Segmental motion timescale

A simple model of an elastomer network is depicted in Fig. 7.1.8. The segmental motion of inter-cross-link chains is fast but anisotropic at temperatures of 100-150 K above the glass transition temperature The end-to-end vector R of such a chain reorients on a much slower timescale because it appears fixed between seemingly static cross-link points. As a result of the fast but anisotropic motion, the dipolar interaction between spins along the cross-link chains is not averaged to zero, and a residual dipolar coupling remains [Cohl, Gotl, Litl]. 

The timescale of fluorescence emission is comparable to that of rotational diffusion of proteins and the timescale of segmental motions of protein domains or individual amino acid residues. The polarization or anisotropy of the emission provides a measure of these processes. Suppose a sample is excited with vertically polarized light (Fig. 11), and that the sample is viscous so that the fluorophores do not rotate during the lifetime of the excited state. Then the emission is polarized, usually also in the vertical direction. This polarization occurs because the polarized excitation selectively excites those fluorophores in the isotropic solution whose absorption... 

In many fluid systems, the rotational diffusion proceeds at the timescales comparable with the fluorescence decay and can be used for studying the viscosity of the microenvironment, local geometrical constraints, segmental motion of polymer chains, etc. In non-viscous solvents, it decays usually faster than fluorescence, but in very viscous systems a full randomization occurs at times much longer than the fluorescence lifetime. The extrapolation tot yields the residual anisotropy, r . 

Steady state anisotropy measurements described in Section 2.7.5 can sometimes be misleading if a number of sources of depolarization are present. For example, as discussed, it can be difficult to differentiate global molecular rotation from local rotational freedom of the fluorophore when it is attached to a larger molecule [ 1,127]. In these cases time resolved single molecule fluorescence anisotropy measurements can be of use since the contributions to the depolarization may well act on different timescales. For example, for a labelled protein segmental motion of the protein backbone near the label and motion in the linker by which... 

Pulsed sequences are used to decouple the various contributions to the nuclear magnetic interaction. Since most spectrometers operate at frequencies of the order of several hundred megahertz, the timescale of the fluctuations observed are of the order of 10 to 10 s and hence are dominated by the segmental motions of the polymer. However, using special pulse sequences, these timescales can be extended to 10 s, when the influence of normal modes becomes evident. Such pulsed measurements are usually made at a single frequency, so it is difficult to obtain a meaningful picture of a distribution of relaxation processes. 

In a small molecule, rotational motion of a fluorophore in solution occurs on a ps timescale and the observed emission is thus averaged over all molecular orientations. In a synthetic polymer whole chain motion is in general very slow, but local motions may occur on the same timescale as fluorescence, and if these local motions, such as segmental motion, determine the rate of a process leading to emission, then the appropriate form of the rate expression for such motion must be employed, as suggested earlier [8]. 

In spin-diffusion studies it is possible to detect not only two but three domain sizes. The third domain can be considered the interface (i) between the other two domains, which can be different chemical species in a polymer blend or rigid crystalline (r) and mobile amorphous (m) material in a semicrystalline polymer. To illustrate this point, a mobility timescale is depicted in Fig. 7.2.25(a) and the simplified ID domain structure of PE underneath in (b). Rigid crystalline and mobile amorphous materials exhibit motion of chain segments with different correlation times Tc. The chains at the interface between both domains exhibit intermediate mobility. The exact ranges of correlation times in the individual domains depend on the particular choice of filters. Therefore, the values of domain sizes derived through spin-diffusion NMR also depend on the type of filters used. In particular, the interface is defined solely by the NMR experiment and can only be detected if the filters are properly chosen. 

NMR is ideally suited to explore molecular motions in the polymer. Different types of motion can be discriminated on behalf of their timescale and geometry of exchange. One-dimensional quadrupole echo lineshapes (see Section 6.2.7.1) are particularly sensitive to segmental dynamics [1-6, 9-12], when there is either fast exchange between discrete geometries (with Tc <1/Avq) or when the motion occurs on the intermediate timescale (tc= 1/Aj q). Dynamic processes in the intermediate to slow motional limit (tc > l/Ar Q) are addressed by 2D exchange spectroscopy (see Section... 

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