NMR Spectroscopy of Liquid Crystal Dendrimers: Experimental Results

NMR of LC Dendrimers and the Investigation of the Biaxial Nematic Phase

Biaxial Nematic Ordering and NMR Spectroscopy

As described in previous chapters, nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for the investigation of liquid- crystalline (LC) systems. This is due to the fact that the anisotropic nature of nuclear magnetic dipolar and quadrupolar interactions gives rise to spectral contributions that depend on the molecular orientation with respect to the external static magnetic field, B0.

In fact, the dipolar splitting of NMR lines associated with proton pairs and the quadrupolar splitting of deuterium in the presence of an electric field gradient (e.g., in a C-D bond) are directly related to the nematic order parameter and the orientation of the director n. These splits result from perturbations of the Zeeman levels associated to the interaction between the nuclear spins and the external static NMR magnetic field B0.

NMR ofLiquid Crystal Dendrimers

Carlos R. Cruz, Joao L. Figueirinhas, and PedroJ. Sebastiao Copyright © 2017 Pan Stanford Publishing Pte. Ltd.

ISBN 978-981-4745-72-7 (Hardcover), 978-981-4745-73-4 (eBook) www.panstanford.com

Both the dipolar interaction between a pair of spins I = 1/2 (typically a proton pair) and the quadrupolar interaction between the spin I = 1 (typically a deuteron) and the electric field gradient (EFG) tensor may be described by second-rank tensors as described in Chapter 4.

In the uniaxial nematic phase, the orientational order can be described by a single order parameter, defined by Eq. 2.2. In that case, the physical properties of the system described by second-rank tensors (e.g., the magnetic susceptibility, the electric permittivity, or the refractive index) can be completely defined by two elements, one corresponding to the direction of a principal axis (z), and another one associated to any direction perpendicular to z. If Q is such a physical parameter it can be expressed in its principal frame (where one of the principal axis coincides with the z direction) by

where Q| is the component of Q in the principal direction (z) and is the value of the component in any direction perpendicular to z. In a uniaxial phase all the directions perpendicular to z are degenerate. The system is symmetric for rotations around the z axis, which in the case of the uniaxial phase, corresponds to the director n. See Fig. 8.1.

In biaxial phases, however, the physical properties depend on the orientation in the plane perpendicular to the principal axis of the phase associated with the nematic director n. The symmetry of rotations around the principal axis is broken and that condition can be described by the emergence of different values for the components of Q in the x and y directions. As schematically represented in Fig. 8.1, such a nematic phase needs a secondary director (m), perpendicular to the principal director (n) to define the corresponding orientational order. The third director (1) is automatically defined by the direction mutually perpendicular to n and m. The physical parameter Q can be represented in its principal frame (with the components defined to fulfill the condition | Qzz| >

| Qyy| > I Qxx I) by

Schematic representation of uniaxial [left) and biaxial [right] nematic phases

Figure 8.1 Schematic representation of uniaxial [left) and biaxial [right] nematic phases.

with Qxx = Qyy contrary to the uniaxial case where Qxx = Qyy = Q±.

As referred in Chapter 2 the search for the biaxial nematic phase, theoretically predicted in 1970 by Freiser [Freiser, 1970), is still a very topical issue in the field of liquid crystals. Especially in the case of thermotropics, the search for the biaxial nematic phase remains an open problem. After more than thirty years of controversial results [Luckhurst, 2001), by the middle of the 2000 decade, several thermotropic LC systems, namely side-chain polymers [Severing and Saalwachter, 2004), bent-core mesogens [Acharya et al., 2004; Madsen et al., 2004), bent-core dimers [Channabasaveshwar et al., 2004), and organosiloxane tetrapodes [Figueirinhas et al., 2005; Merkel et al., 2004), were claimed to exhibit such a phase.

In principle, any physical parameter described by a second-rank tensor is a good candidate to provide evidence of an eventual biaxial nematic phase. Considering Eqs. 8.1 and 8.2, the measurement of the Qxx and Qyy in the principal frame of the tensorial quantity Q

Schematic representation of thermotropic molecules exhibiting phases reported as biaxial nematics in 2004-2005

Figure 8.2 Schematic representation of thermotropic molecules exhibiting phases reported as biaxial nematics in 2004-2005.

(with the z axis coincident with the principal direction), is enough to identify the phase as biaxial if Qxx = Qyy. An asymmetry parameter can be defined by the equation

the phase is recognized as biaxial if n = 0.

Amongst different possible methods, optical techniques, such as polarizing optical microscopy texture defects observations and conoscopy, have been used to identify such a type of phase in LC materials (Luckhurst, 2001; Merkel et al., 2004). However, limitations related to possible biaxiality induced by surface interactions on the LC samples have been frequently questioned in the literature. Contrary, by dealing in general with bulk samples, NMR has been systematically considered as a reference technique to the identification of biaxial nematic behavior in liquid crystals (Galerne, 1988; Luckhurst, 2001; Madsen et al., 2004). Deuterium NMR is particularly useful if partially deuterated samples are used, since each deuterium nucleus in the presence of an electric field gradient (e.g., in a C-D bond) contributes with a single pair of lines to the NMR spectra. Actually, a set of equivalent deuterium nucleus, with the same average angle between the C-D bond and the static external magnetic field B0 gives a single pair of quadrupolar lines. That occurrence is typically identified by the additional amplitude of such a pair of NMR lines. Optionally, if a deuterated sample is not available, mixtures with deuterated materials can be used, assuming that the deuterated molecule used as a probe follows the common phase molecular ordering of the host material. In the case of deuterium NMR, the physical property Q (see Eqs. 8.1, 8.2, and 8.3) used to probe the molecular ordering properties is the electric field gradient (EFG) tensor (V) with components Vy.

 
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