Chromonic Liquid Crystals: A New Form of Soft Matter
Peter J. CollingsDepartment of Physics & Astronomy
Swarthmore College
Department of Physics, Williams College
April 6, 2007
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Acknowledgements
Chemists and PhysicistsRobert Pasternack, Swarthmore CollegeRobert Meyer & Seth Fraden, Brandeis UniversityAndrea Liu & Paul Heiney, University of PennsylvaniaOleg Lavrentovich, Kent State UniversityMichael Paukshto, Optiva, Inc.
Swarthmore StudentsViva Horowitz, Lauren Janowitz, Aaron Modic, Michelle Tomasik,
Nat Erb-Satullo Funding
National Science FoundationAmerican Chemical Society (Petroleum Research Fund)Howard Hughes Medical Institute
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Outline
IntroductionSoft MatterLiquid Crystals
X-ray DiffractionTheory for Fluid SystemsExperimental Results
Simple Theory of Aggregating Systems Electronic States of Aggregates
Exciton TheoryAbsorption 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 CrystalsThermotropic Liquid Crystals
Lyotropic Liquid CrystalsChromonic Liquid Crystals Return to "Recent Talks" Page
Phases of Matter
H2O
solid liquid gas
0 °C 100 °C Temperature
Cholesteryl Myristate
solid liquid crystal gas
71 °C 85 °C Temperature
liquid
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Thermotropic Liquid Crystals
L = 300 J/gm L = 30 J/gm
T
solid liquid crystal liquid
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Orientational Order
n
θ
Order Parameter
S =32cos2 θ−
12
ˆ n =director
0
0.2
0.4
0.6
0.8
S
TC
Temperature
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Liquid Crystal Phases
smectic A smectic C
C10H21O C
O
S C5H11
10S5
60 °C 63 °C 80 °C 86 °C
solid smectic C smectic A nematic liquid
T
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Lyotropic Liquid Crystals
O
OC C15H31
CH3 N
Na
+ -CH3
CH3
CH2
CH2
O P
O
O
OCH2
CHO
CH2
CC C15H31
OC C15H31
O
O+ -
soap phospholipidwater
water
lamellar phasewater
water
water
water
watermicelle
vesicle Return to "Recent Talks" Page
Chromonic Liquid Crystals
Lyotropic SystemsBehavior is dominated by solvent interactionsCritical micelle concentrationBi-modal distribution of sizes (one molecule
vs. many molecules)
Chromonic SystemsIntermolecular and solvent interactions
importantAggregation 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]-2-napthalenesulfonic acid
Anionic Monoazo Dye Liquid Crystalline above 25 wt%
0
5000
1 104
1.5 104
2 104
2.5 104
300 350 400 450 500 550 600
Sunset Yellow FCF(40 µM)
Absorption Coefficient (M
-1cm
-1)
Wavelength (nm)
NN
SO3-
OH
-O3S
Na+
Na+
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Bordeaux Ink (Optiva, Inc.)
Results from the sulfonation of the cis dibenzimidazole derivative of 1,4,5,8- naphthalenetetracarboxylic acid
Anionic dye
Oriented thin films on glass act as polarizing filters
Liquid Crystalline above 6 wt%
0
10
20
30
40
50
60
300 350 400 450 500 550 600 650
Bordeaux Dye(0.0053 wt%)
Wavelength (nm)
N
O
N SO3-
N
N
O
-O3S
NH4+ NH4
+
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Sunset Yellow FCF
20
30
40
50
60
70
0.6 0.7 0.8 0.9 1 1.1 1.2
Sunset Yellow FCF
Concentration (M)
isotropic
nematic
coexistence
Crossed Polarizers
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
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
θ θ
n = 2d sinλ θ
dφ kout - kin = q = (4π/ ) sinλ φ(φ/2)
-kin
kout
wavevector = k = 2π/λ
q = 2π/d
Bragg Condition
q = scattering wavevector
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X-ray Diffraction Results
5
10
15
20
25
0.1 0.15 0.2 0.25 0.3
Sunset Yellow FCF(T = 20°C)
0.30 M0.50 M0.80 M1.08 M
Scattering Wavevector (Å-1
)
0.253
0.254
0.255
0.256
0.257
0.258
0.259
0.26
0.261
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
30 40 50 60 70 80 90
Sunset Yellow FCF1.08 M
Temperature (°C)
nematic isotropic
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Aggregate Shape?
a
d
d
a
Large Planes
Long Cylinders
€
ϕ =ad
=a
2π
⎛ ⎝ ⎜
⎞ ⎠ ⎟q
ϕ = volume fraction
ϕ =πa2
2 3d2 =a2
8π 3
⎛
⎝ ⎜
⎞
⎠ ⎟q
2
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Analysis of Aggregate Shape
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 0.05 0.1 0.15 0.2 0.25 0.3
Sunset Yellow FCF(T = 20 °C)
Volume Fraction
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2
ln(φ)
= 0.53 ± 0.06Slope
Fitting Resultarea of cylinder =
1.21 ± 0.12 nm2
molecular area ~ 1.0 nm2
€
q =2π2 3
cylinder area
⎛
⎝ ⎜
⎞
⎠ ⎟
12
ϕ1
2
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Aggregation Theory (0th Order)
System is held at at constant temperature; volume changes can be ignored; ….. use Helmholtz Free Energy.
Assume energy is lowered by an amount kT for each face-to-face arrangement of two molecules in an aggregate.
