Advances in Modeling Sorption and Diffusion of Moisture in Porous Reactive Materials

Water‐vapor‐uptake experiments were performed on a silica‐filled poly(dimethylsiloxane) (PDMS) network and modeled by using two different approaches. The data was modeled by using established methods and the model parameters were used to predict moisture uptake in a sample. The predictions are reasonably good, but not outstanding; many of the shortcomings of the modeling are discussed. A high‐fidelity modeling approach is derived and used to improve the modeling of moisture uptake and diffusion. Our modeling approach captures the physics and kinetics of diffusion and adsorption/desorption, simultaneously. It predicts uptake better than the established method; more importantly, it is also able to predict outgassing. The material used for these studies is a filled‐PDMS network; physical interpretations concerning the sorption and diffusion of moisture in this network are discussed.     

Kinetics and Mechanism of the Sorption of Some Aromatic Amines onto Amberlite IRA-904 Anion-Exchange Resin

The kinetics of the sorption of aromatic amines such as o-aminophenol (o-AP), o-phenylenediamine (o-PDA), and p-phenylenediamine (p-PDA) onto Amberlite anion-exchange resin in chloride form was investigated in batch experiments spectrophotometrically at different temperatures. The sorption rate is zero order in all amines sorbed, increasing directly in the order: p-PDA相似文献   

Characterization of water vapor transport in glassy polyacrylonitrile by combined permeation and sorption techniques

Diffusion time lags, steady state permeabilities and sorption/desorption kinetics are reported for water vapor in biaxially oriented, solvent cast polyacrylonitrile (PAN) films. A wide range of vapor activities was studied at 15°C, 30°C, and 45°C. The transient and steady state permeation behavior at low and intermediate upstream vapor activities suggests that Fickian transport occurs under most of the conditions studied. Specifically, time lags predicted by Fick's law using the concentration-dependent diffusion coefficient derived from steady state permeation measurements agree reasonably well with experimentally measured values in most cases. p]Integral sorption/desorption kinetics at low and intermediate vapor activities also appear to be Fickian with a concentration-dependent diffusion coefficient. The form of the concentration dependency, evaluated from the “long time” solution of the diffusion equation for sorption experiments, is consistent with the form established for the diffusion coefficient from the steady-state permeation data. The diffusion coefficient exhibits a maximum near the concentration at which clustering is initiated. Presumably, the effective diffusion coefficient of water increases initially due to plasticizing or dual mode sorption effects associated with gap filling in the glassy matrix. As clustering becomes significant, the effective mobility of water is substantially reduced; therefore, the diffusion coefficient decreases at higher activities as clustering becomes the dominant mode of sorption. p]A tendency of the “early time” sorption/desorption kinetic data to exhibit concavity to the square root time axis at high activities suggests that time-dependent reductions in the diffusion coefficient may be occurring. Such reductions could be related to the kinetics of cluster formation at the higher vapor activities during sorption and to slow polymer consolidation during desorption. Any such non-Fickian effects, related to chain segment relaxations occurring over time scales similar to those of a diffusional jump, appear to be of importance only at short times. The short time nature of any such processes is suggested by the fact that diffusion coefficients evaluated from the “long time” solution to the diffusion equation for sorption are consistent with coefficients evaluated from steady state permeation data, in which case all time-dependent relaxation phenomena should be absent.     

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.     

Diffusion of water vapour in polymethyl methacrylate

Certain aspects of the concentration dependence of the diffusion coefficient and on the mechanism of sorption of water vapour in PMMA are investigated. Early time integral sorption kinetics follow the Fickian pattern of initial linearity. Diffusion coefficients deduced from the slopes of these lines are independent of concentration and satisfactorily agree with those obtained from late-time analysis; however, desorption values are higher throughout the whole range of activities than the corresponding absorption ones. On the contrary, typical “non-Fickian” features are discerned in differential absorption kinetics on membranes of different thickness. These anomalies are attributed to rate-determining relaxation processes concurrent with diffusion, whereas other sorption models are incompatible with the general behaviour of this system. General trends of the equilibrium and kinetic data are compared with those of other polymer—water systems and the observed differences are interpreted in terms of the molecular relaxation model.     

