Liquid Crystals: Lecture 1

Basic properties

Support: NSF

Oleg D. Lavrentovich

Liquid Crystal Institute and

Chemical Physics Interdisciplinary Program,

Kent State University, Kent, OH 44242

Boulder School for Condensed Matter and Materials Physics,

Soft Matter In and Out of Equilibrium,

6-31 July, 2015

Acknowledgements

Volodymyr Borshch, Mingxia Gu, Tomohiro Ishikawa, Israel Lazo, Young-Ki Kim, Heung-Shik Park, Chenhui Peng, Oleg Pishnyak, Ivan Smalyukh, Bohdan Senyuk, Jie Xiang, Shuang Zhou (LCI, Kent State University)

Drs. Sergii Shiyanovskii, Antal Jakli (LCI, Kent State University)

Maurice Kleman (Paris), Grigory Volovik (Moscow), Vasyl Nazarenko (Kyiv), Igor Aranson (Argonne NL) Georg Mehl (Hull), Corrie Imrie (Aberdeen)

The lectures are based on the book by

Maurice Kleman and O. D. Lavrentovich

“Soft Matter Physics: An Introduction” (Springer, 2003)

3

Content: Lecture 1

Types of liquid crystalline order Nematic

Cholesteric and blue phases

Twist bend nematic

Smectic A

Lyotropic and Chromonic LCs

Basic Physics Dielectric anisotropy

Surface anchoring

Elasticity

Frederiks effect and modern LCDs

Optics Birefringence

Polarizing microscopy: 2D imaging

Fluorescence Confocal Polarizing microscopy: 3D imaging

4

Content: Lecture 2

Topological defects and droplets Disclinations in uniaxial nematics

Singular

Nonsingular

Homotopy classification

Drops and Conservation laws of topological defects

Cholesteric droplets, Dirac monopole

Chromonic tactoids

Broken chiral symmetry

Wulff construction for liquid crystals

Lamellar phases Free energy density for weak and strong perturbations

Long-range character of deformations; undulations

Focal conic domains

5

Content: Lecture 3

Dynamics of director realignment

Anisotropy of viscosity

Coupling of director reorientation and flow

Statics of colloids in nematic LC

Levitation

Dynamics of colloids in nematic LC

Brownian motion

LC-enabled electrophoresis

LC with patterned orientation as an active medium

Living LC

Swimming bacteria in LC; individual and collective effects

6

Liquid crystal:

a state of matter with long-range orientational order and

complete (nematic)

partial (smectics, columnar phases)

absence of long-range positional order of “building units”

(molecules, viruses, aggregates, etc.)

Our goal: Develop an

intuitive understanding

of what kind of new

physics the orientational

order brings to soft

matter

Crystals, liquid crystals, liquids

pentyl-cyanobiphenyl (5CB):

room temperature nematic

1.2 nm

Temperature

orientational and positional order: Molecular crystal

orientational order; no positional order:

Nematic LC

no orientational and no positional order

Isotropic liquid

Director n = optic axis

7

8

Nematic LC: nema=thread; aka “disclination”

1922, G. Friedel:

Named “nematics”, the simplest

LC, after observing linear defects,

nema=thread, under a polarized

light microscope

Nematic droplet-pancake sheared between two

glass plates; polarizing optical microscope

50 microns

9

Nematic LC: Calamitic and Discotic

10

Nematic LC: Calamitic and Discotic. Biaxial?

Uniaxial

calamitic

Uniaxial

discotic

Existence established

Existence debated, Uniaxial N often mimics biaxiality

Biaxial

Chiral molecule (does not overlap with its chiral

image)

Carbon atom with 4 different attachments

Cholesterol benzoate: Rod-like molecule

with a chiral C atom;

A similar cholesterol derivative was the

subject of the first known publication on

LCs, reporting double melting point and

selective reflection of light, J. Planer, Ann

Chem Pharm 118, 25 (1861)

11

Add chiral molecules to nematic and obtain a

cholesteric:

12

Where do the colors come from? pitch~0.5 mm

Bragg reflection at the periodic structure with period close to the

wavelength of visible light

Why P>>molecular scale? Weakness of chiral contribution to the

intermolecular potential, see Harris et al, Rev Mod Phys 71, 1745

(1999)

Comparative chemistry

CN

Cholesteric CB15 molecule

Nematic 5CB molecule

What would happen when two CB molecules are connected by a flexible

aliphatic chain and form a “bimesogen” or “dimer”?

