Modeling the structure of a polydisperse polymer brush

Numerical self-consistent field theory is used to study the structural characteristics of a polydisperse polymer brush. We consider the relevant case of a Schulz-Zimm distribution and find that even a small degree of polydispersity completely destroys the parabolic density profile. The first moment (average height) of the brush increases with polydispersity, while the average stretching in the brush decreases. The density profiles of separate chain length fractions in a single polydisperse brush are also strongly influenced by polydispersity. Short chains are found to be compressed close to the grafting interface, whereas longer chains have a characteristic flower-like distribution. These longer chains stretch strongly (stem) when surrounded by smaller chains and decrease their stretching (crown) when only surrounded by longer chains. In line with approximate analytical models, our numerical exact results show that the polymer chains in the brush have localized end-point positions (no fluctuations) in strong contrast to the anomalously large fluctuations in the end-point positions of the homodisperse brush. Despite these effects, the scaling of average height with grafting density and number average chain length is unaffected by polydispersity. Many results that we have presented can be understood qualitatively from the bidisperse brush.