Stimuli-Responsive Brushes with Active Minority Components: Monte Carlo Study and Analytical Theory

Abstract

Using a combination of analytical theory, Monte Carlo simulations, and three dimensional selfconsistent field calculations, we study the equilibrium properties and the switching behavior of adsorption-active polymer chains included in a homopolymer brush. The switching transition is driven by a conformational change of a small fraction of minority chains, which are attracted by the substrate. Depending on the strength of the attractive interaction, the minority chains assume one of two states: An exposed state characterized by a stem-crown-like conformation, and an adsorbed state characterized by a flat two-dimensional structure. Comparing the Monte Carlo simulations, which use an Edwards-type Hamiltonian with density dependent interactions, with the predictions from self-consistent-field theory based on the same Hamiltonian, we find that thermal density fluctuations affect the system in two different ways. First, they renormalize the excluded volume interaction parameter v bare inside the brush. The properties of the brushes can be reproduced by self-consistent field theory if one replaces v bare by an effective parameter veff, where the ratio of second virial coefficients Beff/B bare depends on the range of monomer interactions, but not on the grafting density, the chain length, and v bare . Second, density fluctuations affect the conformations of chains at the brush surface and have a favorable effect on the characteristics of the switching transition: In the interesting regime where the transition is sharp, they reduce the free energy barrier between the two states significantly. The scaling behavior of various quantities is also analyzed and compared with analytical predictions.

Dynamic Density Functional Theories for Inhomogeneous Polymer Systems Compared to Brownian Dynamics Simulations

“…The BD scheme presented above can be viewed as an approximate dynamic Monte Carlo (MC) scheme for studying systems with Edwards-type density-based interactions H I . The idea to use such Hamiltonians in MC simulations was first put forward by Laradji et al [60], and later applied in studies of a variety of inhomogeneous polymer systems [45,58,61,[64][65][66]. They have the advantage of being computationally efficient, since the explicit evaluation of the pair interaction, which is often the most time consuming part in a simulation, is circumvented.…”

Polydisperse Polymer Brushes: Internal Structure, Critical Behavior, and Interaction with Flow

“…The nonbonded interaction is formulated in terms of the local monomer density, implying that we have soft interactions. The Hamiltonian thus has the Edwards type [27][28][29][30][31] and can be written as…”

“…The fluctuations enhancement factor also describes the increase in the relaxation time compared to the Rouse time, τ τ R δ −1 1 . Another consequence of the near-critical behavior is the increased chain susceptibility [31,49] leading to effects like the "surface instability" introduced by Sommer and coworkers in Refs. [50][51][52].…”

Responsive polymer brushes for controlled nanoparticle exposure

“…We have considered three different responsive chain lengths (N 2 ): (1) N 2 < N 1 ; (2) N 2 = N 1 and (3) N 2 > N 1 . [48][49][50] Under these conditions, much of the long polymer can already form a dense coil (collapse) without the particle having to penetrate the brush. In the case of N 2 (50) < N 1 (100), the most probable location for the particle is inside of the brush layer, even at χ = 0.…”