Constraints and thermal expansion of the free volume in a micro‐phase separated poly(ester‐adipate)urethane

The free volume behavior of a thermoplastic polyesterurethane (TPU) versus temperature is investigated by positron annihilation lifetime spectroscopy and dilatometry. A discrepancy with the free volume predicted by the lattice‐hole theory is found. The agreement is restored by assuming anisotropic expansion of the free volume holes, which in fact results in expansion mainly in two dimensions. This finding is perfectly compatible with a polymer structure based on rheological, thermal, and TEM data which envisage TPU as formed by short soft segments limited in their movements by chain connectivity and confined by physical crosslinks due to the hard segments. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2104–2109     

Effect of residual water and free volume on the glass‐transition temperature and heat capacity in polystyrene/poly(vinyl acetate‐co‐butyl acrylate) structured latex films

The dynamic heat capacity and glass‐transition temperature of polystyrene (PS)/poly(vinyl acetate‐co‐butyl acrylate) (VAc–BA) (50:50 w/w) structured latex films as a function of annealing time at 70, 77, and 85 °C were examined with modulated‐temperature differential scanning calorimetry. The PS and poly(vinyl acetate‐co‐n‐butyl acrylate) components were considered to be the cores and shells, respectively, in the structured latex. The dynamic heat capacity decreased with time. The glass‐transition temperatures of the PS and VAc–BA phases shifted to higher values after annealing. The results of thermogravimetry showed that there existed about 1.8% residual water in the films. The mean free volume and relative concentration of holes at room temperature (before and after annealing) and 85 °C, as a function of time, were obtained with positron annihilation lifetime spectroscopy (PALS). The PALS results indicated no significant change in free volume during annealing. It is believed that the loss, by diffusion, of residual water mainly caused a decrease in heat capacity and an increase in the glass‐transition temperatures. As little as 1.8% residual water in the structured latex films had a significant influence on the thermal properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1659–1664, 2001     

Influence of the plasticization on free volume in polyvinyl chloride

Positron lifetime measurements in pure polyvinyl chloride (PVC) and in the plasticized PVC have been performed. Tricresyl phosphate was used as a plasticizer. Samples of the PVC were prepared with eight different plasticizer concentrations (from 0 to 35% of the plasticizer in the PVC). All of the measurements were performed in air at room temperature. A conventional fast–slow coincidence lifetime spectrometer was used for the measurements. Mean free volumes radii and fractional free volumes were calculated from the lifetime data. It has been found that the mean free volume radius is in the investigated region of the plasticizer concentrations, a linear function of the concentration of the tricresyl phosphate in the PVC. It seems that a polynomial fit can be used to describe the fractional free volume vs. the plasticizer concentration in the PVC. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1839–1845, 1998     

Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements

Positron annihilation lifetime measurements are reported for four monodisperse polystyrenes with molar mass M = 4,000, 9,200, 25,000, and 400,000. The temperature dependences of orthopositronium (o-Ps) lifetime (τ₃) and intensity (I₃) were measured from 5°C to T_g + 30°C for each sample. From these data, the free volume hole size, 〈v_f(τ₃)〉, and fractional free volume h_ps=CI₃〈v_f(τ₃)〉 were calculated. The temperature dependences of τ₃, 〈v_f(τ₃)〉 and h_ps show a discrete change in slope at an effective glass transition temperature, T_g,ps, which is measurably below the conventional bulk T_g. This suggests that τ₃ is sensitive to large holes which retain their liquid-like mobility in the glassy state. Good agreement was found for T > h_g,ps between h_ps and the theoretical free volume fraction h_th deduced from experimental P-V-T data for polystyrene using the statistical mechanical theory of Simha and Somcynsky. Below T_g,ps, deviations between h_ps and h_th are observed, h_ps falling increasingly below h_th as temperature decreases. Whereas h_ps and h_th depend strongly on M in the melt, each essentially independent of M in the glass. A free volume quantity, computed from the bulk volume, which is in good numerical agreement with the Simha-Somcynsky h-function in the melt, gives improved agreement with h_ps in the glassy state. © 1994 John Wiley & Sons, Inc.     

