Introduction to liquid crystals. Nice webs site on Liquid Crystals. http://abalone.cwru.edu/

Linear Optics: Wave Surfaces Remember that the electric field of light is perpendicular to its direction of propagation. A point source emitting light from the center of an isotropic crystal emanates light outward uniformly in all directions. The position of the wave front defines a sphere (wave surface) whose radius is increasing with time.

Isotropic I

Isotropic II

Cubic

Cubic

If we chose another material with a larger susceptibility (more polarizable), its wave surface would expand more slowly because the susceptibility relates to the square of the refractive index. At an arbitrary time (t), the wave surface shows a radius inversely proportional to the index of refraction.

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Wave Surfaces for Uniaxial Materials For non-cubic single crystals, such as a hypothetical crystal of 2,4hexadiyne, the index of refraction and, hence, the polarizability vary with the direction that the light travels through the crystal.

CH 3 Uniaxial

Anisotropic

Sext.

CH 3

Atom / Molecule

Crystal

Sord.

Wave Surface(s)

The hypothetical crystal of 2,4-hexadiyne is uniaxial, where the unique axis is referred to as the optic axis. Other non-cubic crystals are characterized by two optical axes (i.e. there are three distinct axes) and are said to be optically biaxial. A material then, which has an index of refraction that depends on direction, is called birefringent, or doubly refracting. In the following discussion we limit the discussion of anisotropic crystals to those which are uniaxial.

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Double Refraction When a beam of unpolarized light enters a birefringent crystal at normal incidence (but not along the optic axis), two light beams emerge. This effect (first observed in calcite by the Vikings) is called double refraction: • One ray, which we call the ordinary ray, passes straight through the crystal. • The other ray, called the extraordinary ray diverges as it passes through the crystal and becomes displaced. The relative polarization of the two emerging beams is orthogonal.

Optic Axis

Optic Axis O-ray

O-ray

E-ray

E-ray

We can describe a beam of unpolarized light as the superposition of two orthogonally polarized rays (electric fields at 90 degrees to each other) traversing the same path. When both rays encounter the same index of refraction, as in an isotropic medium, or when the direction of propagation occurs along an optic of an anisotropic crystal, axis (i.e. the light is polarized in a direction perpendicular to the optic axis)the beams remain collinear and in phase. • For light polarized perpendicular to the optic axis, the material appears isotropic and the index of refraction is independent of the direction of propagation. We call this angularly independent index the ordinary index of refraction no. • If light is not polarized perpendicular to the optic axis, the index of refraction varies as a function of the direction of propagation. The angularly sensitive index becomes the extraordinary index of refraction ne.

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Explanation of Double Refraction Generally, for light traveling through a birefringent material in an arbitrary direction, the two orthogonally polarized rays "see" different polarizabilities and thus, different refractive indices. One ray becomes retarded relative to the other (introducing a phase shift) and may take a different path. A uniaxial material will therefore have two wave surfaces, a spherical ordinary wave surface and an ellipsoidal extraordinary wave surface. Note that the magnitudes of the principal axes of the wave surface are inversely proportional to the refractive indices normal to the direction of propagation.

• Light propagates at normal incidence for a wave surface, and your eye selects for rays that strike a normal incidence to the retina. • The origin of the extraordinary ray (unless the ray is traveling along or perpendicular to the optic axis) will appear displaced). • However for the ordinary wave surface ray will be traced back to its real origin (if eminent from within the materials or strikes the material at a normal incidence). Suggested reading: G Gray, Molecular Structure and Properties of Liquid Crystals Academic Press, New York, 1962. A. Saupe Angew Chem. Int Ed. 1968, 7, 98.

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What is a Liquid Crystal? A liquid crystal phase or mesomorphic phase is a phase comprising molecules having a higher degree of orientational order than is found in a liquid and less positional order than is found in a crystal.

