The main purpose of this paper is to test the model of molecular sorption [Vesely D. Polymer 2001;42:4417-22] for Case II type diffusion by measuring the effect of sorption/swelling and resistance to flow through the swollen region on the mass transport of solvents in glassy amorphous polymer. The system of methanol and polymethylmethacrylate (PMMA) has been selected for easy comparison with the existing literature data.The weight loss of penetrant permeating through the polymer has been monitored using a permeability cell placed on a balance (gravimetry). The rate of diffusion and swelling has been measured using light microscopy on samples cut after different elapsed time exposure to the solvent.The contribution of polymer swelling and resistance to flow has been evaluated by comparing the mass transport during diffusion and permeation processes. It is shown that for thin films the thickness independent component of the mass transport process (swelling) makes a significant contribution to the diffusion rate. For thicker samples the thickness dependent component (the resistance to flow through the swollen polymer) dominates both, diffusion and permeation. 相似文献
The application of an interferometric technique (optical thickness meter, OTM) to the measurement of vapor sorption kinetics in both rubbery and glassy polymers is presented. In this technique, the membrane is formed by casting on a suitable glass surface and interferometry is applied in situ. The use of a carrier gas loaded with penetrant vapor introduced a stagnant boundary layer (SBL) effect which had to be corrected, in order to determine true sorption kinetics. The said SBL effect was estimated, on the basis of existing theory for the silicone rubber–methylene chloride (SR/MC) system and found to be more pronounced in the case of desorption. Upon correction for this effect, Fickian sorption curves were obtained; which yielded nearly constant values of the diffusion coefficient, not materially different for absorption and desorption, in line with theoretical expectation.Cellulose acetate–methylene chloride (CA/MC) was then studied as an example of a glassy polymer–vapor system, where the SBL effect distorts the absorption kinetic curve in the same way as the non-Fickian mechanism of sorption inherent in this kind of polymer–penetrant system. Here, the vapor sorption data were corrected using the results obtained from the Fickian SR/MC system. The corrected results were checked by comparison with independent data reflecting the true kinetic behavior of CA/MC, obtained with a vacuum balance apparatus (VBA), which is free of SBL effects. It is shown that this novel method of applying the SBL correction was reasonably successful in favorable circumstances, while a criterion is provided to identify cases where reasonably reliable correction is not possible. 相似文献
Sorption, diffusion, swelling, and tensile stress relaxation measurements were made at room temperature (23°C) for the systems poly(n-butyl methacrylate) (PBMA) with liquid methanol and ethanol, and poly(methyl acrylate) (PMA) with liquid water. Stress relaxation curves for the fully swollen polymers could be superimposed approximately with those for the dry polymers by appropriate shifting along the long axes. For PMA–water the measured curve for stress relaxation with concurrent sorption could be predicted accurately by using a moving boundary theory with data measurements of stress relaxation of the unswollen and swollen polymer combined with sorption data. The modified moving boundary theory is generalized to include the effects of dimension changes through swelling and the larger effects of plasticization associated with sorption of liquids. This improved theory accurately predicts measured curves of stress relaxation with concurrent sorption for the PBMA–alcohol systems from individual stress relaxation, sorption, diffusion and swelling data. The general approach should be applicable to other amorphous polymer–liquid swelling agent systems. The anisotropic nature of swelling of polymer films and its effect on calculated diffusion coefficients are discussed briefly. 相似文献
Recent gravimetric studies of the sorption of organic vapors by poly(vinyl chloride) and polystyrene powders have demonstrated several features which promise to be generally useful in studying the structure and properties of the glassy state. The uptake of vapor can be significantly altered by prior thermal or vapor treatment of the polymer, apparently reflecting changes in the microvoid content or free volume of the polymer. Fickian sorption in sufficiently fine powders proceeds to equilibrium in a few minutes. Upon exposure of a polymer powder to an appreciable pressure of vapor, both a rapid Fickian sorption and a slower, relaxation-controlled sorption are observed. Superposition of these processes leads to widely varied sorption kinetics; a model comprising Fickian diffusion and first-order relaxation terms accurately describes the data and allows estimation of equilibrium and rate constants for both processes. After prolonged exposure, removal of a swelling vapor induces a slow reconsolidation of the polymer structure; this deswelling relaxation can be monitored by the decreasing amounts of vapor sorbed in repeated brief exposures to low vapor pressures, and can also be described by a first-order relaxation model. In this regard, the penetrant vapor serves as a molecular probe, monitoring glassy-state relaxation occurring in the absence of penetrant. The same, presumably true equilibrium is ultimately reached both by swelling from a low free-volume state and by consolidation from a preswollen state of high free volume. The rates of both swelling and consolidation relaxations appear to be retarded by the presence of low concentrations of vapor in the polymer, suggesting that vapor molecules may preempt some of the free volume required for relaxation. 相似文献
