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.     

Water sorption and transport in blends of polyethyloxazoline and polyethersulfone

Water sorption and transport properties for a series of homogeneous blends of hydrophobic polyethersulfone and hydrophilic polyethyloxazoline are reported. Only blends that remained homogeneous after exposure to liquid water were studied in detail. Equilibrium solubility of water in the blend films increases with increasing hydrophilic polymer content. For all materials, equilibrium sorption isotherms show dual-mode behavior at low water vapor activities and swelling behavior at high activities. The sorption/desorption kinetics for PES are generally Fickian, but two-stage behavior is evident in blends containing 10 and 20% polyethyloxazoline. Diffusion coefficients decrease with increasing polyethyloxazoline content, owing to a decrease in the fractional free volume. For all materials, the diffusion coefficient shows a positive dependence on water vapor activity or concentration due to plasticization of the material by high levels of sorbed water, but it becomes a greater function of activity as the composition of hydrophilic polymer in the blend is increased. Since the decrease in the diffusion coefficient is greater than the increase in the solubility coefficient, the permeability coefficient decreases with increasing hydrophilic polymer content. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 993–1007, 1997     

Synthesis and structure–property relationships of poly(sulfone)s for anion exchange membranes

Membranes based on cationic polymers that conduct anions are important for enabling alkaline membrane fuel cells and other solid-state electrochemical devices that operate at high pH. Anion exchange membranes with poly(arylene ether sulfone) backbones are demonstrated by two routes: chloromethylation of commercially available poly(sulfone)s or radical bromination of benzylmethyl moieties in poly(sulfone)s containing tetramethylbisphenol A monomer residues. Polymers with tethered trimethylbenzyl ammonium moieties resulted from conversion of the halomethyl groups by quaternization with trimethyl amine. The water uptake of the chloromethylated polymers was dependent on the type of poly(sulfone) backbone for a given IEC. Bisphenol A-based Udel® poly(sulfone) membranes swelled in water to a large extent while membranes from biphenol-based Radel® poly(sulfone), a stiffer backbone than Udel, only showed moderate water uptake. The water uptake of cationic poly(sulfone)s was further reduced by synthesizing tetramethylbisphenol A and 4,4′-biphenol-containing poly(sulfone) copolymers where the ionic groups were clustered on the tetramethylbisphenol A residues. The conductivity of all samples scaled with the bulk water uptake. The hydration number of the membranes could be increased by casting membranes from the ionic form polymers versus converting the halomethyl form cast polymers to ionic form in the solid state. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1790–1798, 2013     

Synthesis of cellulose derivative based superabsorbent hydrogels by radiation induced crosslinking

Hydrogels with high water uptake were prepared by ionizing radiation induced crosslinking in aqueous solutions of four cellulose derivatives (carboxymethylcellulose sodium salt—CMC-Na, methylcellulose—MC, hydroxyethylcellulose—HEC and hydroxypropylcellulose—HPC). The gel fraction increased with absorbed dose, while water uptake decreased. At high polymer concentrations lower gel fractions were found due to the lower polymer chain mobility and inhomogeneity at low water content. The swelling rate gradually slowed down after 4–5 h. CMC and HEC gels reached equilibrium after 24 h, while HPC and MC gels required longer immersion times. Gels showed second-order swelling kinetics in water. The mechanism of the water diffusion proved to be anomalous. In pure water, CMC gels showed the highest, while HPC and MC gels the lowest water uptake. The derivatives had different sensitivities to ionic strength in the swelling solution. The salt type also proved to be a significant factor at uniform ionic strength. Thus different cellulose derivative based gels may be preferred at various applications depending on the environment.     

Mass and momentum transfer in polymers. III. Effects of liquid penetrants on tensile stress relaxation of amorphous polymers

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.     

