fundamentals of polarization and polarizability
DESCRIPTION
Fundamentals of Polarization and Polarizability. Seth R. Marder Joseph W. Perry Department of Chemistry. Polarizability: A Microscopic View. F = qE (1). Polarization = µ = (2). Effect of Application of an Oscillating Electric Field such as Light. - PowerPoint PPT PresentationTRANSCRIPT
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