Interfacial forces and friction on the nanometer scale: A tutorial M. Ruths Department of Chemistry University of Massachusetts Lowell Presented at the Nanotribology Tutorial/Panel Session, STLE/ASME International Joint Tribology conference, October 20-22, 2008, Miami, Florida, USA.
Expected interaction forces? Many different ones, resulting in a total force van der Waals Electrostatic double-layer (in all systems, but short range) (depends on ionic strength) Oscillatory y( (structural) (layering between surfaces) Steric entropic Capillary (polymer steric forces) (from surface tension)
van der Waals interactions (1) Important for self-assembly, adhesion, colloidal (in)stability Present in all systems, but short-ranged. Molecular interaction energy 1/r 6 Dipole dipole Dipole induced induced dipole Induced dipole induced dipole (fluctuation, dispersion, London) Interaction energy between bodies (surfaces): - Longer-ranged and depends on geometry 1 ( 1/D 2 for two flats, 1/D for two spheres, ) -Bulk dielectric properties can be used. 2 F = A H f (R,D), where F is the force and A H is the Hamaker constant A H = const. f (ε ) + other const. f (n)
van der Waals interactions (2) Symmetric system (common): n 1, ε 1 n 2, ε 2 n 1, ε 1 - always attractive Asymmetric system: n 1, ε 1 n 2, ε 2 n 3, ε 3 How to modify/control interactions: - attractive if n 1, n 3 > n 2 (or < n 2 ) => attractive in vacuum, air, N 2 - repulsive if n 1 > n 2 > n 3 Match n, ε of the separating medium Silicon nitride/diiodomethane/silica 3 n = 2.05 1.74 1.46 to those of the interacting surfaces. ε = 7.5 5.3 3.9 Keep surfaces separated (somehow): - Surfactant layer α-alumina/cyclohexane/ptfe i / l h /PTFE n = 1.7 1.43 1.35 - Double-layer forces ε = 9.0 2.0 2.0 - Polymer steric forces
(Electrostatic) Double-layer forces (1) Important for stability of colloidal suspensions, and in biological systems Typically seen in aqueous systems, can be very long range (microns) Charged surfaces in water (very common): - Dissociation of ions from surfaces - Adsorption of ions from solution + + + + + + Electrostatic double layer: Charged surface + counter-ions in solution Double-layer forces: Osmotic origin (Entropy!!!)
(Electrostatic) Double-layer forces (2) Double-layer repulsion + van der Waals attraction => DLVO theory 5 At large distances (weak overlap), the double-layer force decays exponentially with a characteristic decay length ( Debye length ) that depends only on the solution properties! How to modify/control interactions: Change surface charge or potential Change ion valency or concentration in the solution
Oscillatory forces (structural forces) (1) Alternating repulsion and attraction with increasing confinement of semi-ordered layers formed at separations < 10 molecular diameters. Appear in the regime of boundary lubrication. Ordered structure re can give rise to stick-slip friction avoid this by making systems more fluid-like, i.e., disordered. How to modify/control interactions: Modify surface (to rms roughness > ⅓ molecular diameter 6 ) Use irregularly shaped molecules (branched, bent) to prevent solidification Keep surfaces separated (somehow)
Oscillatory forces (solvation forces) (2) Superposed on (a) attractive or (b) repulsive forces (vdw and double-layer forces) Easily smeared out by surface roughness or poor ordering of the molecules Last layer can withstand high pressures => boundary lubricating layer Aqueous KCl solution
Polymer-mediated forces (without solvent) (1) Complicated rearrangement of chains at the interface between polymer surfaces Entanglement gives strongly time- and rate-dependent adhesion and friction How to modify interactions: Chain mobility: - M w - T g - film thickness
Polymer-mediated forces (in solution) (2) Polymer interactions in solvent: Balance between contraction and expansion: i.e., vdw interactions (and H-bonding) between segments and entropy of mixing. Polymer at surfaces: Homopolymer End-grafted polymer brush 7 loop tail train Steric repulsion, bridging, depletion Repulsion (strongly stretched chains) Polydispersity: it How to modify/control interactions: ti M w /M n > 2 in most commercial polymers. End-grafted vs. adsorbed system Already at M w /M n = 1.05, there are many Grafting density, grafting-to/-from chains twice as long as the most common M w chain! Solvent quality (chemical structure and temperature)
Polymer-mediated forces (in solution) (3) a) Brush (good solvent): No hysteresis No interpenetration and entanglement Elastic energy vs. osmotic pressure 8-12 b) Adsorbed homopolymer (good solvent): Hysteresis Strong rate- and time-dependence Bridging at low coverage
Capillary forces Strong, attractive force due to liquid meniscus, longer range than vdw. Commonly seen in humid air and in other vapors. Also seen for adsorbed layers of molecules with high mobility, and in binary liquid systems. Example: Comparison with vdw for AFM tip and sample wetted by water: 13 How to modify/control interactions: Remove vapor (drying) Increase surface energy Add fluid (immerse system). Keep surfaces separated - patterning
Summary In most systems, more than one type of interaction force might be present check length scales and expected magnitudes! In a controlled environment, some forces can be modified or eliminated, but this is not always easy.
References 1. H. C. Hamaker, Physica 4, 1058-1072 (1937). 2. E. M. Lifshitz, Sov. Phys. JETP (English translation) 2, 73-83 (1956), I. E. Dzyaloshinskii, E. M. Lifshitz, L. P. Pitaevskii, Adv. Phys. 10, 165-209 (1961). 3. A. Meurk, P. F. Luckham, L. Bergström, Langmuir 13, 3896-38993899 (1997). 4. S.-w. Lee, W. M. Sigmund, J. Colloid Interface Sci. 243, 365-369 (2001). 5. B. Derjaguin, L. Landau, Acta Physichochim. URSS 14, 633-662 (1941). E. J. W. Verwey, J. T. G. Overbeek, Theory of the stability of lyophobic colloids,1st ed., Elsevier, Amsterdam, 1948. 6. L. J. D. Frink, F. van Swol, J. Chem. Phys. 108, 5588-5598 (1998). 7. P. G. de Gennes, Adv. Colloid Interface Sci. 27, 189-209 (1987). 8. S. Alexander, J. Phys. (Paris) 38, 983-987 (1977) 9. P. G. de Gennes, Macromolecules 13, 1069-10751075 (1980). 10. S. T. Milner, T. A. Witten, M. E. Cates, Macromolecules 21, 2610-2619 (1988). 11. S. T. Milner, T. A. Witten, M. E. Cates, Macromolecules 22, 853-861 (1989). 12. E. B. Zhulina, O. V. Borisov, V. A. Priamitsyn, J. Colloid Interface Sci. 137, 495-511 (1990). 13. Reprinted figure with permission, from T. Stifter, O. Marti, B. Bhushan, Phys. Rev. B 62, 13667-13673 (2000). Copyright 2000 by the American Physical Society. Black-and-white graphs from M. Ruths and J. N. Israelachvili, Surface forces and nanorheology of molecularly thin films. In Springer Handbook of Nanotechnology, 2nd ed.; B. Bhushan (Ed.), Springer-Verlag, Berlin, Germany (2007). Ch. 30, pp 859 924.