Diffusion through swelling membranes with a Robin boundary condition

A Robin boundary condition at the downstream surface of stretched membrane is used to study diffusion through swollen polymer membranes. Four dimensionless parameters are used to describe the diffusion process. These parameters are associated with the effect of swelling, relaxation, and retardation times of the polymer matrix as well as the normal derivative condition at the downstream side of the membrane. The effect of these four parameters is discussed. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

A rapid and convenient method for measuring the swelling of coals by solvents

The volumetric swelling procedure developed by Liotta was applied to a pair of coals using 10 solvents. The results were compared with the results of gravimetric swelling experiments. Good straight-line correlations having slopes of 0.93 (Bruceton coal) and 1.01 (III. No. 6 coal) were observed. The much more rapid and convenient volumetric swelling procedure gives the same results as the gravimetric procedure. Additionally, no correction for pore volume is necessary with the volumetric procedure. From plots of the gravimetric vs. volumetric swells, the accessbile pore volumes of the coals can be determined. They are 21% and 15% for Bruceton and III. No. 6 coals, respectively.     

Anomalous swelling of a polystyrene matrix in organic solvents

Swelling behavior of a commercial linear polystyrene, containing a small amount (<5% wt) of mineral oil, has been studied in three different classes of organic solvents (alkanes, alcohols and carboxylic acids) using both gravimetry and light microscopy. A comparison has been made with the results presented in earlier publications using a different linear polystyrene, without mineral oil. It is shown that the polystyrene containing mineral oil absorbs much higher amounts of solvent at lower temperatures then at higher temperatures. This anomalous behavior sharply contrasts with the polystyrene without mineral oil, which at lower temperatures absorbs much less solvent. Light microscopy of the diffusion layer reveals that in the polymer with mineral oil precipitation occurs during diffusion at low temperatures, but not at high temperatures. These results clearly show that the presence of small amounts of mineral oil (in quantities below the detection limit of FTIR) can cause significant changes in the sorption behavior of polymers. These results are interpreted by pre‐existing nano‐inhomogeneities, formed by the mineral oil, limited miscibility of oil in the polymer phase and high miscibility of solvent in the oil phase. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Spectrophotometric measurement of swelling of polymer films by very poor solvents

Solvent swelling of polymers is important for many applications, but can be difficult to measure when thin films or very poor solvents are involved. A novel spectrophotometric method is presented that is well suited for measuring swelling of thick or thin polymer films by very poor solvents. In this method, the solvent is stained with iodine, and solvent uptake is measured by observing the change in visible light absorption of the polymer using a spectrophotometer. Using this method, swelling can be accurately measured in thin (< 2 μm) polymer films and with poor solvents that cause little swelling, even water. Results are presented for PMMA films of varying molecular weights swelled by water, by water–alcohol mixtures, and by undiluted alcohols. Swelling of these films is more rapid and more Fickian than has been reported for bulk samples, probably due to differences in PMMA molecular weight and processing. The properties of the iodine–PMMA complex are also explored. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1082–1089, 2005     

Effect of polymer solution concentration on the swelling and mechanical properties of glycol chitosan superporous hydrogels

This study examined the effect of the polymer solution concentration on the swelling and mechanical properties of glycol chitosan (GCS) superporous hydrogels (SPHs). GCS SPHs were synthesized using a gas blowing method using glyoxal as the crosslinking agent at different polymer solution concentrations. A small change in the GCS solution concentration resulted in a remarkable change in compression strength and swelling kinetics without any significant loss in equilibrium water imbibing capacity. The increase in mechanical strength accompanied by the decrease in swelling kinetics was caused by the generation of smaller pores during the gelation process of the reactant systems associated with a higher polymer solution viscosity. The apparent diffusion coefficients for a variety of GCS/simulated gastric fluid solution systems were determined from the theoretical fitting of experimental dynamic swelling data, explaining the effects of the solution concentration and crosslinking density on the swelling kinetics. The diffusion coefficients determined in this study are expected to be used as the basic information in estimating the swelling kinetics of samples in different dimension. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

