dewetting - Universiteit Twente · Afilm + Adry = A = const. V = Ah0 = Afilmh = const. 2(1 cos ) 2...
19
1 dewetting initial state: continuous film of partially wetting liquid final equilibrium state: drops with q = q Y • driving forces • dewetting mechanism? • dewetting dynamics?
Transcript of dewetting - Universiteit Twente · Afilm + Adry = A = const. V = Ah0 = Afilmh = const. 2(1 cos ) 2...
1
dewetting
initial state: continuous film of partially wetting liquid
final equilibrium state: drops with θ = θY
• driving forces• dewetting mechanism?• dewetting dynamics?
2
water drop on teflon: θY=120°
free energy vs. film thickness
h water film with thickness h
• small volume:
equilibrium configuration = drop with c.a. θY if h is not too large
• large volume: equilibrium configuration = thick film
• stability analysis: film is always stable against perturbations
à what is the critical volume (thickness) below which the film is unstable?
à how do unstable films break up?
3
global stability
F
h
filmlvslfilm AhghF
++= 2
2
1)( ρσσflat film:
dry surface:
drysvdry AF σ=
energy of film + dry patch: min!
)( 2
2
1=+
++= drysvfilmlvsldry AAhgAF σρσσ
.. 0 consthAAhVconstAAA filmdryfilm =====+
2/sin2)cos1(2 2. YcYceqh θλθλ =−=
height of a liquid pancake
partial wetting:
0)( <+−= lvslsvS σσσ
)1(cos −= Ylv θσ
heq
4
global stability (II)
F
hheq
tangent construction!
metastable films globally stable films
h0> heq : film is globally stable
h0< heq : film is globally unstable against breakup … but locally stable against small perturbationsà metastable
5
a practical experiment …
nucleation barrier >> kBT : create defect to initiate dewetting
6
nucleated dewetting
hole nucleation at defect sites (e.g. due to surface roughness, chem. heterogeneity, …)
à random distribution of hole locations and time of appearance
7
a second dewetting scenario
Seemann et al. Phys. Rev. Lett. 2001
heterogeneousnucleation
holes appear at random locations and at random times
spinodaldewetting
holes appear at regular distances and at the same time
polystyrene films on Si
à hallmarks of a linear instability
8
wetting and long-range forces
ri
h
h >> ri : lvslF σσ +=
h = O(ri) : )()( hhFF lvsl Φ++== σσ
)(hΦ : effective interface potential
disjoining pressure and effective interface potential (II)
9
properties of Φ(h)
Shh
sllvsv =+−=Φ=→Φ∞→
)(:00:
σσσ
O(Φ) = O(σ) [10 … 100 mJ/m2 (typical organic liquids)]
)(hdhd
Π=Φ
−
:)(hΦ interaction energy / unit area of adjacent interfaces
force / unit area between interfaces: „disjoining pressure“
example: van der Waals interaction
212)(
hAh
π=Φ
A: Hamaker constantA=f(nv,nl,ns,εv,εl,εs)
O(A)=10-20 J (≈2.4kBT @ RT)
h
)()()( lvslhFh σσ +−=Φ
10
contributions to disjoining pressure
n van der Waals interactionn electrostatic interaction (“double layer forces”)n structural solvation forcesn hydrogen bonding forcesn short-range chemical forces
212/)( hAh π=Φ
11
Φ and macroscopic wetting
long range wetting
partial wetting
pseudo-partial wetting
Φ
h)cos1( YlvS θσ −=
h0
homogeneous film
drop + dry substrate
drop + thin film
comment on stability: unstable vs stable
θthin film
12
stability of thin wetting films
( )Phdxdh xt ∂=∂ 3
31µ
00 cos)(),( hhqxthhtxh <<⋅+= δδ
thin film equation:
small perturbation:
Phxx∂=
µ3
30
)(
),(xh
xx dhdhtxP Φ
+∂−= σlocal pressure: hhhdhd
xh
δ⋅Φ+Φ≈Φ )('')(' 00
)(
( ) )()(''3
)( 022
30 thhqqhth δσµ
δ Φ+−=&
Φ’’ > 0: film locally stable for all qΦ’’ < 0: film locally stable for large q but unstable for small q
13
stability of thin wetting films (II)
σ/)('' 0hqc Φ=
fastest growing mode: maximum of prefactor
critical wavevector:
2/* cqq =
characteristic growth time: σ
µτ 43
0
12*cqh
=50* h∝τvan der Waals:
à thin films with an initial thickness, for which Φ’’<0 are linearly unstable
14
interface potential & stability
Φ
h)cos1( YlvS θσ −=
h0
always stable
unstable
15
2222
88
)(12)(11
12)(
dhA
dhhA
hch SiPSairSiOPSair
+−
+−−=Φ −−−−
ππ
example of a complex interfacial potential
Seemann et al. J. Phys. Cond. Matt. 13, 4925 (2001)
air
polystyreneSiOSi
layered substrates: SiO:Si
short range chemical force
vdW: air-liq.-SiO
vdW: air-liq.-Si
16
various dewetting scenarios
Seemann,Jacobs, Herminghaus
17
dewetting dynamics
PDMS (30 µm) on fluorinated SiRedon et al. Phys. Rev. Lett. 1991
18
dewetting dynamics
Redon et al. Phys. Rev. Lett. 1991
observations:- excess material collects in rim- constant dewetting velocity v
- dewetting velocity v ~ θY3
19
model
θD < θYassumptions:- h0<<w<<R; θ <<1- rim profile is circular and symmetric- rim volume: 0
2 hRV rim π=
h0
R(t)
w(t)
A
B
dynamics: balance of viscous dissipation & imbalanced Young force
( ) VdzdxvD DYz ⋅−=∂= ∫ ∫ )cos(cos2 θθσµ=awV
D
ln3 2
θµ
)(2
22DYV θθ
σ−=
point A & B: )(6
22DYD
AA l
V θθθµσ
−= 32
6)0(
6 DDB
DB
B llV θ
µσ
θθµσ
=−−=
:BA VV = ./1
constll BA
YD =
+=
θθ à V=const. ~θY
3
