Langmuir Affinity Constant Research Articles

Adsorption of methylene blue dye from aqueous solution using low-cost adsorbent: kinetic, isotherm adsorption, and thermodynamic studies.

Fig leaf, an environmentally friendly byproduct of fruit plants, has been used for the first time to treat of methylene blue dye. The fig leaf-activated carbon (FLAC-3) was prepared successfully and used for the adsorption of methylene blue dye (MB). The adsorbent was characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), and the Brunauer-Emmett-Teller (BET). In the present study, initial concentrations, contact time, temperatures, pH solution, FLAC-3 dose, volume solution, and activation agent were investigated. However, the initial concentration of MB was investigated at different concentrations of 20, 40, 80, 120, and 200mg/L. pH solution was examined at these values: pH3, pH7, pH8, and pH11. Moreover, adsorption temperatures of 20, 30, 40, and 50°C were considered to investigate how the FLAC-3 works on MB dye removal. The adsorption capacity of FLAC-3 was determined to be 24.75mg/g for 0.08g and 41mg/g for 0.02g. The adsorption process has followed the Langmuir isotherm model (R2 = 0.9841), where the adsorption created a monolayer covering the surface of the adsorbent. Additionally, it was discovered that the maximum adsorption capacity (Qm) was 41.7mg/g and the Langmuir affinity constant (KL) was 0.37 L/mg. The FLAC-3, as low-cost adsorbents for methylene blue dye, has shown good cationic dye adsorption performance.

Adsorption Performance of Acid Dyes on Color-Adsorbing Nonwoven and Its Application in the Washing of Silk Textiles

ABSTRACT In recent years, the use of color-adsorbing nonwoven as a dye transfer inhibitor to prevent the cross-staining of fabrics in home laundering has received great attention. In this work, a color-adsorbing nonwoven was used to adsorb the dyes desorbed from dyed silk textiles and thereby provide an anti-staining effect in the washing. The nonwoven consisted of cationic regenerated cellulose and polyolefin fibers and had an isoelectric point of 7.82. The adsorption properties of acid dyes on the nonwoven and the anti-staining of the nonwoven were studied. The adsorption kinetics and isotherms of acid dyes on the nonwoven followed the pseudo-second-order kinetic and Langmuir adsorption models, respectively. With increasing temperature, the adsorption saturation increased, and the Langmuir affinity constant decreased, indicating an exothermic effect. The adsorption of dyes with high molecular weight showed great temperature dependence. During the washing of dyed silk textiles, the strong adsorption capability of cationic cellulose for desorbed acid dyes contributed to the anti-staining effect of color-adsorbing nonwoven.

Adsorption of Methylene Blue on Nano-Crystal Cellulose of Oil Palm Trunk: Kinetic and Thermodynamic Studies

The adsorption kinetic study of methylene blue using nano-crystal cellulose made from oil palm trunk was investigated. A sample of 0.08 g of nano-crystal cellulose was used to adsorb 300 mL of methylene blue solution, with a varied stirring speed at 100, 200, and 300 rpm. Meanwhile, the concentration of methylene blue was varied at 1, 2, and 3 mg/L. The experimental results showed that the range of adsorption rate constant was 0.0007–0.0130 m/min. For the thermodynamic study, adsorption temperature was varied at 303, 308, 313, and 318 K. The adsorption capacity values for such temperatures were 10.3389, 10.3802, 10.3614, and 10.3464 mg/g, respectively. It was found that ΔH° value of 0.00742 kJ/mol, ΔS° of 0.7758 kJ/mol K and ΔG° value of −242.81 kJ/mol. Based on the curve-fitting using the Henry, Langmuir, and Freundlich isotherm models, this adsorption tended to the Langmuir isotherm model, where the adsorption formed a monolayer covering the surface of the adsorbent. It was also found that the Langmuir affinity constant (KL) value was 4.560 L/mg, and the maximum adsorption capacity (qm) was 8.590 mg/g.

Kinetics, Affinity, Thermodynamics, and Selectivity of Phosphate Removal Using Immobilized Phosphate-Binding Proteins.

