Combined experimental and computer simulation study of the kinetics of solute release from a relaxing swellable polymer matrix. II. Release of an osmotically active solute

The performance of a model monolithic controlled release device, consisting of a swellable polymeric matrix subject to structural relaxation (cellulose acetate), loaded with a simple osmotically active solute (NaCl) and activated by the ingress of solvent (water), was studied experimentally and by computer simulation. The former study involved detailed monitoring of the kinetics of both solute release and solvent absorption (followed in due course by desorption of osmotically imbibed excess solvent). The computer simulation study was based on extensive previous modeling work. Values of the relevant input model parameters were derived from independent experimental measurements of the sorption and diffusion properties of solvent (cf. Part I) and solute (reported in the present article). The resulting simulation was highly successful, considering that it proved possible to simulate closely and consistently the kinetics of both solute release (over practically the whole experimental range) and concurrent solvent absorption (including correct prediction of the magnitude of the osmotically induced excess swelling of the polymeric matrix). Simulation of the final desorption of osmotically imbibed water was facilitated by the realization that this process actually reflects the kinetics of a long‐term deswelling relaxation of the polymer structure back to the state of normal hydration, the rate of which could be measured to a good approximation on the pure deswelling polymer. The results presented here are of obvious practical significance in relation to progress toward computer‐assisted design of monolithic controlled release devices exhibiting relatively complex kinetic behavior. They should also prove useful by calling attention to an important caveat when desorption into water is used as a method for the straightforward determination of solute diffusivity in hydrated polymers, in cases of osmotically active solutes diffusing in nonhydrophilic polymers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2468–2479, 2004     

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     

Diffusion and relaxation in glassy polymer powders: 2. Separation of diffusion and relaxation parameters

Gravimetric sorption measurements for organic vapours in monodisperse glassy polymer powders have shown widely varied non-Fickian kinetic behaviour. These varied kinetics are interpreted by a single mathematical model involving a linear superposition of one or two phenomenologically independent first order relaxation terms upon the ideal Fickian diffusion equation. Analysis of experimental data for submicron powders through this model yields kinetic and equilibrium parameters describing the individual contributions of the diffusion and relaxation processes. This analysis has been applied to both integral and incremental sorption data for vinyl chloride, acetone, and methanol in poly(vinyl chloride) and for n-hexane in polystyrene. Sorption by initially penetrant-free polymer samples is dominated by a rapid Fickian diffusion process, while incremental sorptions show larger relative contributions from slow relaxation processes. The relaxation processes appear to be related to slow redistribution of available free volume through relatively large scale segmental motions in the relaxing polymer. The diffusion—relaxation model seems to provide a meaningful analysis of several non-Fickian ‘anomalies’, including a very slow approach to apparent equilibrium, two-stage and sigmoidal sorption curves, and sorption curves involving an initial maximum followed by temporary desorption and subsequent resorption.     

Guidelines for dryer design based on results from non‐Fickian model

In polymer solution coatings below the glass transition temperature of the pure polymer, the coating can go undergo a glass transition and develop stresses during drying. When stresses develop, a non‐Fickian model accurately describes solvent mass transport in drying polymer coatings. The non‐Fickian model includes the solvent transport due to both stress and concentration gradients. This article presents a non‐Fickian model, which predicts a lower residual solvent than does the corresponding Fickian model. We showed in an earlier article that the non‐Fickian model predicts trapping skinning (higher residual solvent under more intense operating conditions) at higher drying gas‐flow rates. In this article, the non‐Fickian model was used to investigate how the gas‐flow rate, dry film thickness, and substrate thickness affect the residual solvent for a single‐zone dryer. This work recommends guidelines for choosing gas‐flow rates, gas temperatures, and substrate thickness to minimize the residual solvent. The model predictions show that, at any gas temperature, the residual solvent is minimum at an intermediate gas‐flow rate. The trapping skinning effect is less evident in thicker coatings and substrates. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 477–486, 2003     