When a glassy polymer containing a uniformly dispersed solute is brought in contact with a penetrant, solute diffusion will be associated with the transport mechanism and penetration velocity of the penetrant in the polymer. Analysis and prediction of mechanisms of diffusional solute release may be obtained through a new dimensionless number, the swelling interface number, Sw, which compares the relative mobilities of the penetrant and the solute in the presence of macromolecular relaxations in the polymer. It is shown that a sufficient and necessary criterion for time-independent diffusional solute release rates from these swellable systems is that the Sw be smaller than 10?2. The swelling interface number Sw may be related to easily determined structural and thermodynamic parameters of the solute/polymer/penetrant system. Preliminary experimental results of dynamic water swelling of poly(2-hydroxyethyl methacrylate-co-methyl methacrylate) and diffusional release of theophylline from initially glassy copolymers show that decreasing values of Sw are related to increased pseudo-case-II transport kinetics of the solute. 相似文献
The kinetics of sorption of micromolecular swelling agents by polymeric media often deviates from normal Fickian behavior in various ways, which have to be understood and interpreted, with the aid of appropriate models, in terms of the underlying physics. One difficulty which arises in this respect is that salient aspects of the observed kinetic behavior can be mimicked by extraneous effects, in the form of significant deviation from a boundary condition or of imperfect macroscopic homogeneity of the polymer film (modeled in both cases as a surface resistance to penetrant transport). Such effects have, in fact, been invoked (notably by Hansen (2010) [11]) to question the significance of conclusions drawn from modeling approaches based on the effect of intrinsic bulk polymer properties, leading to delayed (viscous) swelling and to build-up and decay of differential swelling stresses. We present here a brief critical account (following the mainstream modeling line initiated by Crank) of typical results concerning various salient aspects of observed non-Fickian sorption kinetics and of the comparative possibility of achieving satisfactory general interpretation thereof, in terms of approaches based on the aforementioned extraneous, versus intrinsic bulk property, effects. We find that the latter approach has been successful so far, both computationally and physically, by establishing a close physically significant analogy between non-Fickian sorption, and (both linear and non-linear) viscoelastic mechanical deformation, behavior. The former approach, on the other hand, proves weak on both counts. 相似文献
A mathematical model was developed to describe diffusion of a penetrant and a solute in a swellable polymer slab. The model was applied to the case of a hydrophilic polymer loaded with a soluble bioactive agent, in which the penetrant (water) is sorbed and solute is desorbed. The model allows the incorporation of any appropriate form of the diffusion coefficients. A Fujita-type exponential dependence on penetrant concentration was chosen and shown to be adequate for prediction of a range of transport behavior. Dimensional changes in the sample were predicted by allowing each spatial increment to expand according to the amount of penetrant sorbed. During the initial period of release, the swelling was restricted to one dimension by the glassy core of the sample. At a later point in the process, the center of the sample had sorbed enough penetrant to plasticize it, and the sample relaxed to an isotropically swollen state; thereafter swelling was three-dimensional. 相似文献
This paper considers the problem of describing quantitatively the process of diffusion in polymers attended by plasticization of their amorphous phase. A consequence of such plasticization is that the volume accessible to the penetrant molecules continuously increases during the course of their sorption. Assuming that the rate of relaxation processes is far greater than that of diffusion, an equation has been generated to describe the sorption in a matrix with varying accessibility. A numerical solution of this equation, using experimental data for a polyamide-water system, demonstrates that sorption in a matrix with increasing accessibility is slower than sorption in a hypothetical matrix with constant accessibility and with the same proportion of the amorphous phase. At the same time, the concentration of the penetrant in the former case proves to be higher at any point in the polymer specimen. The results obtained are important for calculating the rate constants for chemical reactions that proceed in a polymer matrix in the diffusion-kinetic mode. 相似文献
