EntropyEntropy DrivenDriven InteractionsInteractions andand Assembly:Assembly: Spheres,Spheres, RodsRods && PolymersPolymers

Arjun G. Yodh, Department of Physics & Astronomy, University of Pennsylvania

Acknowledgements: National Science Foundation, NASA

U n i v e r s i t y o f P e n n s y l v a n i a OutlineOutline

• Entropy, Phase Transitions, Entropic Forces • Interaction Potential Measurements (mainly spheres) • Self-Assembly (mainly spheres) • Beyond Spheres – Rods (liquid crystal phases) – Rods & Polymers – Rods & Polymer Gels (Carbon Nanotubes)

U n i v e r s i t y o f P e n n s y l v a n i a ParticlesParticles inin WaterWater m μ 73

U n i v e r s i t y o f P e n n s y l v a n i a Forces,Forces, PotentialsPotentials ?? Self-Assembly?Self-Assembly?

U n i v e r s i t y o f P e n n s y l v a n i a LudwigLudwig Boltzman Boltzman

S = ENTROPY W = Number of states (configurations) Accessible to Thermodynamic System with Energy E

U n i v e r s i t y o f P e n n s y l v a n i a NN GasGas ParticlesParticles inin aa BoxBox

LOW ENTROPY HIGH ENTROPY

Number of Configurations that fill box far exceed the number of configurations that fill one quarter of the box.

In the absence of external influences systems tend to maximize entropy (i.e. become more disordered).

U n i v e r s i t y o f P e n n s y l v a n i a EntropyEntropy ofof NN ParticlesParticles inin aa BoxBox

Indistinguishable non-interacting particles in a box

V, T, N S ~ k N ln (V λ3 ) N / deBroglie

ΔV If V → V + ΔV: ΔS ≈ kN ( ) V

U n i v e r s i t y o f P e n n s y l v a n i a FreeFree EnergyEnergy (F)(F)

r F = U - TS

internal energy tendency r associated with to particle positions disorder

Phases of Matter (solid, liquid, gas) minimize free energy

U n i v e r s i t y o f P e n n s y l v a n i a ConventionalConventional SolidsSolids && Liquids/GasesLiquids/Gases

increasing temperature

solid gas U large & negative U ~ 0 TS small TS large U dominates S S dominates U

U n i v e r s i t y o f P e n n s y l v a n i a HardHard SphereSphere SystemsSystems No attractive energy from U !

a F = -TS only depends on entropy r a

U n i v e r s i t y o f P e n n s y l v a n i a MonodisperseMonodisperse Hard Hard SphereSphere PhasePhase BehaviorBehavior

Phase diagram – one-component

Real colloidal crystal

Pusey, P.N., van Megen, W. Nature 320, 340-342 (1986). Zhu, J.X., Li, M., Rogers, R., Meyer, W., Ottewill, R.H., Russell, W.B., Chaikin, P.M. Nature 387, 883-885 (1997). U n i v e r s i t y o f P e n n s y l v a n i a BinaryBinary SystemsSystems

U n i v e r s i t y o f P e n n s y l v a n i a EntropicEntropic Forces Forces Depletion Force: (HARD SPHERES)

inaccessible U(r) = π(ΦS) ΔV(r,aS,aL) to small spheres Osmotic Free pressure Volume Change

Moving 2 large spheres together increases volume accessible to small spheres

Asakura, Oosawa, J. Polym. Sci. v.33, 1983 (1958) Vrij, Pure Appl. Chem. v.48, 471 (1976)

U n i v e r s i t y o f P e n n s y l v a n i a InteractionInteraction MeasurementsMeasurements 1. Basic Technique 2. Large and Small Particles Crocker, J.C., Matteo, J.A., Dinsmore, A.D., and Yodh, A.G., Physical Review Letters 82, 4352-4355 (1999). 3. Particles and Rods Lin, K-H., Crocker, J.C., Zeri, A.C., and Yodh, A.G., Physical Review Letters 87, 088301-1-088301-4 (2001). Lau, A.W.C., Lin, K-H., and Yodh, A.G., Physical Review E 66, 020401-1-020401-4 (2002). 4. Particles and Polymers Verma, R., Crocker, J.C., Lubensky, T.C., and Yodh, A.G., Physical Review Letters 81, 4004-4007 (1998): Macromolecules 33, 177-186 (2000). Owen, R.J., Crocker, J.C., Verma, R., and Yodh, A.G., Physical Review E 64, 011401-1--011401-6 (2001).

