Nature of molecular motion in polymers

The dynamic behaviour of polymer molecules is the bridging element in understanding the relationship between the chemical structure of a polymer and its physical properties. Molecular movement usually involves some change in the conformation of parts of the polymer chain. Since many readers may not have had experience of conformational analysis, it is now appropriate to consider the various forms of motion which are possible for polymers by starting with their small molecule analogues. 

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Fig. 19a-e. Molecular weight dependence of the effective proton and transverse relaxation times T 2=(1/T 2,7)" (see Eq. 160) in different linear polymers at different temperatures. The data were measured at 2.1 T [35, 138, 139]. The classical critical molecular weight Me and a value characteristic for the three-component nature of molecular motions in polymers, M cy reveal themselves as bends in the slopes of the power laws approaching the dependences on the molecular weight Values of the characteristic molecular weights are listed in Table 4. For Mwadditional molecular weight dependence... 

Techniques which are more specific to the various morphological states, especially the amorphous domain, are needed. NMR and ESR are two such molecular probes. By monitoring the mobilities of protons as a function of temperature, Bergmann has defined the onset of molecular motion in various polymers (14). The applicability of NMR as a measure of molecular motion in polymer solids has been the subject of several reviews 15,16,17). ESR monitors the rotational and translational properties of stable radicals, usually nitroxides, and relates their mobilities to polymeric transitions. As stated in several works (18,19), the radical s sensitivity to freedom of motion of the polymer chain is infiuenced by its size, shape, and polarity. The above probes are both high frequency in nature, 10 -10 Hz. Measurement at high frequency has decreased resolving power for the various transitions in contrast to low frequency or static experiments, such a dilatometry with an effective frequency of 10 Hz (20). 

Elucidation of the nature of molecular mobility in LC polymers is inseparable from clarification of the mechanisms of motions of distinct macromolecular fragments. Insufficiency of experimental data does not to date allow to comprehend these problems completely. Some aspects of these will be considered in Chap. 5, dealing with electrooptical phenomena in LC polymers. 

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

The study of the kinetics of EB in rigid-chain polymer solutions is of great importance since it permits the understanding of the physical nature of this phenomenon and provides information on the mechanism of molecular motion in the electric field. 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

The sum must be made over all spin pairs in the proton-rich solid. In the absence of large-amplitude molecular motion this Hamiltonian describes a line shape of width of up to 100 kHz. In the presence of molecular motion the angular part of Equation 13.1 becomes time-dependent, and the partial averaging of this term results in reduced linewidths. In polymers the geometry of main-chain motion is limited by the structure of the polymer chain, and is inherently anisotropic. As a general rule, as the measurement temperature is increased the motion tends to become more isotropic in nature as the free volume increases, and the extent of averaging of the dipolar Hamiltonian increases. This... 

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