Water diffusion in a soft contact lens polymer and its tolerance to UV radiation studied by positron lifetime technique

The kinetics of water sorption, the topology or the free‐volume changes due to the presence of sorbed water in a soft contact lens polymer, poly(2‐hydroxyethyl methacrylate), were investigated by using the positron lifetime technique. It was found that the ortho‐positronium lifetime increases in the beginning of sorption because of microstructural swelling of the polymer matrix. After reaching a maximum, the lifetime decreases and becomes constant, maybe because of the filling of the free‐volume holes with water molecules. The diffusion process is found to be non‐Fickian. By using the dual‐mode sorption model, the Fickian‐controlled part and the relaxation‐controlled part of diffusion were separated. Further, the positron results seem to indicate the existence of water clusters in the sorbed lens material. The tolerance or stability of the soft lens material to UV radiation seems to be satisfactory as revealed by positron results. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1355–1366, 2004     

Three‐dimensional anisotropic moisture absorption in quartz‐reinforced bismaleimide laminates

The three‐dimensional anisotropic moisture absorption behavior of quartz‐fiber‐reinforced bismaleimide (BMI) laminates is investigated by collecting 21 months of experimental gravimetric data. Laminates of six, twelve, and forty plies and various planar aspect ratios are used to determine the three‐dimensional anisotropic diffusion behavior when exposed to full immersion in distilled water at 25°C. The long‐term moisture absorption behavior deviates from the widely used Fickian model, but can be accurately captured by the three‐dimensional, anisotropic hindered diffusion model (3D HDM). Excellent agreement is achieved between experimental gravimetric data and the 3D HDM for all laminate thicknesses. Recovered model parameters are shown to slightly vary with laminate thickness due to the small changes in the cured‐ply thickness. However, model parameters identified for a given laminate thickness are observed to accurately predict the absorption behavior of samples with different planar dimensions. Equilibrium moisture content of 1.72, 1.69, and 1.84% and corresponding diffusion hindrance coefficients of 0.807, 0.844, and 0.671 are recovered for six, twelve, and forty‐ply laminates, respectively, thus confirming strong non‐Fickian behavior. Moisture absorption parameters may be determined successfully at 16.5 months of immersion, before reaching approximately 85% of the equilibrium moisture content at 21 months. Subsequent gravimetric measurements up to 21 months are consistent with the predicted long‐term behavior. POLYM. ENG. SCI., 54:137–146, 2014. © 2013 Society of Plastics Engineers     

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.     

Anomalous sorption kinetics in the methanol vapor–poly(methyl methacrylate) system

The non‐Fickian sorption kinetics of methanol vapor in poly(methyl methacrylate) films 8 and 51 μm thick at 25°C are presented. The behavior of the system was studied in series of interval and integral absorption runs. The relevant diffusion coefficient and viscous relaxation processes were studied separately by kinetic analysis of the first and second stages of sorption kinetic curves. The sorption isotherm concaved upward at high activities, this being typical of Flory–Huggins behavior, whereas it exhibited a convex‐upward curvature at low methanol vapor activities, this indicating sorption in the excess free volume of the polymer matrix. After excess free‐volume fill‐up, the concentration dependence of the diffusion coefficient was found to be well represented by the free‐volume theory of Vrentas and Duda. Relaxation frequencies calculated from the second stage of two‐stage curves exhibited a weak dependence on the concentration. Integral sorption experiments indicated that the system exhibited nearly case II kinetics at high methanol vapor activities. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1184–1195, 2005     

Curing of polyfurfuryl alcohol resin catalyzed by a homologous series of dicarboxylic acid catalysts. II. Swelling behavior and thermal properties

