relate both effects to the competition between
two adversarial mechanisms: the energy gain of localizing one or more
of the knot’s essential crossings on the neutral segment and
the entropic cost of such localization. Tuning the length of the neutral
segment sets the balance between the two mechanisms and hence the
number of localized essential crossings, which in turn modulates the
knot’s size. This general principle ought to be useful in more
complex systems, such as multiblock copolyelectrolytes, to achieve
a more granular control of topological constraints.