In
this study, we investigate the sliding dynamics of small charged
ring chains along the rigid central cyclic diblock polyelectrolyte
of A
n
B
n
in radial charged poly[2]catenane in
the presence of counterions using molecular dynamics simulations and
the Lifson–Jackson formula, and our aim is to study the effects
of electrostatical interaction strength, the size of the charged small
ring chain, and the rigid block length of the diblock polyelectrolyte
on the sliding dynamics of a small ring chain threaded on the rigid
diblock polyelectrolyte. The mean-square displacement g
3(t) of a small ring chain sliding along
the rigid diblock polyelectrolyte of A
10
B
10 exhibits oscillating behavior at
short time scales for the moderate electrostatical interaction strength,
while for the weak or strong electrostatic interactions, it is normal
subdiffusion at short time scales. For n = 1, the
diffusion coefficient D of the small ring chain sliding along the
rigid diblock polyelectrolyte of A
1
B
1 decreases monotonically as the relative electrostatic
interaction strength A increases from A = 0.25–4.
However, for n ≠ 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock
polyelectrolyte of A
n
B
n
first decreases and
then increases with the increase of A, and the nonmonotonous
relationship between D and A becomes more obvious
for larger n. In view of the free energy potential,
the sliding diffusion of a small ring chain is governed by both the
width of the free energy potential well and the height of the free
energy potential barrier. According to the potential of mean force
(PMF) of the small ring chain sliding along the rigid diblock polyelectrolyte,
we find that our results are in good agreement with the theoretical
analysis using the Lifson–Jackson formula. These results may
help us to understand the diffusion motion of a ring chain in radial
poly[n]catenanes from a fundamental point of view and control the
sliding dynamics in molecular designs.