Diffusion coefficient and equilibrium solubility of water molecules in biodegradable polymers

The diffusion coefficient and solubility of water molecules were measured in polyglycolide (PGA), poly(L ‐lactide) (PLLA), poly[(R)‐3‐hydroxybutyrate] (PHB), poly(ϵ‐caprolactone) (PCL), and Skygreen^R (SG). The diffusion coefficient and equilibrium solubility decreased in the order SG > PCL > PLLA > PHB > PGA and PGA > SG > PLLA > PHB > PCL, respectively. The diffusion coefficient and solubility of water at low sorption temperature in PHB varied according to the initial crystallinity of the matrix polymer even though crystallization of PHB molecules took place during the sorption experiment. In contrast, the amorphous PLLA and the crystalline PLLA showed an almost identical diffusion coefficient and solubility of water, in spite of the fact that the amorphous PLLA remained practically amorphous during the whole sorption procedure. A strong correlation existed between the water solubility and the surface tension or contact angle of the polymer matrix. The water diffusivity in PGA was almost 2 orders of magnitude lower while water was more soluble in PGA with a lower heat of sorption than that corresponding to the other more hydrophobic polymers, indicating that the transport of water molecules in PGA followed the solution–diffusion model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1716–1722, 2000     

Molecular Simulation of Oxygen Sorption and Diffusion in the Poly (lactic acid)

Grand canonical Monte Carlo and molecular dynamics simulation methods are used to simulate oxygen sorption and diffusion in amorphous poly(lactic acid) (PLA). The simulated solubility coefficient of oxygen is close to experimental data obtained from the quartz crystal microbalance but much higher than those from the time-lag method. This discrepancy is explained by using the dual-mode sorption model. It is found that oxygen sorption in PLA is predominantly Langmuir type controlled, em.e., through the process of filling holes. The time-lag method only takes into account oxygen molecules that participate the diffusion process whereas a large proportion of oxygen molecules trapped in the void have little chance to execute hopping due to the glassy nature of PLA at room temperature. The simulated diffusion coefficient of oxygen is reasonably close to the data obtained from the time-lag method. The solubility coefficient of oxygen decreases linearly with increasing relative humidity while its diffusion coefficient firstly decreases and then increases as a function of relative humidity.     

Sorption and diffusion of solvent vapours in poly(vinylalcohol) membranes of different crystallinity degrees

Solvent sorption and diffusion are the key processes that control membrane performances in membrane processes. The sorption characteristic of water and ethanol vapours in poly(vinylalcohol) (PVA) membranes of different crystallinity degrees was measured by microgravimetry and the diffusion characteristic was calculated from the sorption kinetics at different water activities by curve fitting. The sorption isotherms for water vapour in membranes of 28, 37, 44 and 56% crystallinity degrees at 40°C obey the Flory equation based on the polymer lattice model. When the sorption extent was corrected by assuming that only the polymer amorphous phase is accessible to the penetrant, a unique Flory χ interaction parameter, 0.3, was obtained for all samples except for the 28% crystallinity sample. For the latter sample, the lower χ value (0.18) obtained can be explained by a change in the sorption behaviour of the original crystalline domains which may undergo partial destruction. The diffusion coefficient increases with the average water content in the membrane according to an exponential relationship characterized by a limit diffusion coefficient and a plasticization coefficient. The higher the crystallinity of the membrane, the lower the values of the limit diffusion coefficient and the plasticization coefficient. The ethanol sorption was also well described by the Flory–Huggins equation. The limit diffusion coefficient for water was two orders of magnitude larger than that for ethanol.     

The measurement of the diffusion coefficient and the sorption isotherm of water in paint films

An experimental technique together with a numerical model is proposed with which the diffusion coefficient and the sorption isotherm of water in paint can be measured. Inside a closed vessel, paint films are on stainless-steel plates. Water is present as water vapour in the air and in the paint. After blowing dry or wet air through the vessel for some time, the situation moves to a new equilibrium. The relative humidity of the air inside the vessel is measured as a function of time. From fitting the theoretical/numerical model against the experimental values, follow the diffusion coefficient and the sorption isotherm of water in the paint. The results show large scattering. When the independently measured sorption isotherm is used as an input parameter in the model, the fitting procedure gives much smaller scattering for the diffusion coefficient.     

