FRICTION OF POLYMER GELS O. Ronsin, T. Baumberger, C. Caroli Institut des NanoSciences de Paris - CNRS - Univ. Paris 6 Gels = soft elastic solid with high content of fluid = poroelastic solid ñ specific frictionnal properties ­ e.g. : gels in biological systems : very low friction (e.g. articular cartilage) ­ Network / solvent contributions to friction ? POROELASTIC EFFECTS : ARTICULAR CARTILAGE (COLLAGEN GEL) Poroelastic transfer of fluid across cartilage Ñ load supported by fluid at short times low friction : fluid lubrication Ñ increasing contribution of matrix as t Õ higher friction : solid friction Wfluid = 1 ¡ (1 ¡ ) µ µ8 φ µ Wtotal ¶ C. W. McCutchen, Wear 5, 1 (1959). G. A. Ateshian, Journal of Biomechanics 42, 1163 (2009). POLYMER GELS = + Æ ­ network chains cross-links (physical or chemical), distance ξ ­ solvent (90–99%), viscosity η η ñ "poro-elastic" material ­ elasticity of entropic origin (rubber) kBT 2 5 ξ G 10 – 10 Pa, ξ 3 – 30 nm. ξ3 ­ solvent/network relative motion ñ diffusive mode ¡ 9 ¡11 2 ¡1 Dcoll. 10 – 10 m .s for aqueous gels (10¡7m2.s¡1 for cartilage) 5 7 ñ 10 ¡ ¡10 s for 1 cm thick sample ñ get rid of time dependence of fluid loaded part. HYDRODYNAMIC FRICTION OF GELATIN GELS Model system : gelatin gel on clean flat glass in plane/plane contact. + Ñ control almost independently solvent viscosity ηS 1 ¡ 4 Pa.s (water glycerol) and network mesh size ξ 6 ¡ 12 nm (gelatin contentration c) gel glass impose ­ sliding velocity V (1 – 2000 µm/s) ­ normal pressure p (0 – 2 kPa) measure ­ stationnary frictionnal shear stress σ(V ). ­ interfacial slip. HYDRODYNAMIC FRICTION OF GELATIN GELS Changing solvent viscosity ηS Changing gelatin concentration 2.5 0% c Õñ G Õñ ξ × 6 21% 2 42% 5% 5 8% 10% 1.5 15% 4 (kPa) 1 3 (kPa) 2 0.5 1 0 0 500 1000 1500 2000 0 V ( m/s) 0 500 1000 1500 2000 V ( m/s) V ñ Response of a confined layer ξ of thickness ξ ? T. Baumberger, C. Caroli and O. Ronsin, Eur. Phys. J. E 11, 85 (2003). HYDRODYNAMIC FRICTION OF GELATIN GELS V layer sheared at a rate γ˙ = V /ξ σξ measured effective visosity ηeff = V ξ relaxation time τR of a chain of size ξ (Rouse) 100 ηeff ¡α = γτ˙ R , α 0.6 compatible ηs with macroscopic¡ ¢ rheology of solutions. s / 10 eff 1 0.01 0.1. 1 10 R HYDRODYNAMIC FRICTION OF GELATIN GELS V layer sheared at a rate γ˙ = V /ξ σξ measured effective visosity ηeff = V ξ relaxation time τR of a chain of size ξ (Rouse) 100 ηeff ¡α = γτ˙ R , α 0.6 compatible ηs with macroscopic¡ ¢ rheology of solutions. Also observed with block copolymer gels s / 10 eff 1 0.01 0.1. 1 10 R K.A. Erk et al., Langmuir, 28, 4472 (2012). EFFECT OF NORMAL STRESS 1.4 1.2 p V 1 0.8 V (kPa) 0.6 σ (1+ε)ξ 0.4 0.2 0 -4 -3 -2 -1 0 1 2 -po p (kPa) = p p = ¡ deformation under compression ǫ ¡ E 3G + ñ layer thickness (1 ǫ)ξ = = p ñ σ(V, p) σ(V, p 0) 1 + (1 + 3α) h 3G i 3G p0 = G 1 + 3α STATIC FRICTION 1.2 1 1 0.8 max 0.8 0.6 0.6 (kPa) (kPa) 0.4 0.4 0.2 0.2 tw 0 0 0 2 4 6 8 10 12 14 16 0 5 10 15 20 65 70 75 80 t (s) t (s) Increase of the number of pinned chains with time. ñ Decrease of the number of pinned chains with velocity. ELASTIC CONTRIBUTION TO GEL FRICTION Schallamach model of rubber friction : dynamics of chain pinning/depinning V thermally activated depinning + advection at velocity V f ñ number of pinned chains × with V F ñ force per chain Õ with V N < µm/s ln V A. Schallamach, Wear, vol. 6, p. 375 (1963) POLYMER GELS FRICTION two contributions: σ ­ chain pinning ­ viscosity of interfacial layer V POLYMER GELS FRICTION two contributions: σ ­ chain pinning ­ viscosity of interfacial layer ñ instability at Vc (compliant system imposed stress) Vc V 0.7 1.2 V > V V < V 0.6 c 1 c 0.5 0.8 0.4 0.6 0.3 0.4 0.2 shear stress (kPa) shear stress (kPa) 0.1 0.2 0 0 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 time (s) time (s) SLEF-HEALING SLIP PULSES IN GELATIN self-healing slip pulses. Healing when local slip velocity reaches Vc . 100 80 60 40 position (mm) 20 0 52 56 60 64 68 time (s ) O. Ronsin, T. Baumberger and C.Y. Hui, J. Adhesion, vol. 87, p. 504 (2011) SLEF-HEALING SLIP PULSES IN GELATIN nucleation favored at the edge(s) of the contact, but also within the contact. 100 80 60 40 position (mm) 20 0 100 80 60 40 position (mm) 20 0 52 56 60 64 68 time (s) CONCLUSION biphasic nature of gels ñ 2 contributions to friction ­ elastic : (rate-dependent) stretching of adsorbed polymer chains ­ hydrodynamic : viscous flow of fluid interfacial layer relative contributions influenced by many parameters (velocity, pressure, charges, surface chemistry, roughness...) ­ Tuning these parameters to achieve very low friction Ñ artificial cartilage : need for tougher gels ñ double network gels (J.P. Gong et al.). ­ their competition can lead to instabilities ñ model system for earth crust (F. Corbi et al., J.G.R. Solid Earth, vol. 118, p. 1483 (2013))..