Transcript PowerPoint Presentation - Liquid Crystals: Robust Physics

Chromonic Liquid Crystals: A New Form
of Soft Matter
Peter J. Collings
Department of Physics & Astronomy
Swarthmore College
Department of Physics, Williams College
April 6, 2007
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Acknowledgements



Chemists and Physicists
Robert Pasternack, Swarthmore College
Robert Meyer & Seth Fraden, Brandeis University
Andrea Liu & Paul Heiney, University of Pennsylvania
Oleg Lavrentovich, Kent State University
Michael Paukshto, Optiva, Inc.
Swarthmore Students
Viva Horowitz, Lauren Janowitz, Aaron Modic, Michelle Tomasik,
Nat Erb-Satullo
Funding
National Science Foundation
American Chemical Society (Petroleum Research Fund)
Howard Hughes Medical Institute
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Outline

Introduction
Soft Matter
Liquid Crystals

X-ray Diffraction
Theory for Fluid Systems
Experimental Results


Simple Theory of Aggregating Systems
Electronic States of Aggregates
Exciton Theory
Absorption Measurements


Birefringence and Order Parameter Measurements
Conclusions
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Motivation

Spontaneous aggregation is important in many different
realms (soft condensed matter, supramolecular chemistry,
biology, medicine).

Chromonic liquid crystals represent a system different
from colloids, amphiphiles, polymer solutions, rigid rod
viruses, nanorods, etc.

Understanding chromonic systems requires knowledge of
both molecular and aggregate interactions.

Chromonic liquid crystals represent an aqueous based,
highly absorbing, ordered phase, opening the possibility
for new applications.
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Soft Matter
Condensed Matter (Fluids and Solids)
Soft Matter (Fluids but not Simple Liquids)
Polymers
Emulsions
Colloidal Suspensions
Foams
Gels
Elastomers
Liquid Crystals
Thermotropic Liquid Crystals
Lyotropic Liquid Crystals
Chromonic Liquid Crystals
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Phases of Matter
H2O
liquid
solid
0 °C
gas
100 °C
Temperature
Cholesteryl Myristate
liquid cryst al
solid
71 °C
liquid
85 °C
gas
Temperature
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Thermotropic Liquid Crystals
solid
liquid crystal
liquid
T
L = 300 J/gm
L = 30 J/gm
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Orientational Order
Order Parameter
n
3
1
2
S  cos  
2
2
0.8

S
0.6
0.4
0.2
0
T
nˆ  director
C
Temperature
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Liquid Crystal Phases
smectic A
10S5
smectic C
O
C10H21O
C
S
solid
smect ic C
60 °C
C5H11
63 °C
liquid
nem at ic
smect ic A
80 °C
86 °C
T
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Lyotropic Liquid Crystals
+
O
+
CH3
CH3
O
Na
O
C C15 H31
N
O
CH2
CH2
O
O P O
CH2
O
CH3
C
CH
CH2
C C15 H31
O
C C15 H31
O
soap
phospholipid
water
water
water
water
water
lamellar phase
water
micelle
water
vesicle
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Chromonic Liquid Crystals

Lyotropic Systems
Behavior is dominated by solvent interactions
Critical micelle concentration
Bi-modal distribution of sizes (one molecule
vs. many molecules)

Chromonic Systems
Intermolecular and solvent interactions
important
Aggregation occurs at the lowest
concentrations (isodesmic)
Uni-modal size distribution
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Sunset Yellow FCF (Yellow 6)
Disodium salt of 6-hydroxy-5[(4-sulfophenyl)azo]-2napthalenesulfonic acid
Anionic Monoazo Dye
Liquid Crystalline above 25 wt%



OH
-O S
3
N
N
Na+
Na+
SO3-
2.5 104
2 104
-1
-1
Absorption Coefficient (M cm )
Sunset Yellow FCF
(40 µM)
1.5 104
1 104
5000
0
300
350
400
450
500
Wavelength (nm)
550
600
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Bordeaux Ink (Optiva, Inc.)
O

Results from the sulfonation of
the cis dibenzimidazole
derivative of 1,4,5,8naphthalenetetracarboxylic acid
O
NH4+
NH4+
-O S
3
N
N
N
N
SO3-
60
Bordeaux Dye
(0.0053 wt%)


Anionic dye
Oriented thin films on glass act
as polarizing filters
Absorption Coefficient (wt% mm)
-1
50
40
30
20
10

