Application of the vacancy solution theory to describe the enthalpic effects accompanying mixed-gas adsorption

The possibility of utilizing vacancy solution theory (VST) to study the enthalpic effects accompanying mixed-gas adsorption equilibria is presented. Besides heterogeneity, the interaction effects by using the regular adsorbed solution, Flory-Huggins, and Wilson models of nonideality in the adsorbed phase are taken into account. To predict adsorption phase diagrams and calorimetric effects in the mixed-gas adsorption system, only a knowledge of the single-gas adsorption isotherms and accompanying calorimetric effects is required. The possibility of simplification of the obtained theoretical expressions is shown. The obtained agreement between theory and experiment is very satisfactory.     

Application of a single model to study the adsorption kinetics of prednisolone on six carbonaceous materials

The knowledge of the adsorption processes of nonelectrolytes from liquid solution on solid materials involves the study of their kinetic and equilibrium aspects as well as the understanding of their thermodynamic functions. However, in most published papers adsorption isotherms are analyzed by using the Giles classification and other proposed equations which are either empirical or based on kinetic or thermodynamic criteria. Our opinion is that both the kinetic and the equilibrium studies must be complementary and that, in general, equations describing the adsorption isotherms come from the kinetic laws governing the different partial processes which determine the global process. These kinetic laws may be derived from single models. In this paper a single model is proposed, which makes it possible to establish a kinetic law satisfactorily fitting a great number of C (concentration) vs t (time) isotherms. This model has been applied to study the adsorption process of prednisolone by six carbonaceous materials from ethanol solution, the specific adsorption rate, and the activation thermodynamic functions being calculated. The results obtained have also been used to analyze the influence of the intraparticle diffusion on the kinetics of the process.     

Application of the NRTL method to correlate solubility of diosgenin

Using the synthetic method, the solubility of diosgenin in 1-hexanol and 1-heptanol was measured at temperatures from 300 K to 329 K by a laser monitoring observation technique at atmospheric pressure. The solubility data were correlated by semi-empirical equations, such as the Apelblat equation, λh model and the ideal model, which agreed well with experimental results. The fusion enthalpy and the melting point determined by differential scanning calorimeter (DSC), are −34064.2 J · mol⁻¹ and 207.09 °C for diosgenin. With collection of over 14 solvents from different references, the NRTL thermodynamic model as one of the activity coefficient models was used to correlate and predict the solubility of diosgenin. The solubility calculated for all solvents showed good agreement with the experimental results within the temperature range studied. Additionally, the solubility of diosgenin in 14 solvents is also investigated at T = 308.15 K, the results of which indicated that solubility of diosgenin in n-alkanols tends to increase with increasing alkanol chain length from methanol to 1-heptanol and n-alkanols presented higher solubility than heterogeneous alcohols for diosgenin, such as 1-butanol > isobutyl alcohol > tert-butanol and 1-propanol > isopropanol. It also shows that solubility of diosgenin decreases with the increasing polarity of solvents. Its corresponding (solid + liquid) equilibrium data will provide essential support for industrial design and further detailed theoretical studies.     

A new approach to the adsorption kinetics of gas mixtures on heterogeneous surfaces

An attempt is made to develop a general theory for describing the adsorption kinetics of gaseous mixtures on heterogeneous surfaces. This can be made by generalization of the equations obtained for equilibrium adsorption of gas mixtures.

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Modeling the kinetics of gas adsorption in multilayer porphyrin films

A kinetic model is proposed to describe the diffusion and adsorption behavior of gas in multilayer films. Numerical solutions are attained on time scales of seconds using a finite differencing approximation to the kinetic equations. Predictions of this model are compared to experimental data for the case of NO2 diffusing through a porphyrin film. The model predicts a binding energy for the NO2 porphyrin interaction of 0.72 eV. It also predicts that for this system diffusion is the limiting factor for the adsorption response time of the film, although the recovery time is determined by both the diffusion coefficient and NO2 binding energy. Comparison with experiment gives a predicted diffusion coefficient of approximately 10(-14) m2.s-1.     

Continuum composition models to describe multicomponent reaction kinetics

Some principles of the construction of kinetic models for multicomponent processes of oil-refining and petrochemistry are suggested in terms of the continuum mixture composition concepts. The results of computer simulation of industrial gasoline fraction hydrocracking processes are presented.