The effect of molecular mass, thermal prehistory, physical state, and three-dimensional chemical crosslinked structure of a polymer on dissolution and diffusion in the PVP-water system has been studied. The kinetic dependences of sorption that correspond to the Fickian or pseudonormal type have been measured. In a certain concentration range, sorption is accompanied by transition of the system to the rubbery state. In the glassy state, the negative concentration dependence of the diffusion coefficient related to the nonequilibrium state of the polymer sorbent is observed. Sorption isotherms are described by S-shaped curves. It has been shown that the thermal prehistory of the polymer sorbent has the most pronounced effect on its sorption behavior. The effect of molecular mass is insignificant, while three-dimensional chemical crosslinks in PVP manifest themselves only in the region of the rubbery state. In accordance with the double sorption model, the experimental isotherms are represented as the superposition of two isotherms described by the Langmuir and Flory-Huggins equations. For the glassy state of the polymer sorbent, the degree of the nonequilibrium state has been estimated. With due regard for the excess free volume, the detailed thermodynamic analysis of isotherms has been performed; namely, the pair interaction parameters and the free energy of mixing have been calculated. The state of water in the polymer has been examined within the framework of hydrate contributions and clusterization theory. 相似文献
The kinetics of ethanol, n-propanol, and n-butanol penetration, sorption, and dimensional swelling in 2 mm poly(methyl methacrylate) sheets were determined over the temperature range 50–95°C. At 50°C, Case II relaxation-controlled transport dominated the observed sorption and penetration kinetics for all three alcohols. At higher temperatures, diffusion of swelling penetrant to the relaxing boundary contributes increasingly to the observed sorption kinetics. In addition, as the temperature is raised, the completion of sorption lags significantly behind the penetration of the relaxing boundary to the sheet midplane. p]The activation energy describing low temperature penetration is significantly higher than the activation energy describing the temperature dependence of high temperature penetration. A distinct transition in the penetration kinetics is apparent for all three alcohols at approximatively 65°C. Independent Clash—Berg determinations of the Tg of the alcohol-swollen sheets indicate that the transition in behaviour is not related to a thermal transition in the polymer, but rather to the generation of diffusional resistance in the high temperature penetration experiments which is comparable to the otherwise rate-determining Case II relaxations dominant in low temperature penetration. At high temperatures, the overall activation energy reflects the combination of diffusional absorption and the more highly activated relaxation-controlled transport. At low temperatures, diffusion of penetrant to the relaxing boundary is rapid compared with the slow, rate determining relaxations and, therefore, the concentration of penetrant is everywhere uniform within the already swollen shell. The extra-ordinarily high apparent activation energy describing the temperature dependence of the initial sorption rate at low temperature reflects the endothermic enthalpy of sorption of alcohols in PMMA as well as the strong coupling between relaxation rate and the penetrant concentration driving the rate determining relaxations. p]Clash—Berg measurements of the temperature dependence of the ten second shear moduli in partially swollen sheets, completely swollen sheets, and unswollen sheets suggest a Tg of approximatively 40°C in the alcohol-swollen PMMA. Moreover, an analysis of the Clash—Berg measurements suggests that the properties of the swollen regions of partially penetrated sheets are identical to the properties of the completely swollen sheets. 相似文献
A comprehensive dynamic diffusion model is developed to calculate the diffusion coefficients of low molecular weight penetrants (i.e., α‐olefins) in semi‐crystalline polyolefins from dynamic sorption measurements. The model also takes into account the extent of polymer swelling on the penetrant diffusion flux, resulting in a moving boundary value problem. The free volume theory is employed to calculate the dependence of the diffusion coefficient on the penetrant concentration. The solubilities and diffusivities of ethylene and propylene in semi‐crystalline high density polyethylene films were measured at different temperatures and pressures, using a Rubotherm® magnetic suspension microbalance operated in series with an optical view cell for the measurement of the degree of polymer swelling. It is shown that model predictions are in excellent agreement with the experimental dynamic measurements on the mass uptake of the sorbed species. Moreover, it is shown that the proposed model can predict correctly the diffusion coefficient of α‐olefins in semi‐crystalline polyolefins.
