Adhesion

지영식 , 이정규 , 이준성

Work of Adhesion and Cohesion

Work of Adhesion: the free energy change, or reversible work done, to separate unit areas of two media 1 and 2 from contact to infinity in vacuum (W12).

1

2

1 unit area

1

2

W12

Work of Adhesion

If 1=2, work of cohesion (W11). Always positive~!!

Surface Energy

Surface Energy: the free energy change when the surface area of a medium is increased by unit area, .

1 unit area

W11

Work of Cohesion (W11)

1

1

1

1

1/2W11 = 1 = s

1/2 UA

1/2W11

1

1 1

1/2W11 = 1 = L

Solid Liquid

Unit: mJ/m2 Unit: mJ/m2 = mN/m (Surface tension)

Surface Energy

Substances such as metals with higher boiling point usually have high surface energies.

Mercury: TB = 357 ℃, = 485 mJ·m-2

Water: TB = 100 ℃, = 73 mJ·m-2

Hydrogen: TB = -253 ℃, = 2.3 mJ·m-2

by strong intermolecular or interatomic attraction

s and L are lowered in a foreign vapor, such as laboratory air, by some absorption of vapor molecule (SV, LV).Mica

in vacuum: = 4500 mJ·m-2

in humid air: = 300 mJ·m-2

Interfacial Energy

Interfacial Energy: the free energy change in expanding their ‘interfacial’ area by unit area when two immiscible liquids 1 and 2 are in contact (12).

1/2 unit area

1

122

1

1

2

1

1

22

-W121/2W11+1/2W22

1

22

1

2

11/2W11+1/2W22 -W12

½ UA

Solid-Liquid

Liquid-Liquid∴ 12=1/2W11+1/2W22-W12 = 1 + 2 -W12

12

=1/2W121

=1/2W212

Interfacial Energy

Liquid 1Surface Energy

Interfacial Energy

W12

With water at

20℃ (2=73)

Cyclohexanol 32 4 101

Diethyl Ether 17 11 79

Benzene 29 35 67

n-Octane 21.8 51 43.8

1-Octene 21.8 - -

Octadecane 28 52 49

Octadecene - 19 -High affinity substances have low interfacial energy and large work of adhesion.

Interfacial Energy

W12 = √(W11d

·W22d)= 2√(1

d·2d)

12 = 1 + 2 - 2√(1d·2

d)

If only dispersion forces are responsible for the interaction between media 1 and 2,

1d : the dispersion force contributions to the surface tensions

Octane-Water

wd = 20, o

d = 21.8 mN·m-1

Theoretically wo = 52.8 mN·m-1

Measuredwo = 50.8 mN·m-1

Work of Adhesion in a Third Medium

unit area

1

2

3

1

2

33

W12+W331

332

-W13-W23

W132 = W12+W33-W13-W23

= (1/2W11+1/2W33-W13)+(1/2W22+1/2W33-W23)-(1/2W11+1/2W22-W12)

= 13 + 23- 12

Positive or Negative~!!

Surface Energy of Transfer

1

2 3

1

2 3

Unit Surface Area

W = 13 – 12

W = W12-1/2W22 + 1/2W33 - W13

= (1/2W11+1/2W33-W13) – (1/2W11+1/2W22-W12) = 13 – 12

Surface Energy of Small Clusters

The concept of surface or interfacial energy remains valid, even for isolated molecules.

-: the pair energy molecular contact

= 1/2

energy gain from molecular contact

effective surface area

Plat Surface

g=1.7/2 (11.33)

Isolated Molecule

g=12/2[4(/2)2]=1.9/2

Small cluster A

g=12×7/2[4(3/2)2]= 1.5/2

A

Very similar~?? ... !!

Surface Energy of Small Clusters

This conclusion is strictly true only for molecules whose pair potentials are additive and where long-range forces and many-body effects are not important.

Success – van der Waals substances

Fail - metal, ionic and H-bonding compounds

Metal – High MP, surface energies and conductivities depend onthe cooperative properties.

Au MP: bulk – 1336 K, 4nm – 1000 K, 2.5nm – 500 K

Water – clusters with 20 molecules: liquid state at 200 K

Example

15.3 Contact Angles and Wetting Films

What is Contact Angle?

3

1

2

θ is Contact angle

Young’s equation defines contact angle by balancing the different interfacial energy terms

The surface energy change of a solid(1)-liquid(2)-vapour(3) system is

With the assumption of no gravity and the constraint of constant droplet volume,

the equilibrium condition is

f1312c23 )( dAdAdW

132312 cos0 dW

1. Even without assumptions on gravity and problem geometry, the equation was found to be valid.

2. The contact angle is independent of the surface geometry.

It is more exact to say that the contact angle is determined by the balance of surface stresses rather than by the minimization of surface free energies.