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Multilayer adsorption equilibrium model for gas adsorption on solids

Adaptation of the ENSIC model to physisorption of nitrogen or argon on a solid surface first led to a 3 parameters model called multilayer adsorption equilibrium model (MAE model). One of these parameters is related to the formation of a multilayer of adsorbate on the solid surface. Exploitation of data from the literature pointed out that this parameter does not depend on the nature of the solid surface and an average value was calculated in the case of N₂ and Ar. As a consequence, the MAE model can be considered as a 2 parameters model. Linearization of the model was established allowing an easy determination of surface areas of macroporous and some mesoporous solids. Fitting of isotherms of meso and macroporous solids has led to promising results compared to the ones obtained with the BET model. Moreover, adaptation of this model to microporous solids can also be used for an uncomplicated determination of porous volume and external surface. Results obtained from data of the literature were close to those obtained with the t-plot model.     

Cellular model for zeolite gas adsorption thermodynamics

Zeolite structures allow one to use a cellular adsorption model of liquid type, which can be used to describe adsorption for a gas mixture in which adsorption forms differing in orientation can arise for molecules of a single kind, which may be accompanied by dissociative or multicentered adsorption, in which an adsorbate molecule occupies several adjacent centers. General adsorption-isotherm equations have been derived together with expressions for the major integral and differential thermodynamic functions (free and internal energies, entropy, and specific heat) in gas-mixture adsorption in the cellular model. The adsorption isotherms in it give a one-to-one correspondence between the gas composition and that in the adsorption layer at all temperatures and degrees of filling, so they can be used for regular-lattice adsorbents, but only outside the critical region.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 5, pp. 584–589, September–October, 1988.     

Study on protein adsorption kinetics to a dye-ligand adsorbent by the pore diffusion model

Adsorption kinetics of bovine serum albumin (BSA) and bovine hemoglobin (bHb) to Cibacron Blue 3GA (CB) modified Sepharose CL-6B has been studied. The effects of liquid-phase ionic strength and CB coupling density on the uptake rates of these two proteins in Tris-HCl buffer (pH 7.5) were evaluated by effective pore diffusivity derived from a pore diffusion model. The results showed that despite their similar molecular masses and sizes, the effects of aqueous-phase ionic strength and CB density on the effective pore diffusivities of BSA and bHb were distinctly different. The effective pore diffusivity of BSA to CB-Sepharose increased significantly with decreasing CB density and increasing liquid-phase ionic strength. This was considered due to the decrease in electrostatic repulsion between the BSA and CB molecules of like charge. That is, the increase in ionic strength and the decrease in CB coupling density reduced the electrostatic hindrance effect on BSA diffusion to CB-Sepharose, facilitating the hindered pore diffusion. In contrast, because of the higher isoelectric point of bHb (7.0) compared to BSA (4.7), bHb suffered little electrostatic hindrance effect during its diffusion to CB-Sepharose. Therefore, the effective pore diffusivity of bHb was unchanged with the change in liquid-phase ionic strength and CB coupling density.     

Use of theory of multimolecular adsorption at heterogenous surfaces to describe the adsorption of hydrocarbon on polymeric sorbents

Theoretical and Experimental Chemistry -     

222Rn gas diffusion and determination of its adsorption coefficient on activated charcoal

The adsorption coefficient is the fundamental parameter characterizing activated charcoal"s ability to adsorb ²²²Rn. The adsorption coefficient is determined for ²²²Rn activated charcoal detectors. In addition, a diffusion and adsorption model is developed for the transport of ²²²Rn in a porous bed of activated charcoal. These processes can be described by parabolic second order differential equation. The equation is numerically solved using the finite differences method. With this model, the ²²²Rn activity adsorbed in the detector is calculated for diverse situations.     