A phosphate (Pi)-selective adsorption system featuring immobilized Pi-binding proteins (PBP) has recently attracted attention for ultralow Pi removal followed by recovery. This study investigated the adsorption kinetics, affinity, thermodynamics, and selectivity, as well as the effect of pH and temperature on Pi adsorption using immobilized PBP (PBP resin). Immobilizing PBP did not affect its Pi affinity. Kinetic studies at 22 °C and pH 7.1 showed that the PBP resin achieved 95% of its equilibrium capacity within 0.64 ± 0.2 min. The estimated Langmuir affinity constant (KL) was 21 ± 5 μM-1 Pi (220 ± 52 L/mg-Pi), which is higher than Pi adsorbents recently reported in literature. The ideal operating ranges for high-affinity Pi adsorption using PBP resin were pH 4.5 to 9 and temperature 14 to 37 °C. The Pi-PBP resin adsorption process was not affected by the presence of common anions (Cl-, Br-, NO2-, NO3-, SO42-, and HCO3-). Adsorption using the Pi-PBP resin was exothermic (ΔH = -6.3 ± 1.3 kJ/mol) and spontaneous (ΔG = -39.7 ± 0.1 to -43.2 ± 0.2 kJ/mol) between 14 and 43 °C. These results indicate that PBP resin's Pi adsorption rate and affinity surpass those of existing adsorbents. Future work to increase the PBP resin's adsorption capacity is important to its application as a viable Pi adsorbent.

Adsorption of Cu(II), Ni(II), Pb(II) and Cd(II) from Ternary Mixtures: Modelling Competitive Breakthrough Curves and Assessment of Sensitivity

This study describes the competitive sorption of Cu(II), Ni(II), Pb(II) and Cd(II) onto grape stalks wastes (GS) in ternary mixtures in a continuous bed up-flow system. The characteristic breakthrough profile was observed for just one of the metals while the other two suffered overshoots. The elution profile showed that (i) lead is not overshot in any mixture, (ii) copper overshoots when lead occurs in the ternary mixture, and (iii) cadmium and nickel exhibit intense overshoots when either lead or copper are present. A kinetic model based on the Homogeneous Surface Diffusion Model (HSDM) was developed to describe the sorption profile of each metal in the mixtures. To simulate the breakthrough curves, the Extended Langmuir Model (MEL) has been incorporated into the HSDM to describe the equilibrium. The values of the Langmuir affinity constant, b, were found to follow the next ranking: Pb (54.5 ± 0.2) >> Cu (15.2 ± 0.3) >> Cd (9.4 ± 0.1) > Ni (8.1 ± 0.2). These constants successfully explain the competence that leads to the observed overshoots in the mixtures. The model successfully fits metal sorption kinetics and elution profile in the mixtures. A study of the model sensitivity was carried out to know how the uncertainty in the experimental data and the model parameters affect the uncertainty in the output of the model. This analysis highlighted the relevance of good estimation of K max , b and η besides the need of gathering high quality experimental data for an accurate determination of the model parameters.

Non‐Metabolic Uptake of Al3+ by Dead Leaves of Rubus ulmifolius: Comparison With Metabolic Bioaccumulation Data

This paper reports a physicochemical study (thermodynamic and kinetic data) describing the ability of Rubus ulmifolius biomass (dead leaves) for metal uptake. The toxicity of aluminum is a major problem for crops in acidic soils and therefore, aluminum has been selected. The results obtained indicate that dead R. ulmifolius leaves uptake up to 10 000 mg/kg on its surface in less than 60 min. This suggests that R. ulmifolius can be an excellent component with adsorbent properties for aquatic environments and in particular for amendments to be used in acidic soils in order to control aluminum levels, thus its toxicity. The results obtained have been critically analyzed and compared with literature on aluminum bioaccumulation. The application of a pseudo‐second order kinetic equation, not previously used in toxicity studies, is discussed. Moreover, a good linear correlation between stability constants for Al3+ complexes with several defined ligands and the Langmuir affinity constants obtained from the corresponding adsorption isotherm has been found. Therefore, in addition to its ethno‐botanical relevance, applications of R. ulmifolius as a detoxifier for aluminum in a simulated acidic gastrointestinal fluid, as phytostabilization agent in amendments or in natural attenuation cycles or as biomass for wastewater treatment containing aluminum, are suggested.

