Mieczyslaw Jaroniec

Thermodynamics of gas adsorption on fractal surfaces of heterogeneous microporous solids

Thermodynamic equations are derived for physical adsorption of gases and vapors on fractal surfaces of heterogeneous microporous solids. The influence of surface geometry on gas adsorption on a microporous solid is studied by analyzing the dependence of the differential molar enthalpy ΔH, the immersion enthalpy ΔHim, and the differential molar entropy ΔS on the fractal dimension D, which is used to characterize the surface irregularity. It is shown that −ΔH, −ΔHim, −ΔS, and the average adsorption potential A increase as the fractal dimension of the surface accessible for adsorption increases. The dependence of these thermodynamic quantities on the fractal dimension D is attributed to the fact that the fraction of small micropores in microporous solids increases as the fractal dimension D increases.

Selectivity of alkylamide bonded-phases with respect to organic acids under reversed-phase conditions

It was shown previously by Czajkowska et al. [J. Chromatogr. A, 691 (1995) 217] that alkylamide phases are better for separating pyridinecarboxylic acids than conventional alkyl packings. They allow separation of these compounds from hydrophobic substances over a wide range of mobile phase compositions. In the current work the retention data for pyridinedicarboxylic acids were measured on monomeric and polymeric alkylamide phases at 35 degrees C by using the acetonitrile-water eluent and utilized to calculate the nonspecific (methylene) and specific (carboxylic and amine) selectivities. Subsequently, the selectivity data were plotted against the pH of the mobile phase. It was shown that while the methylene selectivity does not change much at the pH range from 2 to 5, the specific selectivities studied depend strongly on the pH of the mobile phase. The magnitude of this dependence is determined by the type of the bonded phase and silica support as well as the length of the terminal alkyl groups.

Gradient optimization in elution liquid chromatography : I. Theoretical considerations connected with evaluation of the concentration-time function for stepwise elution

Abstract Using the theoretical treatment of Jandera and Churacek, problems connected with evaluation of the concentration-time function are discussed. It is shown that the linear relationships of the type capacity factor versus concentration of the more efficient eluting component in the binary-solvent mobile phase, measured for different chromatographed compounds, can be used to predict the concentration-time function for stepwise elution with a mobile phase of constant composition in each step.

Statistical thermodynamics of adsorption from multicomponent liquid mixtures on heterogeneous solid surfaces

The statistical thermodynamics of adsorption from multicomponent liquid mixtures on heterogeneous solid surfaces is discussed by assuming the cell adsorption model and ideal adsorbed phase.Two integral representations for the adsorption isotherm are proposed: one based onn-dimensional energy distribution function (i.e., each adsorption site is characterized by adsorption energies of all components), and the other based on distribution of differences of adsorption energies ofn-1 components in relation to adsorption energy of the chosen component (i.e., each adsorption site is characterized byn-1 differences of adsorption energies of the components in relation to adsorption energy of the chosen component).The expressions for differential adsorption heat for adsorption from binary liquid mixtures have been derived from both integral equations.ZusammenfassungDie statistische Thermodynamik der Adsorption von aus mehreren Komponenten bestehenden flüssigen Mischungen auf heterogenen festen Oberflächen wird für das Modell der Zellenadsorption bei ideal adsorbierter Phase diskutiert.Zwei Integraldarstellungen der Adsorptionsisotherme werden vorgeschlagen: eine auf einen-dimensionale Verteilungsfunktion der Energie gestützte (das heißt, jede Adsorptionsstelle wird durch Adsorptionsenergien von allen Komponenten charakterisiert); die andere basiert auf der Verteilung der Unterschiede von Adsorptionsenergien dern-1-Komponenten in bezug auf die Adsorptionsenergie der ausgewählten Komponente (das heißt, jede Adsorptionsstelle wird durchn-1-Unterschiede charakterisiert. Formeln für differentiale Adsorptionswärmen für die Adsorption aus binären flüssigen Mischungen sind von beiden Integral-Gleichungen abgeleitet worden.

