Nano-Structuring and Phase Behavior of Confined Liquids

Transcription

1 Nano-Structuring and Phase ehaior of Confined Liquids NanoScience I Spring 2003 Contents Substrate non-interactie Simple Liquids Hexadecane, OMCTS - Entropic Structuring (Interfacial oundary layer) - oundary-layer effects on lubrication - Discussion in terms of a thermodynamic stress actiation parameter Substrate interactie Polymeric Lubricants Hydroxyl-terminated Perfluoropolyether - Interfacially Modified Monolayer System - 2D Glass Transition s. ulk - Rheologically Controlled Reaction Dynamics 1

2 Scanning Force Microscopy (SFM) Photodiode Laser Topography Piezo Friction Cantileer 100 µm 50 µm A µm Glass Transition µm 0 µm 0 µm 50 µm 100 µm Material Distinction 0 µm 0 µm µm µm Elasticity T g = 374K SFM SPM Enironment Enironmental chamber and heating /cooling stage for scanning probe microscope. 2

3 SFM Modes of Operation Friction Force Measurements x F L Scan Hysteresis ; Liquid Medium SFM Tip k L Lateral Force: F L = k L * x 0 F L x Piezo Scanner/ Solid Interface F static F dynamic Feedback x scan directions Shear Modulation Approach Spectroscopy 7085 Normal Force Response # 04 4., 4:3/,7 #0 20 Probing Distance (D) linearly ramped z-piezo x-modulation input Velocity () D # 04 4., 4:3/,7 #0 20 Lubrication: Friction s. Velocity 1. Linear Relationship: Hydrodynamic Regime of Lubrication homogeneous liquid phase and D Film >> D Molecule F η D F = c f A η D F = 6πR 2 η D Reynolds Relationship Hydrodyn. friction depends on the bulk iscosity, η, the sliding elocity,, and the film thickness, D. Planar Slider (Couette flow) A area c f friction factor (c f =1 for parallel plates) Sphere-Plane (Couette flow) R radius 3

4 Cont.: Lubrication: Friction s. Velocity 2. Ultrathin Compressed Film Regime: SFA Experiments homogeneous liquid but D Film ~ D Molecule F = 6πR 2 η eff D η eff effectie iscosity Confinement and load generally increase the effectie iscosity and relaxation times e.g., Hexadecane (Israelachili): η eff ~10 6 η bulk Interestingly, the coefficient of friction is still low, i.e., ~ Types of friction: (a) Polymers (Mw>1000), branched alkanes show low shear stresses, and smooth frictional sliding. (b) Linear alkanes or spherical molecules (OMCTS) show higher shear stresses as polymers and branched alkanes. => quantized stick-slip sliding Cont.: Lubrication: Friction s. Velocity Critical Velocity: Stick-Slip ehaior homogeneous liquid but D Film ~D Molecule not to be confused with molecular stick slip J. Israelachili (SFA) Liquid film alternately freezes and melts during shear below a critical elocity, critical. --> Phase Transition Model ( critical F static F kin. ) 5K spring τ o or τ o characteristic nucleation time hexadecane: τ o ~5s, crit ~0.4 µm/s H. Yoshizawa, J. Phys. Chem. 97 (1993) 4128 J. Israelachili, in Handbook of Micro/Nano Tribology, ed.. ushan, CRC Press (1995), p. 267 J. N. Israelachili, Intermolecular and Surface Forces (Academic Press, London, 1992) 4

5 Cont.: Lubrication: Friction s. Velocity Critical Velocity: Stick-Slip ehaior Microscopic transport mechanisms are goerned by couplings between atoms or molecules, intra- and intermolecular degrees of freedom, and external forces. Associated with couplings is a spectrum of characteristic times, t: intrinsic (t i ): structural relaxation time, or frequency ν=1/ t i energy distribution and dissipation times extrinsic (t e ): operational dependent times (i.e., rate of the applied external forces) The relationship between the two relaxation times, the Deborah number, De = t i /t e = ν e / ν i, is critical for many processes. Landman and Luedtke: MD simulation (0.1nm perturbation) Gao et al., J. Phys. Chem. 102 (1998) 5033 De=0.75 high friction (stick slip) De=7.5 low friction (superkinetic sliding) Molecular Stick-Slip on Free Surfaces Molecular Stick-Slip Model SFM/AFM on bilayer Lipid Film F ae =24 nn F ae =32 nn Tomlinson Model R. M. Oerney et al., Phys. Re. Lett. 72, 3546 (1994) obsered single molecular jump occurrences below 100 nm/s, and stochastic multiple jump occurrences aboe 800 nm/s 5

