Wetting and adhesion on nano-patterned surfaces,
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1 Wetting and adhesion on nano-patterned surfaces, How geometry couples to physics Olivier Pierre-Louis Oxford Theoretical Physics, Oxford, UK, AND LSP, Univ. J. Fourier, Grenoble, France. 20th May 2009 Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 1 / 38
2 1 Liquid drops 2 Solid clusters 3 Membranes and Filaments 4 Conclusion Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 2 / 38
3 Liquid drops Wetting of solid clusters on nano-patterned surfaces, How geometry couples to physics 1 Liquid drops 2 Solid clusters 3 Membranes and Filaments 4 Conclusion Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 3 / 38
4 Liquid drops Some examples Contact angle Lotus effect Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 4 / 38
5 Liquid drops Young contact angle Surface/Interface free Energies Z Z Z F = ds γ VS (θ) + ds γ SA (θ) + ds γ(θ) VS SA AV Assumptions: (i) flat substrate (ii) fixed total volume: Z Z N = Ω 1 d 2 r A θ 0 s θ A V Equilibrium: δ(f µn) = 0 S Laplace: µ = Ωγ AV κ Young relation (1805): γ SA + γ AV cos θ 0 = γ SV Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 5 / 38
6 Liquid drops Super-hydro-phobic surfaces: Wenzel and cassie-baxter states Bico, Marzolin, Quéré, Europhys. Lett (1999). Effective contact angle: γ eff SA + γ AV cos θ 0 = γ eff SV Wenzel (1936) substrate lengthening r 1 Wenzel and Cassie-Baxter states cos θ W = r cos θ 0 Cassie-Baxter (1944) solid-liquid contact fraction φ AS liquid-vapor contact fraction η AV cos θ CB = φ AS cos θ 0 η AV Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 6 / 38
7 Liquid drops Pinning Gibbs Inequality Condition (1906) θ 0 θ C θ θ 0 + θ C Pinning at corners θ C θ 0 θ θ C π θ 0. Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 7 / 38
8 Liquid drops Dynamics of lifting and collapse Parallel grooves: Electro-wetting experiments Vary θ 0 continuously with V λ/2 λ/2 λ Lattice-Boltzmann simulations Solve the hydrodynamics Movies R. J. Vrancken, H. Kusumaatmaja, K. Hermans, A.M. Prenen, O. Pierre Louis, C. W. M. Bastiaansen, D.J. Broer, preprint Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 8 / 38
9 Liquid drops Capillary filling Seemanet al (2005) Polystyrene drops on Silicon Olivier Pierre-Louis ( Oxford Theoretical Physics, Oxford, Wetting UK, and AND adhesion LSP, Univ. on nano-patterned J. Fourier, Grenoble, surfaces, France. Howolivier.pierre-louis@ujf-grenoble.fr geometry couples 20th Mayto 2009 physics ) 9 / 38
10 Solid clusters Wetting of solid clusters on nano-patterned surfaces, How geometry couples to physics 1 Liquid drops 2 Solid clusters 3 Membranes and Filaments 4 Conclusion ) 10 / 38
11 Solid clusters Experimental equilibrium shape Au/Graphite, Héyraud, Métois, Marseille He 4 crystal, Balibar et al, Paris NaCl, Métois et al ( o C) ) 11 / 38
12 Solid clusters Solids vs liquid Anisotropy: roughnening transition facets ) 12 / 38
