Studies on the free volume and the volume expansion behavior of amorphous polymers

In order to estimate the free volume contribution on the volume change, we investigated the relationship between the volume expansion behavior by Pressure–Volume–Temperature measurement apparatus and the free volume behavior by Positron Annihilation Lifetime Spectroscopy for some amorphous polymers. From these results, the free volume fraction of the amorphous polymers was calculated by assuming that the core volume increases at a constant rate with temperature. It was found that the amount of free volume was not constant even in the glassy state and it played a very important role in the volume expansion.     

Effect of conductive fillers on the cyclic stress-strain and nano-scale free volume properties of silicone rubber

The effect of carbon black(CB) and graphite(G) powders on the macroscopic and nano-scale free volume properties of silicone rubber based on poly(di-methylsiloxane)(PDMS) was studied through thermal and cyclic mechanical measurements, as well as with positron annihilation lifetime spectroscopy(PALS). The melting temperature of the composites(Tm) and the endothermic enthalpy of melting(?Hm) were estimated by differential scanning calorimetry(DSC). Tm and the degree of crystallinity(χc) of PDMS composites were found to decrease with increasing the CB content. This can be explained due to the increase in physical cross-linking which results in a decrease in the crystallite thickness. Besides, χc was found to be dependent on the filler type. Cyclic stress-strain behavior of PDMS loaded with different contents of filler has been studied. Mullins ratio(RM) was found to be dependent on the filler type and content. It was found that, RM increases with increasing the filler content due to the increase in physical cross-linking which results in a decrease in the size of free volume, as observed through a decrease of the o-Ps lifetime τ3 measured by PALS. Moreover, the hysteresis in PDMS-CB composites was more pronounced than in PDMS-G composites. Furthermore, a correlation was established between the free volume Vf and the mechanical properties of PDMS composites containing different fillers. A negative correlation was observed between Vf and RM.     

Positron annihilation studies of chromophore-doped polymers

Doppler-broadening energy spectra and positron annihilation lifetime have been measured as a function of positron implantation energy in pure and chromophore Disperse Red 1 (DR1)-doped poly(methyl methacrylate) (PMMA) polymers. In pure PMMA, the S parameter increases at very short range (<0.02 μm) from the surface to the bulk, while the S parameter of doped PMMA varies with a decrease from a depth of >0.02 μm to about 0.5 μm after an increase, a short distance from the surface. The o-Ps lifetime of the polymers is found to increase from the bulk to the surface, which indicates that the hole size expands near the surface. The o-Ps lifetime distribution becomes broader near the surface. The change of the o-Ps intensity shows the same trend as the change of the S parameter. These results are interpreted as a gradient of DR1 concentration in PMMA, as a function of the depth from the surface to the bulk in the chromophore-doped polymers.     

Change in free volume of polyvinylidene fluoride

Measurement of positron lifetime was carried out on polyvinylidene fluoride as a function of temperature ranging from 193 to 293 K. The local molecular motion, the cooperative motion of long chain, and the thermal expansion are discussed based on the change in free volume concluded with the use of positron lifetime. The different temperature dependence of motions is suggested for an amorphous area constrained by crystalline regions and a free amorphous area.     

Temperature dependence of free volume in atactic polypropylene

Positron annihilation lifetime spectroscopy data are often used to get information on the typical sizes of sub nanometric holes forming the free volume in polymers. To this purpose, the cavities are modelled as spheres or, more generally, using geometries which assume an isotropic expansion with the temperature. However, this guess could be unrealistic owing to the irregular shape of holes and the constrained movements of the macromolecules.In this work positron and dilatometric data are used to estimate the free volume fraction in atactic polypropylene. Comparison with the prediction of the Simha–Somcynsky theory supplies information on the thermal dependence of the volume of holes, whose behaviour can be interpreted in terms of anisotropic expansion.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Positronium hydride formation in collisions of positrons with molecular hydrogen

