Stiffness of the Covalent Bonds

There is also a difference in the stiffness , or elasticity , of these different types of bonds and the relative values of their elastic constants are shown in Table 4.4 [8]. 

Bond type Elastic constant Location in crosslinked rubber 

C-C bonds -100 Main-chain bonds in rubber molecules 

Due to their underlying chemical properties and atomic structures, there is also a difference in the chemical reactivity of the different types of bonds that are present in the rubber matrix and so if chemical agents (sometimes referred to devulcanising agents in the literature) are used that specifically target the sulfur-sulfur and sulfur-carbon bonds, usually aided by other agencies such as heat, this difference in reactivity can be exploited to achieve devulcanisation. 

Because of the nature of rubber processing equipment (i.e., mills and extruders), it is usually the case that two or more of the mechanisms 

---

The glide planes on which dislocations move in the diamond and zincblende crystals are the octahedral (111) planes. The covalent bonds lie perpendicular to these planes. Therefore, the elastic shear stiffnesses of the covalent bonds... 

The Group IV elements also show a linear correlation of their octahedral shear moduli, C44(lll) with chemical hardness density (Eg/2Vm).This modulus is for for shear strains on the (111) planes. It is a measure of the shear stiffnesses of the covalent bonds. The (111) planes lie normal to the bonds that connect the atoms in the diamond (or zinc blende) structure. In terms of the three standard moduli for cubic symmetry (Cn, Q2, and C44), the octahedral shear modulus is given by C44(lll) = 3CV1 + [4C44/(Cn - Ci2)]. Since the (111) planes have three-fold symmetry, they have only one shear modulus. The bonds across the octahedral planes have high resistance to shear which probably results from electron correlation in the bonds (Gilman, 2002). 

What happens if only weak coupling occurs between adjacent molecules This condition can be accomplished by simply changing the values of the force constants such that /i > /2. The force constant /] corresponds to the stiffness of the covalent bond linking pairs of atoms, and /2 represents the much weaker bonding of the molecules together. Now the frequencies become... 

---