Dynamic heterogeneities, boson peak, and activation volume in glass-forming liquids

There are various arguments and models connecting the characteristic length associated with the boson peak vibrations {ξ} to the length scale of dynamical heterogeneity Lₕₑₜ. {ξ} is usually defined as the ratio of the transverse sound velocity to the boson peak frequency. Here we present pressure, temperature, and molecular weight dependencies of {ξ}, estimated using light scattering, in a few molecular and polymeric glass formers. These dependencies are compared with respective dependencies of the activation volume {Δ}V# in the same materials. Good agreement is found for the pressure and molecular weight dependencies of {ξ} and {Δ}V# measured at the glass transition temperature Tg. These results provide more evidence for a possible relationship between the sensitivity of structural relaxation to density (activation volume) and the heterogeneity volume. However, contrary to the expectations for Lₕₑₜ, {ξ} does not decrease with temperature above Tg in most of the studied materials. The temperature dependence of {ξ} is compared to that of Lₕₑₜ in glycerol and orthoterphenyl (OTP) estimated from literature data. The analysis shows a clear difference in the behavior of {ξ}(T) and {Δ}V#(T) at temperatures above Tg, although {Δ}V#(T)1/3 and Lₕₑₜ(T) have similar temperature dependence. Possible reasons for the observed difference are discussed.