Associated-solution model assumptions

The most popular chemical theory postulates stoichiometric chemical species that interact accordingly as a regular solution (regular associated-solution model). The associated-solution model is based usually on the following assumptions ... 

In Section 3.2 the ideal solution model was introduced. The essential assumption of the ideal model is that there is no energy change associated with rearrangements of the atoms A and B. In other words the energies associated with a random distribution of A and B atoms and a severely non-random distribution, in which the A and B atoms are clustered, are equal. 

The matter discussed in sec. 2.3 concerned the phenomenology of adsorption from solution. To make further progress, model assumptions have to be made to arrive at isotherm equations for the individual components. These assumptions are similar to those for gas adsorption secs. 1.4-1.7) and Include issues such as is the adsorption mono- or multlmolecular. localized or mobile is the surface homogeneous or heterogeneous, porous or non-porous is the adsorbate ideal or non-ideal and is the molecular cross-section constant over the entire composition range In addition to all of this the solution can be ideal or nonideal, the molecules may be monomers or oligomers and their interactions simple (as in liquid krypton) or strongly associative (as in water). 

The sequence of models used in these studies constituted a progression from a simple analytical model of the convection-dispersion type with fixed parameters, associated with the assumption of a semi-infinite homogenous profile, to a convection-dispersion numerical model, which incorporated dynamic water and solute movement through a multilayered profile. In brief, the sequence was as follows (a) one-dimensional analytical model with an upper boundary... 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

It is important to note that in formulating the problem in this way, it is a linear formulation, guaranteeing (within the bounds of the assumptions made) a global optimum solution. The potential problems associated with nonlinear optimization have been avoided. Even though the models are nonlinear, the problems associated with nonlinear optimization have been avoided. The approach can use either shortcut models or detailed models and the linearity of the optimization is maintained. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

Still another aspect with a bearing on the selectivity of anion binding of real host-guest systems, that is commonly not addressed when using complementarity models, stems from the crude assumption that the association of the anion host with its target guest is the only relevant and accountable process in solution. This implies that all other ingredients of the system are inert and... 

A stabilization model proposed for AMDH by Zaccai et al. (1989) accounts for all of the observations on the stability of this protein and on its solution structure. It is based on the fact that the AMDH solution particles are different in the different solvents in which the enzyme is active, and on the reasonable assumption that the bound water and salt molecules are not associated separately with the polypeptide but as hydrated salt ions. 

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