Effect of physical ageing on enthalpy relaxation and isothermal contraction in bisphenol-A polycarbonate

The intention of this paper is to correlate the decrease of free volume and the enthalpy relaxation which occur in high polymers during annealing. We used a simple correlation relation, with one chief parameter (the ‘equilibrium temperature’ ?), which can be deduced from different models. Data on polycarbonate (PC) show no correlation between enthalpy relaxation and isothermal contraction using that relation: the assumption that the decrease of free volume in PC in the glassy state obeys a Williams-Landel-Ferry (WLF) type equation could not be confirmed. Moreover, it seems that the changes of configuration occurring during annealing cannot be described with only one parameter.     

Physical properties of polymers–an introductory discussion

Physical characteristics of isolated molecules and bulk polymers are discussed briefly. The broad spectrum of mechanical properties resulting from changes in temperature and experimental time-scale is introduced by first considering the time-independent properties of elastomers under large deformations and then the effect of a progressive decrease in segmental mobility, leading eventually to glassy characteristics. The phenomenological theory of linear viscoelasticity along with time-temperature superposition is outlined, and illustrative data are presented. Finally, phenomena resulting from volumetric relaxation processes are considered briefly.     

Constitutive relations for compressible glassy polymers

Constitutive equations are derived for the isothermal viscoelastic response of glassy polymers at small strains. The model employs the concept of temporary polymeric networks for shear relaxation and the diffusion mechanism for volume recovery of compressible materials. Adjustable parameters are found by fitting experimental data for poly(methyl methacrylate) and polycarbonate in uniaxial tensile tests. It is demonstrated that the stress-strain relations correctly predict nonmonotonic changes in the specific volume observed in creep tests.     

Sorption kinetics and equilibria in annealed glassy polyblends

The sorption kinetics and equilibria of n-hexane in glassy polyblends of polystyrene and poly(2,6 dimethyl-1,4 phenylene oxide) were studied as a function of annealing conditions. Cast film samples were annealed 20°C above their respective glass transition temperatures for two hours and twenty-four hours. The rate of relaxation-controlled (Case II) sorption of n-hexane in these films was reduced markedly consequent to annealing. The effect of annealing on the sorption kinetics and the independently determined film densities was more pronounced for the poly(phenylene oxide)-rich samples. Although sorption rates were reduced by as much as a factor of 100, the sorption equilibrium was insignificantly affected by annealing. Super Case II transport was observed for the slow absorbing annealed samples whereas the more rapid sorption in the unannealed samples followed ideal Case II kinetics. The more pronounced effects of annealing for the poly(phenylene oxide)-rich samples on sorption rates and film densities were explained by considering the increasing difference between the film T_g and the drying temperature used in the original film preparation for the poly(phenylene oxide)-rich samples. These results suggest that glassy polymers, cast and dried well below their glass transition temperatures, will be subject to large long-term reductions in absorption rates and specific volume. Moreover, residual, excess free volume significantly affects relaxation-controlled absorption of vapors in partially annealed glassy polymers.     

Sorption and diffusion of alcohols in amorphous polymers

The effects of polymer composition and penetrant molecular size on the solubility and diffusivity of alcohol vapors in a series of well characterized isoprene-methyl methacrylate copolymers and their corresponding homopolymers has been investigated at room temperature. The rate of sorption behavior changes progressively from Fickian to non-Fickian, to Case II to “Super Case II” transport with increasing methyl methacrylate (MMA) content in the polymers. The equilibrium solubility of the alcohols increases linearly with increasing penetrant molecular size for polymers which are above their glass transition temperature and decreases for polymers which are below their T_g. The solubility also initially increases as an approximately linear function of MMA content in the copolymers. At about 55 mole percent MMA, the sorbed concentration either levels off or passes through a maximum depending on the size of the penetrant. The apparent “diffusion coefficients” (D) decrease with increasing molecular volume of the penetrants. An exponential dependence was found between these two variables for PMMA. These “diffusion coefficients” also decrease exponentially with increasing MMA content in these polymers. However, at 55 mole percent MMA the copolymer undergoes a rubber to glass transition at the temperature of the experiments. On this basis, it is suggested that the hindered chain segmental motion contributes to the sorption process in addition to strictly thermodynamic considerations. Free volume theory can be used to explain the mechanism of diffusion through the rubbery polymers while the “hole” theory can be applied to explain the transport of the penetrants through the glassy polymers.     

