The microstructure of the free volume and its temperature dependence in the epoxy resin diglycidyl ether of bisphenol-A (DGEBA) have been examined using positron annihilation lifetime spectroscopy (PALS, $80–350\mathrm{K}$, ${10}^{-5}\mathrm{Pa}$) and pressure-volume-temperature (PVT, $293–470\mathrm{K}$, $0.1–200\mathrm{MPa}$) experiments. Employing the Simha-Somcynsky lattice-hole theory (S-S eos), the excess (hole) free volume fraction $h$ and the specific free and occupied volumes, $V_f=hV$ and $V_{\mathrm{occ}}=(1-h)V$, were estimated. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, $⟨v_h⟩$, and mean dispersion, ${\sigma }_h$, were calculated. $⟨v_h⟩$ varies from $35\text{to}130{\mathrm{\AA }}^3$. From a comparison of $⟨v_h⟩$ with $V$ and $V_f$, the specific hole number $N_h^{\prime }$ was estimated to be independent of the temperature $[N_h\left(300\mathrm{K}\right)=N_h^{\prime }∕V=0.65{\mathrm{nm}}^{-3}]$. From comparison with reported dielectric and viscosity measurements, we found that the structural relaxation slows down faster than the shrinkage of the hole free volume $V_f$ would predict on the basis of the free volume theory. Our results indicate that the structural relaxation in DGEBA operates via the free-volume mechanism only when liquidlike clusters of cells of the S-S lattice appear which contain a local free volume of $\sim 1.5$ or more empty S-S cells. The same conclusion follows from the pressure dependency of the structural relaxation and $V_f$. It is shown that PALS mirrors thermal volume fluctuations on a subnanometer scale via the dispersion in the ortho-positronium lifetimes. Using a fluctuation approach, the temperature dependency of the characteristic length of dynamic heterogeneity, $\xi$, is estimated to vary from $\xi =1.9\mathrm{nm}$ at $T_g$ to $1.0\mathrm{nm}$ at $T∕T_g>1.2$. A model was proposed which relates the spatial structure of the free volume as concluded from PALS to the known mobility pattern of the dynamic glass transition at low (cooperative $\alpha$-relaxation) and high ($a$-relaxation) temperatures. We discuss possible reasons for the differences between the results of our method and the conclusion from dynamic heat capacity.

• Received 10 October 2005

DOI:https://doi.org/10.1103/PhysRevE.73.031803