Bulk ligand concentration

Equation (15) dictates, for example, that at a mean or bulk ligand concentration of L = KD, a 10% fluctuation in local ligand concentration... 

It has been previously suggested that the addition of cholesterol to the phospholipid membranes increases the availability of the DNP ligand to antibodies in the bulk solution.38 Significantly, we see here that the effect is much larger at lower ligand concentrations then it is at high ligand concentrations. 

The adsorptive stripping response (of the surface-confined species) is directly related to its surface concentration, with the adsorption isotherm - commonly that of Langmuir - providing the relationship between the surface and bulk concentrations of the adsorbate. As a result, calibration curves display an initial linear portion, followed by a curvature, and a leveling off at high concentrations. The response is dependent upon numerous other variables that affect the extent of adsorption, including the electrolyte, pH, accumulation potential and time, convection rate, and ligand concentration. 

In the true dissociative mechanism the reaction should involve an intermediate of reduced coordination number. The rate of substitution should be almost independent of nature of entering ligand. The rate of exchange of solvent molecules from the inner coordination sphere to the bulk should ideally equal the rate of formation of a liganded complex. (The rate of reaction should be independent of the ligand concentration. The latter statement need not always be true however. Consider for example the process... 

Figure 7.1 Distribution of complexes in the bulk of solution (a) and in the adsorption layer (b) versus the total ligand concentration. The first and the second variants of simulations (see text) are presented by full and doted lines, respectively.

On the other hand, bulk concentrations are required for estimation of the respective surface concentrations that are the terms of kinetic equations. To obtain the data for the solution layer adjacent to the electrode surface, mass transport of chemically interacting species should be considered. Quantitative formulation of this problem is based on differential equations representing Pick s second law and supplemented with the respective kinetic terms. It turns out that some linear combinations of these equations make it possible to eliminate kinetic terms. So produced common diffusion equations involve total concentrations of metal, ligand and proton donors (cj j, c, and Cj4, respectively) as functions of time and space coordinates. It follows from the relationships obtained that the total metal concentration varies in the same manner as the concentration of free metal ions in the absence of ligand. Simultaneously, the total ligand concentration remains constant within the whole region of the diffusion layer. This proposition also remains valid for proton donors and acceptors. 

Figure 5a indicates the effect of the CTAB concentration on the rate constants of the complexes of 38b and 38c. In the case of the water soluble 38b ligand, the rate increases with increasing CTAB concentration up to a saturation level. This type of saturation kinetics is usually interpreted to show the incorporation of a ligand-metal ion complex into a micellar phase from a bulk aqueous phase, and the catalytic activity of the complex is higher in the micellar phase than in the aqueous phase. In the case of lipophilic 38c, a very similar curve as in Fig. 4 is obtained. At a first glance, there appears to be a big difference between these two curves. However, they are rather common in micellar reactions and obey the same reaction mechanism 27). 

In addition to the interactions discussed above, which all depend in part on the ioniz-ability, or at least polarizability, of the surface and the adsorbates, hydrophobic parts of ligands may bind to corresponding parts of surfaces. Thus, if a metal ion is complexed or irreversibly bonded to a hydrophobic molecule, the metal may be incorporated into the bulk or surface of a particle via hydrophobic interaction between the molecule and the solid phase. Such interactions may be quantitatively significant in systems with high concentrations of dissolved and particulate organic matter. 

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