Partial molar volume of small molecules in glassy polymers

The 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.     

Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory

Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient D_eff, which depends on the details of the microstructure. D_eff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.     

A generalization of dual mode transport theory for glassy polymers

The polymer matrix, divided in a number of cells in which the penetrant molecules can be sorbed and migrate, is considered. Each cell has been assigned an effective energy value that obeys a particular distribution. The effective diffusion coefficient and its concentration and temperature dependence are determined. The origin of sorbed penetrant mobility is studied. Using a delta-Dirac distribution for the site's energetic values, the model is reduced in the appropriate limit (low pressure) to other formulations of the dual transport model. More general results, allowing the site's energetic values to be drawn from a Gaussian distribution, are also given. © 1994 John Wiley & Sons, Inc.     

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     

Dissolution of rubbery and glassy polymers

A mathematical model is formulated for solvent dissolution of rubbery and glassy polymers. An exact solution to the problem is derived for the constant diffusivity case, and a weighted residual solution is developed for the case of a concentration-dependent diffusion coefficient. The solution is used to calculate concentration profiles, dissolution curves, dissolution half-times, and pseudointerface positions at various times. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2607–2614, 1998     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Effect of end‐tethered polymers on surface adhesion of glassy polymers

The adhesion between a glassy polymer melt and substrate is studied in the presence of end‐grafted chains chemically attached to the substrate surface. Extensive molecular dynamics simulations have been carried out to study the effect of the areal density ∑ of tethered chains and tensile pull velocity v on the adhesive failure mechanisms. The initial configurations are generated using a double‐bridging algorithm in which new bonds are formed across a pair of monomers equidistant from their respective free ends. This generates new chain configurations that are substantially different than the original two chains such that the systems can be equilibrated in a reasonable amount of cpu time. At the slowest tensile pull velocity studied, a crossover from chain scission to crazing is observed as the coverage increases, while for very large pull velocity, only chain scission is observed. As the coverage increases, the sections of the tethered chains pulled out from the interface form the fibrils of a craze that are strong enough to suppress chain scission, resulting in cohesive rather than adhesive failure. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 199–208, 2004     

Atomic mobility in strained glassy polymers: The role of fold catastrophes on the potential energy surface

Deformation is known to enhance the atomic mobility in disordered systems such as polymer materials. To elucidate the origin of this phenomenon, we carry out two types of simulations: molecular dynamics (MD) simulations, which determine the atomic trajectories at finite temperature, and quasi-static simulations, which determine the atomic trajectories in the limit of zero temperature (and in the limit of zero shear rate). The quasi-static simulations show discontinuous changes in properties, such as system energy and atomic mobility. We use a normal mode analysis to show that these discontinuous changes arise from fold catastrophes of the potential energy landscape, in which energy minima flatten out and the heights of energy barriers decrease to zero; this was demonstrated by normal mode frequencies following a power law with an exponent of 0.5 as the discontinuous change is approached. After the fold catastrophe, the system relaxes to a different energy minimum, giving rise to atomic displacements. These fold catastrophes are the only mechanism for diffusive atomic displacements in the quasi-static simulations, where there is no thermal energy. We compared the mean-squared displacements as a function of strain from the quasi-static simulations to those from MD simulations (which do include thermal effects)—the similarity of the values of the mean-squared displacements in these two types of simulations demonstrates that the fold catastrophes underlie the enhanced dynamics in strained polymer systems even at finite temperature. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Modeling of penetrant diffusion in glassy polymers with an integral sorption deborah number

A mathematical model was developed to explain the anomalous penetrant diffusion behavior in glassy polymers. The model equations were derived by using the linear irreversible thermodynamics theory and the kinematic relations in continuum mechanics, showing the coupling between the polymer mechanical behavior and penetrant transport. The Maxwell model was used as the stress–strain constitutive equation, from which the polymer relaxation time was defined. An integral sorption Deborah number was proposed as the ratio of the characteristic relaxation time in the glassy region to the characteristic diffusion time in the swollen region. With this definition, an integral sorption process was characterized by a single Deborah number and the controlling mechanism was identified in terms of the value of the Deborah number. The model equations were two coupled nonlinear differential equations. A finite difference method was developed for solving the model equations. Numerical simulation of integral sorption of penetrants in glassy polymers was performed. The simulation results show that (1) the present model can predict Case II transport behavior as well as the transition from Case II to Fickian diffusion and (2) the integral sorption Deborah number is a major parameter affecting the transition. © 1993 John Wiley & Sons, Inc.     

Fickian diffusion in glassy polymer-solvent systems

A free-volume theory is developed for the analysis of Fickian diffusion processes in glassy polymers. Equations are presented for the prediction of mutual diffusion coefficients in concentrated glassy polymer-penetrant systems. The concentration dependence of the mutual diffusion coefficient is dependent on how much free volume the solvent contributes to the system and on how the addition of solvent affects the densification of the polymer matrix. © 1992 John Wiley & Sons, Inc.     

