Time and temperature dependent sorption in poly-ether-ether-ketone (PEEK)

The possible multimodal sorption mechanisms in glassy amorphous poly-ether-ether-ketone (PEEK) are presented. By varying the penetrant-polymer affinity, experimental temperature, and external solvent activity, a broad range of sorption behaviors from ideal Fickian diffusion to limiting relaxation controlled kinetics is observed. In particular, water, methylene chloride, and n-heptane sorption kinetics are analyzed and interpreted on the basis of the multiple transport mechanisms. Low uptake liquid n-heptane sorption follows ordinary Fickian diffusion. Analogously, water vapor at low activity, is sorbed in small amounts in the same limiting mode while, at higher activities, the moderately higher penetrant uptakes induce slow relaxation coupled with ideal Fickian diffusion. The highly interacting methylene chloride leads to ideal Fickian diffusion only at very low activities, while anomalous non-ideal Fickian diffusion and limiting Case II and diffusion controlled swelling are observed at moderate and at high solvent activities, respectively. Limiting Case II sorption of methylene chloride in PEEK has been observed only at a very low temperature (?32°C). The optical microscopy observations of cryogenically fractured samples contacted with liquid methylene chloride at 5, 20 and 36°C revealed the presence of a sharp front moving linearly with the square root of time. Solvent induced crystallization in methylene chloride swollen samples was detected by means of differential scanning calorimetry (DSC) and wide angle X-ray scattering (WAXS). Finally, sorption from liquid methylene chloride/n-heptane solutions with varying compositions are presented. The progressive increase of the more high sorbing methylene chloride concentration in the solutions, leads to the same wide variety of sorption behavior observed in the methylene chloride vapor sorptions. The gas chromatographic (GC) analysis indicated that the presence of methylene chloride enhanced the n-heptane sorption in the polymer.     

Diffusion of isopropyl nitrate,acetone and water into nitrocellulose

The sorption kinetics of isopropyl nitrate, acetone and water into nitrocellulose films show marked differences from each other. The movement of water is essentially Fickian. That of acetone on all cycles and of isopropyl nitrate on the first cycle are characterized by a boundary between swollen and unswollen material moving at constant velocity into the film (Case II swelling). Sorption of isopropyl nitrate on all but the first cycle is characterized by a uniform concentration at all times throughout the expanding film (Case III swelling). Variations in the equilibrium sorption of isopropyl nitrate have been interpreted as indicating that the degree of crystallinity of the nitrocellulose fibres and films.     

Solvent osmotic stresses and the prediction of Case II transport kinetics

The rate controlling step in Case II transport kinetics is the swelling which occurs at the internal moving boundary. A physical model describing the swelling kinetics of glassy polymers in liquids is presented here. Using a thermodynamic argument, the stress induced by the penetrant on the glassy matrix is evaluated in terms of the penetrant concentration. The velocity of the swelling front is expressed in terms of the solvent stress, using the same functional relationship which gives the mechanical craze propagation rate, in terms of the mechanical stress. The resulting model permits the prediction of the kinetics of the swelling front from an independent characterization of mechanical properties.     

Strain effects in the mass flux of methanol in poly(methyl methacrylate)

Diffusion of organic solvents into glassy polymers often results in a phase transformation of the hard, solid polymer into a swollen, rubbery material. During the sorption, internal stresses exist in the swollen and glassy parts of the polymer and are thought to contribute significantly to the “anomalous” diffusion observed in many penetrant–polymer systems. In this investigation, isothermal sorption data for the methanol–poly(methyl methacrylate) system have been obtained on plates ranging in thickness from 1/32 to ¼ in. The results show features characteristic of both a strain-dependent diffusion coefficient and of a stress gradient contribution to the mass flux. An attempt to reproduce these results by combining a strain-dependent diffusion coefficient model with a stress-induced contribution to the flux is presented.     

