A predictive approach based on the Simha–Somcynsky free‐volume theory for the effect of dissolved gas on viscosity and glass transition temperature of polymeric mixtures

Experimental measurements have been made of the complex frequency-dependent shear modulus for hexachlorobiphenyl (Aroclor 1260) both with and without, in turn, helium- and argon-gas infusion to capacity, over the temperature range 5°–25°C and the pressure range ambient atmospheric to 4000 psi. Static viscosity results derived from the data are presented and analyzed with the aid of the Macedo–Litovitz hybrid equation to find changes in relative free volume brought about by rare-gas impregnation. Limiting high-frequency shear-compliance data are also presented, to which a phenomenological formulation for shear compliance in molecular-bonded liquids is applied as a means for assessing the additional equilibrium number of intermolecular bonds that are bent or broken under rare-gas infusion. Changes are noted in dynamic shear rigidity, loss modulus, and viscoelastic relaxation times brought about by the presence of each rare-gas impregnant in the recipient liquid, all as influenced by temperature and applied static pressure. Some effects on the dynamic shear spectra that are directly related to evaluated changes in free volume and intermolecular bond density are cited. We find that, except at low pressure, an increase in relative free volume is manifest upon Aroclor infusion with helium or argon gas over our temperature and pressure range. This added free-volume characteristic applies for all pressures at low temperatures where the free volume is small. The effect is found to be larger the higher the pressure (greater infusion) at all temperatures. Additional equilibrium numbers of broken bonds occurring upon infusion are enhanced with increasing temperature and, in general, with decreasing pressure. Viscoelastic relaxation times are decreased in Aroclor upon rare-gas impregnation, the reduction being more pronounced the lower the temperature or the higher the applied pressure. Infusion with the larger argon molecule has over all a more prominent impact on changes in free volume, bond density, and shear-rigidity spectra than has impregnation with helium molecules. However, no appreciable differences are detected between the two gas-infusion cases insofar as their impact on the relaxation time is concerned.

The understanding of atomic-scale structure is a prerequisite for establishing the physico–chemical behavior of complex glass systems. To this end, positron annihilation life time spectroscopy (PALS) is an atomic scale probe capable of investigating the subnanoscopic free volume of amorphous materials. In the present work, PALS has been used to quantify the free volume changes as a function of increasing substitution of B2O3 by Al2O3 in strontium borosilicate glasses intended to be used as sealant in solid oxide fuel cells. The free volume parameters; ortho-positronium (o-Ps) life time (τ 3) and intensity (I 3) show composition dependant variations which are correlated to the molar volume and compactness of the glasses through a commutative free volume parameter, $$~\tau _{3}^{3}{I_3}$$ . The effect of change in nanoscopic free volume induced by the substitution of B2O3 by Al2O3 on the glass transition temperature (T g), softening temperature (T s), coefficient of thermal expansion (CTE) and thermal stability of glasses have been studied. A remarkable trend-based variation in these macroscopic properties with change in free volume is observed. We envisage that the findings of this work will provide new insights in establishing subnanoscopic structure and thermo-physical property correlation of complex glass systems containing multiple network former and modifiers.

Several versions of free-volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation-of-state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (Tg) is available from the SS equation. When above the Tg, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free-volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self-diffusion coefficient and the solvent mutual-diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000

Measurements of average free volume hole sizes, 〈vf〉, and the fractional free volumes, fps, 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, 〈vf〉 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 (Tg) but have less influence on the packing density in the glass. Scaling relationships between 〈vf〉, fps, the thermal expansion coefficient αf = dfps/dt, and Tg are examined. We find that 〈vf〉g, the hole volume at Tg, and fps,g, the fractional free volume at Tg, each increase significantly with increasing Tg. 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-Tg 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, Δαf = αf,l − αf,g, increases slowly with Tg, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999

Measurements of average free volume hole sizes, 〈vf〉, and the fractional free volumes, fps, 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, 〈vf〉 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 (Tg) but have less influence on the packing density in the glass. Scaling relationships between 〈vf〉, fps, the thermal expansion coefficient αf = dfps/dt, and Tg are examined. We find that 〈vf〉g, the hole volume at Tg, and fps,g, the fractional free volume at Tg, each increase significantly with increasing Tg. 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-Tg 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, Δαf = αf,l − αf,g, increases slowly with Tg, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999

The kinetics of moisture uptake in a rigid gas-permeable contact lens material, Fluoroperm60, has been investigated. The free volume changes accompanied by the sorption of water were monitored using the positron lifetime spectroscopy (PLS) technique. The positron results indicated swelling in the initial stages of sorption and the filling of vacant free volume sites with water in the later stages of sorption. The sorption curve suggests that the diffusion process in this polymer follows the dual-mode sorption model. Using this model, it was possible to separate Fickian-controlled diffusion and relaxation-controlled diffusion. Furthermore, the positron results combined with the sorption results indicated that Fujita's free volume theory does not seem to be valid for the diffusion process in the present sample under study. The variation of the permeability as a function of the free volume suggests that the amount of water in a contact lens is a measure of its permeability.

