Flat F faces

In Figure 6.18, the flat F faces, stepped S faces, and kinked K faces are shown for a cubic ciystal system. The rougher S and K faces grow very quickly and are rarely, if ever, observed. The ciystal habit is... 

It will be shown first that the growth is governed by the growth of flat F faces and by the generation steps on these faces. Two sources for these steps can be distinguished First, the steps can be generated by 2D nucleation on the surface or by screw dislocations. Second, the rate of incorporation of the building blocks into the steps at the so-called kink positions will be described. 

Hartman and Bennema (1980) proposed the attachment energy model, which relates the energies of the bonds between the crystal-building units to its external shape. Two important concepts were developed as part of this model—the periodic bond chains (PBCs) that define periodically repeated chains of strong intermolecular interactions and the attachment energy (fi tt)- Based on the number of PBCs that are parallel to a face, crystal faces can be classified as flat (F) face with 2 PBCs, step (S) face with 1 PBC, or kink (K) face with 0 PBCs. The morphological importance of the faces follows... 

F-faces (flat) each of which is paralled to at least two PBC veaors. 

Growth on the lateral surface of the cylinder-like crystals present gin activation energy of 30 kcal/mol and is proportional to [Al ] . Thus a stepped surface (S-face, 24) with no defined crystallographic orientation like the (hkO) faces presents a reaction order nearly double than a formally flat face (F-face, 24) like (001). This result seems to be incompatible with the action of the same mechanism of growth on the two kinds of faces. 

FIGURE 6J8 Hypothetical three-dimensional ciystal presenting the three main types of possible faces flat (F), step (S), kink (K) faces. Redrawn, with permission from ElweU and Scheel [28]. 

Ai and A2 are the glass plates, their optically flat surfaces facing each other. At is attached to a spring F of known resilience with the aid of frame B and holder D, both made of brass, A2 rests on the pins T on top of three boxes K. These boxes were fixed to three micrometer movements regulating roughly the position of A2 towards Ai. 

FIGURE 20.9 Schematic illustrating the PBC theory. In a simple cubic crystal, 100 faces are flat surfaces (denoted as F-faces) with one PBC running through one such surface, 110 are stepped surfaces (S-faces) that have two PBCs, and 111 are kinked surfaces (K-faces) that have three PBCs. (From Hartman, R, and Perdok, W.G., Acta CrystL, 8, 49, 1955.)... 

Early work by Hartman and Perdok described crystal growth in terms of the formation of strong bonds between neighboring crystallizing units. Uninterrupted straight chains of these bonds were classified as Periodic Bond Chains (PBC). This theory led to the classification of three types of crystal faces F-faces (flat), S-faces (stepped), and K-faces (kinked) based on the number of PBCs in a slice thickness, dhki- K-faces, which had no PBCs present in a slice, were shown to be... 

In 1955, Hartman and Perdok (18) refined the BFDH model by relating the crystal morphology to its internal structure on an energy basis. They identified that chains of strong intermolecular bonds known as periodic bond chains (PBC) govern the crystal morphology. According to the number of PBC inside a slice of thickness, they classified the crystal faces as (i) F-faces (flat), two or more PBC, (ii) S-faces (stepped), one PBC, or (iii) K-faces (kinked), zero PBC. 

Figure 2.31 Simple cubic C7stal with the three lowest-indexed faces. The faces are flat F, stepped S, and kinks K.

Figure 12 Damping coefficient yr 1(.0 = F/Av obtained from simulating two atomically flat surfaces separated by a simple fluid consisting of monomers at constant temperature and normal pressure. Different coverages were investigated. The numbers in the graph denote the ratio of atoms contained in the fluid Ng relative to the atoms contained per surface layer of one of the two confining walls Nw. The walls are (111) surfaces of face-centered-cubic solids. They are rotated by 90° with respect to each other in the incommensurate cases. Full circles represent data for which Nt-]/Nw is an integer. The arrow indicates the point at which the damping coefficients for commensurate walls increases exponentially.

The key step is the alkylation of the enolate intermediate. F.nolates in five-menibered rings are almost flat and the incoming alkyl halide prefers the less hindered face away from the recently added group R. The example below shows that, if both new groups have double bonds in their chains, it is easier to add a vinyl group as the nucleophile and an allyl group as an electrophile. 

A review of vaginal bioadhesive formulations indicates that bioadhesive tablets have been used for localized treatment of diseases in the vaginal tissue.F ° l For example. Bleomycin, an antitumor agent, was incorporated into a flat-faced disk fabricated from a combination of hydroxypropyl cellulose and poly-(acrylic acid) (Carbopol 934). ° The tablet was designed to release Bleomycin at a slow rate to minimize irritation to healthy mucosa. Another vaginal tablet is formulated from the combination of poly(acrylic acid) with hydroxypropyl methylcellulose and ethylcellu-lose. Other polymer combinations evaluated for potential bioadhesive vaginal delivery include poly(acrylic acid) and sodium carboxymethyl cellulose with Avicel PH102 (methylcellulose) as the diluent. Insulin has been formulated in a cross-linked poly(acrylic acid) gel... 

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