Polyfurfuryl alcohol (PFA), as a bio‐based resin made from lignocellulosic materials, was crosslinked using a homologous series of dicarboxylic acid catalysts consisting of oxalic, succinic, and adipic acids, which are different in their dissociation constants. Swelling behavior, thermal stability, and non‐oxidative char residue of the resulting networks were characterized as a function of the acids strength and their concentration. Swelling of the networks were investigated at room temperature in eight solvents differing in molecular size and solubility parameter. Using acetonitrile as a solvent, the swelling mechanism was explored by applying kinetic models to the swelling data. Dynamic swelling studies during 16–30 days supported non‐Fickian and anomalous diffusion mechanism in highly crosslinked samples supporting PFA chain rigidity and high crosslinking density of the networks. Polymer–solvent interaction parameter, molecular weight between crosslinks and crosslinking densities were also determined. According to the results, the extent of PFA crosslinking and non‐Fickian behavior of the swelling solvent diffusion through the networks are strongly dependent on the concentration and dissociation characteristics of the catalysts used. Thermal stability studies showed no significant differences between the compositions, up to 900 °C. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45770.     

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     

Synthesis and characterization of polyacrylamide‐grafted chitosan hydrogel microspheres for the controlled release of indomethacin

Microspheres of polyacrylamide‐grafted‐chitosan crosslinked with glutaraldehyde were prepared and used to encapsulate indomethacin, a nonsteroidal anti‐inflammatory drug. The microspheres were produced by the water/oil emulsion technique and encapsulation of indomethacin was carried out before crosslinking of the matrix. The extent of crosslinking was analyzed by Fourier transform infrared spectroscopy and differential scanning calorimetry. Microspheres were characterized for drug‐entrapment efficiency, particle size, and water transport into the polymeric matrix as well as for drug‐release kinetics. Scanning electron microscopy confirmed the spherical nature and surface morphology of the particles with a mean particle size of 525 μm. Dynamic swelling experiments suggested that, with an increase in crosslinking, the transport mechanism changed from Fickian to non‐Fickian. The release of indomethacin depends upon the crosslinking of the network and also on the amount of drug loading. This was further supported by the calculation of drug‐diffusion coefficients using the initial time approximation. The drug release in all the formulations followed a non‐Fickian trend and the diffusion was relaxation‐controlled. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1525–1536, 2003     

Enzymatically degradable and pH‐sensitive hydrogels for colon‐targeted oral drug delivery. I. Synthesis and characterization

Cylindrical hydrogels, composed of starch and poly(acrylic acid), were synthesized, and their swelling behavior was studied as a function of the pH of the medium. The gels underwent a sharp transition from Fickian swelling behavior (swelling exponent n = 0.30) to non‐Fickian swelling behavior (n = 0.96) as the pH of the swelling medium changed from 2.0 to 7.4. The hydrogels also underwent partial enzymatic degradation in an amylase‐containing medium of pH 7.4 at 37°C. The effects of the enzyme concentration in the swelling media, the amount of starch present in the gel, the initial water content, the degree of crosslinking, and the diameter of cylindrical hydrogels on the degradation behavior were studied. The degradation of the gels followed Michaelis–Menten kinetics, and the value of the Menten constant was 41.62 × 10^?2. The gels exhibited minimum swelling in an acidic pH medium through the formation of a complex hydrogen‐bonded structure and underwent enzymatic degradation in a medium of pH 7.4 (i.e., simulating intestinal fluid) along with chain‐relaxation‐controlled swelling. Therefore, the gels have potential for colon‐targeted drug delivery. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3630–3643, 2004     

HPMC layered tablets modified with chitosan and xanthan as matrices for controlled‐release fertilizers

Polymeric matrices based on hydroxypropyl methylcellulose (HPMC) with xanthan (X) or chitosan (Q) and using KNO₃ as a model fertilizer were prepared as three‐layered tablets and assayed as controlled release fertilizers (CRFs). The dynamic swelling behavior was analyzed in order to interpret the water uptake mechanism, which in general proved to be non‐Fickian. The presence of HPMC allows a substantially constant rate of fertilizer release. The release mechanism of KNO₃ was analyzed and can be described as non‐Fickian diffusion, with release exponents ranging from 0.85 to 1.01, suggesting polymer relaxation as the major process controlling fertilizer release. Durability in soil indicates the blend Q‐HPMC as the more long‐lasting matrix of those tested, remaining at least 34 weeks. Both blends improve HPMC properties for agronomical applications, with X‐HPMC increasing the swelling rate and Q‐HPMC extending the permanence in the soil. Therefore, layered X‐HPMC and Q‐HPMC matrices can be proposed as suitable materials for the development of CRFs. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40839.     