Analysis of butyl acrylate diffusion in a glassy polystyrene matrix to predict gradient structure

To be able to control composition structure in gradient polymers prepared by sequential polymerization, diffusion phenomena has to be considered, particularly for the first 100% weight increment in a glassy polymer matrix. With that purpose, an analytical model to predict diffusion in that region has been developed for amorphous polymers. The inclusion of a relaxation time to estimate surface concentration changes during sorption led to diffusion coefficients one order of magnitude higher than Fickian coefficients. However, adding a volume increment term to account for polymer swelling, diffusion coefficients went up to 48 times the Fickian values. Experimentally, butyl acrylate with a small amount of photosensitizer was diffused into a slightly crosslinked polystyrene slab matrix at different temperatures in the glassy region. After fixing the gradient composition by photopolymerization, chemical structures throughout the slab were determined by FTIR. The proposed model was confronted with experimental sorption showing a close fit at the different temperatures in the region of interest. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1343–1348, 2001     

Stress‐induced densification of glassy polymers in the subyield region

Constitutive equations are derived for the viscoelastic response of amorphous glassy polymers in the region of subyield deformations. The model treats an amorphous polymer as a composite material consisting of an ensemble of flow units, immobile holes, and clusters of interstitial free volume moving through a network of long chains to and from voids. Changes in macropressure lead to an increase in the equilibrium concentration of interstitial free volume that, in turn, induces diffusion of free‐volume elements from holes. The mass flow results in dissolution of voids that is observed as time‐dependent densification of a glassy polymer. It is demonstrated that the model correctly predicts stress relaxation and a decrease in the specific volume observed in uniaxial tensile and compressive tests on polycarbonate at room temperature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1705–1718, 1999     

Analysis of the solvent diffusion in glassy polymer films using a set inversion method

Within the framework of solvent diffusion in glassy polymers, this paper concerns an experimental study of toluene sorption and desorption in P(MMA/nBMA) copolymer films. Gravimetric experiments (quartz microbalance) are performed in a pressure and temperature controlled chamber. Coupling between solvent diffusion and viscoelastic relaxation is taken into account through the time-dependent solubility model, based on the Fick diffusion equation inside the film and a time variable boundary condition at the film/vapor interface. Viscoelastic relaxation is described by a first order model or by a stretched exponential. In the present paper, a special focus is given on the set inversion method used to analyze the data and to derive well-defined uncertainty intervals upon each determined quantity, taking all the uncertainties on the weight measurements into account. We find that the mutual diffusion coefficient strongly decreases in the glassy state, of about two orders of magnitude for a 0.05 decrease in the solvent weight fraction.     

Molecular motions in bisphenol a polycarbonates as measured by pulsed NMR techniques. II. Blends,block copolymers,and composites

Molecular motions in several polyblends and composites based on bisphenol A polycarbonate were investigated over a wide temperature range by means of two pulsed nuclear magnetic resonance methods: the spin-lattice relaxation time T₁ and the spin-lattice relaxation time in rotating frame T_1ρ. Characteristic changes in the transitions of the polyblends and composites with respect to the transitions of unmodified homopolymers and copolymers were observed. By selecting different types and quantities of materials to modify the matrix (bisphenol A polycarbonate) these changes were analyzed. It was found that the multiple transitions in the composites and polyblends were not always combinations of the transitions present in the constituent materials, but depended on compatibility of the polymers and the type of molecular motions of the individual components. Unlike other methods of investigating polymers in bulk, nuclear magnetic relaxation methods are sensitive to supramolecular structure or morphology. Supplemented with transmission and scanning electron micrographs, the results from these experiments led to the postulation of interaction domains or zones between the two phases in certain nonhomogeneous polymer systems in which the motions in one phase (usually the continuous phase) were affected by the motions in the other phase (usually the dispersed phase). Information on the nature and extent of this interaction was obtained by the NMR relaxation methods. The experimental results reflect not only the presence of separate phases in the nonhomogeneous materials, but also the complex heterogeneity of such systems. The results suggest correlations between internal molecular motions and physical properties of the materials examined. Based on the above concepts, a mechanism of rubber reinforcement was proposed. The impact strength of a rubber-modified polymer is related to the apparent volume of the rubber phase. This volume consists of the actual volume of the rubber plus the affected portion of the surrounding glassy matrix which, assisted by the segmental motions of the rubber, assumes the same motions.     

