Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position q*=2π/ξ by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, ξ∼cBB−0.47, in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions (ξ∼cP−1/2). The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35–0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.
Ising Model on a Triangular Lattice with Three-spin Interactions. I. Free Energy and Correlation Length
