Molecules In Glassy Polymers Research Articles

Glassy Polymers—Diffusion, Sorption, Ageing and Applications

For the past few decades, researchers have been intrigued by glassy polymers, which have applications ranging from gas separations to corrosion protection to drug delivery systems. The techniques employed to examine the sorption and diffusion of small molecules in glassy polymers are the subject of this review. Diffusion models in glassy polymers are regulated by Fickian and non-Fickian diffusion, with non-Fickian diffusion being more prevalent. The characteristics of glassy polymers are determined by sorption isotherms, and different models have been proposed in the literature to explain sorption in glassy polymers over the last few years. This review also includes the applications of glassy polymers. Despite having many applications, current researchers still have difficulty in implementing coating challenges due to issues such as physical ageing, brittleness, etc., which are briefly discussed in the review.

Molecular Modeling Investigations of Sorption and Diffusion of Small Molecules in Glassy Polymers.

With a wide range of applications, from energy and environmental engineering, such as in gas separations and water purification, to biomedical engineering and packaging, glassy polymeric materials remain in the core of novel membrane and state-of the art barrier technologies. This review focuses on molecular simulation methodologies implemented for the study of sorption and diffusion of small molecules in dense glassy polymeric systems. Basic concepts are introduced and systematic methods for the generation of realistic polymer configurations are briefly presented. Challenges related to the long length and time scale phenomena that govern the permeation process in the glassy polymer matrix are described and molecular simulation approaches developed to address the multiscale problem at hand are discussed.

Generalized model for the diffusion of solvents in glassy polymers: From Fickian to Super Case II.

The diffusion of small solvent molecules in glassy polymers may take on a variety of different forms. Fickian, anomalous, Case II and Super Case II diffusion have all been observed, and theoretical models exist that describe each specific type of behavior. Here we present a single generalized kinetic model capable of yielding all these different types of diffusion on the basis of just two parameters. The principal determinant of the type of diffusion is observed to be a dimensionless parameter, γ, that describes the influence of solvent-induced swelling in lowering the potential barriers separating available solvent sites. A second parameter, η, which characterizes the effect of the solvent in reducing the potential energy of a solvent molecule when at rest at an available site, only influences the type of diffusion to a lesser extent. The theoretical analysis does not include any effects that are explicitly non-local in time, an example of which is the inclusion of polymer viscosity in the Thomas-Windle model; it thus represents a variant of Fick's second law utilizing a concentration-dependent diffusivity when η is small. To check the significance of time-delayed swelling, a simulation of a modified model was performed that contained a history-dependent term. The results were found to be very similar to those in the time-local model.

Tuning the transport dynamics of small penetrant molecules in glassy polymers

The effects of network structure of crosslinked poly(methyl methacrylate) (PMMA) discs on dynamic penetrant transport behavior were investigated through gravimetric integral sorption studies. Samples of P(MMA-co-(EG)xDMA) were synthesized via an iniferter-mediated, thermally-initiated free radical polymerization procedure to produce polymers with controlled variations in network structure by altering the comonomer feed ratios of dimethacrylate crosslinkers and changing the crosslinker interchain bridge length. The front velocity in the Case II transport regime was shown to scale directly with the square root of the crosslinking density over varied thermal and structural conditions, and increasing the crosslinker interchain bridge length moved the observed penetrant transport behavior towards the Fickian regime. The demonstrated ability to tune the dynamic transport behavior through modification of the polymer network structure holds promise as a means to mitigate solvent-induced material failure due to cracking and crazing encountered in many high-tech applications.

Calculation of the solubility of liquid solutes in glassy polymers

AbstractThe solubility of liquid molecules in glassy polymers has been considered by using the general results of the Non‐Equilibrium Thermodynamics of Glassy Polymers (NET‐GP), which proved successful to calculate solubility isotherms of gases in glassy polymers for rather different situations, including polymer blends, mixed gases, and mixed matrices. It is shown that the existing model is suitable also for liquid penetrants in a glassy phase: water and ethanol sorption in polycarbonate (PC) and water sorption in polysulfone (PSf) have been examined as examples. The model's ability to predict the solubility from both liquid and vapor phases was tested successfully, using the same values of the parameters for both phases. In the case of PC, the model was also applied to calculate successfully the solubility of liquid water at different temperatures from 25 to 130°C, with a single value of the energetic binary parameter. © 2011 American Institute of Chemical Engineers AIChE J, 2012

Molecular mobility of nitroxide spin probes in glassy polymers: Models of the complex motion of spin probes

AbstractThe rotational mobility of molecules in glassy polymers was investigated by quantitative simulations of electron spin resonance spectra of nitroxide spin probes with molecules of different sizes. The motional models were determined unambiguously when the experimental and calculated spectra coincided within the level of experimental error. Temperature ranges in which different motional models were applicable were determined. Quasi‐librational movements and the distribution of rotational mobility were found to be necessary for the qualitative description of spin‐probe mobility in glassy polymers. The quantitative and empirical characteristics of rotational mobility were examined. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation

The use of hole-filling models is quite common for the sorption of gases into glassy polymers, but these have yet to be explicitly applied to the case of liquid immersion, where extensive use of Flory–Huggins theory dominates. This paper explores how the models based on the idea of sequential filling of a Gaussian distribution of pre-existing free-volume holes within the structure of the glassy polymer can be modified to allow the prediction of the equilibrium solubility of a liquid penetrant. For liquids, the driving force for sorption is more subtle than for gases, with more emphasis on molecular interactions rather than external pressure. For this reason, terms relating to the molecular interactions of a liquid molecule filling a hole were developed, including the effects of elastic constraint for small holes. Consideration of thermal fluctuations show that configurational entropy provides much of the driving force for sorption. Some comparisons with experimental data show a reasonable agreement, and one which is far better than the Flory–Huggins theory.

