Gauche-trans conformational jumps

By comparison of observed and theoretically calculated spectra it can be shown that these carbons are involved in gauche-trans conformational jumps of the C-D bond through a dihedral angle of 103°, and from the correlation times as a function of temperature an activation energy of 5.8 kcal/mol is found. Several seemingly plausible motional models are excluded by these results, but the data agree with models proposed by Helfand (21,22) for motion about three bonds. 

The temperature-dependent spectra were interpreted in terms of a two-site hop model, in which the deuterons undergo jumps through a dihedral angle of 103°. This type of motion is consistent with gauche-trans conformational transitions. At -88"C these motions appear static on the time scale of the deuterium NMR experiment, and at +85 °C the motions are in the fast exchange limit. The rate constants for these motions were obtained from the calculated spectra. An Arrhenius plot of these data show that the apparent activation energy is 5.8 kcal/mol. (Dynamic mechanical data (20 Hz) fall on the Arrhenius plot.) The transitions have an intermediate rate on the deuterium NMR time scale at 20 °C, with the correlation time for the motion being 7 x 10 6 s at this temperature. 

Because the configurations of the chains which predominantly contain the trans and gauche conformations of short parts formed by four C atoms (in sp hybridization) fit fairly well to the tetrahedral lattice (see chapter Conformational and Dynamic Behavior of Polymer and Polyelectrolyte Chains in Dilute Solutions, Fig. 3), to a first approximation they assumed that the basic motion of the fluorophore can be described as a jump-like rotation on the tetrahedral lattice with one characteristic time, p (which depends on the characteristic jump frequency and the conformation structure of the chain), in the form [100, 101] ... 

The other basic model applies to rotational jumps among a few equilibrium sites when the potential barriers are larger than ksT. For aliphatic chains, the j + l)th bond (see Fig. 4.1) is again taking one of three possible orientations (t, g, g ) with respect to the plane defined by the jth and (j — l)th bonds. The potential energy of a trans (t) conformer is about 2.1 kJ/mol [8.10] below that of the gauche states which are assumed... 

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... 

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