Characterization and effects of n-alkane swelling of polystyrene sheets

Detailed penetration kinetics of a series of normal alkanes in 2 mm polystyrene sheets have been determined by an optical method over a broad range of temperatures encompassing the effective glass transition temperature of the resulting sheets. Whereas earlier thin film results, involving identical thermodynamic boundary conditions, have been characterized by ideal Case II transport, the results obtained here appear to be confounded at long times by a significant diffusional resistance in the swollen surface regions surrounding the unplasticized central core of these relatively thick sheets. At relatively low temperatures, the rate determining relaxations, at the boundary between swollen and unswollen polymer, are sufficiently slow to ensure ideal Case II transport over the entire course of the sorption history. These swelling experiments were complemented by Clash—Berg measurements of the temperature-dependence of the 10 sec torsional shear moduli of partly penetrated sheets, completely swollen sheets and unswollen sheets. The Clash—Berg results suggest that the T_g of the n-hexane swollen sheet is approximately 20°C and that the properties of the swollen regions of partly penetrated specimens are identical to the properties of the completely swollen sheet. A model based on the core-shell morphology, induced by the prior swelling, satisfactorily describes the observed mechanical properties of these swelling induced composites.     

A theory of case II diffusion

A theory is proposed to explain the transport behaviour of organic penetrants in glassy polymers in terms of two basic parameters: the diffusivity of the penetrant, D, and the viscous flow rate of the glassy polymer, $\text{1}\text{η}{}_0$. The rate controlling process for transport in these systems is considered to be diffusion of solvent down an activity gradient coupled with time-dependent mechanical deformation of the polymer glass in response to the swelling stress. The theory combines these two factors and is able to predict a wide range of observed transport phenomena from Fickian diffusion kinetics at one extreme to so-called Case II and Super-Case II behaviour at the other. The existence of a sharp front separating swollen and unpenetrated polymer is shown to result from the concentration dependence of the viscous flow rate.     

A deformation model for Case II diffusion

Case II diffusion in glassy polymers is considered in terms of a deformation model. The process is controlled by the mechanical response of the glass just ahead of the sharp front to an osmostic swelling stress. The important factor governing the establishment of the sharp solvent front is taken to be the concentration dependence of the creep response time. These ideas are set in the context of existing models for diffusion in glassy polymers, and experimental evidence is presented to support the deformation mechanism.     

Solvent mixtures sorption in amorphous peek

Summary The sorption kinetics and equilibrium isotherms of methylene chloride, n-heptane and of methylene chloride/n-heptane mixtures in glassy amorphous Poly(aryl-ether-ether-ketone) (PEEK) have been investigated. Ideal Fickian diffusion, anomalous non-ideal Fickian diffusion, “Case II” sorption mechanism and diffusion controlled swelling were observed depending on temperature, on solvent type and on external solvent activity. Gaschromatographic analysis performed on PEEK samples contacted with methylene chloride/n-heptane mixtures indicated that the presence of methylene chloride enhances n-heptane mobility and equilibrium sorbed amount. Dedicated to Prof. Dragutin Fleš on the occasion of his 70th birthday     

Transport models for swelling and dissolution of thin polymer films

Fundamental models have been developed to describe swelling and dissolution of glassy polymer thin films. The models account for solvent penetration by either Fickian or Case II diffusion mechanims. The convective flux due to local swelling as the solvent penetrates is included. Chain disentanglement at the polymer-developer solution interface is scaled with the local solvent concentration and polymer molecular weight using reptation theory. The effective surface concentration during dissolution is estimated by applying thermodynamics of swollen networks to the entangled polymer. Swelling and dissolution of thin polymer films have direct application to microlithography. Various molecular and processing parameters affect the outcome of resist development. The utility of the models for selecting appropriate developer solvents, minimizing resist swelling, and providing a better understanding of the swelling and dissolution of resists is demonstrated.     

