Calculation of the adsorption isotherm from solution on a nonporous adsorbent according to the adsorption isotherms of the components from the gas phase

Conclusions A solution of the problem of calculating the isotherm of excess adsorption from binary liquid solutions on a nonporous (or wide-pored) adsorbent according to the individual adsorption isotherms of the components from the gas phase and the phase diagram of the volume solution is given.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 3–6, January, 1973.     

Calculation of immersion enthalpy data from adsorption isotherms

The thermodynamic equations for the calculation of binary and ternary immersion data in excess formalism are presented. Immersion enthalpies and entropies of the n-hexane/n-octane, n-octane/n-tetradecane and n-hexane/n-tetradecane binary mixtures as well as the n-hexane/n-octane/n-tetradecane ternary mixture on activated carbon are calculated from the temperature dependence of adsorption isotherms. In order to evaluate the quality of the calculations, the calculated immersion enthalpies of the binary mixtures on activated carbon are compared with those that were measured calorimetrically. It is shown that phenomenological thermodynamics can be used successfully to predict calorimetric data on the basis of adsorption excess isotherms.     

Application of water-activated carbon isotherm models to water adsorption isotherms of single-walled carbon nanotubes

The objective of this study is to understand the interactions of water with novel nanocarbons by implementing semiempirical models that were developed to interpret adsorption isotherms of water in common carbonaceous adsorbents. Water adsorption isotherms were gravimetrically determined on several single-walled carbon nanotube (SWNT) and activated carbon samples. Each isotherm was fitted to the Dubinin-Serpinsky (DS) equation, the Dubinin-Astakov equation, the cooperative multimolecular sorption theory, and the Do and Do equations. The applicability of these models was evaluated by high correlation coefficients and the significance of fitting parameters, especially those that delineate the concentration of hydrophilic functional groups, micropore volume, and the size of water clusters. Samples were also characterized by spectroscopic and adsorption techniques, and properties complementary to those quantified by the fitting parameters were extracted from the data collected. The comparison of fitting parameters with sample characterization results was used as the methodology for selecting the most informative and the best-fitting model. We conclude that the Do equation, as modified by Marban et al., is the most suitable semiempirical equation for predicting from experimental isotherms alone the size of molecular clusters that facilitate adsorption in SWNTs, deconvoluting the experimental isotherms into two subisotherms: adsorption onto hydrophilic groups and filling of micropores, and quantifying the concentration of hydrophilic functional groups, as well as determining the micropore volume explored by water. With the exception of the DS equation, the application of other water isotherm models to SWNTs is not computationally tractable. The findings from this research should aid studies of water adsorption in SWNTs by molecular simulation, which remains the most popular tool for understanding the microscopic behavior of water in nanocarbons.     

On numerical classification of solution adsorption isotherms

To numerically classify solution adsorption isotherms, a difference or deviation measure, DS(mc) (the relative difference between two sums of the adsorption maximum's characteristics of selectivity isotherms x 100), is derived. The measure is applicable to completely miscible binary solutions on solids. This quantity evaluates the difference between an adsorption system and the ideal adsorption system (ideal adsorbed and bulk phases, homogeneous surface, and equal molar area solution components) at the point of maximum adsorption. For model systems, DS(mc)s are calculated at several levels of surface heterogeneity (Gaussian distribution of surface energy) and for different signs of phase nonideality (regular solution phases) on a homogeneous surface and on a simple two-site-type heterogeneous surface. All heterogeneous surfaces have negative DS(mc) values, but nonideal phases have DS(mc)s with signs opposite to the sign of deviation from Raoult's law. DS(mc)s from both U- and S-shape isotherms are reported for 16 experimental systems consisting of hydrocarbon mixtures and both alcohol + hydrocarbon and alcohol + water solutions or acetone + carbon tetrachloride on several silica gels and a variety of carbons.     

On the solution of diffusion controlled adsorption kinetics for any adsorption isotherms

Summary The problem of diffusion controlled adsorption kinetics is solved by application of an implicite difference method. Thereby all forms of adsorption isotherms can be used in the calculations. Computation examples are given concerning Langmuir, Freundlich, Volmer, Frumkin, and van der Waals isotherms.

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Zusammenfassung Es wird das Problem der diffusions-kontrollierten Adsorptionskinetik durch Anwendung eines impliziten Differenzenverfahrens gelöst. Dabei können bei der Berechnung alle Formen von Adsorptionsisothermen zugrunde gelegt werden. Rechenbeispiele für die Langmuir-, Freundlich-, Volmer-, Frumkin- und van-der-Waals-Isotherme werden angegeben.

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Nomenclature c concentration - c _o bulk concentration - D diffusion coefficient - x distance from the surface - t time - surface concentration - ₀ equilibrium surface concentration - saturation surface concentration - k _o/c _o - K ₁,K ₂ parameters of Henry and Freundlich isotherm with the dimension of a length - n parameter of Freundlich isotherm - a ₁,a ₂ interaction parameters - B ₁,B ₂,B ₃,B ₄ parameters of different isotherms with the dimension of a concentration - R gas law constant - T absolute temperature dimensionless parameters C c/c _o - / _o - X x/k - X step size ofX - Dt/k ² - step size of - _e time at - 0.95 Zentralinstitut für Organische Chemie,Bereich Grenzflhenaktive Stoffe, der Akademie der Wissenschaften der DDR, Berlin-AdlershofWith 6 figures and 1 table     

Calculation of the sticking coefficient in the case of the linear adsorption isotherm

The expression of the sticking coefficient for the linear adsorption isotherm was derived. The sticking coefficient is an increasing temperature function and directly related to the entropy factor. The limits of applicability of the derived equation are discussed.     

