Coulombic-Poisson-Boltzmann spherical cell model

10 Coulombic-Poisson-Boltzmann Spherical Cell Model 

In order to avoid the assumption of constancy of a (= 1 - P) in the PIE model, attempts have been made to calculate the concentradons of ions at the ionic micellar surface by the use of cell model, which involves the numerical solution of the Poisson-Boltzmann equation (PBE) under specific spherical cell boundary conditions. In this model, the distribution of counterions around an ionic nucellar surface is carried out in terms of coulombic interactions between the 

The validity of most of the assumptions involved in this model has not been tested rigorously. Furthermore, as with other micellar kinetic models, the success of this model is basically claimed on the basis of fairly low residual errors between experimentally determined rate constants (ko,s) and calculated rate constants (kcaicd) in terms of this model. Such a satisfactory statistical fit of observed data to such a micellar kinetic model is necessary for the apparent success of the model but is not sufficient to guarantee the reliability of the values of the calculated parameters from this model. Such a problem has been encountered in both PIE and MA-SB models.  

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Ion distribution around a spherical micelle can also be described with models that consider that polarizable and not very hydrophilic species (such as Br ) interact both coulombically and by a specific, noncoulombic, interaction [26]. This latter interaction allows the ion to intercalate at the micellar surface and to neutrahze an equivalent number of head groups. Ion distribution around a micelle is then calculated by solving the Poisson-Boltzmann equation (PBE) in the spherical symmetry with allowance for specific interactions via a Langmuir or Volmer isotherm [31]. The original kinetic treatment for a micelle of radius a, aggregation number iV in a cell of radius R yields [31] ... 

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