依兰煤在液化溶剂中的溶胀动力学研究

笔者以依兰煤为原料,研究了依兰煤在室温至2000℃范围内在液化起始溶剂和循环溶剂中的溶胀行为,并确定了依兰煤在试验条件下的溶胀动力学参数。试验结果表明：依兰煤在液化起始溶剂和循环溶剂中的溶胀度随溶胀温度的增加和溶胀时间的延长而增大;依兰煤在这2种溶剂中的溶胀都是受Case-Ⅰ扩散控制为主的过程,其溶胀活化能分别为4．18和4．22kJ·mol^-1。     

Influence of dynamic vulcanization and phase interaction on the swelling behavior of the thermoplastic elastomeric blends of nylon-6 and acrylate rubber in various solvents and oil

The swelling behavior of thermoplastic elastomeric blends of nylon-6 and acrylate rubber (ACM) has been studied in various solvents and oil at different temperatures. The blends, both with and without dynamic vulcanization, show excellent solvents and oil resistance at elevated temperature. The interfacial reaction between nylon-6 and ACM phases as well as the dynamic crosslinking of the ACM phase during melt blending tremendously improve the solvent resistance of the blends. A simple thermodynamic model, based on the Flory–Huggins equation, is applied to find out the constraining effect of the continuous nylon-6 matrix (which is the least swellable phase) on the extent of equilibrium swelling of the dispersed ACM phase in toluene at 25°C. The diffusion coefficients of various solvents and the activation energy of diffusion of toluene in 40 : 60 (w/w) dynamically vulcanized blend have been reported. The occurrence of interfacial reaction and the existence of nylon-6–ACM graft copolymers are also supported by the dynamic mechanical thermal analysis of the blends. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 2331–2340, 1998     

Mathematical modeling of water uptake through diffusion in 3D inhomogeneous swelling substrates

Diffusion‐driven water uptake in a substrate (imbibition) is a subject of great interest in the field of food technology. This is a particular challenge for rice grains that are preprocessed to accelerate the water uptake, i.e., to reduce the cooking time. Rice preprocessing disrupts the mesostructural order of starch and induces a microporous structure in the grains. The meso‐ and microstructural length scales have not been considered in joint approach until now. The (re)hydration of rice grains can be modeled by free (concentration‐driven) diffusion or by water demand‐driven diffusion. The latter is driven by the ceiling moisture content related to the extent of gelatinization of the rice substrate network. This network can be regarded as a fractal structure. As the spatial resolution of our models is limited, we choose to model the apparent water transport by a set of coupled partial differential equations (PDEs). Current models of water uptake are often limited to a single dimension, and the swelling of the substrate is not taken into account. In this article, we derive a set of PDEs to model water uptake in a three‐dimensional (3D) inhomogeneous substrate for different types of water diffusion as well as the swelling of the substrate during water uptake. We will present simulation results for different 3D (macroscopic) structures and diffusion models and compare these results, qualitatively, with the experimental results acquired from magnetic resonance imaging. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Challenges in the development of new green solvents for polymer dissolution

As chemical legislation grows more strict and the UK moves towards a bioeconomy, acceptable solvents for industrial dissolution of polymers are growing scarce. An estimated 78% of solvent use in the EU is in sectors such as paints and coatings, printing inks and adhesives, in which polymer dissolution is a critical function. Academic research in safe, sustainable solvents is growing, but largely in the field of reaction solvents, leaving solvents for polymers underdeveloped by comparison. This challenge can be addressed through the adoption of computational tools, improved communication between industry and academia and increased research funding. Recent progress in green solvent development provides a number of models that can be adapted to the problem of polymer dissolution research. © 2020 Society of Chemical Industry     

Dynamics of overall swelling profile of multiresponsive ionic dimethylacrylamide-based hydrogels and cryogels: Diffusion characteristics evaluation of salt-dependent swelling

Due to the importance of ion–polymer interactions in many technological applications, systematic measurements have been investigated on a variety of ionic poly(N,N-dimethylacrylamide) (PDMAAm) hydrogels and cryogels to determine the effect of mono- and multivalent ions on their dynamic properties. Using uniaxial compression, the influence of counter-ion valency on flexibility of charged polymer chains was investigated and the results were discussed as a function of ionic comonomer. To estimate the general swelling features, diffusion process and oscillating swelling–deswelling kinetics of ionic PDMAAm gels in salt solutions have been explained by model equations using early-time approximation as a function of characteristic response time.     

