The possible importance, in nuclear magnetic spin-lattice relaxation, of the magnetic fields produced by molecular rotation was pointed out by Bloembergen, Purcell, and Pound 1 in their classic paper on nuclear relaxation. The purpose of this Letter is to present experimental evidence that spin-rotational interactions provide the dominant relaxation mechanism in certain molecular liquids.Earlier work 2 on the proton and fluorine T x 's at room temperature in CH 2 FC1, CHF 2 C1, CHFC1 2 , and 1, 3, 5-trifluorobenzene demonstrated that the anisotropy in the fluorine nuclear magnetic shielding contributes an appreciable, field-dependent, term to the fluorine T 1 . In these molecules, the direct dipole-dipole interactions among the nuclei are nearly identical for protons and fluorine. Moreover, because of their rigid molecular framework, the molecules should have the same correlation time r c governing the T x of fluorine nuclei as well as of protons. Therefore, even though it is difficult to make a sufficiently accurate estimate of r c to predict quantitative values for T 19 the ratio of the 2ys, R = TIH/TIF, should be predictable to better accuracy. However, it was found that although the predicted ratio of the dipolar contributions to T x , #dip> ranged between 0.4 and 1.0 for the four liquids, the observed ratio ranged between 1.5 and 9.2. In addition, R 0 \^s increased with the applied magnetic field, indicating the presence of a field-dependent interaction which decreased the fluorine T x but had little or no effect upon the proton T x .This behavior agrees qualitatively with the effects calculated on the basis of anisotropy ACT in the chemical shift tensor a inasmuch as the proton shifts are too small for their anisotropy to contribute much to 2\. However, even though the anisotropy is large enough to be important for fluorine, estimates of its magnitude based on chemical shift theory and also on the field dependence of # 0 bs * ec * *° tne result that jR 0 b s should be about 1.5 fl^p for ^V s a * 20 Mc/sec. Therefore, it was concluded that some additional more important factor was shortening the fluorine T x and causing the several-fold difference 1 between R^ip and # 0 bs* That this additional relaxation mechanism involves the spin-rotational interaction is shown by our subsequent measurements of the temperature dependence of the proton and fluorine iys. Results for CH 2 FC1, CHF 2 C1, and CHF 3 are presented in Fig. 1 as a semilogarithmic plot of T x versus 10 3 /T°K; qualitatively similar but less extensive data have been obtained 3 for CHFCL,. The increase of T x with temperature implies that CO 2 T C 2 «1; however, the curvature of the plots for both the proton and fluorine 7\ from straight lines at higher temperatures indicates deviations from "ideal" behavior. 1 Taken individually, such deviations for either the proton or the fluorine T 1 could be attributed to any of several aspects of the liquid-state structure or purity. The significant feature is that the deviations are larger for fluorine than fo...
Nuclear spin relaxation times have been measured for liquid CHFCl2, the values of T1H and T1F between 132° and 298°K at 27, 20 and 17 Mc, and T2H and T2F over the same temperature range at 20 Mc. The results of these measurements are discussed, and the following relaxation mechanisms are shown to be important: (a) intermolecular dipole—dipole interactions, including their effect upon the electronic, scalar coupling of the proton and fluorine nucleus, (b) the quadrupolar relaxation of the chlorine nuclei which are coupled to the proton and the fluorine nucleus by scalar couplings, and (c) the spin-rotation interaction between the fluorine nucleus and the reorientation of the molecule. It is noted that relaxation of the same type as mechanism (b) accounts for the relatively large natural linewidths and poorer resolution often found in spectra of heavier nuclei such as F and P, compared to spectra of protons in the same liquid compound. The statistical assumptions of rotational Brownian motion of the molecule, in the liquid, when applied to the spin-rotation interaction, are found to predict the wrong temperature dependence of T1F at high temperatures. A transient rotation model is proposed in which the molecules ``jump'' from one orientation to another at random times; the spin-rotation interaction is assumed to operate during these ``jumps'' when the molecule is actually rotating. The statistical properties of such a model are calculated, and it is shown that T1F is predicted to have the correct temperature dependence. The model is compared with that developed by Johnson and Waugh for nuclear relaxation by the spin-rotation interaction in gases. The dipole—dipole and quadrupole interactions are discussed in detail, and a treatment of intermolecular dipole—dipole relaxation by Redfield's method is given, with results indicating that the electronic, scalar coupling of nuclei contributes to the inequality T2<T1 often found in liquids.
We study the configurational properties of single polymers in a theta solvent by Monte Carlo simulation of the bond fluctuation model. The intramolecular structure factor at the theta point is found to be distinctively different from that of the ideal chain. The structure factor shows a hump around q approximately 5/Rg and a dip around q approximately 10/Rg in the Kratky plot with Rg being the radius of gyration. This feature is apparently similar to that in a melt. The theoretical expression by the simple perturbation expansion to the first order in terms of the Mayer function can be fitted to the obtained structure factor quite well, but the second virial coefficient cannot be set to zero.
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