Crystal (K)

Liquid

Liquid Crystal Increasing Temperature

H3 C O

CH N

methoxybenzilidenebutylaniline (MBBA) K

liquid

nematic 21°C

45°C

As shown in the diagram above there are discrete phase transitions between the crystal phase, the LC phase and the liquid phase. At each phase transition there is a corresponding heat of enthalpy for the transition.

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History of Liquid Crystals • F Reinitzer (Montash. Chem. 1888, 9, 421) observes two melting points in cholesteryl benzoate. • C. Mauguin (Bull. Soc. Fr. Min. 1911, 34, 71) performs and describes the first electro-optical experiments involving a twisted nematic phase. • M. G. Friedel (Ann. Phys. 1922, 18, 273) recognizes three kinds of LC phases and introduces new terminology. • Smectic smhgma "soapy" • Nematic nhma

"thread"

• Cholesteric (twisted nematic) • W. Friederickz et al. (Z. Phys. 1927, 42, 532) describes the influence of electrical and magnetic fields on smectic, nematic and cholesteric LCs. • Marconi Wireless Telegraph Co is awarded a patent on a light valve in 1936. • W. Maier and S. Saupe (Z. Naturforsch. 1959, 13a, 564) publish what is now known as the Maier-Saupe theory of liquid crystals which is summarized in the equation: Tis = A/4.55kv2 Where A is a molecular parameter including the polarizability anisotropy and v is the molar volume. • W. Richards and G. Heilmeier (RCA Corporation)(J. Chem. Phys. 1963, 39, 384) foresee "TV on a wall".

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• Rediscovery of electro-optical effects and their applications in LC display: Dichroic dye; host guest (G. H. Heilmeier et al. Appl. Phys. Lett. 1969, 13, 46). Phase change displays (G. H. Heilmeier et al. Proc. IEEE. 1969, 57, 34). Twisted nematic field effect (J. L. Fergason US patent # 3,731,986, 1973). • G.W. Gray et al (Electron. Lett. 1973, 9, 130) develops LCD technology based upon cyanobiphenyls. • S. Chandrasekhar et al. (Pramana 1977, 9, 471) discover discotic liquid crystals. • Pierre-Gilles de Gennes, Nobel Prize Physics 1991, studies how extremely complex forms of matter behave during the transition from order to disorder. He showed how electrically or mechanically induced phase changes transform liquid crystals from a transparent to an opaque state, the phenomenon exploited in liquid-crystal.

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Order in Liquid Crystals • There of typically three types of order that characterize liquid crystals: I) orientational order, ii) positional order and iii) bond orientational order • The degree of orientation and positional order in LC phases can vary and depending upon this degree the material may be more liquid-like or more crystal-like. • In general, based on the enthalpy of the transitions, it is concluded that LCs are more liquid-like since the greatest enthalpy of transition occurs upon going from the crystal to the first LC phase. • For a given material it is possible for there to be several discrete LC phases. • As a function of temperature, it is therefore possible to see several transitions with increasing temperature upon a transition the newly created phase has increased disorder. • Liquid crystals are generally oriented with their moments of inertia roughly aligned along an axis that is called the director. Director

q

Orientational order parameter is given by • Thus, when q is 0° for all the molecules, the orientation parameter is one, which is the case for a crystal in the space group P1 for example. When q is 57° the orientational order is by this definition 0. • For most liquid crystals the orinetational order parameter varies between 0.3 and 0.9.

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• The orientational order decreases with increasing temperature and then goes to zero at the clearing temperature (the temperature for the transition to an isotropic phase).

Order Parameter

1

Temperature

T clearing

• Positional order is the degree to which the position of an average molecule or groups of molecules exhibit translational symmetry.

NÆI

KÆN

• Differential scanning calorimetry can be used to characterize the temperature at which phase transitions occur, as can optical microscopy described below.

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Classifications of LC Liquid Crystal

Thermotropic (Liquid crystal phase is a function of the temperature of the material)

Lyotropic (Liquid crystal phase is a function of the concentration of the material)

Low Molar Mass

High Molar Mass (polymers)

Side Chain Polymers

Main Chain Polymers

Rod-like molecules

Nematics (N)

Ordinary Nematics.

