Theoretical study on tethered polymers with explicit grafting points in -solvent

摘要

Systematic studies on the polymers chemically grafted onto a solid substrate with various grafting densities are presented based on the self-consistent mean-field theory (SCMFT). The distribution of the grafting points is explicitly included and all the three coordinates of each grafting point are fixed during the calculations. The existence of solvent molecules is also explicitly considered in the model and the case of θ-solvent is investigated. The structure of the system is derived by solving the SCMFT equations in three-dimensional space. For the cases of low grafting density, the system is highly inhomogeneous and typical mushroom-like structures are derived. On the other hand, when the grafting density is high enough, the system is nearly homogeneous along the substrate and the polymer concentration profile is consistent with the numerical results of one dimensional SCMFT calculations. The crossover between mushroom regime and polymer brush is obtained by tuning the grafting density. In addition, in brush limit, while the root-mean-squared thickness of the brush is linearly dependent on the degree of polymerization, its dependency on the grafting density is in general more complicated than a simple power law.