Discrete functional group model

1 Discrete functional group model. The discrete functional group model makes the 

The study of Lovgren et al. (1987) provides an example of the application of a discrete functional group approach to model the complexation of aluminium with humic substances found in bog-water. The acid-base titration behaviour of the humic material found in Swedish bog-water was modelled as a diprotic acid with the following reactions and acid dissociation constants  

Combining the above expressions with the appropriate MBEs the complexation of aluminium with DOM as a function of pH can be calculated. 

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Electrostatic discrete functional group models. The development of charge on the surface of the humic macromolecule decreases the tendency to dissociate protons from the acid functional groups. To overcome this problem an electrostatic correction factor is introduced into the acid dissociation and complexation constants. This is similar to the approach adopted for the SCMs for inorganic surfaces. 

The model of Tipping et al. (1988) is an example of an electrostatic discrete functional group model. The effects of variable solution ionic strength and pH on the apparent surface acidity constants (polyelectrolyte effects) are accounted for by the incorporation of an electrostatic term exp(—2wzZ) in the equilibrium constants. A brief description of the model is given below. 

One example of this approach has been published by Sposito and coworkers (Sposito and Holtzclaw, 1977 Sposito et al., 1977), who have published proton binding data and a discrete ligand model for fulvic acids derived from sewage sludge. The experimental data, which appear to have been carefully obtained, contain some peculiar anomalies that are difficult to explain. For instance, when low fulvic acid concentrations are titrated with strong base, the low pH region of the titration curve indicates that some functional groups are reprotonated as base is added. Sposito and co-workers have attributed this phenomenon to counterion condensation. The same experimental observation was also reported by Perdue et al. (1980). 

When labeled polypeptides traveling down the axon are analyzed by SDS polyacrylamide gel electrophoresis, materials traveling in the axon can be grouped into five distinct rate components [6], Each rate component is characterized by a unique set of polypeptides moving coherently down the axon (Fig. 28-3). As specific polypeptides associated with each rate class were identified, most were seen to move only within a single rate component. Moreover, proteins that have common functions or interact with each other tend to be moved together. These observations led to a new view of axonal transport, the structural hypothesis [7]. This model can be stated simply proteins and other molecules move down the axon as component parts of discrete subcellular structures rather than as individual molecules (Table 28-1). 

In the second case, if the species mobilities differ greatly, the dimensionality of the system of kinetic equations decreases [103], Let all the components be divided into two groups of species a slow (5) and a rapid (r) one. This yields three types of pair functions. For the rapid species the condition of the equilibrium distribution can be considered as satisfied. Then, for the pair functions of types sr and rr instead of the kinetic Eqs. (32) algebraic relations in Appendix A apply, whose dimensionality can be lowered using the method of substitution variables according to Appendix B. In this case the kinetic Eqs (31) for the local concentrations and Eq. (32) for the pair functions type ss do not change. A similar situation remains in passing to the one-dimensional discrete and point-like models. 

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