Geometrical selection

The textures of polycrystalline aggregates formed by geometrical selection have been widely observed in natural minerals, but the principle has also been actively used in various synthetic methods. 

The most representative example is seen in the comb-like texture of quartz veins formed by the precipitation of quartz crystals on the wall of a vein from a hydrothermal solution that has entered into small fractures in the rocks (Fig. 8.2). 

If there is no epitaxial (coherent) relation between the substrate and the growing crystals, and the nuclei formed initially have completely random orientation, and the growth rate is more or less isotropic, geometrical selection operates in one direction only perpendicular to the substrate surface. When there is an epitaxial and coherent relation between the substrate and the crystals, and the growth rate 

When the substrate surface is curved or spherical, various textures of polycrystalline aggregate appear through geometrical selection. Spherulites will be formed when a sand grain or spherical polycrystalline aggregate formed at the early stage of nucleation acts as a substrate, and wavy banding parallel to the sub- 

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Suzuki S, Yamamura M, Hattori T et al (2007) The subunit composition of hinokiresinol synthase controls geometrical selectivity in norlignan formation. Proc Natl Acad Sci USA 104 21008-21013... 

Spherulites are formed if geometrical selection takes place on a spherical substrate particle. Substrate particles maybe a completely different material from those materials forming the spherulites, such as a sand grain, or a spherical particle of polycrystalline aggregate of the same species formed under a higher driving... 

Figure 8.3. Examples of banding patterns formed by geometrical selection in (a) malachite (b) rhodochrosite (c) agate.

Spherulite formation by geometrical selection may rarely be seen on crystals with isotropic Habitus. Native arsenic. As, occurs in a confeito-like form, and is a type of spherulite grown through the geometrical selection of rhombohedral crystals. Spherical aggregation of calcite crystals with nail-head Habitus is also observed. Semi-spherical aggregates of platy barite crystals known as desert rose are shown in Fig. 8.6. 

Fig. 1 Geometrical selectivity in the recognition of polyatomic anions by 71. Log K values of stability constants determined in an aqueous solution buffered at pH 8. Bite length refers to the distance of the two coordinating donor atoms of the ambidentate anion. Reproduced with permission from [49]...

Nishiyama T et al (2002) Reverse geometrical selectivity in glucuronidation and sulfation of cis- and trans-4-hydroxytamoxifens by human liver UDP-glucuronosyltransferases and sul-fotransferases. Biochem Pharmacol 63 1817-1830... 

This reaction also shows the importance of the entrance channel for the reaction and the resulting products, and it is the first evidence of product control of the reaction path using the geometrical selectivity achieved in van der Waals complexes. 

But with the establishment of thermoeconomic isolation plus the use of the correction factors mentioned above, minimization of the cost per transfer unit Yx becomes a precise criterion. It has already been shown above how the optimum value of the length and diameter of the tubes is obtained—as well as the optimum number of tubes per pass. Further synthesis of such heat exchangers results from minimizing YXrfAoptfUopt with respect to material and geometric selection factors. 

The acid or base elimination of a diastereoisomerically pure p-hydroxysilane, 1, (the Peterson olefination reaction4) provides one of the very best methods for the stereoselective formation of alkenes. Either the E- or Z-isomer may be prepared with excellent geometric selectivity from a single precursor (Scheme 1). The widespread use of the Peterson olefination reaction in synthesis has been limited, however, by the fact that there are few experimentally simple methods available for the formation of diastereoisomerically pure p-hydroxysilanes.56 One reliable route is the Cram controlled addition of nucleophiles to a-silyl ketones,6 but such an approach is complicated by difficulties in the preparation of (a-silylalkyl)lithium species or the corresponding Grignard reagents. These difficulties have been resolved by the development of a simple method for the preparation and reductive acylation of (a-chloroalkyl)silanes.7... 

Motoyoshiya, J., Kusaura, T., Kokin, K., Yokoya, S. i., Takaguchi, Y., Narita, S., Aoyama, H. The Horner-Wadsworth-Emmons reaction of mixed phosphonoacetates and aromatic aldehydes geometrical selectivity and computational investigation. Tetrahedron 2001, 57, 1715-1721. 

Rehwinkel, H., Skupsch, J., and Vorbrtiggen, H., E- or Z-selective Homer-Wittig reactions of suhsti-tuted bicyclo[3.3.0]octane-3-ones with chiral phosphonoacetates. Tetrahedron Lett., 29, 1775, 1988. Tiillis, J.S., Vares, L., Kann, N., Norrby, P.-O., and Rein, T., Reagent control of geometric selectivity and enantiotopic group preference in asymmetric Horner-Wadsworth-Emmons reactions with meso-dialdehydes, J. Org. Chem., 63, 8284, 1998. 

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