chromonic liquid crystals: a new form of soft matter peter j. collings department of physics &...

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


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


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.


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


Thermotropic Liquid Crystals

L = 300 J/gm L = 30 J/gm

T

solid liquid crystal liquid


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


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


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


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+


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

+


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)


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


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


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


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


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



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

⎡ ⎣ ⎢

⎤ ⎦ ⎥



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


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


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)


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:


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


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


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)


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


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


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


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.


chromonic liquid crystals: a new form of soft matter peter j. collings department of physics &...

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