6 Generic Rate Dependences of Sliding Friction I. Dry Sliding Contact II. Lubricated Sliding Contact I.I Rough Surfaces F F low load high load I.2 Single Asperities F ln() intermediate Gnecco, Meyer, PRL 84, 1172 (2000) 2.I Smooth Large Shear Planes F 2.2 Single Asperities F F F ln() riscoe, Eans Proc. R. Lond. A 380, 389 (1982) F ln He, Oerney, PRL in press (2002) () Logarithmic Friction - Velocity Dependence (measured by SFM) Common to SFM experiments is that a discontinuous sliding process causes a logarithmic friction-elocity relationship. riscoe and Eans suggested, based on Eyring s cage model of a liquid at rest, treating shear motion responses with a thermodynamic actiation model that inoles: an actiation energy E (barrier height), and a an Arrhenius representation of the elocity (T).C. riscoe et al., Proc. R. Lond. A (1982) H. Eyring J. Chem. Phys. 3, 107 (1035) 6

7 Logarithmic Friction-Velocity Relationship cont. % 072,.9 ;,9 434/ Eyring considered the following actiation: H. Eyring, J. Chem. Phys. 3, 107 (1935) E = Q + P where E is the total energy, Q is potential barrier height, P is the pressure acting on the olume of the junction, Ω, and τ is the shear strength acting on the stress actiation olume, φ. Arrhenius Law: E / kt = νλ = oe o charact. elocity ν, λ process frequency and jump distance where is the sliding elocity, 0 is the characteristic elocity related to the frequency of the process and the jump distance, k is the otzmann constant and T the absolute temperature. k T τ = ln φ o + 1 φ Ω ( Q + PΩ) τφ. J. riscoe and D. C.. Eans, Proc. R. Lond. A 380, 389 (1982) τφ Q τφ > 1 k T PΩ Logarithmic Friction-Velocity Relationship cont. %$ 4.9, ,8 4,30,3/ 0,/0., ; $.434 /0,107 Å 74: 3088 Load: 100 nn Temp.: 21 o C Silicon wafer x scan directions Logarithmic friction elocity relationship F() = F o + αln([µm/s]); M. He, A. Szuchmacher, G. Oerney, R.M. Oerney, Phys. Re. Lett. in press (2002) The linear fitting constants, F o and α are lubricant specific. 7

8 Thermodynamic Actiation Model cont. 30, ;8%02507,9:70#0, ,80/ / 3,2.,.9 ;,9 4324/0 τ = τ ' o βt ' 1 k τ o ( Q + PΩ); β ln φ φ τ F A o τ: shear stress : sliding elocity T: absolute temperature P: pressure : sliding elocity φ: stress actiation olume Q: potential barrier height Ω: olume of the junction 0 : characteristic elocity k : oltzmann constant F: friction force A: contact area Hexadecane and OMCS show qualitatiely the thermodyn. predicted linear friction-elocity relationship ,3/' %02507,9:70#0, Pa. s* Viscosity s. Temperature OMCTS n-hexadecane Temperature (K) m 2 /s* Kinematic Viscosity s. Temperature OMCTS n-hexadecane Temperature (K) M. He, A. Szuchmacher, G. Oerney, R.M. Oerney, Phys. Re. Lett. in press (2002) T.E. Daubert, R.P. Danner, Physical and Thermodyn. Properties of Pure Chemicals : Data Compilation, Hemisphere Pub. Corp., New York (1989) Opposite absolute relationship between OMCTS and n-hexadecane in friction(t) and iscosity(t) plots. 8

