Structural and Dynamical Coupling in Solvent-Free Polymer Brushes Elucidated by Molecular Dynamics Simulations

Abstract

We investigate the chain configuration and segmental dynamics in interacting solvent-free polymer brushes using molecular dynamics simulations. The brush systems are designed to mimic the interstitial space between a pair of neighboring polymer-grafted nanoparticles in solvent-free nanoparticle–organic hybrid materials. Each brush consists of uniformly grafted chains formed by a given number of monomer beads. In monodisperse systems, two opposing brushes have the same chain length and grafting density. In mixed conditions, we consider binary systems with two surfaces being separately grafted with polymers of distinct chain lengths at different grafting densities as well as bidisperse systems with polymers of two different lengths being tethered to the surfaces at a fixed grafting density. We demonstrate that the brush configuration and interpenetration are both governed by the need that monomer beads have to uniformly fill the space. For systems with longer chain lengths and/or higher grafting densities, the larger interwall separation yields more stretched brush conformations and reduced extents of interbrush mixing. As a result, the polymer configurational entropy is generally decreased and the segment-to-segment relaxation dynamics is slowed down accordingly. The grafting of chains at a high density not only makes the relaxation dynamics deviate from the standard Rouse prediction but also leads to distinct relaxation times for the free and tethered segments. The more slowly relaxing tethered segments play a more important role in determining the overall end-to-end fluctuations. Moreover, the two distinct relaxation processes are consistent with the two-stage decay in the Rouse mode fluctuation autocorrelation function. In the presence of brush bidispersity, the collaboration between polymers of different lengths is evidently observed in the brush profiles. The variations of the chain configuration for the two polymers are complementary, and the associated relaxation dynamics of the two species are significantly coupled.

Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

“…One sees from Figure 1 a that both with increasing chain length (at a fixed grafting density, upper panel) and with increasing grafting density (at a fixed chain length, lower panel), the monomer density distribution becomes more bell-shaped (i.e., more localized at the grafting wall), in agreement with MD simulation results [ 26 ]. Keeping in mind that the two brushes grafted at the left and right walls are identical (and their respective density profiles are mirror symmetric around the gap mid-point), it follows that the overlap between the two opposing brushes decreases both with increasing N (at fixed ) and with increasing (at fixed N ).…”

“…In order to be able to compare our theoretical results directly with MD simulations, we employ a microscopic model that resembles very closely the model used in the recent simulation study [ 26 ]. Specifically, a monodisperse polymer brush is modeled as a flat structureless wall (located in -plane) which is grafted uniformly with polymer chains of length N at grafting density .…”

“…Finally, the interaction between the monomers and the wall is modeled via the following potential [ 26 ]: where z is the distance of the monomer from the wall.…”

“…The value where passes through a minimum corresponds to the equilibrium separation between the two walls. Following the MD simulation study [ 26 ], we define the overlap parameter P between the two brushes at the equilibrium separation as follows: where and are the monomer density distributions of the two brushes grafted at and , respectively.…”

“…Of particular importance for the present work is the recent Molecular Dynamics (MD) simulation study of solvent-free polymer brushes, where detailed results are reported on the equilibrium density profiles and the brush overlap as a function of the grafting density and grafted chain length [ 26 ]. In addition to monodisperse brushes, equimolar bidisperse brushes were also considered, which is important due to the role of bimodal surface ligands in tunability of nanocomposites [ 27 , 28 ].…”