Transport of iodine in poly(ethyleneterephthalate)

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 of dynamics in complex lyophilized formulations: II. Analysis of density variations in terms of glass dynamics and comparisons with global mobility, fast dynamics, and Positron Annihilation Lifetime Spectroscopy (PALS)

A series of poly(styrene-co-vinylphenol) (PSOH) copolymers were prepared and characterized. The miscibility and hydrogen bonding between the partially hydroxylated polystyrene with poly(- caprolactone) (PCL) blend were investigated by differential scanning calorimetry and Fourier transform infrared spectroscopy. The copolymers containing higher than 13 mol % vinylphenol were found to be fully miscible with PCL according to differential scanning calorimetry studies. Quantitative analyses on the fraction of hydrogen-bonded carbonyl groups in the solid state were made by FTIR spectroscopy, and good correlations between thermal behaviors and infrared results were observed. The critical vinylphenol content of 0.1 mol % in PSOH copolymer for the blend to be miscible was predicted from the Painter- Coleman association model and binary interaction model. The discrepancy between the experimental result and theoretical prediction is probably caused by significant free volume increase in this blend system, which is analyzed by the Kovacs' free volume theory. The free volume of the PSOH/PCL is increased which give a positive contribution in the Gibbs free energy. As a result, the polystyrene needs to incorporate more poly(vinylphenol) in PSOH copolymer in order to overcome the free energy increased caused by the free volume increase predicted by the Painter-Coleman association model and the binary interaction model.

Analyses of glass-transition behavior of Pd-based metallic glass with linear solution to non-linear differential equation

PurposeThe purpose of this research paper is to investigate the changes in free volume by adding acrylate modified nanodiamond particles. In this study, a cross-linked thiol-ene (T) network was obtained under ultraviole light. The changes in free volume were analyzed when acrylate-modified nanodiamond (M-ND) particles were added to the nanocomposites obtained. Positron annihilation lifetime spectroscopy (PALS), a well-established method, was used for this analysis. In addition, the effect of nanocomposites containing different ratios of acrylate M-ND particles (1, 2, 3 and 5 Wt. %) on the surface and the thermal properties were also examined.Design/methodology/approachThe impact of different quantities of acrylate M-ND on the free volume and surface morphological properties of thiol-ene polymer networks were studied by using scanning electron microscopy, differential scanning calorimetry, attenuated total reflection, Fourier transform infrared spectroscopy, PALS and thermogravimetric analysis measurements.FindingsThe thermal properties of T/M-ND were found to depend on the weight percentages of the M-ND content. For increasing weight percentages of M-ND added to thio-lene polymer networks, the glass transition temperature (Tg) increased from 103°C to 154°C. The ortho-positronium (o-Ps) lifetime (free volume) and free volume fraction characterization of T/M-ND nanocomposites were investigated using PALS. Increasing temperature caused both the o-Ps lifetime (free volume) to change with increasing saturation and to linearly increase the intensity; however, an increasing weight percentage of M-ND caused no change at all for the o-Ps lifetime (free volume) and the free volume fraction.Originality/valueAccording to published literature, and to the best of the authors’ knowledge, this is the first time a study examining the free volume properties in a thiol-ene system has been carried out.

The kinetics of moisture uptake in a rigid gas permeable contact lens material Paraperm has been investigated. The free volume changes accompanied by the sorption of water have been monitored using Positron Lifetime Spectroscopy (PLS) technique. The positron results indicate the swelling in the initial stages of sorption which seems to be balanced by the rearrangement of chains in the presence of water molecules and filling of vacant free volume sites with water at the later stages of sorption. The sorption curve suggests that diffusion process in this polymer follows dual-mode sorption model. Using this model we have been able to separate the Fickian controlled diffusion and relaxation controlled diffusion. Further, the positron results combined with sorption results indicate that Fujita's free volume theory seems to be not valid for the diffusion process in the present sample under study. The variation of permeability as a function of free volume suggests the amount of water in a contact lens is a measure of its permeability.

The interaction in sorbitol-plasticized starch bionanocomposites via positron annihilation lifetime spectroscopy and small angle X-ray scattering

A free-volume theory is developed based on the defect diffusion model (DDM). In addition, positronium annihilation lifetime spectroscopy (PALS) ortho-positronium free-volume and intensity data are presented for poly(propylene glycol) with a molecular weight of 4000 (PPG 4000) in both the glassy and liquid states and dielectric relaxation and electrical conductivity data are reported for PPG 4000 in the liquid state. The DDM is used to interpret all of the data for PPG 4000 and previously reported PALS and dielectric relaxation data for glycerol. It is shown that while the PPG 4000 data exhibit a preference for the three-halves power law, the data for glycerol favor the first power (standard Vogel-Fulcher-Tammann) law. Good agreement between the DDM and the experimental results is found for all of the electrical data and the PALS free-volume data. While reasonable agreement is also found for the PALS intensity data for PPG 4000, a discrepancy exists between the experimental PALS intensity data and theory for glycerol. For the electrical conductivity for PPG 4000, a transition is observed at the same temperature (about 1.4 T(g) where T(g) is the glass transition temperature) where the PALS free volume changes from steeply rising with temperature to approximately independent of temperature. The same behavior is observed at about 1.5 T(g) for previously reported dielectric relaxation and PALS data for glycerol. Model parameters are presented that show the dominance of mobile single defects above (1.4-1.5) T(g) and the dominance of immobile clustered single defects below T(g) . Finally, a coherent picture of glasses and glass-forming liquids is presented based on the theory and results of the experiments.