Fundamentals of Polarization and Polarizability

Seth R. Marder

Joseph W. Perry

Department of

Chemistry

+-

+

-t1t0 t2

CHARGEDISTRIBUTION

INDUCEDPOLARIZATION

F = qE (1)

Indu

ced

Pola

riza

tion

Electric Field

Polarization = µ = (2)

Polarizability: A Microscopic View

Effect of Application of an Oscillating Electric Field such as Light

APPLIED FIELD

INDUCED POLARIZATION

Application of an oscillating electric field will induce an oscillating polarization in a material.

For linear polarization, this electric field will have the same frequency as the applied electric field, although its phase may be shifted (not shown).

This induced electric field is, itself, light and in the absence of scattering will propagate through the material in the same direction as the light beam that created it.

Mechanisms of Polarization

The oscillating electric field of light affects all charges in the optical

medium, not only the electron.

Vibrational polarization and involves nuclear motion

In dipolar materials molecular rotation can create polarization

In ionic materials, the ions move relative to one another

IONIC MOTIONROTATIONALVIBRATIONALELECTRONIC

__

___

_

_ _

_

__

_

+

++

+

++

+

+

+

++

_

+

+

-

+ -

+

-

No E Field

With E Field

O

M

O

M

Dipoles in Electric Fields

For materials that contain electric dipoles, such as water molecules, the dipoles themselves stretch or reorient in the applied field.

2a

E

+F

–F

P

E

Anisotropic Nature of Polarizability

The polarization of a molecules need not be identical in all directions.

E

E

+-+-+ -+ -+ - +-

H3C CH3H3C CH3

xx xy xzyx yy yzzx zy zz

applied field

indu

ced

pola

riza

tion

Deforming Force

z

x

y

Deforming Force

x'

z'

y'

Polarizability is a tensor quantity as shown below:

Tensorial Nature of Polarization

Each entry of the tensor is a component of the polarizability

The balloon diagram illustrates this point crudely. If a balloon is stretched in one direction (z) then the dimension of the balloon will change in all three directions.

Polarizability: A Macroscopic View

In bulk materials, the linear polarization is given by:

Pi() = ij( Ej( (4)

i,j

where ij() is the linear susceptibility of an ensemble of molecules

The total electric field (the "displaced" field, D) within the material becomes:

D = E + 4P = (1 + 4E (5)

Since P = E (Equation (4)), 4E is the internal electric field created by the induced displacement (polarization) of charges

The Dielectric Constant

The dielectric constant and the refractive index n) are two bulk parameters that characterize the

susceptibility of a material.

in a given direction is defined as the ratio of the displaced internal field to the applied field ( = D/E)

in that direction.

ij() = 1 + 4ij() . (6)

The frequency dependence of the dielectric constant provides insight into the mechanism of charge

polarization.

+e i d+

+e ie

RADIO VISIBLEMICROWAVE

Frequency

The Index of Refraction

The ratio of the speed of light in a vacuum, c, to the speed of light in a material, v, is called the index of refraction (n):

n = c/v. (7)

At optical frequencies the dielectric constant equals the square of the refractive index:

∞() = n2(). (8)

Consequently, we can relate the refractive index to the bulk linear (first-order) susceptibility:

n2() = 1+ (9)

Index of refraction depends therefore on chemical structure.

Role for Materials Chemists

TAKE SUM-OVER-STATES EXPRESSION FOR

ijk ikj e42

rg n j rn n

i rgnk rg n

k rn n i rgn

j n n ngn g

1

n g ng

1

n g ng

rg n

i rn n j rgn

k rg n k rn n

i rgnj 1

n g 2 ng

1

n g 2 ng

rg n j rn n

k rgni rg n

k rn n j rgn

i 1

n g ng 2

1

n g ng2

4 r

gnj rgn

k rni ng

2 42 rgni rgn

k rnj rgn

i rnk ng

2 22 n 1

ng2 2 ng

2 42

TRANSLATE INTO AN OPTIMIZED MOLECULE

INCORPORATE IN AN OPTIMIZED MATERIAL

Bond Length Alternation

Bond-length alternation (BLA) is defined as the average of the

difference in the length between adjacent carbon-carbon bonds in a

polymethine ((CH)n) chain.

SingleBond

DoubleBond

l (2)l (1)

Polyenes have alternating double (1.34 Å) and single bonds (1.45 Å)

and thus show a high degree of BLA (+ 0.11 Å).