Structural changes in glassy polymers

It has previously been shown that glassy poly(ethylene terephthalate) gives rise to endothermal peaks in DTA when annealed at temperatures near to the glass temperature. The present work describes results obtained from DTA and DSC on annealing a number of glassy polymers which have been rapidly cooled from above the glass temperature and on slowly cooled samples of the same polymers. The polymers which have been studied are: poly(ethylene terephthalate), poly(methyl methacrylate), atactic and isotactic polystyrene, bisphenol-A polycarbonate, poly(ethyl methacrylate) and poly(vinyl acetate). In every case, evidence of structural reorganization is observed, and the rate at which this takes place is reported. Separate studies on poly(ethylene terephthalate) reflect density changes which also take place upon annealing. These results are discussed in the context of the calorimetric observations.     

Diffusion and relaxation in glassy polymer powders: 2. Separation of diffusion and relaxation parameters

Gravimetric sorption measurements for organic vapours in monodisperse glassy polymer powders have shown widely varied non-Fickian kinetic behaviour. These varied kinetics are interpreted by a single mathematical model involving a linear superposition of one or two phenomenologically independent first order relaxation terms upon the ideal Fickian diffusion equation. Analysis of experimental data for submicron powders through this model yields kinetic and equilibrium parameters describing the individual contributions of the diffusion and relaxation processes. This analysis has been applied to both integral and incremental sorption data for vinyl chloride, acetone, and methanol in poly(vinyl chloride) and for n-hexane in polystyrene. Sorption by initially penetrant-free polymer samples is dominated by a rapid Fickian diffusion process, while incremental sorptions show larger relative contributions from slow relaxation processes. The relaxation processes appear to be related to slow redistribution of available free volume through relatively large scale segmental motions in the relaxing polymer. The diffusion—relaxation model seems to provide a meaningful analysis of several non-Fickian ‘anomalies’, including a very slow approach to apparent equilibrium, two-stage and sigmoidal sorption curves, and sorption curves involving an initial maximum followed by temporary desorption and subsequent resorption.     

The effects of temperatures and volumetric expansion on the diffusion of fluids through solid polymers

This study examines moisture sorption behaviors of two glassy polymers, epoxy and vinylester, immersed in different fluids at two temperatures below the glass transition temperatures of the polymers. The main purpose of this study is to understand the effect of volume‐dependent temperatures and deformations on the diffusion process of solid polymers. Diffusivity coefficients are first determined by assuming the diffusion to follow the classical Fickian diffusion. In some cases, moisture sorption led to quite significant changes of volume, and the diffusion process cannot be well described by the Fickian diffusion. In such situation, the coupled deformation–diffusion model for linear elastic isotropic materials presented by Gurtin 1 is adopted, as a first approximation. This coupled deformation‐diffusion model reduces to a Fickian diffusion model when the coupling parameters are absent and the volume changes in the solid polymers during diffusion are negligible. A finite difference method is used in order to solve for the coupled deformation‐diffusion model. The model is used to predict the one‐dimensional moisture diffusion in thin plates and the multiaxial three‐dimensional moisture diffusion in dogbone specimens. The multiaxial diffusion in the dogbone specimens is used to validate the calibrated material parameters from the standard thin plate diffusion characterization. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45151.     

