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

Abstract

In the present work, we analyze pulsed deuterium NMR experiments performed on the isotropic and nematic phases of the banana-shaped liquid-crystalline mesogen 4-chloro-1,3-phenylene bis{4-4'-(11-undecenyloxy) benzoyloxy} benzoate (ClPbis11BB) selectively deuterated on the central ring. Starting from a previous evidence of unusual slow dynamics in the isotropic phase (Domenici V. et al., J. Phys. Chem. B 2005, 109, 769), a quantitative and model-supported analysis of the deuterium NMR data is performed here by accounting for slow-motional modulation of the magnetic anisotropies through the full solution of the stochastic Liouville equation. Focusing on the quadrupolar echo experiments performed in the nematic phase, the analysis of the transverse relaxation rate has been carried out by considering single-molecule motions and fluctuations of the local director. The main conclusions are: (a) director fluctuations are not relevant on driving the signal relaxation; (b) molecular reorientations about transverse axes control the dynamic regime of the signal relaxation and impose a full slow-motional treatment; (c) the small amplitude tumbling of the molecule within the wells of orientational potential occurs with characteristic times up to the microsecond. The outcome of our analysis has to be taken as indicative of very slow dynamics concerning out-of-plane motions of the molecules. Besides the specific application, this paper also offers the methodological tools to treat the pulsed deuterium NMR experiment in the slow-motional regime of reorientational motions and provides a detailed comparison with the usually employed fast-motional approximation.

Banana‐Shaped Molecules Peculiarly Oriented in a Magnetic Field:2H NMR Spectroscopy and Quantum Mechanical Calculations

“…c) A complete study [13,14,26] based on a theoretical treatment of the spin-spin relaxation times, measured in this mesophase of the same sample, proves that the origin of the unusual line broadening can be quantitatively evaluated by considering, as the main contribution, the reorientation of the molecule around an axis perpendicular to the molecular plane (D ? ), namely parallel to Z c in Figure 4.…”

“…Each doublet peak has a very broad line width, which remains substantially constant within the investigated temperature range (Dn h/2 % 7500 Hz), as reported in Figure 2. [13] No differences were observed between spectra acquired with and without proton decoupling.…”

“…In the case of banana-shaped molecules, however, complex molecular aggregates may form, in which molecules are not completely free to rotate and molecular dynamics is scaled to the low-frequency range with respect to common calamitic liquid crystals. [9,13,18,20] In this frame, the relation between the molecular and mesophase magnetic susceptibility anisotropy is much stronger.…”

“…[11] Another aspect of great interest is the fact that banana-shaped liquid crystals (BLCs) have a particular behaviour even in the nematic phase. Mesophase biaxiality, [12] slow molecular dynamics, [13] large viscosity, [14] and giant flexoelectricity [15] are some examples of experimental evidence for the unusual behaviour of these molecular systems in the nematic phase. Such properties are certainly related to the distinctive orientation and aggregation of banana-shaped mesogens in this phase, while the effect of external fields can lead to results that are not easily predictable.…”

“…Moreover, the orientational order parameter S, referred to the local aromatic core of bent molecules, was found to be very high (up to 0.85), and the 2 H spinspin relaxation times, as well as the experimental line widths, indicate that molecules are affected by fast reorientational motions. When the same BLC molecules are in the bulk, the 2 H NMR spectra are affected by much slower motions [9,13,16,25,26] and therefore show completely different features. These experimental findings support the idea that BLC molecules have a peculiar packing within the nematic phase under the effect of a magnetic field, as proposed in ref.…”