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. olivier.pierre-louis@ujf-grenoble.fr 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
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
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
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
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
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 00 11 01 00 11 00 11 01 00 11 000 111 000 111 000 111 000 111 000 111 0000 1111 000 111 000 111 000 111 01 0000 1111 000 111 000 111 01 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 cos θ W = r cos θ 0 Cassie-Baxter (1944) solid-liquid contact fraction φ AS liquid-vapor contact fraction η AV 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 0000 1111 00000000 11111111 00000000 11111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 0000 1111 00000000 11111111 00000000 11111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 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
Liquid drops Pinning Gibbs Inequality Condition (1906) θ 0 θ C θ θ 0 + θ C Pinning at corners θ C θ 0 θ 01 000 111 0000 1111 000000 111111 0000000 1111111 θ 00000000 11111111 C 000000000 111111111 00 11 000 111 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
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
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
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
Solid clusters Experimental equilibrium shape Au/Graphite, Héyraud, Métois, Marseille He 4 crystal, Balibar et al, Paris NaCl, Métois et al (620-710 o C) ) 11 / 38
Solid clusters Solids vs liquid Anisotropy: roughnening transition facets ) 12 / 38
Solid clusters Solids vs liquid Anisotropy: roughnening transition facets Energy: elasticity, eletronic energy, etc. ) 12 / 38
Solid clusters Solids vs liquid Anisotropy: roughnening transition facets Energy: elasticity, eletronic energy, etc. Mass Transport: diffusion (surface atoms, or bulk vacancies) ) 12 / 38
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
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
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
Solid clusters Hysteresis ψ = S AV S AS, χ = J s1 J 1 5.0 Ψ a W z y CB 2.0 x 1.0 CF 0.5 CB W CF 0.0 0.2 0.4 0.6 0.8 1.0 Χ ) 16 / 38
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
Solid clusters Dynamics Dynamics limited by peeling or nucleation Combe, Jensen, Pimpinelli, Phys Rev Lett 2000 Mullins and Rohrer, J. Am. Ceram. Soc. 2000 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
Solid clusters Experiments Controlled positionning of mass in holes Ling et al Surf. Sci 2006 McCarty NanoLetters 2006 Ag/W(110) ) 19 / 38
Solid clusters Nucleationless motion Going back to equilibrium height without nucleation on top?? ) / 38
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. 1998 OPL, T.L. Einstein, Phys. Rev.B 2000 z y x x U 00 11 01 000 111 0000 1111 01 00 11 0000 1111 0000000000 1111111111 00000 11111 0000000000 11111111110000 0000000 1111111 0000000000 1111111111 00000000 11111111 0000000000 1111 000000000 111111111 0000000000 1111111111 0000000000 11111111110000 0 1 0000000000 1111111111 000 111000000000 111111111000 0000 111100000000 00000 11111 000000 11111100 0000000 111111100000 h(x) 00000000 111111110000 0000000000 111111111100 110 1 0 1 000 111 0000 1111 000000 111111 0000000 1111111 00000000 11111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 l T x D y+ l T y 00 11 000 111 0000 1111 0000 1111 0000 1111 0000 1111 0000 1111 000 111 00 11 01 ) 21 / 38
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+ 00 11 y 01 000 111 l 01 00 11 x 0000 1111 0000 1111 0000000000 1111111111 y 00000 11111 0000000000 11111111110000 0000000 1111111 0000000000 1111111111 00000000 11111111 0000000000 1111 0000000000 1111111111 0000000000 1111111111 0000000000 11111111110000 00 11 000 111 00 11 01 0000000000 1111111111 000000000 111111111000 00000 11111 0000000 1111111 000000 111111 000000 11111100 h(x) 000 111 00000000 11111111 0000 1111 000000000 111111111 000 1110 1 000 111 01 0 1 000 111 00 11 0000 1111 000 111 00000 11111 0000000 000 111 00000000 11111111 000000000 111111111000 000000000 000000000 11 000000000 000000000 1111111110 1 000000000 111111111 10 0 l T T leading to X t 1/4 (also wetting potential W(h)) 2 2 0 Log (l ) 10 T 2 ) 22 / 38
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 = 0.175... 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 ) 10 0 2 2 0 Log 10(l T) 2 ) 23 / 38
