Characterization of pore size distributions of mesoporous materials from adsorption isotherms

In this article, a new hybrid model for estimating the pore size distribution of micro- and mesoporous materials is developed, and tested with the adsorption data of nitrogen, oxygen, and argon on ordered mesoporous materials reported in the literature. For the micropore region, the model uses the Dubinin-Rudushkevich (DR) isotherm with the Chen-Yang modification. A recent isotherm model of the authors for nonporous materials, which uses a continuum-mechanical model for the multilayer region and the Unilan model for the submonolayer region, has been extended for adsorption in mesopores. The experimental data is inverted using regularization to obtain the pore size distribution. The present model was found to be successful in predicting the pore size distribution of pure as well as binary physical mixtures of MCM-41 synthesized with different templates, with results in agreement with those from the XRD method and nonlocal density functional theory. It was found that various other recent methods, as well as the classical Broekhoff and de Beer method, underpredict the pore diameter of MCM-41. The present model has been successfully applied to MCM-48, SBA's, CMK, KIT, HMS, FSM, MTS, mesoporous fly ash, and a large number of other regular mesoporous materials.

The use of liquid phase adsorption isotherms for characterization of activated carbons

The characterization of three commercial activated carbons was carried out using the adsorption of various compounds in the aqueous phase. For this purpose the generalized adsorption isotherm was employed, and a modification of the Dubinin-Radushkevich pore filling model, incorporating repulsive contributions to the pore potential as well as bulk liquid phase nonideality, was used as the local isotherm. Eight different flavor compounds were used as adsorbates, and the isotherms were jointly fitted to yield a common pore size distribution for each carbon. The bulk liquid phase nonideality was incorporated through the UNIFAC activity coefficient model, and the repulsive contribution to the pore potential was incorporated through the Steele 10-4-3 potential model. The mean micropore network coordination number for each carbon was also determined from the fitted saturation capacity based on percolation theory. Good agreement between the model and the experimental data was observed. In addition, excellent agreement between the bimodal gamma pore size distribution and density functional theory-cum-regularization-based pore size distribution obtained by argon adsorption was also observed, supporting the validity of the model. The results show that liquid phase adsorption, using adsorptive molecules of different sizes, can be an effective means of characterizing the pore size distribution as well as connectivity. Alternately, if the carbon pore size distribution is independently known, the method can be used to measure critical molecular sizes. (C) 2001 Elsevier Science.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips’s work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case. © 2004 American Institute of Physics.

Moisture sorption isotherms and isosteric heat determination in Chilean papaya (Vasconcellea pubescens)

The moisture sorption isotherms of Chilean papaya were determined at 5, 20, and 45 ºC, over a relative humidity range of 10-95%. The GAB, BET, Oswin, Halsey, Henderson, Smith, Caurie and Iglesias-Chirife models were applied to the sorption experimental data. The goodness of fit of the mathematical models was statistically evaluated by means of the determination coefficient, mean relative percentage deviation, sum square error, root-mean-square error, and chi-square values. The GAB, Oswin and Halsey models were found to be the most suitable for the description of the sorption data. The sorption heats calculated using the Clausius-Clapeyron equation were 57.35 and 59.98 kJ·mol-1, for adsorption and desorption isotherms, respectively.

Enthalpy-entropy compensation based on isotherms of mango

Moisture equilibrium data of mango pulp were determined using the static gravimetric method. Adsorption and desorption isotherms were obtained in the range of 30-70 ºC, to water activities (a w) from 0.02 to 0.97. The application of the GAB model to the experimental results, using direct nonlinear regression analysis, provided agreement between experimental and calculated values. The net isosteric heat of sorption was estimated from equilibrium sorption data, using the Clausius-Clapeyron equation. Isosteric heats of sorption were found to increase with increasing temperature and could be well adjusted by an exponential relationship. The enthalpy-entropy compensation theory was applied to sorption isotherms and plots of deltaH versus deltaS provided the isokinetic temperatures, indicating an enthalpy controlled sorption process.

Effect of drying method on the adsorption isotherms and isosteric heat of passion fruit pulp powder

The sorption behavior of dry products is generally affected by the drying method. The sorption isotherms are useful to determine and compare thermodynamic properties of passion fruit pulp powder processed by different drying methods. The objective of this study is to analyze the effects of different drying methods on the sorption properties of passion fruit pulp powder. Passion fruit pulp powder was dehydrated using different dryers: vacuum, spray dryer, vibro-fluidized, and freeze dryer. The moisture equilibrium data of Passion Fruit Pulp (PFP) powders with 55% of maltodextrin (MD) were determined at 20, 30, 40 and 50 ºC. The behavior of the curves was type III, according to Brunauer's classification, and the GAB model was fitted to the experimental equilibrium data. The equilibrium moisture contents of the samples were little affected by temperature variation. The spray dryer provides a dry product with higher adsorption capacity than that of the other methods. The vibro-fluidized bed drying showed higher adsorption capacity than that of vacuum and freeze drying. The vacuum and freeze drying presented the same adsorption capacity. The isosteric heats of sorption were found to decrease with increasing moisture content. Considering the effect of drying methods, the highest isosteric heat of sorption was observed for powders produced by spray drying, whereas powders obtained by vacuum and freeze drying showed the lowest isosteric heats of sorption.

Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

Moisture sorption isotherms of fresh and blanched pumpkin (Cucurbita moschata)

Moisture desorption isotherms of fresh and heat blanched pumpkins (Cucurbita moschata) were determined at three temperatures (30, 50 and 70 °C), using the standard, static-gravimetric method. The GAB, Oswin, BET, Halsey, and Henderson models were tested and, with the exception of the Henderson model, showed satisfactory fits to the experimental data. The GAB model was used to analyze the fitting ability to describe the isotherm type. The shape of the desorption isotherms of fresh and blanched pumpkin at 30 and 50 °C was intermediate to types II and III, and at 70 °C it was of type II for the blanched pumpkin and close to type II for the fresh sample. The influence of blanching on the decrease in equilibrium moisture was very small compared to the fresh samples and it was related to the loss of soluble solids during the pre-treatment. The isosteric heat of sorption measures indicated that a larger amount of heat was required to remove the water from the fresh samples than from the blanched ones.

Study of adsorption isotherms of green coconut pulp

Brazil is considered one of the largest producers and consumers of tropical fruits. Green coconut (Cocos nucifera L.) stands out not only for its production and consumption, but also for the high amount of waste produced by coconut water industry and in natura consumption. Therefore, there is a need for utilization of this by-product. This study aims to study the adsorption isotherms of green coconut pulp and determine its isosteric heat of sorption. The adsorption isotherms at temperatures of 30, 40, 50, 60, and 70 °C were analyzed, and they exhibit type III behavior, typical of sugar rich foods. The experimental results of equilibrium moisture content were correlated by models present in the literature. The Guggenheim, Anderson and De Boer (GAB) model proved particularly good overall agreement with the experimental data. The heat of sorption determined from the adsorption isotherms increased with the decrease in moisture content. The heat of sorption is considered as indicative of intermolecular attractive forces between the sorption sites and water vapor, which is an important factor to predict the shelf life of dried products.

Estimating oceanic heat content change using isotherms

This paper presents a new analysis of ocean heat content changes over the last 50 yr using isotherms by calculating the mean temperature above the 148C isotherm and the depth of the 148C isotherm as separate variables. A new quantity called the ‘‘relative heat content’’ (‘‘RHC’’) is introduced, which represents the minimum local heat content change over time, relative to a fixed isotherm. It is shown how mean temperature and isotherm depth changes make separable and additive contributions to changes in RHC. Maps of RHC change between 1970 and 2000 show similar spatial patterns to a traditional fixed-depth ocean heat content change to 220 m. However, the separate contributions to RHC suggest a more spatially uniform contribution from warming above the isotherm, while isotherm depth changes show wind-driven signals, of which some are identifiable as being related to the North Atlantic Oscillation. The time series show that the warming contribution to RHC dominates the global trend, while the depth contribution only dominates on the basin scale in the North Atlantic. The RHC shows minima associated with the major volcanic eruptions (particularly in the Indian Ocean), and these are entirely contributed by mean temperature changes rather than isotherm depth changes. The depth change contributions to RHC are strongly affected by the recently reported XBT fall-rate bias, whereas the mean temperature contributions are not. Therefore, only the isotherm depth change contributions toRHCwill need to be reassessed as fall-rate-corrected data become available.

Mutant alleles at the rugosus loci in pea affect seed moisture sorption isotherms and the relations between seed longevity and moisture content

Pea (Pisum sativum L.) mutant near-isogenic lines (RRrbrb, rrRbRb, rrrbrb) with lower starch but higher lipid contents, brought about by lesions in the starch biosynthetic pathway, had seed moisture sorption isotherms displaced below that of the wild type (RRRbRb). The negative logarithmic relationship between seed longevity and seed storage moisture content (%, f.wt basis), determined in hermetic storage at 65 degreesC, also differed: longevity in the mutant near-isogenic lines was poorer and less sensitive to moisture content than in the wild type (i.e. C-w was lower). The low-moisture-content limit (m(c)) to this relation also differed, being lower in the mutant near-isogenic lines (5.4-5.9%) than in the wild type (6.1%). In contrast, all four near-isogenic lines showed no difference (P >0.25) in the negative semilogarithmic relationship between equilibrium relative humidity (ERH) and seed longevity. It is concluded that the effect of these alleles at the r and rb loci on seed longevity. was largely indirect; a consequence of their effect on seed composition and hence on moisture sorption isotherms. However, this explanation could not be invoked at moisture contents below mc where differences in longevity remained substantial (RRRbRb double that of rrrbrb). Hence, these mutant alleles affected seed longevity directly at very low moisture contents.