U n i v e r s i t y o f P e n n s y l v a n i a OpticalOptical MicromanipulationMicromanipulation Optical Tweezers Optical Line Tweezers Gradiant Force >> Radiation Pressure

• Strongly Focused Beam Microscope objectives with high NA provide an easy solution

• Non-Destructive Can manipulate small dielectric • Measure Actual 3-Dimensional particles with piconewton Separations forces Particles are confined in the yz- direction

• Confine Motion of Particles Improves Statistics

U n i v e r s i t y o f P e n n s y l v a n i a AA Line-scannedLine-scanned OpticalOptical TweezerTweezer

U n i v e r s i t y o f P e n n s y l v a n i a HarmonicHarmonic PotentialPotential alongalong thethe Line:Line:

U n i v e r s i t y o f P e n n s y l v a n i a MeasuringMeasuring thethe InteractionInteraction

U n i v e r s i t y o f P e n n s y l v a n i a IsolatingIsolating thethe Entropic Entropic Effects Effects ofof thethe BackgroundBackground FluidFluid

Energy Resolution ~ 0.05kT Spatial Resolution ~ 15-30nm

U n i v e r s i t y o f P e n n s y l v a n i a AnAn InteractionInteraction MeasurementMeasurement ExampleExample

U n i v e r s i t y o f P e n n s y l v a n i a EffectEffect ofof AdsorbedAdsorbed PolymerPolymer

PEO (Polyethylene oxide, [CH2CH20]n) Silica Microspheres (~1.1μm diameter) Solvent: Water, pH = 8.0, buffered

U n i v e r s i t y o f P e n n s y l v a n i a LongLong RangeRange PotentialsPotentials δa is “effective thickness” of polymer layer

λ is an exponential decay length

λ, δa Functions of RG?? Owen, Crocker, Verma, Yodh, Phys. Rev. E. 2001 U n i v e r s i t y o f P e n n s y l v a n i a MeanMean FieldField andand ScalingScaling TheoriesTheories

Fleer, van Male, Johner, Macromolecules 32, (1999). Semenov, Joanny, Johner, Bonet-Avalos, Macromolecules 30, (1997).

U n i v e r s i t y o f P e n n s y l v a n i a EntropicEntropic (Depletion) (Depletion) InteractionsInteractions

Dilute Polymer Solution

Hard Spheres

Verma, Crocker, Lubensky, Yodh, Physical Review Letters v. 81, 4004 (1998) Crocker, J.C., Matteo, J.A., Dinsmore, A.D., and Yodh, & Macromolecules v.33, 177 (2000) A.G. Physical Review Letters v. 82, 4352 (1999)

U n i v e r s i t y o f P e n n s y l v a n i a BigBig SpheresSpheres andand LittleLittle SpheresSpheres −3 2 FAO(r) = (kT Φs*) (2as*) (2as* + 2aL -r) (2as* + 2aL + r/2) 3 as* = as + δas ; Φs* = Φs ( 1 + δas/as )

2as = 83 nm (PS) 2aL = 1100 ± 15 nm (PMMA) δas = 7 ± 3 nm Φs from Viscometry LD-H ≈ 3 nm

Crocker, Matteo, Dinsmore, Yodh, Physical Review Letters v. 82, 4352 (1999)

U n i v e r s i t y o f P e n n s y l v a n i a ConcentratedConcentrated SuspensionsSuspensions

Theory: Biben, Bladon, and Frenkel, 1996, Phys. Condens. Matter. 8, 10799. Chu, Nikolov, and Wasan, 1996, Langmuir 12, 5004. Dickman, Attard, and Simonian, 1997, J. Chem. Phys. 107, 205. Gotzelmann, Evans, and Deitrich, 1998, Phys. Rev. E. 57, 6785. Mao, Bladon, Lekkerkerker, and Cates, 1997, Mol. Phys. 92, 151. Piasecki, Bocquet, and Hansen, 1995, Physica (Amersterdam) 218A, 125. Roth R, Evans R, Dietrich S, Phys. Rev E 62 (4): 2000 Roth R, Evans R, Louis AA, Phys. Rev E 64 (5): 2001 Louis AA, Allahyarov E, Lowen H, Roth R, Phys. Rev E 65 (6): 2002

U n i v e r s i t y o f P e n n s y l v a n i a Rod-sphereRod-sphere SystemsSystems

U n i v e r s i t y o f P e n n s y l v a n i a DepletionDepletion Interaction:Interaction: RodsRods && SpheresSpheres

2 U(h;R / L) = – kBTnrRL K(h / L;R / L)

U n i v e r s i t y o f P e n n s y l v a n i a ModelModel ComparisonComparison

Lin, K-H., Crocker, J.C., Zeri, A.C., and Yodh, A.G., Physical Review Letters 87, 088301-1-088301-4 (2001).

U n i v e r s i t y o f P e n n s y l v a n i a RodRod (fd-Virus)(fd-Virus) DepletionDepletion InteractionsInteractions

1.0 μm silica particles

U n i v e r s i t y o f P e n n s y l v a n i a RotationalRotational EntropiesEntropies

U n i v e r s i t y o f P e n n s y l v a n i a AdditionalAdditional DegreeDegree ofof FreedomFreedom

U n i v e r s i t y o f P e n n s y l v a n i a InteractionsInteractions BetweenBetween SpheresSpheres && BentBent RodsRods

Lin, K-H., Crocker, J.C., Zeri, A.C., and Yodh, A.G., Physical Review Letters 87, 088301-1-088301-4 (2001). Lau, A.W.C., Lin, K-H., and Yodh, A.G., Physical Review E 66, 020401-1-020401-4 (2002). U n i v e r s i t y o f P e n n s y l v a n i a Polymer-SpherePolymer-Sphere DepletionDepletion InteractionsInteractions

