Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers

A high‐fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas‐diffusion model is coupled with a triple‐sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0–95 %) and temperatures (30–60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica‐filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.     

Sorption and transport of water in nylon-6 films

Sorption and transport properties of water through films of Nylon-6 were obtained at 5, 23, and 40°C. Commercially available films were used and a Cahn electrobalance was employed for measuring the water uptake by the polymer samples. Values of the water sorption isotherms are accurately described by the Langmuir/Flory-Huggins dual-mode sorption model. At water activity values below 0.15, the volume fraction of water described by the Langmuir portion of the model was greater than the Flory-Huggins population. Solubility and diffusion coefficients of water, as well as the diffusion activation energy and enthalpy of dissolution of water for Nylon-6, were determined from the sorption experiments. Values obtained support the hypothesis of a bimodal water sorption mode, and the formation of water clusters. © 1994 John Wiley & Sons, Inc.     

Sorption and diffusion of water vapor in polyimide films

Sorption and diffusion of water vapor are investigated gravimetrically for polyimide films. The activity dependence of the solubility and diffusion coefficients, S and D, respectively, is classified under four types: (1) constant S and D type, (2) dual-mode sorption and transport type, (3) dual-mode type followed by a deviation due to a plasticization effect at high vapor activity, and (4) constant S and D type followed by a deviation due to water cluster formation at high activity. For the dual-mode type, the Henry's law component is much larger than the Langmuir component except at low activity, and therefore deviation in behavior from the first type is small. S is larger for polyimides with higher content of polar groups such as carbonyl, carboxyl, and sulfonyl. D is larger for polyimides with a higher fraction of free space, with some exceptions. The polyimide from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and dimethyl-3,7-diaminodibenzothiophene-5, 5-dioxide belongs to the third type and displays both large S and large D. The polyimide from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride and 4,4′-oxydianiline belongs to the fourth type, and has the largest D but rather small S because of the hydrophobic C(CF₃)₂ groups. © 1992 John Wiley & Sons, Inc.     

Phase Transitions of MBBA Confined in Porous Solids

The diffusive and dynamic mechanical behaviour of an epoxy system containing tetraglycidyl-4,4′-diaminodiphenylmethane and a multifunctional Novolac glycidyl ether cured with 4,4′-diaminodiphenylsulfone was studied after water sorption. The diffusion of water was performed at 100% relative humidity, by immersion of specimens in water at 20, 40, 70 and 100°C. In all sorption experiments, the water diffusion followed Fick's law. Diffusion coefficients and saturated water concentrations were estimated for these temperatures. The activation energy for diffusion was determined from the relationship linking the diffusion coefficient and the reciprocal of the absolute temperature. The value obtained was 45.7 kJ mol^-1. Dynamic mechanical analysis of samples immersed in water at 25 and 100°C, and with various water contents, showed a shift in T_g> (defined by the tanδ peak) to lower temperatures over the glass transition region, and a slight decrease in the dynamic storage modulus in the presence of water as a result of a plasticization effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sorption and diffusion of gases in a polyimide

Sorption and diffusion of gases (CO₂, N₂, and He) in a polyimide (PI2080) film were measured by using an apparatus which gives the sorption rate curves from the initial state to the equilibrium state. Nonlinear isotherms observed for CO₂ sorption were interpreted successfully in terms of the dual-mode model for sorption in glassy polymers. Linear isotherms observed for N₂ and He seemed to obey Henry's law. Two diffusion coefficients (D_I and D_E) were obtained using the short-time method and the long-time method for a Fickian diffusion model, together with the equilibrium solubility (C_e) from each experiment. The initial sorption rate curves agreed with the calculated curves using D_I, however near sorption equilibrium the curves are in accord with the calculated curves using D_E. These observations suggest that some relaxation process is superimposed on the diffusion process. The non-Fickian transport data were correlated successfully with a model that combines time-dependent diffusion and the Fickian model.     