Competitive permeation of gas and water vapour in high free volume polymeric membranes

ABSTRACTHighly permeable glassy polymeric membranes based on poly (1‐trimethylsilyl‐1‐propyne) (PTMSP) and a polymer of intrinsic porosity (PIM‐1) were investigated for water sorption, water permeability and the separation of CO2 from N2 under humid mixed gas conditions. The water sorption isotherms for both materials followed behavior indicative of multilayer adsorption within the microvoids, with PIM‐1 registering a significant water uptake at very high water activities. Analysis of the sorption isotherms using a modified dual sorption model which accounts for such multilayer effects gave Langmuir affinity constants more consistent with lighter gases than the use of the standard dual mode approach. The water permeability through PTMSP and PIM‐1 was comparable over the water activities studied, and could be successfully modeled through a dual mode sorption model with a concentration dependent diffusivity. The water permeability through both membranes as a function of temperature was also measured, and found to be at a minimum at 80 °C for PTMSP and 70 °C for PIM‐1. This temperature dependence is a function of reducing water solubility in both membranes with increasing temperature countered by increasing water diffusivity. The CO2 ‐ N2 mixed gas permeabilities through PTMSP and PIM‐1 were also measured and modeled through dual mode sorption theory. Introducing water vapour further reduced both the CO2 and N2 permeabilities. The plasticization potential of water in PTMSP was determined and indicated water swelled the membrane increasing CO2 and N2 diffusivity, while for PIM‐1 a negative potential implied that water filling of the microvoids hampered CO2 and N2 diffusion through the membrane. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 719–728

Adsorption Properties of Lac Dyes on Wool, Silk, and Nylon

There has been growing interest in the dyeing of textiles with natural dyes. The research about the adsorption properties of natural dyes can help to understand their adsorption mechanism and to control their dyeing process. This study is concerned with the kinetics and isotherms of adsorption of lac dyes on wool, silk, and nylon fibers. It was found that the adsorption kinetics of lac dyes on the three fibers followed the pseudosecond‐order kinetic model, and the adsorption rate of lac dyes was the fastest for silk and the slowest for wool. The activation energies for the adsorption process on wool, silk, and nylon were found to be 107.15, 87.85, and 45.31 kJ/mol, respectively. The adsorption of lac dyes on the three fibers followed the Langmuir mechanism, indicating that the electrostatic interactions between lac dyes and those fibers occurred. The saturation values for lac adsorption on the three fibers decreased in the order of wool > silk > nylon; the Langmuir affinity constant of lac adsorption on nylon was much higher than those on wool and silk.

Effect of sorption behavior on transport properties of gases in polymeric membranes

The purpose of this work was to study the relationships between the gas sorption and transport properties in polymeric membranes. The intrinsic gas transport properties: permeation, diffusion, and sorption in a series of dense membranes with various carbonyl group densities were investigated. The poly(methyl methacrylate) (PMMA), polycarbonate (PC), and cyclic olefin copolymer (COC) membranes have similar helium permeability, but the helium permeability of poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) membrane was very high. The variation of permeability for these four membranes consists with their fraction free volume. In this study, a direct relationship was found between the carbonyl group density and Langmuir affinity constant. Furthermore, dependence of the fractional free volume on the membrane Langmuir capacity constant was observed.

Effect of Hydrocarbons on the Separation of Carbon Dioxide From Methane through a Polyimide Gas Separation Membrane

The removal of carbon dioxide from natural gas by membrane gas separation is an important process in upgrading the gas for consumers. Hydrocarbons associated with natural gas have the potential to influence the CO2 separation performance of membranes. Here, a glassy polymeric membrane of poly (4,4′-hexafluoroisopropylidene diphthalic anhydride-2,3,5,6-tetramethyl-1,4-phenylenediamine) (6FDA-TMPDA) was exposed to hexane and toluene at different partial pressures in a 90% CH4−10% CO2 gas mixture. The permeability of CO2 and CH4, as well as the selectivity, declined over time as both hexane and toluene competitively sorbed into the membrane. The resulting behavior fit the dual-sorption model for polymeric membrane separation and indicated Langmuir affinity constants of 0.13 ± 0.03 atm−1 for methane, 240 ± 100 atm−1 for hexane, and 980 ± 500 atm−1 for toluene (fugacity basis). The kinetics of the permeability decline were faster than that of the permeability recovery after the hydrocarbon contaminant was removed which may indicate that desorption from the Langmuir voids is the rate controlling step.