U n i v e r s i t y o f P e n n s y l v a n i a PolymersPolymers

U n i v e r s i t y o f P e n n s y l v a n i a INTERACTIONINTERACTION POTENTIALPOTENTIAL forfor varyingvarying DNADNA ConcentrationsConcentrations

λ-DNA •16.5μm = L Dilute • ~50nm = l* • Monodisperse • Non-absorbing

~3nm = LD-H C* ≈ 30-50μg/ml Rg ≈ 500nm

Semi-Dilute ~ 1.2μm Silica

Depth Range

U n i v e r s i t y o f P e n n s y l v a n i a POLYMERPOLYMER DEPLETIONDEPLETION

Dilute polymer solution Concentrated polymer solution

Verma, Crocker, Lubensky, Yodh, Physical Review Letters v. 81, 4004 (1998) Verma, Crocker, Lubensky, Yodh, Macromolecules v.33, 177 (2000) U n i v e r s i t y o f P e n n s y l v a n i a MeanMean FieldField DepletionDepletion PredictionsPredictions

DNA coils / DNA coils / Interaction Measurements Provide Information about Background Complex Fluid!

U n i v e r s i t y o f P e n n s y l v a n i a POLYMERPOLYMER RIGIDITYRIGIDITY

τ=1

Schaefer, Joanny, Pincus, Macromolecules 13 (1980) →

U n i v e r s i t y o f P e n n s y l v a n i a Summary:Summary: InteractionsInteractions

Interaction Measurements • Useful in many contexts • Reveal Structural Correlations in Background Fluids

U n i v e r s i t y o f P e n n s y l v a n i a Self-AssemblySelf-Assembly (mainly(mainly spheres)spheres)

1. Binary Particle Suspensions (Bulk) 2. Wall Effects 3. Wall Structures 4. Directed Colloidal Assembly with Grating Templates

Review: Yodh, A.G., Lin, K-H., Crocker, J.C., Dinsmore, A.D., Verma, R., and Kaplan, P.D., The Philosphical Transactions of the Royal Society of London A 359, 921-937 (2001).

U n i v e r s i t y o f P e n n s y l v a n i a FluidFluid PhasePhase CrystallineCrystalline PhasePhase

Increasing Φs U n i v e r s i t y o f P e n n s y l v a n i a 500μm U n i v e r s i t y o f P e n n s y l v a n i a PhenomenologicalPhenomenological ApproachApproach Fluid Phase: • Gas of Large hard spheres + Gas of Small hard spheres. Carnahan-Starling Equation of State.

Solid Phase: • Close-packed lattice of Large Hard-spheres permeated by hard-sphere gas of Small Spheres.

Critical Feature Emerging from the Solid Model The entropy of the Small spheres increases as the crystal becomes more tightly packed! Equate Osmotic pressures, and chemical potentials of large and small spheres within each phase ⇒PHASE DIAGRAM

U n i v e r s i t y o f P e n n s y l v a n i a PhasePhase DiagramDiagram

Dinsmore, A.D., Yodh, A.G., and Pine, D.J., Physical Review E 52, 4045-4057 (1995).

U n i v e r s i t y o f P e n n s y l v a n i a EntropicEntropic Effect Effect NearNear aa WallWall Depletion Forces at Surface: (HARD SPHERES)

Moving large sphere to wall decreases the Free energy even more!

Kaplan, Rouke, Yodh, Pine, Physical Review Letters v.72, 582 (1994)

U n i v e r s i t y o f P e n n s y l v a n i a RANGERANGE OFOF COMPOSITIONSCOMPOSITIONS WHEREWHERE “EQUILIBRIUM”“EQUILIBRIUM” COLLOIDALCOLLOIDAL EPITAXYEPITAXY ISIS POSSIBLE!POSSIBLE!

Dinsmore, A.D., Warren, P.B., Poon, W.C.K., Yodh, A.G., Europhys Lett 40, 337-342 (1997). Dinsmore, A.D., Yodh, A.G., Pine, D.J., Phys Rev E 52, 4045-4057 (1995).

U n i v e r s i t y o f P e n n s y l v a n i a EntropicEntropic effects effects withwith StructureStructure inin thethe WallsWalls

Dinsmore, A.D., Yodh, A.G., Pine, D.J., Nature 383, 239-242 (1996). Dinsmore, A.D., Wong, D.T., Nelson, P., Yodh, A.G., Phys Rev Lett 80, 409-412 (1998). Dinsmore, A.D., Yodh, A.G., Langmuir 15, 314-316 (1999).

U n i v e r s i t y o f P e n n s y l v a n i a EntropicEntropic repulsionrepulsion fromfrom aa stepstep edge:edge:

Less excluded- volume overlap here glass terrace

Dinsmore, Yodh, Pine, Nature v.3838, 239 (1996)

U n i v e r s i t y o f P e n n s y l v a n i a CORNERSCORNERS

Dinsmore, Yodh, Langmuir v.15, 314 (1999)

U n i v e r s i t y o f P e n n s y l v a n i a VESICLESVESICLES

(PARTICLES PUSHED TO WALLS AND REGIONS OF HIGH CURVATURE)

Large Particles Alone Large and Small Particles

Dinsmore, A.D., Wong, D.T., Nelson, P., Yodh, A.G., Phys Rev Lett 80, 409-412 (1998).

