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Adsorption

One of the most effective for finding relationships between the molecular structure and the thermodynamic characteristics of adsorption, the semi-empirical molecular-statistical theory of adsorption, has been developed for more than 40 years. The theory is based on the use of atom-atom potentials (AAP) - the energies of interaction of sorbent atoms with sorbate atoms.

According to the AA method, the potential adsorption energy Ф is represented as the sum of the interaction energies of each atom of the adsorbate molecule with each atom of the  sorbent. The form of the potential function and its parameters are determined empirically.

According to the molecular statistical theory, Henry's constant is defined as an integral of the distribution function of adsorbed molecules over position and rotation angles. For adsorbents with a mathematically homogeneous surface, the potential field does not depend on the coordinates describing the surface of the adsorbent, but depends only on the distance from the surface. The integrand in the case of an isotropic adsorbent surface obviously does not depend on the angle of rotation of the molecule relative to the perpendicular to the surface.

The values of the potential function are determined by the atomic structure of the molecule, its structural formula; they also depend on the equilibrium distance, which, in turn, depends on the Euler angles that determine the orientation of the molecule relative to the adsorbent surface. The nature of the latter dependence is determined by the shape of the molecule.

An important advantage of this theory is that the actual geometric structure of the molecule, determined from electron diffraction data or built on the basis of regularities in changes in bond angles and bond lengths, is used in the calculation of retention values. In the case of isomers, calculations of the thermodynamic characteristics of adsorption based on real data on the geometric structure of molecules often turn out to be the only reliable criterion for their identification.

Molecular-statistical calculations have received the greatest development for the system "graphitized thermal soot (GTS) - hydrocarbons and their derivatives". The interest in this adsorbent is due to the fact that HTS has a uniform, flat surface, the geometry and chemistry of which have been studied in sufficient detail. GTS, a good model sorbent, has accumulated extensive experimental data on the adsorption of organic compounds of various classes. The main reason for the development and improvement of molecular-statistical calculations on HTS is that adsorption on its surface is extremely sensitive to the structure of molecules and makes it possible to separate geometric isomers. The combination of molecular-statistical calculations and data from chromato-mass-spectrometric studies in most cases makes it possible to unambiguously identify individual isomers in their complex mixtures.

Below is a flowchart for calculating Henry's constant using the molecular statistics method. The shaded element of the scheme indicates its frequent absence in modern methods, which is their obvious drawback.

Despite the external fundamentality and universality, the possibilities of the discussed approach are very limited. This is especially evident when identifying isomers in their mixtures: sometimes the calculation predicts the order in which the isomers emerge from the HTS column, which does not coincide with the experimentally observed one. The reason for this is the difference between the AA parameters for the atoms included in the molecule under study and the parameters found using the reference molecules. Attempts are made to explain the variability of the AA parameters by a change in the nearest environment of the atom or its valence state, which manifests itself in a change in its polarizability. However, the root of the problem lies in the very principle of additivity of atomic contributions to the energy of a molecule. The depravity of this principle is well known, nevertheless, it is applied in the absence of another, more reasonable rule of sums.

Thus, the molecular-statistical method in the given version, which is widely used in modern literature, has a number of disadvantages:

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  • AARP principle;

  • empiricism in choosing the potential of intermolecular interaction;

  • the absence of a term with differential heat capacity in the adsorption energy.

 

In view of the great need in chromatography to apply the theoretical knowledge of adsorption to the study and identification of complex or similar substances, more rigorous approaches are coming to the fore, allowing calculations of van der Waals characteristics ab initio. However, the existing non-empirical quantum-mechanical theories either do not describe real systems that are irresistibly complex for them, or use assumptions (approximations) that give a strong error in the calculation of intermolecular interactions.

So, modern methods of modeling adsorption and related chromatography are either more or less substantiated methods of interpolation of experimental data, or rather rough theoretical approximations that are not capable of predicting the adsorption behavior of molecules.

The approach we describe is based on the molecular-statistical method, which is undoubtedly the most effective in solving the problem. To avoid the disadvantages noted above, this approach is supplemented by the theory of generalized charges (instead of the AA principle), on the basis of which the potential of intermolecular interaction of the Lennard-Jones type is derived, and the differential heat capacity in the adsorption energy is taken into account. The generalized charges participate not only in the expressions for the potential energy of adsorption, but also determine the differential heat capacity of adsorption and the molecular area. The sum rule following from the theory of generalized charges, as well as other consequences of this theory, became the basis for a new approach to adsorption that does not require empirical corrections.

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