Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

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

The gas concentration and pressure effects on the shear viscosity of molten polymers were modeled by using a unified approach based on a free volume theory. A concentration and pressure dependent “shift factor,” which accounts for free volume changes associated with polymer‐gas mixing and with variation of absolute pressure as well as for dilution effects, has been herein used to scale the pure polymer viscosity, as evaluated at the same temperature and atmospheric pressure. The expression of the free volume of the polymer/gas mixture was obtained by using the Simha and Somcynsky equation of state for multicomponent fluids. Experimental shear viscosity data, obtained for poly(ε‐caprolactone) with nitrogen and carbon dioxide were successfully predicted by using this approach. Good agreement with predictions was also found in the case of viscosity data reported in the literature for polystyrene and poly(dimethylsiloxane) with carbon dioxide. Free volume arguments have also been used to predict the T_g depression for polystyrene/carbon dioxide and for poly(methyl methacrylate)/carbon dioxide mixtures, based on calculations performed, again, with the Simha and Somcynsky theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1863–1873, 2006     

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.     

New simple method of measuring the surface glass transition temperature of polymers

A lap‐shear joint mechanical testing method has been probed to measure the surface glass transition temperature (T) of the thick bulk films of high‐molecular‐weight polymers. As T, the temperature transition “occurrence of autoadhesion–nonoccurrence of autoadhesion” has been proposed. The influence of chain flexibility, of molecular architecture, of polymer morphology, and of chain ends concentration on the T has been investigated. The correlation between the reduction in T with respect to the glass transition temperature of the bulk (T) and the intensity of the intermolecular interaction in the polymer bulk in amorphous polymers has been found. The effect of surface roughness on T has been discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2012–2021, 2010     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

Simulated glass transition in free‐standing thin polystyrene films

In this article, we investigate the glass transition in polystyrene melts and free‐standing ultra‐thin films by means of large‐scale computer simulations. The transition temperatures are obtained from static (density) and dynamic (diffusion and orientational relaxation) measurements. As it turns out, the glass transition temperature of a 3 nm thin film is ～60 °K lower than that of the bulk. Local orientational mobility of the phenyl bonds is studied with the help of Legendre polynomials of the second‐order P₂(t). The α and β relaxation times are obtained from the spectral density of P₂(t). Our simulations reveal that interfaces affect α and β‐relaxation processes differently. The β relaxation rate is faster in the center of the film than near a free surface; for the α relaxation rate, an opposite trend is observed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1160–1167, 2010     

Sub‐glass‐transition temperature interface formation between an immiscible glass rubber pair

We used neutron reflectivity to measure the interfacial width in the immiscible system polystyrene/poly(n‐butyl methacrylate) (PS/PnBMA). Measurements were made on the same samples at temperatures ranging from below the glass‐transition temperature (T_g) of PS to slightly above. We observed significant broadening of the interface at temperatures below the T_g of PS, indicating chain mobility below the bulk T_g value. The interfacial width exhibited a plateau at a value of 20 Å in the temperature range of 365 K < T < 377 K. A control experiment involving hydrogenated and deuterated PS films (hPS/dPS) showed no such broadening over the same temperature region. The results are consistent with a reduction of the T_g of PS in the interfacial region of ～20 K. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2664–2670, 2001     

Impact of average free‐volume element size on transport in stereoisomers of polynorbornene. I. Properties at 35 °C

This article demonstrates that transport of gases through glassy polymers is significantly influenced not only by the absolute amount but also by the distribution of free volume. Two stereoisomers of polynorbornene with nearly equivalent total free volume, but markedly different average free‐volume sizes, were evaluated. The free‐volume element size was probed with positron annihilation lifetime spectroscopy, wide‐angle X‐ray scattering, gas sorption, and molecular modeling. The permeation, sorption, and diffusion of light gases were measured in each stereoisomer at 35 °C. All analytical techniques indicated that one isomer (labeled as Architecture II) had a larger average free‐volume element size but fewer elements. This isomer also had a very slightly higher bulk density (1.000 vs 0.992 g/cm³ for the other stereoisomer). Architecture II also had gas sorption and diffusion coefficients that were two to three times those of the less dense counterpart. These differences have been attributed to differences in the free‐volume element size available within the polymer matrix. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2185–2199, 2003     

Physical aging and dye diffusion in polysulfone below the glass transition temperature

The effect of physical aging on the tracer diffusion coefficient D of camphorquinone in polysulfone is investigated. It is shown that if the sample is sufficiently annealed and physical aging is nearly complete, the temperature dependence of D will reflect the primary α-relaxation process of the host polymer. In the temperature range between T_g (=185°C) and 165°C, D is found to be a function of time, and the time dependence of D is given by D = At^?μ, with μ approximately equal to unity. © 1994 John Wiley & Sons, Inc.     

A calorimetric study of the glass transition kinetics in polyisoprene

The connection between the dielectric and calorimetric relaxation behaviours of synthetic polyisoprene Cariflex IR 305 is studied. A similar comparison of dielectric and dilatometric results was described in [1]. The heat capacity was measured during heating of samples prepared with different thermal history. Experimental results were compared with the heat capacity curves calculated for a model based on the multiparameter theory of Kovacs et al. [4]. The model considers the relaxation system as being composed of a set of subsystems characterized by different relaxation times. The distribution of relaxation times and their temperature dependence were taken from the diclectric measurement. The relaxation time of a subsystem from posed to depend, not only on the actual, temperature of the sample, but also on the deviation of this subsystem from equilibrium, or alternatively, on the deviation of the system as a whole. The comparison between the measured and modeled curves shows that both influences must be taken into account in order to explain the experimental results.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday.     

