A. V. Larin

On the interrelation between the Henry constant and retention parameters in chromatography

The relations between the Henry adsorption constant and the parameters of the output elution curve are analyzed based on an exact solution of the direct problem concerning the dynamics of adsorption. The solution is obtained in terms of the model of an equilibrium adsorption layer using the integral representation of the γ-function. Direct proportionality is shown to take place between the Henry constant and the time coordinate of the output curve center of gravity. A linear dependence is revealed between the time corresponding to the output curve center of gravity and the corrected retention time or the time corresponding to the maximum in the output curve determined via the relative length of an adsorbent layer. Recommendations are formulated for the measurement and calculation of the Henry constant in chromatography applying short adsorption layers.

The effect of input pulse duration on the elution curve profile

Numerical simulation and new analytical solutions have been used to study the effect of the duration of the input pulse of an adsorbate on the development of the elution curve profile in the adsorption dynamics. Elution curves calculated with regard to finite input pulse duration have been compared with those determined for the instantaneous injection of an adsorbate in the absence of extracolumn broadening. Quantitative regularities of variations in curve parameters measured as the time corresponding to the maximum of the curve and its width at a fixed height as depending on the length of an adsorbent layer have been estimated. The influence of the input pulse duration on the statistical moments of the elution curve has been determined, with the obtained moments being in agreement with the published solution that was previously found using the Laplace transformations. Correspondence between the theoretical and experimental data has been revealed for argon elution from a helium flowing through an activated carbon layer.

Functions of moments in the elution dynamics of adsorption

An exact solution obtained for the direct problem concerning the elution dynamics of adsorption in terms of the model of an equilibrium adsorption layer using the gamma function is analyzed. Analytical expressions derived for the functions of moments comprise adsorbent layer lengths, mobile phase velocities, and adsorption constants. The functions are found to be interrelated via the slope coefficients of linear equations. The correctness of the results obtained is confirmed by good agreement between the theory and experimental data presented as tabulated values of the moments measured previously for the elution dynamics of Freon 13B1 adsorption on active carbon layers of different lengths.

On the correct measurement of retention and Henry constant on short adsorbent layer

In the discrete model of an equilibrium adsorption bed, the solution of the elution dynamics of adsorption (chromatography) was obtained, which differs greatly from the known direct proportionality between the length of the retention and adsorbent layers. In the novel solution, the retention is linearly dependent on the length of an adsorbent layer, which requires one to define an additional kinetic parameter, namely, the relative length (efficiency) of an adsorbent layer. The methods are suggested to estimate the efficiency of an adsorbent layer based on the parameters of a breakthrough curve and the substantiation is given for the correct calculation of the retention and Henry constant on the adsorbent layers of short length. The discrete theory is amplified with a continuous solution that uses a gamma function. The derived relations can serve as a basis for developing the chromatographic methods for measuring the adsorption Henry constant at small amounts of solid granular materials.

On calculation of the effectiveness of a low-length adsorbent layer

The exact solution of elution linear dynamics of adsorption (chromatography) representing the ratio of the subintegral function of gamma function to the actual Euler gamma function is analyzed. A new equation for calculation of performance of a low-length column is substantiated when an addend in the form of an additional constant is introduced into the known expression determining the number of plates. Additional constants are calculated for three levels of the peak height that little differ from each other and are ∼1.1. The obtained results are compared to the experimental elution curve of trifluorochrloromethane on a low-length active carbon layer and good agreement is found between the theory and experiment.

Effect of component ratio of binary organic solvent on sorption of phenols by silica

Chromatography is employed to measure the adsorption constants of hydroxybenzenes on SiO2 in a low-concentration region at varied compositions of a binary organic solvent (n-hexane-ethyl acetate). It is shown that the Henry constants vary depending on the polar-to-nonpolar component ratio in the binary solvent and the number and position of hydroxyl groups in phenol molecules. It is found that the absolute values of changes Δ(ΔG) in the free energy considerably increase as the content of ethyl acetate in the mixtures diminishes, with the ratios between the Δ(ΔG) values of ortho-, meta-, and para-isomers remaining practically unchanged. The data obtained can be used to optimize the processes of the adsorption separation of mixed polyphenols and the isolation of natural phenolic compounds on a preparative scale.

Measurement of Adsorption Isotherm of Methanol on a Humidified Active Carbon by the Dynamic Method

Elution dynamics of the adsorption of methanol vapors on humidified active carbon is studied. Elution curves are obtained for the various lengths of adsorbent layer. The isotherm of adsorption of methanol–water vapor mixtures on active carbon is calculated, using the model of the equilibrium adsorption layer.

Adsorption of stilbenoids on silica

TLC, HPLC, and statistical methods are used to study the adsorption of stilbenoids from organic solvents on SiO2 in a wide range of concentrations. The dependence of adsorption of trans-stilbene hydroxy and methoxy derivatives on the nature of functional groups, their amount and position in the molecular structure, and also on the concentration and proton-acceptor properties of the polar component of the binary organic solvent is found. It is shown that experimental isotherms of stilbenoid adsorption on aerosil from the mixture of n-hexane and ethyl acetate are well approximated by the Freundlich equation. The adsorption of stilbenoids and phenols on SiO2 is compared. It is found that adsorption properties of phenols and hydroxystilbenes with a similar number of OH groups are practically similar.

Dynamics of the adsorption of freons

The elution adsorption dynamics of some adsorption systems (freon-active carbon) has been studied at two temperatures. The peculiarities of the adsorption dynamics, which are determined by the properties of the adsorption system, have been established. A possibility to calculating elution curves based on the equilibrium adsorption layer model is shown. Preliminary results of the influence of the parameters of the adsorption system on the coefficient of the effective kinetic model are obtained.

Temperature dependences of methane elution on a Cu3(BTC)2 metal-organic framework

Methane elution from a helium flow was studied on a metal-organic framework Cu3(BTC)2 with gas chromatography under temperatures from 20 to 60°C. Specific retention volumes were calculated, and heat of adsorption was determined. The obtained values are characteristic for the microporous adsorbents having relatively large micropores and a low total volume of the micropores. The calculated efficiencies of an adsorbent layer alter slightly and their absolute values are significantly smaller than those of the activated carbons. Efficient kinetic constant has a parabolic dependence on temperature with a minimum at 40°C. Correctness of the developed algorithms to calculate elution constants on adsorbent layers of small length has been confirmed.