Multilayer sorption parameters: BET or GAB values?

The differences between the sets of values for the monolayer capacity and the energy constant obtained by sorption data regressions using two related multilayer sorption isotherms, the two-parameter BET (Brunauer–Emmett–Teller) and the three-parameter GAB (Guggenheim–Andersen–de Boer) isotherms, are analysed. Experimentally, it is found that the GAB monolayer value is always higher than the BET value and the GAB energy constant results always lower than the BET constant. Mathematical and physical reasons are given which explain these differences. The third GAB parameter determines the greater versatility of the GAB equation, which has a quite larger range of applicability than the BET isotherm. It is shown that in terms of the three GAB constants, the two BET parameters are qualitatively and quantitatively reproduced as well as their dependence on the regression interval used in the BET regression, justifying in this way the above-mentioned inequalities. The typical upswing in the BET plots after a (pseudo) linear range at lower activities of the sorbate is also explained. All these findings are exemplified using experimental sorption data of several systems of very distinct chemical nature. A complete regression procedure for sorption data in terms of the GAB isotherm is advanced.     

Analysis of gas sorption in glassy polymers with the GAB model: An alternative to the dual mode sorption model

The suitability of the Guggenheim–Anderson–De Boer (GAB) model for the parameterization of gas sorption isotherms and their dependences on temperature is explored. The GAB model implies that molecules adsorb on inner surfaces of the polymer in multilayers, which contrasts with the assumptions of the classical Dual Mode Sorption (DMS) model which implies the simultaneous occurrence of Henry‐like dissolution and Langmuir's case I adsorption. The GAB model shows similar efficacy of the parameterization of the gas sorption isotherms in polymers as the DMS model. The isosteric heat of adsorption shows clear dependence on relative surface coverage for carbon dioxide sorption in cellulose acetate, polyethylene terephthalate, and the first polymer of intrinsic microporosity (PIM‐1), thus allowing for the occurrence of adsorption multilayers. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1490–1495     

Statistical physics modeling of water vapor adsorption isotherm into kernels of dates: Experiments,microscopic interpretation and thermodynamic functions evaluation

In this paper, water sorption isotherms into date kernels give interesting insights about the sorption mechanism. The equilibrium adsorption data expressing the change in moisture content of date kernels were collected at three different temperatures using the static gravimetric technique. The adsorption isotherm profiles demonstrated that this process was performed via an infinite number of layers. A modified form of the Brunauer, Emett and Teller (BET) model is obtained based on the use of the real gas law and statistical physics treatment so the interaction between molecules is considered. This advanced model is used to fit experimental isotherms by numerical simulation. The sorption mechanism is theoretically explained by the parameters that could be related to the water adsorption process. Based on fitting results, we find that the number of molecules per site (parameter n) has a linear tendency with temperature thanks to the thermal agitation effect. A deeper analysis of adsorption energy demonstrates that the water vapors are physisorbed in the date kernels. Through the exploitation of our model, three classic thermodynamic functions are investigated to interpret the macroscopic aspect of the adsorption mechanism.     

Water vapor adsorption equilibria and mass transport in unmodified and modified cellulose fiber-based materials

Water vapor adsorption isotherms of different unmodified and coated paper samples were studied to determine their suitability as water barrier packaging materials. The sorption behavior of these samples was compared with commercially available paper. The experimental data were analyzed using the Hailwood–Horrobin (H–H), Guggenheim–Anderson–De Boer (GAB) and BET models for extraction of isotherm parameters and determination of monolayer moisture contents. The H–H and GAB models were found to provide good fits to the experimental data. The monolayer moisture content of modified papers was less than 3.0 % (dry basis) as compared to unmodified paper samples (4.20 %), at saturation. It was also observed that the sorption behavior of modified paper samples differed with substrate type. Water vapor permeability (WVP) of unmodified and coated paper samples at the temperatures of 25 and 38 °C were also measured for a wide range of vapor partial pressure gradients. The permeabilities of the modified samples were found to be generally low compared to the unmodified (reference) paper sample. Among the investigated samples, PLA and PHBV coated paper samples showed higher mass transfer resistance to water vapor transport. Furthermore, the water vapor permeabilities of different samples were found to be relatively constant up to the modest relative humidity levels; however, at the higher humidity levels they showed increasing trend with the further increase in relative humidity. Results of this study confirmed that blocking of active surface sites by coating with PLA and PHBV is the most effective way to increase the water vapor barrier properties of modified papers, thus making them the appropriate candidates for green-based food packaging materials.     