9 $ 0,74/:,9 43$5574,. 0,8: Principle Water no boundary layer OMCTS monolayer" n-c 16 H 34 ~ 3 layers OMCS measurements are in agreement with x- ray reflectiity results (S. Sinha): X - ray study: H. Kim et al., in Dynamics in Small Confining Systems V, edited by J.M. Drake et al., (Mat. Res. Soc. Symp. Proc. 2001) Vol 651, p T2.1 Logarithmic Friction-Velocity Relationship cont. % 072,.9 ;,9 434/ F() = F o + αln([µm/s]) k T 1 τ = ln + P φ o φ φ = A kt α ( Q + Ω) n-hexadecane shows a higher shear coordination than OMCTS 9

10 $:22,7 n-hexadecane forms a higher coordinated entropically cooled boundary layer than OMCTS. Reason: Highly anisotropic linear chain molecules. Interfacial liquid structuring was found to reduce friction. Introduced a thermal actiation analysis of nanoscale lubrication, which proide a quantitatie measure for the degree of molecular coordination within the fluid phase close to a solid surface. Mobility in molecularly thin perfluoroether (PFPE) lubricants Fractal bonding kinetics and transitions in the fractal time dependence Nanorheological response unexpected high thermal transition 2D glass-like state (entropic cooling) onding kinetics s. nanorheological response 10

11 Thermal Actiation Processes in Lubrication Nanoasperity Contacts (continuous s. discontinuous motion) Temperature influenced shear strength (friction) indicator for a thermally actiated process Shear behaior of simple liquids (hexadecane, OMCTS) Liquid structuring due to loss in entropy Interfacial confinement and temporal effects Spreading in ultrathin films: Eolution of spreading profile: t 1/2 diffusie transport (reduced mobility) PFPE-OH: X. Ma et al., Phys. Re. E, 59, 722 (1999) Long-time decays in disordered materials (glasses) lack homogenization (implicit assumption in the kinetic scheme of a wellstirred chemical reactor) Reiew: E. lumen et al. Models for Reaction Dynamics in Glasses in "Optical Spectroscopy of Glasses", Ed. I. Zschokke (Reidel Publishing Co., 1986) 11

12 ackground: Zdol Material (molecularly thin): Hydroxyl-terminated perfluoropolyether (PFPE-OH) film: (HO-CH 2 CF 2 O-[CF 2 O] p -[CF 2 CF 2 O] q -CF 2 CH 2 -OH) Tradename: Fomblin Zdol Substrate: Amorphous carbon with surface carbon-oxygen functionalities Interaction: Hydroxylated chain ends form hydrogen bonds with carbon surface. Restriction for bonding: PFPE backbone flexibility. The molecular mobility can be determined two-fold: kinetic measurements (indirect method) rheological measurements (direct method) Representatie Kinetic Data PFPE-OH: 10.7 ±0.5 Å film M n = 2530, polydispersity (M w /M n ) of ~ 1.2, monomer unit ratio (p/q) of 0.87 (stiff backbone) (perfluoromethylene oxide - CF 2 O- and perfluoroethylene oxide -CF 2 CF 2 O-) Fit: k(t) = k t -α, α = 0.5 for T = 50 o C, and α = 1.0 for T = 90 o C. onded Fraction T = 90 o C k(t) α = k o t1-1.0 k(t) = k o t -α k(t) = k o t Time (min) T = 50 o C α =

13 Reaction/onding Kinetics Diffusion controlled or limited Process Classical (steady state, 3D) Second order rate equation n n A = = 4πn An (DA D t t + k = 4 π (D A + )b )b k rate constant (time independent) b critical capture radius for reaction A + -> A n number density D Diffusion constant D Non-Classical (Transient,1D) P.G. de Gennes J. Chem. Phys. 76, 3316 (1982) dn dt A = k (n k time-dependent rate coeff. A k(t) = k o t 1 2 ; k o = 4πDb n ) Smoluchowski M. V., Z. Phys. Chem. 92, 129 (1917) Reaction/onding Kinetics Actiation arrier controlled or limited Process Classical (steady state, 3D) Second order rate equation n n A = = 4πn An (DA D t t + k = 4 π (D A + )b )b k rate constant (time independent) b critical capture radius for reaction A + -> A n number density D Diffusion constant D Non-Classical (Transient,1D) P.G. de Gennes J. Chem. Phys. 76, 3316 (1982) dn dt k(t) A = k (n = k t 1 o ; k time-dependent rate coeff. A k n o ) = 4πDb Smoluchowski M. V., Z. Phys. Chem. 92, 129 (1917) 13