In the present paper we further test a model of stress-dependent diffusion previously used with success to simulate the variation from Case I to Case II penetration kinetics in the system liquid methylene chloride-uniaxially oriented cellulose acetate film, according to whether penetration occurs across or along the axis of preferred macromolecular orientation. Data on penetration rates, optical density profiles (using a colored tracer), and the corresponding birefringence profiles, characteristics of these penetration modes in the aforesaid system, are presented and compared with appropriate model uptake kinetic curves and penetrant concentration and compressive differential swelling stress profiles. It is shown that the salient features of the observed experimental behavior are in general accord with model predictions based on physically realistic assumptions. 相似文献
The possibility of predicting the breakthrough curves of a phospholipid (PL) during its sorption by mesoporous composites based on MCM-41 using models of the dynamics of sorption that consider the kinetics of adsorption (the Thomas model) and mixed diffusion (the asymptotic model) is demonstrated using phosphatidylcholine (PC) as an example. The effect the kinetic parameters have on the tailing of the sorption front with respect to the mixed diffusion limitation of the sorption of nonpolar biologically active substances (BASes) is shown. It is found that the ordered structure of composite materials based on MCM-41 ensures a high rate of mass transfer and thus little tailing of the sorption front, when compared to sorbents with a lower degree of order (silica gel and polymer materials) during the sorption of a phospholipid under dynamic conditions. Based on calculations of the parameter of pattern Λ under the conditions of the dynamic mode of sorption in mixed diffusion kinetics, it is shown that the sorption of phosphatidylcholine from hexane solutions by mesoporous composites based on MCM-41 allows the sorption chromatographic process to proceed in the most advantageous (quasi-equilibrium) mode. 相似文献
Solubility (sorption) and transport measurements of water vapor in poly(acrylonitrile) reported by Stannett, Haider, Koros, and Hopfenberg have been re-interpreted in terms of an extension of the “dual-sorption” model for glassy polymers. The extension of the model assumes solubility and diffusion coefficients that are dependent on concentration, and partial immobilization of some of the penetrant species dissolved in the polymer. Satisfactory agreement has been obtained between theory and the experimental data. 相似文献
The effects of plasticization on the transport of gases and vapors in and through glassy polymers are examined from the viewpoint of the “dual-mode” sorption model with partial immobilization. The analysis assumes the existence of two penetrant populations with different mobilities in the Henry's law and Langmuir domains of the glassy polymers. These mobilities are characterized by their mutual diffusion coefficients DD and DH. The plasticization of the polymer by penetrant gases is reflected in the concentration dependence of DD and DH. Expressions for the effective (apparent) diffusion and permeability coefficients are derived assuming that DD and DH are exponential functions of the penetrant concentration in the polymers. The results of this study are compared with a similar analysis which assumed the existence of a single mobile penetrant population. The present analysis provides information on the effects of plasticization on the penetrant transport in the Henry's law and Langmuir domains separately. The effects of antiplasticization or clustering of penetrant molecules on the effective diffusion and permeability coefficients are also examined. 相似文献