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S‐shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S‐shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Finite difference modeling of the gas transport process in glassy polymers

Finite difference modeling has been used to predict the results of gas transport experiments for a concentration-dependent diffusion coefficient. Experiments on the transport of CO₂ in poly(ethylene terephthalate) and poly(ethylene naphthalate) had previously shown a difference between the effective diffusion coefficients for absorption and desorption runs of a double-sided experiment, but this effect had not been seen for single-sided experiments. The finite difference calculations show that such results are to be expected, and the parameters included in the models that attempt to describe the diffusion process in glassy polymers, such as the dual-mode model, and which lead to concentration-dependent diffusion coefficients, can be found by fitting the experimental data for the double-sided experiment using finite difference modeling. The dependence of the effective diffusion coefficient on pressure for the single-sided experiment can be correctly predicted using results from the double-sided experiment for an identical sample. © 1996 John Wiley & Sons, Inc.     

Application of direct (hetero)arylation in constructing conjugated small molecules and polymers for organic optoelectronic devices

Direct (hetero)arylation, as a sustainable, atom-economic and environmentally benign synthetic protocol compared to conventional coupling techniques, has been extensively applied to the sustainable preparation of π-conjugated materials for organic optoelectronic devices. In this review, we will highlight recent advances made in direct arylation for conjugated small molecules and polymers toward high performance organic optoelectronic devices. Some important insights in direct arylation for synthesizing organic optoelectronic materials are given, together with the challenges and outlook in this significant and hot research field.     

Processing‐induced properties in glassy polymers: Application of structural relaxation to yield stress development

A method is presented to predict the yield stress distribution throughout an injection‐molded product of an amorphous polymer as it results from processing conditions. The method employs the concept of structural relaxation combined with a fictive temperature, following the Tool–Narayanaswamy–Moynihan formalism. The thermal history, as it is experienced by the material during processing, is obtained by means of numerical simulation of the injection molding process. The resulting predictions of yield stress distributions are shown to be in excellent agreement with experimental findings, both for different mold temperatures and for different part thicknesses. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1212–1225, 2006     

Simulation of plastic deformation in glassy polymers: Atomistic and mesoscale approaches

The mechanism of deformation in glasses is very different from that of crystals, even though their general behavior is very similar. In this study, we investigated the deformation of polycarbonate on the atomistic scale with molecular dynamics and on the continuum scale with a new simulation approach. The results indicated that high atomic/segmental mobility and low local density enabled the formation (nucleation) of highly deformed regions that grew to form plastic defects called plastic shear transformations. A continuum-scale simulation was performed with the concept of plastic shear transformations as the basic region of deformation. The continuum simulations were able to predict the primary and secondary creep behavior. The slope of the secondary creep depended on the interactions between the plastic shear transformations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 994-1004, 2005     

On the Origin of Heterogeneous Diffusion in Glassy Poly(alkyl methacrylates)

The diffusion of small molecules through amorphous polymers proceeds by the thermally activated jumps whose rate changes from one region to another due to polymer heterogeneity. Little is known at present about the origin of diffusion heterogeneity. The oxidation of triplet nitrene and quenching of phenanthrene phosphorescence have been used to study the movement of molecular oxygen on a nanometer length scale in glassy poly(ethyl methacrylate) and poly(n‐butyl methacrylate) far below the glass transition temperature. It has been found that, as temperature increases, the jump rates in all regions increase by the same factor. This finding points to the equality of the activation energies of oxygen jumps in different regions of the polymers. We conclude that the correlated elastic displacements of polymer chains inside regions about several nanometers in size provide molecules jumps. Due to the large size of these regions, the activation energy of jump does not depend on local polymer structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1097–1104     

Analysis of gas sorption in glassy polymers with the GAB model: An alternative to the dual mode sorption model

The suitability of the Guggenheim–Anderson–De Boer (GAB) model for the parameterization of gas sorption isotherms and their dependences on temperature is explored. The GAB model implies that molecules adsorb on inner surfaces of the polymer in multilayers, which contrasts with the assumptions of the classical Dual Mode Sorption (DMS) model which implies the simultaneous occurrence of Henry‐like dissolution and Langmuir's case I adsorption. The GAB model shows similar efficacy of the parameterization of the gas sorption isotherms in polymers as the DMS model. The isosteric heat of adsorption shows clear dependence on relative surface coverage for carbon dioxide sorption in cellulose acetate, polyethylene terephthalate, and the first polymer of intrinsic microporosity (PIM‐1), thus allowing for the occurrence of adsorption multilayers. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1490–1495     

Transport properties of small molecules in zwitterionic polymers

Despite great interests in using zwitterionic polymers for membrane surface modification to enhance antifouling properties, there lacks fundamental understanding of the relationship between polymer structure and water/salt separation properties. In this study, two series of zwitterionic polymers were prepared from sulfobetaine methacrylate and 2‐methacryloyloxyethyl phosphorylcholine. Both are crosslinked by poly(ethylene glycol) diacrylate (PEGDA). These copolymers were thoroughly characterized in terms of sol‐gel fraction, density, glass transition temperature, contact angle, water and salt transport properties, and pure‐gas permeability. Interestingly, the zwitterionic polymers exhibit water sorption and permeability similar to noncharged poly(ethylene glycol)‐based materials. These zwitterionic polymers exhibit lower NaCl diffusivity and permeability and thus higher water/NaCl selectivity than the non‐charged PEG‐based materials at similar water volume fractions, demonstrating their promise for membrane surface modification for desalination and wastewater treatment. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1924–1934