Water sorption kinetics in poly(aryl ether ether ketone)

The kinetics of diffusion of water from different activity vapors and liquid phase have been investigated in glassy amorphous poly(aryl ether ether ketcne) (PEEK) films at the temperature of 60°C and in glassy semicrystalline PEEK sheets at different temperatures, respectively. In the case of the amorphous PEEK films (250 μm thick) the data at low activity levels were interpreted by means of a purely Fickian mechanism. At higher activity levels the material has shown the presence of a relaxation process; in this case the data have been interpreted using a model proposed by Berens and Hopfenberg. Equilibrium sorption isotherm is also reported. Liquid water sorption in semicrystalline (30%) PEEK sheets (2 mm thick) has been determined to follow the classical Fickian mechanism. The water uptake values obtained for both amorphous and semicrystalline PEEK, confirm the good moisture and liquid water resistance of this kind of high performance thermoplastic polymer.     

Non‐fickian three‐dimensional hindered moisture absorption in polymeric composites: Model development and validation

A new, three‐dimensional, anisotropic non‐Fickian diffusion model is developed to characterize moisture absorption in polymeric composites. The new hindered diffusion model extends the classical Fickian theory to include the effects of the interaction of diffusing molecules with the chemical and physical structure of polymeric composites. The numerical solution of the hindered diffusion model is obtained for a three‐dimensional, anisotropic domain by using a forward‐time, centered‐space finite difference technique. The moisture weight gain over time predicted by the model is shown to mimic a wide variety of anomalous absorption behavior, often exhibited by anisotropic composite laminates. The accuracy of the numerical solutions is verified by comparing the results to known analytical solutions of a one‐dimensional, “Langmuir‐type” diffusion model and for the limiting case of the three‐dimensional Fickian model. The utility of the proposed hindered diffusion model is demonstrated by accurately recovering the absorption behavior of three different material systems reported in literature. First, it is shown that the hindered diffusion model can accurately predict the moisture absorption data for unidirectional glass‐reinforced epoxy plates of varying dimensions exposed to a relative humidity of 80%. Second, the one‐dimensional version of the model is applied to experimental moisture absorption data for isotropic epoxy resin samples of different thicknesses. Anomalous effects due to sample thickness reported in the original article are accurately captured. Third, the proposed model is shown to be more accurate than a two‐stage diffusion model applied to moisture absorption data obtained from a woven 3‐ply carbon fiber reinforced bismaleimide composite. POLYM. COMPOS., 34:1144–1157, 2013. © 2013 Society of Plastics Engineers     

Multiscale fluid transport theory for swelling biopolymers

Fluid flow through a (bio) polymeric matrix has multiscale characteristics and is affected by the relaxation of surrounding polymers. Models developed in the past were either single scale (Polymer (1982) 23 (4) 529; Chemical Engineering Science (1992) 47 (12) 3037) or were limited to systems with a short memory (Achanta, 1995; Moisture transport in shrinking gels during drying, Ph.D. thesis, Purdue University, West Lafayette, IN). To address these limitations, we use the generalized Darcy's law equations of Singh (Effect of viscoelastic relaxation on fluid and species transport in biopolymeric materials, Ph.D. thesis) and the mass balance equations of Bennethum and Cushman (International Journal of Engineering Science (1996) 34 (2) 125) to develop a multiscale fluid transport model. The effect of viscoelastic relaxation of solid polymers on the flow of vicinal (adsorbed) fluid is considered at the mesoscale. At the macroscale two bulk fluids are incorporated, one of which is identical to the vicinal fluid. The mass balance equations for the vicinal fluid and its bulk counterpart are coupled via source/sink terms. The resulting fluid transport equation includes a novel integral term related to viscoelastic properties of the biopolymeric matrix. This term incorporates viscoelastic effects with both short and long memory. The model can describe both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport. The model suggests fluid transport is Darcian in the rubbery and glassy states when the biopolymers are sufficiently far from the glass transition region. In the proximity of glass transition the flow of fluids is anomalous or non-Darcian. These predictions are in agreement with the experimental observations of Kim et al. (Chemical Engineering Science (1996) 51 (21) 4827). In spite of its multiscale characteristics, the resulting transport equation is simple and can be easily solved. The experimental parameters needed to solve the equation are the effective diffusivity, a sorption or drying curve and viscoelastic properties of the material.     

