Structure of bottle-brush polymers in solution: a Monte Carlo test of models for the scattering function

Extensive Monte Carlo results are presented for the structure of a bottle-brush polymer under good solvent or theta solvent conditions. Varying the side chain length, backbone length, and the grafting density for a rigid straight backbone, both radial density profiles of monomers and side chain ends are obtained as well as structure factors describing the scattering from a single side chain and from the total bottle-brush polymer. To describe the structure in the interior of a very long bottle brush, a periodic boundary condition in the direction along the backbone is used, and to describe effects due to the finiteness of the backbone length, a second set of simulations with free ends of the backbone is performed. In the latter case, the inhomogeneity of the structure in the direction along the backbone is carefully investigated. We use these results to test various phenomenological models that have been proposed to interpret experimental scattering data for bottle-brush macromolecules. These models aim to extract information on the radial density profile of a bottle brush from the total scattering via suitable convolution approximations. Limitations of this approach and the optimal way to perform the analysis of the scattering data within this approach are discussed.