Spin Probe Determination of Molecular Orientation Distribution and Rotational Mobility in Liquid Crystals: Model-Free Approach

Abstract

A model-free approach for simulation of EPR spectra of nitroxide spin probes in liquid-crystalline materials was suggested and used to obtain parameters of molecular orientation and rotational mobility. The developed method is based on experimental recording and numerical simulation of the angular dependence of EPR spectra, which is shown to be much more informative in comparison with a single EPR spectrum. Quantitative spectral simulations considering both local orientational ordering and distribution of local directors in the sample were used for discrimination of models of rotational mobility and orientational alignment. The method was applied for detailed quantitative characterization of axial, orthorhombic, and low-symmetry non-orthorhombic molecular orientation distributions. It is shown that the ordinarily used model of rotational diffusion in a mean-field potential is suitable for the description of molecular mobility and orientational ordering only for relatively low sample temperatures and low-mobility probe molecules with large sizes. In cases of high molecular mobility, the more realistic jump mechanism of molecular moves can be approximately described as quasi-librations. For ordered liquid crystals it was found that mostly the order parameters up to rank 12–14 are essential and easily determined. When well-aligned materials are described, the order parameters up to 18th rank or even higher become meaningful. Both molecular and sample biaxiality is analyzed and quantitatively characterized. The local molecular ordering and sample orientational alignment are quantitatively characterized separately.

Orientation Distribution of Molecules in a Smectic Liquid Crystal with a Distorted Director Geometry

“…Modeling of the angular dependences of the EPR spectrum was carried out according to the technique developed in ref . This technique is based on the explicit consideration of the director orientation inhomogeneity in real samples of liquid crystal material, that is, taking into account the orientation distribution of local directors of the liquid crystal material.…”

“…It is assumed that in each of the local ordered regions, the probe is oriented in accordance with the orientational potential of the mean field where (0, β m , γ m ) are Euler angles that transform the director reference frame into the molecular reference frame, k B is Boltzmann constant, and c n l are coefficients of the potential decomposition. It has been shown in the literature that the EPR spectra of spin probes in deformed liquid crystals can be well approximated by the superposition of spectra of individual local ordered regions described by a simple molecular field potential such as in eq . ,− This approach would fail if the spin probe molecules would predominantly be localized in the regions with a low orientation order, such as defects and interdomain boundaries. The spin probe chosen in the present work is embedded well in the bulk structure of the smectic mesophase, which is corroborated by the experimentally observed strong angular dependences of EPR spectra, and the absence of dipolar and exchange broadening in the recorded spectra.…”

“…Among many techniques used to determine the orientational ordering of liquid crystals, special attention is attracted by the spin probe method, which has been used for this purpose for a long time. − The principle of this technique consists in introducing into the studied medium an admixture of stable free radical having an electron paramagnetic resonance (EPR) spectrum. Thus, the free radical serves as a spin probe.…”

Rotational Dynamics of Nitroxide Biradical in Room-Temperature Ionic Liquids Measured by Quantitative Simulation of EPR Spectra

“…We note that other ways to improve sensitivity toward the determination of the principal rotation axis are the use of high-field EPR 26,27 or the study of nitroxides in aligned media. 28 The temperature dependence of the spin-exchange integral J is shown in Figure 6a. Its value characterizes the overlap of the orbitals of the two unpaired electrons, or, equivalently, the energy separation between singlet and triplet states of the biradical.…”

“…Note that because the monoradical was obtained from the corresponding biradical by reduction of one of the nitroxide groups, one would expect close rotation characteristics for the two cases. We note that other ways to improve sensitivity toward the determination of the principal rotation axis are the use of high-field EPR , or the study of nitroxides in aligned media …”