yodh phys295 entropic forces
DESCRIPTION
Entropic ForcesTRANSCRIPT
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropic Forces &Phase TransitionsEntropic Forces &Phase Transitions
Arjun G. Yodh, Dept. of Physics & Astronomy
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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
• General Motivations
• Entropy, Phase Transitions, Entropic Forces
• Interaction Potential Measurements(mainly spheres)
• Self-Assembly (mainly spheres)
• Beyond Spheres
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U n i v e r s i t y o f P e n n s y l v a n i a
Particles in WaterParticles in Water73
μm
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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, Potentials ? Self-Assembly?Forces, Potentials ? Self-Assembly?
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U n i v e r s i t y o f P e n n s y l v a n i a
(1) Self-Assembly / Collective Properties• Novel Phases (Equilibrium Statistical Physics)
• Role of shape, charge, concentration,conformation, size, ...
• Structure, Dynamics, Rheology, Optical Properties, ...• Beyond Equilibrium: Metastable phases, glasses, …
Templates, Nucleation,…Sedimentation (Microgravity!)
(2) Interactions / Forces• What are the interactions between constituents in What are the interactions between constituents in
suspension?suspension?•• How do these interactions arise?How do these interactions arise?•• How do these interactions affectHow do these interactions affect
selfself--assembly, structure,assembly, structure,dynamics, dynamics, rheologyrheology,,transport properties?transport properties?
MOTIVATIONS / FUNDAMENTALMOTIVATIONS / FUNDAMENTAL
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U n i v e r s i t y o f P e n n s y l v a n i a
MOTIVATIONS / PRACTICALMOTIVATIONS / PRACTICALCreation of Novel Structures for “High-Tech” ApplicationsPhotonics, Sensors, MicroArrays, Bragg-Switches, Advanced Composites …
Understanding, CONTROL ofmany “Practical” soft materials
Insight about crowdedenvironments: cellular interiors
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U n i v e r s i t y o f P e n n s y l v a n i a
Ludwig BoltzmanLudwig Boltzman
S = ENTROPYW = Number of states (configurations)
Accessible to ThermodynamicSystem with Energy E
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U n i v e r s i t y o f P e n n s y l v a n i a
N Gas Particles in a BoxN Gas Particles in a Box
E.g.,
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).
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropy of N Particles in a BoxEntropy of N Particles in a Box
Indistinguishable non-interacting particles in a box
V, T, N
S ~ k N ln ( λ3deBroglie )N
V /
ΔS ≈ kN (ΔVV
)If V → V + ΔV:
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U n i v e r s i t y o f P e n n s y l v a n i a
Free Energy (F)Free Energy (F)
F = U - TS
internal energyassociated with
particle positions
tendencyto
disorder
Phases of Matter (solid, liquid, gas) minimize free energy
r
r
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U n i v e r s i t y o f P e n n s y l v a n i a
Conventional Solids & Liquids/GasesConventional Solids & Liquids/Gases
U dominates S S dominates U
solid liquid, gas
increasing
temperature
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U n i v e r s i t y o f P e n n s y l v a n i a
Hard Sphere SystemsHard Sphere Systems
No attractive energy from U !
F = -TSonly dependson entropy
a
ar
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U n i v e r s i t y o f P e n n s y l v a n i a
Monodisperse Hard Sphere Phase BehaviorMonodisperse Hard Sphere Phase Behavior
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).
