Material Properties and Characterization

Transcription

1 ETH lecture: Material Properties and Characterization Materials Science & Technology Manfred Heuberger Advanced Fibers, Empa, 9014 St. Gallen 8h about Surfaces Part 1 Introduction When the material property depends on the surface 1.5h Surface Properties What are the relevant quantities? Analysis and Characterization of Surfaces (XPS, SIMS) 1.5h Intermolecular Interactions intermolecular forces (Van der Waals, electrostatic forces, entropic forces) Integration: from intermolecular to surface forces Macroscopic forces (Kapillary Forces, Young-Laplace equation) 1h Exercises (magnitudes, ranges, XPS spectra) 1.5h Static Surface Forces Lifschitz Theory Part 2 Hamaker constant Forces at solid-liquid interfaces (Hydrophilic, double-layer, depletion, structural forces) Forces at polymer interfaces (steric forces, brush, bridging, ) Forces on biological surfaces (membranes, specific interaction) 1.5h Dynamic Surface Forces Adhesion hysteresis (dynamics of surfaces, WLF) Macroscopic friction (with / without lubrication) Introduction to Nanotribologie Measurement of surface forces (AFM, SFA) 1h Exercises (integration, Hamaker, steric repulsion) 1

2 Static Surface Forces When the medium matters The Hamaker constant Definition: A = π 2 C 1 ρ 1 ρ 2 simplification (geometry-independent) material-pair constant typical values Joules positive for attraction 2

3 Effects of a medium Surface Forces in a Medium Interactions with a medium modified forces/energies complications ordered molecules adsorbed molecules chemical reactions 3 1 medium 3 2 The Lifshitz Theory Surface Forces in a Medium Continuum approach continuum electrodynamics frequency dependent integral, ε(ω) difficult calculation (absorption data) retardation effects gives expression for Hamaker constant 3 1 medium 3 2 3

4 Frequency integration: The Lifshitz Theory A 3 4 kt ε ε 1 3 ε ε 2 3 ε 1 + ε 3 ε 2 + ε 3 + 3h ε 1 (ν) ε 3 (ν) ε (ν) ε (ν) 2 3 dν 4π ε 1 (ν) + ε 3 (ν) ε 2 (ν) + ε 3 (ν) ν 1 ε(ν) not measurable over entire spectrum retardation effects at higher frequencies The Lifshitz Theory Simplification after Israelachvili for visual frequencies A = A ν =0 + A ν> 0 3kT 4 ε 1 ε 3 ε 2 ε 3 ε 1 + ε 3 ε 2 + ε 3 + 3h 8 2 (n 2 1 n 32 ) (n 22 n 32 ) (n 12 + n 32 ) (n 22 + n 32 ) (n 12 + n 32 ) + (n 22 + n 32 ) [ ] 4

5 Van der Waals repulsion: The Lifshitz Theory Hamaker constant can be negative i.e. repulsion for ε 1 <ε 3 <ε 2 or ε 1 >ε 3 >ε 2 Analogy with gravity, ρ 1 <ρ 3 <ρ 2 Typical Hamaker constants 5

6 Superfluidic helium in CaF2 container Contact Angle Surface Forces in simple liquids Surface Tension Contact Angle cosϑ γ SV γ SL γ LV θ 6

7 Energetics of surface wetting Wetting coefficient Ξ = γ SV γ SL γ LV liquid γsl γlv vapor γsv solid Surface wetted by liquid if Ξ <0 Disjoining Pressure of Liquids For Liquids between two surfaces Definition introduced by Derjaguin: Π(D) = E D Change of free energy per surface with surface separation in a liquid 7

8 Surface Forces in simple liquids Structural Surface Forces mica/ethanol/mica Structural Surface Forces Confinement -induced ordering Periodicity similar to molecular dimensions Complex dynamics viscosity relaxation Strongest for spherical molecules plastic crystals 8

9 Surface Forces in simple liquids Forces in aqueous solutions Abundance of water Hydrogen bonding capability Permanent dipole moment r -3 Ionic complex formation Importance in biologic interactions Amphiphilic structures (e.g. membrane) hydrophilic balance Hydrophobic Effect Structured water around hydrophobic molecules (entropy of water) Hydrophobic Interaction Hydrophobic attraction 9