Summary The feasibility of observing the threshold for the formation of positronium hydride, PsH, in collisions of low-energy positrons with hydrogen molecules in a mass spectrometric application is considered. The expected count rate of the signature ion H⁺ using existing positron beams depends upon the cross section for a dissociative attachment reaction. The estimation of this cross section relies on knowledge of certain potential energy curves and leptonic wave functions. This knowledge does not yet exist. The curves are roughly estimated by considering the binding of a positron to the ionicB state of H₂. Methods of calculating the wave functions are briefly considered.A preliminary version was presented at the Third International Workshop on Positron and Positronium Chemistry, Milwaukee, July 1990 (Ref. [1])     

Positronium annihilation in liquids in the framework of non-local interaction

In the bubble model of ortho positronium (o-Ps) annihilation in liquid the origin of the trapping of o-Ps is the electron-exchange repulsive interaction between the electron of o-Ps and the electron of the medium. The corresponding effective interaction is non-local in nature. However, in the prevalent bubble model, this effective interaction is usually treated as local (model) potential (sharp or smooth). In the present study, we have taken an approach to consider this trapping interaction as non-local in nature, which is included through a model separable non-local function to tackle the problem in analytically solvable manner. The analytical calculations show that this non-local interaction effectively acts as a gauge potential in the energy of the Ps atom in parameter (bubble radius) space. The computed bubble variables obtained using experimental Ps annihilation data are shown. A comparison between the present data with the calculated results using prevalent bubble model has been presented. Discussions have been made on the input parameter dependencies of the computed data.     

Evidence for the existence of two kinds of orthopositronium in condensed rare gases and for irreversible transitions between them

With reference to time-differential measurements of the momentum distribution of annihilating positron–electron pairs (AMOC) in the condensed rare gases Ne, Ar, and Kr, the paper discusses the question whether in condensed matter positronium (Ps) forms only at predetermined trapping sites or “anywhere”, with subsequent processes leading to Ps trapping or to the formation of Ps bubbles. Ne, in which Ps bubbles are formed not only in the liquid but also in the solid state, may serve as model material for more complex Ps-formers, such as polymers.     

The free volume in acrylic resin/laponite nanocomposite coatings

The morphological features and the free volume properties of an acrylic resin/laponite nanocomposite are investigated using X-ray diffraction and Positron Annihilation Lifetime Spectroscopy. The effects of particle loading on the degree of exfoliation is examined. The measured lifetime spectra and the relative intensities of samples with different particle loading, as well as the shape parameters of the Doppler line broadening are correlated to the free volume in the nanocomposite and the measured CO₂ gas solubility. The effect of the exfoliated nanoclay on the free volume of the composite is found to be very small for clay volume fraction up to 0.2%.     

Positronium formation in NaY-zeolites studied by lifetime, positron beam Doppler broadening and 3-gamma detection techniques

Results of positron annihilation measurements on NaY pressed powders and deposited thin films using slow positron beam and conventional fast positron techniques are presented. In lifetime experiments using an external ²²Na source an averaged long lifetime of 1.8 ns with a sum intensity of 27% was observed in pressed powders in the presence of air at room temperature (RT). In literature this lifetime is ascribed to positrons annihilating in water filled or β cages Habrowska, A.M., Popiel, E.S., 1987. Positron annihilation in zeolite 13X. J. Appl. Phys. 62, 2419. By means of isotopic exchange some of the Na was replaced by ²²Na. These powders showed a long lifetime component of 7–8 ns with an intensity increasing from 1 to 12% when heated under normal atmosphere from RT to 200°C. No significant increase of the shorter (1.5 ns) lifetime was observed, while its intensity dropped from 13.4 to 6.6%. Both effects are ascribed to the loss of water from cages only. The beam experiments revealed a high fraction of 3-gamma annihilations in the pressed powder and thin film samples, indicating the annihilation of o-Ps and thereby the existence of large open volumes.     

Positron age–momentum correlation studies of free volumes in polymers

Positron age–momentum correlation (AMOC) spectroscopy, which can sensitively probe momentum distributions of positrons and positronium (Ps), was conducted for studying the pick-off process of the triplet bound state ortho-Ps (o-Ps) with electrons at the walls of the free volumes in polymers. Influences of different chemical elements forming free volume were investigated. It was found that the momentum distribution of o-Ps pick-off annihilation sensitively depends on the electronic state in the free volumes. The feasibility of the chemical analysis relevant to the free volume in polymers is discussed.     

