Anisotropic fluid

Liquid crystals represent a state of matter with physical properties normally associated with both soHds and Hquids. Liquid crystals are fluid in that the molecules are free to diffuse about, endowing the substance with the flow properties of a fluid. As the molecules diffuse, however, a small degree of long-range orientational and sometimes positional order is maintained, causing the substance to be anisotropic as is typical of soflds. Therefore, Hquid crystals are anisotropic fluids and thus a fourth phase of matter. There are many Hquid crystal phases, each exhibiting different forms of orientational and positional order, but in most cases these phases are thermodynamically stable for temperature ranges between the soHd and isotropic Hquid phases. Liquid crystallinity is also referred to as mesomorphism. 

Leslie, F. M., Some constitutive equations for anisotropic fluids. Quart J Mech Appl Math, 1966,19(3), 357 370. 

Being bordered by the solid and liquid states, the liquid crystal state has some of the order of a solid, combined with the fluidity of a liquid. As such, it is an anisotropic fluid and it is this anisotropy that has led to the widespread application of liquid crystals. 

In this book we consider only fluids that are isotropic, meaning that the fluid properties are independent of direction. By contrast, solids can readily have spatially oriented properties. Consider, for example, a common material like graphite, whose molecular structure has strongly oriented layers. Both mechanical and thermal properties are vastly different normal to and parallel to the layers. While ordinary fluids exhibit no such properties, it is possible to have anisotropic fluids. For example, long-chain polymeric fluids can exhibit properties that are oriented relative to the flow directions. 

Anisotropic fluids, of which nematic liquid crystals are the most representative and simplest example, are characterized by an anisotropic dielectric permittivity. The nematic phase has D,yuh symmetry, and in a laboratory frame with the Z axis parallel to the C , symmetry axis (the director) the permittivity tensor has the form ... 

The model of a dipole in a spherical cavity can only provide qualitative insights into the behaviour of real molecules moreover, it cannot explain the effect of electrostatic interactions in the case of apolar molecules. More accurate predictions require a more detailed representation of the molecular charge distribution and of the cavity shape this is enabled by the theoretical and computational tools nowadays available. In the following, the application of these tools to anisotropic liquids will be presented. First, the theoretical background will be briefly recalled, stressing those issues which are peculiar to anisotropic fluids. Since most of the developments for liquid crystals have been worked out in the classical context, explicit reference to classical methods will be made however, translation into the quantum mechanical framework can easily be performed. Then, the main results obtained for nematics will be summarized, with some illustrative... 

The basic concepts of deuterium (2H) NMR and its application to anisotropic fluids have been described in numerous references [1,4-7]. This technique has some specificities which make it particularly relevant to investigate fluid, partially ordered systems ... 

In case of anisotropic motions (an anisotropic fluid), the quadrupolar interaction is partially time-averaged to a residual tensor. This residual interaction A modulates the time relaxation function via a reversible dephasing MYt)=exp[-t/T2]cosAt. For motions uniaxial around a symmetry axis, the effect on the spectrum is to split the resonance line into a symmetric doublet with a splitting (in frequency units) ... 

The big difference between normal isotropic liquids and nematic liquids is the effect of anisotropy on the viscous and elastic properties of the material. Liquid crystals of low molecular weight can be Newtonian anisotropic fluids, whereas liquid crystalline polymers can be rate and strain dependent anisotropic non-Newtonian fluids. The anisotropy gives rise to 5 viscosities and 3 elastic constants. In addition, the effective flow properties are determined by the flow dependent and history dependent texture. This all makes the rheology of LCPs extremely complicated. 