Positron annihilation lifetime studies of free volume in a polymer electrolyte PEO complexed with NH4I

Positron lifetime spectroscopy has been applied to study the temperature dependence of free-volume properties in a solvent-free polymer–salt complex polyethylene oxide (PEO) doped with ammonium iodide (NH₄I, with NH ≈ 0.076) in the temperature range of 298–353 K. The observed lifetime spectra were resolved into three components and the longest lifetime, τ₃, was associated with the pick-off annihilation of ortho-positronium (o-Ps) trapped by the free volume. The lifetime component, τ₃, and its intensity, I₃, both showed a significant variation with temperature, which followed a different course in the heating and cooling cycle. Changes in the temperature coefficient of τ₃ and I₃ were observed at T ≈ 328 K, the melting point of the sample. This behaviour is correlated to the temperature variation of the electrical conductivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 969–976, 1998     

Effect of physical aging of poly(1‐trimethylsilyl‐1‐propyne) films synthesized with TaCl5 and NbCl5 on gas permeability,fractional free volume,and positron annihilation lifetime spectroscopy parameters

The effect of physical aging on the gas permeability, fractional free volume (FFV), and positron annihilation lifetime spectroscopy (PALS) parameters of dense, isotropic poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) films synthesized with TaCl₅ and NbCl₅ was characterized. As‐cast films were soaked in methanol until an equilibrium amount of methanol was absorbed by the polymer. When the films were removed from methanol, film thickness initially decreased rapidly and was almost constant after 70 h in air for both catalysts. This timescale was much longer than the timescale for complete methanol desorption (ca. 5 h). From the film‐thickness data, the reduction in FFV with time was estimated. For samples prepared with either catalyst, the kinetics of FFV reduction were well‐described by a simple model based on the notion either that free‐volume elements diffuse to the surface of the polymer film and are subsequently eliminated from the sample or that lattice contraction controls polymer densification. Methane permeability decreased rapidly during the first 70 h, which was the same timescale for the thickness change. The decrease in methane permeability was smaller in films prepared with NbCl₅ than with TaCl₅. The logarithm of methane permeability decreased linearly as reciprocal FFV increased, in accordance with free‐volume theory. The PALS results indicate that the concentration of larger free‐volume elements (as indicated by the intensity I₄) decreased with aging time and that the other PALS parameters were not strongly influenced by aging. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1222–1239, 2000     

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

Free 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     

Positron annihilation lifetime spectroscopy study of polyvinylpyrrolidone-added polyvinylidene fluoride membranes: Investigation of free volume and permeation relationships

Polyvinylidene fluoride (PVDF) membranes were prepared via the phase inversion method from casting solutions containing PVDF, dimethylformamide (DMF), and polyvinylpyrrolidone (PVP) as pore former. PVP was used in the casting solution in a range of 0–5 wt % and extracted. The effect on membranes of using PVP in the casting process was analyzed by X-ray diffraction, differential scanning calorimetry, scanning electron microscopy, viscosity, and water permeability techniques. With an increase of PVP from 0 to 5 wt %, the PVDF casting solution viscosities increased from 858 to 1148 cP; the resulting PVDF membrane thickness increased; and the crystallinity of PVDF membranes decreased from 40.0 to 33.3%, which indicates that the addition of PVP inhibits the degree of crystallization in the PVDF membranes. SEM results revealed the shape and size of macropores in the membranes; these macropores changed after PVP addition to the casting solutions. The impact of structural changes on free-volume properties was evaluated using positron annihilation lifetime spectroscopy (PALS) studies. PALS analysis indicated no effect on the average radius (~3.4 Å) of membrane free-volume holes from the addition of PVP to the casting solution. However, the percentage of o-Ps pick-off annihilation intensity, I₃, increased from 1.7 to 5.1% with increased PVP content. Further, increasing the PVP content from 0.5 to 5% resulted in an increased final pure water permeability flux. For instance, the 210 min flux for a 14% PVDF + 0.5% PVP membrane was found to be 3.3 times greater than a control membrane having the same PVDF concentration. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 589–598     

