Order out of Chaos

Liquid Crystals

• Liquid: “A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material”

• “In the liquid state, atoms or molecules have sufficient kinetic energy to overcome the chemical bonds that held them in their crystal lattice and move independently..”

• Crystal: “a solid formed by the solidification of a chemical and having a highly regular atomic structure”

• Liquid Crystal: “a phase of matter similar to a liquid, in which the molecules are arranged regularly in one or two dimensions”

• How can we get a liquid in which we have highly ordered structures, or even “lattices”?

• Order requires that we restrict degrees of freedom

Types of Liquid Crystals

Lyotropic – phase transitions depend on

concentration (and temperature)

Order arises from the chemistry of the amphiphilic

molecules in (at least) bicomponent systems

• Thermotropic – phase transitions depend on

temperature

Order arises from the shape and rigidity of the

molecules

Order in 1 DimensionLangmuir-Blodgett Films

"At length at Clapman where there is, on the common, a large pond, which I observed to be one day very rough with the wind, I fetched out a cruet of oil, and dropped a little of it on the water. I saw it spread itself with surprising swiftness upon the surface.. the oil, though not more than a teaspoonful, produced an instant calm over a space several yards square, which spread amazingly and extended itself gradually until it reached the leeside, making all that quarter of the pond, perhaps half an acre, as smooth as a looking glass.”

Benjamin Franklin, 1774

Report to the Royal Society

Langmuir-Blodgett Films

Amphiphilic molecules have a hyrodphobic (“water hating”) and a hydrophilic (“water loving”) end

The hydrophilic part is generally polar (-OH, -COOH, -NH3+, -PO4-(CH2)2NH3+ etc.)

The hydrophobic part is generally a hydrocarbon or fluorocarbon chain

At a water-oil interface, amphiphilic molecules align –lowest energy state. Forces driving the aggregation include Van der Waals forces, hydrophobic interactions and, electrostatic interactions between charged groups on the surface

The film of aligned molecules at the interface is a Langmuir-Blodgett Film

Making LB films

LB technique allows the density of the molecules to be

controlled

Makes a film a single molecule thick (Langmuir)

Can be used repeatedly to build up films (Blodgett)

Highly ordered films can be made ( why is this good?)

An aside on nonlinear optics

{ }TOHEEEEEEP lkjijklkjijkjiji ..321

0+++= χχχε

• The polarisation of a material can be written

• Where P is the induced polarisation, E is the incident electric

field and χ is the susceptibility.

χ1 processes: linear optics, absorption, reflection

χ2 processes: second harmonic generation, sum and difference generation, hyper Raleigh scattering.. REQUIRES NON CENTRO SYMMETRIC SAMPLE

χ3 processes: multiphoton absorption, 3rd harmonic generation…

Second order nonlinear effects

where Ns is the density of molecules, β is the molecular hyperpolarisibility and the brackets denote the average

molecular orientation.

This is why LCs are used for second order optics experiments- because the orientational average can be

very high.

ijksijk N βχ =2

Applications of LB films

The LB technique is widely used in optics and other areas.

One of the most important is in non-linear optics, where the highly ordered polar alignment of molecules allows a χ(2) response giving effects such as second harmonic generation.

• Other important areas are sensing, optical interference filters optical image sensors , resists, membranes, lubrication layers, alignment layers for liquid crystals biocompatible layers, optical recording and catalytic surfaces

From surfaces to mixtures

Growth of micelles

At dilute amphiphile concentrations, micelles can grow in one and two dimensions, with the

restriction that one dimension of the micelle twice the hydrophobic tail length (2l).

Because in the absence of any other hydrophobic component there can be no space

between the sheets of hydrophobic tails inside the micelle.

Minimize surface energy -> minimize exposed surface area

Macroscopic micelle demonstrationhttp://www.youtube.com/watch?v=u_1RfqMH-KM

Higher concentrations: formation of

“crystalline” states

Typical sequence of phases observed in lyotropic mixtures as amphiphile concentration

Increases from left to right.

(a) Disordered micellar, (b) cubic micellar, (c) hexagonally packed cylinders, (d) cubic

bicontinuous, (e) lamellar sheets, followed by the same sequence in reverse

with the two components swapped in position.

Lyotropic transitionsCritical micelle concentration

hexagonal

cubic

Krafft Temperature

Surfactant solubility dramatically higher above Krafft temperature.

Micelles are much more soluble than isolated molecules.

Lyotropic Liquid Crystals and optics

• Lyotropic liquid crystals were discovered in 1850 in a biological system (a

mixture of myelin and water). There are many important biological examples

of amphiphilic- molecular ordering in this case can be studied by techniques

such as second harmonic microscopy. Aside: this is a very hot research

area

• Apart from LB films, optics seems mostly to have overlapped with lyotropic

LCs as a means of studying naturally occurring systems, rather than as the

basis of technologies

• However, there is a growing interest in self-assembly as a means of

making structured new materials.

• New types of materials we might want to make include 3D photonic crystals-

preferably high contrast refractive index structured materials, periodic in 3D

on below with periodicity similar to the wavelength of light.

2 and 3D photonic structures

in butterfly scalesThese may have developed because of templating from an

amphiphillic self assembly processes.

