Electrostatics, different formulations

Such small particles usually are generated by air-jet micronization and less frequently by controlled precipitation or spray drying. As bulk powder, they usually tend to be very cohesive and exhibit poor flow and insufficient dispersion because of large interparticle forces such as van der Waals and electrostatic forces (Zeng et al. 2001 Podczeck 1998 Hickey et al. 1994). The control of sufficient powder flow and deaggregation (dispersion) is thus of utmost importance to ensure efficient therapy with a dry-powder aerosol. Two different formulation approaches are used currently in marketed DPI preparations to fulfill the requirements. Most often, coarse particles of a pharmacologically inactive excipient, usually a-lactose monohydrate, are added that act as a carrier and provide sufficient powder flow to the mixture. Other carbohydrates, amino acids, and phospholipids have been suggested frequently (Crowder et al. 2001). 

Because the various SCM s have different formulations for treating adsorption reactions and the electrostatic terms, parameters fit to one model may not he applicable to other models (Morel et al, 1981). For example, Gao and Mucci (2001) determined different Log K s for As(V) adsorption by goethite when the data were fit to the Constant Capacitance Model, the Basic Stem Model, and the Triple Layer Model. 

In the virial methods, therefore, the activity coefficients account implicitly for the reduction in the free ion s activity due to the formation of whatever ion pairs and complex species are not included in the formulation. As such, they describe not only the factors traditionally accounted for by activity coefficient models, such as the effects of electrostatic interaction and ion hydration, but also the distribution of species in solution. There is no provision in the method for separating the traditional part of the coefficients from the portion attributable to speciation. For this reason, the coefficients differ (even in the absence of error) in meaning and value from activity coefficients given by other methods. It might be more accurate and less confusing to refer to the virial methods as activity models rather than as activity coefficient models. 

Note that Gp 0p of eq. (9) can be written in several equivalent but different looking forms, as is typical of electrostatic quantities in general. For example, it is often convenient to express the results in terms of the electrostatic scalar potential ( )(r) instead of the electric vector field E(r). In the formulation above, the dielectric displacement vector field associated with the solute charge distribution induces an electric vector field, with which it interacts. In the electrostatic... 

At the potential of zero charge, the difference in electrostatic inner potential,. d c, across the electrode interface is related to the difference in outer potential, /lippK, between the free surface of metal electrode and the fi surface of aqueous solution as formulated in Eqn. 5-14 and shown in Fig. 5-14 ... 

Nevertheless, the data in Table 3.5 reveal an important difference between classical hydrogen bonding and dihydrogen bonds. In fact, since in O- - -H conventional bonds the electrostatic component is followed by charge transfer energy while the polarization contribntion iipL is very small, classical hydrogen bonds can be formulated as... 

In the 2-level limit a perturbative approach has been used in two famous problems the Marcus model in chemistry and the small polaron model in physics. Both models describe hopping of an electron that drags the polarization cloud that it is formed because of its electrostatic coupling to the enviromnent. This enviromnent is the solvent in the Marcus model and the crystal vibrations (phonons) in the small polaron problem. The details of the coupling and of the polarization are different in these problems, but the Hamiltonian formulation is very similar. ... 

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