U n i v e r s i t y o f P e n n s y l v a n i a ControlledControlled ColloidalColloidal EpitaxyEpitaxy

• PMMA beads with Polymer, index matched for 3D confocal microscopy.

• Slight density mis-match for 3D growth (decalin)

Lin, K-H, Crocker, J.C., Prasad, V., Schofield, A.,Lubensky, T.C., Weitz, D.A., Yodh, A.G., Physical Review Letters, 85 (2000)

Steven Chou. J. Vac. Sci Tech: B 15 No.6 (1997). Xia, Y., et al, Science 273, 347-349 (1996).

U n i v e r s i t y o f P e n n s y l v a n i a 2D2D AssemblyAssembly onon Line-gratingsLine-gratings

d = mean spacing above groove 2p scissor angle tan θ = d U n i v e r s i t y o f P e n n s y l v a n i a 2D2D AssemblyAssembly onon Crossed-Crossed- gratingsgratings

d = mean spacing above groove

U n i v e r s i t y o f P e n n s y l v a n i a U n i v e r s i t y o f P e n n s y l v a n i a FCCFCC CrystalCrystal

Confocal Image Reconstruction

2020 Layer Layer Portion Portion Within Within Larger Larger Colloidal Colloidal Crystal Crystal

Lin, K-H, Crocker, J.C., Prasad, V., Schofield, A.,Lubensky, T.C., Weitz, D.A., Yodh, A.G., Physical Review Letters, 85 (2000)

U n i v e r s i t y o f P e n n s y l v a n i a Summary:Summary: Self-AssemblySelf-Assembly

• Small species plus Geometric Structures produce Unusual and Useful Entropic Forces for Materials Synthesis.

U n i v e r s i t y o f P e n n s y l v a n i a BEYONDBEYOND SPHERESSPHERES

• Rods • Rods & Polymers • Rods & Polymer Gels (Carbon Nanotubes)

U n i v e r s i t y o f P e n n s y l v a n i a ExcludedExcluded VolumeVolume DependsDepends onon PhasePhase

2D

L πD2 2L ~2DL2

isotropic nematic

Ratio : L/πD D volume fraction at transition φ = 4 πD2 L

U n i v e r s i t y o f P e n n s y l v a n i a ConcentrationConcentration drivendriven Isotropic-Isotropic- NematicNematic phase phase transitiontransition inin hardhard rodsrods

increasing concentration

isotropic phase nematic phase D - rod diameter φ(θ)−orientational distribution L – rod length functions π φ - rod concentration I −N order parameterθ S : at I - N phase transition θ D φ φ = 4 3 2 1 θ I −N S = 2 sin( )( cos − ) ( )dθ L ∫ 2 2

Onsager, 1949 U n i v e r s i t y o f P e n n s y l v a n i a colloidalcolloidal liquidliquid crystalscrystals

900 nm

• fd virus : 900 nm length 7 nm diameter • L/D=130 • higher monodispersity then chemical rod-like colloids

• semiflexible rods – persistence length 2.2 μm

hard core repulsion dominates interaction potential virus particles – often used to study liquid crystaline behavior

Experiment J. D. Bernal (1936), Onsager (1949)

U n i v e r s i t y o f P e n n s y l v a n i a BackgroundBackground onon Lyotropic Lyotropic Rod Rod SuspensionsSuspensions isotropic-nematic (cholesteric) smectic phase phase coexistance four mutants – periodicty 0.3 to 1.2 μm

isotropic

nematic

crossed polarizers

fd virus – model system of monodisperse hard rods phase diagram isotropic phase nematic phase smectic phase (cholesteric) concentration Tang and Fraden, Liq. Cryst, 1995 Dogic and Fraden, PRL 1997 U n i v e r s i t y o f P e n n s y l v a n i a PolymersPolymers inin Nematic Nematic Suspensions Suspensions

Semi-flexible Biopolymer Nematic Liquid Crystal

+ = ?

DNA, Neurofilaments, Wormlike Aqueous suspension of fd virus micelle and Actin quantitatively understood • Directly Visualization with Fluorescence Microscopy • Quantitative Image Analysis Possible

U n i v e r s i t y o f P e n n s y l v a n i a Semi-flexibleSemi-flexible biopolymersbiopolymers DNA Neurofilament

16 micron length 5 - 20 micron length 2 nm in diameter 12 nm in diameter 40 nm persistence length ~ 220 nm persistence length Wormlike Micelle Actin ( polybutadiene-polyethyleneoxide )

10 – 50 micron length 2 – 30 micron length ~ 15 nm in diameter 7-8 nm in diameter ~ 500 nm persistence length ~ 16 micron persistence length

U n i v e r s i t y o f P e n n s y l v a n i a ImagesImages ofof PolymersPolymers inin IsotropicIsotropic && Nematic Nematic SuspensionsSuspensions ofof fd fd Virus Virus Isotropic Nematic

