Elastic constants and dimensions of imprinted polymeric nanolines determined from Brillouin light scattering

Elastic constants and cross-sectional dimensions of imprinted nanolines of poly(methyl methacrylate) (PMMA) on silicon substrates are determined nondestructively from finite-element inversion analysis of dispersion curves of hypersonic acoustic modes of these nanolines measured with Brillouin light scattering. The results for the cross-sectional dimensions, under the simplifying assumption of vertical sides and a semicircular top, are found to be consistent with dimensions determined from critical-dimension small-angle x-ray scattering measurements. The elastic constants C11 and C44 are found to be, respectively, 11.6% and 3.1% lower than their corresponding values for bulk PMMA. This result is consistent with the dimensional dependence of the quasi-static Young's modulus determined from buckling measurements on PMMA films with lower molecular weights. This study provides the first evidence of size-dependent effects on hypersonic elastic properties of polymers.