Amorphous state long-range interactions

It will be shown later (Section 3.1.7) that in good solvents the coil is expanded and a is large whereas in the O condition a is equal to unity. It is worth pointing out at this stage that it has recently been shown from neutron scattering measurements that a is also close to 1 in an amorphous polymer in the solid state since in this condition the effect of long-range interactions on the chain dimensions is small. 

For many years, during and after the development of the modem band theory of electronic conduction in crystalline solids, it was not considered that amorphous materials could behave as semiconductors. The occurrence of bands of allowed electronic energy states, separated by forbidden ranges of energy, to become firmly identified with the interaction of an electronic waveform with a periodic lattice. Thus, it proved difficult for physicists to contemplate the existence of similar features in materials lacking such long-range order. 

The disorder of the atomic structure is the main feature which distinguishes amorphous from crystalline materials. It is of particular significance in semiconductors, because the periodicity of the atomic structure is central to the theory of crystalline semiconductors. Bloch s theorem is a direct consequence of the periodicity and describes the electrons and holes by wavefunctions which are extended in space with quantum states defined by the momentum. The theory of lattice vibrations has a similar basis in the lattice symmetry. The absence of an ordered atomic structure in amorphous semiconductors necessitates a different theoretical approach. The description of these materials is developed instead from the chemical bonding between the atom, with emphasis on the short range bonding interactions rather than the long range order. 

The liquid crystal state (LCS) shows order in one or two dimensions it lacks the three-dimensional long-range order of the crystalline state. LCS has characteristics intermediate between those of the crystalline and the disordered amorphous states. These phases are called liquid crystals because many of them can flow like ordinary liquids but they display-birefringence and other properties characteristic of crystalline soHds. In liquid crystal phases the molecules can move but the orientational order is conserved in at least ne direction. The LCS can be displayed by small molecules and by polymersj but in both cases a characteristic chemical structure is needed. The existence of the liquid crystal state is related to the molecular asymmetry and the presence of strong anisotropic intermolecular interactions (19-21). Thus, molecules with a rigid rod structure can form highly ordered... 

In the bulk state each polymer molecule is surrounded by other polymer molecules of the same type. Expansion of a given chain to relieve long-range intramolecular steric interactions only serves to create an equal number of intermolecular steric interactions with neighboring chains. These opposing volume exclusion effects exactly counteract each other and so in a bulk amorphous polymer the polymer molecules adopt their unperturbed dimensions (i.e., a = 1). 

---