Time-correlation function segmental motion

In Chapter 3, we used the Rouse model for a polymer chain to study the diffusion motion and the time-correlation function of the end-to-end vector. The Rouse model was first developed to describe polymer viscoelastic behavior in a dilute solution. In spite of its original intention, the theory successfully interprets the viscoelastic behavior of the entanglement-free poljuner melt or blend-solution system. The Rouse theory, developed on the Gaussian chain model, effectively simplifies the complexity associated with the large number of intra-molecular degrees of freedom and describes the slow dynamic viscoelastic behavior — slower than the motion of a single Rouse segment. 

The anisotropy of segmental motion exhibited in Fig. 19 may arise, as noted above, either from the intramolecular or from the intermoleoilar ccmstraint to the rotational motion. The anisotropy d orioitational condadon decay was indeed noted already by Weber and Helfand [47] in their Brownian dynamics simulation of polyethylene of infinite chain length. Their orioitational time-correlation function of the chord vector ( = 0°) decayed much more slowly than those of either the bisector vector ( = 0°, = 0°) or the out-of-plane vector ( = 0°, = 90°). What they modeled was a phantom chain having no... 

An important class of magnetization filters are mobility filters which select magnetization based on the time scale of segmental motions ((19), and references therein). The parameters for discrimination are the amplitude and characteristic frequency or the correlation time tc of molecular motions. The effect a filter exerts on a NMR signal can be represented by the filter transfer function. Examples are given in Figure 30 (163,164) with transfer function for filters, which select magnetization based on the time scale of molecular motion. 

Our experimental measurements of the orientation autocorrelation function on sub-nanosecond time scales are consistent with the theoretical models for backbone motions proposed by Hall and Helfand(ll) and by Bendler and Yaris(12). The correlation functions observed in three different solvents at various temperatures have the same shape within experimental error. This implies that the fundamental character of the local segmental dynamics is the same in the different environments investigated. Analysis of the temperature dependence of the correlation function yields an activation energy of 7 kJ/mole for local segmental motions. 

Fig. 6.2.2. Left Simulated NMR lineshapes that are averaged by various characteristic segmental motions. In the case of fast rotation, y represents the angle between the rotation axis and the C—bond. For a two-site jump, j3 denotes the angle between the C—bond in the two configurations, and the effective asymmetry parameter becomes 17 7 0. Right Calculated 2D exchange spectra for a two-site jump with /3 = 120° (top), and for continuous diffusion (bottom). The distribution functions P(/3) of the reorientation angle are shown, together with the contour maps of the corresponding spectra. All data are displayed on the reduced frequency scale in units of Cq, and mixing times are set equal to the motional correlation time r,..

Stock-Schweyer et al. [112] reported a high-pressure effect on molecular motions in the paraelectric phase of a (70/30) VDF and TrFE copolymer. Fluorine-19 NMR relaxation times (Ti and Tjp) were studied over a range of pressures from 0.1 to 200 MPa. Correlation times of the molecular motions, as functions of pressure and temperature, were obtained and the activation parameters determined. The experimental data confirmed the presence of a slow motion in the amorphous phase in addition to the fast anisotropic motion. The results indicated that the relaxation times of the copolymer are controlled by the effects of both temperature and volume. The authors concluded that 40-50% of the mobility increase of segments with increasing temperature under constant pressure results from volume expansion. 

F%. IX Time dependence of dipole-dipole correlation function for segmental motion of polyisop-rene in the bulk state. Feints denote results of DRIS calculations, filled circles are obtained in the absence of intermolecuiar correlations. The two stroigla lines are best fits to idiort and long time regions. The empty circles show DRIS results in the presence of environmental fluctuations. Values of the KWW exponents are shown on each curve... 

---