Relaxation modes of metaphosphate glasses with entropic shrinkage

We have reconfirmed the anomalistic reversible strain (shrinkage) after tensile creep in the specific metaphosphate glass melts with entropic elasticity in a wide range of applied stresses. We attempted to elucidate the origin of the anomalistic shrinkage by focusing on the relaxation modes. The fast mode was identified for all glasses by two different measurements, i.e., the dynamic viscoelasticity in the linear range and the creep recovery in the non-linear range. In contrast, the slow mode in addition to the fast mode was confirmed only for the glasses showing the anomalistic shrinkage. The slow mode induced the essential shrinkage at whole tensile stresses, whereas the fast mode, especially at higher tensile stresses, contributed to the moderate shrinkage. As the most likely mechanism in the linear range, the local segmental motion with mobile cation motion and the large-scale relaxation of the connected molecules through scission and renewal of the bond between alkali cations and the oxygen anion were assigned to the fast and the slow modes, respectively. In the non-linear range, the dimensionless strain-rate dependence of the reversible strains for both modes had a similar characteristic to that of the viscosity.