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

Different definitions of the free volumes are discussed and related to the total specific volume and to the local free (hole) volume. Positron lifetime measurements are reported for polyethylene, polytetrafluoroethylene, and CR39-copolymers. Two long-lived components appear in polyethylene and polytetrafluoroethylene, which were attributed to o-Ps annihilations in crystalline regions and in holes of the amorphous phase. From a relation between the coefficients of the thermal expansion of macroscopic and hole volume, the fractional hole volume h and from this the number of holes, N, is estimated. Values of Tg = 195 K, hg = 4.5% (polyethylene) and 5.7% (polytetrafluoroethylene) and Ng = 0.73 nm -3 (polyethylene) and 0.36 nm -3 (polytetrafluoroethylene) were obtained. In semicrystalline polymers these values agree with estimates obtained from the densities of the crystalline and amorphous phases. The effect of cross-linking on the free-volume properties of CR39-copolymer networks was studied. The comparison of the hole volume with the specific volume allowed us to estimate the number density of holes to = 1 nm -3 . PACS numbers: 61.41.+e, 65.70.+y, 78.70.—g

We present experiments on glucose-gelatin compounds using positron annihilation lifetime spectroscopy (PALS) in order to study the behavior of the free volume dependent on H2O loading, drying, and uniaxial pressure. A semiempirical quantum mechanical model was applied in order to correlate the lifetime of orthopositronium in nanoscaled voids to the void size. This allowed us to determine the absolute value of the mean void radius in the biopolymer samples. In addition, the variation of the total free volume of the differently treated samples is quantified and illustrated by a log-normal distribution function. Most interesting results have been obtained after saturation loading with H2O that leads to the formation of voids with a mean size of 84.3(1.9) Å(3) and to an increase of the total free volume by a factor of 2.5. This observation in the swelled sample is explained by the entropy elastic regime well above the glass transition temperature that greatly facilitates the formation of free volume. Differential scanning calorimetry (DSC) measurements were performed in order to determine the glass transition temperature and to support the interpretation of the results obtained by PALS.

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.

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

Two distinct oligomeric species of similar mass and chemical functionality (M w≈2,000 g/mol), one a linear methyl methacrylate oligomer (radius of gyration R g≈1.1 nm) and the other a hybrid organic–inorganic polyhedral silsesquioxane nanocage (methacryl-POSS, r≈1.0 nm), were subjected to thermal and rheological tests to compare the behaviors of these geometrically dissimilar molecules over the entire composition range. The glass transition temperatures of the blends varied monotonically between the glass transition temperatures of the pure oligomer (T g=−47.3°C) and the pure POSS (T g=−61.0°C). Blends containing high POSS contents (with volume fraction φ POSS≥0.90) exhibited enhanced enthalpy relaxation in differential scanning calorimetry (DSC) measurements, and the degree of enthalpy relaxation was used to calculate the kinetic fragility indices m of the oligomeric MMA (m=59) and the POSS (m=74). The temperature dependences of the viscosities were fitted by the free-volume based Williams–Landel–Ferry (WLF) and Vogel–Fulcher–Tammann (VFT) framework and a dynamic scaling relation. The calculated values of the fragility from the WLF–VFT fits were similar for the POSS (m=82) and for the oligomer (m=76), and the dynamic scaling exponent was similar for the oligomeric MMA and the POSS. Within the range of known fragilities for glass-forming liquids, the temperature dependence of the viscosity was found to be similarly fragile for the two species. The difference in shape of the nanocages and oligomer chains is unimportant in controlling the glass-forming properties of the blends at low volume fractions (φ POSS<0.20). However, at higher volume fractions, adjacent POSS cages begin to crowd each other, leading to an increase in the fractional free volume at the glass transition temperature and the observed enhanced enthalpy relaxation in DSC.

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.