Ortho‐positronium lifetime distribution analyzed with MELT and LT and free volume in poly(ε‐caprolactone) during glass transition,melting, and crystallization

Positron annihilation lifetime spectroscopy (PALS) was used to study the free volume behavior in the temperature range between 100 and 370 K in semicrystalline poly(ε‐caprolactone) (PCL). For the analysis of the spectra we used the well‐known routine MELT as well as the new program LT8.0, which allows both discrete and log‐normal distributed annihilation rates. From experiments, confirmed by the analysis of simulated spectra, we found that MELT returns too large values for the o‐Ps lifetime τ₃ associated with too small intensities I₃. This is due to the underestimation of the width of o‐Ps lifetime distribution in MELT (the spectra analyzed contained 3 million counts). The same effects were observed in the parameters obtained from the discrete term analysis. LT, however, returns, when allowing the o‐Ps lifetime to be distributed, rather accurate values for τ₃, I₃, and the width (standard deviation σ₃) of the o‐Ps lifetime distribution. The effect of the glass transition, melting, and crystallization on the annihilation parameters was observed. These results were compared with differential scanning calorimetry (DSC) and pressure–volume–temperature (PVT) experiments. From this comparison, the number density of holes and the fractional free (hole) volume have been estimated. At a “knee” temperature T_k ≈ 1.5 T_g, a leveling off of the o‐Ps lifetime τ₃ and a distinct decrease in the width, σ₃, of its distribution was observed; the latter effect was detected for the first time. Fast motional processes and/or the disappearance of the dynamic heterogeneity of the glass and the transition to a homogeneous liquid are discussed as possible reasons for these effects. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3077–3088, 2003     

Pressure‐volume‐temperature and glass transition behavior of silica/polystyrene nanocomposite

The pressure‐volume‐temperature (PVT) behavior and glass transition behavior of a 10 wt % silica nanoparticle‐filled polystyrene (PS) nanocomposite sample are measured using a custom‐built pressurizable dilatometer. The PVT data are fitted to the Tait equation in both liquid and glassy states; the coefficient of thermal expansion α, bulk modulus K, and thermal pressure coefficient γ are examined as a function of pressure and compared to the values of neat PS. The glass transition temperature (T_g) is reported as a function of pressure, and the limiting fictive temperature (T_f′) from calorimetric measurements is reported as a function of cooling rate. Comparison with data for neat PS indicates that the nanocomposite has a slightly higher T_g at elevated pressures, higher bulk moduli at all pressures studied, and its relaxation dynamics are more sensitive to volume. The results for the glassy γ values suggest that thermal residual stresses would not be reduced for the nanocomposite sample studied. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1131–1138     

Thermally stimulated current and DSC studies of the broadened glass transition in liquid crystalline polymers

The high sensitivity of the thermally stimulated current, thermal sampling (TS) method is emphasized in a study of the breadth of the glass transition in several liquid-crystalline polymers (LCPs). Differential scanning calorimetry (DSC) was performed on all samples to further quantify the glass transition regions. For “random” copolyester LCPs with widely varying degrees of crystallinity, including highly amorphous samples, very broad glass tran-sition regions were observed. One semicrystalline alternating copolyester and a series of semicrystalline azomethine LCPs were studied as examples of structurally regular polymers. These exhibited relatively sharp glass transitions more comparable to ordinary isotropic amorphous or semicrystalline polymers. The broad glass transitions in the random copolyesters are attributed to structural heterogeneity of the chains. In one example of a moderate-crystallinity random copolyester LCP (Vectra), glass transitions ranging up to ca. 150°C in breadth were determined by the thermal sampling (TS) method and DSC. In other lower crystallinity copolyester LCPs, the main glass transition temperature as determined by DSC was comparable to that determined by TSC although cooperative relaxations of a minor fraction of the overall relaxing species were detected well below the main T_g, by the TS method and not by DSC. Rapid quenches from the isotropic melt to an isotropic glass were possible with one LCP. The anisotropic and isotropic glassy states for this LCP were found to have the same breadth of the glass transition as was determined by the TS method, although TSC and DSC show that T_g is shifted downward by ca. 15°C in the anisotropic glass as compared to the isotropic glass. © 1993 John Wiley & Sons, Inc.     

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     

Temperature modulated calorimetry and dielectric spectroscopy in the glass transition region of polymers

The results from temperature modulated DSC in the glass transition region of amorphous and semicrystalline polymers are described with the linear response approach. The real and the imaginary part of the complex heat capacity are discussed. The findings are compared with those of dielectric spectroscopy. The frequency dependent glass transition temperature can be fitted with a VFT-equation. The transition frequencies are decreased by 0.5 to 1 orders of magnitude compared to dielectric measurements. Cooling rates from standard DSC are transformed into frequencies. The glass transition temperatures are also approximated by the VFT-fit from the temperature modulated measurements. The differences in the shape of the curves from amorphous and semicrystalline samples are discussed.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthday     

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