ABSTRACT
The effect of temperature on the response of viscoelastic systems to pertur bation fields can be qualitatively observed in Figure 8.1, where the time dependence of the deformation is schematically represented for a viscoelas tic liquid. It can be seen that at the glass transition temperature the defor mation remains nearly constant for comparatively long times. However, as the temperature of the system increases, the deformation undergoes a dra matic increase, which is larger the higher the temperature. If the shear stress is canceled out after steady-state conditions are reached, the time 306
dependence of the recoverable deformation [er(t) = e(t) — a t / rj] is obtained. Note that the higher the temperature, the greater the unrecoverable contri bution to the shear deformation, i.e., the viscous deformation
A real example of the effect of temperature on the viscoelastic functions at T > Tg is shown in Figure 8.2. Here double logarithmic plots of the compliance function J( t) versus time are shown at several temperatures for a solution of polystyrene ( M v = 860,000) in tri-m-tolyl phosphate (l) in which the weight fraction of polymer is 0.70. Because the glass transition temperature of the solution is 15°C, the isotherms were registered at
According to Eq. (5.16), J{t) can be written as
where J r(t) is the recoverable compliance function, which involves the Hookean (Jg) and the entropic [/^ (f)] contributions. Separation of the recoverable compliance from the compliance function can be achieved by canceling out the shear stress once steady-state conditions are reached (see Sect 5.3.1). Owing to the fact that at temperatures close to Tg a time much larger than the time scale of the experiment could be needed to reach steadystate conditions, the experimental determination of the recoverable compli ance function in these cases can be performed by using the following method: A shear step stress a is imposed on the material at temperatures well above Tg, and once steady-state conditions are reached the system is cooled to the required temperature. Then the shear stress is canceled out and Jr(t) is obtained from the ratio of the recoverable deformation to the shear stress, taking as the origin of the time scale the time at which the stress was canceled out. By comparing the isotherms of J(t) and J r(t) obtained for the polystyrene-tri-m-tolyl phosphate (70%) solution, plotted in Figures 8.2 and 8.3, respectively, one finds that the two functions nearly coincide at tem peratures close to Tg. This is consequence of the fact that at these tempera tures, and in the interval of time in which the measurements were performed, the viscous contribution to the deformation is nearly negligible, and consequently only the elastic contributions are important. To detect differences between J(t) and J r(t) at a low temperatures would surely require unattainably large times. However, large differences between the values of J(t) and Jr{t) are observed at high temperatures because, in this case, the viscous contribution to the deformation is dominant. The values of J( t) and Jr{t) at these temperatures are similar only at short times.