Disc-like molecules (Discotics)

Smectic (S)

Twisted Nematic (Cholesteric)

C5H 11

Perpendicular Arrangment (S a)

Tilted Long Axis (S c)

CN

R

R

F OC4H9

C5H 11

R R

N C11H23O

R R

C8H 17 N

Rod-Like (Calamtic)

Disc-like (Discotic)

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Classifications of Liquid Crystals According to Degree of Order Nematics (from the Greek: nematon- thread-like) are uniaxial liquid crystals in which the average direction of the long axes of the molecules defines the direction N:

http://abalone.cwru.edu/tutorial/enhanced/files/lindex.html F O

C5H 11

CN

C8H 17 O

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Cholesteric Phase Cholesteric is the nematic state superimposed with a natural twist between layers including the long axis of the molecules induced by the incorporation of chiral group to give helical twist to the orientation of the director. The pitch of the twist is quite sensitive to temperature.

F

*

O C8H 17 O

Chiral Nematic LC Adding a chiral dopant to a nematic liquid crystal will induce a helical twist to create a chiral nematic phase. Remember it is the phase that is chiral not necessarily the molecule itself. A cholesteric liquid can diffract light differently depending upon the pitch of the liquid crystal according to the equation l = np, where l is the wavelength of light, n is the refractive index and p is the pitch. The pitch is very sensitive to temperature and accordingly, cholesteric LC have temperature dependent optical properties. Page - 12

Smectic Phases Smectic A is a phase in which the molecules are parallel to one another and are arranged in layers with the long axes perpendicular to the layer plane.

Smectic C is a smectic A like structure in which the long axes of the molecules of a tilted average angle differing from 90° with respect to the plane of the layer.

N HC

CH N

terephthal-bis-p-butylaniline (TBBA) K

B 113°C

C 144°C

A 172°C

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N 200°C

I 200°C

Smectic C* If a smectic phase is chiral and has an off axis dipole then as you go from layer to layer the director will maintain a tilt angle with respect to the layer plane but that rotates about a cone from layer to layer.

Thus, the off axis dipole will average to zero in the bulk material.

*

Illustration of several planes of smectic C*

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Illustration of off axis dipole

Ferroelectric Smectic C* If the helix can be unwound such that all the dipoles (and directors stay at the same angle as shown below) then the molecules will form a ferroelectric phase. The bulk material will have a net alignment of all the dipoles and therefore a bulk dipole moment.

2q

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Discotic Phase A discotic phase in one is which flat molecules typically with threefold or four fold symmetry that have a rigid core and several floppy side chains stacked with their planes lying roughly parallel to one another. Thus, the director is oriented roughly perpendicular to the plane of the molecule.

Nematic Discotic

Columnar Discotic

In nematic discotics phases there is no position order between the molecules but only orientational order. In the case of columnar discotic phases the molecules themselves lie roughly on top of each other, so there is some degree of positional order.

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Summary of Phases and Order phase

order

Isotropic liquid

full continuous translational and rotational

Nematic

symmetry (on average molecular orientation breaks rotational symmetry

untilted

tilted

Smectic-A

Smectic-C layering breaks translational symmetry; in smectic-C molecules are tilted

Hexatic SB

SI SK

Like the smectic A they are stacks of liquid layers but the molecules tend to be positioned along a hexagonal lattice within each plane

Plastic crystals Smectic (Crystal) -B

Crystal-

the rigid part of the crystals stay ordered but the long chain aliphatic tail melt (according to de Gennes), more appropriately called a crystal molecular rotation freezes out

The degree of order increases from the top to the bottom of the table. In general, phases from the top of the table are expected at high temperatures, and phases from the bottom at low temperatures.

