where βe is the electron Bohr magneton, h is Plank's constant, I is the peak amplitude, and the subscripts +1, 0, -1 are nuclear quantum numbers for 14N. ΔHpp0 is the peak-to-peak line-width of the central line. The values of giso and b are calculated from the parameters for the immobilized spin probe:

[MATHEMATICAL EXPRESSION OMITTED] (3)

[MATHEMATICAL EXPRESSION OMITTED] (4)

Evila et al. performed the EPR study on the order parameters and molecular dynamics using spin probe 2 in a reentrant nematic (RN) liquid crystal mixture, 6OCB-8OCB. The order parameter is shown as a function of temperature in the different phases (Fig. 3). The ordering decreases slightly at the N-SmA and SmA-RN transitions in the cooling run.

Although the EPR spin probe method is an excellent technique, non-LC spin probes may actually cause phase separation when they are mixed with the host LC materials. In this case, the true molecular dynamics and microenvironment in the host LC phases cannot be evaluated. In fact, although this is another type of soft materials, the studies using the ionic liquid imidazolium nitroxide radical (±)-6 as an EPR spin probe revealed that the τR value of (±)-6 in the host ionic liquid 10 became much smaller than that simply estimated from the viscosity Z of 10, implying the existence of local structures in the host ionic liquid (Fig. 4). This behavior was not observed when typical neutral nitroxide spin probes such as TEMPO were employed with the same host 10. Accordingly, it is desirable to use an LC spin probe in a diamagnetic host LC material.

3 LC nitroxide spin probes in diamagnetic LC hosts

Since two or more different materials showing the same LC phase are generally miscible, LC nitroxide radical materials could be used as appropriate spin probes for the diamagnetic host materials showing the same LC phase.

3.1 First-generation of rod-like LC nitroxide radical materials

Only a few rod-like LC nitroxide radical materials containing a DOXYL or TEMPO group within the terminal alkyl chain had been synthesized before 2003 (Fig. 5). Dvolaitzky et al. synthesized the first LC nitroxide radicals 11–13 showing several smectic phases. The EPR spectra of the spin probe 12 dissolved in diamagnetic host LC materials changed at LC-to-LC phase transition. However, when the LC nitroxide radical materials illustrated in Fig. 5 were employed as spin probes, it was difficult to determine the exact direction of molecular alignment of the spin probes and host materials to the applied magnetic field, due to the free rotation of the nitroxide radical unit inside the molecule and the possible phase separation (see Section X.2).

3.2 Second-generation of rod-like LC nitroxide radical materials

In 2004, the design and synthesis of a new type of chiral LC nitroxide radical materials 18 (Fig. 6), which could satisfy the following four requirements and showed chiral (or achiral) nematic [N* (N)] and/or smectic C [SmC* (SmC)] phases at wide temperature range below 90 1C, were reported by the present authors.

(1) Spin source: A nitroxyl group with a large electric dipole moment (ca. 3 Debye) and known principal g-values (gxx, gyy, gzz) should be the best spin source, because i) the dipole moment is large enough for the source of the spontaneous polarization (Ps) and ii) the principal g-values are useful to determine the direction of molecular alignment in the LC phase by EPR spectroscopy (Fig. 7).

(2) High thermal stability: A molecule with 2,2,5,5-tetraalkyl-substituted pyrrolidine-1-oxy (PROXYL) unit is stable enough for repeated heating and cooling cycles below 150 °C in the air.

(3) Molecular structure: (a) To avoid the free rotation of the nitroxide radical unit inside the molecule so as to maximize the [MATHEMATICAL EXPRESSION OMITTED] and [MATHEMATICAL EXPRESSION OMITTED], a geometrically fixed chiral cyclic nitroxide radical unit should be incorporated into the rigid core of LC molecules. (b) To obtain a slightly zigzag molecular structure and a negative Δε advantageous for the appearance of a ferroelectric SmC* phase, a trans-2,5-dimethyl-2,5-diphenylpyrrolidine-1-oxy (PROXYL) skeleton in which the electric dipole moment orients to the molecular short axis is the best choice (Fig. 7).

(4) Chirality: Since both chiral and achiral LC materials are required for comparison of their optical and magnetic properties in the various LC phases, the molecules should be chiral and both enantiomerically enriched and racemic samples need to be available.

