The stability of thin (soft) films

Transcription

1 The tability of thin (oft) film Lecture 5 Stability of thin film Long range force* November, 9 e.g. Diperion, electrotatic, polymeric

2 Review of Lecture The dijoining preure i a jump in preure at the boundary. It doe not vary between the plate. G Π ( h) = A h T P,,,, Ni P h P π RR F y Π h dh R + R Force between phere: G(h) y G h Π ( h) = h G = = S G = l lv 3 h Curve Stable Curve Metatable Curve 3 - Untable Ian Morrion 9 Lecture 5 - Stability of thin film

3 Review of Lecture G ( h ) A h Π = = + μi i + Ψ +Ψ Π i=, r dg S dt dn A d d A dh = μ Ψ + Ψ Π dg S dt Nid i A d d A dh i=, r T, P,,, N i N i Π= dμi A μ h h μ i,, Ψ, Ψ i a modified Gibb equation. n i d= dμ = Γdμ A i i i N A i Π Γ i = A μ h i h, dh i the exce adorption due to dijoining preure. Note that we do not know how much exce i on either plate! Ian Morrion 9 Lecture 5 - Stability of thin film 3

4 Review of Lecture 3 ε Π ( h) = ( Eh E Ψ o ) Ψ lim 4nkT inh h Π = 4 nkt π lim Π = h κh Φ κhh d Φ = coh coh Φ m ( Φ Φ ) m For the approach of urface at contant t potential, ti Φ i contant. t For the approach of urface at contant urface charge denity Φ i: zen = ( coh Φ coh Φm ) κ Ian Morrion 9 Lecture 5 - Stability of thin film 4

5 A 3 3kT Δ G3 = A3 = 3 Reln () l πh Δ Δ Review of Lecture 4 n= Lifhitz (954) The ditance derivative of the tanding, ocillatory EM wave between two flat plate i the force per area. Convert optical data to dielectric data: n ref ab ε ω = κ Reflectivity normal = ( nref ) ( nref ) + κ + + κ ( ω) ab ab ωε ε ( iξ) = + dω π ω + ξ ε Fit dielectric data to empirical equation: d j j ( iξn ) = + + j + ξτ ω + g ξ + ξ n j j j j n n f The Matubara frequencie: ( i n) ( i n) ( iξn ) ( iξn ) ( i n) ( i n) ( i ) ( i ) ε ξ ε ξ Δ = ε ξ +ε ξ 4π kt ξ n = n h The dielectric difference: ε ξ ε ξ 3 Δ 3 = ε 3 ξ n +ε ξ n The Lifhitz contant: A 3kT = Δ Δ Rel n 3 3 n= ( l ) Ian Morrion 9 Lecture 5 - Stability of thin film 5

6 From lecture. G Π ( e) = A h Energy of thin liquid film P Between urface: /e P( ) = Range of P(e): For polymer: ize of coil Electrotatic: nm in water nm in oil Ian Morrion 9 Energy = ( l + lv + P e ) m Energy a e m Energy a e l + m l lv = = S TP,,,, N i *de Genne, P-G; Brochard-Wyart, F.; Quéré, D. Capillarity and wetting phenomena: Drop, bubble, pearl, wave. Springer: New York; 4. Lecture 5 - Stability of thin film 6 lv

7 Energy at contant volume Energy E = = l + lv + P e m = = + + or = + + Differentiating give: Conider change at contant volume = Ae The urface tenion of the film i the change in energy with area: E l lv P e A dp e de = l + lv + P( e) da + A de de = l + lv + P e da AΠde A e Ade + eda = or = da de film de = da Ae= contant film = l + lv + P e + eπ e Ian Morrion 9 Lecture 5 - Stability of thin film 7

8 Stability of thin film dgbwq, Fig. 4.3 The energy of a film at contant volume i: The differential with repect to thickne i: film = l + lv + P e + eπ e d film d P e d P e = + Π ( e) +Π ( e) + e = e de de de A film i table (locally)only if: d P e > de (c) repreent the plitting of the film in (a) into two thickne of partial area, α and α + α < α P e P e P e α + α = Thi i the energy at contant Ae! Ian Morrion 9 Lecture 5 - Stability of thin film 8

9 dgbwq, Fig. 4.4 Total wetting S = > lv l Film greater than e c are table. Ian Morrion 9 Lecture 5 - Stability of thin film 9

10 Thickne of a large drop. Small drop are pherical egment. Large drop are flattened. To pread the drop require an force per unit length: + v lv l The hydrotatic preure integrated over the depth of the drop i a force per unit length puhing to pread the drop: e P = ρ g e z dz = ρ ge ρ v lv + l + ρge = lv coθe = ρge At equilibrium the um of the two i zero: Subtituting the Young-Dupré equation: Re-arranging give: e e κ = in dgbwq, Fig..4 θ Ian Morrion 9 Lecture 5 - Stability of thin film

11 dgbwq, Fig. 4.4 Partial wetting S lv l = < = coθ + lv l Ian Morrion 9 Lecture 5 - Stability of thin film

12 Peudo partial wetting dgbwq, Fig. 4.4 S = < lv l π = = co θ + e v lv l p L π e SV θ SL Gibb adorption iotherm: p π e = RT Γd ln p Ian Morrion 9 Lecture 5 - Stability of thin film

13 film = l + lv + P ( e) + eπ( e) Wetting, ga adorption, and contact angle p L = coθ + v lv l π e SV θ SL If the liquid ha a finite contact angle, then ga adorption i finite at p. d de film = ep e ( Γ ) π Γ = p ( Γ) RT Γ d ln p Ian Morrion 9 Lecture 5 - Stability of thin film 3

14 A π e film = l + lv + P e + eπ e Pe = = ( e= e) Wetting contact angle ga adorption lv c L p π e SV θ SL From a thermodynamic argument by degenne et al: P( e ) e ( e ) = ( coθ ) Π = + coθ l lv m m m l lv P e m lv From a thermodynamic argument by Adamon: lv ( co ) Area = θ The contact angle on mall particle! Ian Morrion 9 Lecture 5 - Stability of thin film 4

15 Slab of thickne a, eparation l: A + π l l a l a + + Interaction on treated urface Silane treatment of gla (a) Water pread on clean gla thick film are table. (b) On thinly ilanized gla, thick film or water are table, thin film of water are untable. Gold film on platic (a) Thin film of water are untable on platic. (b) Thin film of water are table on gold-coated platic. Ian Morrion 9 Lecture 5 - Stability of thin film dgbwq, p