Nonlinear Relaxation and Aging

If an equilibrated glass is subjected to only a few-degree change in temperature AT, the glass structure will not be far from equilibrium even immediately after the temperature change and the process of relaxation toward equilibrium can be described by a linear spectrum of relaxation times. The shape of the relaxation spectrum governing densification 

The asymmetry is easily explained by consideration of the effect of free volume on T. Equilibration at a low temperature produces a low free volume after an increase in temperature, the process of volume dilation is therefore sluggish until the free volume has expanded, and the rate of dilation then accelerates autocatalytically. The reverse occurs after a downward jump in temperature the rate of volume shrinkage slows as the free volume collapses. Similar phenomena occur when the pressure, rather than the temperature, is increased or decreased (Ferry 1980). 

In general, the prediction of the asymmetric volumetric relaxation processes in glassy materials requires that expressions such as (4-6) and (4-10) that describe the dependence of the characteristic relaxation time on free volume or entropy be extended so that they can describe the nonequilibrium state. Several different expressions for in the nonequilibrium glassy state have been proposed (Scherer 1992). One simple expression is obtained by applying the free volume expression (4-6) to the nonequilibrium state. Then 

As the glass or liquid ages and its volume decreases, the fictive temperature also decreases, finally reaching the actual temperature T if and when the glass or liquid reaches thermodynamic equilibrium. From Figs. 4-10 and 4-17, it can readily be deduced that Tf can be related to the fractional free volume by  

From this, and the definitions of ai,ag, and /, we obtain for the volume r at a time t after a step change in temperature from T to T2  

---