Lecture handout including QS - Department of Materials Science ...

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BH4 Course B: Materials for Devices BH4 Liquid Crystals • Crystalline materials have long-range order. This means that they are anisotropic: their properties (e.g. refractive index, thermal expansion coefficient, electrical conductivity) may differ, depending upon the direction of measurement. • In contrast, liquids, which have no long-range order, are isotropic: they are invariant with respect to direction. The absence of long-range order means that all directions are equivalent. • Somewhere in between there are Liquid Crystals, which are anisotropic liquids. Their anisotropy, or directionality, comes from molecular shape. Liquid crystals often consist of rod-shaped molecules, with a rigid long axis: e.g. Methoxybenzylidene Butylaniline, or MBBA The central region of the molecule (between the rings) is rigid, whilst the ends are flexible. These rod-shaped molecules are free to move relative to each other and flow past each other, so that there is no long-range positional order. However, because of their shape, they tend to line up, with their long axes lying roughly parallel, i.e. they have some orientational order. This alignment stems from packing considerations, and also electrostatic interactions. Nematic Liquid Crystal (LC) structure No positional order. Long range orientational order, defined by a Director, D. D This leads to useful anisotropic optical properties, which are the basis for electronic displays.
BH5 Course B: Materials for Devices BH5 The degree of orientational order in a LC is temperature dependent: • at high temperature thermal agitation overcomes the alignment interaction, leading to randomisation of the molecular orientation, i.e. the liquid crystal becomes a ‘normal’ isotropic liquid. • at low temperature the system may crystallise into a ‘normal’ crystal structure. crystal liquid crystal liquid Director, D highly ordered, no intrinsic order, no translational freedom increasing temperature, isotropic decreasing order An order parameter, Q, is used to describe the degree of orientational order. Q = 3 cos2 θ −1 2 Director, D θ where .... represents an average over all molecules. With all molecules aligned: cos 2 θ = 1 ⇒ Q = 1 For an isotropic liquid, with randomly oriented molecules: cos 2 θ = 1 € 3 ⇒ Q = 0 € € Consider a hemisphere: The probability of the molecule lying at an angle, € θ, is proportional € to the circumference, 2πr = 2πd sinθ r (Higher angles are more likely.) A small increment in angle, dθ , corresponds to a d surface area of 2πr × d × dθ = 2πd sinθ d dθ To calculate cos 2 θ , we integrate over the surface of the hemisphere (from θ = 0 to π / 2 ), and divide by the total surface area (for the hemisphere, this is 2πd 2 ): ∫ 0 π 2 cos 2 θ 2πd sinθ d dθ = − 1 π ⎡⎡ ⎤⎤ 2 2πd 2 3 cos3 θ ⎣⎣ ⎢⎢ ⎦⎦ ⎥⎥ = 1 3 0 €
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Lecture handout including QS - Department of Materials Science ...

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