Conformational probes in study of glassy polymers

This work is devoted to development of FTIR spectroscopic method of conformational probes in glassy polymers. A new approach is employed to model the freezing of conformational transitions in probe molecules in glassy polymers. This method is based on introducing small molecules (probes) in a polymer and following conformational dynamics in the probe molecules at different temperatures. For each polymer-probe system, freezing of conformational transitions is observed by FTIR at a certain individual temperature, T f . A linear correlation between the freezing temperature T f of conformational transitions of probe molecules and the size of rotational fragments of probe molecules is observed. The magnitude of T f increases with the size of rotational fragments of the probe molecules and decreases with the free volume fraction of the studied polymers. The obtained results were interpreted in terms of existing “mobile” and “fixed” free volume entities in glassy polymers. The new representations about the processes occurring in polymeric matrices at T f are given. Finally, relaxation transitions observed in the polymers at the temperatures T f were assigned to certain types of molecular mobility of their lateral groups.

Effect of long-term aging on oxygen sensitivity of luminescent Pd-tetraphenylporphyrin/PMMA films

The phosphorescence quenching by molecular oxygen of Pd-tetraphenylporphyrin molecules encapsulated into thin films of PMMA was monitored during long-term aging. The quenching-dependent part of the phosphorescence decay law was described by a stretched exponential, whereas the value of stretching factor β = 0.79 remained constant during the whole aging period of 9 months. The average values of quenching rates decreased more than four times during this time. The diffusion constants, determined from the response of phosphorescence to a step change in oxygen pressure, decreased by a similar amount. The results contribute to a deeper understanding of the factors influencing the long-term stability of oxygen sensors based on dye molecules in glassy polymers. The magnitudes of the sensitivity drift, caused by physical aging, were determined for Pd-TPP/PMMA at different aging temperatures: the aging rates of Stern–Volmer factors in logarithmic timescale were 0.22 and 0.12 at 20 and 70 °C, respectively. The lower temperature aging process was solvent assisted, whereas at 70 °C a relatively fast change involving the solvent evaporation was followed by slower relaxation.

Solubility of Gases in Vitreous Silica Described by a Distribution of Dissolution Energies

The solubility of gases in vitreous silica complies well with Henry's Law at low pressures. Deviations observed at high pressures have been explained by site saturation, i.e., the number of dissolved molecules approaches the number of available sites that are assumed to have all the same energy of solution. In the present study, the observed deviations from Henry's Law are explained by a gradual saturation of sites of increasing energy. Experimental data of the solubility of hydrogen, helium, and neon in vitreous silica can be described by a Gaussian distribution of dissolution energies and Fermi-Dirac statistics. The solubility of hydrogen in metallic glasses, as well as the solubility of small molecules in glassy polymers, has been interpreted, and now, glasses in vitreous silica fit into this general concept of small particles in amorphous matrices.

Rotational mobility of guest molecules studied by method of oriented spin probe

Oriented spin probe method was used for study of rotational mobility of di-p-anisylnitroxide in low-temperature ethanol, toluene and isopropylbenzene glasses as well as in glassy polystyrene, poly-(N-vinylpyrrolidone) and polyvinyl butyral matrixes. Alignment of probe molecules in initially isotropic samples was induced by polarized light irradiation (photoselection phenomenon). The temperature dependencies of relaxation of alignment were measured. The rotational relaxation of light-induced alignment in low-temperature glasses was found to complete near the glass transition temperature. A step-type relaxation of alignment on a time scale of minutes has been found in the temperature range 150–300 K for polystyrene, poly-(N-vinylpyrrolidone) and polyvinyl butyral. The results are in dramatic contradiction with the commonly known rotational correlation times of probe molecules in glassy polymers obtained by the traditional spin probe method. The nonlinear least-squares fitting of experimental EPR spectra has been used for treatment of this contradiction. Quantitative agreement of simulated and experimental EPR spectra in the temperature range 77–300 K has been achieved simply by using the model of quasi-libration. By this term we mean that the probe molecules are in stochastic fast angular motion in the anisotropic cage of the matrix. The average angular displacement at ∽300 K has been estimated as 5–15°.