Sorption of basic dyes onto granulated pillared clays: thermodynamic and kinetic studies

Effect of the granulation process onto the thermodynamic and kinetic sorption parameters of two basic dyes (Basic Yellow 28-BY 28 and Basic Green 4-BG 4) was evaluated in the present work. The charge surface properties of the surfactant-modified aluminium-pillared clay (CTAB-Al-Mont-PILC) particles were not modified, and the isoelectric point remains constant after high shear wet granulation. The Gibbs free energy of both BY 28 and BG 4 sorption was negative and decreased with the granulation; the endothermic nature of the sorption process was confirmed by the positive values of ΔH°. Adsorption kinetics of the two dyes, studied at pH 6 and 150 mg L(-1), follow the pseudo-first order kinetic model with observed rate constants of 2.5-4.2×10(-2) min(-1). The intraparticle diffusion model, proposed by Weber and Morris, was applied, and the intraparticle plots revealed three distinct sections representing external mass transfer, intraparticle diffusion and adsorption/desorption equilibrium. Diffusion coefficients, calculated from the Boyd kinetic equation, increased with the granulation and the particle size. Pseudo-first order kinetic constants, intraparticle diffusion rate constants and diffusion coefficients were determined for two other initial concentrations (50 and 100 mg L(-1)) and include in a statistical study to evaluate the impact of granulation and initial concentration on the kinetic parameters. Kruskal-Wallis tests, Spearman's rank order correlation and factor analysis revealed a correlation between (i) the diffusion coefficients and granulation, and between (ii) the intraparticle diffusion rate constants and initial concentration.     

Water sorption/desorption kinetics in poly(ethylene naphthalene-2,6-dicarboxylate) and poly(ethylene terephthalate)

Water sorption/desorption experiments were carried out on films (～ 220 μm thick) of amorphous poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) stored in ambient conditions for different periods of time (0.5-4 years) and of poly(ethylene terephthalate) (PET) with different degrees of crystalinity levels (0-29%) by means of FTIR spectroscopy. Water sorption/desorption kinetics follows Fick's law for all samples investigated. Water sorption isotherms, obtained from gravimetric methods, indicate a larger sorption capacity in the case of PEN materials. The apparent diffusion coefficients (D) are larger in the case of PET samples. The observed D values decrease with storage time (physical aging) of PEN samples and with the crystallinity of PET samples. © 1995 John Wiley & Sons, Inc.     

Sorption of rubidium chloride by crown-containing polymer

The kinetics and mechanism of the sorption of rubidium chloride from ethanol by granulated polymer containing immobilized dibenzo-18-crown-6 are studied. The sorption of RbCl is controlled by internal diffusion accompanied by complex formation in the polymer. The equilibrium constants of the sorption and diffusion coefficients of the electrolyte in the sorbent are calculated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1025–1028, June, 1995.     

Thermodynamic interactions in binary mixtures of anisole with ethanol, propan-1-ol, propan-2-ol, butan-1-ol, pentan-1-ol, and 3-methylbutan-1-ol at T = (298.15, 303.15, and 308.15) K

In this paper, excess thermodynamic functions have been computed from the measured values of density, viscosity, and refractive index at T = (298.15, 303.15, and 308.15) K, ultrasonic velocity at T = 298.15 K over the entire mixture composition range of (anisole with ethanol, propan-1-ol, propan-2-ol, butan-1-ol, pentan-1-ol, or 3-methyl butan-1-ol). Excess molar volume, V^E has been calculated from densities, whereas deviations in viscosity, Δη, were computed from the measured viscosities. From ultrasonic velocities, isentropic compressibilities were calculated, from which deviations in isentropic compressibility, Δk_s have been computed. Lorenz-Lorentz mixture rule was used to compute molar refractivity, R from refractivity index data and from these data, deviations in molar refractivity, ΔR have been computed. Computed thermodynamic quantities have been fitted to Redlich and Kister polynomial equation to derive the coefficients and standard errors between experimental and predicted quantities. Intermolecular interactions between anisole and alkanols have been studied based on the computed excess thermodynamic quantities.     