Experimental Studies and Modelling of Sorption and Diffusion of Water and Alcohols in Cellulose Acetate

The sorption characteristics of water, methanol and ethanol vapours in cellulose acetate (CA) films were measured by microgravimetry. The sorption isotherms for water vapours in the CA film at different temperatures in the range 20–40°C do not obey the Flory equation over the whole water activity range. At high water activities, the sorption extent increases much faster with the water activity than it should according to the Flory approach. The isotherms over the whole water activity range can be fitted well by the ENSIC model, a new mechanistic model developed to account for the possibility of solvent cluster formation in the polymer material. Similar behaviour was observed for ethanol, which shows a lower tendency to form clusters, but higher affinity to CA. The sigmoidal shape found for the methanol sorption isotherm suggests a strong sorption on CA sites at low methanol activities. The Guggenheim–Anderson–De Boer equa-tion fitted well this isotherm. The diffusion coefficient, which was calculated from Fickian sorption kinetics at different solvent activities by curve fitting, was constant for water but increased with ethanol content in the membrane according to an exponential relationship characterized by a limit diffusion coefficient and a plasticization coefficient. The limit diffusion coefficient for water was two orders of magnitude larger than that for ethanol, but the activation energy for ethanol was twice as large. Methanol diffusion was only Fickian at a low solvent activity; the diffusion coefficient was one order of magnitude lower than that for water. © of SCI.     

Determination of diffusion coefficients of water in cellulose acetate membranes

The determination of the diffusion coefficient for water in various porosity cellulose acetate membranes by a gravimetric method, using a humidified carrier gas, is described. It was found to be impossible to obtain meaningful results for very porous membranes, although dense membranes gave limiting values of diffusion coefficient at high carrier gas velocities. This phenomenon is explained in terms of the dissipation of the heat of sorption by the forced convection provided by the carrier gas. The variation of diffusion coefficient with concentration of water in dense cellulose acetate is explained in terms of clustering of water molecules in the polymer at high concentration.     

Modeling of the limiting step of water sorption by composite sorbents of the “calcium chloride in porous matrix” type

A nonstationary model is proposed to describe the water sorption from air by composite sorbents of the “salt in a porous matrix” type via the interaction of water with the salt to form a salt solution in pores. It is shown that the dynamics of the moisture content at the adsorber outlet cannot be described under the assumption of constancy of the effective sorption rate constant. The limiting step of water sorption is analyzed, and it is supposed that the limiting step is the water diffusion through the solution layer forming near the external surface of a granule. An expression for the sorption rate constant as a function of the moisture content of the sorbent is proposed that takes into account the monotonic decrease in this constant with an increase in the amount of water sorbed. The effective diffusion coefficient at the limiting step of sorption is determined, which turns out to be close to the effective diffusion coefficient in an aqueous calcium chloride solution.     

Evidence of dual mobility in sulfur dioxide-polyarylate system: An integral sorption analysis

Integral sorption/desorption measurements were carried out for the sulfur dioxide-glassy polyarylate polymer system at 25°C, 40°C, 55°C, and 63°C. The transport of sulfur dioxide in the glassy polyarylate polymer was governed by Fickian diffusion. The effective diffusion coefficient of sulfur dioxide increased with increasing penetrant concentration. The concentration dependence of the effective diffusion coefficient is explained on the basis of the partial-immobilization model developed by Paul and Koros. The mobility of the molecules sorbed in the Langmuir mode is shown to be significantly lower than the mobility of the molecules in Henry's law dissolution mode. The predictions of permeability values as a function of upstream gas pressure are presented. The equilibrium sorption isotherms for this system are well represented by the dualmode sorption model. The eltergetics and the temperature dependence of the dual-mode parameters are also discussed.     