Liquid Crystalline above 6 wt%
0
300
350
400
450
500
550
600
650
Wavelength (nm)
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Sunset Yellow FCF
Crossed Polarizers
70
Sunset Yellow FCF
Temperature (°C)
60
50
isotropic
40
coexistence
30
nematic
20
0.6
0.7
0.8
0.9
1
1.1
1.2
Concentration (M)
V. R. Horowitz, L. A. Janowitz, A. L. Modic, P. A. Heiney, and P.J. Collings,
Phys. Rev. E 72, 041710 (2005)
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X-ray Diffraction
wavevector = k = 2š /


kout - kin = q = (4š /) sin

d
q = scattering wavevector
-kin

kout
Bragg Condition
n = 2d sin
q = 2š /d
Sunset Yellow
(1) Peak at q = 18.5 nm-1 (d = 0.34 nm): concentration independent
(2) Peak at q ~ 2.0 nm-1 (d ~ 3.0 nm): concentration dependent
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X-ray Diffraction Results
Sunset Yellow FCF
1.08 M
Sunset Yellow FCF
(T = 20°C)
-1
15
10
0.30 M
0.50 M
0.80 M
1.08 M
5
0.26
0.14
0.259
0.13
0.258
0.12
nematic
0.257
isotropic
0.11
-1
Scattering Intensity (arb. units)
20
0.15
0.256
0.1
0.255
0.09
0.254
0.08
0.253
0.1
0.15
0.2
0.25
-1
Scattering Wavevector (Å )
0.3
FWHM (Å )
Peak Scattering Wavevector (Å )
25
0.261
0.07
30
40
50
60
70
80
90
Temperature (°C)
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Aggregate Shape?
a  a 
    q
d 2 
Large Planes
d
a
  volume fraction
d
a
Long Cylinders
 a 2
a 2
=
 
2
2 3d 8
 2
q
3 
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Analysis of Aggregate Shape
0.08
-2
Peak Scattering Wavevector Squared (Å )
-1.4
0.07
0
ln(q )
-1.5
0.06
1
 2 3  2 12
q  
 
cylinder area 
2
-1.3
Slope = 0.53 ± 0.06
-1.6
-1.7
-1.8
0.05

-1.9
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
-1.2
Fitting Result
area of cylinder =
1.21 ± 0.12 nm2
ln()
0.04
0.03
Sunset Yellow FCF
(T = 20 °C)
0.02
0
0.05
0.1
0.15
0.2
0.25
molecular area ~ 1.0 nm2
0.3
Volume Fraction
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Aggregation Theory (0th Order)


System is held at at constant temperature; volume changes
can be ignored; ….. use Helmholtz Free Energy.
F  E  TS
Assume energy is lowered by an amount kT for each
face-to-face arrangement of two molecules in an aggregate.

E   N n n1kT
n1
n  number of molecules in an aggregate
N n  number of aggregates of size n
Assume for entropy considerations that aggregates act like
ideal gas molecules.

 2nmk  5 
V  system volume
 S  N kln V  3 ln T 3 ln
 2  
 n  N 2
m  mass of a molecule


2
h
2

n
n1

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Aggregation Theory (0th Order)
To see what size aggregates contribute the most to the free
energy, let’s imagine all the aggregates have the same
number of molecules n.
n 1
N
N  total number of molecules
Nn 
 "E"   
NkT
 n 
n

N  nV 3
3 2nmk  5
"S"  kln  lnT ln 2  
n  N 2
2  h  2

This competition between the two terms means there is a
distribution of aggregate sizes that minimizes the free

energy.
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Aggregation Theory (1th Order)

Goal: find the distribution of sizes that minimizes the free
energy. But this means minimizing a function of an
infinite number of variables (Nn)!


