Reduced-strain closure

As experimental evidence has shown that the standard Folgar-Tucker model predicts a faster transient orientation evolution than that observed experimentally. Tucker et al. (2007), Wang et al. (2008) and Phelps and Tucker (2009) have proposed a new evolution equation, i.e., the so-called reduced-strain closure (RSC) model, to slow down the fiber orientation kinetics. Their approach is based on the spectral decomposition theorem. The theorem states that if T is a symmetric second-order tensor, then there is a basis e, i — 1, 2, 3 consisting entirely of eigenvectors of T and the corresponding eigenvalues Aj, i — 1, 2, 3 forming the entire spectrum of T, thus T can be represented by T = A,e,e,. 

A mixed cyclothiophene including phenylene units was synthesized by Tobe et al. [423], Macrocycle 4.55 (Chart 1.56) was made, which includes four alternating 2,5-thienylene and 1,3-phenylene units and is similar in shape to cyclo [8]thiophene 4.31. The meto-branched phenylene units helped to form the macrocycle and reduced strain energy, but interrupted the overall conjugation. The synthesis of a corresponding pyridine-containing macrocycle 4.56 was attempted, but the ring-closure reactions of penta- and heptacyclic precursors failed [424]. 

In Tsai [7], an elasticity solution for stresses in a pressurized thick cylindrical vessel is presented. In this analysis, the longitudinal bending deformation due to end closures is neglected, the formulation of the elasticity problem then reduces to a generalized plane strain analysis. The effects of material selection, layup sequence, and winding angles on the burst strength of thick multilayered cylinders are also addressed. 

We note that Pa = 0 in each case. Equation (77a) is Daly and Harlow s form, with slightly different constants. Equations (77b)-(77d) are suggested by the notion that interactions between the mean strain rate and fluctuation fields contribute to the pressure fluctuations. The closures Eqs. (77a) and (77b) were unsatisfactory. For the (T2) flow, Eq. (77c) with C4 = 5 works very well (Fig. 26c,d), but it is not adequate for the (C4) flow (Fig. 25c,d). Equation (77d) reduces to Eq. (77c) for irrotational mean flow, i.e. the (T2) flow, and with C4 = 5 and C5 = Eq. (77d) predicts the (C4) flow reasonably well (Fig. 25c,d). 

The Jacobson-Stockmayer cyclization theory is based on the assumption that all rings are strainless and that the conformational probability of ring closure is given by Eq. 3-2, i.e. conformational restrictions or preferences are absent. This assumption apparently cannot be fulfilled in real systems for small rings (as shown in Sect. 3.2.2). In some systems this leads to a lowering of the concentration of cydics when compared with their equilibrium concentration. This is because the probability of small ring closure is reduced due to the strain caused not only by bond angle deformation but also by bond opposition and transannular interactions. In such a case, as in the discussed earlier l,3-dioxolane-BF3 system, the concentration of small cycles (up to 25-30 bonds) is lower than the calculated one 141... 

To reduce the strain associated with cyclization, we next stndied acyclic piperidine precursors as nucleophiles to ultimately intercept the Mazzocchi, discovery, and cyanohydrin approaches. Diethyl glutaconate 35 coupled readily with fluoro-4-nitroarenes 30a or 30b to give 36 (95%, HPLC Scheme 3.12)." ° Again, however, ring closure to 37 did not proceed by either S Ar (36a, X = F) or palladium catalysis (36b, X = Br). The newly formed ally lie anion of 36 presumably delocalized into the nitroaromatic ring to generate electron-rich character inhibiting subsequent nucleophilic S Ar substitution or the oxidative addition required to enter palladium catalysis pathways. 

A synthesis of the 1,3,4,5-tetrahydropyrrolo-[3,3,2-de]quinoline ring, which appears in several natural products, was accomplished by using an indole ring closure. The cyclization would be expected to be disfavored by the strain which must be overcome in the ring closure. The successful approach was to construct the dihydroquinoline 48 which was then reduced to the amine 49. Cyclization to 50 occurred in 58% yield under acidic conditions. <94T7879>... 

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