Time-resolved small-angle x-ray scattering measurements of a polymer bicontinuous microemulsion structure factor under shear

In situ synchrotron x-ray scattering is used in conjunction with a novel annular cone and plate shear cell to study the nonequilibrium structure factor of a polymer bicontinuous microemulsion within the flow-gradient plane. At equilibrium the scattering is well described by the Teubner-Strey structure factor. In steady shear, the structure factor becomes highly anisotropic, owing to loss of scattering intensity along the flow direction and growth of intensity in peaks that progressively rotate towards the velocity-gradient direction. These results contrast with the predictions of a time-dependent Landau-Ginzburg model of Patzold and Dawson, which generally predicts suppression of scattered intensity. The model assumption of a uniform velocity profile at the microemulsion length scale may be inappropriate owing to high viscosity contrast between the constituents of this sample. While the model anticipates a "stress-x-ray" rule, the data do not support its existence in this system. Nevertheless, strong connections do exist between x-ray anisotropy and stress during transient flow inception experiments. These connections break down upon flow cessation, where stress decays much more rapidly than anisotropy in the structure factor. The mechanical response of this sample exhibits a Rouse-like spectrum of relaxation times, whereas the second moment tensor used to characterize anisotropy in the structure factor exhibits nearly single-exponential relaxation. A phenomenological upper-convected-Maxwell/Lodge model for the second moment tensor provides essentially quantitative predictions of the structural response in step strain and oscillatory shear flow at moderate strains, although additional nonlinearity is found at higher strains.