Answer: depends on odd-even character of aliphatic chain

even number m of CH2 groups

How can we pack these molecules in space?

odd number m of CH2 groups

Packing bimesogens

Even m, rod-like molecules:

Easy! Nematic!

Odd m, bent shape:

Difficult…cannot

sustain uniform bend in

2D…

Predictions:

R.B. Meyer (1973, Les Houches)

R. Kamien, J. Phys II 6, 461 (1996)

I. Dozov, EPL 56, 247 (2001)

J. Selinger et al, PRE 87, 052503

(2013)

E. Virga, PRE 89 052502 (2014)

0 0 0ˆ sin cos , sin sin , costz tz =n

Go to 3D:

Uniform bent

is achieved

through twist!

Freeze Fracture TEM, “planar” fractures

0 . 1 µ m0 . 1 µ m

FFT

t̂

Period 8.05 nm (molecular scale!!! Frozen rotations?

Not visible under regular optical microscope; need an electron microscope)

Borshch, Gao et al, Nature Comm 4, 2635 (2013)

Chen, Walba, Clark et al, PNAS 110, 15931 (2013)

CB7CB quenched from the “X” temperature range and viewed under TEM

Freeze-Fractures in TEM: most likely to occur parallel to the long axes of molecules, thanks to the lowest molecular density

8 nm period

Freeze Fracture TEM, “planar” fractures

The 8 nm period is not visible in X-ray studies; thus there is no

modulation of density

How do we know that the structure is indeed twist-bend as opposed

to a simple cholesteric, or, say, splay-bend, also predicted to exist?

Tilted fractures: Bouligand arches are

different in Ch and Ntb

Cholesteric:

Bouligand

arches are

symmetric

0

0

z'

0

0

0 0

0

ln 2cos sin sin 'sin tan cot

sin cos

tb

tb

t yx x

t

=

Ntb: Bouligand arches

are either asymmetric or

incomplete

Bouligand et al, Chromosoma 24, 251 (1968)

FF TEM, Asymmetric Bouligand arches

Both types of Ntb asymmetric Bouligand arches are observed

Borshch et al, Nature Comm 4, 2635 (2013)

Nematic and Cholesteric are merely two point ends

of The Twist-Bend Nematic World…

Cholesteric

: molecular tilt angle

Twist-bend Nematic

0 0 =

0 0 0ˆ sin cos , sin sin , cos =n

0 / 2 =00 / 2

2 /t P=0

Nematic

tz =

Add a 1D positional order to obtain a smectic…

1-4 nm

Smectic A (SmA)

Periodic modulation of density (verified by X-

ray experiments), unlike in Ntb phase

1910, G. Friedel, F. Grandjean:

Deciphered SmA structure

from observation of

focal conic domains;

X-ray was not available

Smectics and focal conic domains

mm40

21

22

Smectics: Optical Microscopy at its best

Smectic A

1 nm

1910, G. Friedel, F. Grandjean:

Deciphered SmA structure

from observation of

focal conic domains;

X-ray was not available,

but the mere fact of existence of

ellipses and hyperbolae led to a

correct conclusion: SmA is a

system of equidistant flexible

fluid layers, i.e, a 1D periodic

structure

mm40

Smectics A, C, C*, etc

23

SmC SmC*

Smectic A: Molecules normal to the layers; Smectic C; molecules are tilted

Chiral smectic C; molecules are tilted and follow an oblique helicoid

Twist Grain Boundary Phases

24

Combination of smectics and cholesterics; formed by chiral molecules;

sophisticated analog of Abrikosov phase in superconductors; smectic is

penetrated by a lattice of screw dislocations that allows the smectic to twist

1989, Renn, Lubensky, Pindak, Goodby et al.:

Crystals, thermotropic liquid crystals, liquids

pentyl-cyanobiphenyl (5CB):

room temperature nematic

1.2 nm

Temperature

orientational and positional order: Molecular crystal

orientational order; no positional order:

Nematic LC

no orientational and no positional order

Isotropic liquid

Director n = optic axis

25

Lyotropic Liquid Crystals: Power of Entropy

Concentration, c

Onsager (1949): Nematic order in solution

of long thin rods, thanks to translational vs

orientational entropy trade-off

Lyotropic Liquid Crystals: Power of Entropy

Onsager (1949): Nematic order in solution

of long thin rods, thanks to translational vs

orientational entropy trade-off

Concentration, c

Tobacco mosaic virus (TMV)

J. Bernal and I. Fankuchen, J. Gen. Physiol. (1941): tactoids as N nuclei in tobacco mosaic virus dispersions (1939: First images of TMVs)

Phase diagram does not depend on

temperature

Molecular structure of phospholipids

Molecular structure of phospholipids. The

number of carbon atoms in the aliphatic

chains varies, usually between 16 and 20.

Two chains might be of different length.

phosphatidylcholine (lecithin) phosphatidylserine

phosphatidylethanolamine

N

O

N

O

N

N

SO3NH4NH4O3S

+ +

2 nm

Chromonic molecules:

1. Rigid plank-like polyaromatic core

2. Ionic groups at periphery

Lyotropic Chromonic LCs: special case

Violet 20

Mechanism of LC formation: through

aggregation: balance of entropy and

association energy d; average length

of aggregates

n

d

exp2 B

L ck T

d

29

LCLCs=Mesomorphic phases (N and Col) resulting from 1D non-covalent molecular self-assembly

Common occurrence in dyes, drugs, proteins, nucleic acids

Similar to living polymers, wormlike micelles of surfactants

Promising applications as sensing material, in optical components, organic semiconductors, alignment of nanotubes, assembly of nanorods, etc.

Nakata, Clark et al. Science 318, 1276

(2007)

Kuriabova, Betterton, Glaser,

J. Mat. Chem. 20,10366 (2010)

Lyotropic Chromonic LCs: special case

Chromonics :

controlled by both c

and T

Thermotropic LC (in your

displays): same molecules,

c=const, aligned at low T

Onsager systems:

same rods,

athermal,

aligned at high c

T

c

T

c

HS Park, ODL in Liquid crystals beyond displays, Editor Q. Li (2012)

Lyotropic Chromonic LCs: special case

HS Park, ODL in Liquid crystals beyond displays, Editor Q. Li (2012)

Columnar phase: 2D positional order of

columns (aggregates)

Nuclei of columnar

phase in isotropic

fluid: Bend

deformations that

preserve the

equidistance of 2D

lattices

Toroids rather than

spheres

Disodium

cromoglycate + water

+PEG

Content

Types of liquid crystalline order Nematic

Cholesteric and blue phases

Twist bend nematic

Smectic A

Lyotropic and Chromonic LCs

Basic Physics Dielectric anisotropy

Surface anchoring

Elasticity

Frederiks effect and modern LCDs

pentyl-cyanobiphenyl (5CB)

Anisotropy of uniaxial nematic

Director n=optic axis

Anisotropy of all properties: Optical, Dielectric, Diamagnetic,

Electric conductivity, Elasticity, Viscosity, etc.

