Multiscale Elasticity\nof Epoxy Networks by Rheology\nand Brillouin Light Spectroscopy

The response of soft materials to an imposed oscillatory\nstress\nis typically frequency dependent, with the most utilized frequency\nrange falling in the range of 10<sup>–2</sup>–10<sup>2</sup> rad/s. In contrast to most conventional contact techniques\nfor measuring material elasticity, like tensile or shear rheology\nand atomic force microscopy, or invasive techniques using probes,\nsuch as microrheology, Brillouin light spectroscopy (BLS) offers an\noptical, noncontact, label-free, submicron resolution and three-dimensional\n(3D) mapping approach to access the mechanical moduli at GHz frequencies.\nCurrently, the correlation between the experimental viscoelastic (at\nlower frequencies) and elastic (at higher frequencies) moduli has\nfundamental and practical relevance, but remains unclear. We utilize\na series of solvent-free epoxy polymer networks with variable cross-link\ndensity as models to compare the storage modulus, <i>G</i>′, (in the MPa range) obtained from shear rheology and the\nlongitudinal modulus, <i>M</i>′, (in the GPa range)\nextracted from BLS. Our results show that <i>G</i>′\nexhibits a much stronger increase with increasing cross-link density\nthan <i>M</i>′ (by a factor of about 3.5). This finding\nis 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\nfast hypersonic dispersion compared to its uncross-linked precursor.\nThese results testify the importance of obtaining reliable information\nabout the elasticity of networks and will hopefully trigger further\ninvestigations in the direction of bridging the elasticity of soft\nmaterials at different scales.