Multiscale Elasticity of Epoxy Networks by Rheology and Brillouin Light Spectroscopy

The response of soft materials to an imposed oscillatory stress is typically frequency dependent, with the most utilized frequency range falling in the range of 10^-2-10² rad/s. In contrast to most conventional contact techniques for measuring material elasticity, like tensile or shear rheology and atomic force microscopy, or invasive techniques using probes, such as microrheology, Brillouin light spectroscopy (BLS) offers an optical, noncontact, label-free, submicron resolution and three-dimensional (3D) mapping approach to access the mechanical moduli at GHz frequencies. Currently, the correlation between the experimental viscoelastic (at lower frequencies) and elastic (at higher frequencies) moduli has fundamental and practical relevance, but remains unclear. We utilize a series of solvent-free epoxy polymer networks with variable cross-link density as models to compare the storage modulus, <i>G</i>', (in the MPa range) obtained from shear rheology and the longitudinal modulus, <i>M</i>', (in the GPa range) extracted from BLS. Our results show that <i>G</i>' exhibits a much stronger increase with increasing cross-link density than <i>M</i>' (by a factor of about 3.5). This finding is discussed in the context of the phantom network model for <i>G</i>' and Wood's inverse rule of mixtures for <i>M</i>'. The epoxy polymer network displays an unexpectedly fast hypersonic dispersion compared to its uncross-linked precursor. These results testify the importance of obtaining reliable information about the elasticity of networks and will hopefully trigger further investigations in the direction of bridging the elasticity of soft materials at different scales.