Water sorption and water‐resistance properties of poly(vinyl alcohol)/clay nanocomposite films: Effects of chemical structure and morphology

A series of poly(vinyl alcohol)/sodium montmorillonite (PVA/NaMMT) nanocomposite films were prepared via a solution method, and their water sorption and water‐resistant properties were investigated as a function of clay content. The water sorption and water resistance properties were strongly dependent on the chemical structure and film morphology originating from the NaMMT content. The water diffusion coefficient and water uptake of the PVA/NaMMT nanocomposite films were obtained by best fits to a Fickian diffusion model. The diffusion coefficient and water uptake in the PVA/NaMMT nanocomposite films varied between 8.16 × 10⁻¹⁰ and 3.60 × 10⁻¹⁰ cm² s⁻¹ and 35.6 and 29.9 wt%, respectively. Both the diffusion coefficient and water uptake decreased as the content of NaMMT in pure PVA was increased. Additionally, the water resistance pressure (mm) of the PVA/NaMMT nanocomposite films increased with increasing NaMMT content. Contact angle analyses showed that the chemical affinity to water and the surface energy of the nanocomposite films decreased with increasing NaMMT content. Furthermore, the well‐dispersed and exfoliated structure in the nanocomposite films not only induced an increased tortuous path for water molecules to pass through, but also increased the molecular order. However, to enhance the water sorption properties and water resistance of hydrophilic PVA, further studies to increase the dispersion of clay particles and ensure desired morphological qualities such as crystallinity and molecular packing order in the PVA/clay nanocomposite films are required. POLYM. COMPOS., 36:660–667, 2015. © 2014 Society of Plastics Engineers     

In situ characterization of moisture sorption/desorption in thin polymer films using optical waveguide spectroscopy

The kinetics of moisture sorption/desorption in poly(terephthalate-co-phosphate) thin films was investigated in situ at T = 25 °C using optical waveguide spectroscopy (OWS). At low water activities, Fickian diffusion was observed for the initial phase of the sorption process, while at high activities, due to the clustering of water, a complex sorption behavior was found. The moisture sorption isotherms were analyzed according to both the Zimm and Lundberg model as well as the Brown model, which suggests the formation of clusters of water molecules in poly(terephthalate-co-phosphate) at water activities of α₁ = 0.58 or higher. The water diffusion coefficient decreases with increasing water activity, which also suggests water cluster formation. A biphasic desorption behavior was also observed upon decreasing the water activity from α₁ = 1 to 0. This study demonstrated the unique advantages of OWS in characterizing in situ the sorption/desorption behavior of penetrants in polymer thin films.     

Sorption and transport studies of water in Kapton polymide. I

Sorption isotherms and diffusion coefficients of water in a 0.3-mil Kapton polyimide film at 30, 45, and 60°C are reported. The data are well described by the dual mode sorption and transport models at low activities. At high penetrant activities, clustering of water is suggested by a Zimm–Lundberg analysis of the sorption data and the fact that the diffusion coefficient for water decreases with increasing external vapor activity. The effect of temperature on the diffusion coefficients at infinite dilution and the dual mode sorption parameters k_D, b, and C are presented and discussed. The magnitude of the activation energy of the diffusion coefficient at infinite dilution, 5.4 kcal/mol, is smaller than the corresponding activation energy in more flexible chain polymers, perhaps suggesting that rather small backbone motions are associated with diffusion of water through the Kapton matrix. The predictions for the isosteric enthalpy of sorption from the dual mode model are presented and compared with the values determined from graphical analysis of the sorption isotherms performed independently without reference to the dual mode sorption model.     

Water vapor sorption and transport in dense polyimide membranes

The sorption and transport of water vapor in five dense polyimide membranes were studied by thermogravimetry. The sorption isotherms of water vapor in the polyimides could be successfully interpreted by both the dual‐mode sorption model and the Guggenheim–Anderson–de Boer equation. The water vapor diffusion behavior was found to be nearly Fickian at higher water vapor activities, whereas non‐Fickian diffusion was observed at lower water activities. The phenomena could be well described by the mechanism of combined Fickian and time‐dependent diffusion. The diffusion coefficient and water vapor uptake in the polyimides were strongly dependent on the polymer molecular structure. Except for the polyimide prepared from 3,3′,4,4′‐diphenylsulfone tetracarboxylic dianhydride and 1,3‐bis(4‐aminophenoxy) benzene, the permeability of water vapor in the dense polyimide membranes predicted from the sorption measurement at 30°C corresponded well with the water vapor permeability measured at 85°C. Among the polyimides studied, pyromellitic dianhydride–4,4′‐diaminophenylsulfone (50 mol%)/4,4′‐oxydianiline (50 mol%) showed both high water sorption and diffusion and, therefore, high water vapor permeability, which for vapor permeation membranes is necessary for the separation of water vapor from gas streams. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 2306–2317, 2003     