BUT: the length scale of the typical amphiphilic system is approximately

100°A, whereas in the butterfly it is closer to 100nm

Liquid crystals for lumberjacks

Liquid crystals for lumberjacks

• Long, rigid logs or molecules align naturally

• Note formation of domains

• Alignment effects at interfaces

Liquid crystals as plates

Plate-shaped things also order naturally- stacking

Αχτυαλλψ, τηερµοτροπιχ λιθυιδ χρψσταλσ ωερε δισχοϖερεδ βψ σοµεονε στυδψινγ χαρροτσ

Rod and plate-like molecules

Sub-species of Thermotropic LCs

Nematic Liquid Crystals

• Rod or disk-like molecules

Isotropic state

Nematic stateorientational order but no positional order

Chiral nematic(aka cholesteric)Get this if your molecules are chiral,

or by doping with chiral molecules.

Pitch of the order of λ

Sub-species of Thermotropic LCs

Smectic Liquid Crystals

Smectic A

Smectic C At certain temperatures, the liquid

crystal material may gain some

positional order. When this happens the liquid crystal forms

into smectic phase where the molecules,

although still forming a fluid, prefer to lie

on average in layers. This is called the

smetic phase. There are several smectic Phases some of which are sufficiently

ordered to be considered soft crystals

chiral smectic C material,

denoted by smectic C*

Smectic C(Alternative form)

Alignment of Liquid crystals

• Define an define an average direction of the molecules called the director and denoted by the vector n

• Order parameter S

where <> denotes a thermal averaging and is the angle between each molecule and the director n.

Alignment can be due to electric or magnetic fields, shear flow fields, substrate surface texturing, stretched liquid crystal polymer films, use of polarised light within the absorption band

1cos32

1 2 −= θS

Characterising transitions- DSC

Use Differential Scanning Calorimetry (DSC)

Measure the difference in the amount of heat required

to increase the temperature of a sample and reference

are measured as a function of temperature.

When a sample undergoes a phase transition it uses

either more (if endothermic) or less heat (exothermic)

than the reference to maintain both at the

same temperature

Tg

TNI

Characterising transitions- Textures

• Aligned liquid crystals are highly birefringent. In thin liquid crystal sample

cell is placed temperature controlled platform and viewed between two

crossed polarizers under an optical microscope. “Textures” characteristic of

the phase can be observed.

A nematic texture

Chiral or cholesetic textures

Optics and Thermotropic Liquid

Crystals

• Allow a dynamic (eg: switching) response, or

tuning

• Highly birefringent or circularly birefingent

• Order allows χ2 response. Attached to polymers, this can be made into films.

• Wide variety of ways of switching between 2 or

more different phases: temperature, E, B,

polarised light, shear

• Very large number of applications

Displays• Various configurations. Most use twisted nematic LC. A

layer of molecules is sandwiched between 2 transparent electrodes (eg: ITO on glass), with 2

crossed polarisers

• Applied voltage is used to “untwist” the LC in the liquid

crystal molecules in the center of the layer, so it is

blocked by the second polariser- Voltage allows the transmission to be controlled

One example of LCs in PCFs

shifting bandgapssee Vol. 11, No. 20 / OPTICS EXPRESS 2594

“.. the LC shows large thermo-optical effects, whereby the photonic bandgaps of the cladding may be shifted spectrally. We found bandgap location sensitivities

of 3nm/°C and 1nm/°C at infrared and visible wavelengths, respectively.

However, whenoperating the LC around the phase transition temperatures,

significantly stronger effects were observed”

Different temperatures

Smart Glass

http://www.switchlite.com/home.html

Dynamic Wavelength Processor Optical Scheme (Simplified)

1 input

2. All polarisation

to horizontal

3. Spreading by “grism”

4. “ProgrammableMirror”

5 output

29© 2008 Finisar Corporation, Confidential

Liquid Crystal On Silicon (LCOS)

• An array of 1280 x 768 pixels, each pixel is 13 x 13 microns

• Wafer is highly polished, less than 20 microns warp over 200mm

• 4000 pixels per channel, 50-100 channels

• Response time ~70 ms

• Programmable mirror: optics problem converted to software problem

30© 2008 Finisar Corporation, Confidential

LCOS: Cross section• Backplane is built on an standard 8 inch CMOS wafer

• 0.35 micron feature size with mixed analogue, digital, HV

and LV processes

• 2 polymer alignment layers and 5 metal layers, with

additional passivation to flatten the pixel layer

Each pixel in each column can be individually

addressed via the backplane

Phase returns to zero after 2π

Formation of Phase Grating

Phase retardance of each cell can be set via the

applied voltage

Differential retardance can be established in

adjacent cells to generate a phase

ramp

A sawtooth phase grating is thus

created

V

Formation of Phase Grating

sawtooth phase grating written over entire channel area

Area 14 pixel columns wide addresses each

100 GHz channel

References

1. Introduction to Liquid Crystals: Chemistry and Physics

by P. J. Collings and M. Hird, published by Taylor and

Francis (1997)

2. Liquid Crystals: Nature's Delicate Phase of Matter by P.

J. Collings, Adam Hilger (1990)

3. The Physics of Liquid Crystals

by P. G. de Gennes and J. Prost, OUP (1993, 2nd edition)

4. Liquid Crystals by S. Chandrasekhar, CUP (1992)