Nematic ordering

For structures with a high curvature (e.g., small micelles) or situations where orientational interactions become important (e.g., the gel phase of a membrane) lattice-based models might be inappropriate. Off-lattice models for amphiphiles, which are quite similar to their counterparts in polymeric systems, have been used to study the self-assembly into micelles [ ], or to explore the phase behaviour of Langmuir monolayers [ ] and bilayers. In those systems, various phases with a nematic ordering of the hydrophobic tails occur. 

Disc-like particles can also undergo an Onsager transition—here tire particles fonn a discotic nematic, where tire short particle axes tend to be oriented parallel to each other. In practice, clay suspensions tend to display sol-gel transitions, witliout a clear tendency towards nematic ordering (for instance, [22]). Using sterically stabilized platelets, an isotropic-nematic transition could be observed [119]. 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

Lattice models have the advantage that a number of very clever Monte Carlo moves have been developed for lattice polymers, which do not always carry over to continuum models very easily. For example, Nelson et al. use an algorithm which attempts to move vacancies rather than monomers [120], and thus allows one to simulate the dense cores of micelles very efficiently. This concept cannot be applied to off-lattice models in a straightforward way. On the other hand, a number of problems cannot be treated adequately on a lattice, especially those related to molecular orientations and nematic order. For this reason, chain models in continuous space are attracting growing interest. 

On the theoretical side, Marcelja [26] was first to account explicitly for flexible tail chains in nematic ordering, using the Maier-Saupe model potential (Eq. 1) for each segment of the molecule. More complex models were proposed by Samulski et al. [27] and Emsley et al. [28]. In these approaches alkyl chains are assumed to exist in a discrete set of conformers described by... 

Figure 10.13. (a) SEM image of ZnO nanorods coated with octylamine. Scale bar, 200 nm. (b) Uniform nanorod film fabricated by spin coating of ZnO nanorods. Scale bar, 500 nm. The nanorods assemble into domains with nematic ordering, (c) Saturated transfer characteristics for a thin-film transistor fabricated by spin coating of ZnO nanorods with different ligands octylamine (solid line), butylamine (dashed line). Vi = 60V. (d) Output characteristics of a spin-coated device made from octylamine-stabilized ZnO nanorods.The device structure is shown in the inset in (c). Reproduced from Ref. 83, Copyright 2006, with permission from the American Chemical Society. 

Mesophase with a helicoidal supramolecular structure of blocks of molecules with a local smectic C structure. The layer normal to the blocks rotates on a cone to create a helix-like director in the smectic C. The blocks are separated by plane boundaries perpendicular to the helical axis. At the boundary, the smectic order disappears but the nematic order is maintained. In the blocks the director rotates from one boundary to the other to allow the rotation of the blocks without any discontinuity in the thermomolecular orientation. 

From these measurements of linear dichroism, it can be concluded, that the linkage of l-l.c. s to a polymer backbone generally reduces the nematic order. This effect has been found so far for poly(acrylates), poly(methacrylates) and poly-(siloxanes) and is established by NMR 59,60), ESR61) and birefringence measurements. 

When the polar groups are ordered on the micellar face in two-dimensional nematic order, x and y correspond to the directions on the micellar face corresponding to the minimum and maximum values of R respectively (3). 

Thermotropic liquid crystalline PPV derivatives 43 were prepared by the coupling of dihalodialkoxybenzene and divinylbenzene in the presence of a palladium catalyst, as outlined in Scheme 47 [133]. Polarized light microscopy, as a function of temperature, showed evidence of a nematically ordered structure in the material. X-ray diffraction analysis of the pristine polymers showed them to be semi-crystalline in nature, although the crystallinity of the polymer changed dramatically upon heating above 100 °C. 

Nematic order in which there is statistical alignment with a director. 

In the framework of irreversible thermodynamics (compare, for example, [31, 32]) the macroscopic variables of a system can be divided into those due to conservation laws (here mass density p, momentum density g = pv with the velocity field v and energy density e) and those reflecting a spontaneously broken continuous symmetry (here the layer displacement u characterizes the broken translational symmetry parallel to the layer normal). For a smectic A liquid crystal the director h of the underlying nematic order is assumed to be parallel to the layer normal p. So far, only in the vicinity of a nematic-smectic A phase transition has a finite angle between h and p been shown to be of physical interest [33],... 

Equation (39) shows that nematic degrees of freedom couple to simple shear, but not the smectic degrees of freedom the modulus of the nematic order parameter has a non-vanishing spatially homogeneous correction (see (39)), whereas the smectic order parameter stays unchanged. The reason for this difference lies in the fact that J3 and /3 include h and p, respectively, which coupled differently to the flow field (see (22) and (23)). Equation (38) gives a well defined relation between the shear rate y and the director tilt angle 9o, which we will use to eliminate y from our further calculations. To lowest order 0O depends linearly on y ... 

In contrast to the director tilt the lowest order correction to the nematic order parameter is quadratic in the shear rate (tilt angle) ... 

Fig. 11 Out of the material parameters connected with the order parameter, only /3 jn — has a measurable effect on the critical values. Some more parameters can influence the amplitudes of the order parameter undulation, namely L and Mo (the latter is only present in the case of the nematic order parameter). All amplitudes have been normalized such that = 1. Note that...

In the previous sections we have shown that the inclusion of the director of the underlying nematic order in the description of a smectic A like system leads to some important new features. In general, the behavior of the director under external fields differs from the behavior of the layer normal. In this chapter we have only discussed the effect of a velocity gradient, but the effects presented here seem to be of a more general nature and can also be applied to other fields. The key results of our theoretical treatment are a tilt of the director, which is proportional to the shear rate, and an undulation instability which sets in above a threshold value of the tilt angle (or equivalently the shear rate). 

Following the lines proposed above will give a prediction of the pattern formed above onset. For a transition from undulating lamellae to reorientated lamellae or to multilamellar vesicles, defects have to be created for topological reasons. Since the order parameter varies spatially in the vicinity of the defect core, a description of such a process must include the full (tensorial) nematic order parameter as macroscopic dynamic variables. 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

Typical 23 Na NMR spectra recorded within dense Laponite dispersion are shown in Figure 2, clearly exhibiting a large residual quadrupolar splitting [9] fingerprint of the macroscopic nematic ordering of these dense Laponite dispersions (more than 23% w/w). The cancellation of this residual quadrupolar... 

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... 

Porion, P., Al-Mukhtar, M., Meyer, S., Faugere, A.M., van der Maarel, J.R.C. and Delville, A. (2001) Nematic Ordering of Suspensions of Charged Anisotropic Colloids Detected by 23Na Nuclear Magnetic Resonance. The Journal of Physical Chemistry B... 

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