Thermodynamic analysis of sorption isotherms of bentonite

Sorption isotherms of water vapour on commercial bentonite clay are determined at T = (303, 323, and 343) K. The sorption isotherms have a sigmoid shape (Type II). At a given water activity, moisture content decreases with increasing temperature. Hysteresis between adsorption and desorption isotherms is shown over most the range of water activity varying from 0.1 to 0.9. The fitting of the experimental data by using two theoretical models (Guggenheim–Anderson–DeBoer (GAB) and Henderson) shows that the two models reproduce experimental data with acceptable accuracy. The GAB model, however, is largely superior. The isosteric sorption enthalpy is determined and its dependency on the amount of water retention is investigated. It is found that the enthalpy reaches a maximum value when a monolayer of water covers the adsorbant surface. The enthalpy decreases asymptotically to a finite value when the amount of adsorbed water increases.     

Sorption of methanol,dimethyl carbonate,methyl acetate,and acetone vapors in CTA and PTMSP: General findings from the GAB Analysis

Sorption of vapors of four organic compounds in two glassy polymers, cellulose triacetate (CTA) and poly[(trimethylsilyl)propyne] (PTMSP), has been reported and analyzed in terms of Guggenheim‐Anderson‐De Boer (GAB) model. These two structurally and physicochemically different glassy polymers both independently showed that one sorption site was formed by about three monomeric units. This finding held true for vapors of all characterized compounds; that is, for methanol, for its derivatives dimethyl carbonate and methyl acetate, and for acetone. The “rule of three” might thus also be applicable to other sorbates and glassy polymers. Further, an original modification of the GAB model for the sorption of alcohols in PTMSP was derived and successfully tested. Overall, the analyses of the sorption isotherms, heats of sorption and diffusion coefficients supported the view that the sorption of vapors in glassy polymers has adsorptive nature. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 561–569     

Thermo-physical characterization of Pharmacoat? 603, Pharmacoat? 615 and Mowiol? 4-98

Hydroxypropyl methylcellulose (HPMC) and polyvinyl alcohol (PVA) are important polymers in pharmaceutical, food and other industries being largely used as encapsulation agents. The characterization of two reference grades of HPMC (Pharmacoat^? 603 and Pharmacoat^? 615) and one reference grade of PVA (Mowiol^? 4-98), through X-ray diffraction (XRD) and thermogravimetry (TG) is described. Specific analyses were performed by means of dynamic vapour sorption analysis of water adsorption/desorption from vapours at 10, 25, 40, 55 and 70?°C. Guggenheim?CAnderson?Cde Boer (GAB), Brunauer?CEmmett?CTeller (BET), Park and n-layer BET models were successfully used to fit the experimental data. The glass transition temperature as function of water content was measured by means of differential scanning calorimetry (DSC). The experimental data were analysed according to Linear, Gordon?CTaylor, Fox and Roos equations. XRD studies revealed amorphous structure for the Pharmacoat^??603 and Pharmacoat^??615 and crystalline for Mowiol^??4-98. Single and multi-step temperature degradation point was found for Pharmacoat^??603 and Pharmacoat^??615 and Mowiol^??4-98, respectively. The water uptake is higher for Pharmacoat^??603 and Pharmacoat^??615 than Mowiol^??4-98. The influence of temperature on water uptake is opposite for the two types of polymers. GAB and n-layer BET were found to better model Pharmacoat^??603 and Pharmacoat^??615 and Mowiol^??4-98 data, respectively. The water makes the glass transition to decrease quite drastically. Gordon?CTaylor is better fitting the experimental data both for Pharmacoat^??603 and Pharmacoat^??615 and Mowiol^??4-98.     

Investigation of Moisture Sorption,Permeability, Cytotoxicity and Drug Release Behavior of Carrageenan/Poly Vinyl Alcohol Films

This work describes moisture sorption behavior and water vapor permeability of glutaraldehyde-crosslinked carrageenan/polyvinyl alcohol (Carr/PVA) films. The moisture uptake has been studied under various relative humidity (RH) and the data obtained has been interpreted in the terms of various isotherm models such as GAB, Oswin and Halsey models. The moisture permeability through the films has been characterized in the terms of various parameters like water vapor transmission rate (WVTR), permeance (P) and water vapor permeability (WVP). It was found that these parameters are greatly affected by the degree of crosslinking of the films. Finally, the model drug Gentamycin Sulphate was loaded in to the films and its release was monitored kinetically in the physiological buffer (PF) at 37°C. The films exhibited diffusion controlled release mechanism. The films are non-cytotoxic.     

