Periodic bond chain theory

According to the periodic bond chain theory [89-92] and the defect density mechanism, diamond (111) surface is most stable in resisting oxidation than other faces [92]. However, dry oxygen roughens the (111) surface very fast, while the (100) surface is largely inert to oxygen below 1,220 K [93]. 

Hartman and Perdok f6Q-62 > in 1955 developed a theory which related crystal morphology to its internal structure on an energy basis. They concluded that the morphology of a crystal is governed tty a chain of strong bonds (called periodic bond chains (PBC)), which run through the structure. The period of these strong bond chains is called the PBC veaor. In addition, Hartman and Perdok divided the crystal face into three types. These types are ... 

These observations were made and explained by P. Hartman and W.G. Perdok in their periodic bond chain vector (PBC) theory (see the Chapter 1 references), which we introduced in Section 1.2.1. This theory takes into account the fact that 3D crystals are far more complicated structures, which are full of partial bonds and preferred directions. When the PBC vector is parallel with a crystal face, there is maximum growth along that crystal face. 

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... 

Sometimes the estimation of the electronic structures of polymer chains necessitates the inclusion of long-range interactions and intermolecular interactions in the chemical shift calculations. To do so, it is necessary to use a sophisticated theoretical method which can take account of the characteristics of polymers. In this context, the tight-binding molecular orbital(TB MO) theory from the field of solid state physics is used, in the same sense in which it is employed in the LCAO approximation in molecular quantum chemistry to describe the electronic structures of infinite polymers with a periodical structure -11,36). In a polymer chain with linearly bonded monomer units, the potential energy if an electron varies periodically along the chain. In such a system, the wave function vj/ (k) for electrons at a position r can be obtained from Bloch s theorem as follows(36,37) ... 

Studied the effects of bond and atom alternations and of chain pairing on the NLO properties of one-dimensional periodic semiconductors, with special emphasis on polydiacetylenes (PDA). The properties were referred to as and but we prefer and this is more correct to write 3(A)/A and y(N)/N with N, the number of units, tending toward infinity. Another Hiickel investigation [174] concentrated on (a) the second-order NLO responses of asymmetric unit cell polymers that modeled polymethineimine (PMI) and (b) the relations between bond alternation, atom alternation, and the sign and magnitude of p(/V)//V. At this level of theory the equations reduced to the non-self-consistent scheme detailed above and can be called uncoupled. 

Block copolymers are molecules composed of two or more distinct monomers chemically bonded in the same chain. We consider the simplest case where there are two types of elementary units A and B. These units are arranged into bonded linear sequences, or blocks, of variable length that are then repeated a variable number of times. To date, only one-component fluids composed of periodic block copolymers where the A and B block lengths are unique have been studied based on PRISM theory. However, random or statistical copolymers where there is quenched chemical or sequence disorder associated with the polymerization process are also of great interest. ... 

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