Viscoelasticity and dynamical gaps: rigidity in crystallization and glass-forming liquids

Rigidity plays an important role on the relaxation properties of glass forming melts, yet it is usually determined from the average co-ordination number through the chemical composition. A discussion is presented on how viscoelasticity can be used as an alternative way to determine glass rigidity and to give clues about the relaxation processes. In particular, it is shown that the transverse current dynamical structure factor of dense glass and crystal forming fluids contain rich information about rigidity that can be related with the presence of a dynamical-gap for transversal vibrational modes. As a result, the number of floppy modes can be related with the size of the dynamical gap and with the liquid relaxation time. From this, a dynamical average effective coordination number can be defined. As an example, numerical simulations for hard-disks in a dense fluid phase are provided. Finally, a discussion is presented on the need to improve glass viscoelasticity models to describe consistently non-exponential stress and strain relaxation.