Sorption of water and organic solutes in polyimide films and its effects on dielectric properties

The effect of structure on the sorption kinetics of water and of various organic solutes into polyimide (PMDA-ODA) thin films was studied. The major techniques employed include measurements of sorption kinetics, density, and dielectric relaxation. More solute uptake, lower densities and higher diffusivities were observed for films cured at lower temperatures. By measuring both changes of mass and of density, the volume expansion of the polymer due to each solute was obtained; this was found to be proportional to the molar volume of the solute. The two dielectric relaxation peaks (denoted by γ₁ and γ₂) due to water (and other solutes) were studied in detail to obtain the relevant activation energies and the separate dipole moments. While water and methylene chloride appear in both γ₁ and γ₂ configurations, methyl and ethyl alcohol appear mainly as γ₂, while acetic acid is primarily γ₁. It was concluded that the γ₁ configurations are relatively homogeneously distributed throughout the polymer, involving loose bonding to the polymer structure, while the γ₂ configurations involve small clusters, probably chains of molecules. © 1993 John Wiley & Sons, Inc.     

Sorption and diffusion of water vapour on edible films

Two types of films consisting of sodium salt of carboxymethyl cellulose (NaCMC) and hydroxypropyl cellulose (HPC) as film forming materials and glycerin as plasticizer were prepared, characterized and their water vapour sorption properties were determined. The water sorption isotherms of the films were measured using a magnetic suspension balance. Results show that diffusion of water vapour in NaCMC based film is faster than that in HPC based films, due to the heterogeneous structure and larger pore dimensions of the NaCMC films.     

Sorption of Hydrophobic Organic Compounds by Aqueous Latexes

Summary: Optical absorption measurements are used for the first time to investigate the uptake of pure organic solvents or solutions by latex particles. Sorption into glassy polymer particles is a two‐stage process with distinctly different characteristic times, which reflects that an initial softening of the outer particle layer facilitates further uptake. The sorption of solutions containing highly water‐insoluble compounds allows the preparation of composite nanoparticles, which are hardly accessible by other routes.

Photograph of the neat 100 nm latex (right) particles and the particles after dying by sorption with the hydrophobic pigment Sudan IV (left).     

Calorimetric Studies and Structural Aspects of Ionic Liquids in Designing Sorption Materials for Thermal Energy Storage

The thermal properties of a series of twenty‐four ionic liquids (ILs) have been determined by isothermal titration calorimetry (ITC) with the aim of simulating processes involving water sorption. For eleven water‐free ILs, the molecular structures have been determined by X‐ray crystallography in the solid state, which have been used to derive the molecular volumes of the ionic components of the ILs. Moreover, the structures reveal a high prevalence of hydrogen bonding in these compounds. A relationship between the molecular volumes and the experimentally determined energies of dilution could be established. The highest energies of dilution observed in this series were obtained for the acetate‐based ILs, which underlines their potential as working fluids in sorption‐based thermal energy storage systems.     

Diffusion of Solvents and Cations in Porous Sol-Gel Glass

Diffusion coefficients for water, cyclohexane, toluene, chloroform, acetone and acetonitrile in porous sol-gel glass were determined using the diaphragm and radioactive tracer techniques. Polar solvents were found to diffuse faster than nonpolar solvent within porous sol-gel glass. The diffusion coefficients of Nd³⁺ and Er³⁺ inside porous sol-gel glass were determined from concentration profiles within monoliths impregnated by 1.6 M rare earth salts dissolved in either acetone or water. To study the effects of ligands on the diffusion, four different erbium salts were used: nitrate, chloride, bromide, and perchloride. It was found that the diffusion rate increases with decreasing radius of rare earth coordination sphere.     