Influence of segmental swelling of an asymmetric block copolymer on the morphology of melt-mixed immiscible polymer blends

We investigate the influence of an asymmetric PS-b-PMMA block copolymer (bcp) on the morphology of melt-mixed immiscible binary polymer blends containing poly(styrene-co-acrylonitrile) random copolymer (SAN) and poly(cyclohexylmethacrylate) (PCHMA). By varying the SAN copolymer composition, the balance between the swelling of each block segment located at the interface between the two phases is altered and the effect on blend morphology is studied. As in earlier studies using a symmetric bcp, we find that for a specified shear history, there is a zone of effective emulsification of the blend bounded by regions of internal and external emulsification failure. However, the locations of the boundaries between stable and unstable emulsification differ for an asymmetric versus a symmetric bcp. Thus the morphology depends not only on the segmental swelling ratio but also on the difference in the effective size of each bcp segment. Scaling arguments successfully correlate the limits of stable emulsification for both symmetric and asymmetric bcp.     

The effect of swelling agents and characterization of polyurethane/polymer electrolytes/clay composites

This study discusses the interaction model and characterization of a clay organic processed with different swelling agents blended with PU/polymer electrolytes. The change in d‐spacing of the clay and modified clay in the PU/polymer electrolytes blends was analyzed using X‐rays. A rigid‐body pendulum rheometer was used to determine the curing behavior of PU/polymer electrolytes matrix in the clay and modified clay with different proportions. Dynamic mechanical analysis has been applied to discuss the intermolecular interaction between clay and organoclay with different proportions and PU/polymer electrolytes blends. We have also analyzed the mechanical properties, stress, and strain. As a result, the compatibility of polymer electrolytes, clay, and organoclay is better. The swelling agent that intercalated among the layers of clay will be crowded out and adsorbed onto the surface of clay. The curing time, intermolecular interaction, thermal properties, and mechanical properties of composites were clearly influenced by the clay and swelling agent. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1206–1214, 2005     

A transport model for the absorption of mixed solvents in glassy polymer membrane

Transport model for mixed solvents in glassy polymer membrane is rare in literature. In our previous work, a new experimental method has been developed and absorption kinetic curves for two mixed solvent systems (ethanol/1,2-dichloroethane and ethanol/ethyl acetate) in polyurethane (PU) membrane at have been measured. In this work, based on Liu et al.'s transport model for single solvent/polymer membrane system, a transport model for the absorption of mixed solvents in glassy polymer membrane is established. Three model parameters in this model can be obtained by correlating the experimental data of the corresponding single solvent/polymer membrane systems; the other three should be determined by correlating the experimental data of mixed solvents/polymer membrane system. The effect of model parameters on diffusion is studied by numerical simulation. The correlated results agree well with the experimental absorption curves. The model has the ability to predict the transport phenomena of mixed solvents in polymer membrane.     

Determination of the kinetics of diffusion in coals by solvent swelling techniques

A simple technique has been developed for measuring the kinetics of solvent diffusion in coals at various temperatures. The technique is based on a well-known method for measuring the volumetric swelling of coals by solvents. Several coals have been examined in both pyridine and tetrahydrofuran, at temperatures between 298 and 332 K. The diffusion follows the well-established case II rate law at ambient temperatures, implying that the processes are controlled by relaxation in the coal network structure. As temperatures are increased, the process becomes more Fickian in nature. The activation energies for the diffusion-relaxation processes are in the range 31 to 82 kJ mol⁻¹.     