Actin 16 μm Actin in Nematic Fd

Wormlike Micelle 500 nm

Neurofilament 200 nm

DNA 50 nm

Hairpin defects 10 μm 10 μm Dogic Z, Zhang J, Lau AWC, Aranda-Espinoza H, Dalhaimer P, Discher DE, Janmey PA, Kamien RD, Lubensky TC, Yodh AG, Phys. Rev. Lett. 92 (12): 2004 U n i v e r s i t y o f P e n n s y l v a n i a ObtainObtain orientational orientational distribution distribution functionfunction (ODF)(ODF) fromfrom realreal spacespace imagesimages

π θ θ Extract S φ 3 2 1 θ from ODF: S = 2 ∫sin( )( cos − ) ( )dθ 2 2 U n i v e r s i t y o f P e n n s y l v a n i a ActinActin OrderOrder ParameterParameter Vs.Vs. LengthLength

41 mg/ml

28 mg/ml

U n i v e r s i t y o f P e n n s y l v a n i a TangentTangent –– Tangent Tangent CorrelationsCorrelations t(s’) t(s’+s) h(s)

Isotropic phase – quasi 2D actin in nematic phase

−s / 2L 〈tr(s'+s)⋅tr(s')〉 = e p Orientational correlations decay exponentially

Lp – persistence length actin in isotropic phase

U n i v e r s i t y o f P e n n s y l v a n i a TangentTangent tangenttangent correlationcorrelation functionfunction forfor differentdifferent fd fd concentrations concentrations

fd concentration 0.010 39 mg/ml 50 mg/ml 98 mg/ml

>

)

s

(

x

t ) 0.005

0

(

x

t

<

0.000 0123 s [μm] U n i v e r s i t y o f P e n n s y l v a n i a β FreeFree energyenergy ofof aa polymerpolymer inin aa nematicnematic liquid liquid crystalcrystal δ Bending Energy Coupling Energy Elastic Energy L 2 l r L p ⌠ ⎛ ∂t ⎞ Γ r r 2 1 r 2 3 F = ⎮ ⎜ ⎟ dz + ∫(t (z) − n(0, z)) dz + K ∫ ∇δn d r 2 ⌡ ⎝ ∂z ⎠ 2 0 2 0 splay bending

low energy Twist l p Persistence Length high energy Γ Coupling Constant K Elastic Constant δnr Local Fluctuation of Nematic Director *R.D. Kamien et al, Phys. Rev. A. 45, 8727(1992). U n i v e r s i t y o f P e n n s y l v a n i a TheoreticalTheoretical predictionprediction forfor tangent-tangent- tangenttangent correlationcorrelation functionfunction

U n i v e r s i t y o f P e n n s y l v a n i a ExtractExtract physicalphysical parametersparameters fromfrom thethe datadata fittingfitting

fd conc. Odijk def. l. gamma K [μm] [kT/μm] [dyne 10-8]

39 0.080 78 1.23

50 0.050 200 1.64

98 0.036 386 2.17

*K ≈ 3×10-8 (dyne/cm)

*Z. Dogic and Seth Fraden, Langmuir 16, 7820(2000).

U n i v e r s i t y o f P e n n s y l v a n i a Summary:Summary: BiopolymersBiopolymers inin Lyotropic Lyotropic NematicsNematics

• Polymers (except DNA) couple strongly to nematic and stretch out. • Polymers more “ordered” than nematic • Theory + Experiment yield coupling parameter, Odijk length

Dogic Z, Zhang J, Lau AWC, Aranda-Espinoza H, Dalhaimer P, Discher DE, Janmey PA, Kamien RD, Lubensky TC, Yodh AG, Phys. Rev. Lett. 92 (12): 2004

U n i v e r s i t y o f P e n n s y l v a n i a RodsRods inin PolymerPolymer SolutionsSolutions

•• fdfd/NIPA/NIPA mixturesmixtures –– aa thermotropicthermotropic suspensionsuspension •• MeltingMelting ofof LamellarLamellar phasesphases

•• SingleSingle--layerlayer rodrod membranesmembranes

A. Alsayed, Z. Dogic and A.G. Yodh, to be published in Physical Review Letters (2004).

U n i v e r s i t y o f P e n n s y l v a n i a RodsRods andand PolymerPolymer inin GoodGood SolventSolvent

N

• Hard to observe melting directly

Z. Dogic and S. Frade, Phil. Trans. R. Soc. Lond. A v. 359 (2001). U n i v e r s i t y o f P e n n s y l v a n i a Temperature-SensitiveTemperature-Sensitive NIPANIPA PolymerPolymer

N-isopropyl acrylamide

acylamide group (hydrophilic)

Propyl group (hydrophobic)

o Mw~250k Increasing temp ~32 C

o * at 10 C C ~ 0.01 gm/ml Rg~ 55 nm Tanaka T. et al , Nature, 325 (1987) 796-798. C. Wu and X. Wang, Phys. Rev. Lett. 80, 4092 (1998) U n i v e r s i t y o f P e n n s y l v a n i a OurOur ExperimentExperiment

