Transverse nuclear spin relaxation due to director fluctuations in liquid crystals. II. Second-order contributions of the fluctuating director

Abstract

Recently, we have introduced a slow-motional theory for transverse nuclear spin relaxation due to director fluctuations [D. Frezzato, G. Kothe, and G. J. Moro, J. Phys. Chem. B 105, 1281 (2001)]. This method is now generalized to second-order contributions of the fluctuating director. We consider the specific case in which the director is aligned orthogonal to the magnetic field. By exploiting the Gaussian character of director fluctuations, the stochastic Liouville equation for the coupled spin and director dynamics is solved in terms of a characteristic function whose time dependence is determined by a nonlinear integral equation. A convenient solution of the integral equation is obtained by decomposing the characteristic function according to the relaxation rates of the director fluctuations. In a first application, we evaluate the free induction decay and the corresponding absorption spectrum for quadrupolar probe nuclei in nematic liquid crystals. It is shown that the transverse magnetization is well represented by a monoexponential decay, i.e., a Lorentzian lineshape in the frequency domain. Explicit relations are derived for the linewidths and frequency shifts under slow-motional conditions where the Redfield theory cannot be applied anymore

Slow Dynamics of Banana-Shaped Molecules: A Theoretical Approach to Analyze2H-NMRT2Relaxation Times

“…In this situation, it has been demonstrated that the DF contribution prevails yielding the characteristic dependence (τ) ≅ (τ) ∝ τ 1/2 at large values of τ, while the contribution of the molecular motions dominates at short τ. Unfortunately, low molecular weight nematics are macroscopically aligned by the instrumental magnetic field, and in such a situation an almost τ-independent relaxation rate is predicted. , This is also the present case; in fact, angular measurements in the nematic bulk have been unsuccessful because of the fast reorientation of the molecules with respect to the magnetic field . In the following, we also will show that a reasonable model for molecular reorientational dynamics may yield a basically τ-independent relaxation rate.…”

“…The theoretical description of nuclear magnetic relaxation driven by DF has been developed. − With reference to the case of average director aligned parallel to the magnetic field and to a single deuteron per molecule, a monoexponential dependence of the maximum QE signal vs τ is predicted (i.e., a τ-independent relaxation rate). Because the three deuterons of the central ring of ClPbis11BB-d 3 are basically indistinguishable from the DNMR spectrum within the resolution of the line, one can analyze the data as if a single nucleus would be present.…”

Collective Fluctuations in Ordered Fluids Investigated by Two-Dimensional Electron−Electron Double Resonance Spectroscopy

“…We choose the ADF frame with the y axis collinear with the Y axis of the LF (see Figure ), therefore the transformation from the LF to the ADF can be specified by the Euler angles Ω = (0, θ B , 0), where θ B is the angle between the static magnetic field B 0 and the average director n̄ at the probe location. The g-tensor component required in eq 2 can be written as ( Z is the unit vector along the static magnetic field) where g ZZ 0 is the component in the absence of director fluctuations ( n ≡ n̄ ), while δ g ZZ is its fluctuating part in the linear approximation with respect to the stochastic variables , Clearly the average vanishes because = 0. It should be stressed that the linear approximation holds in the case of small fluctuation amplitudes, allowing one to neglect in eq 6 higher-order terms (with respect to powers of n x and n y ).…”

“…Notice that eq 8 leads to a vanishing δ g ZZ if θ B = 0°, 90°, that is, for the so-called canonical geometries with the average director parallel or perpendicular to the magnetic field. In those situations, second-order terms have to be necessarily accounted for in the expansion of δ g ZZ . However, in the case of vesicles where all orientations θ B contribute, the minor correction to eq 8 due to the appearance of second-order terms can be safely ignored.…”

“…It should be mentioned that this methodology has already been applied to the analysis of transverse nuclear spin relaxation rates measured in vesicles 14,15 and in polymeric liquid crystals . An extended version of the theory is reported in ref .…”