Sorption/desorption,diffusion, and swelling characteristics of geomembranes in the presence of halo‐organic liquids

Sorption/desorption results of halogen‐containing liquids into high‐density polyethylene, linear low‐density polyethylene, very low‐density polyethylene, and polypropylene geomembranes are presented at 25, 50, and 70°C. Sorption results are obtained by a gravimetric method, and diffusion coefficients have been calculated by using Fick's equation from the initial linear portions of the sorption/desorption curves. Swelling of the geomembranes was studied from a measurement of the increase in volume, thickness, and diameter. From a temperature dependence of sorption and diffusion coefficients, the Arrhenius parameters have been calculated. Liquid concentration profiles have been computed using Fick's equation for the appropriate initial and boundary conditions. The results of this study may have relevance in selecting the suitable geomembrane for a specific application in hazardous waste chemical ponds and other similar situations.     

The effects of temperatures and volumetric expansion on the diffusion of fluids through solid polymers

This study examines moisture sorption behaviors of two glassy polymers, epoxy and vinylester, immersed in different fluids at two temperatures below the glass transition temperatures of the polymers. The main purpose of this study is to understand the effect of volume‐dependent temperatures and deformations on the diffusion process of solid polymers. Diffusivity coefficients are first determined by assuming the diffusion to follow the classical Fickian diffusion. In some cases, moisture sorption led to quite significant changes of volume, and the diffusion process cannot be well described by the Fickian diffusion. In such situation, the coupled deformation–diffusion model for linear elastic isotropic materials presented by Gurtin 1 is adopted, as a first approximation. This coupled deformation‐diffusion model reduces to a Fickian diffusion model when the coupling parameters are absent and the volume changes in the solid polymers during diffusion are negligible. A finite difference method is used in order to solve for the coupled deformation‐diffusion model. The model is used to predict the one‐dimensional moisture diffusion in thin plates and the multiaxial three‐dimensional moisture diffusion in dogbone specimens. The multiaxial diffusion in the dogbone specimens is used to validate the calibrated material parameters from the standard thin plate diffusion characterization. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45151.     

Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties

The swelling and mechanical properties of various interpenetrating polymer networks (IPNs) were studied. Six networks made from permutations of a moderately crosslinked polyelectrolyte network (ref), a moderately crosslinked neutral polymer network (net1), and a highly crosslinked polyelectrolyte network (net2) were first swollen in water and structural properties such as end-to-end chain lengths and radial distribution functions were compared with the component networks' equilibrium properties. The swelling of composite IPNs was discussed in terms of a balance between the osmotic pressure due to mobile counterions and the restoring force of the network chains, which act in parallel to counteract the osmotic swelling. For the ref-net2 system, the strong stretching of net2 chains increases the network restoring force and the further swelling due to the counterions is suppressed. The swollen networks were then uniaxially stretched, and equilibrium stress-strain plots were obtained up to high extension ratios. The equilibrium volume decreased upon uniaxial extension, and the elastic moduli of IPNs of the A-A type were slightly greater than that of their respective single networks.     

Adsorption of anionic dyes on a reversibly swelling cationic superabsorbent polymer

A cationic monomer [2‐(methacryloyloxy)ethyl]trimethylammonium chloride was polymerized using N,N′‐methylenebisacrylamide as the crosslinker to obtain a cationic superabsorbent polymer (SAP). This SAP was characterized by Fourier transform‐infrared spectroscopy, and the equilibrium swelling capacity was determined by swelling in water. The SAP was subjected to cyclic swelling/deswelling in water and NaCl solution. The conductivity of the swelling medium was monitored during the swelling/deswelling and was related to the swelling/deswelling characteristics of the SAP. The adsorption of five anionic dyes of different classes on the SAP was carried out and was found to follow the first‐order kinetics. The Langmuir adsorption isotherms were found to fit the equilibrium adsorption data. The dye adsorption capacity of the SAP synthesized in this study was higher than that obtained for other hydrogels reported in the literature. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Calculation of optimum multicomponent solvent compositions for polymers using a multiple regression program

A useful prediction of the solubility of a polymer in a particular solvent can be obtained by comparing their respective solubility parameters. The solution to the problem of finding solvent mixtures with maximum polymer interaction, already available for binary and ternary mixtures, has been extended to cover any number of components. This report also points out that the theoretical optimum composition (for two or more components) can be calculated by using a multiple regression program. The easy availability of such a program on most computers offers the occasional user an alternative to writing a special program for the purpose.