Solvent quality tunes interactions fd rods NIPA

Repulsive polymer-polymer Steric - Low Temperature rod-rod rod-polymer Homogeneous Samples

heat

polymer-polymer attractive → Inhomogeneous - High Temperature rod-rod repulsive Samples rod-polymer repulsive

U n i v e r s i t y o f P e n n s y l v a n i a NIPANIPA polymerpolymer && fd fd rods rods atat LowLow TemperaturesTemperatures

7.5 mg/ml fd + 37.5 mg/ml NIPA 50 mg/ml fd + 7.5 mg/ml NIPA

isotropic lamellar C o C o T < 17 T < 5

•Low temperature, low rod • Low temperature, small concentration is miscible with amount of polymer in polymer. concentrated rod suspension destabilizes nematic phase and stabilizes smectic layers

U n i v e r s i t y o f P e n n s y l v a n i a BehaviorBehavior ofof fd/NIPA fd/NIPA mixture:mixture: LargeLarge [fd][fd] andand LowLow [NIPA][NIPA]

50 mg/ml fd + 0.7 % NIPA in 20 mM trizma buffer solution, pH 8.15. Temperature increase leads to unbinding of smectic layers and creation of nematic droplet when NIPA polymer is fully expelled 5oC7oC12oC15oC 16oC

scale bar is 5 microns 17oC

U n i v e r s i t y o f P e n n s y l v a n i a BehaviorBehavior ofof fd/NIPA fd/NIPA mixture:mixture: LargeLarge [fd][fd] andand LowLow [NIPA][NIPA] 50 mg/ml fd + 0.7 % NIPA in 20 mM trizma buffer solution, pH 8.15. lamellar swollen lamellar isotropic nematic

dislocation nucleation of nematic nematic swollen lamellar isotropic droplet droplet at the dislocation position

Temperature U n i v e r s i t y o f P e n n s y l v a n i a BehaviorBehavior ofof fd/NIPA fd/NIPA mixture:mixture: lowlow [fd][fd] andand highhigh [NIPA][NIPA] isotropic 7mg/ml fd + smectic T=15oC 3.75% NIPA in T=20oC 20 mM trizma buffer solution, pH 8.15. 5 μm 5 μm 20 - 31oC 5 μm nematic T=29oC

5 μm

5 μm U n i v e r s i t y o f P e n n s y l v a n i a BehaviorBehavior ofof fd/NIPA fd/NIPA mixture:mixture: lowlow [fd][fd] andand highhigh [NIPA][NIPA] 7mg/ml fd + 3.75% NIPA in 20 mM trizma buffer solution, pH 8.15. nematic droplet isotropic smectic droplet

membrane membrane

membrane melting Temperature isotropic smectic nematic T=15oC T=20oC T=29oC 5 μm 5 μm 5 μm 20 - 31oC 5 μm 5 μm U n i v e r s i t y o f P e n n s y l v a n i a MeltingMelting ofof lamellarlamellar dropletdroplet

22oC26oC

5 μm 5 μm

28oC29oC

5 μm 5 μm 7mg/ml fd + 3.75% NIPA in 20 mM trizma buffer solution, pH 8.15.

U n i v e r s i t y o f P e n n s y l v a n i a MeltingMelting ofof ColloidalColloidal MembranesMembranes

31oC

after 1 minute after 1.5 minutes

Kinetic barrier to create nematic 3d droplet after 2 minutes out of 2d membrane Melted totally to nematic droplet isolated 2D membrane

Colloidal membranes can be prepared in a metastable state - easily superheated nucleation barrier for melting 2D smectic layer into 3D nematic droplet !!!

U n i v e r s i t y o f P e n n s y l v a n i a DisturbingDisturbing colloidalcolloidal membranemembrane mechanicallymechanically (colloidal(colloidal membranemembrane isis aa stablestable object)object) • temperature is 28 oC (near melting temperature) • scale bar is 5 microns time

pull membrane metastable Condensing smectic Two colloidal membranes slide many times with nematic back to layers and join. tweezer and droplet smectic coalesce silica bead (tweezer off) onto membrane

U n i v e r s i t y o f P e n n s y l v a n i a Summary:Summary: RodsRods inin NIPANIPA SolutionsSolutions • Solvent effects lead to Temperature-dependent phase transitions in Lyotropic Systems. • Solvent effects at low fd-concentration lead to heterogeneous nucleation of nematic/smectic droplets. (Isotropic - Smectic/Lamellar – Nematic) • Solvent effects at high fd-concentration lead to swelling of Lamellar phase, defects/nematic droplets, and eventually isotropic droplets in Nematic background. • Melting of Lamellar structures: Kinetic barriers

U n i v e r s i t y o f P e n n s y l v a n i a RodsRods inin PolymerPolymer GelsGels

“Nematic nanotube gels,” Islam MF, Alsayed AM, Dogic Z, Zhang J, Lubensky TC, Yodh AG, Phys. Rev. Lett. 92 (8): 2004

U n i v e r s i t y o f P e n n s y l v a n i a AnAn ImportantImportant Rod:Rod: SingleSingle WallWall CarbonCarbon Nanotubes Nanotubes