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U n i v e r s i t y o f P e n n s y l v a n i a
Binary SystemsBinary Systems
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropic ForcesEntropic ForcesDepletion Force: (HARD SPHERES)Depletion Force: (HARD SPHERES)
Moving 2 large spheres together increases volume accessible to small spheres
inaccessibleto
small spheres
Asakura, Oosawa, J. Polym. Sci. v.33, 1983 (1958)
Vrij, Pure Appl. Chem. v.48, 471 (1976)
U(r) = π(ΦS) ΔV(r,aS,aL)
Osmoticpressure
FreeVolume Change
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U n i v e r s i t y o f P e n n s y l v a n i a
Optical MicromanipulationOptical MicromanipulationOptical TweezersGradiant Force >> Radiation Pressure
• Strongly Focused BeamMicroscope objectives with high NA provide an easy solution
• Non-DestructiveCan manipulate small dielectric particles with piconewtonforces
• Measure Actual 3-Dimensional SeparationsParticles are confined in the yz-direction
• Confine Motion of ParticlesImproves Statistics
Optical Line Tweezers
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U n i v e r s i t y o f P e n n s y l v a n i a
A Line-scanned Optical TweezerA Line-scanned Optical Tweezer
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U n i v e r s i t y o f P e n n s y l v a n i a
Measuring the InteractionMeasuring the Interaction
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U n i v e r s i t y o f P e n n s y l v a n i a
Isolating the Entropic Effectsof the Background Fluid
Isolating the Entropic Effectsof the Background Fluid
Energy Resolution ~ 0.05kTSpatial Resolution ~ 15-30nm
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U n i v e r s i t y o f P e n n s y l v a n i a
Big Spheres and Little SpheresBig Spheres and Little Spheres
Crocker, Matteo, Dinsmore, Yodh, Physical Review Letters v. 82, 4352 (1999)
FAO(r) = (kT Φs*) (2as*)−3 (2as* + 2aL - r)2 (2as* + 2aL + r/2)as* = as + δas ; Φs* = Φs ( 1 + δas/as )3
2as = 83 nm (PS)2aL = 1100 ± 15 nm (PMMA)δas = 7 ± 3 nmΦs from ViscometryLD-H ≈ 3 nm
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U n i v e r s i t y o f P e n n s y l v a n i a
Concentrated SuspensionsConcentrated Suspensions
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U n i v e r s i t y o f P e n n s y l v a n i a
Fluid Phase Crystalline PhaseFluid Phase Crystalline Phase
Increasing Φs
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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
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U n i v e r s i t y o f P e n n s y l v a n i a
Phase DiagramPhase Diagram
Dinsmore, A.D., Yodh, A.G., and Pine, D.J., Physical Review E 52, 4045-4057 (1995).
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropic Effect Near a WallEntropic Effect Near a WallDepletion 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)
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U n i v e r s i t y o f P e n n s y l v a n i a
RANGE OF COMPOSITIONS WHERE “EQUILIBRIUM”COLLOIDAL EPITAXY IS POSSIBLE!
RANGE OF COMPOSITIONS WHERE “EQUILIBRIUM”COLLOIDAL EPITAXY IS 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).
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropic effects with Structure in the WallsEntropic effects with Structure in the Walls
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).
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U n i v e r s i t y o f P e n n s y l v a n i a
Entropic repulsion from a step edge:Entropic repulsion from a step edge:
Less excluded-volumeoverlap
here glass terrace
Dinsmore, Yodh, Pine, Nature v.3838, 239 (1996)
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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)
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U n i v e r s i t y o f P e n n s y l v a n i a
VESICLES VESICLES
(PARTICLES PUSHED TO WALLS ANDAND REGIONS OF HIGH CURVATURE)
Dinsmore, A.D., Wong, D.T., Nelson, P., Yodh, A.G., Phys Rev Lett 80, 409-412 (1998).
Large Particles Alone Large and Small Particles
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U n i v e r s i t y o f P e n n s y l v a n i a
• 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)
Controlled Colloidal EpitaxyControlled Colloidal Epitaxy
Steven Chou. J. Vac. Sci Tech: B 15 No.6 (1997).Xia, Y., et al, Science 273,347-349 (1996).
