Wychodząc z ogólnego wyrażenia na kanoniczną sumę stanów mobilnej jednoskładnikowej monowarstwy adsorpcyjnej przedstawiono kolejne etapy procesu formułowania równania adsorpcji gazu na homogenicznej powierzchni stałego adsorbentu. Szczegółowo omówiono sposób wyprowadzenia całki konfiguracyjnej proponowanego modelu podkreślając rolę zarówno przyciągania jak i odpychania pomiędzy zaadsorbowanymi cząsteczkami. Zmodyfikowano wyrażenie na prawdopodobieństwo znalezienia molekuły w określonym punkcie powierzchni adsorbentu uzależniając tę wielkość od koncentracji adsorbatu. Wyrażenia na tzw. efektywną powierzchnię adsorbentu otrzymano adaptując dwuwymiarowe analogi równań stanu sztywnych kul, odpowiednio van der Waalsa (2D-vdW) oraz Reisa-Frischa-Lebowitza (2D-RFL). W rezultacie wyprowadzono dwa nowe równania adsorpcji różniące się szczegółami dotyczącymi odpychania adsorbat-adsorbat. Każde z tych równań poddano analizie teoretycznej w aspekcie dwuwymiarowych przejść fazowych. W obu przypadkach wykazano, że proponowane rozwiązanie dopuszcza możliwość wystąpienia dwóch przemian fazowych pierwszego rodzaju, to jest kondensacji gaz-ciecz oraz krzepnięcia, ciecz-ciało stałe. Weryfikację przedstawionej koncepcji uzupełniono opisem literaturowych danych doświadczalnych otrzymując bardzo dobrą zgodność teorii z eksperymentem.
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The subsequent stages of the process of formulation of the equation for gas adsorption on a homogenous surface of a solid adsorbent were presented based on the general expression for the canonical ensemble of the mobile single-component adsorption monolayer. The method of formulating the configuration integral of the proposed model was discussed in detail where the role both of the attraction and repulsion between adsorbed molecules was emphasised. The expression for the probability of finding a molecule in a specified point on a surface of an adsorbent was modified by determining its magnitude by the adsorbent concentration. The expression for the so-called effective surface of the adsorbent was obtained by adapting a two-dimensional analogue equation of state hard spheres – Van der Waals equation (2D-vdW) and Reis-Frisch-Lebowitz equation accordingly (2D-RFL). As a result, two new adsorption equations were formulated which differ in detail concerning the adsorbate-adsorbate repulsion. On each of these equations theoretical analysis was performed in terms of two-dimensional phase transformation. In both cases it was proved that the proposed solution allows for the presence of two-phase transformations of the first type which is the gas-liquid condensation and solidification liquid-solid. The verification of the given approach was supplemented by the description of the experimental data given in reference literature and by obtaining a very good correlation between the theory and experiment.
Methods for obtaining optically active compounds in enantiopure form are commonly classified into three categories: utilization of chiral pool starting materials (stereoselective multistep synthesis), creation of chirality from achiral precursors (asymmetric synthesis) and separation of racemates into their enantiomer constituents (crystallization, chromatography on chiral phases, kinetic resolution). The most important method for the separation of enantiomers is the crystallization. The crystallization can be carried out in the variants: direct crystallization of enantiomer mixtures (homo- and heterochiral aggregates – Scheme 2, 3) and separation of diastereoisomer mixtures (classical resolution) (Scheme 1) [1–5]. The most widely used method for the separation of enantiomers rests on the crystallization of diastereoisomers formed from a racemate and an enantiopure reagent – resolving agent (resolution via salt-formation and complex-formation). The pair of diastereoisomers exhibit different physicochemical properties (e.g., solubility, melting point, boiling point, adsorbtion, phase distribution). For this reason, the crystalline material can be separated from the residue by filtration (Scheme 22) [4, 27], distillation (Scheme 23, 24) [28, 29], sublimation (Scheme 25) [4, 30], or extraction (Scheme 26) [2, 31]. The composition of crystalline diastereoisomers is influenced by resolving agent (structure (Scheme 4) [4] and amount of resolving agent (Scheme 5) [4]), structure of racemates (Scheme 10) [2, 15], the character and amount of supplementary additives (Scheme 6–9) [4, 12–15], nature of the solvent (crystallization with solvent) – Scheme 11–18 [2, 4, 16–23] and time of crystaillzation (Scheme 19–21) [4, 14, 25, 26].
The enantioseparation of a racemate through diastereomeric salt formation with a resolving agent is one of the most attractive methods for obtaining an enantiopure compound, with advantages such as its simplicity in operation, recyclability of the chiral source, and applicability on an industrial scale. In this method the enantiomers are converted into a diastereomeric salt pair by reaction with a single enantiomer of resolving agent. The diastereomers are then separated by crystallization taking advantage of the different solubility of the two compounds [1–3]. The formation of diastereomers, to be separated afterward, usually consists of salt formation with a resolving agent of opposite acide-base character (Scheme 1, 9). In this process, the molecules of opposite character (amine and acid) recognize each other by various interactions on the basis of their molecular structures and functional groups [3]. Using this method can be obtained a series of enantiomerically pure amines (Scheme 2–8) [4–26] and acids (Scheme 10–17) [27–41] which may be valuable substrates for asymmetric synthesis. The conditions for enantioseparation play an important role. On the efficiency of the enantioseparation has an effect the resolving agent, nature of the solvent or just its dielectric constant and the character and amount of some supplementary additives.
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