The Design of an Automatic System for the Gravimetric Measurement of Water Sorption

An understanding of the mechanisms by which water molecules are held within a substance or at its surface, either by physical or chemical processes, is of importance in the formulation, preparation and storage of a wide variety of substances. The traditional experimental techniques which have been used to make measurements on samples exposed to specific levels of relative humidity, (e.g. using desiccators containing saturated salt solutions), are slow, laborious, inaccurate, and provide a limited amount of data. This paper describes the conception, operation, and facilities of a new system which by employing recently developed electronic components and transducers, significantly advances the performance capability for moisture sorption analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sorption and diffusion of aliphatic hydrocarbons into crosslinked natural rubber

The sorption and transport of four aliphatic hydrocarbons into natural rubber crosslinked by different vulcanization systems [conventional (CV), efficient (EV), peroxide (DCP) and a mixed system consisting of sulfur and peroxide (mixed)] were investigated in the temperature interval of 28–60°C. Of the four systems, natural rubber vulcanized by DCP exhibited lowest penetrant uptake. It was observed that the kinetics of liquid sorption in every case deviates from the regular Fickian trend, characteristic of sorption of liquids by rubbers. The diffusion coefficient, activation energy of sorption, enthalpy, entropy, and the rubber-solvent interaction parameter were evaluated for the four systems from the swelling data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 725–734, 1997     

Measurement and Modeling of Th Sorption onto TiO(2)

The sorption and desorption of Th onto TiO₂ (10 g/L) was studied as a function of pH (1–11), ionic strength (0.005–0.1 M NaCl, NaClO₄), thorium concentration (from 1 × 10⁻⁹ to 3 × 10⁻² M), and carbonate concentration (up to 10⁻² M) using ²³⁴Th tracer. The results indicate the reversible formation of an inner sphere complex with a strong pH dependence. No effect of the carbonate on sorption could be measured in the pH range investigated (5–10.5). The data were fitted with five different conceptual models (constant capacitance, diffuse layer, Stern, triple layer, and a nonelectrostatic model) using FITEQL. Different hydroxy complex surface reactions were tried, one at a time, varying the site density (1–12 sites/nm²). The reaction that provided the best fit depended strongly on the surface site density and the model used. To be able to fit a reaction to the pH-dependent data with the compact layer models, the effect of the electrostatic term had to be decreased by decreasing the site density below 5 sites/nm². None of the electrostatic models could be used to fit all of the isotherm data. The nonelectrostatic model could be used to reasonably fit both the pH-dependent and isotherm data.     

Water sorption in poly(ammonium sulfopropylbetaines). II. Sorption isotherms

Water sorption by four amorphous acrylic and methacrylic poly(zwitterions) bearing ammonium sulfopropylbetaine side groups () was studied at a constant temperature of 23°C and over a broad range of water activity (0.14-0.90). Whatever the physical state of the hydrated polymer, glassy or viscoelastic, water diffusion is Fickian (average diffusion coefficient D?_s in the range 2-16 × 10^?8 cm² s^?1), and the sorption isotherms may be quantitatively analyzed according to the Guggenheim-Anderson-De Boer amended BET equation for multilayer sorption processes. The number of sitebound water molecules per monomeric unit is in the range 1.5–2.0, and apparently there is no great energy difference between direct site binding and indirect binding in the successive solvation layers. The polymer-water interaction parameter (?0.6 < χ Flory < 0.6) is an increasing function of the water content of the hydrated poly(zwitterions) over the whole composition range (water volume fraction < 0.5), without any clear transition from the glassy to the viscoelastic state. Clustering of water molecules (Zimm-Lundberg theory) is never observed, even at high water content. Because of the charged structure of their dipolar units, the poly(zwitterions) show a water sorption process similar to that of the corresponding poly(electrolytes) of the tetra-alkylammonium sulfonate type. © 1992 John Wiley & Sons, Inc.     