Characterization of glassy state relaxations by low pressure carbon dioxide sorption in poly(methyl methacrylate)

Poly(methyl methacrylate) (PMMA) microspheres were swollen in methanol vapor, the swelling penetrant was quickly evacuated, and the subsequent relaxation of the polymer under vacuum was monitored by determination of the rate of settling of rapidly measured low pressure pseudoequilibrium CO₂ sorption isotherms. The decrease in CO₂ sorption capacity occurred very rapidly at short times, but the final stages of consolidation were protracted. In all cases, the microspheres were under vacuum between isotherm determinations. A single relaxation time is not sufficient to describe the relaxation processes characterized by the time-dependent sorption measurements. The sorption relaxation curves are similar in shape to volume relaxation curves for glassy polymers following imposition of a large pressure or temperature step change. The observed similarity between the sorption relaxation curves and classical volume relaxation curves is consistent with the notion that the excess sorption capacity introduced by methanol preswelling results from excess unrelaxed volume introduced into the glass by the quickly removed alcohol. As the excess volume relaxes, the excess sorption capacity decreases. One can, therefore, monitor the subtle process of consolidation using CO₂ as a probe of the excess volume introduced by the swelling perturbation. Subatmospheric pressure CO₂ sorption isotherms measured between 20 and 40°C for two different diameter microsphere samples (5436 Å and 1453 Å) for pressures up to 700 mm Hg were concave to the pressure axis. Such general isotherm shapes can be described by a two-term expression consisting of a Henry's law term and a Langmuir term. The Langmuir term, which arises due to unrelaxed volume in the nonequilibrium glass, is responsible for the observed concavity in the sorption isotherm. Annealing the sample, increasing the temperature of the sorption experiment closer to the T_g of the PMMA or permitting the preswollen sample to relax tends to reduce the concavity of the isotherm relative to the corresponding case for sorption in the preswollen sample measured at 25°C. This trend is presumably a consequence of the reduction in unrelaxed volume in the glass which attends either annealing, approaching the glass transition temperature of the polymer, or consolidation of excess volume following exposure to a swelling penetrant.     

The effect of molecular orientation on the physical ageing of amorphous polymers-dilatometric and mechanical creep behaviour

The objective of this study was to determine whether molecular orientation has an effect on the rate of physical ageing in amorphous glassy polymers. To achieve this, samples of atactic polystyrene and bisphenol-A polycarbonate were uniaxially hot-drawn to various stretch ratios and then quenched into the glassy state to freeze in orientation. Physical ageing rates were then measured as a function of orientation with dilatometry and tensile creep measurements. The volume relaxation rate, β, was approximately 50% higher for the stretched samples and did not vary with orientation over the range of stretch ratios tested. This was true despite the fact that the initial free volume was actually decreasing with increasing elongation. In contrast, creep measurements showed a slight decrease in the horizontal shift rate, μ_h, upon stretching (i.e. a decreased ageing rate). Possible explanations for these unusual trends in terms of a stretch-induced activated state are discussed.     

Creep behaviour of annealed UPVC and PMMA

The 20°C creep compliance of UPVC is temporarily increased by prior annealing at temperatures above ～45°C and below T_g. This effect increases with decreasing annealing time. Similar behaviour is observed with PMMA which suggests that this may be a general phenomenon shared by polymers in the ‘glassy amorphous state’. The temporary, and therefore unstable nature of the annealed state is inappropriate for a test specimen, particularly for tests of long duration. It is suggested that volume relaxation in UPVC below 45°C proceeds by short range separation into regions of molecular order and disorder. This state is rapidly disrupted at temperatures above 45°C.     

