Order parameter of nematics

An overview of the apphcation of NMR to the field of liquid crystals over the past 50 years has been presented and the important aspects of proton and deuterium NMR have been delineated. The use of liquid crystals as solvents in NMR spectroscopy has been reviewed." Reviews on NMR studies of orientational order with 20 references, rotational diffusion of liquid crystals in the nematic phase and NMR spectroscopy in liquid crystals and membranes are available. A review on the application of spectroscopic methods to liquid crystalline phases has appeared during the period under report and it includes a discussion of the NMR methods. NMR and other methods used to determine the order parameters of nematics have been reviewed. ... 

The order parameter of nematic networks is obtained as a function of temperature and the crosslink density. For nematic networks crosslinked at the isotropic phase, the nematic to isotropic transition is lower than that of the constituent nematic polymers which are the same length as the strands in the networks, while the transition temperature increases for the... 

Fig. 3.5 a Order parameter of nematic dried films made with CNT dispersions that have been sonicated during different times tus- All of the used dispersions have undergone a single step of 1 h. b Order parameter of nematic dried films made with CNT dispersions that has been ultracentrifuged during different times tuc- All of the used dispersions were sonicated during 2 h. Reproduced with permission from [76], Copy right 2011 American Chemical Society... 

Neutron scattering from mixtures of normal hydrogenous molecules with deutoiated versions of the same compound provides a route to the orientational order parameters of nematic phases. Reliable results exist for and in PAA. Higher wder parameters have been determined in other materials but the experimental conditions used suggest that the values are not yet accurate. 

Note 2 For rod-like molecules, the order parameter of the effective molecular symmetry axis at the nematic-isotropic transition is about 0.3 and can increase to about 0.7 in the... 

In addition to lowering V th, ferroelectric nanoparticles such as BaTi03 or Sn2P2S6 [144, 156, 318-323] have also been shown to increase the nematic-to-isotropic phase transition temperature (TN/Iso) and the order parameter of the nematic host [142, 320, 324-326], which are thought to have their origin in a coupling of the electric dipole moment of the particles with the orientational order of the surrounding nematic molecules (Fig. 6). 

Lemaire, B J., Panine, P., Gabriel, J.C.P. and Davidson, P. (2002) The measurement by SAXS of the nematic order parameter of laponite gels. Europhysics Letters 59, 55-61... 

Recently, the surface tensor model has been used together with the dielectric continuum model to calculate the orientational order parameters of solutes in nematic solvents [8,9,27], Figure 2.32 shows the theoretical results for anthracene and anthraquinone in nematic solvents with different dielectric anisotropy. Considering only the surface tensor contribution, positive Szz and Sxx and negative are obtained, with Szz > Sxx > Syy. This corresponds to what could be expected on the basis of the molecular shape the long axis (z) is preferentially aligned with the director, and the normal to the... 

FIG. 15.50 Order parameters of rodlike molecules in the isotropic and the nematic states. Kindly provided by Prof. SJ. Picken (2003). 

Both with thermotropics and lyotropics, a large number of properties can be studied. For example, NMR can be used to obtain the order parameter of the cholesteric phase (2 ). Rheooptic studies (27) (for example, the variation of the refractive index under shear) describe the way cholesteric phase reorganizes to nematic after orientation by a strong shear. 

Strzelecki has studied the orientation of a nematic polymer in its LC state in a 0.3 T magnetic field by X-ray diffraction and found that the sample had an order parameter of 0.64 The orientation of LC polymers in a magnetic field has also been observed by others using X-ray techniques I Extruded fibers have been studied by Roviello and Sirigu to measure the degree of orientation achievable in mesomorphic polymers by shear field, but only solid samples were studied and even though they were oriented, the results gave little quantitative indication of the order of the mesophase... 

Worked Example 10.5 of Chapter 10 shows how the Maier-Saupe potential can be used to predict the order parameter of a nematic. 

Transient EMR has also been reported on the triplet state of retinal dissolved in liquid crystalline phase (Munzenmaier et al., 1992). The simulation of the transients with the stochastic Liouville equation provides the motional and order parameters of the pigment. The anisotropy ofmotional correlation times is high as expected for such an extended linear molecule and the correlation times couldbe followed with temperature over a range of two orders of magnitude in the nematic and smectic phase. 

The fairly good quality of the fits validates both Leadbetter s assumptions and the Maier-Saupe distribution function. However, the values of S obtained and even the quality of the fits obviously depend on the odd or even number of (CH2) groups in the flexible spacer. This odd-even effect is widespread and well known in the field of main-chain LCPs and will be discussed later in this article. The nematic order parameter of main-chain LCPs may reach values as high as 0.85 which demonstrates the very high orientation of the nematic phase of these polymers. Such a large orientation is undoubtedly responsible for the good mechanical properties of this type of materials. The treatment described above therefore provides a very easy way of characterizing the orientational order of a nematic phase. It has also been tested for thermotropic side-chain LCPs and found to be satisfactory as well [15]. Unfortunately, it has not been used yet in the case of lyotropic LCPs except for some aqueous suspensions of mineral ribbons (Sect. 5) which are not quite typical of this family of materials. 

Lowering the temperature increases Szz for all systems to the same limiting value of Szz 0.65 in the nematic phase [35, 99, 100]. Note, that the order parameter curve of polymer 1 exhibits a horizontal slope at the glass transition. A further jump of Szz. observed for the polymers 2, indicates an additional smectic A phase with a limiting value of Szz 0.9. No such discontinuity is detected for the monomeric liquid crystal 5, exhibiting a smectic A phase, likewise. Comparison of the order parameters of Fig. 17 with those of NMR [108-110] and birefringence studies... 

A good fit of (2.14) to the experimental data is obtained by varying only two parameters, Sq and the temperature independent contribution C. The value obtained for Sq is 0.08 0.03 and does not vary with temperature in the whole temperature range of about 15 K above Tni- It is larger than the surface order parameter of the same liquid crystal in contact with inorganic Anopore membrane, but still considerably smaller than the bulk nematic value at the transition temperature. This indicates that only a partial orientational wetting takes place in the isotropic phase of the PDLC material and that the... 

It is useful to rewrite the quantities into a dimensionless form. Usually, coordinates are measured in terms of the film thickness d (or another t5q)ical dimension in the case of a non-planar geometry) and the correlation length = Qd= y/27CL/B fs 10 nm. The order parameter is rescaled in units of the scalar order parameter of the nematic phase at the phase transition temperature, = 2B/Z /6C 0.2 — 0.6, and the temperature is controlled by d = (T — — T ) the reduced temperatures 0 = 1, 0, and 9/8... 

---