13 Solid clusters Solids vs liquid Anisotropy: roughnening transition facets Energy: elasticity, eletronic energy, etc. ) 12 / 38
14 Solid clusters Solids vs liquid Anisotropy: roughnening transition facets Energy: elasticity, eletronic energy, etc. Mass Transport: diffusion (surface atoms, or bulk vacancies) ) 12 / 38
15 Solid clusters The Wulff and Kaishev constructions Isotropic solid γ(θ) = γ µ = Ω γκ R = Ω γ µ γ cos(θ 0 ) = γ S h s = Ωγ S µ Polygonal shape h i = Ωγ i µ h s = Ωγ S µ R θ 0 h s h s h i h j Global geometry ψ = S AV S AS ) 13 / 38
16 Solid clusters 3D KMC Model 3D KMC Hopping along the surface ν = ν 0 e (n 1J 1 +n 2 J 2 +n s1 J s1 +n s2 J s2 )/T J bond energy, n i nb neighbors i = 1 NN adsrobate i = 2 NNN adsorbate i = s1 NN substrate i = s2 NNN substrate Moves to NN/ surface Shape parameter ζ = J 2 J 1 = J s2 J s1 Wetting controlled by χ = J s1 J 1 isotropic: χ = (1 + cos θ 0 )/2 ) 14 / 38
17 Solid clusters Flat substrate vs parallel nanogrooves N = 10 4, λ = 20, ζ = 0.2, χ = 0.4, T/J 1 = 0.5 Flat substrate Parallel grooves 3 states Wenzel, Cassie-Baxter, Capillary Filling W z y x CB CF λ/2 λ/2 λ ) 15 / 38
18 Solid clusters Hysteresis ψ = S AV S AS, χ = J s1 J Ψ a W z y CB 2.0 x 1.0 CF 0.5 CB W CF Χ ) 16 / 38
19 Solid clusters Surface Diffusion Mullins Model Local chemical potential µ = Ω γκ. Mullins model: j = Dc k B T sµ V n = Ω sj Triple Line Equilibrium contact angle θ = θ 0 Scaling v n ssκ Relaxation time t L 4 θ 0 s j θ A S V ) 17 / 38
20 Solid clusters Dynamics Dynamics limited by peeling or nucleation Combe, Jensen, Pimpinelli, Phys Rev Lett 2000 Mullins and Rohrer, J. Am. Ceram. Soc Activation energy: lateral size R Cost: γ step2πρ Gain: γ rough (1/R) per atom Total: E = γ step2πρ γ rough R πρ2 E b = π γ2 step γ surf R Slow relaxation time t e E b/k B T Eb E ρ ρ 1/R ) 18 / 38
21 Solid clusters Experiments Controlled positionning of mass in holes Ling et al Surf. Sci 2006 McCarty NanoLetters 2006 Ag/W(110) ) 19 / 38
22 Solid clusters Nucleationless motion Going back to equilibrium height without nucleation on top?? ) / 38
23 Solid clusters Model X = (x U + x D )/2, and H = X tan(θ) l T = x U x D, l = y + y Einstein-like relation tx = D C k B T XE T. Diffusion limited dynamics D C Ω2 Dc eq H 2 l T l Khare, Bartelt, Einstein, Phys. Rev. Lett OPL, T.L. Einstein, Phys. Rev.B 2000 z y x x U h(x) l T x D y+ l T y ) 21 / 38
24 Solid clusters Interfacial and Wetting energies Free energy E I γ(h U + h D )(l + l T ) + 2γ(1 χ)l T l X l T Maximum aspect ratio r = l /l T r I max Drift dynamics tx = Ω2 Dc eq k B T «1 χ 1/4 r 3/2 init tan θ 2γ(1 χ) X 3 tan 2 (θ) 2Log (l ) z x U x D y y l x y h(x) l T T leading to X t 1/4 (also wetting potential W(h)) Log (l ) 10 T 2 ) 22 / 38
25 Solid clusters Elastic energy Exp: Tersoff Tromp, 1993 Ag/Si(100) Exp: Xu et al 2007, Ge/Si(111) E E 1 Z Z dr j dr k G j,k `rj r k fj (r)f k (r) 2 Maximum aspect ratio r = l /l T r E max = C V 1/2 tan(θ) 1/2 d 3/2 0 e 3(3+σ)/8(1 σ) where C = Drift dynamics tx = Ω2 Dc eq k B T α 2 (1 σ 2 ) e 1/(1 σ) 1 πyd 0 X where Y is the Young modulus. Scaling law X t 1/2. 2Log (l ) Log 10(l T) 2 ) 23 / 38
