Free Volume Size Distribution Research Articles

Where do Proteins Fit in the Structural Classification of Condensed Matter?

In this work, we use Bond Orientational Order Parameters(BOOP)[1] as the universal descriptors of local packing in proteins. To classify proteins as a distinct family, this local view is combined with a global one which is portrayed by translational order parameters and the free volume distribution. We find that the organization of first coordination shells carries strong signatures of close packed crystalline order in BOOP space. We also show that proteins exhibit no icosahedral bond orientational order at the heavy-atom level and at coarse grained level where residue packing is considered. Close packedness is characterized by the space filling ratio of 0.74048 and is achieved through stacking of hexagonal arrays. Depending on stacking order, this creates Face Centered Cubic(FCC) and Hexagonal Close Packed(HCP) crystals as well as an infinite variety of FCC-HCP mixtures. Using radial distribution formalism, we show that protein-crystal correspondence is strictly local and it extends up-to second nearest neighbors. Due to local correspondence, arbitrarily stacked systems capture protein properties as accurate as ideal crystals.In passing from bulk crystals to proteins we propose a robust route which randomly distributes free volume pockets in a close packed lattice. Remarkably, our results suggests that such protein-like structures automatically possess an exponential size distribution of free volume. This is in accordance with Cohen-Turnbull theory of dense liquids and glasses[2]. We conclude that proteins constitute a unique glassy phase with no icosahedral order.1. Steinhardt, P.J., D.R. Nelson, and M. Ronchetti, Bond-orientational order in liquids and glasses. Physical Review B, 1983. 28(2): p. 784.2. Cohen, M.H. and D. Turnbull, Molecular Transport in Liquids and Glasses. Vol. 31. 1959: AIP. 1164-1169.

Gas transport and free volume in hexafluoropropylene polymers

Amorphous perfluorinated polymers reveal interesting gas permeation and sorption properties. However, the number of the polymers of this class described in literature is limited. In this work, synthesis and physicochemical properties of two novel perfluorinated polymers: poly(hexafluoropropylene) (PHFP) and the copolymer of hexafluoropropylene (90 wt.%) and perfluoromethylvinyl ether (10 wt.%) (copoly-HFP–PFMVE) are reported. PHFP and copoly-HFP–PFMVE are completely amorphous polymers with T g of 150 and 142 °C, respectively. PHFP exhibits a relatively high gas permeability ( P(O 2) = 124 Barrer) and so the gas permeation properties are intermediate between those of AF1600 and Hyflon copolymers. As is the case for other perfluorinated polymers, the data points of PHFP and copoly-HFP–PFMVE are located above upper bounds (1991) of Robeson diagrams for He/H 2 and He/CH 4 pairs. Enhanced selectivity of separation of these pairs as well as for N 2/CH 4 separation can be explained by reduced permeability and solubility of hydrogen containing molecules in perfluorinated polymers. Positron annihilation lifetime spectroscopy showed monomodal size distribution of free volume in these polymers with the concentration of microcavities of about 6–7 × 10 20 cm −1 and the corresponding average size of 392 and 364 Å 3 in PHFP and copoly-HFP–PFMVE, respectively. Solubility and diffusivity selectivity in the two novel polymers are compared to those reported for other perfluorinated polymers.

Free volume change in Zr50Cu40Al10 glassy alloy by the annealing studied by positron annihilation spectroscopy

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.

Free volume in imidazolium triflimide ([C3MIM][NTf2]) ionic liquid from positron lifetime: Amorphous, crystalline, and liquid states