Fortunately, there is a constraint:
N
n
N
n1


Use a Lagrange multiplier :
F
N

0
N n
N n

and solve for Nn in terms of 
 the constraint equation, yielding 
Substitute Nn back into
and thereby also yielding Nn.
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Results of 1st Order Aggregation Theory
0.14
0.35
Sunset Yellow FCF
( = 22)
0.3
Fraction of Aggregates
Fraction of Molecules
 = 0.01
<n> = 3.3
0.25
0.2
0.15
0.1
 = 0.25
<n> = 14.4
0.05
Sunset Yellow FCF
( = 22)
0.12
 = 0.01
peak = 3
0.1
0.08
0.06
0.04
 = 0.25
peak = 14
0.02
0
0
0
10
20
30
40
50
Number of Molecules in an Aggregate
60
0
10
20
30
40
50
Number of Molecules in an Aggregate
60
Nv
volume fraction   
, where v  volume of a single molecule
V
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Absorption Experiments
2.5 104
Sunset Yellow FCF
0.04
0.20
0.50
2.00
5.00
8.00
11.0
14.0
17.0
20.0
-1
-1
Extinction Coefficient (M cm )
2 104
1.5 104
mM
mM
mM
mM
mM
mM
mM
mM
mM
mM
1 104
5000
0
300
350
400
450
500
550
600
W av elength (nm )
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Exciton Theory


Strong molecular absorption is due to a collective
excitation with some charge separation (two state system)
Aggregation results in a coupling between the excited
states of identical nearest neighbor two state systems
No Coupling
E
With Coupling
E-
E+
0 0
0 


H  0 E  

0  E

For n aggregated molecules:
m 
E mn  E 2cos

n 1
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Exciton Theory

The transition probability for absorption is proportional to
the intensity of the light and the square of the transition
dipole moment. For single excited molecule states, |1>,
2
2
2
|2>, |3>, etc:
1  0 1

˜
 2  0 2
˜
2
2

2
The transition dipole moment of a coupled state is given by
its superposition of single molecule excited states.
1
1
2
2
2
1 
1
2
1  0  1  
E  E
2
2
1
1
2
2
2 
1
2
 2  0  2  0
E  E 
2
2
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
Exciton Theory
Graphs of ||2/n for different values of n:
n=2
n=1
E
E
n=3
n=4
E
n=5
E
n=6
E
E
Prediction
Aggregation causes a shift in wavelength and broadening!
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Sunset Yellow FCF
2.4 10 4
Sunset Yellow FCF
Fitting Results
a   958010 M 1cm 1
 = 22.6 ± 0.1
2.2 10
-1
Absorption Coefficient (M cm )
2 104
-1
Exciton Theory
Absorption coefficient:
  
a n  a1  a   a1  cos

n 1
4
1.8 10 4
1.6 10 4
1.4 10 4
1.2 10 4
1 104
0
0.005
0.01
0.015
0.02
Concentration (Molal)
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Bordeaux Ink
X-ray Results
Absorption Results
Cylinder area = 3.24 ± 0.04 nm2
a   24.00.1 wt%1 cm 1
Molecular area ~ 1.2 nm2
 = 24.5 ± 0.1
34
Intensity (arb. units)
4
32
-1
Bordeaux Ink
-1

5
Absorption Coefficient (wt% cm )
Bordeaux Ink
4.3 wt%
5.9 wt%
7.3 wt%
8.6 wt%
3
2
1
30
28
26
24
0
0.05
0.1
0.15
0.2
Concentration (wt%)
0
0.004
0.005
0.006
0.007
0.008
-1
q (A )
0.009
0.01
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Birefringence
-0.05
Birefringence
n  n|| n
Notice:
(1) Birefringence decreases
with increasing temperature

(2) Birefringence is negative
Sunset Yellow FCF
-0.06
0.94 M
-0.07
coexistence
-0.08
-0.09
1.08 M
nem ati c
1.17 M
N=N
-0.1
N
=
N
Birefringence
0.99 M
1.25 M
-0.11
N=N
-0.12
20
30
40
50
60
70
80
N=N
o
T em perature C)
(
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Order Parameter
-0.2
Order Parameter of Aggregate
Order Parameter of the N=N Bond
0.8
-0.25
Sunset Yellow FCF
1.25 M
0.75
0.7
0.65
0.6
-0.3
n|| A||  n  A
SNN 
n|| A||  2n  A
0.55
20
30
40
50
60
Temperature (°C)
70
80
-0.35
-0.4
20
Measure:
(1) indices of refraction
(2) absorption of polarized
light
30
40
50
Temperature (°C)
60
70

80
SNN  P2 cos S
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Conclusions

Sunset Yellow FCF forms linear aggregates with a crosssectional area about equal to the area of one molecule.

The energy of interaction between molecules in an aggregate is
fairly large (~22 kT).

The aggregates probably contain on the order of 15 molecules
on average.

Bordeaux Ink appears to behave similarly, except the crosssectional area is about equal to two or three molecules.
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