Mechanically robust hydrophobized double network hydrogels and their fundamental salt transport properties

Water swollen polymer networks are attractive for applications ranging from tissue regeneration to water purification. For water purification, charged polymers provide excellent ion separation properties. However, many ion exchange membranes (IEMs) are brittle, necessitating the use of thick support materials that ultimately decrease throughput. To this end, novel double network hydrogels (DNHs) with variable water content are prepared and characterized in terms of mechanical and ion transport properties to evaluate their potential utility as tough membrane materials. The first network contains fixed anionic charges, while the other is comprised of a copolymer with varied ratios of hydrophobic ethyl acrylate (EA) and hydrophilic dimethyl acrylamide (DMA) repeat units. Characterization of freestanding DNH films reveals a reduction in water content from 88 to 53 wt% and a simultaneous increase in ultimate stress and strain by ~3.5× and ~4.5×, respectively, for 95%/5% EA/DMA, relative to 100% DMA. Fundamental salt transport properties relevant to water purification, including permeability, solubility, and diffusivity, are measured and systematically compared with conventional membrane materials to inform the development of DNHs for membrane applications. The ability to simultaneously reduce water content and increase mechanical integrity highlights the potential of DNHs as a synthetic platform for future membrane applications.     

Water sorption and transport in blends of poly(vinyl pyrrolidone) and polysulfone

Water sorption and transport properties for a series of miscible blends of hydrophobic bisphenol A polysulfone and hydrophilic poly(vinyl pyrrolidone) are reported. Study was restricted to blends that remained homogeneous after exposure to liquid water. The solubility of water in the blend films increased with increasing hydrophilic polymer content. Equilibrium sorption isotherms show dual-mode behavior at low activities and swelling behavior at high activities. The sorption kinetics are generally Fickian for blends containing 20% poly(vinyl pyrrolidone) or less, but exhibit two-stage behavior in blends containing 40% poly(vinyl pyrrolidone). Diffusion coefficients extrapolated to zero concentration decrease with increasing poly(vinyl pyrrolidone) content, owing to a decrease in the fractional free volume. However, the diffusion coefficient becomes a greater function of activity as the composition of hydrophilic polymer in the blend is increased, due to plasticization of the material by large levels of sorbed water. Permeability coefficients generally decrease with increasing poly(vinyl pyrrolidone) content for blends containing 20% poly(vinyl pyrrolidone) or less because the decrease in the diffusion coefficient is greater than the increase in the solubility coefficient. Blends containing 40% poly(vinyl pyrrolidone) have permeability coefficients greater than those of polysulfone due to high water solubility. The permeability coefficients depend on water concentration in approximately the same way for all blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 655–674, 1997     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Nanochannels and nanodroplets in polymer membranes controlling ionic transport

Polymer materials with low water uptake exhibit a highly heterogeneous interior characterized by water clusters in the form of nanodroplets and nanochannels. Here, based on our recent insights from computer simulations, we argue that the water cluster structure has large implications for ionic transport and selective permeability in polymer membranes. Importantly, we demonstrate that the two key quantities for transport, the ion diffusion and the solvation free energy inside the polymer, are extremely sensitive to molecular details of the water clusters. In particular, we highlight the significance of water droplet interface potentials and the nature of hopping diffusion through transient water channels. These mechanisms can be harvested and fine-tuned to optimize selectivity in ionic transport in a wide range of applications.     

Synthesis of anion conducting polymer electrolyte membranes by Pd-Catalyzed Buchwald-Hartwig Amination coupling reaction

A novel aryl bromine bearing polymer was synthesized by Friedel-Crafts polycondensation. This precursor polymer substrate was used for C–N coupling via Buchwald-Hartwig amination to incorporate 9 examples of aryl amines into the polymer chains with high conversions (80–100%). Two aminated polymers were subsequently quaternized to give anion conducting polymers. These quaternary ammonium polymers show promising electrochemical membrane property because of their ability to transport mobile anions through the material while being electrically insulating. Membrane characteristics crucial to high electrochemical performance including ion exchange capacity, anion conductivity, water uptake, swelling ratio, and alkaline stability were evaluated.     

