Bending rigidity and induced persistence length of molecular bottle brushes: A self-consistent-field theory

The two-gradient version of the Scheutjens-Fleer self-consistent-field (SF-SCF) approach is employed for the analysis of the average conformations of side chains and corresponding contribution to the bending rigidity, or equivalently the induced persistence length, of molecular bottle brushes both under good and theta solvent conditions. This study is targeted to unravel conformational properties of poly(L-lysine)-graft-poly(ethylene glycol) copolymers in dilute aqueous solutions, where variation of temperature changes the solvent strength for poly(ethylene glycol) in a wide range. We focus on molecular brushes with moderate and high grafting density and large degree of polymerization of grafted chains. In this limit the predictions of an analytical mean-field theory for the dependences of the structural properties of the bottle brush on the architectural parameters are well confirmed. Both the induced persistence length and the ratio between the induced persistence length and the cross-sectional thickness of the bottle brush increase with increasing grafting density and/or increasing degree of polymerization of the grafted chains. However, in the range of moderate chain lengths and grafting densities this ratio remains small, which explains why the effects of the induced bending rigidity on the apparent persistence length have not been observed in earlier numerical experiments. We argue that only molecular bottle brushes with densely grafted long chains possess the potential for lyotropic ordering, both in solutions and at interfaces, due to the expected high effective segment asymmetry.