Magnetic Properties of Liquid Crystals

Just as many other macroscopic properties, magnetic susceptibility of liquid crystal is also anisotropic, i.e., it can be described by a tensor, which, in a uniaxial system fixed to the director, can be expressed as  

In Ihis expression X and Xl are the susceptibility along the director and normal to it. They relate to the average molecular susceptibility Xmu (unit m /kg), the mass-density p, and the uniaxial order parameter S as  

The magnetic susceptibility tensor is a very useful measure of the macroscopic symmetry it gives the direction of the uni-axis with large precision. The weighted average of the X and Xi give the average susceptibility density  

Sometimes it is also useful to determine the relahve anisotropy as  

These expressions show that the magnetic anisotropy Ax a is proportional to the order parameter, and its temperature dependence gives the temperature dependence of the order parameter.  

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Dunmur, D., Toriyama, K. Magnetic properties of liquid crystals. In Demus, D., Goodby, J., Gray, G.W., Spiess, H.-W., Vill, V. (eds.) Physical Properties of Liquid Crystals, pp. 102—112. Wiley-VCH, Weinheim (1999)... 

D. Dunmur, K. Toriyama, Magnetic properties of liquid crystals, in Physical Properties cf Liquid Crystals, Vol. 2, Ch. 4, Ed. D. Demus, J. Goodby, G.W. Gray, H.-W. Spiess, V. Vill, Wiley-VCH, Weinheim, (1999). 

Muller, K., Kothe, G., and Wassmer, K.-H. Dynamic Magnetic Resonance of Liquid crystal Polymers Molecular Organization and Macroscopic Properties. Vol. 95, pp. 1 — 56. 

One of the most specific and unique features of low-molecular liquid crystals is their ability for orientation in external fields — mechanical, electric and magnetic. It is this property that establishes wide capabilities for technical application of liquid crystals. Today electric and magnetic optics of liquid crystals are an independent and useful for practics branch of the physics of the condensed state of matter 42 43 ... 

Fast separations of 16 PAHs were achieved within 6-7 min using packed columns. A comparison study of the PAH molecular shape recognition properties of liquid-crystal-bonded phases in packed-column SFC and HPLC found that the selectivity was enhanced in SFC. The result of an interlaborotory round-robin evaluation of SFC for the determination of PAHs also shows that SFC possesses distinct advantages over GC-mass spectrometry (MS) and nuclear magnetic resonance (NMR) including speed, cost, and applicability. 

Dynamic Magnetic Resonance of Liquid Crystal Polymers Molecular Organization and Macroscopic Properties... 

Generally, properties of liquid crystals depend on direction, they are tensorial. Some of them (like density in nematics) may be scalar. A scalar is a tensor of rank 0. It has one component in a space of any dimensionality, 1 = 2° = 3 ... = 1. Other properties, like spontaneous polarization P (e.g., in chiral smectic C ) are vectors, i.e., the tensors of rank 1. In the two-dimensional space they have 2 = 2 components, in the 3D space there are 3 = 3 components. For instance in the Cartesian system P = iP + jPy + kP. Such a vector can be written as a row (Px> Py, Pz) or as a coluirm. Properties described by tensor of rank 2 have 2 = 4 components in 2D space and 3 = 9 components in the 3D-space. They relate two vector quantities, such as magnetization M and magnetic induction B, M = xB, where % is magnetic susceptibility. Each of the two vectors has three components and, generally, each component (projection) (a = x,y,z) may depend on each of Bp components (p = x,y,z) ... 

Leslie, F.M. Introduction to nematodynamics. In Dunmur, D., Fukuda, A., Luckhurst, G., INSPEC (eds.) Physical Properties of Liquid crystals Nematics, pp. 377-386, London (2001). Parodi, O. Stress tensor for nematic liquid crystals. J. Phys. (Paris) 31, 581-584 (1970) Miesowicz, M. The three coefficients of viscosity of anisotropic liquids. Nature 158, 27 (1946) Influence of the magnetic field on the viscosity of para-azoxyanisole. Nature 136, 261 (1936). 

Properties of Liquid Crystal Epoxy Thermosets Cured in a Magnetic Field... 

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