The Hydrolysis of Protactinium(V) Studied by Capillary Diffusion

The mean diffusion coefficient of ²³³Pa has been measured simultaneously with those of ²²Na and ¹⁵²Eu in 0.5 M (Na, H)ClO₄ solutions with the pH ranging from 0.3 to 13, by the open-end capillary method optimized in order to obtain reproducible and reliable D values at T = 25°C. In the case of Eu(III), the results tend to give higher ₁₃ and ₁₄ hydrolysis constants than the values generally acccepted, but these data are probably affected by the formation of polynuclear or colloidal species as soon as the hydrolysis process is involved. For Pa(V), results are in agreement with the existence of the following two equilibria (I = 0.5 M, T = 25°C):

Sorption and diffusion of low molecular weight gases and vapors in glassy polymers at high concentration of sorbate

A theoretical approach has been developed to describe the sorption and diffusion processes of low weight molecular gases and vapors in polymers at wide ranges of sorbate concentration. The equation of an S‐shaped gas sorption isotherm in glassy polymer matrix has been derived. The concentration dependence of the sorbate molecule diffusion coefficient has been established. For an S‐shaped sorption isotherm, this dependence is nonmonotonous. The conditions of cluster formation of sorbate molecules have been analyzed within the proposed approach, in which it is possible to determine a correlation between these conditions and parameters of sorption isotherm. The comparison of the experimental and theoretical data provides an assessment of the microscopic characteristics of investigated polymer–vapor systems, such as the distances between vapor molecules in a matrix corresponding to intermolecular repulsion and attraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2314–2323, 1999     

Sorption of Water Vapour on Exinite Concentrates

Maceral concentrates of the exinite group, isolated from the hard coals from the Janina and Brzeszcze Mines were studied. Sorption studies in the coal-water vapour system and the concentrates maceral-water vapour system were carried out using the volumetric method (under isothermal-isobaric conditions) at 298 K, at the following relative sorbate pressures: 0.19; 0.34; 0.52; 0.70 and 0.88.The presented sorption isotherms show that the exinites isolated from coals have higher water vapour sorption capacities than the coals from which they were isolated. Their sorption capacity is closely related to the accessibility of their porous structure during the interfacial-volumetric process of water vapour interaction in the coal substance.     

Study of Sorption Processes of Selected Pesticides on Soils and Ceramic Porous Cups used For Soil Solution Sampling

Abstract

Soil sorption constants of four organochlorine (lindane, dicofol, chlorfenson and tetradifon) and three organophos-phorus pesticides (dimethoate, fenitrothion and methidathion) were measured using two different soils at six concentrations.

Soil samples were collected at depths of 0-20 cm and around 100 cm from an experimental citrus crop field. Effects of soil properties (organic matter, moisture content, pH and texture) on the sorption processes were also investigated.

Partitioning of pesticides between soil and solution was investigated after batch equilibration, using pesticide concentrations ranging from 10 to 200 μg1^?1. The equilibration time was estimated in 2 h for organochlorine, and 72 h for organophosphorus pesticides. Data fitted to Freundlich types adsorption isotherms.

Analytical determinations were carried out by gas chromatography with ECD and NPD detectors, after liquid-liquid extraction with dichloromethane of the water supernatant.

Moreover, a validation of the use of suction samplers used to collect soil solution samples from the vadose zone, based on a short term study in the laboratory was determined.     

Modeling Diffusion in Foamed Polymer Nanocomposites

Two‐way multicomponent diffusion processes in polymeric nanocomposite foams, where the condensed phase is nanoscopically reinforced with impermeable fillers, are investigated. The diffusion process involves simultaneous outward permeation of the components of the dispersed gas phase and inward diffusion of atmospheric air. The transient variation in thermal conductivity of foam is used as the macroscopic property to track the compositional variations of the dispersed gases due to the diffusion process. In the continuum approach adopted, the unsteady‐state diffusion process is combined with tortuosity theory. The simulations conducted at ambient temperature reveal distinct regimes of diffusion processes in the nanocomposite foams owing to the reduction in the gas‐transport rate induced by nanofillers. Simulations at a higher temperature are also conducted and the predictions are compared with experimentally determined thermal conductivities under accelerated diffusion conditions for polyurethane foams reinforced with clay nanoplatelets of varying individual lamellar dimensions. Intermittent measurements of foam thermal conductivity are performed while the accelerated diffusion proceeded. The predictions under accelerated diffusion conditions show good agreement with experimentally measured thermal conductivities for nanocomposite foams reinforced with low and medium aspect‐ratios fillers. The model shows higher deviations for foams with fillers that have a high aspect ratio.