SWNTs have extraordinary properties: • Strength (~100x steel) • Tensile strength 100-200 GPa • Stiffness 1.4 TPa • Elongation 20-30% • Electrical conductivity (~Copper) • Ballistic electron transport mechanism • Highest known current density • Thermal conductivity (~3x Diamond) • Thermally stable polymer (anaerobic)

Products incorporating SWNTs can benefit from all of these properties simultaneously. ~1 nm

100 nm – 10,000 nm U n i v e r s i t y o f P e n n s y l v a n i a DispersingDispersing SWNTs SWNTs van der Walls attaction: 40 KBT/nm Surfactant: SDS TX-100 NaDDBS Laser-oven SWNTs: 0.5 mg/ml 0.8 mg/ml 20 mg/ml HiPCO Time: 5 days 5 days 2 months 5.00

2.50

0 0 2.50 5.00 μm Islam, Rojas, Bergey, Johnson, Yodh NanoLett. 3, 269 (2003) U n i v e r s i t y o f P e n n s y l v a n i a SurfactantSurfactant AdsorptionAdsorption onon Nanotubes Nanotubes

Popular belief Our suggestion

Recent experimental evidence

Richards, Balavoine, Schultz, Ebbesen, and Mioskowski Science 300, 775 (2003) U n i v e r s i t y o f P e n n s y l v a n i a SWNTsSWNTs Behave Behave likelike RigidRigid RodsRods

I 100 I I(0.5% NaDDBS/D O) -2 2 Q I I(1.0% NaDDBS/D2O) 10 Q-1 (a) 1

0.1% HiPco/D O 0.1 2 with 1% NaDDBS

1E-3 0.01 0.1 Q (Å-1)

Zhou, Islam, Wang, Ho, Yodh, Winey, Fischer Chem. Phys. Lett. 384, 185 (2004)

U n i v e r s i t y o f P e n n s y l v a n i a SWNTSSWNTS areare AttractiveAttractive RodsRods

concentration

Isotropic (I) Nematic (N)

Onsager Ann. N. Y. Acad. Sci. 51, 627 (1949)

U n i v e r s i t y o f P e n n s y l v a n i a NematicNematic ElastomersElastomers

Volume compression

Isotropic (I) Nematic (N)

Lacoste, Lau and Lubensky Euro. Phys. J. E 8, 403 (2002) Lubensky, Mukhopadhyay, Radzihovsky and Xing PRE 66, 011702 (2002)

U n i v e r s i t y o f P e n n s y l v a n i a PropertiesProperties ofof NIPANIPA gelgel

N-isopropylacrylamide (NIPA) gel: F. Ilmain et al. Nature 349, 400 (1991)

Temperature

Pelton R., Temperature-sensitive aqueous microgels, Tanaka’s website Adv. Colloid Interface Sci., 85 (2000) 1-33. U n i v e r s i t y o f P e n n s y l v a n i a fd-virusfd-virus inin GelGel betweenbetween CrossedCrossed Polarizers Polarizers

Before shrinking After shrink

U n i v e r s i t y o f P e n n s y l v a n i a SWNT-NIPASWNT-NIPA GelsGels

SWNT dispersed in NaDDBS + (NIPA) pre-gel polymerized for 3h at T=22°C

8.25 mg/ml 2.47 mg/ml

U n i v e r s i t y o f P e n n s y l v a n i a TemporalTemporal andand ConcentrationConcentration DependenceDependence(P)

(A)

Islam, Alsayed, Dogic, Zhang, Lubensky, Yodh PRL 92, 088303 (2004) U n i v e r s i t y o f P e n n s y l v a n i a DeterminationDetermination ofof Nematic Nematic Order Order

O.A. (P)

(A)

Stronger O.A. α absorption σ || ⎡ I // ⎤ ln⎢ ⎥ = −NLSΔσ ⎣ I ⊥ ⎦ α α Independently S = ∫ f( ) 1(3cos2 −1)dΩ σ ⊥ 2 Determined

U n i v e r s i t y o f P e n n s y l v a n i a Isotropic-NematicIsotropic-Nematic Transition: Transition: NematicNematic NanotubeNanotube Gels Gels O.A. α (P)

⎡ I // ⎤ ln⎢ ⎥ = −NLSΔσ ⎣ I⊥ ⎦ (A)

Islam, Alsayed, Dogic, Zhang, Lubensky, Yodh PRL 92, 088303 (2004) U n i v e r s i t y o f P e n n s y l v a n i a DefectsDefects

(P)

(A)

4 extinction branches

Defects and buckling in nematic lyotropic gels, M. F. Islam, M. Nobili, T. C. Lubensky and A. G. Yodh (in preparation) U n i v e r s i t y o f P e n n s y l v a n i a MechanicalMechanical PropertiesProperties

U n i v e r s i t y o f P e n n s y l v a n i a DirectDirect MeasurementMeasurement ofof PolarizedPolarized AbsorptionAbsorption Cross-SectionCross-Section

2.0 σ || 1.5 E22 E33 /mole C) /mole 2 1.0 cm 6 0.5 σ Experiment ⊥ σ (10 0.0 E 5 11 No Depolarization 4 E22 /mole C)

2 3 E E 12 33 σ

cm 2 || 6 Theory 1 σ ⊥ σ (10 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Energy (eV) With Depolarization

Direct Measurement of the Polarized Absorption Cross-Section of Single-Wall Carbon Nanotubes, M. F. Islam, D. E. Milkie, C. L. Kane, A. G.Yodh and J. M. Kikkawa (to be published in Phys. Rev. Lett. (2004)).

