Grafted polymer layers under shear: A Monte Carlo simulation

Abstract

Endgrafted polymers at surfaces exposed to a shear flow are modeled by a nonequilibrium Monte Carlo method where the jump rate of effective monomers to neighboring lattice sites against the flow direction is smaller than in the flow direction, assuming that this difference in jump rates is proportional to the local velocity of the flowing fluid. In the dilute case of isolated chains, the velocity profile is assumed linearly increasing with the distance from the surface, while for the case of polymer brushes the screening of the velocity field is calculated using a parabolic density profile for the brush whose height is determined self-consistently. Linear dimensions of isolated chains are obtained over a wide range of shear rates γ̇, and the deformation of the coil structure by the shear is studied in detail. For brushes it is found that the density profile and the distribution for the perpendicular coordinate zN of the free ends differ only little from the shear-free case, while the distribution of the free end coordinate xN parallel to the wall in the flow direction gets strongly modified. It is shown that the average scaled chain trajectory (〈zi〉/〈zN〉 as a function of 〈xi〉/〈xN〉, i labels the monomers along the chain) is a universal function independent of shear rate, while 〈xN〉 depends on γ̇, chain length N and grafting density σ in scale form, 〈xN〉/(σ1/3N3γ̇) is a function of N2σ5/3 only. Our results are compared with the recent theories of Rabin and Alexander or Barrat, respectively, and both similarities and differences are noted and discussed. The observed increase of the coil radius with the inclination of the chain produced by the flow is somewhat smaller in our model than it was in those theories.

Rheology of Polymer Brushes: A Brownian Dynamics Study

“…Brushes at smaller areal fractions deform at a smaller value of Wi due to the increased penetration of the velocity into the brush. Many of these trends had been witnessed in previous simulations, 16,[31][32][33][34][35][36][37][38] but in addition we derived scalings for brush rheology observed in the simulations and compared steady to oscillatory shear. As in previous simulations, 16,31-37 we found no brush thickening under steady shearing which contrasts with many theoretical studies.…”

“…[31][32][33][34]37,38 Monte Carlo simulations by Lai and Binder 31 and Miao et al 33 for weak flows covering a decade of shear rates found no appreciable change in brush height. Lai and Lai 32 simulated larger shear rates (about 6 times the largest shear rate in Lai and Binder's simulations) and found no appreciable change in the brush thickness.…”

“…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 …”

“…We have calculated a measure of the chain tilt: 31 where r 1 cm /|r i cm | is the "1" component of the unit vector directed from the chain-tethering point to the chain center of mass and 90 -θ is the angle of inclination from the "2" axis. A smaller value of 〈θ〉 corresponds to a larger chain tilt or inclination.…”

Dynamic Compression of in Situ Grown Living Polymer Brush: Simulation and Experiment

“…The brush structure and its properties can be controlled by tuning the grafting density, and variation of polymer molecular weight, temperature, and solvent quality [18]. Numerous theoretical [19][20][21][22][23][24][25][26], experimental [27][28][29][30][31], and simulational [32][33][34][35][36][37][38][39][40][41][42][43][44][45] studies have examined the structure and properties of polymer brushes. There exist, however, sometimes significant differences between the theoretical and the experimental investigations of polymer brushes.…”