Interfacial forces and friction on the nanometer scale:

A tutorial

M. Ruths

Department of ChemistryUniversity 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 (in all systems, but short range)

• Electrostatic double-layer (depends on ionic strength)

• Oscillatory (structural) (layering between surfaces) y ( ) ( y g )

• Steric−entropic (polymer steric forces)

• Capillary (from surface tension)• Capillary (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/r6

Dipole–dipole

Dipole–induced dipoleDipole induced dipole

Induced dipole–induced dipole (fluctuation, dispersion, London)

• Interaction energy between bodies (surfaces):- Longer-ranged and depends on geometry1 (∝ 1/D2 for two flats,

1/D for two spheres,…)- Bulk dielectric properties can be used.2

F = AH × f (R D) where F is the force and AH is the Hamaker constantF AH × f (R,D), where F is the force and AH is the Hamaker constant

AH = const. × f (ε ) + other const. × f (n)

van der Waals interactions (2)

Symmetric system (common):

n1, ε1 n2, ε2 n1, ε1

- always attractive

Asymmetric system:Asymmetric system:

i if ( )

n1, ε1 n2, ε2 n3, ε3

- attractive if n1, n3 > n2 (or < n2)=> attractive in vacuum, air, N2

- repulsive if n1 > n2 > n3

How to modify/control interactions:

• Match n ε of the separating mediumMatch n, ε of the separating medium to those of the interacting surfaces.

• Keep surfaces separated (somehow):- Surfactant layer

Silicon nitride/diiodomethane/silica3

n = 2.05 1.74 1.46ε = 7.5 5.3 3.9

Al i / l h /PTFE4 Surfactant layer- Double-layer forces- Polymer steric forces

α-Alumina/cyclohexane/PTFE4

n = 1.7 1.43 1.35ε = 9.0 2.0 2.0

(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)

Ch d f i t ( )• 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 theory5

At large distances (weak overlap), the double-layer force p) ydecays exponentially with a characteristic decay length(“Debye length”) that dependsonly on the solution properties!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.formed at separations 10 molecular diameters.

• Appear in the regime of boundary lubrication.

Ordered str ct re can gi e rise to• Ordered structure 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• Modify surface (to rms roughness > ⅓ molecular diameter6)

• Use irregularly shaped molecules(branched bent) to prevent “solidification”(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

A KCl l tiAqueous 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:interactions:

• Chain mobility:- Mw- T- Tg- 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:End-grafted polymer “brush”7

Polymer at surfaces:Homopolymer

tailloop

train

H t dif / t l i t ti

Repulsion (strongly stretched chains)Steric repulsion, bridging, depletion

P l di it How to modify/control interactions:

• End-grafted vs. adsorbed system• Grafting density, grafting-to/-from• M

Polydispersity:Mw/Mn > 2 in most commercial polymers.

Already at Mw/Mn = 1.05, there are manychains twice as long as the most common • Mw

• “Solvent quality” (chemical structureand temperature)

chains twice as long as the most commonchain!

Polymer-mediated forces (in solution) (3)

a) Brush (good solvent): • No hysteresis• No interpenetration and entanglement• Elastic energy vs osmotic pressure8-12

b) Adsorbed homopolymer (good solvent):• Hysteresis• Strong rate- and time-dependence• Bridging at low coverageElastic energy vs. osmotic pressure 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 tipand 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!present –check length scales and expected magnitudes!

• In a controlled environment, some forces can be modified or eliminated,but this is not always easy.y y

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 3899 (1997)3. A. Meurk, P. F. Luckham, L. Bergström, Langmuir 13, 3896-3899 (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 1948Elsevier, 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 1075 (1980)9. P. G. de Gennes, Macromolecules 13, 1069-1075 (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 6213. 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 nanorheologyof molecularly thin films In Springer Handbook of Nanotechnology 2nd ed ; B Bhushan (Ed )of molecularly thin films. In Springer Handbook of Nanotechnology, 2nd ed.; B. Bhushan (Ed.), Springer-Verlag, Berlin, Germany (2007). Ch. 30, pp 859–924.