10 Depletion Interaction Surface Forces in simple liquids PEG in water concentration dependent temperature dependent Depletion free energy for small separations W(D 0) ρr kt 10

11 Surface Forces In the presence of ions permanent surface charge strong electrostatic forces counter-ion cloud thermal agitation complex formation in water Effect of counter-ions 11

12 a) differential ion solubility b) surface group dissociation c) ion substitution d) adsorption of ionic groups e) anisotropic crystals (mica) Important: ph-dependence (isoelectric point) Sources of Surface Charge Double-layer model Boltzmann distribution ρ = ρ 0 e zeψ kt Poisson equation d 2 ψ zeρ = εε 0 dx 2 12

13 The Poisson-Boltzmann equation d 2 ψ = zeρ = zeρ 0 dx 2 e zeψ kt εε 0 εε 0 general solution: parameter K: <=> ψ = kt log cos 2 Kx ze e zeψ 1 kt = cos 2 Kx K 2 = ( ze)2 ρ 0 2εε 0 kt ( ) solution for low surface potentials ψ = ψ 0 e κx Double-layer structure Debye screening length 1 κ = εε 0 kt e i 2 ρ i z i 2 13

14 Static Surface Forces Double Layer & Van der Waals The DLVO Theory Derjaguin-Landau Verwey-Overbeek (DLVO) secondary minimum clays, slurries ceramic colloids 14

15 Measurement of DLVO forces exponential longrange decay short range hydration forces Israelachvili, 1983 Structure and Complexity simple liquids complex fluids ionic solutions polymer polymer-bearing monolayers steric and entropic forces bilayers teathered groups 15

16 Polymer-bearing surfaces Forces at complex surfaces mushroom-regime brush-regime Rg RF Steric energy (mushroom) D R W(D) 36kTΓe g Radius of gyration: R g = l n 6 16

17 Steric force (brush) P(D) kt s 3 2L D 9 4 D 2L 3 4 Forces at complex surfaces Membrane fluctuations Biological surface interactions undulation peristaltic 17

18 The undulation repulsion Disjoining pressure: P(D) = 3π 2 ( kt ) 2 64κ b D 3 The peristaltic repulsion Disjoining pressure: P(D) 2 kt ( )2 π 2 κ t D 5 18

19 The specific interaction streptavidin-biotin thethered direct force measurement The specific interaction electrostatic repulsion strong specific attraction steric repulsion strong adhesion lipid pullout membrane seizure 19

20 The specific interaction strong specific fast at full tether extension Summary Forces in Nature Coulomb forces van der Waals forces Lifshitz continuum theory structural forces ionic double-layer forces forces at complex surfaces 20

21 Exercises 2) Plot the Lennard-Jones pair-potential and the resulting pair- force in a graph. At what separation, r, is the equilibrium distance (F=0)? Below which separation does the repulsive term start to dominate? 3) To directly measure Lennard-Jones-type forces between macroscopic bodies, does one need the entire bodies to be present? What is the critical exponent, n, in a potential of type w(r)=-a/r n, below which the total energy of interaction starts to depend on the entire body? 4) Compare the Keesom energy to kt. Up to what distance are dipolar typically molecules oriented? The dipole moment of water is µ=1.854d (Debye), where 1D= *10-30 Cm, the relative permittivity of water is ε=78.54 and the permittivity of vacuum is ε 0 =8.854*10 12 As/Vm, the Boltzmann constant is k=1.38*10-23 J/K. 5) The DLVO theory is known to fail at high salt concentrations and/or small distances. What could be the reason(s) for this, and, in which sense do you expect the real forces to deviate from the theory? 6) Using Archimedes law, show that two bodies of mass m 1 =V 1 *ρ 1 and m 2 =V 2 *ρ 2 are experiencing a repulsive gravitational force if immersed in a medium of density ρ 3 when either one of the conditions ρ 1 <ρ 3 <ρ 2 or ρ 2 <ρ 3 <ρ 1 applies.? Question! What objects are shown in the background? What are their properties? 21

22 Answer Multi-walled carbon nano tubes (CNT) high tensile strength el. conductive 1nm-10nm diameter -> use in Advanced Fibers Dynamic Surface Forces When the rate matters 22

23 Static versus Dynamic? Friction is a dynamic surface force! The difference between static and dynamic friction is important (e.g. rail ways) 2001: Jana L. Heuberger (7) What is the molecular origin for the difference between static and dynamic surface forces? Is friction velocity-dependent? Why? Everything experiencing a force, is flowing... a structure stands a structure flows lifetime Log(time scale) 23