A model to describe the settling behavior of fractal aggregates

A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200x, which can capture images of particles/flocs down to 2 microm in diameter was used. The performance and technique of the settling rig were validated by comparing the measured settling rates of 30- and 50.7-microm standard particles with their theoretical settling rates calculated using Stokes' law. The measured settling rates were within 10% agreement with the calculated Stokes' velocities. The settling rates and sizes of the particles/flocs were analyzed using image analysis software called WiT 5.3. The maximum temperature gradient across the settling column was 0.1 degrees C, which effectively eliminated convective currents due to temperature differences in the settling column. A total of 1000 calcium phosphate flocs were analyzed. Calcium phosphate flocs with fractal dimensions varying from 2.3 to 2.8 were generated via orthokinetic aggregation. Measurements of fractal dimensions, using light scattering, were done simultaneously with the settling experiments and they were found to be constant. The fractal dimensions calculated using the model agreed with those obtained by light scattering to within 12%.     

Gas adsorption in active carbons and the slit-pore model 1: Pure gas adsorption

We describe procedures based on the polydisperse independent ideal slit-pore model, Monte Carlo simulation and density functional theory (a 'slab-DFT') for predicting gas adsorption and adsorption heats in active carbons. A novel feature of this work is the calibration of gas-surface interactions to a high surface area carbon, rather than to a low surface area carbon as in all previous work. Our models are used to predict the adsorption of carbon dioxide, methane, nitrogen, and hydrogen up to 50 bar in several active carbons at a range of near-ambient temperatures based on an analysis of a single 293 K carbon dioxide adsorption isotherm. The results demonstrate that these models are useful for relatively simple gases at near-critical or supercritical temperatures.     

Applying structural transition theory to describe enzyme kinetics in heterogeneous systems

Enzyme action was investigated by assuming the occurrence of different states of enzyme-substrate affinities. These states were considered to involve enzyme species with distinct abilities to form reaction product. The results obtained showed strong agreement with the experimental data for the action of peroxidase. This approach provides a powerful tool for predicting the kinetic behavior of other enzymatic processes in conditions not described before. An additional feature of this approach is the ability to characterize processes at any enzyme-substrate concentration ratio, including high enzyme-substrate ratios and enzyme inhibition by substrate or product. This proposal can also be used in systems with heterogeneity concerning the investigated enzyme.     

Application of the LBET class models to describe the structure of microporous activated carbons on the basis of argon and benzene adsorption isotherms

The reported research is concerned with the properties of the new LBET class models designed to describe the heterogeneous adsorption on microporous carbonaceous materials. In particular, the new adsorption models were applied to a computer analysis of the microporous structure of two active carbons on the basis of argon and benzene adsorption isotherms. This paper provides for more thorough information on the properties of the proposed models and identification technique presented in the earlier papers.     

Modification of the NRTL model for ternary and quaternary liquid-liquid equilibrium calculations

The original NRTL model is modified for the correlation of ternary liquid-liquid equilibria. The ternary expression of the modified NRTL model includes three additional ternary parameters and the ternary terms vanish when a ternary system degenerates to a binary. The ability of the modified NRTL model has been evaluated in the calculations of ternary vapor-liquid-liquid equilibria and quaternary liquid-liquid equilibria.     

Analysis of a chemostat model with variable yield coefficient: Tessier kinetics

We investigate a chemostat model in which the growth rate is given by a Tessier expression with a variable yield coefficient. We combine analytical results with path-following methods. The washout conditions are found. When washout does not occur we establish the conditions under which the reactor performance and reactor productivity are maximised. We also determine the parameter region in which oscillations may be generated in the reactor. We briefly discuss the implications of our results for comparing the performance of a single bioreactor against a cascade of two bioreactors.     

Thermodynamical model and prediction of gas/solid adsorption isotherms

A thermodynamic model of gas/solid adsorption has been constructed from two elements. One of those is the original Gibbs equation. The second is functions psi(theta) or psi(P) calculable from measured isotherms. The model provides the possibility of calculating the relative change in free energy of the surface, and based on the model, implicit isotherm equations of general validity and in integral form can be derived. The prediction of isotherms can be made based on characteristic adsorption functions (CAFs). The CAFs concentrate in one function all measured isotherms having the same change in relative free energy of the surface. From CAFs any isotherm can be predicted if one measured point is known or one required datum of the isotherm can be defined. The maximum average deviation between the measured adsorbed amounts and those calculated from the CAFs is +/-10%. The CAFs are very sensitive to the internal structure of adsorbents (micro-, meso-, and macropores and nanostructures). It is the goal of future investigations to determine the exact connections related to the CAFs and to the structure of adsorbents.