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     

Non-fickian diffusion with reaction in glassy polymers with swelling induced by the penetrant—effects of consecutive and parallel reactions

A mathematical model is presented for non-Fickian diffusion of a penetrant A into a granular glassy polymer containing a reactive group B, resulting in the desired product P. Further, both a consecutive reaction between A and P (producing X) and a parallel reaction between A and C (producing Y) are incorporated, with C initially present in the particle. The swelling of the polymer, induced by the penetrant, is described by power-law kinetics for the velocity of the swelling front. Kinetics are considered to be first order in each of the two reactants. Concentration profiles in the particle and selectivity to desired product are calculated as function of the swelling behavior of the polymer grain. In case of a consecutive reaction the local concentration of P reaches a maximum value independent of the swelling rate. However, the position of the maximal concentration of P moves towards the center of the grain with a rate depending on the kinetics of swelling. For Case II diffusion this velocity equals the velocity of the advancing front between glassy and rubbery polymer. The selectivity of the desired reaction decreases with decreasing swelling rate. A low swelling rate also results in an inhomogeneous product distribution within the granule. A criterion is derived predicting under what conditions the consecutive reaction can be neglected and a pure product is obtained. The analysis further reveals that both a more homogeneous product and a higher selectivity toward a desired product can be obtained by realizing preswelling of the polymer with an inert swelling agent. For Case II diffusion the concentration profiles of the side product of the parallel reaction, Y, are flat in the rubbery part of the polymer. This is caused by the relatively low swelling rate allowing Y to redistribute in the swollen polymer. If additional C is continuously supplied from the gas phase, then the selectivity decreases continuously with increasing conversion of B.     

Transport of swelling penetrants in glassy polymers: Influence of convection

The transport of a solute by diffusion into a glassy polymer can lead to swelling of the material. For certain types of polymers, a sharp interface is formed between the swollen region and the glassy core. When the density of the swollen material is much smaller than the density of the glass, a significant convective mass-average velocity is generated within the sample. Previous models have neglected the role this convection plays in solute transport and in the proper calculation of the sample dimensions as a function of time. In this paper, we study the contribution of convective terms to the solute transport process, including the motion of the swollen polymer/solution interface. We also compute the eulerian strains that result from the calculated velocity fields and the stresses that would be generated if a linear viscoelastic model is used as a constitutive equation relating the stress to the strain. We show that serious errors can be generated in the calculations if convective terms are neglected. Furthermore, a comparison of the strains and stresses acting on the polymer with those acting on the mixture of solute and polymer shows that they can be significantly different. The stresses and strains acting on the polymer alone offer the most rational physical picture of the material deformation.     

Effect of the thermal histories on case II sorption kinetics: Test of a kinetic theory for swelling

Case II sorption kinetics have been analyzed for PS–n-hexane systems. Samples of polystyrene characterized by several different annealing histories were used. For all thermal histories, the n-hexane sorption kinetics at several temperatures were measured, as well as some relevant mechanical properties of the glassy matrix, e.g., density and initial stress for crazing. The main influence of the thermal history is to appreciably alter the initial stress for crazing σ_c, as well as the swelling kinetics. The σ_c curve vs. annealing time is seen to go through a minimum which is paralleled, at 40°C, by a maximum in the swelling kinetics. The independent mechanical and sorption data obtained were compared with a recently proposed [G. C. Sarti, Polymer, 20 , 827 (1979); G. C. Sarti and A. Apicella, Polymer, 21 , 1031 (1980)] theory for Case II kinetics, which is shown to be particularly suitable to describe the observed behavior.     