Water sorption and diffusion through saturated polyester and their nanocomposites synthesized from glycolyzed PET waste with varied composition

A new system of saturated polyester and their nanocomposites synthesized from glycolyzed PET with varied composition is investigated for the sorption and diffusion studies in water. The kinetics of sorption is studied by using the equation of transport phenomena. The values of ‘n’ from transport equation are found to be below ‘0.5’, showing the non-Fickian or pseudo-Fickian transport in the polymer. The dependence of diffusion coefficient on composition and temperature has been studied for all polymeric samples. The diffusion coefficient of saturated polyester samples decreases with an increase in glycolyzed PET contents. The nanocomposite samples show less diffusion coefficient than pristine polymer and it decreases with an increase in nano-filler up to 4 wt%. The diffusion coefficient increases with an increase in temperature for all the samples. The sorption coefficient shows a little change with variation in composition as well as temperature for all the samples and it is in a range of 1. The activation energy for diffusion and permeation is positive for all the samples. The heat of sorption is also positive for all the samples, indicating Henry type mode of sorption.     

Morphology effect on water sorption behavior in a thermoplastic modified epoxy resin system

Water sorption behavior in polyetherimide (PEI) modified diglycidyl ether bisphenol-A/4,4′-diaminodiphenyl sulfone (DGEBA/DDS) systems was investigated by gravimetric analysis, positron annihilation lifetime spectroscopy and scanning electron microscopy. The equilibrium water uptake showed strong composition-dependent, which suggested that hydrophilic groups rather than free volume were more significant in determining ultimate water sorption. While besides the number of hydrophilic groups and fractional free volume, morphology induced by phase separation was another key factor that decided the value of diffusion coefficient, which was chiefly responsible for the anomalous diffusion behavior observed at the beginning of co-continuous phase. In addition, morphology not only had the function of decreasing fractional free volume, but also changed the number of hydrophilic groups in epoxy rich regions, which obviously distinguished water sorption behavior in the blends from that in single component systems.     

Sorption and desorption parameters of water or ethanol in light‐cured dental dimethacrylate resins

Two cycles of sorption/desorption of water or ethanol by light‐cured dental resins of bisphenol A glycol dimethacrylate (Bis‐GMA), bisphenol A ethoxylated dimethacrylate (Bis‐EMA) urethane dimethacrylate (UDMA) triethylene glycol dimethacrylate and decanediol dimethacrylate (D₃MA) were studied. The experimental curves m_t = f(t) taken for the first water sorption by poly‐Bis‐GMA, poly‐Bis‐EMA and poly‐UDMA showed a maximum. A maximum was also observed in the curve obtained for first sorption of ethanol by poly‐Bis‐GMA. In all other cases, the curves for sorption or desorption of water or ethanol showed Fickian behavior. The experimental data obtained for first sorption of water or ethanol were perfectly fitted to a new proposed equation, which predicts water or ethanol sorption with simultaneous extraction of unreacted the monomer. This equation gave us the possibility for the determination of the diffusion coefficient of the extraction of the unreacted Bis‐GMA during the water and ethanol sorption, as well as the diffusion coefficient of the extraction of the unreacted Bis‐EMA and UDMA during the water sorption. The maximum water or ethanol absorbed at equilibrium and the diffusion coefficient are determined from the second sorption/desorption cycle during which the extraction of the monomer is negligible. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

The influence of binder content on the water transport properties of waterborne acrylic paints

Diffusion coefficients and sorption isotherms of water in waterborne acrylic paint films and in the pure binder of the paints have been measured by gravimetric sorption. Solubility of water was found to enhance with the increased binder content in the paint films while the diffusivity of water decreased significantly. Sorption isotherms in the paint and pure copolymer films were correlated with the Flory Huggins theory and ENSIC model, respectively. Fickian diffusion was observed in both types of films and the kinetic data were best correlated with a numerical model which takes into account the concentration dependency of the diffusion coefficient and the dimensional change of the film due to sorption. It was concluded that the utilization of a simplified analytical solution may lead to significant errors in the estimation of diffusivities.     