Ionic liquid crystals are liquid crystals containing ionic moieties. Ionic hquid crystals having ammonium and pyridinium salts were reported to show stable thermotropic liquid crystalline behavior [35 0]. Seddon, Bruce, and coworkers showed that some imidazolium and pyridinium salts exhibit low melting points and liquid crystalline behavior [41]. Ionic liquid crystals with lower temperature mesophase ranges are called hquid crystalline ionic liquids. A large variety of thermotropic liquid crystaUine ionic liquids exhibiting anisotropic fluid states were prepared. In particular, the ionic liquid crystals based on imidazolium salts 1 [42-46], 2... 

R.J.Gordon, W.R.Schowalter, Anisotropic fluid theory a different approach to the dumbbell theory of dilute polymer solutions, Trans Soc. Rheol. 15(1972), 79-97. 

For anisotropic fluids, including water, moving parallel to the wall, 12.2.3] has... 

Many computers, such as laptops, have flat-panel screens or displays that contain liquid crystals (Bahadur 1990). Liquid crystals are composed of small semirigid molecules that are elliptical or oblong in shape and spontaneously orient, forming anisotropic fluids (Collings 1990). Liquid crystals commonly used in flat-panel displays have orientational order but do not have long-range positional order. The direction of the preferred orientation in a liquid... 

S. Hess, Transport Phenomena in Anisotropic Fluids and Liquid Crystals, J. Non-Equilib. Thermodyn. 11 (1986) 175. 

We recall, finally, that the interpretation of energy relaxation results, in pure anisotropic fluids and simple solutions, is more limited by the lack of precise knowledge of the full intermolecular potential than of theoretical tools. 

Interest in this topic w as stimulated by the intense experimental research on phase transitions in disordered media in the 1990s. Tire experimental studies have involved simple fluids such as He or N2 [131, 132, 280], fluid mixtures (e.g., isobutjTic acid and water [115]), and anisotropic fluids such as nematic liquid crystals [281-284]. One main conchtsion from these. studies was that fluids in dilute aerogels can indeed undergo true phase transitions. 

The expression after the first equal sign in Eq. (7.18) provides the statistical definition of the singlet density in the disordered system where 5 q — qt) — S r — Vi) for a simple fluid without internal degrees of freedom, whereas q — qi) — 6 r - Vi) d u - (jJi) for anisotropic fluid particles. The second... 

Hensel Bielowka, S., Psurek, T., Ziolo, J., and Paluch, M. (2001) Test of the fractional Debye-Stokes-Einstein eqnation in low-molecnlar-weight glass-forming liqnids nnder condition of high compression, Phys. Rev. E 63, 062301 Wang, C. H. (2002) Enhancement of translational diffusion coefficient of a probe in a rotationally anisotropic fluid, Phys. Rev. E 66, 021201... 

There is an orientational order in the liquid crystals which are anisotropic fluids. The director field n(r) or its components n affect the hydrodynamic behavior, so that is dependent on the distortion of the director field as well. For convenience, we designate a vector N for the angular velocity of liquid crystal directors with respect to the background fluid,... 

By far the most important application of liquid crystals is display devices. Liquid crystal displays (LCDs) are used in watches, calculators, and laptop computer screens, and for instrumentation in cars, ships, and airplanes. Several types of LCDs exist. In general their value is due to the fact that the orientation of the molecules in a nematic phase substance can be altered by the application of an external electric field, and that liquid crystals are anisotropic fluids, that is, fluids whose physical properties depend on the direction of measurement. It is not pure liquid crystalline compounds that are used in LCDs, but liquid crystal mixtures having optimized properties. 

Freedericksz V and Zolina V 1933 Forces causing the orientation of an anisotropic fluid Trans. Faraday... 

This result is identical to the expression which is obtained from the perturbation expansion of A for a pure fluid. Thus, referring to Equation 2, the first-order conformal solution relation for anisotropic fluids is... 

When viewed through such a microscope, an isotropic liquid would appear black as the plane-polarized light would pass through unaffected and be absorbed by the analyzer. Flowever, liquid crystals are anisotropic fluids and their birefringence causes the plane polarization to be lost the light becomes elliptically polarized instead (i.e., there are... 

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