Rigid hybrids

Let us return to the simple shear distortion that was illustrated in Fig. 8-1. Focusing on the central atom and the four nearest neighbors tetrahedrally bonded toil, we sec that the distortion twists the tetrahedron as illustrated in Fig. 8-2, where 

A distortion in the zincblcnde lattice, corresponding to 3 = —i 2 all other strains are zero. Atoms a and c lie in the positive. v-direction from the origin by o/4 h and d lie in the negative, v-direction by the same amount. 

The shear distortion of Fig, 8-1 exerts a twist on each set of tetrahedral bonds. Rehybridization cannot accommodate to this so the hybrids may be imagined rigidly fixed. 

To calculate the angle of misalignment of the two hybrids in each bond, take the dot product of the nearest-neighbor vector distance in the distorted and undistorted crystal and divide by the distance before and after distortion that is, divide by and (3 + 2c ) a/4, respectively  

The meaning of 0, the angle of misalignment, is seen in Fig. 8-3. Expanding Eq. (8-7) for small 0 and small we obtain 0 = 2fi /3 the same result applies for every bond. We write the change in hybrid covalent energy, quadratic in 9, in the form 

---

For a crystal having the symmetry of diamond or /.incblende (thus having cubic elasticity), there are three independent clastic constants, c, t 12, and C4.4. The bulk modulus that was discussed in Chapter 7 is B = (c, + 2c,2)/3. We can discuss the bulk modulus, and the combination c, — c,2, entirely in terms of rigid hybrids, and therefore the two elastic constants c, and c,2 do not require deviations from this simple picture. This will not be true for the strain, which is relevant to c 44, and this is a complication of some importance. 

Trivalent ( classical carbenium ions contain an sp -hybridized electron-deficient carbon atom, which tends to be planar in the absence of constraining skeletal rigidity or steric interference. The carbenium carbon contains six valence electrons thus it is highly electron deficient. The structure of trivalent carbocations can always be adequately described by using only two-electron two-center bonds (Lewis valence bond structures). CH3 is the parent for trivalent ions. 

By far the most common lead salt used for PVC stabilization is tribasic lead sulfate. It can be found either alone or combined with another lead salt in almost every lead-stabilized PVC formulation. Many of the combinations are actually coprecipitated hybrid products, ie, basic lead sulfophthalates. Dibasic lead stearate and lead stearate are generally used as costabilizers combined with other primary lead salts, particularly in rigid PVC formulations where they contribute lubrication properties dibasic lead stearate provides internal lubrication and lead stearate is a good external lubricant. Basic lead carbonate is slowly being replaced by tribasic lead sulfate in most appHcations due the relatively low heat stabiHty of the carbonate salt which releases CO2 at about 180°C during PVC processing. 

Ereeze casting (59) is a hybrid of sHp casting, gel casting, and freeze drying in which a slurry is poured into a rigid mbber mold, frozen, and the frozen Hquid is removed by sublimation, ie, by freeze drying (see Cryogenics). 

As an organic polymer, poly(tetramethylene oxide) was also used for the preparation of ceramers. The mechanical properties in these cases were much improved in comparison with those for hybrids from polysiloxanes. In these poly (tetramethylene oxide)-silica hybrids, the effect of the number of functional triethoxysilyl groups was examined [13]. As shown in Fig. 2, more multifunctional organic polymer produced more crosslinked hybrid networks. This means that the more rigid the structure in the hybrids is, the higher the modulus and the lower swelling property. 

In diamond, each carbon atom is sp3 hybridized and linked tetrahedrally to its four neighbors, with all electrons in C C cr-bonds (Fig. 14.30). Diamond is a rigid, transparent, electrically insulating solid. It is the hardest substance known and the best conductor ol heat, being about five times better than copper. These last two properties make it an ideal abrasive, because it can scratch all other substances, yet the heat generated by friction is quickly conducted away. 

In diamond, carbon is sp hybridized and forms a tetrahedral, three-dimensional network structure, which is extremely rigid. Graphite carbon is sp2 hybridized and planar. Its application as a lubricant results from the fact that the two-dimensional sheets can slide across one another, thereby reducing friction. In graphite, the unhybridized p-electrons are free to move from one carbon atom to another, which results in its high electrical conductivity. In diamond, all electrons are localized in sp3 hybridized C—C cr-bonds, so diamond is a poor conductor of electricity. 

The structure of a-C H films may be thus pictured as sp--carbon atoms in condensed aromatic clusters, dispersed in an sp- -rich matrix, which confers to the network its characteristic rigidity. This situation can also be regarded as a random covalent network in which the sp" clusters of a defined size take part in the structure as an individual composed atom with its corresponding coordination number [17]. Such kinds of models have been successfully used to describe the dependence of a-C H film mechanical properties on composition, hybridization, and sp" clustering [23]. 

Because of the necessity of spatially appropriate overlap of the 2p. .-orbital on boron with the adjacent jp3-hybridized carbon orbital (12) or with the tt-MO of the double bond (13), any such ir-bonding should be most sensitive to molecular conformation. Hence, the occurrence of such 7r-bonding might be more evident in certain highly rigid cyclic structures, such as 14 and 15. 

---