Wetting When It Isn’t Simple!

P.S. Pershan, Harvard Univ.

Simple Wetting

D ~ Δμ−1/3

Van der WaalsμVapor

Bulk (T ) = μ LiquidBulk (T ) − VdW / D3

μLiquidBulk (T ) > μVapor

Bulk (T )

(T>Tboiling)

D

• 1) Casimir Effect: Critical Binary Liquid• Fisher and de Gennes (1978), Krech and Dietrich (1991, 1992)

• Correlation Length:

Three Different Experiments

D

ξ ~ 1 / T − Tc

−ν

M. Fukuto,Y. Yana

2) Structured SurfaceC. Rascon and A. O. Parry, Nature 407, 986 (2000).

y =L(x / x0 )γ

γ1 γ

O. Gang, B.Ocko,, K.Alvine, T. Russell,M. Fukuto, C. Black

3) Reconstructing Surface

Nanoparticles & Controlled Solvation

Thiol Stabilized Au Particles(~ 2 to 8 nm)

Dry Monolayer Adsorption (Wetting Liquid)

D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ockio, F. Stellacci

Control of Film Thickness

Saturated vapor Bulk liquid reservoir:

at T = Trsv.

Wetting film on Si(100) at T = Trsv + ΔTμ.

Outer cell: 0.03CInner cell: 0.001C

Vapor Pressure Thickness

μP1 ~ ΔTμ

Van der Waals

ΔTμ ~μ ~D−3

Delicate Control:Delicate Control:

X-Ray Reflectivity: Film Thickness

Qz = 4π λ( )sinα

€

Φ(Qz )2

~ A2 + B2 + 2AB cos QzD[ ]

R(Qz ) =RF (Qz) Φ(Qz)

exp −Qz

σeff

( )

exp[−Qz

σeff ]

Example of 1/3 Power LawMethyl cyclohexane (MC) on Si at 46 °C

ΔTμ [K]

Thi

ckne

ss L

[Å

]

L (2Weff /Δμ)1/3 (ΔTμ)1/3

Δμ [J/cm3]

• Via temperature offset

ΔμComparisons

• Via gravity

For h < 100 mm,

Δμ < 105

J/cm3

L > ~500 Å

small Δμ, large L

• Via pressure under-saturation

For ΔP/Psat > 1%,

Δμ > 0.2

J/cm3

L < 20 Å

large Δμ, small L

Critical Casimir Effect in NanoThick Liquids: Binary Liquid

47.7 °C

46.2 °C

45.6 °C

[Heady & Cahn, J. Chem. Phys. 58, 896 (1973)]

Tc = 46.13 0.01 °C, xc = 0.361 0.002

Methylcyclohexane (MC)

Perfluoro-methylcyclohexane

(PFMC)

Fisher and de Gennes (1978), Krech and Dietrich (1991, 1992)

x (PFMC mole fraction)

Tem

pera

ture

[C

]PFMC rich

MC rich

Thermodynamics

Bulk MC + PFMC reservoir:(x ~ xc = 0.36) at T = Trsv.

wetting film on Si(100)

T = Trsv + ΔTμ.

Outer cell: 0.03C

Inner cell: 0.001C

Same Experiment: Thickness of Absorbed Film

T=(T-Tc)/Tc

ΔμFilm-TRes2 Phase

Coexistence

Vapor Phase

Liquid Phase

Critical Point

ExperimentalPaths

ExperimentalPaths

qz [Å1]

R/R

F

X-ray reflectivity & Film thickness D

Paths

Tfilm [°C]

Film

thic

knes

s L

[Å

]

0.50 K

0.10 K

0.020 K

x = 0.36 ~ xc

Tc =

46.

2 °C

ΔTμ

D vs........ T-Tc

Theory( ) ( )

22 L

LTk

L

WLLF cBeff ξθ

μ ++Δ≈ΔExcess free energy/area of a wetting film:

Casimir term

( ) 3/12⎥⎦

⎤⎢⎣

⎡Δ

Θ+≈⇒

μ

ξLTkWL cBeff “Force” or “pressure” balance: 0=

∂Δ∂−LF

y = (L/ξ)1/ = t (L/ξ0+)1/ y = (L/ξ)1/ = t (L/ξ0

+)1/

+

,(y

) (+,)

+

,(y

) /

+,(

0)

(+,)

(+, +)(+, +)

d = 4 Ising (mean field)[M. Krech, PRE 1997]

d = 2 Ising (exact)[R. Evans & J. Stecki, PRB 1994]

Experiment vs. Theory

y = (L/ξ)1/ = t (L/ξ0+)1/

ΔTμ 0.020 K0.10 Kd = 2 (exact)

d = 4 (MFT)

+,(y)

+,(0)

Theory for y-dependence in d=3 does not exist!

