Pearl-necklace structures of molecular brushes with rigid backbone under poor solvent conditions: A simulation study

Abstract

Bottle-brush polymers, where flexible side chains containing N=20 to 50 effective monomers are grafted to a rigid backbone, are studied by molecular dynamics simulations, varying the grafting density σ and the solvent quality. Whereas for poor solvents and large enough σ the molecular brush is a cylindrical object, homogeneous in axial direction, for intermediate values of σ an axially inhomogeneous structure of "pearl-necklace" type is formed. The "pearls," however, have a strongly nonspherical ellipsoidal shape, due to the fact that several side chains cluster together in one pearl, qualitatively consistent with predictions of Sheiko et al. [Eur. Phys. J. E 13, 125 (2004)] We analyze the structure of these pearls and study both the transition to the axially uniform cylinder at high σ and to the trivial pearl-necklace structure at small σ, where each pearl contains a single collapsed chain only.

Molecular dynamics simulations of single-component bottle-brush polymers with flexible backbones under poor solvent conditions

“…For bottle-brush polymers with a flexible backbone, no sharp phase boundaries [27] are expected to occur as it has been shown by MD simulations for bottle-brush polymers with a stiff backbone [29,30]. Thus, we shall not describe any detailed calculations on how to derive phase boundaries here, but only give (background) qualitative arguments to understand the phenomena observed in our simulations.…”

“…For bottle-brush polymers with flexible backbones under poor solvent conditions [29,30] we describe both the backbone chain and the side chains by a bead-spring model [48,49,50], where all beads interact with a truncated and shifted Lennard-Jones (LJ) potential U LJ (r) and nearest neighbors, bonded together along a chain, also experience the finitely extensible nonlinear elastic (FENE) potential U FENE (r), r being the distance between the beads. Thus,…”

“…Thus, the total surface free energy of a collapsed bottlebrush polymer with a flexible backbone is of the order of R 2 c γ = N 2/3 τ 4/3 = (Nτ 2 ) 2/3 . For rigid backbones, when the distance h and the radius R c of the collapsed chain [as described by equation (4)] become comparable, the system can minimize its free-energy cost if two, or more neighboring globular chains, coalesce [27,29,30,33]. If we assume that the number of thermal blobs remains constant, the bulk free energy decides on the stability of the different structures.…”

“…However, computer simulations have been very useful to validate approximations needed to interpret experimental data [10,12,16,17,18,19,20,21,22,23,24,25,26]. Since some of the suggested applications require to consider bottle-brush polymers under poor solvent conditions, first steps to consider this case by theory [27] and simulations [28,29,30] have been taken. In particular, for bottle-brush polymers with a single type of side chains and rigid backbone, interesting pearl-necklace structures have been theoretically predicted [27] and validated by numerical simulations [29,30].…”

“…Since some of the suggested applications require to consider bottle-brush polymers under poor solvent conditions, first steps to consider this case by theory [27] and simulations [28,29,30] have been taken. In particular, for bottle-brush polymers with a single type of side chains and rigid backbone, interesting pearl-necklace structures have been theoretically predicted [27] and validated by numerical simulations [29,30]. These studies were also extended to bottle brushes with two different types of side chains grafted alternately onto the backbone [31,32,33], where such pearl-necklace structures were observed at intermediate grafting densities.…”