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,
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) approximately 1750 g/mol , T(g)=332 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(occ)=(1-h)V, and the size distribution (mean,
The microstructure of the free volume was studied for an amorphous perfluorinated polymer (Tg = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, Vf = hV and Vocc = (1 − h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass Vocc has a particular high compressibility, while the compressibility of Vf is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈vh〉, and mean dispersion, σh, were calculated. From a comparison of 〈vh〉 with Vf a constant hole density of Nh′ = 0.25 × 1021 g−1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈VSV〉 ∝ 1/σh2, is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈vh〉 and σh show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from Nh′ = Vf/〈vh〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007
Changes in the microstructure of the free volume and its temperature dependence in ethylene-norbornene copolymer and bisphenol-A polycarbonate due to densification under pressure and swelling with CO2 gas have been examined using positron annihilation lifetime spectroscopy (PALS) and pressurevolume- temperature (PVT) experiments. Employing the Simha-Somcynsky equation of state the specific hole free and occupied volumes were estimated. From the PALS spectra analyzed with the new routine LT9.0 the size distribution of subnanometre holes and its mean and mean dispersion were calculated. Above Tg, the dispersion mirrors the thermal fluctuations in the free volume. From comparison of PALS and PVT data the specific number of holes was estimated. It was found that the occupied volume has a constant and identical compressibility in the glassy and rubbery state. It shows no memory for the history of the glass and mirrors only the pressure and temperature during the measurement. The change in the total volume due to the pre-treatments of the polymers occurs exclusively in the hole free volume Vf and the relative change in Vf is one order of magnitude larger than in the total volume. PALS data show that the mean hole size and its dispersion in the glassy state is decreased due to densification and increased due to swelling. PVT data show that the volume changes are frozen in the polymer glasses and that, when heating the samples, the volume begins to recover at temperatures ca. 50 K in gas swollen and 20 K in densified polymers below Tg. The PALS data show a corresponding behaviour.
In porous media, the vacuum lifetime of ortho-positronium (o-Ps) of τ = 142 ns can be reduced markedly by pick-off annihilation (interaction with electrons of the host material). So the o-Ps lifetime is determined by the pore size which can be extracted by utilising approved models like the Tao-Eldrup model for pore sizes smaller than 1 nm and the Tokyo model or RTE model for larger pore sizes. The RTE model contains an explicit temperature dependence of the o-Ps lifetime. Experiments on controlled pore glasses (CPG) with different pore sizes (2 -70 nm) at different temperatures (50 -500 K) were performed to verify the RTE model. A general agreement for T = 300 K could be found. The temperature dependence of the lifetime, especially for low temperatures, could not be approved sufficiently. 1 Introduction The growing interest of science and industry in the development of porous glass for various applications (low-dielectric thin films, catalysis, molecular filter) necessitate an adequate characterisation of its properties, especially of the pore size. Positronium annihilation lifetime spectroscopy (PALS) allows its non-destructive measurement. In dielectric amorphous material a part of the positrons is formed to a bound state of a positron and an electron which is called positronium (Ps) [1]. There are two spin states of Ps. The singlet spin state (para-positronium, p-Ps) has a very short self-annihilation lifetime of τ S = 0.125 ns and is not suitable to deliver information about the pore size. The long vacuum lifetime of the triplet spin state (ortho-positronium, o-Ps) of τ T = 142 ns is, however, an adequate sensor for measuring the pore size. The vacuum lifetime of o-Ps can be reduced markedly by pick-off annihilation (interaction with electrons of the host material). So the annihilation lifetime contains information about the pore size which can be extracted by calculating the annihilation rate of o-Ps:
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