There is prediction for 0for 3D.

Universal “Casimir amplitudes”

• At bulk Tc (t = 0), scaling functions reduce to:

For d = 3 Ising systems Δ Δ

Renormalization Group (RG)

Monte Carlo [M. Krech, PRE 1997]

-0.326

-0.345

2.39

2.450

“Local free energy functional” theory (LFEF)[Z. Borjan & P. J. Upton, PRL 1998]

-0.42 3.1

Our Result N/A 3 ± 1

For recent experiments with superfluid He (XY systems), see: R. Garcia & M.H.W. Chan, PRL 1999, 2002; T. Ueno et al., PRL 2003

Δ (0) = (0)/(d – 1)

Adsorption vs..... Shape: Phase Diagram

1/γ

Sculpted SurfacesTheory: Rascon & Parry, Nature (2000)

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Variety of Shapes (γ0

Long Channels

Planar CrossoverGeometry to Planar

GeometryDominated

Height =L

xL

⎛

⎝⎜⎞

⎠⎟

γ Adsorbed Liquid ∞

Parabolic Pits: Tom Russell (UMA)

Diblock Copolymer in

Solvent

Self Alignment on Si

PMMA removal by UV

degradation & Chemical RinseReactive Ion

EtchingC. Black (IBM)

~40 nm Spacing

~20 nm Depth/Diameter

Height ~ r2

γ ≈

X-ray Grazing Incidence Diffraction (GID) In-plane surface structure

Diffraction Pattern of Dry PitsHexagonal Packing

Thickness D~Δμ13Cross over to other filling!

Liquid Fills Pore: Scattering Decreases:

X-ray Measurement of Filling

GID

Electron Density vs..... ΔT

Filling

Reflectivity

Filling

Results for Sculpted Surface

Γc ~ ΔT( )

−βc

R-P Predictionβc~3.4

βc13

Uncertainties?

Flat Sample

Sculpted is Thinner than Flat

Tasinkevych & Dietrich

Volume of Liquid FillingPores: Γp

Volume of Liquid above Pores: Γt

Film only coats Flat PartArea_Flat/Area Total:

l =hmaxl = hliq

Reconstructing Surface:Gold Nanoparticles & Controlled Solvation

Controlled Wetting:Dry Monolayer Adsorption

LangmuirIsotherms

Formation

Liftoff AreaOf Monolayer

Stellacci et al (MIT)OT: MPA (2:1)OT=CH3(CH2)7SHMPA=HOOC(CH2)2SH

Bimodal Size Distribution of Particles

GID: X-ray vs. Liquid Adsorption(small particles)

GIDAdsorpt

ion

Return to Dry

Qz

QxyQxy Qxy

Three FeaturesThat Can Be Understood!

Solid lines are just guides for the eye!

Temperature Dependence of Reflectivity:

1-Minimum at low qz

2-Principal Peak Reduces and Shifts

3-2nd Minima Moves to Lower qz

Construction of Model: Dry Sample

Core size distribution

Vertical electrondensity profile

Model Fit: Based on Particle Size Distribution

Fits of Physical Model

1-Minimum at low qz

2-Principal Peak Reduces and Shifts

3-Second Minima Moves to Lower qz

Evolution of Model with Adsorption

Thin wetting film regime

Beginning of bilayer transition

Thick wetting film regime

DRY

toluene ΔT~3K

tolueneΔT~0.5K

tolueneΔT~15mK

tolueneΔT~0.5K

tolueneΔT~3K

Bimodal Au nanocrystals in equilibrium with undersaturated vaporGood Solvent Poor vs..... Good

Solvent

Rev

ersi

ble

Aggregation in Poor Solvent

Dissolution in GoodSolvent

Self Assembly

(1) dry

(2) ethanol ΔT~1K

(3)ethanolΔT~15mK

(4)dryagain(etOHextracted)

(5)tolueneΔT=15K

(6)tolueneΔT~15mK

(7)tolueneΔT~3K

Summary of Nano-particle experiments

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Summary

• Delicate Control of Wetting: ΔμΔ• Wetting of Critical Liquid (Casimir)

M. Fukuto,Y. Yana

• Wetting of Structured Surface (Rascon/Parry & Tasikevych/Dietrich)O. Gang, B.Ocko,, K.Alvine, T. Russell,M. Fukuto, C. Black

• Nano-Particles: Self Assembly D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ockio, F. Stellacci