26 Solid clusters Other energy Metallic layers: Electronic confinement energy Z. Zhang et al, Phys.Rev.Lett.1998,1999 Metals/Semiconductor 1) Quantum confinement of electrons 2) Charge spilling in the substrate 3) Friedel oscillations Van der Waals forces U VdW = A 12πh 2 A can be either > 0 or < 0??? A J Z. Suo and Z. Zhang, Phys Rev B (1998) Magic thicknesses (as in metal clusters) ) 24 / 38
27 Membranes and Filaments Wetting of solid clusters on nano-patterned surfaces, How geometry couples to physics 1 Liquid drops 2 Solid clusters 3 Membranes and Filaments 4 Conclusion ) 25 / 38
28 Membranes and Filaments Carbon nanostructures Nanotubes on ripples (or grids) Derike et al, NanoLetters (2001). Graphene on rough SiO 2 E.D. Williams et al, NanoLetters (2007); scale-bar 2nm. ) 26 / 38
29 Membranes and Filaments Lipidic membranes Simple (fluid) lipid membrane on a nonflat surface L. Tan et al PNAS (2003); scale-bar 10µm M. Abkarian A. Viallat, Biophys J. (2005); D = 130µm ) 27 / 38
30 Membranes and Filaments 1D model: Filament or membrane on ripples Fakir Carpet Total energy Z E = ds» C 2 κ(s)2 + σ + V(r(s)) Wavelength λ Amplitude ǫ Crenellated Sinusoidal Saw tooth outside solid V = 0, surface V = γ, inside V = +. i.e. Deformations l eq Adhesion energy γ Bending rigidity C Tension σ h(x) h S(x) x ) 28 / 38
31 Membranes and Filaments Equilibrium equations for the Euler elastica with adhesion κ>0 κ<0 Free parts C ssκ + C 2 κ3 σκ = 0. s B F (BC1) Boundary conditions BC1 F B (BC2) (BC3) Euler-Bernoulli elastica model κ F = κ B κ eq, Cut-off length d = (C/σ) 1/2 where κ eq = (2γ/C) 1/2 BC2 κ B κ eq κ F κ B + κ eq. d Similar to the Gibbs Inequality Condition for the wetting contact angle BC3 κ + = κ, and sκ + sκ, ) 29 / 38
32 Membranes and Filaments Patterned substrates: a 1D model Natural parameters Constructing solutions from n-bridges n=1 n=2 n= β = λ d β 1 tension dominates β 1 curvature dominates All possible solutions Non-overlapping reduces the number of possible states «1/2 κeq α = κ g geometrical curvature κ g = 4π 2 ǫ/λ 2 α 1 Floating state α 1 Membrane follows patterns β ε σ C λ γ 0 α ) 30 / 38
33 8α Membranes and Filaments Ground state Transitions α 0, ,5 F β 5 1P 0 3P 4P 2P β ε σ C λ γ np, n 0 8 α ) 31 / 38
34 Membranes and Filaments Metastability n m α > α [β] n m α 0, ,5 F n m α < α [β] n m α n m [β] > α n m+1 [β] α n m [β] = α m n [β] α n m [β] > α n m+p [β] But no total order, e.g. α 5 5 [0] < α 4 9 [0], and α 5 5 [1] > α 4 9 [1] β-dependent decimation order Non-sticky F ground state at α < α [β] β β ε 8α3 α 8 8 α 2 2 α 1 2 8α2 α1 α3 3 8 σ C λ α 8α α 1 1 3P 4P np, n γ 8 2P 1P ) 32 / 38
35 Membranes and Filaments Sinusoidal surfaces n=1 n=2 n= λ 3 x A single family of bridges for: fakir carpet and sinusoidal, more for other surfaces σ C λ β 0 ε α γ Sinusoidal surface 30 F β β np n 0 8 α 1 1,5 2 2,5 α 0,8 0,82 0,84 0,86 0,88 0,9 F P 1P P P P P ) 33 / 38