Hydration mechanism of polysaccharides: A comparative study

Water sorption was studied at 20 °C on films composed of different natural polymers. Three polysaccharides were investigated: chitosan, cellulose, and alginate. The major differences between these polymers, from a structural point of view, lay in the substitution of an OH group by an NH₂ function for chitosan and by an ionic COO^?Na⁺ group for alginate. An analysis of the experimental water sorption isotherms, expressed as the number of water molecules sorbed per repeating unit in the amorphous phase, associated with an analysis of the enthalpy profile related to the water sorption allowed us to propose a water sorption mechanism in two steps for all the polymers: water sorption on polymer‐specific sites in the first step and water clustering around the first sorbed water molecules in the second step. It was determined that two water molecules interacted with the polymer chains for cellulose and chitosan, whereas four water molecules were bonded to alginate chains. The specific sorption sites were identified as OH groups for cellulose, OH and NH₂ groups for chitosan, and ionic and OH groups for alginate. A systematic reduction of the half‐sorption time was observed in the activity range corresponding to this first sorption step, and it was explained by a water plasticization effect. On the other hand, an increase in the half‐sorption time was observed in the second sorption step, at a high activity (>0.8), for chitosan and alginate. A modelization associating the Guggenheim–Anderson–de Boer model and the clustering theory, applied to our systems, allowed us to relate the occurrence of this last phenomenon to the formation of water clusters containing more than two water molecules. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 48–58, 2005     

Water‐mediated transport in ion‐containing polymers

Water‐mediated ion conduction enables high conductivity in hydrated polymer membranes commonly used in electrochemical devices. Understanding the coupling of the absorbed water with the polymer matrix and the dynamics of water inside the polymer network across the full range of length scales in the membrane is important for unraveling the structure–property relationships in these materials. By considering the water behavior in ion‐containing polymers, next‐generation fuel cell membranes are being designed that exceed the conductivity of the state‐of‐the‐art materials and have optimized conductivity and permeability that may be useful in other types of devices such as redox flow batteries. Water–polymer associations can be exploited to tune the transport and mechanical property tradeoffs in these polymers. Measurements of water motion provide important criteria for assessing the factors that control the performance of these types of materials. This review article discusses current understanding of water behavior in ion‐containing polymers and the relationship between water motion and ion and molecular transport. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Role of additives in the water vapor transport through block co-poly(amide/ether) membranes: effects on surface and bulk polymer properties

In the last years there has been a growing industrial interest in modifying the performance of traditional polymers by using additives, working as modifiers for processing, rheological, transport, bonding, and pigmentation properties. This work was focused on the understanding of the relationships between chemical structure and water vapour transport through a polymer matrix modified by different additives regarding hydrophilicity and molecular structure. A screening of the changes in surface energies and bulk morphology, as a function of the chemical nature and weight percent modifier, allowed estimating the effects on the water vapour transport through polymer membranes. Static and dynamic contact angle measurements explained the difference in surface wettability and affinity to polar species such as water molecules. Modifiers having polar groups improved the surface hydrophilicity, enhancing the breathability of the membranes, while hydrophobic components such as aromatic structures led to a reduction of the water vapour mass uptake onto the membrane surface. On the other hand, thermal analyses showed a tendency of the polymer structure to reduce its own mobility with consequent slowdown of the diffusion through polymer matrix. Modification with large and bulky structures disrupted the polymer packing density, but simultaneously increased the stiffness of the polymer chains, inhibiting the penetrant migration. As a result, balancing the effects due to modifier polarity and bulky structure, it is possible to change the performance of a polymer in terms of transport, going from breathable membranes to barrier films.     