=

||e

e

e

e

00

00

00

10414 == eee ||a

1.7 1.5 0.2e on n n =

Field-induced reorientation of LC optic axis caused by diamagnetic or

dielectric anisotropy: Frederiks effect (Leningrad, USSR, 1920-1930ies);

Optic axis: Easily deformable by E-field: Frederiks effect

Optical response to the electric field puts liquid crystals

at the heart of modern informational displays technologies

n̂

E

Guide to eye, director line

1927, Vsevolod Frederiks and Antonina Repiova

Magnetic field reorients LC

Frederiks effect: Field reorients LC

1934, V. Frederiks and V. Tsvetkov: Electric field reorients LC

(1885-1943)

cB d const=

1969, Kent, Ohio: James Fergason

patents Twisted nematic cell, the first field-operated LCD

(M. Schadt and W. Helfrich filed a similar patent in Europe and

also published an article)

Field effects = LC displays

First product,

Fergason’s ILIXCO (Kent, 1970)

1934-2008

2006: Lemelson-MIT $500,000 award

LC displays: Control of polarized light

Dielectric anisotropy and birefringence of LC enabled

revolution in informational portable displays

3.5 billion LCD panels sold in

2014 (all sizes)

39

Elasticity vs. Anchoring

Elasticity: Director gradients cost energy

2

2

1~

2

i

j

n Kf K

x L

=

~F f dV KL=

Elasticity vs. Anchoring

Elasticity: Director gradients cost energy

Surface anchoring

2

2

1~

2

i

j

n Kf K

x L

=

~F f dV KL=

Elasticity vs. Anchoring

Elasticity: Director gradients cost energy

Surface anchoring

2 212

; ~s sf W F WL

External Torque

2

2

1~

2

i

j

n Kf K

x L

=

~F f dV KL=

Elasticity vs. Anchoring

Elasticity: Director gradients cost energy

Surface anchoring

2 212

; ~s sf W F WL

2

2

1~

2

i

j

n Kf K

x L

=

~F f dV KL=

Elasticity vs. Anchoring

Elasticity: Director gradients cost energy

Surface anchoring

Anchoring extrapolation length

W/K=

2 212

; ~s sf W F WL

2

2

1~

2

i

j

n Kf K

x L

=

~F f dV KL=

Material parameters: orders of magnitude

263 J/m1010 ~W

Anisotropy of surface tension: Intuition fails; experiments say

(weak as compared to surface tension)

? ? ?K W 21

9

5 10 J~ ~ ~ 5 pN

10 m

B NIk TK

a

asizemolecular~W

K

==

μm10nm10J/m1010

N10263

11

21-2 2

2 18

5 10~ ~ ~10 J/m

10

Bk T

a

Surface tension

Elastic constants

Elasticity of N: Oseen, 1933, Frank, 1958

F. C. Frank, Disc. Faraday Soc. 25, 19 (1958)

ˆ ˆ x, y,z=n n

Elastic free energy density-?

2

0 ....i iij ijkl

j j

n nf f

x xa

=

1

molecular size

i

j

n

x

Requirements:

-n and n are invariant;

-central inversion about any point;

-invariance under any rotation around n.

ˆdivn ˆ ˆcurln nTwo scalar invariants linear in derivatives:

2

curln n…thus can also be 2 2 2

ˆ ˆ ˆ ˆ ˆcurl curl curl= n n n n n

Invariant and Quadratic in derivatives: 2

ˆ ˆcurln n 2

ˆcurln 2

ˆdivn

2 2 2

1 2 3

1 1 1ˆ ˆ ˆ ˆ ˆdiv curl curl

2 2 2FOf K K K= n n n n n

splay twist bend

Frank-Oseen elastic free

energy density:

divn=1

r

nx = cos, ny = sin, nz = 0

divn=2

r

nx =x

r, ny =

y

r, nz =

z

r

2D and 3D splay

q = n curl n

nx = cosqz, ny = sinqz, nz = 0

q =a

d=

2

p

Twist (one-directional)

n curln

nx = sin, ny = cos, nz = 0

Bend

Elasticity vs Anchoring: Hybrid-Aligned Nematic Film

1. Infinitely strong anchoring

Fixed boundary conditions

Problem: Find the director dependence on z in equilibrium

Assumption #1:

2

3

2

1 cos2

1sin

2

1

=

dz

dK

dz

dKfFO

ˆ , , sin , 0, cosx y zn n n z z = =nn̂

K1 = K3 = KAssumption #2:

2

12FO

df K

dz

=

00z = = dz d = =

The problem reduces to finding (z) that minimizes the integral

2

12

0

z d

FO

z

dF K dz

dz

=

=

=

Euler-Lagrange eq. (next slide gives the outline, home assignment if you do not know it yet):

2

20 0

'

FO FOf fd d

dz dz

= =

0

0

d zz

d

=

2

012

d

FOF Kd

=

eq z

za=

z = eq z a z

z= 0 = z = d = 0

where is such that

z

F z = f eq z a z , 'eq z a' z , z dz0

d

F a

a

a=0

=0 Condition of the extremum:

Euler-Lagrange equation for 1D problem, fixed boundary conditions (leisure time reading)

FFO = f FO ,' ,z dzz =0

z=d

FFO = 12 K '

2dz

z=0

z=d

?

F a

a=

f

af

'

'

a

dz

0

d

=f

z

f

'

d z

dz

dz

0

d

d z

dz

f

'dz

0

d

= z f

' z=0

z=d

0

z d

dz

f

'dz

0

d

f

d

dz

f

'

z dz = 0

0

d

f

d

dz

f

'

ddz

0

d

= aF a

a

a =0

= dF = 0or

f

d

dz

f

'= 0

Euler-Lagrange equation for 1D problem; its solution

has 2 constants of integration defined

from the boundary conditions, for example, = z,c1,c2

z = 0 = 0 z = d = dand

F = f ,' ,z dz0

d

f s0 0 0 f sd d d

zzz eq ad ==

z is not necessarily 0 at the boundaries!

dfs 0 0 da

=d

dafs 0 0,eq a z = 0 = 0

dfs0

d0

F a

a=

f

af

'

'

a

dz

0

d

dfs 0

d0

0 dfsd

dd

d

d z

dz

f

'dz

0

d

= z f

' z=0

z=d

0

z d

dz

f

'dz

0

d

f

d

dz

f

'

z dz

f

'

dfs0

d

z=0

0 f

'

dfsd

d

0

d

z=d

d = 0

f

d

dz

f

'= 0

Euler-Lagrange equation for 1D problem; its solution

has 2 constants of integration defined

from the boundary conditions = z,c1,c2

f

'

dfs0

d

z = 0

= 0f

'

dfsd

d

z= d

= 0and

Euler-Lagrange equation for 1D problem, soft boundary conditions (leisure time reading)

Elasticity vs Anchoring: Hybrid-Aligned Nematic Film

2. Finite (weak) anchoring

Problem: Find the director vs z in equilibrium with new

boundary conditions:

0

0

0'

FO s

z

f df

d =

=

n̂

2

12FO

df K

dz

=

21

0 0 0 02sf W = 2

12sd d d df W =

n̂

0'

FO sd

z d

f df

d =

=

0

0

d zz

d

=

0 0

0 0

0

d

d

L

d L L

=

2

012

0

d

FO

d

F Kd L L

=

0 0 0 0 0dK W d = 0 0d d d dK W d =

0

0

d d

d d

d

L

d L L

=

Finite anchoring makes the director gradients weaker

and the energy smaller, effectively increasing the cell

thickness

0 0/L K W=

/d dL K W=

0

0

d zz

d

=

Summary of hybrid aligned N film

Ld = K /Wd

0

0

d zz

d

=

2

012

d

FOF Kd

=

0

0

d zz

d

=

0 0

0 0

0

d

d

L

d L L

=

0

0

d d

d d

d

L

d L L

=

2

012

0

d

FO

d

F Kd L L

=

0 dd d L L

L: anchoring extrapolation length

Infinitely strong Finite anchoring

NB: at large scales, surface anchoring takes over, enslaving the director field, the director follows the “easy axis” prescribed by surface anchoring potential

~FOF Kl2~anchoringF Wl

00z = =

dz d= =

End of story for hybrid aligned films?