36 Membranes and Filaments Orders of magnitude Orders of magnitude Graphene C = 0.9eV, γ 6meVÅ 2, σ 0 ǫκ eq 1. ǫ = 1nm, and λ = 10nm, α 2 larger than 100nm follow Orders of magnitude lipid membranes(swain and Andelman) C = J, and σ = Jm 2 γ = Jm 2, l eq = 3nm Choosing ǫ 50nm l eq, λ 500nm ǫ, we obtain α 1.5 and β 5 A. Incze, A. Pasturel and P. Peyla, Phys.Rev.B (2004) Nanotubes Oxygen adsorption tunes bending rigidity: σ 0, C = 20eV.nm, and γ 1eV.nm % oxygen C = 40eV Peyla et al Choosing ǫκ eq < 1. ǫ = 5nm, λ = 50nm ǫ = 1nm, and λ = 10nm, α 0.6. we obtain Oxygen adsorption scan tranisiton region α 2 (Nevertheless ǫκ eq 1) ) 34 / 38
37 Conclusion Wetting of solid clusters on nano-patterned surfaces, How geometry couples to physics 1 Liquid drops 2 Solid clusters 3 Membranes and Filaments 4 Conclusion ) 35 / 38
38 Conclusion Summary Liquids on micro-grooves: R. J. Vrancken, H. Kusumaatmaja, K. Hermans, A.M. Prenen, OPL, C. W. M. Bastiaansen, D.J. Broer, preprint ) 36 / 38
39 Conclusion Summary Liquids on micro-grooves: R. J. Vrancken, H. Kusumaatmaja, K. Hermans, A.M. Prenen, OPL, C. W. M. Bastiaansen, D.J. Broer, preprint Solids on nano-grooves: OPL, Y. Saito, EuroPhys. Lett ) 36 / 38
40 Conclusion Summary Liquids on micro-grooves: R. J. Vrancken, H. Kusumaatmaja, K. Hermans, A.M. Prenen, OPL, C. W. M. Bastiaansen, D.J. Broer, preprint Solids on nano-grooves: OPL, Y. Saito, EuroPhys. Lett Drift of solid islands: M. Dufay, OPL, preprint ) 36 / 38
41 Conclusion Summary Liquids on micro-grooves: R. J. Vrancken, H. Kusumaatmaja, K. Hermans, A.M. Prenen, OPL, C. W. M. Bastiaansen, D.J. Broer, preprint Solids on nano-grooves: OPL, Y. Saito, EuroPhys. Lett Drift of solid islands: M. Dufay, OPL, preprint Membranes and filaments on patterns OPL, Phys. Rev. E 2007 ) 36 / 38
42 Conclusion Perspectives Coupling between physics and morphology ) 37 / 38
43 Conclusion Perspectives Coupling between physics and morphology Nonlinear phenomena, Statistical Physics, Non-equilibrium processes ) 37 / 38
44 Conclusion Perspectives Coupling between physics and morphology Nonlinear phenomena, Statistical Physics, Non-equilibrium processes Dewetting of solid films on flat substrates OPL, A. Chame, Y. Saito, Phys. Rev. Lett ) 37 / 38
45 Conclusion Perspectives Coupling between physics and morphology Nonlinear phenomena, Statistical Physics, Non-equilibrium processes Dewetting of solid films on flat substrates OPL, A. Chame, Y. Saito, Phys. Rev. Lett Nonlinear dynamics, instabilities, and fluctuations of extended fronts OPL, Europhys. Lett. 2005; C. Misbah, OPL, Y. Saito, Rev. Mod. Phys ) 37 / 38
46 Conclusion Elastica: variation of the energy s < s B free s > s B adhesion Z sb» Z» C C E = ds 2 κ2 + σ + ds s B 2 κ2 + σ γ. t s B = t s +, B Variation δr(s) with δr(s) = 0 for s > s B. δe = Z sb» ds(δr n) C ssκ + C 2 κ3 σκ + [ (δr n)c sκ + ( sδr n)cκ] s B» «C + ds B 2 κ2 + σ s B C 2 κ2 + σ γ «s + B ) 38 / 38
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