dewetting driving forces dewetting mechanism? dewetting dynamics? final equilibrium state: drops with θ = θ Y

Transcription

1 dewetting initial state: continuous film of partially wetting liquid final equilibrium state: drops wit θ = θ Y driving forces dewetting mecanism? dewetting dynamics? 1

2 free energy vs. film tickness water drop on teflon: q Y =10 water film wit tickness small volume: equilibrium configuration = drop wit c.a. q Y if is not too large large volume: equilibrium configuration = tick film stability analysis: film is always stable against perturbations wat is te critical volume (tickness) below wic te film is unstable? ow do unstable films break up?

3 global stability F flat film: 1 Ffilm ( ) = σ sl + σ lv + ρ g A film dry surface: F dry = σ sv A dry eq energy of film + dry patc: F( A dry ) 1 = σ sl + σ lv + ρ g Afilm + σ sv Adry! = min 3 partial wetting: S = σ sv sl lv ( σ + σ ) < = σ lv (cosθy 1) 0 Afilm + Adry = A = const. V = A0 = Afilm = const. = λ (1 cosθ ) = λ sin eq. c Y c Y eigt of a liquid pancake θ /

4 global stability (II) metastable films globally stable films F tangent construction! eq 0 > eq : film is globally stable 4 0 < eq : film is globally unstable against breakup but locally stable against small perturbations metastable

5 a practical experiment 5 nucleation barrier >> k B T: create defect to initiate dewetting

6 nucleated dewetting ole nucleation at defect sites (e.g. due to surface rougness, cem. eterogeneity, ) random distribution of ole locations and time of appearance 6

7 a second dewetting scenario polystyrene films on Si eterogeneous nucleation spinodal dewetting oles appear at random locations and at random times oles appear at regular distances and at te same time allmarks of a linear instability 7 Seemann et al. Pys. Rev. Lett. 001

8 wetting and long-range forces disjoining pressure and effective interface potential (II) r i >> r i : F = σ + σ sl = O(r i ) : F = F( ) = σ + σ + Φ( ) lv sl lv Φ () : effective interface potential 8

9 properties of F() Φ( ) = F( ) ( σ sl + σ lv ) : = 0 : Φ 0 Φ = σ sv ( σ lv + σ sl ) = S O(F) = O(σ) [ mj/m (typical organic liquids)] Φ() : interaction energy / unit area of adjacent interfaces dφ d = Π() force / unit area between interfaces: disjoining pressure example: van der Waals interaction Φ( ) = A 1π A: Hamaker constant A=f(n v,n l,n s,ε v,ε l,ε s ) O(A)=10-0 J (.4k B RT) 9

10 contributions to disjoining pressure van der Waals interaction Φ( ) = A/1π electrostatic interaction ( double layer forces ) structural solvation forces ydrogen bonding forces sort-range cemical forces 10

11 F and macroscopic wetting F long range wetting partial wetting omogeneous film drop + dry substrate pseudo-partial wetting drop + tin film 0 S = σ 1 cosθ lv ( Y ) θ tin film comment on stability: unstable vs stable 11

12 stability of tin wetting films tin film equation: t = 1 3µ d dx 3 ( P) x 3 0 = xx P 3µ small perturbation: ( x, t) = 0 + δ( t) cos qx δ << 0 local pressure: P( x, t) = σ xx + dφ d ( x) dφ d ( x) Φ' ( 0 ) + Φ''( 0 ) δ δ& 3 t) = 3µ ( σ q + Φ' '( )) δ( ) ( 0 q t 0 F > 0: film locally stable for all q F < 0: film locally stable for large q but unstable for small q 1

13 stability of tin wetting films (II) critical wavevector: q c = Φ' '( 0 ) /σ fastest growing mode: maximum of prefactor q * = qc / caracteristic growt time: van der Waals: τ 5 * 0 1µ 3 σ τ* = 4 0q c tin films wit an initial tickness, for wic F <0 are linearly unstable 13

14 interface potential & stability F always stable 0 S = σ 1 cosθ lv ( Y ) unstable 14

15 example of a complex interfacial potential Φ( ) = c 8 8 A air PS SiO 1π 1 1 ( + d) A 1π ( + d) air PS Si sort range cemical force vdw: air-liq.-si vdw: air-liq.-sio air polystyrene SiO Si layered substrates: SiO:Si 15 Seemann et al. J. Pys. Cond. Matt. 13, 495 (001)

16 various dewetting scenarios Seemann, Jacobs, Hermingaus 16

17 dewetting dynamics PDMS (30 µm) on fluorinated Si 17 Redon et al. Pys. Rev. Lett. 1991

18 dewetting dynamics observations: -excess material collects in rim - constant dewetting velocity v - dewetting velocity v ~ q 3 Y 18 Redon et al. Pys. Rev. Lett. 1991

19 model 0 R(t) w(t) B q D < q Y assumptions: - 0 <<w<<r; θ <<1 -rim profile is circular and symmetric -rim volume: V rim = π R 0 A dynamics: 3µ V θ D ln balance of viscous dissipation & imbalanced Young force w a = ( v) dxdz = σ (cosθ cosθ V D = µ ) z Y D σ = V ( θ Y θ D ) σ point A & B: VA = θd ( θy θ ) D 6µ l A V B σ σ 3 = θd (0 θ ) = θ D D 6µ l 6µ l B B 19 θy V A = V B : θ D = = const. V=const. ~θ 3 Y 1+ l / l A B