Resonance Structures and BLA

(CH3)2N

(CH3)2N O O -(CH3)2N+

+N(CH3)2 N(CH3)2(CH3)2N+

-+

Decreasin

g Magn

itud

e of BL

A

Decreasin

g En

ergy Gap

Electric Field Perturbation of Structure

-0.1

-0.05

0

0.05

0.1

BLA

BO

A

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

0 2 4 6 8 10 12 14F (10

7 V/cm)

(+) (-)

(+) (-)N O

Me

Me

N O

Me

Me

N O

Me

Me

APPLIED FIELD

An electric field can increase charge separation in the ground –state of molecules

This in turn modifies the BLA, the Bond Order Alternation (BOA) and the dipole moment

Linear Polarizability and BOA

( 2ge

 Ege )

20

40

60

80

100

120

xx (10

-24

esu

)

(arb

. un

its)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6BOA

Legend:

: xx

O: model

² : 2ge

r : 1

 E  ge

The linear polarizabilty is peaked at BOA = O called the cyanine limit

First Hyper-polarizability and BOA

( 2ge(ee-gg)

 E 2ge

)Oudar, Chemla, Garito and Lalama

-800

-600

-400

-200

0

200

400

600

800

xxx

(10

-30

esu

)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6BOA

Legend:

: xxx

O: model

+: (ee-gg)

is peaked between polyene and cyanine limit

Beyond cyanine limit is negative

Most aromatic molecules tend to be near polyene limit with small

Factors Affecting Charge Separation

(CH3)2N O O-(CH3)2N+

CHARGE SEPARATION

(CH3)2N+ O-(CH3)2N O

CHARGE SEPARATION & LOSS OF AROMATICITY

NO

CH3O-

NCH3

+

CHARGE SEPARATION & GAIN OF AROMATICITY

Manipulation of BLA Through Topology

+(CH3)2N (CH3)2N

ON

ON

O

Ph Ph

O-

.. ..

(CH3)2N

SO

ONC

NC

(CH3)2N

SO

ONC

NC

+

–

SSN

CNNC

CNS

SN

CNNC

CN

_

+

Tradeoff on Aromatic Stabilization EnergyBetween Donor and Acceptor in Neutraland CT VB Structure

Decreasse Aromatic Stabilization Energy in Neutral VB Strucutre

Increasse Effective Conjugation Length in CT VB Strucutre

Good, But Not Good Enough

(CH3CH2CH2CH2)2N

SO

O

NC

CN

= ~13,500 x 10-48 esu at 1.907 m; = ~4,000 x 10-48 esu.

Material n reff.(pm/V)

n3reff.(pm/V)

n3reff./(pm/V)

LiNbO3 2.2 31 330 12

SandozPolymer

1.7 55 270 ~45

However: sub-optimal thermal stability: 60%decomposition after 20 min. @ 150 C.

Second Hyper-polarizability and BOA

– ( 4ge

 E 3ge

) + e'

( 2ge

 E 2ge

2ee'

 E  ge') + ( 2

ge(ee-gg)2

 E 3ge

)Pierce, Garito, Kuzyk and Dirk

-2.500 104

-2.000 104

-1.500 104

-1.000 104

-5000

0

5000

1.000 104

1.500 104

xxxx

(10

-36

esu

)

-0.6 -0.4 -0.2 0BOA

0.2 0.4 0.6

Legend:

: xxxx

O: model

X: e'

( 2ge

 E 2ge

2ee'

 E  ge')

+: ( 2ge(ee-gg)2

 E 3ge

)

³ : – ( 4ge

 E 3ge

)

has a rich structure as a function of BOA

Imaginary part of gives rise to two-photon absorption

hF

Two-photon

Absorptivity

Fluorescence

fl

hA

S0

S2

S1

Sn

hA Electron Transfer

Energy TransferPhotochemistry

hA

Two-Photon Excited Processes

Two-Photon Processes Provide 3-D Resolution

z

TPA I2

TPA z-4

I -2

Excitation by two photons is confined to a volume very close to focus where intensity is highest , giving rise to pinpoint 3D resolution

Excitation by one photon results in absorption along the entire path of the laser beam in the cuvette.

TPA Provides Improved Penetration Into Absorbing Materials

Excitation by one photon results in absorption by surrounding medium before beam reaches sample

Excitation by two photons of half the energy allows for penetration through the material, and then two photons can be absorbed by the sample

Effect of bis-Donor Substitution

≈ 10 x 10-50 cm4 s photon-1 ≈ 200 x 10-50 cm4 s photon-1

NN

E

1Ag

1Bu

2Ag

7.4 D

8.9 D

3.9 eV

4.8 eV

E=1.5 eV7.2 D

3.1 D4.5 eV5.4 eV

E=1.8 eV

S0 S2

M01

2 M122

(E1 E0 )

Proposed Model to Enhance TPA in Symmetrical Molecules

-0.15

-0.1

-0.05

0

0.05

0.1

N Phenyl Vinyl Phenyl N

Group

-C

harg

e D

iffer

ence

N

N

BDAS has large and symmetrical charge transfer from nitrogens to central vinyl group that is associated with large transition moment between S(1) and S(2).

