Free volume of an epoxy resin and its relation to structural relaxation: Evidence from positron lifetime and pressure-volume-temperature experiments

Abstract

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, 80-350K, 10(-5) Pa) and pressure-volume-temperature (PVT, 293-470 K, 0.1-200MPa) 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, Vf=hV and Vocc=(1-h)V, were estimated. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, <Vh>, and mean dispersion, sigma h, were calculated. <Vh> varies from 35 130 A3. From a comparison of <Vh>with V and Vf, the specific hole number N'h was estimated to be independent of the temperature [Nh(300 K)=N'h/V=0.65 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 Vf 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 approximately 1.5 or more empty S-S cells. The same conclusion follows from the pressure dependency of the structural relaxation and Vf. 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 nm at Tg to 1.0 nm at T/Tg>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 (alpha-relaxation) temperatures. We discuss possible reasons for the differences between the results of our method and the conclusion from dynamic heat capacity.