Zero-point energy linear chain

Leonard-Jones Parameters of the Linear Chain with Zero-Point Energy... 

Consider a monoatomic linear chain of atoms with mass m and nearest-neighbour interactions of the Lennard-Jones type with (p(r) given by (4.2). Prove that the zero-point energy... 

For many applications it is permissible to simplify the equation of state (5.76) by using the fact that the changes in volume due thermal expansion are generally small. and can, therefore, be expanded about the volume Y(T = 0) that the system has at T = 0. Neglecting the zero-point energy, we have V(T = 0) = Vq, where Vq is the volume at which has its minimum (see the corresponding discussion for the linear chain in Sect.4.1). Thus we write... 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

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