Water transport properties of thermoplastic polyurethane films

Two linear segmented polyurethanes, based on poly(oxyethylene) (POE) as a soft segment and 4,4′‐diphenylmethane diisocyanate and 1,4‐butanediol as hard segments and differing in their soft segment length, have been studied from a water vapor transport point of view. For both polyurethanes, the water sorption is governed by a Fickian process, and the thermoplastic polyurethane with the longer POE segments displays the higher water diffusion rate. The water sorption isotherms are Brunauer Emmet Teller (BET) type III for both thermoplastic polyurethanes, and the water uptakes are directly related to the polymer POE content. The Flory–Huggins theory cannot correctly describe the sorption isotherms. More sophisticated approaches (Koningsveld–Kleinjtens or Guggenheim‐Anderson‐de Boer (GAB) models) are needed to fit the experimental water uptakes. The positive deviation from Henry's law and the decrease in the apparent diffusion coefficient observed at a high activity have been particularly studied. In this activity range, an isotherm analysis based on the cluster integral of Zimm and Lundberg suggests some clustering phenomenon, which seems consistent with the diffusion coefficient variation. In agreement with the sorption results, the water permeability coefficients are small at low activities, and they increase greatly with the relative pressure of water. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 473–492, 2004     

Water Sorption Properties and Antimicrobial Action of Zinc Oxide Nanoparticles-Loaded Cellulose Acetate Films

In this work, ZnO nanoparticles loaded cellulose acetate (ZOLCA) films have been prepared and characterized by XRD, SPR and SEM analysis. The moisture permeation properties of the films have been investigated. The GAB isotherm model has been found to fit well on the moisture uptake data obtained at different temperatures. The monolayer sorption capacity χ_m was found to decrease from 0.059 to 0.0079 g water/g dry film with increase in temperature from 20 to 37°C. The isosteric heat of sorption, when studied in the lower water activity range of 0.04 to 0.10, was evaluated to be 46.55 to 87.29 kJ/mol. The water vapor permeability across the ZOLCA films was found to increase with temperature and activation energy of moisture sorption process was found to be 48.57 kJ/mol. These films have shown excellent antibacterial action against model bacteria E-Coli when investigated by qualitative and quantitative methods. Films exhibit great potential to be used as edible films to protect food stuff against microbial infections.     

The Thermal Characteristics,Sorption Isotherms and State Diagrams of the Freeze-Dried Pumpkin-Inulin Powders

Powders based on plant raw materials have low storage stability due to their sorption and thermal properties and generate problems during processing. Therefore, there is a need to find carrier agents to improve their storage life as well as methods to evaluate their properties during storage. Water adsorption isotherms and thermal characteristics of the pumpkin powder with various inulin additions were investigated in order to develop state diagrams. Differential scanning calorimetry (DSC) was used to obtained glass transition lines, freezing curves and maximal-freeze-concentration conditions. The glass transition lines were developed using the Gordon–Taylor model. Freezing data were modeled employing the Clausius–Clapeyron equation and its development–Chen model. The glass transition temperature of anhydrous material (Tgs) and characteristic glass transition temperature of maximum-freeze-concentration (Tg′) increased with growing inulin additions. Sorption isotherms of the powders were determined at 25 °C by the static-gravimetric method and the experimental data was modeled with four different mathematical models. The Peleg model was the most adequate to describe the sorption data of the pumpkin–inulin powders. Guggenheim-Anderson-de Boer (GAB) monolayer capacity decreased with increasing inulin concentration in the sample.     

Moisture sorption in polyamide 6.6: Experimental investigation and comparison to four physical-based models

Water sorption in polyamide 6.6 has been characterized for a wide range of temperature (25°C to 80°C) and various water activities using a Dynamic Vapor Sorption testing machine. Complex sorption mechanisms govern the water uptake in the material. The competition between two main temperature dependant mechanisms has been observed: a Henry's sorption mechanism that mainly governs the sorption curve at low water activities, and a second mechanism at high water activities that could be related to the formation of water clusters. It is observed that the temperature dependency can mainly be attributed to the Henry's contribution. Four physically based models are then used and identified thanks to the extended experimental database. It is shown that a simple Flory-Huggins model is not able to capture the experimental observations at very high water activities for all the temperatures tested. The ENSIC model is a better choice, but good prediction for very high water activity cannot be obtained. Both modified Park and GAB models can accurately predict the volume fraction of water for the whole ranges of water activity and temperature, although the modified Park model should be preferred considering the number of parameters and the mathematical simplicity.     

