Polymer brushes computer simulations

Another approach to study the penetration depth is to use computer simulations of simple shear flow. Computer simulations can check the validity of certain assumptions implicit in the theories, such as the assumption that the shear flow does not distort the density profile. However to do this solvent molecules must be included explicitly in the simulation. Almost all previous simulations of polymer brushes have modeled the solvent as a continuum to save CPU time. 

This name covers all polymer chains (diblocks and others) attached by one end (or end-block) at ( external ) solid/liquid, liquid/air or ( internal ) liquid/liq-uid interfaces [226-228]. Usually this is achieved by the modified chain end, which adsorbs to the surface or is chemically bound to it. Double brushes may be also formed, e.g., by the copolymers A-N, when the joints of two blocks are located at a liquid/liquid interface and each of the blocks is immersed in different liquid. A number of theoretical models have dealt specifically with the case of brush layers immersed in polymer melts (and in solutions of homopolymers). These models include scaling approaches [229, 230], simple Flory-type mean field models [230-233], theories solving self-consistent mean field (SCMF) equations analytically [234,235] or numerically [236-238]. Also first computer simulations have recently been reported for brushes immersed in a melt [239]. 

In our computer studies of the conformational behavior of the shell-forming chains, we used MC simulations [91, 95] on a simple cubic lattice and studied the shell behavior of a single micelle only. Because we modeled the behavior of shells of kinetically frozen micelles, we simulated a spherical polymer brush tethered to the surface of a hydrophobic spherical core. The association number was taken from the experiment. The size of the core, lattice constant (i.e., the size of the lattice Kuhn segment ) and the effective chain length were recalculated from experimental values on the basis of the coarse graining parameterization [95]. 

This suggests that these structures, which are the reason for the clear separation of the time scales of the local chain motion and the isotropization in PEMA, are significantly affected by the presence of the nanoparticle. One can compare this effect with the significant reduction in the chain reptation in star polymers, where the star point does not move and chain motion can only occur via arm-retraction [45]. In fact, from NMR on selectively deuterated four-arm star poly(butadiene), Brereton el al. [46] found a similar behavior, namely almost uniform dynamics for the middle part of the arm, yet significantly shorter correlation times for the chain ends. Our work also motivated computer simulation of chain dynamics of grafted chains. It was found that the repeat units at the end relax faster than units further inside along the chain, as previously observed for planar brushes but at variance with theoretical expectations [47]. 

To summarize the part devoted to the general behavior of nonpolar polymers in organic solvents, we would like to mention that both linear chains and those with more complicated molecular architectures (stars, brushes, copolymers, etc.) have been intensely studied experimentally, theoretically, and by computer simulations, and their properties are now well understood. The message we would like to convey... 

D. Dimitrov, A. Milchev, and K. Binder. Polymer brushes on flat and curved substrates scaling concepts and computer simulations. 

A. G. Koutsioubas, N. SpiUopoulos, D. L. Anastassopoulos, A. A. Vradis, and G. Toprakcioglu. Formation of polymer brushes inside cylindrical pores a computer simulation study. T. Chem. Pkus.. 131 044901, 2009. 

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