U n i v e r s i t y o f P e n n s y l v a n i a BackgroundBackground

0.6

Optical Absorption at E , E , E , … 0 11 22 33 123 Energy

E11, E22-0.6, E33 WaveKp Vector

Lin, Phys. Rev. B 62, 13153 (2000)

U n i v e r s i t y o f P e n n s y l v a n i a LinearLinear AbsorptionAbsorption AnisotropyAnisotropy

• Linear Absorption is a fundamental optical quantity σ || • Needed for proper interpretation of optical spectra

• Comparison to theory σ ⊥ • Offers new methods to measure alignment in suspensions and composites

U n i v e r s i t y o f P e n n s y l v a n i a MagneticMagnetic AlignmentAlignment Combine SWNT with Pre-Gel ingredients Monomer

N-isopropylacrylamide (NIPA) Cross-linker

Align Sample in 9T Magnetic Field

UV Polymerization Locks in NT Alignment

U n i v e r s i t y o f P e n n s y l v a n i a QuantifyQuantify AlignmentAlignment (Raman(Raman Scattering)Scattering)

` 1.2 θ 1.0 VV 0.8

0.6

0.4 5.68x10-2 mg/ml f (θ) 0.2 1.43x10-3 mg/ml (Arbitrary Units) θ Fit 0.0 θ 0 90 180 270 360 G-Band Peak Intensity G-Band Peak Intensity Rotation (Degrees) 2 1 ⎛ 3cos − 1⎞ S ≡ f ( )⎜ ⎟ d(cosθ ) ∫−1 ⎜ ⎟ ⎝ 2 ⎠ NEMATIC Order Parameter

Concentration Order Parameter 5.68x10-2 (mg/ml) S = 0.18 1.43x10-3 (mg/ml)

5.85x10-2 (mg/ml) S = 0.11 2.93x10-3 (mg/ml)

U n i v e r s i t y o f P e n n s y l v a n i a CombineCombine RamanRaman ScatteringScattering withwith PolarizedPolarized OpticalOptical AbsorptionAbsorption toto ObtainObtain AbsorptionAbsorption Cross-SectionCross-Section

σ ||

−nα⊥d T⊥ = e −nα d α || σ ⊥ T|| = e σ α σ 2 σ 1 σ || = ()|| − σ⊥ S + ()|| + 2σ ⊥ 3 3 1 1 σ Independently = − ()− S + ()+ 2σ measure using ⊥ || ⊥ || ⊥ Raman 3 3 scattering

U n i v e r s i t y o f P e n n s y l v a n i a MeasurementMeasurement && TheoryTheory •No free parameter 2.0 model agrees within σ 1.5 || factor of 2. E22 E33 /mole C) /mole 2 1.0 cm 6 0.5 Depolarization Effect σ ⊥ σ (10

• Experiment 0.0 critical in calculation. E 5 11 No Depolarization 4 E22 /mole C) /mole

2 3 E E 12 33 σ

cm 2 || 6 Theory 1 σ ⊥ σ (10 0

ED 0.5 1.0 1.5 2.0 2.5 3.0 3.5 EIN Energy (eV) With Depolarization

C.L. Kane and E.J. Mele, cond-mat/0403153 (2004). H. Ajiki and T. Ando, Physica B 201, 349 (1994). U n i v e r s i t y o f P e n n s y l v a n i a Summary:Summary: BeyondBeyond SpheresSpheres

• Measurements of Isolated Biopolymers in Hard Rod Suspensions. • Hard Rods in Polymer Solutions (NIPA) – Temperature-dependent phase transitions in lyotropic systems – Melting of Smectic Phases • Hard Rods in Cross-linked Polymer Solutions (NIPA) – Nematic Nanotube Gels

U n i v e r s i t y o f P e n n s y l v a n i a CollaboratorsCollaborators

Mohamad Islam, Zvonimir Dogic, Jian Zhang, Keng-hui Lin, Tony Dinsmore, John Crocker, Ritu Verma, Andy Lau, Peter Kaplan, Ahmed Alsayed, Larry Hough, Joe Matteo, Daniel Chen, Jenifer Rouke, Paul Dalhaimer, Helim Aranda-Espinoza, Enrique Rojas, Daniel Bergey

Tom Lubensky (PENN) Dave Pine (UCSB) Dave Weitz (Harvard) Dennis Disher (PENN) Paul Janmey (PENN) Charlie Johnson (PENN) Randy Kamien (PENN)

U n i v e r s i t y o f P e n n s y l v a n i a . . .

U n i v e r s i t y o f P e n n s y l v a n i a