These results suggest that a large change in quadrupole moment between S(0) and S(1) is leads to enhanced

Strategies for the Design of New Materials

D--D

DD

n

D

D

A

A

Increase conjugation length

Also:

DD

ADA

Add electron acceptors to the backbone

Chain-Length Dependence

With increasing chain length: increases (2)

max red-shifts

Method: Two-photon induced fluorescence (TPF)

Pulse duration: ≈ 5 ns

I

II

III

IV

NN

BuBu

BuBu

N

NBu

Bu

Bu

Bu

OMe

MeO

NBu

Bu

NBu

Bu

OMe

MeO

NBu

Bu

NBu

Bu

OMe

MeO

OR

RO

OMe

MeOR=C12H25

Design of TPA Chromophores

NN

N

N

N

NMeO

OMe

D-A-D D--D A-D-A

N

NCN

NC

N

N CN

NCBu

Bu

Bu

Bu

Hex

Hex

Hex

Hex

C12H25O

OC12H25

S

CN

NCO

O

S

NC

CNO

O

OMe

MeO

OMe

MeO

12

53

210

995

1250

1940

2300

4700

in 10-50 cm4 s/photon Albota et al., Science 1998

Photochemistry Generated via an Intramolecular Electron Transfer

Photoactive

Donor

h

PET

+.

-.

Photoproducts2) Rearrangement

1) Bond Cleavage

Two-Photon Dye

Media: Negative Tone Resist

UnexposedUnexposed ExposedExposed DevelopedDeveloped

Two-photon radical initiator

0.1% 2h radical initiator70% polymer precursor30% binder

Two-photon negative resist

100 x more sensitive than 100 x more sensitive than commerical radical initiatorscommerical radical initiators

N

N

N S O

O

O

OO

O

Why 3D Micro and Nanofabrication

Technology pull towards miniaturization of devices and patterned materials.

Need to free form fabricate 3 dimensional structures Increasing need for ability to pattern a variety of materials Need to couple nano-scale object with micro-scale objects

Areas impacted by 3D micro- and nano-fabrication Tissue

engineeringMicrofluidicsMEMS Photonics

Design of a Donor-Acceptor Linked Two-Photon Dye Photoacid Generator

1. Non-basic Electron Donor: Ar3N

(Ph3N+H, pKa = -5)

2. Electron Acceptor Sulfonium group

Separated from a π-Conjugation

System of Two-Photon Dye (π* > *)

3. Decrease of Perturbation of Sulfonium

Group on Electron Donor

4. Non-nucleophilic Anions (X- = BF4-,

PF6-, AsF6

-, SbF6-, (Ph-F5)4B- , etc.)

R’ = π-Conjugation System

R = methyl, benzyl

N S+

Me

R

'R

Quantum Yields of Acid Generation

N

N

S+

S+Me

Me

Me

Me 2 SbF6-

n-Bu

n-Bu

N

N

n-Bu

n-Bu

S

S

Me

Me

2SbF6-

2SbF6-

N

N

n-Bu

n-Bu

n-Bu

n-Bu

S

S

Me

Me

Me

Me+

+

H+

0.59

0.60

~0.02

Me

Me

+

+

O

O

O

NNEt

Et Et

Et

Rhodamine B, Base

O NNEt

Et Et

Et

COOH

+

H+OH-

max = 556 nm

Rhodamine B, acid

Rhodamine B as an Indicator

Media: Positive Tone Resist

UnexposedUnexposed ExposedExposed DevelopedDeveloped

1% 2h photoacid generator 99% positive resist

Two-photon positive resist

N

N

S

S

Bu

Bu

2SbF6- O

O

CH2CH2

O

O

O

OHO

CH20.57 0.40 0.03

50 x more sensitive than 50 x more sensitive than commercial photoacid initiatorscommercial photoacid initiators

Positive-Tone Resist

Grating with buried channels

Grating plane: 10 m below surface Film surface

Vertical cross-section

8 m

50 m

100

20

20

Acknowledgments

Marder GroupDianne McCord-Maughon

Timothy ParkerHarald RoeckelYadong ZhangWenhui Zhou

Molecular CharacterizationAnd Multiphoton Processing

Joe PerrySteve Kuebler

Kamjou MansourCristina Rumi

Stephanie PondKevin Braun

FUNDING: National Science Foundation

Office of Naval ResearchAir Force Office of Scientific Research

National Science Foundation STCNational Institutes of Health

DARPA

TheoryJean-Luc BrédasDavid BeljonneThierry KogejEgbert Zöjer

Postive ResistChris Ober

Tianyue Yue