Positron annihilation lifetime spectroscopy (PALS) is used to study the ionic liquid 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide [C(3)MIM][NTf(2)] in the temperature range between 150 and 320 K. The positron decay spectra are analyzed using the routine LifeTime-9.0 and the size distribution of local free volumes (subnanometer-size holes) is calculated. This distribution is in good agreement with Fürth's classical hole theory of liquids when taking into account Fürth's hole coalescence hypothesis. During cooling, the liquid sample remains in a supercooled, amorphous state and shows the glass transition in the ortho-positronium (o-Ps) lifetime at 187 K. The mean hole volume varies between 70 Å(3) at 150 K and 250 Å(3) at 265-300 K. From a comparison with the macroscopic volume, the hole density is estimated to be constant at 0.20×10(21) g(-1) corresponding to 0.30 nm(-3) at 265 K. The hole free volume fraction varies from 0.023 at 185 K to 0.073 at T(m)+12 K=265 K and can be estimated to be 0.17 at 430 K. It is shown that the viscosity follows perfectly the Cohen-Turnbull free volume theory when using the free volume determined here. The heating run clearly shows crystallization at 200 K by an abrupt decrease in the mean <τ(3)> and standard deviation σ(3) of the o-Ps lifetime distribution and an increase in the o-Ps intensity I(3). The parameters of the second lifetime component <τ(2)> and σ(2) behave parallel to the o-Ps parameters, which also shows the positron's (e(+)) response to structural changes. During melting at 253 K, all lifetime parameters recover to the initial values of the liquid. An abrupt decrease in I(3) is attributed to the solvation of e(-) and e(+) particles. Different possible interpretations of the o-Ps lifetime in the crystalline state are briefly discussed.

Subnanometre size free volumes in amorphous Verapamil hydrochloride: A positron lifetime and PVT study through Tg in comparison with dielectric relaxation spectroscopy

Positron annihilation lifetime spectroscopy (PALS), a method well established for the study of polymers, is employed to characterize the temperature dependence of the free volume through T g in the amorphous pharmaceutical Verapamil hydrochloride. From the PALS spectra analyzed with the routine LifeTime9.0 the size (volume) distribution of local free volumes (subnanometre-size holes), its mean, 〈 v h 〉 , and mean dispersion, σ h, were calculated. A comparison with the macroscopic volume from PVT-experiments delivered the hole density and the hole free volume fraction and in that way a complete characterization of the free volume microstructure. These data are used in correlation with structural ( α-) relaxation data from broad-band dielectric spectroscopy in terms of the Cohen–Turnbull free volume model. An extension of this model, distinctions in the free volume behaviour of the glassy and supercooled-liquid state and different ways of extrapolating the equilibrium part of the free volume into the temperature range of the glass are discussed. The potential of the PALS method for the study of pharmaceuticals is briefly reviewed and some recently developed applications (analysis of density fluctuations) are illuminated.

Free volume from positron lifetime and pressure–volume–temperature experiments inrelation to structural relaxation of van der Waals molecular glass-forming liquids

Positron annihilation lifetime spectroscopy (PALS) is employed to characterizethe temperature dependence of the free volume in two van der Waals liquids:1, 1′-bis(p-methoxyphenyl)cyclohexane(BMPC) and 1, 1′-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC). From the PALSspectra analysed with the routine LifeTime9.0, the size (volume)distribution of local free volumes (subnanometer size holes), its mean,⟨vh⟩, and meandispersion, σh, were calculated. A comparison with the macroscopic volume from pressure–volume–temperature (PV T) experiments delivered the hole density and the specific hole free volumeand a complete characterization of the free volume microstructurein that sense. These data are used in correlation with structural (α)relaxation data from broad-band dielectric spectroscopy (BDS) in terms of the Cohen–Grest andCohen–Turnbull free volume models. An extension of the latter model allows us to quantifydeviations between experiments and theory and an attempt to systematize these in terms ofTg or of the fragility. The experimental data for several fragile and less fragile glass formers areinvolved in the final discussion. It was concluded that, for large differences in the fragilityof different glass formers, the positron lifetime mirrors clearly the different character ofthese materials. For small differences in the fragility, additional properties like the characterof bonds and chemical structure of the material may affect size, distribution and thermalbehaviour of the free volume.

Relationship between free volume properties and structure of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) membranes via various crystallization conditions

