Stern region

The propulsor, in a steady situation, has to provide the thrust equivalent to the resistance of the ship. The prediction of this balance between ship resistance and propeller thrust is a complex process because the water flow in the stern region of the ship interacts with the flow through the propeller. The ship resistance may be modified by the action of the propeller, while the propeller efficiency usually is influenced by the disturbed flow regime near the stern of the ship. 

Micellar catalysis, conducted in the absence of Lewis acid tends to inhibit the Diels-Alder reaction, relative to the reaction in water. The reason is that the local reaction medium in the Stern region is less favorable than bulk water. However, by combining Lewis-acid and micellar catalysis, enzyme-hke rate accelerations can be obtained (Table 7.5) in case the Lewis acid acts as the counterion for the miceUe. " ... 

For spherical micelles, one of the more commonly accepted models for the micellar structure is that proposed by Gruen (Fig. 1). This model features a rather sharp interface between a dry hydrophobic hydrocarbon core and a region filled with surfactant headgroups, part of the counterions (for ionic surfactants), backfolding surfactant tails, and water, namely, the Stern region. In the remainder of this chapter, intramicelle volumes with specific features such as the Stern region and the hydro-phobic core will be referred to as zones. ... 

Table 1 Calculated salt concentrations in the micellar Stern region of selected surfactants...

Both the Menger-Portnoy model and the model by Berezin were effectively derived on the assumption that micellar solutions contain two pseudophases, namely the micellar pseudophase and bulk water. However, both models can be expanded to take more than one micellar pseudophase into account. For example, this could be done when the micellar pseudophase is seen to consist of two separate pseudophases (zones) itself, namely a pseudophase corresponding to the hydrophobic core and a pseudophase corresponding to the micellar Stern region. " If one then assumes a reaction to occur with a rate constant k in the Stern region while the reaction does not occur in the micellar core, the expression for k includes the distribution of the reactant over different zones [Equation (6)]. " ... 

Here, k is the rate constant for hydrolysis in the Stern region, Fstem and Fmic are the volumes of the Stern region and of the micelle, respectively, AvS and Pm are the water-to-Stern region and water-to-micelle partition coefficients, respectively. Equation (6) shows that, for the assumptions described above, the micellar rate constant is given by the rate constant for the reaction in the Stern region, multiplied by a factor representing the distribution of the reactant within the micelle. Further subdivision of the micellar pseudophase is (mathematically) possible " " " but may not be warranted. 

For the first case, one can use the so-called pseudophase ion exchange (PIE) model.The PIE model is based on the Menger-Portnoy model but additionally allows for ion exchange to occur in the micellar Stern region where a reactive counterion competes with nonreactive counterions (Scheme 5). 

Because the majority of reactants appears to bind to micelles in the micellar Stern region (vide supra), we will focus on this zone. A number of approaches has been... 

A particularly successful approach in probing the micellar Stern region was developed by the group of Romsted, who realized that the dediazoniation of substituted arenediazonium ions results in the rate-determining production of highly reactive (and rather unselective) aryl cations which will react at a diffusion controlled rate even with weak nucleophiles such as chloride anions and urea (Scheme 7). 

With respect to the reduced water concentration (1), it seems as if all but one of the hydrolysis reactions following the mechanism shown in Scheme 10 are retarded in micellar solutions (the exception being the hydrolysis of 4-nitrophenyl chloroformate la in cationic micelles ) and the lower water concentration in the micellar Stern region (estimated to be 45 mol dm for and 33 mol dm for SDS ) will... 

The lower polarity of the mieellar Stern region (2) is also widely thought to make a signifieant eontribution to the rate retarding effects of micelles in fact, the transition state of the type of hydrolysis reactions commonly used to probe the micellar pseudophase is thought to be more polar than the reactants, indicating that a more polar medium would be favorable for reaction to occur. 

Not surprisingly, it is rather difficult to separate the different contributions of the different interactions as they occur in the micellar Stern region. In an attempt to solve this problem, the group of Engberts used a series of hydrolysis reactions of activated esters and amides to probe the reaction environment offered by micelles. The reactions initially involved the water-catalyzed pH-independent hydrolysis reactions of i-methoxy-phenyl dichloroacetate 4 and l-benzoyl-3-phenyl-l,2,4-triazole 5, as extensive information on the rate retarding effects of added cosolutes on this reaction was available. ... 

Table 2 Molalities m and concentrations c of 1-propanol and tetramethylammonium bromide (TMAB) in solutions mimicking the Stern regions of DTAB and CTAB micelles...

Literature on reactions involving micellar counterions is particularly rich and for good reasons. The local concentration of counterions in the micellar Stern region is extremely high compared to typical aqueous solutions. As a result, bimolecular reactions involving bases such as hydroxide and acetate or oxidants such as perchlorate can be accelerated significantly by using these as a counterion for cationic surfactants. Discussion here will be restricted to a selected number of relatively recent examples of particular interest. This should not, however, distract from the merit of many of the other publications in this field. 

Finally, as an example of the effect of ion-pairing of surfactant counterions with co-moving ions, the reaction of methyl 4-nitrobenzenesulfonate with Br was accelerated when the concentration of Br in the Stern region was increased through the appropriate choice of cation. 

One other aspect of nonprimitive electric double layer theories which is particularly relevant to the inner Stern region are the models for the water molecule and the ions. The simplest models for a water molecule and an ion are a hard-sphere point dipole and point charge, respectively. A more realistic model of the hard-sphere water molecule would include quadrupoles and octupoles and also polarizability. However the hard-sphere property is best avoided and replaced, for example, by a Lennard-Jones potential. An alternative to a multipolar water model are three point charge sites associated with the atoms within the water molecule. 

Stern [4] introduced the concept of the nondiffuse part of the double layer for specifically adsorbed ions, the remainder being diffuse in nature this is shown schematically in Figure 7.4, where the potential is seen to drop linearly in the Stern region, and then exponentially. Grahame distinguished two types of ions in the Stern plane, namely physically adsorbed counterions (outer Helmholtz plane) and chemically adsorbed ions that lose part of their hydration shell (inner Helmholtz plane). 

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