No. At submicron thicknesses, the director is unstable

w.r.t. in-plane deformations (similar to buckling)

2

2

1 1

1 2

1 1 1 1ˆdiv ~

2 2K K

R R

n

Int. J. Mod. Phys 9 2389 (1995)

1 2

1 1ˆ ˆ ˆ ˆdiv div curl

2R R= n n n n 24

24

1 2

2ˆ ˆ ˆ ˆdiv div curl

KK

R R =n n n n

Free Energy of a Nematic in an External Field

Dielectric case (no ions, no flexoelectric/surface polarization)

21

02ˆ

FO af f e e= n E

211

02ˆ

FO af f m = n B m0 = 4 107

Henry / m

Energy density should depend on two vectors, the field and the director

ˆ ˆ= n nE

E D= e0eE2 e0ea n E

2

a = e e e

0i ij jD E= e e

||

0 0

0 0

0 0

e

e e

e

=

Electric displacement:

Energy density (x 2):

FFO = f FO dV

U=const

FE = f E dV =12 E D dV

dFE = 12 E dD dV

dDz

The energy of the electric field

and its change:

Which leads to a change in the

surface charge density by

When n reorients, surface charge density changes;

to keep the voltage constant at the electrodes, one

needs to supply energy from the electric source:

dFG = dDz

A

dA= div dD dVElectric potential

div dD =divdDdD

E =

dFG = E dD dV = 2dFE

The minimum of the total bulk free energy is achieved when dFFO dFE dFG = d FFO FE = 0

D = e0eE e0e| |E| | = e0eE e0ea E n n E D= e0eE2 e0ea n E

2

21

02ˆ

FO af f e e= n E

211

02ˆ

FO af f m = n B m0 = 4 107

Henry / m

Free Energy of a Nematic in an External Field

Dielectric case (no ions, no flexoelectric/surface polarization)

Splay Frederiks Transitions

2 21

1 0

1 1ˆ ˆdiv

2 2af K = m n B n

Assuming deviations are small:

m

221

0

2

2

1 sin2

1cos

2

1B

dz

dKf a

=

221

0

2

12

1

2

1m

B

dz

dKf a

=

=0 at z=0, z=d

E-L equation: 02

22 =

dz

d

za

za sincos 21 =General solution: Boundary conditions yield and 01 =a nd =/

, the critical field for the Frederiks tra nsition Non-trivial solution at a

c

K

dBB

m

1

0

1

=

a

K

B m

1

0

11

=

, , cos ,0, sinx y zn n n z z=

Three basic geometries of Frederiks effect

a

c

K

dB

m

1

0

1

=

a

c

K

dB

m

1

0

2

=

a

c

K

dB

m

1

0

3

=

Electric field case can be treated similarly

Splay deformation

Twist deformation

Bend deformation

Heliconical director in electric field

0cE

p PE

=

Bimesogens: Ideal for electrically induced twist bend, since the bend constant is

very small

A cholesteric with a small bend-twist ratio K3 /K2 =1 and e>0 adopts an

oblique helicoidal shape in an electric field with the field-dependent pitch:

EE

0e

Color tuning: Vertical field

E

J. Xiang et al, Advanced Materials, 3014 (2015)

E

Liquid Crystals. Lecture 1.2

Optics

Support: NSF

Oleg D. Lavrentovich Liquid Crystal Institute and

Chemical Physics Interdisciplinary Program,

Kent State University, Kent, OH 44242

Boulder School for Condensed Matter and Materials Physics,

Soft Matter In and Out of Equilibrium,

6-31 July, 2015

LCs: Birefringent materials

1.7

extraordinary wave

en

Director n

=Optic axis

1.5

ordinary wave

on

Polarization E of light

Birefringence: Double refraction of light in an ordered material,

manifested through dependence of refractive indices on

polarization of light

0.2e on n n =

Birefringence revealed through pair of

polarizers: textures and LCDs

LCs: Ordinary and Extraordinary waves

/ t = E B / t = H D 0 =B 0 =D

0i ij jD Ee e= 0i ij ij jB Hm d =

||

0 0

0 0

0 0

e

e e

e

=

Light propagation in a homogeneous medium

El. displacement Mag. field induction El. field Mag.field strength

0, exp , , ...t i i t t= =E r E k r H r

=k E B =k H D 0 =k H0 =k D

Consider a plane monochromatic wave:

Eliminating mag. field H: 2 2

0 k m = D E k Ek

2 0ij i j ij jN N N Ed e =0 0

1 c

v e m= N kRefractive index “vector”

and using constitutive eq. for D:

2 2

0 0 ij j i i j jE k E k E k= m e e

Fresnel equation; Propagation of Light in LC

The three homogeneous equations have a nontrivial solution only if the

determinant of coefficients vanishes (Fresnel equation):

2 2 2 2

|| ||Det , 0z x yN N N N e e e e e = =

k

Two waves: ordinary, with

and extraordinary, with refractive index that

depends on the angle between the wave-vector

and the optic axis:

oN n e= =

,2 2 2 2cos sin

o ee eff

e o

n nN n

n n = =

on e=

en e=

optic axis

2 0ij i j ij jN N N Ed e =

Polarizing microscopy: Principle

sin

cos:Entry

A

A

Phase difference =2d

0

ne no

dntA

dntA

e

o

0

0

2cossin

2coscos

:Exit

nematic slab

n X

Y d

polarizer

aryextraordinc

dn

ordinaryc

dn

e

o

,

,:propagate toTime

Projected onto analyzer’ direction:

=

=

dntAA

dntAA

e

o

0

2

0

1

2coscossin

2coscossin

Acos t Resulting vibration:

with amplitude 2

2 2

1 2 1 22 cosA A A A A =

= oe nn

dII

0

22

0 sin2sin

nematic slab

n X

Y d

polarizer

Y

X

analyzer

Polarizing microscopy: Principle

= oe nn

dII

0

22

0 sin2sin

Dark Brushes:

regions where n is || or to polarizers

0; / 2; ... =

P A

Polarizing microscopy: Principle

Polarizing microscopy:

Degeneracy of two director fields

= oe nn

dII

0

22

0 sin2sin

P A

Polarizing microscopy: Degeneracy of two

director fields: Radial or Circular?

= oe nn

dII

0

22

0 sin2sin

P A

PM problem: Two orthogonal n fields

Solution: optical compensator (quartz wedge, Red plate, etc.)

en

on

en

on

en

on

en

on

en

on

Lower retardation,

yellow of the

first order of

interference

Higher retardation,

blue of the

second order of

interference

Radial and circular patterns produce different pattern

of interference colors when the compensator is added

Ultimate Compensator: LC PolScope

R. Oldenburg, G. Mei, US Patent 5,521,705

YK Kim et al, J Phys Cond Phys 25, 404202 (2013)

LC PolScope image of chromonic: shows both

the in-plane director and retardance

(a) T = 32.9 oC (c) T = 30.6 oC, t = 0 s (d) T = 30.6 oC, t = 156 s (b) T = 30.7 oC

0 nm

136 nm

50 μm

1

2

1 2

1

2

1

2

1 2 1 2 Retardance:

; e o

eff

d n planar n n n

d n titled director

= =

=

PolScope creates a map of the orientation of the optic axis in the sample and of the local value of the

optical phase retardation;

Nematic

Isotropic

Polarizing microscopy

= oe nn

dII

0

22

0 sin2sin

Interference colors: 0I I =

Visible when 0~ 1 3e od n n

Limitation: 2D image

Why the interference colors change?

= oe nn

dII

0

22

0 sin2sin

Limitation: 2D image

= oe nn

dII

0

22

0 sin2sin

Derived in approximation of planar director,

and constant thickness d ˆ , ,0x yn n=n

BTW! When , how does the texture look like? , , 0, 0,1x y zn n n =

Limitation: 2D image

2 2

0

0

sin 2 sin , , , , , , ,

d

effI I f x y z n x y z d x y dz

= n

When and , one deals with: , ,x y z=n n ,d d x y=

Limitation: 2D image

??????????????