The relationship between the crystalline structure and the free volume properties within the amorphous phase of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) membranes, which were prepared via isothermal crystallization processes at various crystallization temperatures, was investigated. From the data of positron annihilation lifetime (PAL) spectroscopy over a temperature range of 25–90°C, the temperature dependence of free volume size, amount, distribution, and relative fractional free volume and thermal expansion behaviors of free volume were discussed. The existence of a rigid-amorphous fraction (RAF) which constrained long-range motions in the semi-crystalline polymer was demonstrated by DSC trace and considered to interpret the temperature dependence of those free volume properties. Based on the crystallization conditions, the effect of the crystallization rate of PHBV polymer was proposed to explain the thermal expansion coefficients of free volume size. The membranes crystallized at faster crystallization rate would accompany higher thermal expansion coefficients of free volume size and the larger free volume size at higher temperatures. Larger distribution of the free volume size and higher thermal expansivity of o-Ps lifetime dispersion (dσ/dt) of isothermally melt-crystallized membranes were observed as a result of the bimodal distribution of the lamellar periodicity, which was obtained by small-angle X-ray scattering (SAXS), and less amount of RAF than that of a cold-crystallized membrane. Conclusively, free volume size and thermal expansion of the free volume in PHBV membranes were affected by the kinetics of crystallization; comparatively, the total amount of free volume and fractional free volume were determined by the final crystallinity. The size distribution of free volume was associated with the crystalline lamellar structure which was dominated by the crystallization conditions.

Effect of thermal history on the free volume properties of semi‐crystalline poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) membranes by positron annihilation lifetime spectroscopy

AbstractFree volume properties of a series of poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) (PHBV) membranes, which were produced by various nonisothermal crystallization processes (rapid‐, step‐, and slow‐cooling processes), were investigated using positron annihilation lifetime (PAL) spectroscopy over a temperature range of 25–90 °C. From the annihilation lifetime parameters, the temperature dependence of free volume size, amount, size distribution, and fractional free volume and thermal expansion properties of free volume were discussed. A model which assumed that amorphous phase was subdivided into mobile and rigid amorphous fractions (MAF and RAF) in the semicrystalline polymer was considered to interpret the temperature dependence of those free volume properties. Morphological observation of the semicrystalline polymer by small‐angle X‐ray scattering (SAXS) indicated that the rapid‐cooled (cold‐crystallized) membranes showed a much thinner thickness of the repeating lamellar/amorphous layers and most likely higher amount of RAF, which restrained the chain motion, than the step‐ and slow‐cooled (melt‐crystallized) membranes. The difference of free volume properties among various PHBV membranes was created according to the crystalline structure of the polymer from different thermal history. The polymer crystallized with slower cooling rate induced higher crystallinity and resulted in less free volume amount and lower fractional free volume. In addition, the thermal expansion coefficients of free volume size were affected by the crystallization rate of PHBV polymer. Larger distribution of the free volume size of melt‐crystallized membranes was observed as a result of the bimodal distribution of the lamellar periodicity and less amount of RAF than that of the cold‐crystallized membranes. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 855–865, 2009

Fluctuation approach for the estimation of the dynamic heterogeneity in glass-forming liquids from the dispersion in o-Ps lifetimes: Free volume fluctuations in polymers

Positron annihilation lifetime spectra are analyzed with respect to the mean, τ3, and mean dispersion, σ3, of ortho-positronium lifetimes using the new routine LifeTime, version 9.0, which assumes a log-Gaussian distribution of annihilation rates λ=1/τ. From these data the size distribution of subnanometer local free volumes (holes) characterized by their mean, 〈vh〉, and mean dispersion, σh=〈δvh2〉1/2, is derived. Pressure–volume–temperature experiments are analyzed employing the Simha–Somcynsky equation of state in order to obtain the fractional, h, and the specific, Vf=hV, hole free volume and its expansivity and compressibility. From comparison of Vf with 〈vh〉 the specific number of holes Nh′ is estimated. It is assumed that the hole size dispersion mirrors directly the fluctuation in the free volume as long as the relaxation time of structural motion is larger than the ortho-positronium lifetime of a few nanoseconds. The mean fluctuation in the fractional and specific free volume is calculated. Starting from a fluctuation approach the mean size of the smallest subvolume 〈VSV〉 representative for structural relaxations is estimated. This volume is assumed to be closely related to the volume of a cooperatively rearranging region and to mirror the dynamic heterogeneity. Limits of this interpretation and specific features of PALS are discussed. The variation of the subvolume with temperature and pressure is analyzed. A different behavior of 〈vh〉 and σh is interpreted in terms of Donth’s theory of dynamic glass transition heterogeneity.