Correlation between fractional free volume and diffusivity of gas molecules in glassy polymers

Despite its oversimplifications, the free-volume approach has proven to provide very useful correlative and even semipredictive capabilities. This article is concerned with the correlation between the diffusivity, D, of gas molecules in glassy polymers and the fractional free volume, FFV, determined by the Bondi method. The diffusivities were taken from a database, generated by the authors in connection with work on the new Landolt Börnstein series “Diffusion in Non-Metallic Solids”, which encompasses a very large variety of glassy polymers. For a given diffusant log D is a linear function of 1/FFV as predicted by the free volume theory. However, the deviations from this relationship are significant and strongly correlated between O2, N2, CO2, and CH4. The systematic deviations are opposite to the predicted effect of the polymer jumping unit size in the free-volume concept of Vrentas and Duda and are interpreted in terms of an increase in the activation energy with increasing chain stiffness. Correlation analysis further suggests that the diffusion mechanisms of H2 and particularly of He differ markedly from that of larger gas molecules. Furthermore the influence of the cohesive energy and the glass-transition temperature of the polymers is investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3344–3358, 1999

On the Solubility of Gas Molecules in Glassy Polymers and the Nonequilibrium Approach

The recent nonequilibrium approach of Doghieri and Sarti for the solubility of gases in glassy polymers is reexamined. Analytical expressions for the equilibrium and nonequilibrium contributions to the chemical potential of the penetrant are presented. Volume dilation of the glassy matrix is explicitly taken into consideration. The role of the apparent partial molar or specific volume of the sorbed gas is also examined. The model is tested against the experimental data of Fleming and Koros for the solubility of CO2 in Bisphenol A polycarbonate.

Relevance of Elastic Energies during Sorption of CO2 Molecules in Glassy Polymers Demonstrated for Two Very Similar Polyimides

Data on CO2-sorption in and corresponding volume changes of three polyimides are evaluated in the framework of a recent model where elastic distortion of glassy polymers during dissolution of small molecules is taken into account. Due to the chemical identity and structural similarity of the polymers, differences in the behavior of CO2 can be attributed solely to differences in the distribution of the intermolecular space (holes). Thus the polyimide with the lowest volume change has the smallest elastic energy and, therefore, the largest solubility of CO2. The evaluation yields values of the average free energy of sorption and the width and average volume of the distribution of holes.

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO2 in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO2 pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2397–2408, 1997

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

Partial molar volume of small molecules in glassy polymers

AbstractThe sorption of atoms or molecules in glassy polymers is assumed to occur within a variety of sites belonging to the intermolecular volume and providing different space for the dissolved molecules. If the size of the small molecule is larger than the size of the site, the glassy polymer is elastically distorted during sorption of the solute molecules. Minimizing the total free energy yields the result that large sites are occupied first, giving rise to small volume changes only. By increasing the solute concentration, smaller sites have to be occupied as well and the corresponding volume changes are larger. Thus the molecules can be considered to act as probes for the intermolecular space. A quantitative analysis and comparison with experimental results provides information on the intermolecular space in a glassy polymer. Compared to the dual‐sorption model, the model of this study is able to explain the nonlinear relationship between volume change of the polymer and the partial pressure of the solute. At large solute concentrations, swelling of the glassy polymer or its transformation into the rubbery state occurs, which gives rise to structural changes after desorption. © 1993 John Wiley & Sons, Inc.

Sorption and partial molar volume of small molecules in glassy polymers

The sorption of atoms (He, Ar) or molecules (N 2 , CO 2 , H 2 O, SO 2 , CH 4 , C 2 H 6 , C 3 H 8 ) in polymers is described by assuming a continuous distribution of dissolution energies. The energy distribution arises from a volume distribution of the intermolecular space yielding different elastic distortion energies when occupied by solute molecules. On the basis of statistical fluctuations of the free volume and Eshelby's elasticity theory, it will be shown that a gaussian distribution of sorption energies is appropriate for small molecules in glassy polymers. The width of the Gaussian distribution can be calculated and it agrees well with values obtained by fitting experimental sorption data

A jump motion of small molecules in glassy polymers: A molecular dynamics simulation

Motions of small molecules in an amorphous polymer below its glass transition temperature Tg have been studied using molecular dynamics simulation. An infinite length chain model having 600 interacting sites, each representing a CH2 unit, is used. The system, which is composed of the infinite length chain and ten spherical molecules representing oxygen, is examined at 30 deg below Tg. Although most of the molecules are trapped by cages created by the chain, a molecule reveals clear jump motions. During the jump, no significant change is found in the local free volume as well as in the nonbonded energy acting on the molecule. Potential energy surfaces for the molecules clearly show the cooperative process of jump and chain motions: a generation of a vacant cage and a channel which connects two cages. It is found that the molecule passes through the channel without significant energy barrier and concentration of free volume.

The dual‐mode solution and transport of water in poly(acrylonitrile)

AbstractSolubility (sorption) and transport measurements with water in solvent‐free poly (acrylonitrile)(PAN) (23) have been interpreted in terms of an extension of the “dual‐sorption” model for transport of small molecules in glassy polymers. Satisfactory agreement has been obtained between theory and experimental data. An earlier analysis of similar data for water in PAN containing 0.26 percent (by weight) of a residual solvent (1) has been compared with the present results in order to investigate the effects of residual solvent on the dual‐sorption and transport parameters for the water‐PAN system.