Diffusion mechanics of the system PMMA-methanol

Case II diffusion of penetrants in polymer sheet is associated with constrained swelling of the material and the generation of internal stresses. The work reported here is based on data from the model system PMMA-methanol. Specimen dimensions have been measured during swelling and these are related to the mechanics of the diffusion process. In particular the discontinuous reduction in sheet specimen thickness when the fronts meet has been compared with behaviour predicted from a simple model of Case II diffusion. The fact that there is a quantitative discrepancy indicates that the specimen shape change, as the fronts meet, is also accompanied by an increase in the degree of ‘equilibrium’ solvent uptake as the hydrostatic stress component on the swollen layers is relaxed. This increase is accounted for in terms of thermodynamic equations incorporating the work of deformation of a rubber network and it is apparent that a measurement of the volume change in a swelling polymer, when approaching Case II fronts meet, can give a measure of the Flory-Huggins interaction parameter x. At elevated temperatures a substantial concentration gradient develops behind the advancing fronts, which complicates the prediction of the discontinuous shape change observed at 42°C, 52°C and 62°C. The generation and partial relaxation of molecular orientations behind the advancing Case II fronts has been observed by optical birefringence. The technique has also been used to study the development of biaxial tensile stresses in the surface layers during desorption of partially swollen specimens. These stresses readily exceed that necessary for crazing, and a sorption-desorption cycle has been shown to induce such mechanical damage in the absence of any external or prior internal stress.     

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.     

The effect of penetrant activity and temperature on the anomalous diffusion of hydrocarbons and solvent crazing in polystyrene part I: Biaxially oriented polystyrene

The effects of temperature and penetrant activity on the sorption kinetics and equilibria of a series of alkanes in glassy, biaxially oriented polystyrene were studied. Normal isomers of pentane, hexane, and heptane cause crazing of polystyrene film samples at high penetrant activities (> 0.85). Crazing kinetics are identical to the kinetics of Case II transport. Transport of these normal hydrocarbons in glassy polystyrene in the temperature range 25 to 50°C is markedly non-Fickian; limiting Case II transport is observed at activities in exces of 0.6. Sorption appears to be controlled by highly activated relaxation processes including primary bond breakage at these high penetrant activities. Fickian diffusion behavior is approached, however, as penetrant activity is reduced. Sorption of the branched isomers of these compounds does not result in polymer microfailure. The sorption kinetics of the branched isomers, although time dependent, appear to be controlled primarily by thermally activated diffusion rather than large scale polymer relaxations which control Case II transport.     

Swelling-controlled,constant rate delivery systems

Materials and conditions required for constant rate absorption of a liquid into a glassy polymer (Case II transport) have been exploited to produce prototype devices for constant rate delivery of a solute, molecularly dispersed within the polymer, to the surrounding liquid environment. Absorption of n-hexane in polystyrene films, containing between one and two percent of Sudan Red IV dye, resulted in constant rate liberation of the colored solute to the surrounding fluid. The rate of dye release was controlled by the constant rate absorption of n-hexane in these dye-containing films. Companion experiments involving microtome sectioning and photomicrographic recording of dye-loaded films, consequent to immersion in n-hexane for various time intervals, revealed that the unpenetrated central core retained the dye originally dispersed within the film sample and, conversely, the swollen outer regions were completely denuded of dye consequent to n-hexane penetration. The constant rate advance of the microscopically observable sharp boundary, between dye-containing and dye-denuded polymer, was quantitatively consistent with the independently determined kinetics of dye accumulation in the supernatant n-hexane. These results indicate that diffusion of invading n-hexane to the relaxing boundary and back diffusion of dye in the previously swollen outer shell are both rapid compared with the rate-determining Case II transport of n-hexane in these dye-containing films. The delivery of Sudan Red IV to the n-hexane was not confounded by an initial burst of solute, typically common to so-called membrane-reservoir controlled delivery devices. Swelling-induced delivery from glassy matrices appears useful, therefore, for the design of monolithic devices for constant rate delivery over the entire course of the delivery cycle. The concept is not limited to monolithic devices; membrane-reservoir devices could be constructed involving a glassy, solute-containing reservoir which could be activated by penetration of invading liquid consequent to placement in a suitable fluid environment. Development of devices, suitable for swelling-controlled release of drugs to target organs, will be based upon glassy, hydrophilic polymeric hosts.     

Differential sorption in glassy polymers

Anomalous sorption curves have often been observed for differential sorption experiments in glassy polymers. A model is proposed to describe this non‐Fickian behavior. This model is based on the presence of interfacial resistance caused by slow rate processes at the phase boundary. Predictions of the model are compared with general experimental observations. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1431–1440, 1999     

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.     

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.