14 Temperature Dependence of the Reaction Coefficient k(t) PFPE-OH film: 10.5 ±0.5 Å M n =2530,, M w /M n ~ 1.2, p/q =0.87 Diffusion-limited reaction in the low temperature regime, T < 57 o C Onset of changes in the bonding kinetics at T > (52 ± 7) o C Actiation barrier-limited reaction in the high temperature regime, T>90 o C k k(t) = k o t -α k(t) α = 0.5 k k(t) = k t -1.0 t -0.5 α = Temperature, C Temperature induced Transition Measurements with SM-SFM Shear Response x L Cantileer Tip Sample Shear Displacement x mod 0 x L Heating/Cooling Stage T g Oerney, R. M.; ueniaje, C.; Luginbuhl, R.; Dinelli, F. Journal of Thermal Analysis and Calorimetry 2000, 59,

15 Nanorheological Response PFPE-OH film: 10.5 ±0.5 Å M n =2530,, M w /M n ~ 1.2, p/q =0.87 Local rheological properties measured by Shear-Modulated Scanning Force Microscopy (SM-SFM) (1-14 khz, 2-4 nm mod. amplitude, 10 nn load) The response amplitude is sensitie to changes in the shear modulus and contact stiffness. The phase shift is sensitie to energy dissipation. Transition temperature T = 52 o C (bulk polymer T g = -115 o C) Amplitude, a.u Phase shift, degrees "glass-like" "liquid-like" Temperature, C Temperature, C Rheological s. Kinetic Response T < 52 o C : Diffusion-limited reaction is explained with a glass-like state of the PFPE-OH film (i.e., chain mobility limited by hole propagation). T > 52 o C : The deliery of the hydroxyl moiety to the surface is no longer limited to hole diffusion, due to enhanced segmental mobility (i.e, backbone flexibility). (glass-like to liquid-like transition) k k(t) = k o t -α α k(t) = k k(t) k t -1.0 t -0.5 α = 1 Phase shift, degrees T = 87 o C T = 52 o C "glass-like" "liquid-like" Temperature, C Temperature, C 15

16 Entropic Cooling Shift in the glass transition attributed to interfacial confinement, affecting the PFPE backbone flexibility The entropic cooling effect (assuming a completelywetting low free energy liquid and a high free energy surface) can be expressed in form of a thickness, h, dependent film entropy, S: * A = 12π(D + h) S 2 1 T A* effectie Hamaker constant T Temperature D cutoff constant The asymmetric nature of the confinement (normal to the surface) will preferentially "freeze" the out-of-plane torsional motions in the energetically confined PFPE backbones. Perfluoropolyether (Zdol) Monolayer Lubricant Anisotropy in Entropy T g h[nm] => Anisotropy in the Film Entropy manifested in T g (h) 16

17 INITIAL ONDING RATE CONSTANT k b ackbone Composition Effect onding Kinetics Zdol 4000/CHx at 64ºC k(t) ~ t -0.5 k(t) ~ t ºC C1:C2 RATIO Waltman, et al., Trib Lett. 1999, 7, 91 Increase C1/C2 ratio increases chain flexibility Increased bonding rate constant obsered with increased C1/C2 ratios Abrupt increase seen at C1/C2 between k(t) X -(CF 2 O) y (CF 2 CF 2 O) z CF 2 - X = k t o α α = 0.5 diffusion α = 1.0 conection Summary Nanorheology is driing the bonding kinetics ackbone flexibility Transition temperature shifted from bulk. Discontinuous rate behaior Properties and bonding kinetics of Zdol effected by: substrate confinement molecular affinity chain flexibility temperature Confinement is primarily determined by Configurational entropy Interfacial interactions 17

18 Attachment : Oscillatory Solation Forces Local confinement and normal stresses generate discrete ordering in een such simple liquids as OMCTS. SFA squeezing experiments reeal oscillatory solation forces 1 1 J. N. Israelachili, Intermolecular and Surface Forces, Academic Press, London,