The discotic phase, consisting of disk-shaped molecules, and the columnar phases, in which translational symmetry is broken in not one but two spatial directions, leaving liquid-like order only along columns.

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Disclinations When viewed under a microscope with crossed polarizers, one of the most striking features of liquid crystals is the appearance of texture. • An isotropic material placed between crossed polarizers will allow no light to pass through the polarizer. • If a birefringent material is viewed between cross polarizers the optic axis not perfectly aligned along one of the axes of the polarizer light will be transmitted. • Such is the case for an LC if the director is not aligned along one of the axes of the polarizer. When the director is aligned along such an axis the image will appear dark. • Textures occur which appear as sudden change in the image, going from light to dark. In such a case there is a discontinuity in the direction of the director. Such a defect in the order is called a disclination.

Spatial variations of the director causing thread-like images. From Jurgen Nehring and Alfred Saupe, Journal of The Chemical Society, Faraday Transactions II, 1972, vol. 68, 1-15; Copyright 1972 by The Chemical Society, London

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Orientation of the Director with Respect to a Substrate Surface In principle, the director can be oriented at an angle with respect to a substrate. The two limiting cases are called homeotropic alignment and homogeneous alignment.

Homeotropic orientation of the director relative to the surface of the plane of the substrate has the director more or less normal to the surface.

Homogenous orientation of the director relative to the surface of the plane of the substrate has the director more or less parallel to the surface.

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• The alignment of the liquid crystal is very sensitive to the polarization and polarizability of the surface in which it is in contact. • It is therefore possible to judiciously modify the surface in such a manner as to control the orientation. • My understanding is that it is in part art, in part science, and in part engineering. • It has been found that if a very thin layer of a polyimide is placed onto the substrate surface and then rubbed in one direction only (not back and forth), that it is possible to favor a homogenous alignment of nematic phases. • If the surface is treated with a long chain lethicin or long chain trichlorosilanes it is possible to favor a homeotropic alignment.

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Freedericksz Transition Recall that for materials that contain electric dipoles, such as water molecules, the dipoles themselves stretch or reorient in the applied field.

P

q

+F

2a

E

q

E

–F

t

• If then an electric field is applied orthogonal to this direction the liquid crystal will tend to rotate to align the director with the electric field assuming that the director and the dipole moment (more precisely the larger component of the dielectric anisotropy) are essentially colinear. • This reorientation as depicted below is called a Freedericksz transition. It should not be confused with a phase transition because the LC remains in the same LC phase. Simply, the orientation of the director is perturbed.

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Factors that Affect the Voltage at which LC Change Orientation

Splay Twist Bend K11

K22

K33

K1 1 + 14 (K 3 3 - 2K3 3) Vc = p e 0D e

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Displays • Dynamic scattering mode displays The first LCD, demonstrated at RCA Corporation laboratories in 1963, used an effect known as the dynamic scattering mode (DSM), which caused the liquid crystal to turn cloudy and scatter light under an applied voltage. Today this is not often used, however in polymer disperse LC light scattering is still used for specialty windows Basic Physics of common displays:

abalone.cwru.edu/tutorial/enhanced/files/lindex.html

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• Twisted nematic displays The next generation of LCDs used the twisted nematic (TN) effect, developed at Hoffmann-La Roche, Inc., in 1971 and is still used in watches and calculators today.

Figure 3: A twisted-nematic cell. (A) The assembly is transparent to light in the absence of an electric field. (B) An applied field destroys the twist of the nematic, rendering the assembly opaque.

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Addressing of displays Passive matrix: In passive matrix there are rows and columns of electrodes which are serial energized sequentially allowing one pixal at a time to be addressed.

Thin-film transistor display (TFT) developed in 1973 at the Westinghouse Electric Corporation, Here a thin-film transistor (TFT) is used to addres each pixel. pixels

transparent electrode electrode TFT wire

In color displays this is ususally a while backlight and then filtered on pixel are used to impart color.

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Ferroelectric Display

2q Ele

ctri c

fiel

d

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