Self-Consistent Connected-Rod Model for Small-Angle Scattering from Deformed Semiflexible Chains in Flow

Quantifying the microstructure and dynamics under nonlinear deformations is critical for designing flow processes and rheological models for semiflexible polymers and molecular assemblies. Although flow-small angle neutron and X-ray scattering (flow-SANS/SAXS) are suitable for studying how a material's microstructure deforms in flow, scattering models to describe the molecular anisotropy of semiflexible chains in flow have yet to be developed due to the challenge of describing the coupled effects of global (chain-level) deformation and local (segment-level) orientation. To address this challenge, we develop a detailed scattering model for anisotropic semiflexible chains based on a connected-rod chain model that incorporates an orientation distribution for the segments that is thermodynamically self-consistent with the overall stretch and orientation of the chain. We validate the model by comparing its predictions with flow-SANS experiments on wormlike surfactant micelles and find excellent quantitative agreement for the shape of the scattering anisotropy between experiment and simulation across a large range of shear rates. The development of a thermodynamically consistent scattering model for semiflexible chains in flow opens up new possibilities for obtaining microstructural information from flow-SANS/SAXS experiments that can be compared with molecular theories and simulations of flowing polymers and complex fluids.