Optimum isotherm equation and thermodynamic interpretation for aqueous 1,1,2-trichloroethene adsorption isotherms on three adsorbents

Aqueous 1,1,2-trichloroethene (TCE) adsorption isotherms were obtained on Ambersorb^1® 563 and 572 adsorbents and Filtrasorb^2® 400 granular activated carbon (GAC). The data for Ambersorb 563 adsorbent covers TCE concentrations from 0.0009 to 600 mg/L. The data for each adsorbent was fit to 15 isotherm equations to determine an optimum equation.The best equation for the TCE adsorption isotherms is the Dubinin-Astakov (DA) isotherm. The DA isotherm coefficients were used to estimate the TCE micropore volume and the adsorption potential distribution. For each adsorbent, the TCE micropore volume is equivalent to the N₂ porosimetry micropore volume. The mean adsorption potential is 18.8, 13.0, and 8.9 kJ/mol, with coefficients of variation of 0.37, 0.53, and 0.67, for Ambersorb 563 and 572 adsorbents and Filtrasorb 400 GAC, respectively. Thus, Ambersorb 563 adsorbent has the most energetic and most homogeneous adsorption volume, while Filtrasorb 400 GAC has the least energetic and most heterogeneous adsorption volume. For these reasons, Ambersorb 563 adsorbent has the highest TCE capacity at low concentrations, whereas Filtrasorb 400 GAC has the highest TCE capacity at high concentrations. The performance of Ambersorb 572 adsorbent is generally intermediate to the other two adsorbents.     

Application of spline functions in calculating the surface excess isotherm according to the gibbs isotherm

Spline functions are proposed for computing the surface excess isotherms for the adsorption of 2-hydroxy-5-alkyl-benzophenone oximes at toluene/water and octane/water interfaces. The proper choice of boundary conditions, sub-intervals and type of the functions used to compute the first derivative is discussed. The spline functions give the values of the surface excess which can then be used in describing the kinetics and mechanism of copper extraction by hydroxyoximes.     

Empirical development of a binary adsorption isotherm based on the single-component isotherms in the framework of a two-site model

The adsorption behavior of mixtures of the enantiomers of 2,2,2-(trifluoro)-1-(9-anthryl)-ethanol (TFAE) on a quinidine carbamate bonded stationary phase was studied as an example of competitive binary adsorption on a Pirkle-type chiral adsorbent. A model of the adsorption isotherms is proposed and discussed. Binary adsorption isotherms derived by combination of the single-component isotherms of the two enantiomers in the framework of the classical bi-Langmuir model allow the correct prediction of the retention times of the elution bands of the components of binary mixtures but fail properly to predict the separation of the two enantiomers. Use of a quadratic model was needed to improve the agreement between calculated and experimental chromatograms of binary mixtures. The existence of a third type of adsorption sites besides the high-energy enantioselective and the low-energy nonselective sites was assumed. These sites have a low interaction energy, exhibit some affinity toward (S)-TFAE, but none toward (R)-TFAE.     

Substantiation of the method of an “ideal adsorption solution” for calculating the adsorption of binary vapor mixtures from the individual isotherms

Conclusions Substantiation was offered for the method of an ideal adsorption solution, which was proposed by Myers and Prausnitz to calculate the adsorption equilibrium of binary vapor mixtures with a solid adsorbent from the individual isotherms, for the particular case of adsorption systems for which is fulfilled the condition of an affinity of the adsorption isotherms of the vapor mixtures at a constant composition of the adsorption solution, and the condition of the additivity of the affinity coefficient of such a solution.Translated from Izvestiya Akademii Nauk SSSR, Seriya, Khimicheskaya, No. 1, pp. 171–173, January, 1972.     

Determination of the average heat and characteristic energy from the adsorption isotherm

The isotherms of the total content, isosteric and average heats of adsorption, as well as characteristic energies of adsorption were determined from the isotherms of excess adsorption of carbon dioxide on six different carbon adsorbents at temperature ranging from 293 to 423 К at pressures up to 6 MPa. The average isosteric heats are in agreement with the average heats of adsorption, which were determined from the equation relating the heat of adsorption with the characteristic energy of adsorption.     

Determination of the energetic topography of bivariate heterogeneous surfaces from adsorption isotherms

The reversible adsorption process occurring on patchwise heterogeneous bivariate surfaces is studied by Monte Carlo simulation and mean-field approximation. These surfaces are characterized by a collection of deep and shallow adsorbing patches with a typical length scale l. Patches can be either arranged in a deterministic chessboard structure or in a random way. Previous studies showed that the topography of a given surface can be obtained from the knowledge of the corresponding adsorption isotherm and a reference curve. In the present work, we discuss the advantages and disadvantages of using different reference curves. One of the main consequences of this analysis is to provide an improved method for the determination of the energetic topography of the surface from adsorption measurements.     

Neural network modelling of adsorption isotherms

This paper examines the possibility to use a single neural network to model and predict a wide array of standard adsorption isotherm behaviour. Series of isotherm data were generated from the four most common isotherm equations (Langmuir, Freundlich, Sips and Toth) and the data were fitted with a unique neural network structure. Results showed that a single neural network with a hidden layer having three neurons, including the bias neuron, was able to represent very accurately the adsorption isotherm data in all cases. Similarly, a neural network with four hidden neurons, including the bias, was able to predict very accurately the temperature dependency of adsorption data.