Previous work in diffusion of whole extender oil and extender oil fractions in practical rubber compounds has shown the nature of the rubber matrix to be the major controlling factor. Therefore, a sensitive diffusivity approach, using radiotracer labeled hydrocarbon penetrants of sizes comparable to the size of a rotating segment, was used to study various aspects of the matrix structure on penetrant diffusion for polybutadiene, styrene—butadiene, and Butyl rubbers. These results were compared with fractional free volume measurements made by a thermal expansion technique. Neither fractional free volume nor diffusivity of phenyldodecane, benz-a-anthracene, or n-octadecane was affected by 5-fold variations of crosslink density or by variations in loading of 10 to 80 parts of carbon black (HAF-LS); nor were they affected by changes from FEF to SAF black at a 50 phr level. Glass transition temperature and fractional free volume are both affected by increasing percentages of benzene or phenyldodecane, While diffusivity rises with increasing dilution, states of equal free volume in different elastomers are not states of equal diffusivity; for example, at a fractional free volume of 0.10, corresponding to 20% benzene in both polybutadiene and Butyl at 70° C, the diffusivity of benzene in Butyl is lower by a factor of 15. Comparison of diffusivity of large penetrants with their cross-sectional area gives two basic curves, one for flexible penetrants and another for molecularly rigid species. These results are explained in terms of a distribution of free volumes, wherein only holes above a critical size are effective in diffusion. Swelling the system with aromatic diluent greatly increases the total fractional free volume, but only slightly the number of holes above this critical size. To understand the diffusivity of rigid molecules in elastomers, a probability factor must be applied in estimating their effective cross-sectional area.

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).

Transitions from solid to liquid in isotactic polystyrene studied by thermal analysis and X-ray scattering

When we keep an amorphous polymer at a temperature below its glass transition temperature T g or when we vary the cooling rate of the polymer from its melting temperature to a temperature below T g , it is not in a true thermodynamical equilibrium state and many of its properties change such as the free volume, the enthalpy and other properties. This behavior is called Physical ageing. In this paper, the study of this phenomenon in partially crystallized poly (ethylene terephtalate) (PET) (14%) is done by differential scanning calorimetry (DSC). The sample of PET is aged in two different ways: the first one consists on annealing the material at temperatures T a below the glass transition temperature T g for different ageing times Δt a . The second one consists of cooling the polymer from a temperature higher than T g (95°C) to the room temperature following various cooling rates b. An endothermic peak appears at a temperature situated just above T g . We notice that for a slow cooling rate and higher annealing time, the area's peak increases and the temperature shifts toward a higher value. Examining the results reveals that the influence of the polymer's thermal history is important for a slow cooling rate and a significant annealing time.

The effects of hydrogen on viscoelastic relaxation in Zr–Ti–Ni–Cu–Be bulk metallic glasses: implications for hydrogen embrittlement

Positron lifetime, UV-VIS absorption and differential scanning calorimetric (DSC) measurements were performed on pristine polycarbonate (PC) and Ag2+-ion-implanted polycarbonate before and after isochronal annealing treatment. UV absorption results indicated the formation of silver clusters in the polymer matrix. The cluster sizes and number of atoms in these clusters were evaluated from UV results. DSC scans for the sample before and after implantation revealed the diffusion of silver ions in the matrix. Further, these results reveal that the Tg of the implanted PC decreased from its pristine value before annealing whereas it increased after annealing. This was inferred to be due to the formation of cross-links by Ag2+ ions when implanted but after annealing, the cross-link seemed to decrease, which resulted in increased diffusion. Positron results as a function of annealing temperature revealed that small size clusters may have been formed in the available free volume and there was migration of silver atoms in the polymer matrix due the rearrangement of the polymer chains. From the positron results the activation energy for the diffusion of silver atoms was determined to be 0.6 eV.

Phase separation in amorphous hydrophobically modified starch–sucrose blends: Glass transition, matrix dynamics and phase behavior

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 ).

A combined experimental and computational approach is applied to amorphous polycarbonates (PCs) to link the macroscopic behavior and molecular features. The Simha–Somcynsky equation of phase (EOS) provides a more accurate description than the Tait EOS for describing the pressure–volume–temperature (PVT) relationship and thermal expansivity. The relationship between the specific volume and the hole free volume was investigated using PVT measurements, positron annihilation lifetime spectra, and molecular dynamics (MD) techniques, to examine the correlations between changes in the behavior of specific volume and molecular packing. We found that the specific volume and hole free volume have linear relationships with temperature. However, the occupied volume displayed remarkable compressibility. The analyses revealed that the PC with side methyl groups and long C–Si bonds contributed to the formation of large free volume. The MD results validate the effectiveness of molecular simulation techniques in designing materials at the molecular level.