The microenvironment in polymer solids with added plasticizers. An attempt to measure the size and distribution of free volume in poly(methyl methacrylate) solids

Various amounts of n-alkylbenzenes (C n : C 6H 5–C n H 2 n+1 ( n = 3–16)) were doped into poly(methyl methacrylate) (PMMA) films, and the emission and thermal properties of each film were measured in detail together with their solid-state 13C NMR spectra. The aim of the present work was to estimate the size distribution of free volume in amorphous regions of polymer solids heavily doped with plasticizers by using C n as models of a plasticizer. The excimer fluorescence yields of C n in PMMA were found to depend on both the amount of C n and the length of the alkyl chains of C n , although the fluorescence spectra of all of the C n s in dilute fluid solution were almost the same. The quantitative analysis showed: (1) C n with n ⩾ 12 induces a phase separation in PMMA, in which almost all of the C n molecules are in a separated phase, and thus they cannot penetrate regions in which PMMA chains are aggregated. This means that C n with n ⩾ 12 cannot enlarge the space between PMMA chains. (2) Smaller C n ( n < 11) can enter free volumes between PMMA chains that correspond to their molecular size, but they can enlarge them only to a limited extent. Thus, the amount by which plasticization can increase the free volume of PMMA is limited by the size of the dopant and the inherent free volume of the polymer matrix. (3) The efficiency of excimer formation was found to reveal the maximum amount of C n that could fit in the free volume of PMMA. Thus our fluorescence measurements showed that PMMA solids that were plasticized to their limit had a free volume that was larger than the volume occupied by all the conformers of C 5 and smaller than the volume occupied by almost all the conformers of C 12. In conclusion, we were able to obtain information on plasticization and to demonstrate a method of monitoring microenvironments in polymer solids after they have been doped with plasticizers.

MD and MC simulation analyses on the effect of solvent types on accessible free volume and gas sorption in PMMA membranes

The effects of solvent types on accessible free volume and dynamic conformation of polymer chains in atactic poly(methyl methacrylate)s (a-PMMA)s were studied by molecular simulation techniques. Five well-minimized amorphous packing models were constructed to form a-PMMA membranes with different casting solvents by utilizing the amorphous builder module of Cerius 2 Software. The fractional free volume, fractional accessible free volume and free volume size distribution of PMMA membranes in various solvent environments were analyzed. The solubility coefficients were also calculated for oxygen and nitrogen by using the Grand Canonical Monte Carlo (GCMC) method. Simulated results indicated that the gas diffusivity of the membrane is mainly affected by free volume and accessible volume, while the gas solubility is highly dependent on the free volume size distribution at the interface.

Free Volumes and the Anomalous Self-Diffusivity of Attractive Colloids

Free volume theories for the dynamics of dense fluids commonly assume (i) that diffusivity increases with average free volume per particle and (ii) that the size distribution of free volumes can be approximated by that of an equivalent hard-sphere reference system. We use molecular simulations to demonstrate that these assumptions break down when one considers concentrated suspensions of particles with short-range attractions. In these systems, self-diffusivity shows nonmonotonic dependencies on both average free volume and the strength of the interparticle attraction. Moreover, when interparticle attractions are strong, the shape of the free volume distribution is qualitatively different than that of the corresponding hard-sphere reference fluid. We propose a conceptual revision to the traditional free volume perspective that takes into account both the size distribution and the persistence time of the free volumes, and we demonstrate that it can qualitatively capture the disparate behaviors of a model fluid with short-range attractions and its hard-sphere reference fluid.

70 MeV Carbon [formula omitted] ion induced modification in polystyrene by positron annihilation

Polystyrene is the radiation resistant polymer and occupies a unique position in the study of radiation effects. The bombardment with swift heavy ions (SHI) results in the change of free volume properties which have strong correlation with macroscopic properties of the polymeric material. Positron annihilation lifetime spectroscopy (PALS) provides direct information about the dimension, content and hole size distribution of free volume in polymers. Polystyrene films were irradiated with C 5 + ions of energy 70 MeV to fluences of 10 10 , 10 11 , 10 12 and 10 13 ions / cm 2 from 15 UD Pelletron accelerator at Nuclear Science Centre (NSC), New Delhi, India. The effect of ion irradiation characterized by PALS has been studied. Observed lifetime spectra were resolved into three components and o-Ps lifetime component was associated with the pick off annihilation of positronium trapped by the free volume. o-Ps lifetime, free volume hole radius and the average free volume are found to be decreased on irradiation. The average free volume of the micro-voids decreased from 0.4% to 7.6% for fluences of 10 10 – 10 13 ions / cm 2 , respectively.