Assume for entropy considerations that aggregates act like ideal gas molecules.
€
F = E−TS
€
E = Nn n −1( )n=1
∞
∑ −αkT( )
€
S = Nnk lnVNn
+32
ln T+32
ln2πnmk
h2
⎛ ⎝ ⎜
⎞ ⎠ ⎟+
52
⎡
⎣ ⎢
⎤
⎦ ⎥
n=1
∞
∑€
n = number of molecules in an aggregate
Nn = number of aggregates of size n
€
V = system volume
m = mass of a molecule
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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.
This competition between the two terms means there is a distribution of aggregate sizes that minimizes the free energy.
€
Nn =Nn
⇒ "E" = −n −1
n
⎛ ⎝ ⎜
⎞ ⎠ ⎟NαkT
€
N = total number of molecules
€
"S" =Nn
k lnnVN
+32
ln T+32
ln2πnmk
h2
⎛ ⎝ ⎜
⎞ ⎠ ⎟+
52
⎡ ⎣ ⎢
⎤ ⎦ ⎥
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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:
Use a Lagrange multiplier :
and solve for Nn in terms of
Substitute Nn back into the constraint equation, yielding and thereby also yielding Nn.
€
Nn
n=1
∞
∑ = N
€
∂F∂Nn
+ λ∂N∂Nn
= 0
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Results of 1st Order Aggregation Theory
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 10 20 30 40 50 60
Sunset Yellow FCF(α = 22)
Number of Molecules in an Aggregate
φ = 0.25< > = 14.4n
φ = 0.01< > = 3.3n
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 10 20 30 40 50 60
Sunset Yellow FCF(α = 22)
Number of Molecules in an Aggregate
φ = 0.01 = 3peak
φ = 0.25 = 14peak
€
volume fraction = φ =NvV
, where v = volume of a single molecule
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Absorption Experiments
0
5000
1 104
1.5 104
2 104
2.5 104
300 350 400 450 500 550 600
Sunset Yellow FCF0.04 mM0.20 mM0.50 mM2.00 mM5.00 mM8.00 mM11.0 mM14.0 mM17.0 mM20.0 mM
Wavelength (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
€
H =
0 0 0
0 ΔE β
0 β ΔE
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
€
ΔEm≤n = ΔE +2β cosmπn +1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
No Coupling With Coupling
ΔE ΔE+βΔE-β
For n aggregated molecules:
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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>, |3>, etc:
The transition dipole moment of a coupled state is given by its superposition of single molecule excited states.
€
ψ1 =12
1 +12
2 μ12 = 0 μ ψ1
2= μ 2 E = ΔE+β
ψ2 =12
1 −12
2 μ 22 = 0 μ ψ2
2= 0 E = ΔE−β
€
μ12 = 0 ˜ μ 1
2= μ 2
μ 22 = 0 ˜ μ 2
2= μ 2
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Exciton Theory
Graphs of | |2/n for different values of n:
PredictionAggregation causes a shift in wavelength and broadening!
ΔE
ΔE
ΔE
ΔE
ΔE
ΔE
n = 1 n = 2
n = 3 n = 4
n = 5 n = 6
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Sunset Yellow FCF
Exciton TheoryAbsorption coefficient:
€
an = a1 + a∞ − a1( )cosπ
n +1
⎛ ⎝ ⎜
⎞ ⎠ ⎟
Fitting Results
= 22.6 ± 0.1
€
a∞ = 9580±10( ) M−1cm−1
1 104
1.2 104
1.4 104
1.6 104
1.8 104
2 104
2.2 104
2.4 104
0 0.005 0.01 0.015 0.02
Sunset Yellow FCF
Absorption Coefficient (M
-1cm
-1)
Concentration (Molal)
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Bordeaux Ink
X-ray Results
Cylinder area = 3.24 ± 0.04 nm2
Molecular area ~ 1.2 nm2
0
1
2
3
4
5
0.004 0.005 0.006 0.007 0.008 0.009 0.01
Bordeaux Ink
4.3 wt%5.9 wt%7.3 wt%8.6 wt%
Intensity (arb. units)
q (A-1
)
Absorption Results
= 24.5 ± 0.1
24
26
28
30
32
34
0 0.05 0.1 0.15 0.2
Bordeaux Ink
Absorption Coefficient (wt%
-1cm
-1)
Concentration (wt%)
€
a∞ = 24.0±0.1( ) wt%−1cm−1
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Birefringence
-0.12
-0.11
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
20 30 40 50 60 70 80
Sunset Yellow FCF
Temperature (oC)
coexistence
nematic
0.94 M
0.99 M
1.08 M
1.17 M
1.25 M
Notice:(1) Birefringence decreases with increasing temperature(2) Birefringence is negative
€
Δn = n|| −n⊥
Birefringence
N=N
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Order Parameter
-0.4
-0.35
-0.3
-0.25
-0.2
20 30 40 50 60 70 80
Sunset Yellow FCF1.25 M
Temperature (°C)
0.55
0.6
0.65
0.7
0.75
0.8
20 30 40 50 60 70 80Temperature (°C)
€
SN=N =n||A|| − n⊥A⊥
n||A|| + 2n⊥A⊥
€
SN=N = P2 cosβ( ) S
Measure:(1) indices of refraction(2) absorption of polarized light
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Conclusions
Sunset Yellow FCF forms linear aggregates with a cross-sectional 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 cross-sectional area is about equal to two or three molecules.
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