Effect of Cu(II), Cd(II) and Zn(II) on Pb(II) biosorption by algae Gelidium-derived materials

Biosorption of Pb(II), Cu(II), Cd(II) and Zn(II) from binary metal solutions onto the algae Gelidium sesquipedale, an algal industrial waste and a waste-based composite material was investigated at pH 5.3, in a batch system. Binary Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II) solutions have been tested. For the same equilibrium concentrations of both metal ions (1 mmol l −1), approximately 66, 85 and 86% of the total uptake capacity of the biosorbents is taken by lead ions in the systems Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II), respectively. Two-metal results were fitted to a discrete and a continuous model, showing the inhibition of the primary metal biosorption by the co-cation. The model parameters suggest that Cd(II) and Zn(II) have the same decreasing effect on the Pb(II) uptake capacity. The uptake of Pb(II) was highly sensitive to the presence of Cu(II). From the discrete model it was possible to obtain the Langmuir affinity constant for Pb(II) biosorption. The presence of the co-cations decreases the apparent affinity of Pb(II). The experimental results were successfully fitted by the continuous model, at different pH values, for each biosorbent. The following sequence for the equilibrium affinity constants was found: Pb > Cu > Cd ≈ Zn.

A novel model equation for the permeation of hydrogen in mixture with carbon monoxide through Pd–Ag membranes

Hydrogen permeance decrease, owing to the covalent interaction of carbon monoxide with the Pd–Ag membrane surface, represents a considerable drawback, since this decreases the efficiency of the alloy membranes. This work proposes a novel Sieverts–Langmuir's model taking into account the mentioned adsorption. The proposed model equation, in order to take into account the fraction of the membrane surface not active for hydrogen permeation, introduces Langmuir's isotherm, which is the surface loading in the classical Sieverts’ permeation equation. The evaluation of the α parameter and the Langmuir affinity constant involved in the proposed model was carried out using experimental data measured using a 60 μm thick Pd–Ag commercial membrane at 647 K (374 °C), up to a total pressure of 700 kPa. The presented model yields, in a parametric form, a quantitative assessment of hydrogen permeance decrease caused by the adsorption of gases on Pd–Ag membrane surfaces. Therefore, this novel Sieverts–Langmuir's equation models hydrogen permeation through Pd–Ag-based membranes in the presence of inhibitor gases such as CO. In addition, by ab initio evaluation of the α and the Langmuir affinity constant, the proposed Sieverts–Langmuir's equation can identify a new membrane with better efficiency.

The sorption of a syntan on nylon and its resist effectiveness towards reactive dyes

The sorption behavior of a commercial syntan on nylon and its resist effectiveness towards the uptake of reactive dyes on both nylon and nylon/cotton blend fabrics were investigated. The sorption isotherms of the syntan on nylon at pH 4 fitted a dual sorption mechanism consisting of partition and Langmuir type models. Whereas Langmuir sorption saturation was little influenced by temperature in the range of 50–80 °C, partition coefficients and Langmuir affinity constants increased with increasing temperature, indicating that syntan sorption was endothermic. The ability of the syntan to resist the uptake of reactive dyes was greatly influenced by the nature of the dye and the temperature of syntan application; the observed increase in resist effectiveness that accompanied an increase in the temperature of syntan application can be attributed to a corresponding larger uptake of syntan and greater extent of diffusion of the syntan within the nylon substrate, together with a lower extent of syntan desorption during reactive dyeing.

Cadmium adsorption isotherms onto clay separates of a yermic cambisol soil from central Jordan valley

Soils of central and southern Jordan Valley (JV) are partially irrigated with waste waters relatively enriched with heavy metals, such as Pb and Cd. A composite surface soil sample (0–25 cm) was collected from a central JV field of Deir‐Alla. The clay fraction (reference clay: <2 μm primarily of carbonate, mica, and kaolinite minerals) was fractionated from a subsample and employed in studying Cd adsorption isotherms (10, 20, or 30° C) from 0.05 M NaCl (Cd 2+ and CdCl+ chemical species) or NaClO4(Cd 2+ species only) background solutions. Twelve Cd initial concentrations ranging between 0.4 and 10 mg L ‐1 were employed in the adsorption study. Cadmium adsorption onto OM‐free or CO3‐free clay suspensions in 0.05 M NaClO4 background solutions was also studied. Equilibrium Cd concentrations were determined using Differential Pulse Anodic Stripping Voltammetry. For the reference clay suspensions in NaClO4 or NaCl solutions. Cd2+ adsorption isotherms conformed to linear Langmuir plot. Maximum adsorption capacity (B) from the ClO4 background solutions increased slightly with increasing temperature from 1020 (at 10° C) to 1099 μg g‐1 clay (at 30° C). This was accompanied by a respective increase in the Langmuir's affinity constant (K) from 16.0 to 30.3. Changing the background solution to NaCl resulted in a marked increase in B values and decrease in K values with increasing temperature. This was attributed to concurrent adsorption of CdCl+ and Cd2+ ionic species from the Cl solutions. Adsorption of CdCl+ species decreased from 367 to 254 μg g‐1 with increasing temperature from 20 to 30° C due to decreasing stability of that complex ion. Removal of organic matter slightly increased the B values of Cd2+ due to the exposure of internal surfaces as a result of deflocculation of clay particles. To the contrary, acid removal of CaCO3 caused a substantial reduction in the adsorption capacity of Cd2+ due to flocculation of clay particles by Ca2+.