Oxidation of alcohols by chlorine dioxide in organic solvents

The kinetics of oxidation of a series of alcohols (propan-2-ol, 2-methylpropan-1-ol, butan-1-ol, butan-2-ol, 3-methylpentan-1-ol, heptan-4-ol, decan-2-ol, cyclohexanol, borneol) by chlorine dioxide in organic solvents was studied using spectrophotometry. The reaction is described by the second-order rate equation w = k[ROH][ClO₂]. The rate constants were measured in the range of 10–60 °C, and the activation parameters of the processes were calculated. The products were identified, and the yields were determined.     

Chitosan derivatives as biosorbents for basic dyes

The scope of this study was to prepare and evaluate chitosan derivatives as biosorbents for basic dyes. This was achieved by grafting poly (acrylic acid) and poly (acrylamide) through persulfate induced free radical initiated polymerization processes and covalent cross-linking of the prepared materials. Remacryl Red TGL was used as the cationic dye. Equilibrium sorption experiments were carried out at different pH and initial dye concentration values. The experimental equilibrium data for each adsorbent-dye system were successfully fitted to the Langmuir, Freundlich and pH-dependent Langmuir-Freundlich sorption isotherms. Thermodynamic parameters of the adsorption process such as DeltaG degrees, DeltaH degrees, and DeltaS degrees were calculated. The negative values of free energy reflected the spontaneous nature of adsorption. The typical dependence of dye uptake on temperature and the kinetics of adsorption indicated the process to be chemisorption. The grafting modifications greatly enhanced the adsorption performance of the biosorbents, especially in the case of powdered cross-linked chitosan grafted with acrylic acid, which exhibited a maximum adsorption capacity equal to 1.068 mmol/g. Kinetic studies also revealed a significant improvement of sorption rates by the modifications. Diffusion coefficients of the dye molecule were determined to be of the order 10(-13) - 10(-12) m2/s. Furthermore, desorption experiments affirmed the regenerative capability of the loaded material.     

Magnetic chitosan grafted with polymerized thiourea for remazol brilliant blue R recovery: Effects of uptake conditions

Magnetic chitosan was prepared by co-precipitation with polymeric Schiff’s base resulting from the reaction of thiourea with glutaraldehyde. This material has great potential as high-effective sorbent for Remazol Brilliant Blue R (RBBR): maximum sorption capacity reached 0.441?mmol?g^?1 at pH 1.6 and at 25°C. Kinetic plots, pH dependence, isotherm data, and influences of ionic strength were reported. The data from equilibrium sorption experiments are well fitted to the Langmuir isotherm and the pseudo-second-order sorption kinetics indicates that chemisorption controls the process. The distribution coefficient was calculated at different temperatures and the thermodynamic parameters have been calculated: the sorption reaction is endothermic, spontaneous, and increases the entropy of the system. Alkaline solution (0.5?M NaOH) was used for desorbing RBBR from loaded sorbent. The sorbent exhibited good regenerability over several repeated adsorption/desorption cycles.     

Measuring the radon concentration and investigating the mechanism of decline prior an earthquake (Jooshan, SE of Iran)

Batch equilibrium studies were conducted at 20 ± 0.5 °C with indigenously synthesized spherical resorcinol–formaldehyde resin beads, using radioanalytical technique, to determine their capacity for sorption of cesium ions from alkaline medium. Equilibrium isotherm studies were carried out, by varying the initial concentrations of cesium from 0.1 to 50 mM. The liquid-to-solid phase ratio of ~100 ml:1 g was maintained for all the sorption experiments. The equilibrium data were fitted to Langmuir and Freundlich isotherm models. It was observed that Freundlich isotherm explains sorption process nicely. The effect of resin size on percentage cesium ion uptake was also investigated, and 20–40 mesh size was found to be the optimum particle size. The cesium sorption capacity of the beads was determined to be ~238 mg/g. The kinetics of the sorption was studied at different initial cesium ion concentrations, and the kinetics data were fitted into various kinetics models. The kinetics of the cesium ion sorption was found to be pseudo second-order. The mechanistic steps involved were found to be complex, consisting of both film diffusion and intraparticle diffusion with film diffusion as the rate limiting step.     