Estimation of free volume in poly(trimethylsilyl propyne) by positron annihilation and electrochromism methods

The free volume of poly(trimethylsilyl propyne) (PTMSP), a glassy polymer distinguished by extremely high gas permeability and diffusion coefficients, was determined by means of two probe techniques—the positron annihilation method and the electrochromism method. Lifetime analysis of positron annihilation spectra revealed an additional long-lived component that is not typical for most of previously studied polymers. A model that has been developed earlier predicts that this lifetime corresponds to the larger size of free-volume elements having an intrinsic radius of about 6 Å. Therefore, PTMSP should be similar to porous inorganic sorbents. A comparison with the literary data for zeolites and silica gel confirms this. According to the electrochromism method, the temperature dependence of the size of free-volume elements for PTMSP is much weaker than that for regular glassy polymers like polystyrene. It was concluded that the great free volume in glassy PTMSP is associated with very loose packing of the chains. © 1993 John Wiley & Sons, Inc.     

Numerical simulation of anomalous penetrant diffusion in polymers

This work introduces a new numerical algorithm that can be used to analyze complex problems of penetrant transport. Penetrant transport in polymers often deviates from the predictions of Fick's law because of the coupling between penetrant diffusion and the polymer mechanical behavior. This phenomenon is particularly important in glassy polymers. This leads to a model consisting of two coupled differential equations for penetrant diffusion and polymer stress relaxation, respectively. If the polymer relaxation is the rate-limiting step, both the concentration and stress profiles are very steep. A new algorithm based on a finite difference method is proposed to solve the model equations. It features the development of a tridiagonal iterative method to solve the nonlinear finite difference equations obtained from the finite difference approximation of the differential equations. This method was found to be efficient and accurate. Numerical simulation of penetrant diffusion in glassy polymers was performed, showing that the integral sorption Deborah number is a major parameter affecting the transition from Fickian to anomalous diffusion behavior. © 1993 John Wiley & Sons, Inc.     

A Model for the Diffusion of Moisture in Adhesive Joints. Part I: Equations Governing Diffusion

A methodology is proposed to relate the diffusion coefficient of small penetrant molecules in polymers to temperature, strain, and penetrant concentration. The approach used is based on well-known free volume theories. It is assumed that the transport kinetics is governed by the constant redistribution of the free volume, caused by the segmental motions of the polymeric chains. An expression for the diffusion coefficient is inferred from the temperature, strain, and penetrant concentration dependence of the free volume. The stress dependence of solubility is predicted from the Hildebrand theory. It is shown that the resulting constitutive equations exhibit many features desirable for joint durability studies. Finally, a non-Fickian driving force arising from differential swelling is included in the governing equations.     

Nonlinear stress-strain behavior of glassy polymers

We have attempted to provide a unified account of the structural relaxation and mechanical properties of glassy polymers by reviewing recent results of a predictive model. One would like to understand how the effects of structural relaxation influence the performance of amorphous solids. The physics of glassy polymers is still evolving and the functional relationships between relaxation and deformation have not been firmly established. However, significant progress has already been made that can be utilized in solving problems in the large deformation of polymers. Equations have been derived that can be applied to provide quantitative prediction of the nonlinear stress-strain relationships as a function of physical aging, strain rate, temperature, external stress field, and the filler concentration in composites.     

The effect of fusion and physical aging on the toughness of poly(vinyl chloride)

It is well known that during aging or annealing, materials become stiffer and more brittle, and creep and stress relaxation rates decrease. Research in this area is very important because physical aging (annealing) plays a large role in the production of products, and it also occurs during the use of the objects or products. The decrease of free volume with time is unavoidable even at ambient temperatures. The influence of fusion and physical aging on the toughness of extruded PVC profiles was investigated. It is known that the toughness of PVC is influenced by secondary crystallization—after primary particles of PVC are partially melted. Recrystallization upon cooling or annealing forms a three-dimensional structure tying together the primary particles. This three-dimensional structure normally produces a tougher PVC product. The density of glassy PVC can be changed by changing the quenching rate. The density can be further changed by annealing below T_g. The densification of a glassy polymer normally leads to a less tough PVC product. This study uses density measurements and differential scanning calorimetry scans to measure the amount of enthalpy relaxation (related to densification) and crystalline melting energy (related to the amount of crystallinity) for various annealed samples. These are related to toughness as measured by notched Izod and droppeddart impact tests.