Relations between elastic modul

As opposed to the liquid-crystal transformation, the liquid-glass transformation is not a phase transition and therefore it can not be characterized by a certain transition temperature. Nevertheless, the term "the vitrification temperature , Tv, is widely used. It has the following physical meaning. As opposed to crystallization, vitrification occurs when the temperature changes continuously, i.e. over some temperature interval, rather than jump-wise. Inside this interval, the sample behaves as a liquid relative to some of the processes occurring in it, and as a solid relative to other processes occurring in it. The character of this behaviour is determined by the ratio between the characteristic time of the process, t, and the characteristic relaxation time of the matrix, x = t//G, where tj is the macroscopic viscosity and G is the matrix elasticity module. If t x, then the matrix should be considered as a solid relative to the process, and if t > x it should be considered as a liquid. The relation tjx = 1 can be considered as the condition of the matrix transition from the liquid to the solid (vitreous) state, and the temperature Tv at which this condition is realized as the temperature of vitrification. Evidently, Tv determined by such means will be somewhat different for the processes with different characteristic times t. However, due to the rapid (exponential) dependence of the viscosity rj on T, the dependence of Tw on t (i.e. on the kind of process) will be comparatively weak (logarith-... 

Pig. 4 23 Relation between the elastic module of inorganic solid emd their melting... 

The sample-tip-cantilever system can be modeled as a mechanical system with springs and dash-pots 11,12). Solving the motion equations of this model at low frequency (i.e. below the cantilever resonance frequency) and neglecting the damping constants (i.e. neglecting viscoelastic effects in polymers) leads to the following relation for the ratio between the sample modulation amplitude, z, and the tip response amplitude, also called the dynamic elastic response ... 

---