Sorption extraction of palladium(II) with modified polysiloxane

Sorption of palladium(II) from model solutions with polysiloxanes modified with amine and thiourea groups was stidied and it was found that the maximum sorption on aminopropyl polysiloxane is shifted slightly to alkaline region compared with a sulfur-containing sorbent. First time an effect of a series of external factors on a sorption kinetics of palladium with polysiloxanes was researched, diffusion coefficients of sorbate ions were calculated, and evaluation of their dependence on an initial concentration of metal, a grain diameter of the sorbent, and a temperature of sorption environment was carried out. It is shown that quantitative desorption of palladium from thiocarbamoylated polysiloxane is achieved by double treating the sorbent with hydrochloric acid solution of thiourea at high temperature.     

The determination of isosteric heats of sorption of leather: Experimental and mathematical investigations

Knowledge of sorption isotherms of leather products is necessary to control rehydration/dehydration and storage processes and it is valuable tool for prediction of the stability and shelf life of products but the impact of the controlled climate on moisture sorption isotherms of leather remains unclear. The aim of this work is to predict moisture desorption isotherms of leather of bovine variety. The static gravimetric method was used to determine sorption isotherms at four temperatures (30, 40, 50 and 60 °C) and the equilibrium moisture content of leather samples was measured within the range of 5–90% relative. All the curves exhibited type II behavior, according to Brunauer’s classification. Equilibrium moisture contents are observed to drop as the temperature is enhanced. Many models available in the literature were used to describe the experimental data. The agreement between experimental and calculated sorption isotherms is seen to be satisfactory (correlation coefficients from 0.93 to 0.99). Furthermore, DENT model is found to be the most appropriate for describing the relationship between the equilibrium moisture content, the water activity and temperature. On the other hand, the isosteric heats of desorption were determined from sorption isotherms and then correlated with corresponding equilibrium moisture contents. Besides, the isosteric heats of desorption decreased continuously with increasing of the equilibrium moisture content.     

Sorption of methanol/MTBE and diffusion of methanol in 6FDA–ODA polyimide

This article discusses the diffusion and solubility behavior of methanol/methyl tert‐butyl ether (MTBE) in glassy 6FDA–ODA polyimide prepared from hexafluoroisopropylidene 2,2‐bis(phthalic anhydride) (6FDA) and oxydianiline (ODA). The diffusion coefficients and sorption isotherm of methanol vapor in 6FDA–ODA polyimide at various pressures and film thicknesses were obtained with a McBain‐type vapor sorption apparatus. Methanol/MTBE mixed‐liquid sorption isotherms were obtained by head‐space chromatography and compared with a pure methanol sorption isotherm obtained with a quartz spring balance. Methanol sorption isotherms obtained with the two methods were almost identical. Both methanol sorption isotherms obeyed the dual‐mode model at a lower activity, which is typical for glassy polymer behavior. The MTBE was readily sorbed into the polymer in the presence of methanol, but the MTBE sorption isotherm exhibited a highly nonideal behavior. The MTBE sorption levels were a strong function of the methanol sorption level. Methanol diffusion in the polymer was analyzed in terms of the partial immobilization model with model parameters obtained from average diffusion coefficients and the dual‐mode sorption parameters. Simple average diffusion coefficients were obtained from sorption kinetics experiments, whereas the dual‐mode sorption parameters were obtained from equilibrium methanol sorption experiments. An analysis of the mobility and solubility data for methanol indicated that methanol tends to form clusters at higher sorption levels. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2254–2267, 2000     