Confocal Microscopy: 3D image of 3D

Usual

microscope

objective Confocal

microscope

Voxel=3D pixel

~1 mm 3

objective

Pinhole #1 Pinhole #2

(Minsky, 1957)

Computer 3D image Scanning

PMT PMT

Light

source

Light

source

Confocal Microscopy: Principle

Pinzhole #1 Pinhole #2

Fluorescence Confocal Microscopy

3D image of concentration (positional distribution) of

fluorescent dopant….

Fluorescent tag increases contrast of tissues

Living cell

PMT PMT

Light

source

Light

source

1980 M. Petran and A. Boyde

Two distinctive features:

1. Anisometric fluorescent dye aligned by LC

2. Polarized light

….but we are interested in orientations

rather than in concentrations…

Fluorescence Confocal Polarizing Microscopy

FCPM: Fluorescent anisometric dyes

N,N'-Bis(2,5-di-tert-butylphenyl)-3,4,9,10-

perylenedicarboximide)

BTBP

t

BTBP

350 400 450 500 550 600 650

Wavelength, nm

Ab

sorp

tion

, arb

.u

Ar Laser Excitation at

=488nm

Flu

ore

scen

ce E

mis

sion

, arb

.u.

A | |

A |

F | |

F |

0.01 % of BTBP in ZLI-3412

FCPM: Anisotropic Fluorescence

Fluorescence signal = f (orientation of dye)

n

n

P

minimum signal

n

n

P P

a

I ~ cos4a

n

n

P P

maximum signal

I. Smalyukh et al, Chem Phys Lett 336, 88 (2001)

FCPM: Anisotropic Fluorescence

Objective:

40X NA0.6;

60x NA1.4

Sample

Focal plane

PMT

Light source

Illuminating aperture

Confocal aperture

Beam splitter

filter

488 nm,

100 nW

510nm-550 nm

z

Polarizer/Analyzer

mznnn oe m10;1.0/||

mz m1~

/e oz n n z n

I. Smalyukh et al Chem Phys Lett 336, 88 (2001)

FCPM: Frederiks Effect

Relative Intensity scale:

Imin Imax

I ~ cos4a

P 0V

a=0

d=15mm

3V

a= f(z)

P

d=15mm V

I. Smalyukh et al Chem Phys Lett 336, 88 (2001)

FCPM: Planar Cholesteric

P

8 mm

Pn/2 <1 (to avoid the Mauguin regime)

I. Smalyukh et al, Phys. Rev. Lett. 90, 085503 (2003)

Summary: What have you learned Liquid crystals: Orientationally ordered media

Thermotropic (t-driven), lyotropic (c-driven), chromonic (t,c-driven)

Uniaxial nematic, twist bend, cholesteric, smectic, columnar, dramatic dependence on molecular structure…

Orientational elasticity vs surface anchoring Frank elastic constants ~ 5 pN

Equilibrium director defined by boundary conditions (anchoring), elasticity, and external field

As the system become larger, anchoring imposes stronger restrictions on the director

Frederiks transitions @ heart of modern LCDs

Optics LCs are birefringent; ordinary and extraordinary waves

Polarizing microscope: 2D image of 3D sample

Fluorescence confocal polarizing microscopy: 3D image of 3D orientational order

Cholesteric structure of DNA in chromosomes:

Bouligand arches

Chromosoma (Berl.) 24, 251--287 (1968)

La structure fibrillaire et l'orientation des chromosomes

chez les Dinoflagellés

Y. BOULIGAND, M.-O. SOYER et S. PUISEUX-DAO

89

Double twisted cylinders stabilized by a 3D network of topological defects –

disclinations.

BPII

BPI

100 nm

Main problem for applications:

Temperature range of BPs is narrow,

~1oC

One approach: Polymerization

H. Kikuchi et al, Nature Mat. 1, 64

(2002)

0ˆ || Zn

n̂

X

Y

Clolesteric: 1D twist; Blue phases: 3D twist

90

Polymer mesh formed in BPII

Can be refilled with N for

electro-optic applications

J. Xiang et al, APL 103, 051112

(2013)