Calculation of carbon-13 relaxation times and nuclear Overhauser enhancements in a hydrocarbon chain undergoing gauche-trans isomerism

Abstract

An analytically tractable model has been developed for calculating the relaxation times of a hydrocarbon chain undergoing gauche-trans isomerization about each carbon-carbon bond and overall isotropic motion. Each internal rotation is described by two parameters, tau/sub t/, the lifetime of a trans state, and sigma, the equilibrium ratio of gauche to trans states: sigma = ((g/sup +/) + (g/sup -/))/2(t). Spin lattice relaxation times (T/sub 1/), spin-spin relaxation times (T/sub 2/), and nuclear Overhauser enhancements (NOE) have been calculated for a six-bond chain. As a result of the restriction introduced into the internal motion, properties associated with the slowly tumbling end of the molecule such as a reduced NOE, T/sub 1/ much greater than T/sub 2/, and a frequency dependence of T/sub 1/ propagate far into the chain in contrast to the free internal rotation mode. Analysis of data obtained for n-hexadecyltrimethylammonium bromide micelles and for sonicated dimyristoyl lecithin lipid vesicles indicates that restriction of internal rotation is not sufficient to explain the observed T/sub 1/ and T/sub 2/ values. For this reason, the effects of correlated motions such as kink formation and diffusion have been treated semiquantitatively and a correlation factor f introduced to reflect the degree of motionalmore » correlation. The three possible contributions to the observed T/sub 1/ gradient (cumulative effects of successive internal gauche reversible trans isomerizations as modified by an appropriate correlation factor, a gradient in the isomerization rate as described by tau/sub t/, and a gradient in sigma) are evaluated in light of available experimental data. In general, T/sub 1/ values measured in systems undergoing multiple isomerizations are found to be sensitive to the order of the system as well as to the rate of internal motion. For typical parameters, T/sub 2/ values are found to be sensitive to the degree of motional correlation and to the value of sigma, but not to the isomerization rate.« less