Effect of tacticity of PMMA on gas transport through membranes: MD and MC simulation studies

The effects of tacticity of poly methyl methacrylate (PMMA) on the morphology and size distribution of free volume and gas molecules transport through PMMA matrix were conducted by molecular simulation techniques. How the spatial structure of PMMA affects the glass transient temperature T g of stereoregular PMMA membranes and the solution and diffusion mechanisms in the stereoregular PMMA membranes were conducted by molecular simulation techniques and were compared with experimental data. The polymer chains conformation, gas diffusion mechanism, the time course of the accessible free volume, free volume size distribution, free volume morphology and glass transient temperature, in the various stereoregular PMMA were obtained by a molecular dynamics simulation technique, while the gas solubility in different stereoregular PMMA was calculated by a Monte Carlo technique. A comprehensive comparison of the physical and transport properties of the stereoregular PMMA membranes between simulated and experimental results are provided based on a microscopic interpretation of chain flexibility, free volume morphology and size distribution of free volume in the stereoregular PMMA membranes and gas molecule transport mechanisms through the stereoregular PMMA membranes.

Glass transition and free volume in the mobile (MAF) and rigid (RAF) amorphous fractions of semicrystalline PTFE: a positron lifetime and PVT study

The structure of the free volume and its temperature dependence in poly(tetrafluoroethylene) (PTFE) and of its copolymer with perfluoro(propyl vinyl ether) (PFA) was studied by pressure–volume–temperature (PVT) experiments ( T=27–380 °C, P=0.1–200 MPa) and positron annihilation lifetime spectroscopy (PALS, T=−173–250 °C, P=10 −5 Pa). From the analysis of these experiments we conclude on the volumetric properties of the mobile (MAF) and rigid amorphous fractions (RAF) in these semicrystalline polymers. The specific volumes of the MAF and RAF, V MAF and V RAF, were estimated assuming that V MAF agrees with the specific volume of the melt extrapolated down to lower temperatures using the Simha–Somcynsky equation of state (S–S eos). V RAF was then estimated from the specific volume of the entire amorphous phase, V a, and the known V MAF. The specific free volume V f= V a− V occ was also estimated from V a using the S–S eos hole fraction h, V occ=(1− h) V a. From the analysis of PALS data with the routine LT9.0 the mean volume, 〈 v h〉, and the width, σ h, of the local free volume size distribution (holes of subnanometre size) were obtained. A comparison of 〈 v h〉 with V f delivered the hole density N ′ h . The volume parameters show that the RAF which is formed during crystallisation from the melt has a distinctly smaller specific free and total volume than the MAF. During cooling the contraction of the RAF slows down and finally, below room temperature, the RAF possesses a larger free volume than the MAF shows. Obviously, the restriction of the segmental mobility in the RAF by the crystals limits at high temperatures the free volume expansion and at low temperatures dense packing of the polymer chains. These conclusions from the analysis of the specific volume are confirmed by PALS experiments.

Microstructure of free volume in SMA copolymers II. Local free volume from PALS

The structure of the free volume and its temperature dependence between, at maximum 133 and 503K of copolymers of styrene with maleic-anhydride, SMA (0–35mol% MA), is studied by pressure–volume–temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this second part of the work, PALS data are reported from which the temperature dependence of the mean size and size distribution of local free volumes (subnanometer size holes) is analysed. The mean hole volume, νh, varies in PS between 80Å3 (133K) and 212Å3 (503K) and shows a systematic decrease with increasing MA content for a given temperature above Tg. The specific number of holes, Nh′, estimated from a comparison of PVT and PALS results, increases slightly with MA content from Nh′=(0.60±0.02)×1021g−1 to Nh′=(0.70±0.02)×1021g−1 which corresponds to Nh(Tg)=Nh′/Vg=0.62–0.82nm−3 (Vg is the material's specific volume at Tg) and 1/Nh(Tg)=1.6–1.2nm3 for the volume which contains one hole. The analysed size distributions of the holes above Tg follow the compressibility of the free volume as it is predicted by the theory of thermal volume fluctuation. We also comment on the connection between the hole size as measured by PALS and the size of a cluster of randomly distributed unoccupied cells as defined by the Simha–Somcynsky theory.

