Relations Between Hole Volume and Macroscopic Volume in Various Polymers

Positron annihilation lifetime spectroscopy (PALS) was used to investigate the phase transitions, mainly the glass transition, of poly(ethylene terephthalate) (PET) and nylon-6 during the thermal treatment of these polymers. The longest-lived component lifetime and intensity, indicative of ortho-positronium pick-off, exhibit thermal dependencies that can be attributed to the free-volume changes associated with structural transitions. Glass transition temperatures and the volume of intermolecular-space holes among polymer chains were obtained from the lifetime, τ3 and intensity of formation, I3, of the long-lived component of ortho-positronium. For PET, the free-volume fraction and thermal expansion coefficients related to the free-volume fraction were also obtained. Double glass transition behavior was noted in the analyzed polymers, which was consistent with their semicrystalline nature as revealed by differential scanning calorimetry. Increases in the slope of the lifetime-temperature plots for nylon-6 and PET were interpreted to suggest that glass transitions are followed by an increased free-volume cavity expansion as temperature is increased. The intensity response for PET was consistent with the association of glass transition with the reduction of crystalline consraint on segmental mobility in the amorphous phase. In contrast, the intensity behavior during the thermal treatment of nylon-6 seems to be governed more by the electronic effects occurring when the polymer chains acquire mobility than by free-volume changes. Since the sensitivity of PALS is in the order of nanometers, it is expected to give an alternative novel technique to estimate phase transitions and relaxations in polymers from the point of view of the free volume. © 1996 John Wiley & Sons, Inc.

The local free volume in metallocene-catalysed poly(α-olefin)s: a positron lifetime study

Positron annihilation lifetime has been utilized for the first time to investigate the free - volume hole properties in thermolumenscent dosimeter ( TLD ) as a function of gamma-dosc . The hole volume, free volume fraction determined form orthopsitronium lifetime are found to be ?lamatically increase to large values , and then to minimum values as a function ofgamma-dose . The free - volume holes size is found to be 0.163nm’ and to have maximum of 0.166nm^ at the gamma-dose of 0.1 and 0.8 Gy, respectively-

Free volume evolution in polyoxymethylene studied by positron annihilation spectroscopy

An analysis of interatomic space is presented for atomic models of amorphous ${\mathrm{Pd}}_{52}$${\mathrm{Ni}}_{32}$${\mathrm{P}}_{16}$ in the as-quenched state and in an annealed state. Interstitial voids are constructed as clusters of overlapping spheres that are placed in Delauney tetrahedra. It is found that the difference between as-quenched and annealed ${\mathrm{Pd}}_{52}$${\mathrm{Ni}}_{32}$${\mathrm{P}}_{16}$ predominantly lies in the quantity of the relatively large voids. More specifically, the number of voids surrounded by nine or less atoms (``intrinsic voids'') increases, whereas the number of voids surrounded by ten or more atoms (``holes'') strongly decreases. The interpretation is that during structural relaxation the holes break up into two or more intrinsic voids. Since in the annealed state the diffusivity is a factor 25 smaller than in the as-quenched state, the diffusion process is explained in terms of the occurrence of holes. The analysis of the volumes and shapes of the holes shows that (1) the volume distribution becomes narrower on structural relaxation, and (2) although holes with a volume of one atomic volume or more do occur, their shape is strongly nonspherical, and they certainly do not resemble crystalline vacancies. It is furthermore argued that, because of the importance of holes for the atomic mobility, the hole volume is to be regarded as the free volume appearing in the well-known free-volume model by Turnbull and Cohen.

Change in free volume during volume phase transition of poly( N-isopropylacrylamide) gel as studied by positron annihilation lifetimes: temperature dependence

Variations of ortho-positronium (o-Ps) lifetime and gas permeability of the Aquivion® E8705 membrane were studied as functions of temperature under vacuum and relative humidity at room temperature. When the temperature was varied between 0 and 100 °C in vacuum, the hole volume of Aquivion® E8705, deduced from the ortho-positronium lifetime, gradually increased. However, when the relative humidity was changed at room temperature, the hole volume was essentially unchanged. Good linear correlations between the logarithm of permeabilities of O2 and H2 and reciprocal hole volume at different temperatures indicates the importance role of free volume in gas permeation in dry Aquivion® E8705. However, for hydrated Aquivion® E8705 the permeability less depends on hole volume.

Direct relationships between volume variations at macro and nanoscale in epoxy systems. PALS/PVT measurements

Positron annihilation lifetime (PAL) spectroscopy was used to study the effect of water uptake on the free volume in 6FDA-ODA polyimide (PI2566, DuPont). Orthopositronium (o-Ps) lifetime (τ3) and intensity (I3) data were analyzed assuming a Gaussian size distribution of preexisting (excess free volume) holes and further assuming that holes occupied by water molecules would not be detected in the measurement. When exposed to humidity, both the mean hole volume and the number of holes not occupied by water molecules decrease with increasing relative humidity, as indicated by decreasing τ3 and I3. Our PAL results correlated with humidity-induced mass uptake and volume expansion support a model according to which water absorption in polyimides occurs in two stages. At relative humidities smaller than about 30%, water is absorbed mostly in large, preexisting holes, with each hole typically occupied by a single water molecule. At larger humidities, an increasing fraction of the sorbed water molecules will occupy sites other than preexisting empty holes. A multiple occupation of larger holes by water molecules is discussed as a possible mechanism.

