Brushes in 0 and poor solvents

Brushes under variable solvent conditions have been simulated by Lai and Binder using a bond fluctuation model and by Grest and Murat using MD. The 0 temperature for the bond fluctuation model was calculated from an independent study of a single chain to be Te =. 9e. The MD simulations used a FENE potential, eq. (9.6), between bonded monomers 

Both MC and MD simulations find that the density cannot be fitted by this functional form. The agreement does not seem to get better with increasing chain length. While the scaling suggested by eq. (9.33), namely, that p z)/p]J versus z/Npy should exhibit a data collapse, seems to be confirmed in the MC simulations, the plots are for a very limited range of 

The reason for the disagreement is presumably the relatively large monomer densities reached within the brush. In principle, for very long chains and very low pa, one may reach a situation in which the monomer density is small even near To. This regime has not been reached in any of the simulations. On the basis of the mapping of the coarse-grain model treated in the simulations to the experimental systems, it is difficult experimentally to satisfy both the conditions of strong chain overlap and dominance of binary interactions, imphcit in the analytical SCF study. This is consistent with the numerical SCF calculations of Whitmore and Noolandi.  

Below To, simulations show that the monomer density becomes almost uniform up to the brush height, which grows roughly linearly with Npa. The monomer density in this regime becomes quite high, close to the melt density, making the simulations difficult to perform. In MC simulations, the acceptance rate of the MC moves becomes very low, while in MD simulations, chain relaxation slows down considerably. However, for moderate N, equihbration can be reached, but needs to be checked carefully by verifying that identical results are obtained by different paths. 

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