Positron annihilation lifetime studies of changes in free volume on cross-linking cis-polyisoprene,high-vinyl polybutadiene,and their miscible blends

Measurements of average free volume hole sizes, 〈v_f〉, and the fractional free volumes, f_ps, in vulcanized cis-polyisoprene (CPI), high-vinyl polybutadiene (HVBD), and their 50 : 50 blend were made via determination of orthopositronium annihilation lifetimes. The results are compared to corresponding data on the uncured materials. On crosslinking, 〈v_f〉 decreases in the rubbery state but remains essentially unchanged in the glass. This is consistent with the expectation that the crosslinks greatly restrict the thermal expansion of the chains above the glass transition temperature (T_g) but have less influence on the packing density in the glass. Scaling relationships between 〈v_f〉, f_ps, the thermal expansion coefficient α_f = df_ps/dt, and T_g are examined. We find that 〈v_f〉_g, the hole volume at T_g, and f_ps,g, the fractional free volume at T_g, each increase significantly with increasing T_g. This behavior is consistent with previous observations reported in the literature and has been interpreted as a manifestation of the kinetic character of the glass transition. High-T_g polymers need a larger free volume to pass into the liquid state. The change in expansion coefficient on passing from the glass to the liquid, Δα_f = α_f,l − α_f,g, increases slowly with T_g, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999     

Free volume changes on optical switching in azobenzene‐polymethylmethacrylate blends studied by a pulsed low‐energy positron beam

Polymers including chromophores, which can be switched by light, have been studied extensively during the last years due to a host of potential applications which arise from the marked changes in physical properties on switching. Even though there is clear evidence that the free volume has a significant influence on the isomerization kinetics, the question of free volume changes on switching was only addressed recently. Using a pulsed low‐energy positron beam the ortho‐positronium lifetime τ₃ was taken as a very sensitive free volume probe, and no change in free volume was detected on isomerization in an azobenzene‐polymethylmethacrylate (PMMA) copolymer containing about 8 wt % of the azobenzene moiety. Here, we report for the first time on free volume changes in an azobenzene‐PMMA blend with an azobenzene moiety concentration as high as 40 wt %. Using the same pulsed low‐energy positron beam, small but significant changes of τ₃ were observed between the structurally relaxed dark and the UV‐illuminated states suggesting a decrease in free volume of the order of 10%. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Characterization,optical, and nanoscale free volume properties of Na‐CMC/PAM/CNT nanocomposites

Polyblend and nanocomposite films of sodium salt of carboxymethylcellulose (Na‐CMC)/polyacrylamide (PAM) and Na‐CMC/PAM modified with carbon nanotubes (CNT) were synthesized by the solution casting technique. The effect of PAM and CNT loading on the structural, optical, and nanoscale free volume properties of Na‐CMC was studied. X‐ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy exhibited the existence of strong interactions between Na‐CMC and PAM and the non‐destructive effect of CNT on Na‐CMC/PAM structure. The HR‐TEM revealed the multi‐walled structure of CNT with a 7.06‐nm wall thickness and a 6.92‐nm wall inner diameter. Positron annihilation lifetime spectroscopy (PALS) was done, in a vacuum and at 30°C to 200°C, to investigate the nanoscale free volume properties by using a conventional fast‐fast coincidence spectrometer. It was found that the o‐Ps lifetime (τ₃ ) and free volume (V_h) increase with increasing CNT percentage in the Na‐CMC/PAM blend. The distribution of the o‐Ps lifetime was broadened with increasing CNT ratios. Furthermore, the glass transition temperature (T_g) increases with increasing loads of CNT. For the first time, a correlation was done between Urbach energy (E_U) and V_h. Finally, the results were represented and discussed in the frame of free volume properties. Optical measurements showed that the transmittance T% of Na‐CMC/PAM was 91.12% and decreased to 68.42% and 36.45% after loading with 1.0 and 2.0 wt % CNT. In addition, the blend shows higher insulating properties compared with the individual polymers. The CNT incorporation reduces the band gap significantly and increases the E_U in the films.     

