The unique architecture of bottlebrush
polymers gives
rise to multiple
molecular parameters consisting of the bottlebrush backbone length
(N
bb), side chain length (N
sc), and grafting density (f). These
macromolecules can thus be engineered to exhibit a wide range of desired
properties, enabling their use in applications ranging from soft elastomers
to self-assembled photonic crystals. However, understanding the physical
behavior throughout this wide design space is challenging due to the
significant computational cost of molecular models. In this work,
we designed a coarse-grained model based on the recently developed
implicit side-chain (ISC) framework to describe the conformation of
bottlebrush polymers in melts. Using single chain in mean-field (SCMF)
simulations, we used molecular observables such as the end–end
distance
⟨
R
bb
2
⟩
and radius of gyration
⟨
R
normalg
2
⟩
to parametrize an ISC model with wormlike
cylinder model parameters; effective Kuhn length λ–1, cylinder length L and width D. We considered a wide range of bottlebrush architectures, systematically
varying the backbone and side-chain lengths (N
bb and N
sc, respectively) and the
grafting density f. We observed that the conformations
of bottlebrush polymers follow Gaussian chain conformations at sufficiently
long N
bb and are much more flexible than
the analogous chains in solution. These bottlebrush polymers exhibit
modest stretching, which becomes much more pronounced at high grafting
densities (f = 5) to accommodate the crowded side
chains. Each architecture varying N
bb, N
sc, and f could be mapped to
a unique set of wormlike cylinder model parameters, so that they can
be represented by an ISC model consisting of N
ISC beads of size D with a bending parameter k
θ related with effective Kuhn length λ–1. The effective pairwise interaction potential for
this ISC model was determined by using an iterative Boltzmann inversion
(IBI) procedure to match the structural features in the ESC model.
The resulting interaction potential determined by IBI was consistent
with the original architectures, showing similar forms relative to
the width D. However, we observed several trends,
such as the emergence of a stronger repulsive potential for longer
side chains and higher grafting densities, which we attribute to the
increased exclusion of neighboring bottlebrushes due to the higher
concentration of grafted side chains. The final ISC model results
in a significant reduction of the degrees of freedom needed to model
the melt state, and we expect that our melt ISC model for bottlebrush
polymers will enable efficient large-scale simulation to relate macroscopic
properties to molecular structure.