Properties of diclofenac sodium sorption onto natural zeolite modified with cetylpyridinium chloride

In this study an investigation of a model drug sorption onto cationic surfactant-modified natural zeolites as a drug formulation excipient was performed. Natural zeolite was modified with cetylpyridinium chloride in amounts equivalent to 100, 200 and 300% of its external cation-exchange capacity. The starting material and obtained organozeolites were characterized by Fourier transform infrared spectroscopy, zeta potential measurements and thermal analysis. In vitro sorption of diclofenac sodium as a model drug was studied for all surfactant/zeolite composites by means of sorption isotherm measurements in aqueous solutions (pH 7.4). The modified zeolites with three levels of surfactant coverage within the short activation time were prepared. Zeta potential measurements and thermal analysis showed that when the surfactant loading level was equal to external cation-exchange value, almost monolayer of organic phase were present at the zeolitic surface while higher amounts of surfactant produced less extended bilayers, ordered bilayers or admicelles at the zeolitic surface. Modified zeolites, obtained in this manner, were effective in diclofenac sodium sorption and the organic phase derived from adsorbed cetylpyridinium chloride was the primary sorption phase for the model drug. The Langmuir isotherm was found to describe the equilibrium sorption data well over the entire concentration range. The separate contributions of the adsorption and partition to the total sorption of DS were analyzed mathematically. Results revealed that that adsorption and partitioning of the model drug take place simultaneously.     

Water sorption in hybrid silica gels containing colloidal nontronite

Hybrid silica gels (HSGs) were prepared according to an acid-catalyzed sol–gel method using tetraethoxysilane (TEOS) as silica precursors and colloidal suspension of nontronite clay mineral. The silica surfaces were hydrophilic in relation to silanol groups and it was of interest to increase hydrophobicity by substituting silanol by methylated groups through addition of methyltrimethoxysilane (MTMS) in a molar ratio TEOS: MTMS equaled to 1:0.4. The aim of the present paper was to predict effects of water content in soil on HSG hydration by characterizing HSG water desorption and sorption with dynamic vapor sorption device. From desorption kinetics, TEOS HSGs showed higher ability to water surface evaporation and diffusion compared to the TEOS–MTMS HSGs. After complete dehydration, water sorption isotherms Type II were obtained for HSGs. Isotherms were fitted with Brunauer-Emmett-Tellet (BET) and Guggenheim, Andersen, de Boer (GAB) models. The higher monolayer values of water adsorbed for HSGs containing nontronite suggested a major influence of clay minerals on overall hydration. However, the water binding energy depended upon the nature of silica matrix indicating weaker bonds with methylated groups at solid surface in MTMS–TEOS HSGs. Apparent water sorption diffusivities, D_app were calculated according to Fick’s diffusion model. Maximal D_app values were obtained in the range 0.2??.3 a_w after which the D_app decreased in relation with capillary condensation.     

Water sorption and permeation in chitosan films: Relation between gas permeability and relative humidity

The water sorption of chitosan has been studied at 20 °C. Water transport is governed by a Fickian process for relative humidities lower than 0.4, and in that range of partial pressures, the diffusion coefficient is concentration‐dependent. At a higher activity, anomalous diffusion is observed. The sorption isotherm is well described by the Guggenheim‐Anderson‐de Boer (GAB) model, and the clustering phenomenon observed at high relative pressures can be studied with the parameters of this model. The water permeability coefficient greatly increases with the relative pressure, and the water plasticization effect leads to a loss of the gas barrier properties under wet conditions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3114–3127, 2001     

Rigid sphere molecular model enables an assessment of the pore curvature effect upon realistic evaluations of surface areas of mesoporous and microporous materials