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U n i v e r s i t y o f P e n n s y l v a n i a
FCC CrystalFCC CrystalConfocal Image Reconstruction
20 Layer Portion Within Larger Colloidal 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)
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U n i v e r s i t y o f P e n n s y l v a n i a
BEYOND SPHERESBEYOND SPHERES
• Rods• Rods & Polymers• Rods & Polymer Gels
(Carbon Nanotubes)
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U n i v e r s i t y o f P e n n s y l v a n i a
Rods: colloidal liquid crystalsRods: colloidal liquid crystals
Experiment J. D. Bernal (1936), Onsager (1949)
• fd virus : 900 nm length 7 nm diameter • L/D=130
• semiflexible rods – persistence length 2.2 μm
• higher monodispersity then chemical rod-like colloids
virus particles – often used to study liquid crystaline behavior
hard core repulsion dominates interaction potential
900 nm
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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 nematic
πD2 2L
πD2
~2DL2
2D
L
Ratio : L/πD
Excluded Volume Dependson Rod Orientation
Excluded Volume Dependson Rod Orientation
Orientational Entropy ↔ Packing Entropy
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U n i v e r s i t y o f P e n n s y l v a n i a
Concentration driven Isotropic-Nematic phase transition in hard rods
Concentration driven Isotropic-Nematic phase transition in hard rods
isotropic phase nematic phase
increasingconcentration
Onsager, 1949
LD
NI 4=−φ
D - rod diameterL – rod length
n transitiophase N-Iat ionconcentrat rod -NI−φ
order parameter S :
f(θ)−orientational distribution functions
∫ −= θθfθθπ 2 )()21cos
23)(sin(2 dS
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U n i v e r s i t y o f P e n n s y l v a n i a
Phases of Lyotropic Rod SuspensionsPhases of Lyotropic Rod Suspensions
isotropic
nematic
crossed polarizers
isotropic-nematic (cholesteric) phase coexistance
smectic phasefour mutants – periodicty 0.3 to 1.2 μm
fd virus – model system of monodisperse hard rods
phase diagram isotropic phase nematic phase smectic phase
concentration(cholesteric)
Tang and Fraden, Liq. Cryst, 1995Dogic and Fraden, PRL 1997
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U n i v e r s i t y o f P e n n s y l v a n i a
Concentration driven Isotropic-Nematic phase transition in hard rods
Concentration driven Isotropic-Nematic phase transition in hard rods
isotropic phase nematic phase
increasingconcentration
Onsager, 1949
LD
NI 4=−φ
D - rod diameterL – rod length
n transitiophase N-Iat ionconcentrat rod -NI−φ
order parameter S :
φ(θ)−orientational distribution functions
∫ −= θθφθθπ 2 )()21cos
23)(sin(2 dS
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U n i v e r s i t y o f P e n n s y l v a n i a
Polymers Plus RodsPolymers Plus Rods
+ = ?
900 nm
Increasing temp ~32oC
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U n i v e r s i t y o f P e n n s y l v a n i a
lamellar swollen lamellar
nematic
nematicisotropic
isotropic dropletswollen lamellardislocation nucleation of nematic droplet at the
dislocation position
Temperature
50 mg/ml fd + 0.7 % NIPA in 20 mM trizma buffer solution, pH 8.15.
Behavior of fd/NIPA mixture:Large [fd] and Low [NIPA]
Behavior of fd/NIPA mixture:Large [fd] and Low [NIPA]
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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
isotropic smectic droplet
membrane
nematic droplet
membrane
membrane melting
7mg/ml fd + 3.75% NIPA in 20 mM trizma buffer solution, pH 8.15.
5 μm
isotropic T=15oC
smecticT=20oC
5 μm5 μm
nematic T=29oC
20 - 31oC
5 μm
Behavior of fd/NIPA mixture:low [fd] and high [NIPA]
Behavior of fd/NIPA mixture:low [fd] and high [NIPA]
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U n i v e r s i t y o f P e n n s y l v a n i a
Melting of Lamellar DropletMelting of Lamellar Droplet
smectic droplets (cylindrical shape)
nematic droplets(elongated shape)
isolated 2D membrane
2 μm
5 μm
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U n i v e r s i t y o f P e n n s y l v a n i a
SummarySummary
• Entropy is a pervasive effect in Condensed Matter Physics.
• In this talk we have used Model Systems to illustrate its effect.
• In practice Spheres & Rods can be small Molecules.