Adsorption of Clostridium thermocellum cellulases onto pretreated mixed hardwood, avicel, and lignin

Adsorption of Avicel-hydrolyzing activity was examined with respect to: mixed hardwood flour pretreated with 1% sulfuric acid for 9 s at 220 degrees C (PTW220), lignin prepared from PTW220 by either acid or enzymatic hydrolysis, and Avicel. Experiments were conducted at 60 degrees C for all materials, and also at 25 degrees C for PTW220. Based on transient adsorption results and reaction rates, times were selected at which to characterize adsorption at 60 degrees C as follows: PTW220, 1 min; lignin, 30 min; and Avicel, 45 min. Similar results were obtained for adsorption of cellulase activity to PTW220 at 25 and 60 degrees C, and for lignin prepared by enzymatic and acid hydrolysis. For all materials, adsorption was described well by a Langmuir equation, although the reversibility of adsorption was not investigated. Langmuir affinity constants (L/g) were: PTW220, 109; lignin, 17.9; Avicel, 4.3; cellulose from PTW220, > or =187. Langmuir capacity constants were 760 for PTW220 and 42 for Avicel; the cellulase binding capacity of lignin appeared to be very high under the conditions examined, and could not be determined. At low and moderate cellulase loadings at least, the majority of cellulase activity adsorbed to PTW220 is bound to the cellulosic component. The results indicate that PTW220, and its cellulose component in particular, differ radically from Avicel with respect to adsorption. Avicel-hydrolyzing activity and CMC-hydrolyzing activities were found to bind to Avicel with a constant ratio of essentially one, consistent with adsorption of a multi-activity complex.

Effect of anions on adsorption of bile salts by colestipol hydrochloride.

The Langmuir affinity constant and adsorptive capacity for the adsorption of citrate anion or cholate anion by colestipol hydrochloride at pH 7.5, 37 degrees C, were similar. Prior exposure of colestipol hydrochloride to citrate anion caused the adsorption of cholate anion to decrease slightly in comparison to a control utilizing only cholate anion. The concentration of citrate anion was found to be directly related to the decrease in cholate anion adsorption. Simultaneous exposure of colestipol hydrochloride to citrate and cholate anions at pH 7.5, 37 degrees C, resulted in the same adsorption of cholate anion as sequential exposure to citrate anion followed by cholate anion. Sequential exposure of colestipol hydrochloride to simulated gastric fluid and simulated intestinal fluid containing cholate anion resulted in a small decrease in cholate adsorption which was attributed to competition with phosphate anion in simulated intestinal fluid. Pepsin in the simulated gastric fluid did not affect adsorption of cholate anion from simulated intestinal fluid. Preexposure to components of tomato juice and orange juice also slightly reduced the adsorption of cholate anion by colestipol hydrochloride.

A mathematical model of diffusion under saturated conditions to assess the pollution potential of herbicides to aquatic systems

Abstract The physicochemical dynamics of a pesticide-sediment-water system were studied utilizing a one-dimensional numerical model of diffusion under saturated conditions, with nonlinear Freundlich/Langmuir adsorption-desorption. Specifically, the model was formulated to assess the pollution potential of pesticides to aquatic systems, based upon their ability to migrate within the aquatic environment. Initial physical and chemical characterization of eight freshwater sediments, and adsorption studies using two chemically dissimilar herbicides—bromacil and diquat—revealed insightful positive relationships between adsorption coefficients and sediment properties. Bromacil showed a high positive correlation between the Freundlich sorption partition coefficient and the organic carbon content. Diquat adsorption, as characterized by a Langmuir-type adsorption, showed a high positive correlation between the Langmuir affinity constant and the surface area, while the Langmuir adsorption maxima correlated highly with the cation exchange capacity of sediments treated for the removal of organic matter. Apparent heats of adsorption for bromacil at 5° and 25°C were low, indicating a predominantly physical type of adsorption. Temperature change was found to have little or no effect upon the adsorption of diquat over the range of observed temperatures, 5° and 25°C. Rates of adsorption for both bromacil and diquat were very rapid, especially on sediments with small organic matter fractions. In general, diquat took slightly longer than bromacil to attain equilibrium. The slower adsorption rate of diquat on high-organic-matter sediments confirms previous findings indicating a possible redistribution of diquat from adsorption sites on the organic fraction to adsorption sites on the clay surface. Varying the initial solution concentration of either bromacil or diquat did not significantly affect the reaction rates. Desorption studies for bromacil and diquat showed that for each sediment, a unique linear relationship existed between the adsorbate concentration at which desorption began and the slope of the desorption isotherm.