24 length scale The experimental window system of interest experimental window (limited) time scale Non-equilibrium systems Relationship between potential and force F(r) = w(r) r potential suggests quasi-equilibrium time-dependence often not explicit forces represent more elegant description ALL INTERACTIONS CAUSE NON-EQUILIBRIUM 24

25 Length and time scales on surfaces Surface Length- and Time-Scales acoustic radiowaves microwave IR visible light energyfrequency [ev] [Hz] time [sec] years 1 year 1 day nuclear reactions confinement surface forces SFA stretch chemical reactions corrosion SPM esfa rotations conformation evolution microscopy XPS nuclei atoms molecules cells life forms 1nm/s 1µm/s 1mm/s 1m/s 1Km/s speed of light length [m] Degrees of freedom Translation Rotation Stretch Twist storage of thermal energy 0.5. kt equipartition principle (in equilibrium) 25

26 Non-equilibrium in the kitchen microwave oven water at equilibrium microwaves (1GHz) excite rotation collisions distribute energy no melting of ice (ω res ~10KHz) cup of water hν equilibrium rotation 3. impact Mechanical Oscillator spring, k mass, m x(t) = x 0 sin(ωt) ω = k m F = mx & = kx describes one degree of freedom equation of motion harmonic oscillator general solution resonance frequency 26

27 Damped oscillator spring, k damping, η mass, m F = mx & = kx ηx& x(t) = x 0 e λt mλ 2 +ηλ + k = 0 λ 1,2 = η 2m ± η 2 4m 2 k m Damped oscillator spring, k mass, m damping, η low damping solution F = mx & = kx ηx& δ rel = η mk < 2 η x(t) = x 0 e 2m t cos( k m η2 4m 2 t) 27

28 spring, k mass, m Damped oscillator with harmonic drive damping, η amplitude external drive phase shift The Deborah number Definition: De i = τ i τ ext = ω ext ω i Dynamically dissipated energy (adhesion hysteresis, friction force...) close to thermodynamic equilibrium T far from thermodynamic equilibrium v, ω, L, Mw, confinement T, temperature v, velocity ω, frequency M w, molecular weight Deborah number, log(de) confinement 28

29 Time-Temperature Superposition P is the probability that a molecular transition takes place τ is the elapsed time Assumption: τ. P must reach a certain (constant) value T-T Superposition Activation barrier (Boltzmann) ln(τp) =Γ= ΔE act kt ΔE act kt P = e + ln(τ ) ln(τ ) =Γ+ ΔE act kt ln(τ ) = ΔE act kt 2 T 29

30 Time-Confinement Superposition Probability of transition depends on free volume V ΔE act kt P = e = e C V Assumption ΔE act kt = C V Time-Confinement Superposition ΔE act kt P = e = e C V ln(τp) =Γ= C V + ln(τ) ln(τ) =Γ+C V ln(τ) = C' ( 1 V ) 30

31 Example 1 Adhesion pull-off force contact area Poly-n-(Buthyl Methacrylate) H H H backbone C C (PnBMA) Dynamics of a polymer surface O H H H H C C C H O C C C H H H H H side chain H 31

32 Adhesion hysteresis 100 C Contact Diameter [micrometer] c t D 20 i amete r [ µm] PMMA T=2 1 C PBMA T=15 C PBMA T=25 C JKR Force [N] JKR Pull-off force JKR model: F pull off = 3πRγ eq 32

33 Energy dissipation effective surface energy: F separation = 3πRγ eff rate dependence τ-t superposition confinement not well-defined The Deborah number Definition: De i = τ i τ ext = ω ext ω i Dynamically dissipated energy (adhesion hysteresis, friction force...) close to thermodynamic equilibrium T far from thermodynamic equilibrium v, ω, L, Mw, confinement T, temperature v, velocity ω, frequency M w, molecular weight Deborah number, log(de) confinement 33

34 Example 2 Friction friction force, F sliding velocity, v Dissipated energy per unit time = F. v Molecular Tribology friction coefficient µ boundary lubrication boundary lubrication transition region transition region hydrodynamic lubrication hydrodynamic lubrication Sommerfeld number Sommerfeld ( number ( viscosity ( * viscosity * speed * / speed / load / ) load )) 34

