aggregation behavior and liquid crystal properties of water-soluble dyes

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Aggregation Behavior and Liquid Crystal Properties of Water-Soluble Dyes

Peter J. CollingsDepartment of Physics & Astronomy, Swarthmore College

Department of Physics & Astronomy, University of Pennsylvania

21st ILCC

July 4, 2006

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Acknowledgements

Chemists and Physicists

Robert Pasternack, Swarthmore College

Robert Meyer and Seth Fraden, Brandeis University

Paul Heiney, University of Pennsylvania

Oleg Lavrentovich, Kent State University

Michael Paukshto, Optiva, Inc. Swarthmore Students

Viva Horowitz, Lauren Janowitz, Aaron Modic, Michelle Tomasik Funding

National Science Foundation

American Chemical Society (Petroleum Research Fund)

Howard Hughes Medical InstituteReturn to "Recent Talks" Page

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Outline

IntroductionChromonic Liquid Crystals

Materials: Sunset Yellow FCF, Bordeaux Ink

Theoretical ConsiderationsSimple Theory of Aggregation

More Rigorous Theory of Aggregation and Liquid Crystal Phases

Experimental ResultsAbsorption Measurements in Dilute Solutions

X-ray Diffraction Measurements Over a Wide Concentration Range

Birefringence Measurements

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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Lyotropic Liquid Crystals

Amphiphilic 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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Chromonic Phases

M phase(positionally and orientationally

ordered columns)

N phase(orientationally ordered columns)

J. Lydon, in Handbook of Liquid Crystals, editedby J. Goodby, G. W. Gray, H.-W. Spiess, and V. Vill (Wiley-VCH, New York, 1998), Vol. 2B,Chap. XVIII, p. 981.


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Disodium Cromoglycate

Drug developed for the treatment of asthma. Liquid crystal phases at room temperature for concentrations

greater than about 10 wt%. X-ray measurements: 0.34 nm spacing between rings, column

diameter of 2-3 nm, column spacing about 4 nm. NMR points to a high value of the order parameter. Light scattering and viscosity measurements suggest a column

diameter of about 2 nm and an average length of about 20 nm at the nematic-isotropic transition.

Cross-sections of one and four molecules have been suggested. Birefringence of the nematic phase is small and negative.


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Chromonic Structures

J. Lydon, in Handbookof Liquid Crystals,edited by J. Goodby, G. W. Gray, H.-W.Spiess, and V. Vill (Wiley-VCH,New York, 1998),Vol. 2B,Chap. XVIII,p. 981.


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Sunset Yellow FCF

Disodium salt of 6-hydroxy-5-[(4-sulfophenyl)azo]-2-napthalenesulfonic acid

Anionic Monoazo Dye Food Color (Yellow 6)

N

N

SO3Na

OH

NaSO3

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) Return to "Recent Talks" Page

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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

N

O

N SO3H

N

N

O

HO3S

0

10

20

30

40

50

60

300 350 400 450 500 550 600 650

Bordeaux Dye(0.0053 wt%)

Wavelength (nm)Return to "Recent Talks" Page

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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) Return to "Recent Talks" Page

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Simple Theory

The partition function Q for a collection of non-interacting aggregates is

where n is the number of molecules in an aggregate, qn is the partition function of a single aggregate with n molecules, and Nn is the number of aggregates with n molecules.

The chemical potential per molecule n for an aggregate with n molecules is then

At equilibrium, all chemical potentials per molecule are equal.

€

Q =qn

Nn

Nn!,

n

∏

€

n =kTn

lnNnqn

.


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Simple Theory (continued)

Including translational degrees of freedom and a decrease in energy of kT for each pair of neighboring molecules in an aggregate,

where V is the sample volume, n is the thermal wavelength of an aggregate with n molecules (assumed to be constant), and n is the internal energy of an aggregate with n molecules.

Equating chemical potentials and denoting the volume fraction of aggregates with n molecules as xn, one obtains

€

qn =V

Λn3

exp−εkT

⎛ ⎝ ⎜

⎞ ⎠ ⎟ =

V

Λ3exp α n −1[ ]( ),

€

xn = nΛ3

veα

⎛

⎝ ⎜

⎞

⎠ ⎟n−1

x1n , where v is the molecular volume.


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Simple Theory (continued)

But the total volume fraction for all molecules is

The volume fraction of single molecules is therefore:

€

φ = xn

n=1

∞

∑ = nΛ3

veα

⎛

⎝ ⎜

⎞

⎠ ⎟n−1

x1n

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

n=1

∞

∑ =x1

1−Λ3

veα x1

⎛

⎝ ⎜

⎞

⎠ ⎟2

.

€

x1 =1 + 2φz( ) − 1 + 4 φz

2z2φ, where z =

Λ3

veα .


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Results of Simple 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( = 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( = 22)

Number of Molecules in an Aggregate

φ = 0.01 = 3peak

φ = 0.25 = 14peak


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More Rigorous Theory

M. P. Taylor and J. Herzfeld, Langmuir 6, 911 (1990); Phys. Rev. A 43, 1892 (1991)

Linear aggregates:

hard-core potentials

short-range repulsions

pair-wise attraction

For = 0.26:

S = 0.65

<n> = 6Return to "Recent Talks" Page

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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 Model

Strong molecular absorption is due to a collective excitation with some charge separation (two state system)

Aggregation results in a coupling between identical nearest neighbor two state systems

€

H =ΔE β

β ΔE

⎡

⎣ ⎢

⎤

⎦ ⎥

€

ΔEm≤n = ΔE1 +2β cosmπn +1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

No Coupling With Coupling

ΔE ΔE+βΔE-β

For n aggregated molecules:


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Theory-Experiment Comparison

AssumptionAbsorption coefficient =

€

an = a1 + a∞ − a1( )cosπ

n +1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Fitting Results

€

a∞ = 9580±10( ) M−1cm−1

α = 22.6 ± 0.11 104

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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X-ray Diffraction

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

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

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

€

=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 ± 0.06SlopeFitting Result

area of cylinder = 1.21 ± 0.12 nm2

molecular area ~ 1.0 nm2


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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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Bordeaux Ink (Absorption)

24

26

28

30

32

34

0 0.05 0.1 0.15 0.2

Bordeaux Ink

Absorption Coefficient (wt%

-1cm

-1)

Concentration (wt%)

AssumptionAbsorption coefficient =

€

an = a1 + a∞ − a1( )cosπ

n +1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Fitting Results

€

a∞ = 24.0±0.1( ) wt%−1cm−1

α = 24.5 ± 0.1


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Bordeaux Ink (X-ray)

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

)


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Analysis of Aggregate Size

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.03 0.04 0.05 0.06 0.07

φ

Bordeaux Ink

-2.9

-2.8

-2.7

-2.6

-2.5

-2.4

-3.6 -3.4 -3.2 -3 -2.8 -2.6(ln φ)

= 0.51 ± 0.03slope Fitting Resultarea of cylinder = 3.24 ± 0.04 nm2

molecular area ~ 1.2 nm2


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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.


aggregation behavior and liquid crystal properties of water-soluble dyes

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