Equilibria solvation/desolvation

Solvation—Desolvation Equilibrium. From the observation of migration of plasticizer from plasticized polymers it is clear that plasticizer molecules, or at least some of them, are not bound permanently to the polymer as iu an internally plasticized resia, but rather an exchange—equiHbrium mechanism is present. This implies that there is no stoichiometric relationship between polymer and plasticizer levels, although some quasi-stoichiometric relationships appear to exist (3,4). This idea is extended later ia the discussion of specific iateractions. 

The analyte solvation-desolvation equilibrium inside the column could be written in the following form ... 

Assuming that solvation-desolvation equilibrium is fast, we can express the overall retention factor of injected analyte as a sum of the retention factor of solvated form multiplied by the solvated fraction (9) and the retention factor of the desolvated form multiplied by the desolvated fraction (1-9), or... 

However, if the van t Hoff plots are linear, it indicates that the retention and/or selective processes governing the separation are unchanged over the temperature range studied. Furthermore, it can be assumed that a separation is a) thermodynamically reversible, b) (AH) and (AS) values are temperature independent, c) the enantiomers are retained in single associative mechanism, and d) a solvation-desolvation equilibrium does not obscure the association process of the enantiomers with the... 

Expression (4-36) shows that the solvated fraction of the analyte is dependent on the counteranion concentration and desolvation equilibrium parameter. 

The first example concerns systems where one or more solid phases exists in a state of equilibrium with a single vapor phase. This type of situation would exist for solvation/desolvation equilibria whose transition temperatures are substantially less than the fusion point corresponding to generation of a liquid phase, and it is certainly the most commonly encountered type of solvate system of pharmaceutical interest. For most compounds, the solid substance in question has no appreciable vapor pressure, so that the sole component of the vapor phase will be the volatile solvent. The usual occurrence where the evolved solvent passes entirely into the vapor phase will be assumed, where it does not form a discrete liquid phase of its own. 

Chaotropic Model. If the counteranion concentration is low, some analyte molecules have a disrupted solvation shell, and some do not due to the limited amount of counteranions present at any instant within the mobile phase. If we assume an existence of the equilibrium between solvated and desolvated analyte molecules and counteranions, this mechanism could be described mathematically [151]. 

This equation has three parameters ks is a limiting retention factor for solvated analyte, k s is a limiting retention factor for desolvated analyte, and K is a desolvation parameter [151], The description of the experimental results with function (4-39) is shown in Figure 4-50. Expression (4-39) in principle allows for the calculation of the solvation equilibrium constant from experimental chromatographic data. 

Conversions of a metastable phase into a more stable phase may include the transformation of one polymorphic phase into another, the solvation of an anhydrous phase, the desolvation of a solvate phase, the transformation of an amorphous phase into a crystalline anhydrate or solvate phase, the degradation of a crystalline anhydrate or solvate phase to an amorphous phase, or in the case of digoxin, the conversion of imperfect (less crystalline, more amorphous) crystals with a high density of defects into more perfect (more crystalline) crystals with a lower density of defects. While it is straightforward to determine the equilibrium solubility of a phase that is stable with respect to conversion, the measurement of solubilities of metastable phases that are susceptible to conversion is not a trivial matter. 

This theory also explains plasticization by nonsolvents (softeners). When introduced into the polymer mass, these molecules act by holding apart the polymer molecules and so breaking some unions between active centers on the polymer. It was also explained why internally plasticized systems behave worse with the temperature than the externally plasticized, since molecules of a separate plasticizer are free to solvate and desolvate the active centers on the resin macromolecules to a given extent, determined by the concentration, the temperature and the equilibrium involved in the system. Permanently bound side chains have no such freedom. Other properties such as the tear strength or the creep behavior of plasticized systems were also explained. 

Figure 1.12 Host-guest binding equilibrium showing the desolvation of both species required prior to the binding occurring. The final complex is still solvated but overall there are more free solvent molecules present, hence increasing the entropy of the system.

Thermodynamic or Mechanistic Theory. From the observation of migration of plasticized polymers it is clear that plasticizer molecules are not boimd permanently to the polymer, but rather a dynamic equilibrium exists between solvation and desolvation of the polymer chains by plasticizer. Different families of plasticizers are attracted to the pol5uner by forces of different magnitude but the attraction is not permanent. There is a continuous exchange where a plasticizer molecule becomes attached to an active group on the polymer chain only to be dislodged and replaced by another plasticizer molecule. 

When complexing the ligand with the lanthanide ion, many processes occur, including desolvation/solvation processes and successive formation of intermediate species Lanthanides Coordination Chemistry). In most cases, the complex is formed within seconds, with some exceptions such as l,4,7,10-tetraazacyclododecane-l,4,7,10-tetraacetic acid (DOTA) complexes. In the latter, the reaction is very slow and the equilibrium will take several days to establish. As a consequence, at room temperature, the solution will be stirred for more than 5 days, whereas on gentle warming of the solution, the delay can be reduced to half (this is the golden rule in kinetics on increasing the reaction fl om room temperature to 10 °C more, the rate should be increased by approximately a factor of two). 

The mechanism of plasticization is not completely understood. There are many theories aimed at explaining the specific interactions between the plasticizer and PVC, e.g., the gel theory, the grease theory, and the theory of equilibrium between the processes of solvation and desolvation. Based on the most recent studies, it is assumed that the plasticizer particles permeate into polymer chains during the swelling process. The... 

The first equilibrium shows an enthalpy change of —3.6 kJ/mol (1 M) and —6.3 kJ/mol (2 M), whereas for the second, the AH value is 17.1 kJ/mol. Although the overall effect of an increase in temperature would be to increase the ionic association because the second equilibrium is strongly endothermic, the exothermic nature of the first step is rather surprising because it involves the loss of two DMF molecules from the first solvation sphere of the lithium ion and the formation of only one Li —N03 bond. Furthermore, in the second step, the substitution of one molecule of DMF by one nitrate ion in the Li first solvation sphere has an enthalpy cost of 17.1 kJ/mol, which demonstrates that, as expected, the desolvation of the lithium ion is an endothermic process, which is partially compensated by the likely exothermic nature of the ion-pair formation. 

In summary, the synergy of experiment and theory extends from ion mobility studies to equilibrium studies covered here and provides important insight into energetic and structural aspects of fully desolvated, partially solvated, and—together with other methods—fully solvated biomolecules. 

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