Damage‐depth profiling of ion‐irradiated polyimide films with a variable‐energy positron beam

Various polyimide layers [2.2–2.6 μm of hexafluoroisopropylidene bis(phthalic anhydride‐oxydianiline), pyromellitic dianhydride‐oxydianiline, and 3,3′‐4,4′‐biphenyltetracarboxylic dianhydride‐p‐phenylenediamine] spin‐coated on silicon substrates were studied with a variable‐energy positron beam in combination with a Doppler‐broadened annihilation radiation technique. From the experiments, the thickness of the layers was estimated with the VEPFIT routine. These values corresponded well to the values determined from interferometry and ellipsometry. Irradiation of the polyimides with 1 × 10¹⁵ boron ions/cm² at an energy of 180 keV led to a strong chemical modification of the irradiated top layer. This caused the inhibition of positronium formation in the irradiated layer, which was observed as a lowering of the annihilation line S parameter. The thickness of the modified layer was estimated to be 700–800 nm. This value did not agree with the ellipsometric measurements but corresponded to the maximum implantation depth of boron ions calculated with TRIM (Transport of Ions in Matter) code. The positron results appeared somewhat larger than the TRIM estimates. Reasons for these relations are discussed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3062–3069, 2000     

Free‐volume change in volume phase transition of polyacrylamide gel as studied by positron annihilation: Salt dependence

Variation of free‐volume parameters—average radius size, number concentration, and size distribution—of a polyacrylamide (PAAm) gel containing 4 mol % carboxylate anions is studied during a volume phase transition (VPT) caused by a change of sodium chloride (NaCl) concentration. A positron annihilation lifetime technique is used for the determination of the free‐volume characteristics. The measurement is performed in an acetone–water 3 : 2 (v/v) [0.27 : 0.73 (mol/mol)] mixed solvent at 20°C, and the free‐volume parameters deduced from the analysis of a positron annihilation curve are utilized. An average free‐volume size of the swollen PAAm gel, ∼ 0.32 nm in radius, almost agrees with that of the mixed solvent for a corresponding salt concentration, while the size of the collapsed gel, which is ∼ 0.28 nm in radius, is smaller than that of the mixed solvent. The results for the collapsed gel indicate that the hydrogen bond plays a significant role in the nanoscopic environment. The radius of the free‐volume of the swollen PAAm gel seems to be influenced by the composition between acetone and water. An inhomogeneity of the nanoscopic structure inside the PAAm gels is discussed in terms of a dispersion of a size distribution of the free‐volume. It is concluded that a change of the nanoscopic environment of the PAAm gel during the VPT can be monitored through the free‐volume parameters obtained by the positron annihilation lifetime technique. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2634–2641, 1999     

The hydrogen bond and free volume property of poly(ether‐urethane) irradiated by neutron

Poly(ether‐urethane) (PEU) was irradiated by neutron in different atmospheres. The hydrogen bonding interaction was analyzed by Fourier transform infrared (FTIR), and the microstructure of PEU had been investigated by positron annihilation lifetime spectroscopy (PALS). The gas products were detected by gas chromatography after irradiation. The results demonstrated that the irradiation led to more hydrogen bonded carbonyl in PEU, smaller relative free volume fraction, and narrower free volume distribution. It suggested that increasing hydrogen bonds would result in the collapse of free volume. The irradiation induced micro‐phase merging together and the presence of oxygen would accelerate this tendency, which was revealed by PALS. All the results indicated that the chain relaxation led to more hydrogen bonds, and the hydrogen bonding interaction suppressed the free volume. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 381–388, 2010     