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 10 20 J Z. Suo and Z. Zhang, Phys Rev B (1998) Magic thicknesses (as in metal clusters) ) 24 / 38
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
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
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
Membranes and Filaments 1D model: Filament or membrane on ripples 000 111 000 111 000 111 000 111 000 111 Fakir Carpet Total energy Z E = ds» C 2 κ(s)2 + σ + V(r(s)) 0000 1111 0000 1111 0000 1111 0000 1111 0000 1111 0000 1111 0 1 0 1 0 1 0 1 00 11 00 11 000 111 000 111 0000 1111 01 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 01 00 11 00 11 000 111 00 11 00 11 00 11 00 11 00 11 01 000000000 111111111 000000000 111111111 000000000 111111111 000000000 111111111 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 00 11 00000 11111 00000 11111 000000 111111 000000 111111 h(x) 000000 111111 00000000 11111111 00000000 11111111 h 000000000 111111111 S(x) 00000000 11111111 0000000000 1111111111 000000000 111111111 000000000 111111111 0 1 x ) 28 / 38
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 0000000 1111111 000000000 111111111 0000000000 1111111111 0 1 0 1 000 111 0000 1111 (BC1) 0000 1111 Boundary conditions BC1 F 00 11 11111 B000000 111111 0 1 00000000 11111111 0000000000 1111111111 0 1 00 11 (BC2) 000 111 + 00 11 00000 11111 000000 111111 00000000 11111111 00000000 11111111 0000000000 1111111111 0 1 00 11 (BC3) 000 111 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 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 000 111 Similar to the Gibbs Inequality Condition for the wetting contact angle BC3 κ + = κ, and sκ + sκ, ) 29 / 38
Membranes and Filaments Patterned substrates: a 1D model Natural parameters Constructing solutions from n-bridges n=1 n=2 n=3 0000 1111 0000 1111 0000 1111 0000 1111 0000 1111 β = λ d β 1 tension dominates β 1 curvature dominates 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 0000000 1111111 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
8α Membranes and Filaments Ground state Transitions α 0,5 10 1 1,5 F β 5 1P 0 3P 4P 2P β ε σ C λ γ np, n 0 8 α ) 31 / 38
Membranes and Filaments Metastability n m α > α [β] n m α 0,5 10 1 1,5 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 0 5 0 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
Membranes and Filaments Sinusoidal surfaces n=1 n=2 n=3 000 111 000 111 000 111 0000 1111 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 0000000000 1111111111 000 111 00 11 01 000 111 000 111 01 0 1 0 1 0 1 0 1 0 1 0000 1111 0000 1111 0000 1111 0000 1111 0000 1111 λ 3 x 3 00 11 00 11 000 111 000 111 000 111 01 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 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 0000000 1111111 00000000 11111111 00000000 11111111 20 β β 10 3 2 1 0 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 0000000 1111111 00000000 11111111 00000000 11111111 4P 1P 00000000 11111111 000000000 111111111 000000000 111111111 0000000 1111111 0000000 1111111 0P 00000000 11111111 000000000 111111111 000000000 111111111 0P 00000000 11111111 00000000 11111111 00000000 11111111 2P 00000000 11111111 000000000 111111111 000000000 111111111 3P 00000000 11111111 000000000 111111111 000000000 111111111 ) 33 / 38
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 = 1.4 10 19 J, and σ = 1.7 10 5 Jm 2 γ = 5 10 6 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 1 12.5% 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
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
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
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. 2009 ) 36 / 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 Solids on nano-grooves: OPL, Y. Saito, EuroPhys. Lett. 2009 Drift of solid islands: M. Dufay, OPL, preprint ) 36 / 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 Solids on nano-grooves: OPL, Y. Saito, EuroPhys. Lett. 2009 Drift of solid islands: M. Dufay, OPL, preprint Membranes and filaments on patterns OPL, Phys. Rev. E 2007 ) 36 / 38
Conclusion Perspectives Coupling between physics and morphology ) 37 / 38
Conclusion Perspectives Coupling between physics and morphology Nonlinear phenomena, Statistical Physics, Non-equilibrium processes ) 37 / 38
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. 2007 ) 37 / 38
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. 2007 Nonlinear dynamics, instabilities, and fluctuations of extended fronts OPL, Europhys. Lett. 2005; C. Misbah, OPL, Y. Saito, Rev. Mod. Phys. 2009 ) 37 / 38
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