Conformational correlation rotational jump

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

As an introduction, our previous studies on the conformations of maleic acid copolymers with aromatic vinyl monomers are summarized. To characterize the compact form and the pH-indueed conformational transition of the maleic acid copolymer with styrene in aqueous NaCl, 400 MHg H-NMR spectra were measured. The spectral form depended on the molecular conformation. Because each of proton resonance peaks could not be separated, the spin-lattice relaxation time T was estimated by using the inversion recovery technique (tf-t-tf/2). The T s for both side chain and backbone protons reflected the transition, and the protons were considered to be in a more restricted motional state in the compact form than in the coil form. Also, from temperature dependence of each Tj, motion of the copolymer in the coil form was described in terms of the local segmental jump (D) combined with the isotropic rotational motion (O), when a ratio between both the correlation times tq and Tq was about 0.07. For the compact form, the ratio was found to be about 10. By referring to theoretical diagram of Tj vs. tq for the methylene protons on the backbone, value of Tn for the compact form was compared with that for the coil form at 35 C. 

The assumption of free rotation about each C-C bond in an alkyl chain can give conformations of molecules that are precluded on grounds of excluded-volume effects. Following Tsutsumi, a jump model was employed [8.11] to describe trans-gauche isomerisms in the chain of liquid crystals by allowing jumps about one bond at any one time. To evaluate internal correlation functions gi t), not only the equilibrium probabilities of occupation given by Eq. (8.4) are needed, but also the conditional probability P(7, t 7o,0), where 7 and 70 denote one of the three equilibrium states (1, 2, 3) at times t and zero, respectively,... 

Chachaty and co-workers [8.20, 8.37, 8.38] were first to describe correlated internal motions in alkyl chains of surfactant molecules that form lyotropic liquid crystals. The last section described an extension of the master equation method of Wittebort and Szabo [8.4] to treat spin relaxation of deuterons on a chain undergoing trans-gauche jump rotations in liquid crystals. This method was also followed by Chachaty et al. to deal with spin relaxation of nuclei in surfactants. However, they assumed that the conformational changes occur by trans-gauche isomerization about one bond at a time. In their spectral density calculations (see Section 8.3.1), they used a transition rate matrix that was constructed from the jump rate Wi, W2, and Ws about each bond. Since W3 is much smaller than Wi and W2, the time scale of internal motions was practically governed by Wi and W2 of each C-C bond. Since... 

The dynamic terms in eqn (1) depend upon the assumptions used to describe the motion. For the intermolecular motion a diffusive process is assumed (rotation through a sequence of small angular steps). In that case intermolecular reorientation can be characterized by two rotational correlation times, and Tru. The correlation time for reorientation of the symmetry axis of a molecular diffusion tensor is Tr, while Tru refers to rotation about the axis. For the intramolecular motion a random jump process is assumed. Thus, isomerization occurs through jumps between different conformations with an average lifetime Tj. 

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