Contributions of the nanovoid structure to the moisture absorption properties of epoxy resins

Epoxy resins absorb significant quantities of moisture, typically 1 to 7% by weight for various formulations, which can greatly compromise their physical properties. It is known that polarity of the epoxy is a significant factor in determining the ultimate moisture uptake. However, the contribution from molecular topology still remains vague. In this work, the effects of molecular topology are elucidated by synthesizing novel epoxies where the polarity is maintained constant but the topology is systematically altered. The molecular topology is quantified in part via Positron Annihilation Lifetime Spectroscopy (PALS) in terms of the nanometer-sized voids, or nanovoids, that are also commensurate with typical interchain distances. The nanovoids are separated into their absolute zero and thermally fluctuating fractions by performing PALS measurements over a wide range of temperatures. A strong correlation is observed between the absolute zero hole volume fraction and the ultimate moisture uptake. Although the correlation is clear, the absolute zero hole volume fraction alone is not sufficient to predict the ultimate moisture uptake, and network polarity must also be considered. It is surmised that the role of the nanovoids is to open the epoxy matrix and alleviate steric hindrances that may prevent a water molecule from associating with a polar group. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3035–3048, 1998     

Physicochemical testing of free films containing non‐soluble components

Eudragit® L 30D‐55 films containing diclofenac sodium in different concentrations (0%, 1%, and 5%) were studied by conventional physicochemical methods and positron annihilation spectroscopy. Diclofenac sodium was found to change the properties of the film formed significantly. Positron annihilation spectroscopy was applied to track the Eudragit–diclofenac interaction. The presence of diclofenac initially led to significant distortion of the structure of the pure Eudragit film. However, during storage (17°C, 65% relative humidity), the distorted structure relaxed because of water uptake from the air. At the end of the storage period, the free‐volume size was almost the same in all films. Copyright © 2011 John Wiley & Sons, Ltd.     

Free‐volume change during the volume phase transition of polyacrylamide gel studied by positron annihilation: Solvent‐composition dependence

Changes in the free‐volume parameters of polyacrylamide (PAAm) gels during the volume phase transition (VPT) were studied with the positron annihilation lifetime technique. The VPT was induced through the variation of the solvent composition in a mixture of acetone and water. The PAAm gels containing 0 and 4 mol % carboxyl groups in their polymer chains were adapted to compare the effect of the presence of ionic groups on the microscopic environment. The change of the free‐volume property is discussed on a nanoscopic scale, with attention paid to the interactions between the polymer chains and the solvent molecules. It is proven that the variations of the free‐volume parameters correlate significantly with the VPT phenomenon. The results of the free volume for both gels are well‐explained when an interaction parameter, ε_g, is assumed. The interpretation suggests that the state of the interactions among the components (the polymer chain, acetone, and water molecules) plays an important role in the change of the free volume of PAAm gels during the VPT. An increase of the dispersion of the free‐volume size near the VPT point was observed for the ionized PAAm gel. The broadened size distribution of the free volume of the ionized PAAm gel around the VPT point lay between those of pure water and the corresponding mixed solvent, suggesting that a local minimum of the average free‐volume size at the VPT point is caused by the increase of a specific interaction, hydrogen bonding. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 922–933, 2000     

Free Volume and Swelling in Thin Films of Poly(N‐isopropylacrylamide) End‐Capped with n‐Butyltrithiocarbonate

The free volume in thin films of poly(N‐isopropylacrylamid) end‐capped with n‐butyltriocarbonate (nbc‐PNIPAM) is probed with positron annihilation lifetime spectroscopy (PALS). The PALS measurements are performed as function of energy to obtain depth profiles of the free volume of nbc‐PNIPAM films. The range of nbc‐PNIPAM films with thicknesses from 40 to 200 nm is focused. With decreasing film thickness the free volume increases in good agreement with an increase in the maximum swelling capability of the nbc‐PNIPAM films. Thus in thin hydrogel films the sorption and swelling behavior is governed by free volume.