FRICTION OF POLYMER GELSO. Ronsin, T. Baumberger, C. CaroliInstitut des NanoSciences de Paris - CNRS - Univ. Paris 6

Gels = soft elastic solid with high content of fluid = poroelastic solidñ 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 cartilageÑ load supported by fluid at short timeslow friction : fluid lubricationÑ increasing contribution of matrix as tÕhigher friction : solid friction

µ=µ8 (1� (1�φ)WfluidWtotal

)

C. W. McCutchen, Wear 5, 1 (1959).G. A. Ateshian, Journal of Biomechanics 42, 1163 (2009).

POLYMER GELS

network = chains + cross-links Æ

(physical or chemical), distance ξ solvent (90–99%), viscosity η

ñ "poro-elastic" material

elasticity of entropic origin (rubber)G � kBT

ξ3

� 102 – 105 Pa, ξ� 3 – 30 nm. solvent/network relative motionñdiffusive modeDcoll.� 10�9 – 10�11 m2.s�1for aqueous gels (10�7m2.s�1 forcartilage)ñ 105��107 s for 1 cm thick sampleñ get rid of time dependence of fluidloaded part.

ξ

η

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)

glassgel

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

0

0.5

1

1.5

2

2.5

0 500 1000 1500 2000

0%

21%

42%

(k

Pa)

V ( m/s)

Changing gelatin concentrationcÕñGÕñ ξ×

0

1

2

3

4

5

6

5%

8%

10%

15%

0 500 1000 1500 2000

(k

Pa)

V ( m/s)

ñ Response of a confined layerof thickness � ξ ? ξ

V

T. Baumberger, C. Caroli and O. Ronsin, Eur. Phys. J. E 11, 85 (2003).

HYDRODYNAMIC FRICTION OF GELATIN GELS

layer sheared at a rate γ̇=V /ξ

measured effective visosity ηeff =σξ

Vrelaxation time τR of a chain of size ξ (Rouse) ξ

V

1

10

100

0.01 0.1 10

ef

f/

s

R

1.

ηeff

ηs

� (γ̇τR)�α, α= 0.6 compatiblewith macroscopic rheology of solutions.

HYDRODYNAMIC FRICTION OF GELATIN GELS

layer sheared at a rate γ̇=V /ξ

measured effective visosity ηeff =σξ

Vrelaxation time τR of a chain of size ξ (Rouse) ξ

V

1

10

100

0.01 0.1 10

ef

f/

s

R

1.

ηeff

ηs

� (γ̇τR)�α, α= 0.6 compatiblewith macroscopic rheology of solutions.

Also observed with block copolymer gels

K.A. Erk et al., Langmuir, 28, 4472 (2012).

EFFECT OF NORMAL STRESS

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-4 -3 -2 -1 0 1 2

σ (

kP

a)

p (kPa)-po

V(1+ε)ξ

Vp

deformation under compression ǫ=�pE

=� p3Gñ layer thickness (1+ǫ)ξñ σ(V , p)=σ(V , p = 0)[1+ (1+3α) p

3G

]

p0 =3G

1+3α

�G

STATIC FRICTION

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16

(

kP

a)

t (s)

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 65 70 75 80

(kP

a)

t (s)

tw

max

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/depinningV

thermally activated depinning+ advection at velocity Vñ number of pinned chains× withVñ force per chainÕ with V

f

N

F

ln V< µm/s

A. Schallamach, Wear, vol. 6, p. 375 (1963)

POLYMER GELS FRICTION

two contributions:

chain pinning viscosity of interfacial layerσ

V

POLYMER GELS FRICTION

two contributions:

chain pinning viscosity of interfacial layerñ instability at Vc (compliant system� imposed stress)

σ

VVc

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25 30 35 40

shea

r st

ress

(kP

a)

time (s)

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70 80

shea

r st

ress

(kP

a)

time (s)

V > Vc

V < Vc

SLEF-HEALING SLIP PULSES IN GELATIN

self-healing slip pulses. Healing when local slip velocity reaches Vc .

0

20

40

60

80

100

52 56 60 64 68

po

siti

on

(m

m)

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.

0

20

40

60

80

100

po

siti

on

(m

m)

0

20

40

60

80

100

52 56 60 64 68

po

siti

on

(m

m)

time (s)

CONCLUSION

biphasic nature of gelsñ 2 contributions to friction elastic : (rate-dependent) stretching of adsorbed polymer chains hydrodynamic : viscous flow of fluid interfacial layerrelative contributions influenced by many parameters (velocity, pressure,charges, surface chemistry, roughness...) Tuning these parameters to achieve very low frictionÑ artificial cartilage :

need for tougher gelsñ double network gels (J.P. Gong et al.). their competition can lead to instabilitiesñ model system for earth crust(F. Corbi et al., J.G.R. Solid Earth, vol. 118, p. 1483 (2013)).

Poroelastic effects : Articular cartilage (collagen gel)Polymer gelsHydrodynamic friction of gelatin gelsHydrodynamic friction of gelatin gelsHydrodynamic friction of gelatin gelsHydrodynamic friction of gelatin gelsEffect of normal stressStatic frictionElastic contribution to gel frictionPolymer gels frictionPolymer gels frictionSlef-healing slip pulses in gelatinSlef-healing slip pulses in gelatinConclusion