Chumakova et al. reported the ordering of the LC spin probes (S, S)-18a (m=n=15, Fig. 6) and (±)-18a dissolved in the magnetically aligned nematic matrix of achiral N-(4-methoxybenzylidene)-4-butylaniline (MBBA) in detail. This work demonstrated that the change of the orientation distribution of 18a reflects only the structural change of the host LC material, irrespective of the chirality of spin probes (Fig. 8), and that the LC nitroxide radical molecules are better probes for the diamagnetic LC material than non-LC TEMPO radical.

4 Magnetic properties of second-generation of rod-like LC nitroxide radical materials

When the concentration of a nitroxide spin probe in a diamagnetic host material is low enough, the conventional methodologies to estimate the orientational order of the spin probe by using ΔH and A values can be employed. In contrast, when the nitroxide radical material is not diluted by the diamagnetic host material, the radical spin-spin interactions prevail over the hyperfine coupling interactions between electron and nuclear spins, resulting in the ΔH increase and the loss of hyperfine coupling structure (Fig. 9). In this case, orientational order and intermolecular magnetic interactions can be evaluated by analysing the g-values and changes in ΔH, respectively.

In this section, the following four findings by the present authors are described: (1) The principal g-values (g// and g[perpendicular to]) and molecular orientation of the LC nitroxide radical molecule 18b (m=8, n=7) confined in a surface-stabilized LC cell were determined by EPR spectroscopy. (2) The magnetic-field-induced molecular orientation in the bulk nematic and SmC phases of (±)-18c (m=n=13) was determined by EPR spectroscopy. (3) The unique spin glass-like intermolecular ferromagnetic interactions ([bar.J] > 0), which were referred to as positive "magneto-LC effects", were discovered in the various LC phases of 18 in weak magnetic fields by EPR spectroscopy and SQUID magnetization measurement. (4) The existence of anisotropy in the intermolecular ferromagnetic interactions responsible for the positive magneto-LC effects was proved by the measurement of the electric field dependence of molecular orientation and magnetic interactions in a surface-stabilized ferroelectric LC cell of (S,S)-18c showing an SmC* phase.

4.1 Molecular orientation in the N and N* phases confined in a surface-stabilized LC cell

It is well-known that the orientation of LC molecules can be controlled by using a surface-stabilized LC cell. However, until 2005 there was no report on the study of the orientation of LC molecules in a surface-stabilized LC cell by EPR spectroscopy. The present authors reported for the first time the molecular orientation in the N and N* phase of 18b confined in surface-stabilized LC cells (Fig. 10).

First, the angular dependence of g-value for the N and N* phases of (±)-18b and (S,S)-18b, respectively, was measured by EPR spectroscopy. For the N phase of (±)-18b, the angular profile of the vertically rubbed cell was flat, while that of horizontally rubbed cell oscillated significantly (Fig. 11a). In contrast, for the N* and crystalline phases of (S,S)-18b, the angle profiles of both rubbed cells were almost identical (Fig. 11b, c). These experimental results can be explained by the orientation models shown in Fig. 12. In the LC phases, the rotation axis fluctuates from the director (the average direction of the molecular long axis). To take this fluctuation into account, g// was defined as the ensemble g-value observed when the magnetic field is applied parallel to the director and g[perpendicular to] as the ensemble g-value observed when the magnetic field is applied orthogonally to the director.

The orientation model for the N phase of (±)-18b indicates that the LC molecule rotates around the long axis of the molecule, which is aligned with the rubbing direction on the cell surface, and that the direction of the long axis is uniform throughout the cell (Fig. 12a). Since the angle between the magnetic field direction and the long axis of the molecule varies between 0 and 90° for the horizontally rubbed cell ([??]), g// or g[perpendicular to] is alternately observed. For the vertically rubbed cell (O), only g[perpendicular to] is observed since the magnetic field is always orthogonal to the director.

The orientation model for the N* phase of (S,S)-18b indicates that the LC molecule rotates around the long axis of the molecule, which aligns with the rubbing direction on the cell plane, and that the long axis between the two cell planes rotates to form a helical superstructure (Fig. 12b). The agreement between the angular profiles of horizontally and vertically rubbed cells is due to this helical superstructure.

To determine the g// and g[perpendicular to] values, the temperature dependence of the g-value was measured for the N phase of (±)-18b confined in a horizontally rubbed cell at the angles of 0 and 90° (Fig. 13a). The temperature dependence of the g-value followed the Haller equation:

g//(T) = g// (1 - T/T*)β (5)

g[perpendicular to](T) = g[perpendicular to] (1 - T/T*)β (6)

where T is the temperature (K), T* is the transition temperature (K) between the N and isotropic phases, and β is the exponent parameter.