Equilibrium, kinetics, mechanism, and process design for the sorption of methylene blue onto rice husk

Batch experiments were carried out for the sorption of methylene blue onto rice husk particles. The operating variables studied were initial solution pH, initial dye concentration, adsorbent concentration, and contact time. Equilibrium data were fitted to the Freundlich and Langmuir isotherm equations and the equilibrium data were found to be well represented by the Langmuir isotherm equation. The monolayer sorption capacity of rice husks for methylene blue sorption was found to be 40.5833 mg/g at room temperature (32 degrees C). The sorption was analyzed using pseudo-first-order and pseudo-second-order kinetic models and the sorption kinetics was found to follow a pseudo-second-order kinetic model. Also the applicability of pseudo second order in modeling the kinetic data was also discussed. The sorption process was found to be controlled by both surface and pore diffusion with surface diffusion at the earlier stages followed by pore diffusion at the later stages. The average external mass transfer coefficient and intraparticle diffusion coefficient was found to be 0.01133 min(-1) and 0.695358 mg/g min0.5. Analysis of sorption data using a Boyd plot confirms that external mass transfer is the rate limiting step in the sorption process. The effective diffusion coefficient, Di was calculated using the Boyd constant and was found to be 5.05 x 10(-04) cm2/s for an initial dye concentration of 50 mg/L. A single-stage batch-adsorber design of the adsorption of methylene blue onto rice husk has been studied based on the Langmuir isotherm equation.     

Aroma scalping characteristics of polybutylene succinate based films

The removal of aroma compounds from packaged food items - aroma scalping – can be primarily controlled by the choice of packaging materials. Although the utilization of biodegradable polymers as packaging materials can greatly contribute to the sustainability of the packaging industry, only limited data on their aroma scalping properties are available. In this work, the aroma scalping characteristics of a series of films made from biodegradable polybutylene succinate (PBS) and polybutylene succinate-co-addipate (PBSA) for common aroma compounds in foods (ethyl acetate, ethyl butyrate, ethyl hexanoate, hexan-1-ol, heptanal and (R)-(+)-limonene) are reported. The aroma scalping characteristics of a film made from poorly biodegradable low density polyethylene (LDPE) are reported for comparison.The aroma scalping characteristics, namely sorption and diffusion coefficients, of the tested aroma compounds were determined at 23 °C by means of sorption microgravimetry, and the permeability coefficients were estimated using the solution-diffusion model. The permeability coefficients for the films made from PBS, PBSA and LDPE were comparable for the more polar compounds: hexan-1-ol, ethyl acetate and ethyl butyrate. Conversely, the permeability coefficients of the less polar aroma compounds (ethyl hexanoate, heptanal and (R)-(+)-limonene) in PBS and PBSA-based films were by one to two orders of magnitude lower than those of the LDPE. In addition, a new mathematical model was proposed for the kinetics of the transient sorption of aroma compounds of low volatility (p^sat < 1 kPa).     

Sorption and diffusion of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) blend membranes

The diffusion and sorption of methyl substituted benzenes through cross-linked nitrile rubber/poly(ethylene co-vinyl acetate) (NBR/EVA) blend membranes has been studied. The influence of blend composition, cross-linking systems, temperature and size of penetrants on the transport behaviour has been analysed. It was observed that as the EVA content increases in the blends, the solvent uptake decreases. An increase in the penetrant size also decreases the solvent uptake. The diffusion experiments were carried out in the temperature range 23–75 °C. As temperature increases the equilibrium uptake also increases. The transport coefficients namely diffusion coefficient, sorption coefficient and permeation coefficient have been calculated. The sorption data has been used to estimate the activation energies for permeation and diffusion. The van’t Hoff relationship was used to determine the thermodynamic parameters. The affine and phantom models for chemical cross-links were used to predict the nature of cross-links. Models for permeability were used and the theoretical values compared with the experimental results.