Conformation of Polymer Brushes under Shear: Chain Tilting and Stretching

Abstract

We have studied the conformation of a polymer brush in equilibrium with a solvent that is subject to a shear flow. The interplay between the polymer brush and the hydrodynamic flow of the solvent has been modeled, with simple but largely justifiable approximations. The main technique used in our study is a Monte-Carlo simulation algorithm that is distinct from many standard numerical methods used in studies of polymer brushes in that it combines an off-lattice description of polymer brushesthe Edwards Hamiltonianwith a modification of the standard Metropolis Monte-Carlo transition probability to take into account the effective force acting upon the polymer molecules by the moving solvent. The conformation of the polymer brush, the configurations of each individual chain in particular, is investigated in detail. It is found that the significant response of the brush to the solvent shear flow manifests principally in the form of the chain tilting toward and stretching along the direction of the flow, whereas the overall conformational properties, such as the averaged local monomer density, and the linear span of the brush in the direction normal to that of the flow remain essentially unaffected by the flow. Such response can be understood both qualitatively and semiquantitatively in terms of a notion of the mechanical balance of the different physical forces involved, which was used in the theory of Rabin and Alexander (Rabin, Y.; Alexander, S. Europhys. Lett. 1990, 13, 49). The relevance of our study to some recent experiments is briefly discussed.

Off-lattice Monte Carlo simulation of the discrete Edwards model

“…Scaling Relations and Distribution Functions subsection) do not depend on the numerical value of w 2 . In accordance with the choice made in our previous studies, [17][18][19][20] we use the value w 2 ϭ 0.5 in our simulations.…”

“…Estimates for the scaling exponents of the Domb-Joyce model are known from a field-theoretic analysis of high-precision MC data. 15,16 Recently we used discretized Edwards chains in conjunction with off-lattice Monte Carlo simulation schemes for a variety of polymer systems including grafted polymer brushes in a good solvent 17 as well as in a poor solvent, 18 binary brushes in both good and poor solvent, 19 polymer brushes in a good solvent under shear, 20 and diblock copolymer melts. 21,22 The characteristic feature of the models used in these studies is that the volume interaction is formulated as a "virial expansion" in terms of coarse-grained number densities of the effective chain monomers ("vertices").…”

Rheology of Polymer Brushes: A Brownian Dynamics Study

“…We have confirmed that 〈f1(x1)〉 ) 〈u1(x2)F(x2)〉 and 〈f2-(x1)〉 ) 0 elsewhere. 46 Other authors have invoked the Brinkman equation in theoretical approaches 15,18,20,26 and MonteCarlo simulations 31,33 of brushes, and also in studying single tethered chains via Brownian dynamics. 23 …”

Simulating Tethered Polymer Layers in Shear Flow with the Dissipative Particle Dynamics Technique

“…Several simulation techniques have been used, such as Brownian dynamics, [22][23][24] stochastic dynamics, 25 and dynamic Monte Carlo. [26][27][28] One would expect the most exact results from molecular dynamics simulations, and such simulations have indeed been carried out for symmetric systems consisting of two layers of short grafted polymer chains which are sheared against each other. 29,30 However, most simulations of flow past polymer brushes tend to leave out the solvent molecules and model the solvent as a continuum to save CPU time.…”