35 Interfacial excitation v < ω > 2π < λ > excitation frequency, sliding velocity external load (confinement) temperature not well-defined Energy dissipation friction coefficient: dissipation peak below Tg log(velocity) <-> log(de) 35

36 . Superkinetic sliding The superkinetic state of sliding? Superkinetic sliding close to thermodynamic equilibrium 'super kinetic' regime dissipated energy, kinetic friction v s << v m v p = 0 T m v m, L m v s >> v m v s - v m v p = 0 v p >> v m De << 1 De = 1 De >> 1 36

37 . Controlled superkinetic sliding via sub-nanometer out-of-plane oscillations 4 3 f = 929 Hz, A = 8.9 nm f = 5 KHz, A = 8.9 nm piezo off µ3 = 0.62 friction force springs, k F piezo amplitude, A sliding mechanism piezo ~ A = κ + ²L k L load measuring springs, k L dilatency κ surfaces 2 1 kinetic friction F [mn] µ 0 = 0.48 µ 2 = 0.16 µ 1 < L c load, L [mn] load modulation, ²L ultra-low friction controlled friction dynamic regimes frequency dependence history effects Molecular Tribology Intermittent Friction (stick-slip) molecular oredeing time effects Examples: squeaky door Violine 37

38 Macroscopic Stick-Slip Poly-n-(Buthyl Methacrylate) H H H backbone C C (PnBMA) Dynamics of a polymer surface O H H H H C C C H O C C C H H H H H side chain H 38

39 Friction measurement F s F k time static friction F s friction force [arb. units] 0 'slip' 'stick' below T g kinetic friction F k above T g in-plane cycle N Shear-induced transition 50 L=13.1mN static friction F s error: friction force [mn] kinetic friction F k driver velocity [nm/s] v c 2 39

40 Temperature dependence around Tg kinetic friction Fk [mn] C L=5.2mN v=67nm/sec 25 C 2 35 C 20 C sliding cycle N C sliding cycle N temperature [ C] The role of sub-tg relaxations Friction <- side chains (Sub-Tg relaxations) Reduction <- backbone orientation δ δ δ β δ K. Shimuzu et al., Journal of Polymer Science, Vol. 13, (1975). 40

41 Measuring Surface Forces Direct force measurement contact geometry and contact mechanics different continuum models available The role of the contact geometry F : external load F : external load R : radius of the spheres R : radius of the spheres a : radius of contact area a : radius of contact area K : elastic modulus K : elastic modulus τ : normal deformation ζ : displacement / deformation elastic elastic R1 R2 a F F 3 a = R1 R = * R2 R1 + R2 F R K limit Ri -> ES -> HERTZ 3 τ = elastic rigid F 2 R K 2 R a F F K = ν ν2 2 E1 E2 3 ( + ) F : external load F : external load a : contact radius R : radius of the spheres E : Young's modulus a : radius of contact area ν : Poisson's ratio K : elastic modulus σ : normal deformation ζ : displacement / deformation F F = 1 2 (1 - ν 2 ) rigid spherical punch elastic SNEDDON E ( (a + R ) ) 2 2 ln ( R + a ) - a R R - a σ = 1 2 a ln R + a ( R - a ) 41

42 The JKR theory L pull off = 3πRγ adhesive continuum model pull-off force contact area a 3 = R L + 6πRγ + 12πRγL + 6πRγ K ( )2 4 K = 3 1 ν ν 2 2 E 1 E 2 R = R 1 R 2 R 1 + R 2 The AFM spherical tip on flat surface tip shape not well-defined spring constant not well-defined lateral scanning -> images rather high speed of operation 42

43 The AFM Contact modes: Constant force mode Constant height mode Lateral force mode The AFM Non-contact modes: Constant amplitude mode Constant phase mode 43

44 The AFM Tapping mode on a gold surface AFM Calibration grid 44

45 The SFA The Surface Forces Apparatus principle The SFA setup F = k x (D-M) D k M 45

46 The SFA optics Interferometric surface distance measurement 46

47 The electric field (1) (3) (2) (4) Flash-Back every interaction causes non-equilibrium length- and time scales important dissipative processes (damped oscillator, Deborah number) adhesion hysteresis molecular tribology (superkinetic friction) measurement (indirect, AFM, SFA) 47