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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