Terminal stage of highly viscous flow

The shear misfit model for highly viscous flow is based upon a theoretical prediction for its terminal stage in terms of irreversible Eshelby relaxations in five-dimensional shear space. The model is shown to predict a small $\delta$-function (Debye peak) in the dielectric spectrum, in agreement with experimental evidence. It is extended to density fluctuations, and a relation between adiabatic and isothermal compressibility jumps at the glass transition is derived. The model is applied to high-precision measurements of the shear, dielectric, and bulk relaxation data in two vacuum pump oils and in squalane, a short chain polymer with a strong secondary relaxation peak. The terminal stage of aging data in squalane demonstrates that the adiabatic density fluctuations contribute a fast component to the thermal expansion, explaining why the thermal expansion seems to equilibrate a bit faster than the dynamic heat capacity.

Figure 1

Fit of dielectric data at 255 K in PPE [14] with (continuous line) and without (dashed line) the Debye peak from the irreversible processes. The inset shows the dashed line misfit at the peak.

Figure 2

Fit of dynamic adiabatic compressibility data (a) at 218 K in DC704 [14], and (b) at 257.5 K in PPE [14] in terms of the spectrum of Eq. (14) (continuous line).

Figure 3

Secondary relaxation peak in squalane in the glass phase [16], together with fits in terms of a Cole-Cole function [16] and in terms of the Gaussian barrier distribution of the present paper.

Figure 4

(a) Measurement [15] of $G\left(\omega \right)$ in squalane; fit in terms of Eq. (11) with the parameters in Table 3. (b) Fit of dielectric data for the same sample in the same cryostat [15] with Eq. (14), with a factor of 0.4 weaker secondary relaxation peak; fit of new adiabatic compressibility data [18] at the slightly lower temperature 171.65 K in terms of Eq. (14) with $a=0$ and a factor 2.6 stronger secondary relaxation peak than the shear data (see the text).

Figure 5

Vogel-Fulcher fit of the values $5{\tau }_{\alpha }$ from the shear relaxation data [16] in the electric-circuit equivalent model (open circles), and of the ${\tau }_c$ values of the shear misfit model in Table 3 (full squares). The value ${\tau }_c=200$ s (full diamond) at 167.73 K is needed for the fit of the aging data in Fig. 6.

Figure 6

(a) Measurement [17] of the density decrease of squalane at 167.73 K on cooling from a 0.06 K higher temperature (down triangles), and of the density increase on heating from a 0.06 lower temperature (up triangles), plotted with the opposite sign to demonstrate the near equality of both curves. The theoretical predictions are calculated for ${\tau }_c=200$ s, the dashed curve only for the irreversible spectrum of Eq. (3), and the continuous curve adds the adiabatic spectrum fitted to the data in Fig. 4 with an appropriate factor (see the text).