High-pressure sorption of carbon dioxide in solvent-cast poly(methyl methacrylate) and poly(ethyl methacrylate) films

Carbon dioxide sorption isotherms in poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (PEMA) are reported for pressures up to 20 atm. Temperatures between 35 and 80°C were studied for PMMA and temperatures between 30 and 55°C were studied for PEMA. Typical dual mode sorption isotherms concave to the pressure axis were observed in all cases. The measured Langmuir sorption capacities of both polymers extrapolated to zero at the glass transition (Tg) consistent with the behavior of other glassy polymer/gas systems. Sorption enthalpies for CO2 in the Henry's law mode for PMMA and PEMA are in the same range (−2 to −4 kcal/mole) as has been reported for a variety of other glassy polymers such as poly(ethylene terephthalate), polycarbonate, and polyacrylonitrile. Some of the data suggest that postcasting treatment of the PEMA films left a small amount of residual solvent in the film. the presence of the trace residual solvent during quenching from the rubbery to the glassy state after annealing appears to cause a dilation of the Langmuir capacity and an alteration in the apparent Langmuir affinity constant of the PEMA film. These results suggest the possibility of tailoring physical properties of glassy polymers such as sorptivity, permeability, impact strength, and craze resistance by doping small amounts of selected residuals into polymers prior to quenching to the glassy state from the rubbery state.

Model for sorption of mixed gases in glassy polymers

AbstractA model is presented for analysis of the sorption of mixed gases in glassy polymers at concentrations below which significant plasticization occurs. The well‐known dual‐mode sorption model comprised of a Henry's law term and a Langmuir isotherm term, which has been used extensively for interpretation of single‐component gas sorption data, forms the basis for the analysis of binary mixtures discussed here. Measurements using pure gases provide dual mode parameters which can then be used to predict the resultant sorption isotherms for binary mixtures of any of the pure gases. The proposed analysis is based upon recognition that the Langmuir component of the overall sorption concentration should be governed by competition between the two penetrants for the fixed unrelaxed volume in the polymer, which is believed to be the locus of the Langmuir capacity. This effect may result in a significant depression of the measured sorption of similar penetrants competing for the limited Langmuir capacity. A numerical example is considered which illustrates the range of behavior expected for CO2 and CH4 in polycarbonate. Deviations from the theoretical predictions of the simple dual‐mode model for binary systems are discussed in terms of plasticizing effects on the Henry's law constant and the Langmuir affinity constant. The analyses proposed here are of direct and critical interest to the applied problems of migration of trace contaminants in glassy polymers and analysis of barrier packaging for foods since all of these applied problems involve mixed‐penetrant sorption. Specifically, it is predicted that the presence of residual monomers or solvents in glassy polymers can produce both anomolously low Langmuir sorption affinity constants and sorption enthalpies compared with the residual‐free case.

Energetics of gas sorption in glassy polymers

The molar enthalpy for gas sorption in glassy polymers at a fixed concentration, often called the isosteric enthalpy of sorption, exhibits a clearly discernable minimum when plotted as a function of penetrant concentration. This unexpected behaviour has been observed in several glassy polymer systems including poly(ethylene terephthalate), polyacrylonitrile and polycarbonate. The behaviour can be modelled by analysing the temperature dependence of the various equilibrium parameters comprising the so-called dual mode sorption model for gas sorption in glassy polymers. The fundamental significance of the various enthalpies describing the temperature dependence of the Henry's law solubility constant, the Langmuir affinity constant and the Langmuir capacity constant are included in the discussion. Provision is made for non-ideal vapours and gases by introduction of the compressibility factor in the expression for the isosteric enthalpy. Application of relationships for calculating both the isosteric and the isothermal enthalpies of sorption is made to the case of CO 2 in poly(ethylene terephthalate) in the temperature range 35° to 115°C. These results and analyses complement the wealth of equilibrium and transport data which are consistent with the dual mode sorption model for penetrant sorption in glassy polymers.