Water diffusion in polymer coatings containing water-trapping particles. Part 2. Experimental verification of the mathematical model

The influence of the water microtraps (cross-linked poly(methacrylic acid) sodium salt spherical particles) with high sorption capacity and low diffusion coefficient on the water penetration through the epoxy coating has been investigated. Water diffusion coefficients for the pure epoxy coating as well as composite coatings with 5% and 3.7% content of water traps have been estimated by attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) and microbalance measurement methods. Experimental results were compared with the mathematical model of diffusion in composite media. The presence of the particles capable of binding water reversibly (water traps) significantly slows down the diffusion rate. Composites with water traps dispersed in the whole volume of the coating and sandwich-structured coatings composed of 3 layers with particles located only inside the middle layer have been examined. The diffusion rate has been found to depend not only on the concentration of the water traps but also on the location of the particles inside the coating. Both kinds of composites exhibit lower diffusion coefficient in comparison with the pure coating, however in the case of the sandwich-structured composites this effect is significantly stronger and much closer to that predicted by the model. Water diffusion coefficient for the sandwich-structured composite with 5% addition of water traps is ca. three times lower than for the pure epoxy coating.     

EFFECTS OF GLASS MICROFILLERS ON THE WATER-TRANSPORT BEHAVIOR OF POLYURETHANE COMPOSITES

Glass microspheres with unique composition and diameter, and modified by different surface treatments, were blended with polyurethane (PU) in various proportions to improve the liquid transport properties of the PU composites. Transport properties such as diffusion, permeability, and sorption coefficient were measured on various filler-filled PU composites at three different temperatures. These temperature-dependent parameters were used to provide a quantitative way to examine the effects of filler loading and the surface properties on the improvement of the water transport properties of PU composites. Results show that due to trapping at interfacial boundaries between filler and polymer, a high water affinity and large space for water activity is expected inside all the filler-filled composites. As a result, lower water diffusion (or high water resistivity) was found among all the filler-filled composites compared to that of filler-free composites. Besides, the more filler present in the composite, the longer the paths of the water molecules within the composites as the water penetration proceeds. Thus, lower diffusion coefficient values were observed for composites with large amounts of filler addition.     

Water transport in densely crosslinked networks: A comparison between epoxy systems having different interactive characters

Water transport in a densely crosslinked epoxy network, TGDDM-HHPA, was investigated by coupling time-resolved FTIR spectroscopy and gravimetric measurements. Vibrational analysis yielded information on the different water species present in the system and allowed a quantitative estimation of their population at sorption equilibrium.The transport of water molecules was found to follow a Fickian behaviour characterized by an effective diffusion coefficient which increases with total water concentration. The dependence of the effective diffusion coefficient, D_eff(C), on concentration, as obtained from integral sorption curves, was interpreted by introducing a concentration dependent term, D(C), and an “interaction factor”, ?, which accounts for the effect of the molecular interactions which effectively slow down the diffusion process.The results were compared with those obtained on another epoxy network, TGDDM-DDS, characterized by the presence of stronger interacting sites. Differences and similarities of the spectroscopic and gravimetric results are critically discussed in the light of the structure of the two networks.     

Distribution of morphology and transport properties of water vapor in injection‐molded biodegradable aliphatic polyester

A biodegradable polyester, poly(tetramethylene dodecanedioate), was injection molded in a rectangular cavity. Thin sections were sliced from molded samples starting from the skin. The morphology distribution inside the molded samples was studied by X‐ray analysis. The diffusion and solubility coefficient of water vapor were then measured using the microgravimetric method at the temperature of 30°C. Results show that morphology developed during the process influences the diffusion of water molecules through the polymer matrix. In particular, a direct influence of crystalline degree on the sorption and diffusion parameters was identified. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010