Mutant alleles at the rugosus loci in pea affect seed moisture sorption isotherms and the relations between seed longevity and moisture content

Pea (Pisum sativum L.) mutant near-isogenic lines (RRrbrb, rrRbRb, rrrbrb) with lower starch but higher lipid contents, brought about by lesions in the starch biosynthetic pathway, had seed moisture sorption isotherms displaced below that of the wild type (RRRbRb). The negative logarithmic relationship between seed longevity and seed storage moisture content (%, f.wt basis), determined in hermetic storage at 65 °C, also differed: longevity in the mutant near-isogenic lines was poorer and less sensitive to moisture content than in the wild type (i.e. CW was lower). The low-moisture-content limit (mc) to this relation also differed, being lower in the mutant near-isogenic lines (5.4–5.9%) than in the wild type (6.1%). In contrast, all four near-isogenic lines showed no difference (P >0.25) in the negative semi-logarithmic relationship between equilibrium relative humidity (ERH) and seed longevity. It is concluded that the effect of these alleles at the r and rb loci on seed longevity was largely indirect; a consequence of their effect on seed composition and hence on moisture sorption isotherms. However, this explanation could not be invoked at moisture contents below mc where differences in longevity remained substantial (RRRbRb double that of rrrbrb). Hence, these mutant alleles affected seed longevity directly at very low moisture contents.

Can carbon surface oxidation shift the pore size distribution curve calculated from Ar, N(2) and CO(2) adsorption isotherms? Simulation results for a realistic carbon model

Using the virtual porous carbon model proposed by Harris et al, we study the effect of carbon surface oxidation on the pore size distribution (PSD) curve determined from simulated Ar, N(2) and CO(2) isotherms. It is assumed that surface oxidation is not destructive for the carbon skeleton, and that all pores are accessible for studied molecules (i.e., only the effect of the change of surface chemical composition is studied). The results obtained show two important things, i.e., oxidation of the carbon surface very slightly changes the absolute porosity (calculated from the geometric method of Bhattacharya and Gubbins (BG)); however, PSD curves calculated from simulated isotherms are to a greater or lesser extent affected by the presence of surface oxides. The most reliable results are obtained from Ar adsorption data. Not only is adsorption of this adsorbate practically independent from the presence of surface oxides, but, more importantly, for this molecule one can apply the slit-like model of pores as the first approach to recover the average pore diameter of a real carbon structure. For nitrogen, the effect of carbon surface chemical composition is observed due to the quadrupole moment of this molecule, and this effect shifts the PSD curves compared to Ar. The largest differences are seen for CO2, and it is clearly demonstrated that the PSD curves obtained from adsorption isotherms of this molecule contain artificial peaks and the average pore diameter is strongly influenced by the presence of electrostatic adsorbate-adsorbate as well as adsorbate-adsorbent interactions.

Adsorption Isotherms for Removal of Linoleic Acid from Ethanolic Solutions Using the Strong Anion Exchange Resin Amberlyst A26 OH

Adsorption isotherms for the removal of linoleic acid from aqueous ethanol were measured using a strong anion exchange resin (Amberlyst A26 OH). The data for linoleic acid were compared with previously published results for oleic acid. The equilibrium data were correlated using the Langmuir and Freundlich isotherms. Lower average deviations between experimental and calculated results were obtained with the Langmuir model. The capacity of the resin for adsorbing linoleic acid was evaluated at different water contents in ethanol, 100 w = 0.50 to 15.27, and at 298.15 K. The water content in ethanol does not influence significantly the equilibrium behavior, and the strong anion exchange resin has a good performance in the removal of linoleic acid from the liquid phase.

Effect of chemical treatment on the mechanical properties, water vapour permeability and sorption isotherms of gelatin-based films

Proteins contain hydrophilic groups, which can bind to water molecules through hydrogen bridges, resulting in water vapour adsorption. An increase in the degree of cross-linking can be a method to improve the cohesiveness force and functional properties of protein-based films. Thus, the objective of this work was to evaluate the effect of chemical treatment of gelatin with formaldehyde and glyoxal on the mechanical properties, water vapour permeability (WVP) and water vapour sorption characteristics of gelatin-based films. Films were produced using gelatin, with and without chemical treatment. The formaldehyde treatments caused a significant increase in the tensile strength and a reduction in the WVP of films. The Guggenheim-Anderson-De Boer and Halsey models could be used to model the sorption isotherms of films. It was observed that an increase in temperature produced a decrease in water sorption, and the chemical modifications did not affect the monolayer moisture content. Copyright (c) 2007 John Wiley & Sons, Ltd.