The Structure of the Free Volume in Poly(styrene‐co‐acrylonitrile) from Positron Lifetime and Pressure Volume Temperature (PVT) Experiments

AbstractSummary: The structure of the free volume and its temperature dependence between 25 and 190 °C of copolymers of styrene with acrylonitrile, SAN (0 to 50 mol‐% AN), is studied by pressure volume temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this second part of the work, PALS data are reported from which the temperature dependence of the mean size and size distribution of local free volumes (subnanometer size holes) is analysed. The mean hole volume, vh, varies in PS between 105 Å3 (27 °C) and 220 Å3 (190 °C), and shows a systematic decrease with increasing AN content, at Tg from 121 Å3 for PS to 102 (±2) Å3 for SAN50. The specific number of holes, $N_{\rm h} '$, estimated from a comparison of PVT and PALS results, is independent on the temperature and the composition of SAN, $N_{\rm h} '$ = (0.56 ± 0.02) × 1021 g−1 which corresponds to Nh(Tg) = $N_{\rm h} '$/V(Tg) = 0.59 nm−3 and 1/Nh(Tg) = 1.7 nm3 for the volume which contains one hole. The analysed size distributions of the holes above Tg follow the compressibility of the free volume as it is predicted by the theory of thermal volume fluctuation. Moreover, we showed that the bulk elasticity modulus follows mastercurves as a function of vh above and below Tg.Free volume hole radius distribution n(rh) in PS for three different temperatures.magnified imageFree volume hole radius distribution n(rh) in PS for three different temperatures.

SHI induced modification in CR-39 polycarbonate by positron annihilation lifetime studies

CR-39 is a polycarbonate widely used as SSNTD for recording nuclear charged particles and in other applications. Latent ion tracks produced in the polymers due to the damage produced by the passage of Swift Heavy Ions contain amorphous material with highest degree of disorder, changing the free volume properties which have strong correlation with the macroscopic properties of the material. Positron annihilation lifetime spectroscopy (PALS) provides direct information about the dimension, content and hole size distribution of free volume in polymers. The effect of irradiation of 40 Ar (14.9 MeV/n) ions on CR-39 polycarbonate by Positron Annihilation Lifetime Spectroscopy (PALS) is reported here. PALS provides a non-destructive and non-interfering probe, having high detection efficiency for free volume hole properties. From o-Ps lifetime mean free volume hole radius and average free volume of the micro-voids have been calculated. PAL measurement shows an increase in free volume on irradiation.

Crystallinity dependence of free-volume size and its distribution of ethylene-vinyl alcohol copolymer evaluated by positronium lifetime measurement

The size distribution of free-volume (<~0.1 nm3) of ethylene-vinyl alcohol copolymer with various crystalline degrees was estimated by positronium lifetime measurement. With increasing degree of crystallinity, the size distribution significantly narrowed and the intensity of positronium decreased. This indicates that the inhomogeneity reduces with the increase of the degree of crystallinity. It is found that the free-volume fraction estimated is reflected by the fraction of the amorphous region.

Positron Annihilation Study of Hyper-Cross-Linked Polystyrene Networks

Hyper-cross-linked polystyrene sorbents with various degree of cross-linking ranging from 25% to over 100% were studied using positron annihilation lifetime (PAL) spectroscopy. Long-lived components of the lifetime distribution of positron annihilation, orthopositronium (o-Ps) lifetimes, give information on the effective size of elementary free volumes (unoccupied spaces), responsible for the properties of sorbents. Experiments were carried out in a vacuum, in air and also in oxygen and nitrogen. Narrow size distribution of elementary free volumes having radius of about 1.5 nm and concentration estimated as ∼1019 cm-3, were found in the samples with cross-linking higher than 40%. Some of the hyper-cross-linked samples gave positronium lifetime τ5 > 50 ns, which is among the highest values ever measured for organic polymer compounds. Positronium quenching (shortening of o-Ps lifetime) due to Ps exchange interaction with oxygen, dissolved in sorbents, gave information about the character of distribution of ...