高吸水性树脂

用热力学理论和相转变理论阐明了高吸水性树脂的吸水机理。解释了高分子链上的电荷密度、外界溶液离子强度以及交联度对吸水倍数的影响，并指出了影响吸水速率的因素。介绍了淀粉类、纤维素类、共聚合类、复合类以及可生物降解类高吸水性树脂近30年来的研究状况以及存在的问题，简要介绍了高吸水性树脂的应用。     

用脉冲梯度场核磁共振技术研究乙醇-水混合液在壳聚糖渗透汽化膜中的自扩散过程

用脉冲梯度场核磁共振技术(PFG—NMR)研究了水、乙醇和乙醇一水混合液在硫酸交联的壳聚糖渗透汽化膜和未交联的壳聚糖渗透汽化膜中的自扩散过程,得到了乙醇和水的溶解度和自扩散系数,阐述了水和乙醇透过壳聚糖膜的机理;实验结果表明：水和乙醇是分别由两种不同类型的扩散通道透过膜的;水是由亲水性的离子化通道扩散透过膜,而乙醇是由亲油性的高分子无定形区扩散透过膜;PFG—NMR方法所得到的结果与渗透汽化实验所得到的结果完全一致。     

Non-Fickian water vapor sorption dynamics by Nafion membranes

Dynamics of water absorption from a saturated vapor and water desorption into dry air for Nafion 1100 EW ionomers have been measured for film thicknesses between 51 and 606 microm and at temperatures ranging from 30 to 90 degrees C. Water absorption and desorption exhibit two distinct non-Fickian characteristics: (1) desorption is 10 times faster than absorption and (2) the normalized mass change does not collapse to a single master curve when plotted against time normalized by membrane thickness squared, t/l2, for either absorption or desorption. Water desorption data were fit well by a model in which diffusion is rapid and interfacial mass transport resistance is the rate-limiting process for water loss. Water absorption is described by a two-stage process. At early times, interfacial mass transport controls water absorption, and at longer times, water absorption is controlled by the dynamics of polymer swelling and relaxation.     

P(AA-DAC)两性聚电解质水凝胶的合成及性质

以丙烯酸(AA)和丙烯酰氧乙基三甲基氯化铵(DAC)为单体, 采用水溶液聚合法制备了P(AA-DAC)聚电解质水凝胶. 采用红外光谱和核磁共振等方法对其结构进行了表征. 研究了不同组成比的聚电解质水凝胶在去离子水、不同pH值溶液以及不同离子强度盐溶液中的溶胀行为. 研究结果表明, 摩尔比为1∶1的聚电解质水凝胶表现出典型的两性聚电解质凝胶的溶胀行为. 离子强度对其溶胀行为有着显著影响, 在溶液离子强度较高时, 凝胶网络的溶胀主要受溶剂向凝胶内部扩散所控制, 满足Fick型扩散规律n≤0.5, 随着溶液离子强度的增加, 凝胶网络平衡含水量增加, 扩散系数增大.     

Transport of water in polyvinyl alcohol films: Effect of thermal treatment and chemical crosslinking

Data on sorption and transport of water in polyvinyl alcohol films, modified by thermal treatment above T_g, or by chemical crosslinking with glutaraldehyde at different crosslinking degrees, are presented. Equilibrium swelling is constrained by both treatments, except for low degrees of crosslinking where the said reduction is counterbalanced by the partial loss of crystallinity. Analysis of the resulting water uptake kinetics indicates that viscous relaxation effects are, at least partly, responsible for the observed non-Fickian kinetic behavior. Thermodynamic diffusion coefficients of water, D_W, and relaxation frequencies of the swelling polymer, β_W, are determined by application of a theoretical model accounting for relaxation-dependent sorption kinetics in glassy polymers. The results indicate that the effect of both heat-treatment and chemical crosslinking is more intense on the macromolecular relaxation process than on the diffusion coefficient of water. Comparison of the release kinetics of a model drug from as-prepared, non-crosslinked and from crosslinked matrices indicate that the retardation of macromolecular relaxations process induced by crosslinking results in a more uniform release rate.     

The evolution of steep fronts in non-fickian polymer-penetrant systems

We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.