Theory of free volume in polymers

A number of theoretical approaches to the problem of free volume in polymers are discussed. Because some questions in the Bueche approach remain unresolved, the lattice-gas model was studied. Inconsistencies in the independent-vacancy approximation led to consideration of a mean-field model and then a precise Padé-approximant solution, neither of which gave satisfactory agreement with experiment. Introduction of an internal pressure parameter to model the effects of the chainlike structure of polymers restores agreement with experiment.     

Free volume microstructure of amorphous polymers at glass transition temperatures from positron annihilation spectroscopy data

The analysis of annihilation characteristics of ortho-positronium at conventional calorimetric glass transition temperatures for a series of amorphous polymers reveals empirical correlations of average lifetime of o-Ps , and of its product with a relative intensityI _3g with appropriateT _g ^DSC values. These trends in terms of free volume mean that both the average size of free volume hole entityv _hg and the fractional free volume grow with increasingT _g ^DSC . The results are discussed considering the chemical microstructure as well as possible mechanisms acting in glass transition. A relation is indicated between geometric and flexibility characteristics of chains and thev _hg andf _g parameters of free volume microstructure on the one side and potential motional processes responsible for solidification of the amorphous system on the other side.     

Positronium as a probe of structure and stability of solid phases in binary n-alkane mixtures

Annihilation of triplet ortho-positronium (o-Ps) in binary mixture of odd numbered n-alkanes was investigated. Sensitivity of o-Ps lifetime to the size of free volumes in the sample structure allows to distinguish not only the phases of solid but also some details of their structure. It was found that in the rigid phase o-Ps locates in the interlamellar gap. In mixed systems the o-Ps lifetime in that phase is longer than in neat compounds due to the change of molecular arrangements around the gap. In the case of n-tricosane + n-nonadecane mixture a transient structure appears when the n-tricosane content is between 3% and 10%. Directly after the increase of temperature to the range of 285–292 K the sample transforms to the rotator phase, but returns (at least partially) to the previous rigid structure with recovery time constant of many hours. Above 292 K the structure is stable.     

Focused cryogenic trapping for dynamic headspace and pyrolytic analysis of polymers on a fused silica capillary column

Focused cryogenic trapping has been used to maximize the high resolution capabilities of fused silica capillary columns during dynamic headspace and pyrolytic polymer analyses. Mass spectrometric detection with data system recording/processing provide sensitive, selective, and rapid results. The techniques described herein demonstrate the power of both dynamic headspace and pyrolytic analyses for troubleshooting applications with complex industrial polymer products.     

Study of the size and numerical concentration of the free volume of carbon filled HDPE composites by the positron annihilation method

In this paper, the size and numerical concentration of free volume of high density polyethylene/carbon black (HDPE/CB) composite were investigated by positron annihilation lifetime spectroscopy (PALS). The PALS were measured in two series of samples, one with various CB contents in the composites and the other with changing the temperature of HDPE/CB composite containing 25 phr CB. It was found that the important parameters of PALS show their fluctuation around the percolation threshold. The conductivity of HDPE/CB is controlled by CB contribution, and that can be reflected in o-Ps lifetime. The temperature dependence of positron lifetimes reveals that the existence of glass transition temperatures and the size of free volume holes increases when temperature increases above glass transition. The results observed from the second set of samples suggest that positive temperature coefficient is in some way related with free volume expansion. The experiment facts implied that the conductivity of HDPE/CB was related with not only the size of free volume holes but also the number of free volume holes. The Doppler-broadening of HDPE/CB was also investigated.     

Single-molecule conformations probe free volume in polymers

In this communication, we showed that the conformational dynamics of the tetraphenoxy-perylenetetracarboxy diimide single dye molecule embedded in different polymer matrixes allows a direct visualization of the local free volume. By monitoring the fluorescence lifetime of the dye molecule in time and at different locations in the matrix, different lifetimes were observed. Attributed to two distinct stable conformations of the dye molecule, the lifetime variations permitted characterization of the spatial distribution and temporal dynamics of free volume.