Gradient optimization in elution liquid chromatography : II. Theory of multi-step elution with a mobile phase of constant composition in each step

Abstract Equations describing multi-step elution with a mobile phase of constant composition in each step have been derived. These equations are very useful for calculating the concentration-time function if the experimental relationships between the capacity factors and the concentration of the more efficient eluting component in the binary-solvent mobile phase are known for different sample compounds.

Dependence of the capacity ratio on the composition of the binary mobile phase in liquid—solid adsorption chromatography

Abstract The dependence of the capacity ratio on the composition of the binary mobile phase is discussed in terms of Snyders treatment. The relationships obtained for the capacity ratio have been tested on experimental data. The derivation of the relationship for the capacity ratio discussed by Jandera and Churacek has been examined.

Multilayer adsorption from multicomponent liquid mixtures on solid surfaces

Multilayer adsorption of multicomponent liquid mixtures on homogeneous and heterogeneous solid surfaces is discussed. Heterogeneity effects of the adsorbent surface have been taken into account in calculation of mole fractions of the components in the first adsorbed layer. The model calculations, illustrating multilayer and heterogeneity effects, have been performed for adsorption of ternary liquid mixtures.ZusammenfassungEs wird die Mehrschichtadsorption auf homogenen und heterogenen Oberflächen diskutiert. Bei der Berechnung der Molbrüche der Komponenten der ersten adsorbierten Schicht wurden Heterogenitäts-Effekte berücksichtigt. Die Modellrechnungen wurden an ternären flüssigen Mischungen vorgenommen.

Correlation between the fractal dimension and the microporous structure of a solid

SummaryA theoretical description of gas adsorption on heterogeneous microporous solids is compared with that based on the fractal nature of these solids. It is shown that the structural parameters of a microporous solid correlate with the fractal dimension that characterizes the geometrical irregularities of microporous solids. Numerical studies performed for model solids with different degrees of microporosity show that the root-mean-square value of micropore size depends linearly on the fractal dimension.ZusammenfassungEine theoretische Beschreibung der Gasadsorption an heterogenen mikroporösen Feststoffen wird mit der auf der Bruchstruktur dieser Körper basierenden verglichen. Es wird gezeigt, daß die Strukturparameter eines mikroporösen Feststoffs mit den Bruchdimensionen, die die geometrischen Ungleichmäßigkeiten des mikroporösen Körpers charakterisieren, in Korrelation zu setzen sind. Numerische Untersuchungen an Modellfeststoffen mit verschiedenem Grad an Mikroporosität zeigen, daß die Wurzel aus den mittleren Quadraten der Mikroporengröße linear mit der Bruchdimension verknüpft ist.

Gas adsorption on structurally heterogeneous microporous solids

Isotherm equations for gas adsorption on microporous adsorbents are derived for four distribution functions that characterize the structural heterogeneity of the solids. Since these functions represent the size distributions of micropores, they are physically meaningful for describing gas adsorption on heterogeneous microporous solids. Presentation of relationships between the distribution functions describing either structural or energetic heterogeneity of a solid increases the utility of previous distribution functions for characterization of microporous adsorbents.

Application of a partially mobile model of monolayer adsorption to multilayer phenomena

Two multilayer adsorption models are discussed, assuming partially mobile adsorption in the first layer, and theBET orKim-Oh (KO) mechanisms for formation of higher layers. The theoretical multilayer adsorption isotherms corresponding to these models have been calculated for differing degrees of mobility of the first layer.ZusammenfassungZwei Mehrschicht-Modelle, bei der Annahme einer partiell mobilen Adsorption der Erst-Schicht, und desBET, bzw.Kim-Oh (KO) Mechanismus für die Ausbildung höherer Schichten, werden diskutiert. Die theoretischen Mehrschicht-Adsorptionsisothermen, die diesen Modellen entsprechen, werden für verschiedene Grade von Mobilität der ersten Schicht berechnet.