Four kinds of epoxy resins: cresol novolac, tris‐hydroxyphenylmethane, tetramethylbiphenol, and bisphenol A, were cured with phenol novolac epoxy resins. Characteristics of these epoxy compounds were studied by the positron annihilation lifetime (PAL) technique. Glass transition temperatures, thermal expansion coefficients, and volume of intermolecularspace holes among polymer chains were obtained from the lifetime, τ3, of the long‐lived component of ortho‐positronium. It was revealed that, at the glass transition temperature, Tg, the volume of the hole created among polymer chains expanded 1.4 times the volume at room temperature. The smaller flexural modulus of tris‐hydroxyphenylmethane than that of the other samples was explained by the volume of intermolecular‐space holes obtained from τ3. Aging effects were seen in the data of the intensities, I3, of ortho‐positronium, which became smaller after heating the samples above Tg. I3 and τ3 were strongly affected by the density of cross‐linkings, and their chemical structures. The larger the density of cross‐linkings, the smaller I3 and higher Tg were obtained. Epoxy compounds with the higher water‐absorption rates had larger intermolecular‐space holes. © 1993 John Wiley & Sons, Inc.

A phenomenological model linking the macroscopic volume from dilatometry with the microscopic free volume from positron annihilation lifetime spectroscopy is presented. The temperature dependences of both quantities enable to obtain the so-called initial temperature Ti at which dynamic free volume change sets in, the corresponding initial volume Vi, and subsequently, all free volume characteristics. Application of this model on the literature data of a typical low-molecular weight glass former, o-terphenyl, leads to the findings that (i) Ti ≅ TK the Kauzmann temperature and (ii) a packing fraction of the extrapolated equilibrium liquid at Ti is close to the closest regular packing of hard spheres. The published viscosity−temperature data over 12 decades of magnitude are correlated with the free volume hole fraction fh, as determined from the PALS results, via the WLF−Doolittle type equation. These findings indicate that the orthopositronium (o-Ps) is able to detect the part of the total free volume distribution which is relevant for the viscosity over the measured temperature interval from Tg up to ∼ 1.5Tg. In addition, the change of the free volume hole behavior above Tr = 1.25Tg, lying in the vicinity of the crossover temperature Tc from the idealized version of mode-coupling theory, is critically analyzed within a modified bubble concept (the equilibrium interaction of o-Ps with the soft matrix).

Compositional and temperature dependence of free volume in segmented copolymer PET/PEO studied by positron annihilation lifetime measurement

It is well known that structural relaxation in a bulk metallic glass affects some properties such as viscosity, electrical conductivity, and ductility. The free volume in glassy alloy, which is open volume retained by rapidly solidification from liquid state, has a significant roll for those properties. In order to discuss the nature of free volume in a Zr50Cu40Al10 bulk metallic glass, positron lifetime measurements have been performed for this metallic glass before and after annealing, and all positron lifetime spectra have been decomposed into multi components as a size distribution function by use of CONTIN-PALS II program. The positron lifetime distribution for this metallic glass has a broad spectrum comparing to crystal metal including a single vacancy, and its average lifetime corresponds to the free volume size. This width of positron lifetime (free volume size) distribution decreases by the annealing at 673 K. This change of the positron lifetime distribution can be attributed to a free volume relaxation.

Effect of crosslinking on the mobility of PDMS filled with polysilicate nanoparticles: Positron lifetime, rheology and NMR relaxation studies

Analysis of the temperature dependence of viscoelastic and dielectric relaxation processes in several individual polymers by the equation of Williams, Landel, and Ferry provides values of the fractional free volume at the glass transition temperature and its thermal expansion coefficient which are rather similar in different systems and of reasonable magnitude, with one exception (poly-n-butyl methacrylate). The friction coefficient per monomer unit atT g , derived from viscoelastic data, varies from 103 to 106 dyn-sec/cm; it is believed to depend on the magnitude of intermolecular forces as well as the disposition of local free volume in the packing of chain segments, which will be affected by detailed geometry even though the average fractional free volume atT g is apparently not much affected. The friction coefficient of a foreign molecule of comparable size to a chain monomer unit, derived from diffusion measurements, is similar in magnitude to that of a chain unit for polyisobutylene 96° aboveT g ; but is very much smaller than that of chain unit for polyvinyl acetate only 12° aboveT g . The temperature dependences of these quantities are similarly related. It is suggested that a foreign molecule is provided with local excess free volume which is relatively unimportant when the average free volume is considerable (well aboveT g ) but greatly reduces the friction coefficient when the average free volume is small (nearT g ).