From positron annihilation lifetime spectroscopy analyzed with the new routine LT9.0 and pressure-volume-temperature experiments analyzed employing the equation of state (EOS) Simha-Somcynsky lattice-hole theory (SS EOS) the microstructure of the free volume and its temperature dependence of an oligomeric epoxy resin (ER6, $M_n\approx 1750\mathrm{g}∕\mathrm{mol}$, $T_g=332\mathrm{K}$) of diglycidyl ether of bisphenol-$A$ (DGEBA) have been examined and characterized by the hole free-volume fraction $h$, the specific free and occupied volumes $V_f=hV$ and $V_{\mathrm{occ}}=(1-h)V$, and the size distribution (mean, $⟨{\nu }_h⟩$, and mean dispersion, ${\sigma }_h$) and the mean density $N_h^{\prime }=V_f∕⟨{\nu }_h⟩$, of subnanometer-size holes. The results are compared with those from a previous work [G. Dlubek et al., Phys. Rev. E 73, 031803 (2006)] on a monomeric liquid of the same resin (ER1, $M_n\approx 380\mathrm{g}∕\mathrm{mol}$, $T_g=255\mathrm{K}$). In the glassy state ER6 shows the same hole sizes as ER1 but a higher $V_f$ and $N_h^{\prime }$. In the liquid $V_f$, $⟨{\nu }_h⟩$, $d{V}_f∕dT$, and $d{V}_f∕dP$ are smaller for ER6. The reported dielectric $\alpha$ relaxation time $\tau$ shows certain deviations from the free-volume model which are larger for ER6 than for ER1. This behavior correlates with the SS EOS, which shows that the unit of the SS lattice is more heavy and bulky and therefore the chain is less flexible for ER6 than for ER1. The free-volume fraction $h$ in the liquid can be described by the Schottky equation $h\propto \exp (-H_h∕k_{B}T)$, where $H_h=7.8$–$6.4\mathrm{kJ}∕\mathrm{mol}$ is the vacancy formation enthalpy, which opens a different way for the extrapolation of the equilibrium part of the free volume. The extrapolated $h$ decreases gradually below $T_g$ and becomes zero only when $0\mathrm{K}$ is reached. This behavior means that no singularity would appear in the relaxation time at temperatures above $0\mathrm{K}$. To quantify the degree to which volume and thermal energy govern the structural dynamics, the ratio of the activation enthalpies $E_i=R\left[\right(d\ln \tau ∕d{T}^{-1}){]}_i$, at constant volume $V$ and constant pressure $P(E_V∕E_P)$, is frequently determined. We present arguments for necessity to substitute $E_V$ by $E_{Vf}$, the activation enthalpy at constant (hole) free volume, and show that $E_{Vf}∕E_P$ changes as expected: it increases with increasing free volume, i.e., with increasing temperature, decreasing pressure, and decreasing molecular weight. $E_{Vf}∕E_P$ exhibits smaller values than $E_V∕E_P$, which leads to the general inference that the free volume plays a larger role in dynamics than concluded from $E_V∕E_P$. The same conclusion is obtained when scaling $\tau$ to $T^{-1}{V}_f^{-\gamma }$ instead of to $T^{-1}{V}^{-\gamma }$, where both $\gamma$’s are material constants.

• Received 22 September 2006

DOI:https://doi.org/10.1103/PhysRevE.75.021802