Influence of the conformational order of glassy isotactic polypropylene on its crystallization and melting behaviour

The influence of conformational order of glassy isotactic polypropylene (iPP) on its crystallization and melting behaviour was studied by wide‐angle X‐ray diffraction (WAXD), Fourier‐transform infrared spectroscopy (FTIR) and differential scanning calorimetry (DSC). The glassy iPP samples with various conformational orders were prepared by freeze‐drying procedure from very dilute solution. WAXD and FTIR results suggest that although freeze‐dried samples are non‐crystalline, their conformational order is rather high and increases with decreasing concentration of parent solutions. With increasing conformational order of glassy samples, the cold crystallization peak shifts to lower temperature, indicating acceleration of crystallization. At low fusion temperature, the conformational order of melt obtained from freeze‐dried samples is high so that the relaxation time of single‐ and pauci‐chains to re‐entangle is long and the interpenetration between single‐ and pauci‐chain collective particles is slow. However, at high fusion temperature, the interpenetration process can be completed very quickly. Copyright © 2004 Society of Chemical Industry     

Surface resistance and diffusion characteristics of toluene into calcium carbonate‐ and polymer‐coated calcium carbonate‐filled natural rubber composites

Solvent absorption has been followed in compression‐molded rubber vulcanizates for toluene in natural rubber (gum), calcium carbonate (CC)‐filled natural rubber composites, and polymer‐encapsulated calcium carbonate (PCC)‐filled natural rubber composites. The surface resistance is found to affect the absorption process of the composites. Diffusion from the sample sides is considered for thickness and the diffusion coefficients corrected accordingly. Aspects of the effect of PMMA on the equilibrium toluene take up, Fickian mode of transport; transport coefficients; activation parameters; and crosslink density are studied. The sorption results have been interpreted in terms of first‐order kinetic model. The crosslink densities calculated from equilibrium sorption successfully to explain the transport coefficient values of the composites. POLYM. ENG. SCI., 53:2487–2497, 2013. © 2013 Society of Plastics Engineers     

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.     

Synthesis and characterization of POSS hybrid organogels using Menschutkin quaternization chemistry

The present research describes a series of organic–inorganic hybrid gels based on polystyrene and polyhedral oligomeric silsesquioxanes (POSSs) prepared using free radical copolymerization and Menschutkin chemistry techniques. In the first step, poly(styrene‐co‐chloromethylstyrene) is readily achieved by thermally initiated radical copolymerization and the subsequently obtained copolymer reacts with diethanolamine functional POSS nanoparticles which are employed as the crosslinker. The resulting hybrid network possesses ionic moieties and inorganic POSS nanoparticles. The POSS‐containing hybrid gels exhibit excellent organic solvent absorption and show good mechanical behaviour. Gel containing 0.8 × 10^?3 mmol of POSS(DEA)₈ (DEA, diethanolamine) reached the highest swelling ratio; hence, the corresponding gel can absorb organic solvent up to 20× its weight. The rate constant, coefficients and diffusional behaviour of hybrid organogels in organic solvent were examined as well. The organic solvent intake of the hybrid gel follows a non‐Fickian type diffusion. © 2018 Society of Chemical Industry