Hybrid Closure

The following hybrid closure was proposed by Advani and Tucker (1990)  

The hybrid closure is exact when the fibers are in both random state and perfect alignment. It however tends to accelerate the orientation transients in transient shearing flows. 

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It also needs to be mentioned that, in Bay s work, the hybrid closure was used to model the data. With this closure, the values of C/ were found around 0.01 to match the experimental an values. However, if one uses the orthotropic closure, the data are matched with C/ = 0(0.001). Therefore, it is important to notice that, although the measured values of an are irrelevant to any closure schemes, the data of Cl, and hence the coefficients of the empirical equation (5.25), depend on the closure-scheme chosen. 

To solve the orientation tensor equation (Equation [3.31]), a closure approximation equation is needed to replace the fourth-order orientation tensor by a function of the second orientation tensor. A widely accepted one is the hybrid closure approximation (Advani, 1990b) whereas many other closure approximations have been recently proposed (Cintra and Tucker, 1995). 

An alternative approach to determining the degree of fiber orientation without having to solve Eq. (12.32) has been suggested (Advani and Tucker 1987 Folgar and Tucker 1984), namely, a hybrid closure approximation that may cover the entire range of orientation with the form... 

A systematic effort to correlate ease of ring closure with the stereoelectronic requirements of the transition state has been developed by Baldwin and co-workers. They classify ring closures with respect to three factors (a) ring size, (b) the hybridization of the carbon at the reaction site, and (c) the relationship (endocyclic or exocyclic) of the reacting bond to the forming ring. Certain types of ring closures are found to be favorable whereas others are unfavorable for stereoelectronic reasons. The relationships are summarized in Table 3.12. 

Just one reaction has been described where lithiated methoxyallene 42 reacted with bicyclo[3.2.0]heptenone 175 to form the triquinane derivative 176 via a tandem oxy-Cope-transannular ring closure sequence (Eq. 8.31) [111]. However, cycloocta-none 177 was isolated as a major product, which is unusual since other alkenyl-lithium compounds and 175 provide only triquinanes. The authors assumed that the additional sp2-hybridized C-atom in the eight-membered ring intermediate (eno-late of 177) induces a conformation which is less susceptible to transannular ring closure. 

Frankel, S.H., T.-L. Jiang, and P. Givi. 1992. Modeling of isotropic reacting turbulence by a hybrid mapping-EDQNM closure. AIChE J. 38(4) 535-43. 

Two substrates of special interest are 2-(2-hydroxyethoxy)-3-nitro-thiophene and its 3-(2-hydroxyethoxy)-2-nitro isomer. Both compounds form Meisenheimer-type spiro adducts, 135 and 136, by ring closure at the 2-and 3-positions, respectively.177 Intramolecular cyclization brings in an extra driving force for the formation of the adduct, which is also observed in the trinitrobenzene series.31 This would account for the structure of adduct 136, which exceptionally bears the sp3-hybridized carbon on a ft position. No other examples of such a structure from 5-membered heteroaromatic substrates is known even for transient species, except for benzoannelated derivatives (see Section III,A,3). 

The Michael-type addition of an aniline to an unsaturated ester, generated in situ, provided an example of a type a ring closure in which the electrophilic center is sp2-hybridized <2004BML4147>. This reaction represents a synthetically useful procedure to access tetrahydro-1,4-benzodiazepines. 

The type d ring closure to access monocyclic 1,4-diazepines is typically accomplished by uniting a nucleophilic nitrogen atom with an electrophilic carbon atom examples, where the latter is in either an spz or an sp3 hybridization state, have been described. 

Other developments include the introduction of hybrid lines resistant to glyphosate and glufosinate. Glyphosate-resistance technology was rapidly adopted for soybean, but was more slowly adopted for field corn due to corn s slower canopy closure. Acceptance of glufosinate-resistant weed control technology faced the same obstacles, but has been even less competitive economically due to product cost. 

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