A gas adsorption rigid spheres model (RSM) was incorporated into the CPSM model (corrugated pore structure model) to correlate the pore surface areas obtained from the BET and CPSM methods. The latter is a method simulating the gas sorption hysteresis loop and enables the evaluation of surface areas S(CPSM) through the integration of the pertinent pore size distributions. Thus, S(CPSM) values are inherently influenced by pore curvature. The new CPSM-RSM version estimates surface areas S(CPSMfs) that are independent of pore curvature and can be compared with the pertinent S(BET) values. The RSM exploits the fact that a curved pore surface accommodates fewer molecules, assumed to behave as rigid spheres, than an equal flat one. Thus, the RSM accounts for a higher molecular surface coverage Ac (nm2/molec.) in pores with marked curvature than that (i.e., Af) on a flat surface. The ratio Ac/Af for nitrogen adsorbed on single pore sizes varies in the range Ac/Af = 1.44-1.03 for pore sizes D = 1.5-15 nm, respectively. Also for D = 1.5-5.0 nm the S(CPSMfs) and S(BET) values are lower by approximately 10-45% than the S(CPSM) estimates. From the application of the CPSM-RSM model on several porous materials exhibiting all known types of sorption hysteresis loops, it was confirmed that S(BET) approximately S(CPSMfs) (+/-5%) and (S(CPSM) - S(BET))/S(BET) = 3-68% for the materials examined. In conclusion, the BET method may produce quite conservative surface area estimates for materials exhibiting pore structures with appreciable pore curvature, whereas the CPSM-RSM model can reliably predict both S(CPSM) and S(CPSMfs) = S(BET) values.     

Modeling of water vapor adsorption isotherms onto polyacrylic polymer

The adsorbed amounts of water vapor onto polyacrylic polymer (polymer ×10) were measured using a thermogravimetry method as a function of pressure at 298 and 313 K. The adsorption isotherms are categorized to type II isotherms by IUPAC classification leading to a hysteresis loop between adsorption and desorption branches. The current study was completed by the measurement of the adsorption heats at 298 K using a differential scanning calorimetry. The calorimetric curves showed two adsorption heats domains. These domains have been attributed to the adsorption of “equivalent monolayer” and the condensation of water between polymeric chains. The correlation of experimental data to some chosen theoretical models shows that the GAB model is the most adequate to describe water vapor sorption isotherms.     

Preferential sorption in ion-exchange pervaporation membranes: sorption of water-ethanol mixture by sodium polyethylene sulphonate

Sorption of water and ethanol from aqueous ethanol solutions by sulphonated polyethylene membrane is studied both theoretically and experimentally, particular attention being paid to the effect of ionogenic-group content (capacity) on the sorption and sorption selectivity. A theoretical model is proposed based on models of salting-out and swelling of ion-exchangers. Examination of the experimental results obtained using the isopiestic method reveals a satisfactory agreement with the model, i.e. with a modified BET equation for sorption of water and a modified Setschenow equation for salting-out. Based on the results of this study, the following conclusions may be drawn: sorption selectivity toward water increases as capacity increases; the per equivalent uptake of water is determined primarily by water activity in the outside solution and the presence of ethanol plays only a minor role; the osmotic effect associated with deformation of the matrix has a negligible influence on selectivity. The model makes it possible to estimate sorption selectivity and may have applications in the calculation of pervaporation membrane performance. The sorption of water by the polymer was found to be far more pressure-dependent than that expected from thermodynamics, presumably due to the nonelastic behavior of the noncrosslinked polyethylene matrix.     

Effects of pore structure and surface chemical characteristics on the adsorption of organic vapors on titanate nanotubes

Effects of pore structure and surface chemical characteristics of titanate nanotubes (TNTs) on their adsorptive removal of organic vapors were investigated. TNTs were prepared via a hydrothermal treatment of TiO₂ powders in a 10 M NaOH solution at 150?°C for 24?h, and subsequently washed with HCl aqueous solution of different concentrations. Effects of acid washing process (or the sodium content) on the microstructures and surface chemical characteristics of TNTs were characterized with nitrogen adsorption-desorption isotherms, FTIR, and water vapor adsorption isotherms. For the adsorption experiments, gravimetric techniques were employed to determine the adsorption capacities of TNTs for four organic vapors with similar heats of vaporization (i.e., comparable heats of adsorption) but varying dipole moments and structures, including n-hexane, cyclohexane, toluene, and methyl ethyl ketone (MEK), at isothermal conditions of 20 and 25?°C. The experimental data were correlated by well-known vapor phase models including BET and GAB models. Isosteric heats of adsorption were calculated and heat curves were established. Equilibrium isotherms of organic vapors on TNTs were type II, characterizing vapor condensation to form multilayers. The specific surface area (and pore volume) and hydrophilicity of TNTs were the dominating factors for the determination of their organic vapors adsorption capacity. The GAB isotherm equation fitted the experimental data more closely than the BET equation. The heats of adsorption showed that the adsorption of organic vapors on TNTs was primarily due to physical forces and adsorbates with larger polarity might induce a stronger interaction with TNTs.