,cos0f

c

dVdA

dA

SEM picture of a drop of cooled glass on Fernico metal. × 130

For example, for water on SAMs on Gold surface

1. Octanethiol on Au

S SSSS

Au

1 = 21.8, 2 = 73 → 12 = 51 mJ/m2 with water at 20℃

Calculated : Contact Angle 115°Observed : Contact Angle = 109° at 22℃

2. Undecenethiol on Au

For example, for water on SAMs on Gold surface

S S S S S

Au

Expected : Contact Angle ℃Observed : Contact Angle = 103 at 22℃

Ichimura, K.; Oh, S.-K.; Nakagawa, M. Science 2000, 288, 1624.

Dynamic Surfaces:Light-Driven Motion of Liquids

(365 nm)

(436 nm)

-N=

N-

15.4 Hysteresis in contact angle and adhesion measurements

Contact angle hysteresis : advancing contact angle θA > receding contact angle θR

Hysteresis in the adhesion energy of two phases

(a) Surface roughness mechanical equilibrium

(b) Chemical heterogeneity chemical equilibrium

(c) Molecular rearrangement thermal equilibrium

(d) Surface deformation and interdigitation thermodynamically irreversible dissipation of energy occurs

Drop of water on an alkylketene dimer surface: (a) fractal surface D=2.29; (b) flat surface

r : length of rulerσ : area of rulerN : number of segmentsD : fractal dimension

2)(

)(D

D

CN

rCrN

(a) Equilibrium configuration of liquid droplet on another liquid.

(b) Non-equilibrium (but stable) configuration of liquid droplet on a solid surface.

(c) Microscopic and molecular-scale deformations that can occur to relax the unresolved vertical component of the interfacial tension.

These stress relaxation effects usually act to reduce the final contact angles θ' and θ'' below θ.

All the previously described effects (due to the absence of mechanical, chemical, thermal equilibrium) can lead to hysteresis and aging effects of contact angles and adhesion energies. In general,

But these differences also depend on dynamic factors.

ARAR WW

15.5 Adhesion force between solid particles

The adhesion force of two rigid (incompressible) macroscopic spheres is simply related to their work of adhesion by the Derjaguin approximation (Eq. (10.18)).

For identical solid materials, W121 = 2γ12. For the following special cases:

F = 2πRγSL (two identical spheres in liquid)

F = 4πRγSV (sphere on flat surface in vapor)

13221

2112

21

21 2)(2)( WRR

RRFDW

RR

RRDF

Theories that count the elasticity of solid particles in;

– Hertz theory : calculates elastic deformation due to external pressure internal stress.

– JKR theory : elastic deformation + surface tension (interaction between solid elements implicitly included via surface tension = surface energy)

Hertz theory :

Where E = Young modulus

ν = Poisson ratio

σ = uniaxial stress

21

21

2

021

021

21210

)(4

3

)(4

3

3

3

RR

RRFkk

FRR

RRkka

xy

zz

z

y

z

xzz A

FE

E

vk

,,,

1 2

JKR theory :

2

2/1

122

2/3

02

2121212

1

1

2

31

2

3)(

3

21

)3(633

xa

KWx

R

KaxP

a

a

R

a

RWFRWRWFK

Ra

forceexternalwithout,)(3

4,, 0

2121

21 aakk

Ka

rx

RR

RRR

For a sphere of radius R on a flat surface of the same material, R=R1 and W12 = 2γ12.

a remains real positive for F > -3πRγSV = -(3/2)πRW12

For F < -3πRγSV, (energy in deformed shape > undeformed) abrupt separation occurs

Maximum adhesion force FMax = -3πRγSV (JKR approximation)

-4πRγSV (Derjaguin approximation for rigid particles)

The contact between two elastic solids both in the presence (contact radius a1) and absence (contact radius a0) of surface forces.

(a) shows the contact between two convex bodies of radii R1 and R2 under a normal load of P0;δ is the elastic displacement.

(b) indicates the distribution of stress in the contacting spherical surfaces.When surfaces are maintained in contact over an enlarged area by surface forces, the stresses between the surfaces are tensile (T) at the edge of the contact and only remain compressive (P) in the center.Distribution A is the Hertz stress with a=a1 and P=P1;distribution B the JKR stress with a=a1 and P=P0 anddistribution C the Hertz stress with a=a0 and P=P0.

(c) represents the load-displacement relation for the contacting surfaces.

– JKR theory is a continuum theory and implicitly assumes that the attractive forces between the two surfaces act over an infinitesimally small range. It predicts an infinite stress at the edge of the contact circle(x=1).

In the limit of small deformations, the adhesion force becomes Fs = -4πRγSV (DMT approximation – VdW force assumed) -3πRγSV (JKR approximation)

– Apart from its breakdown within the last few nanometers of the bifurcation boundary, most of the equations of the JKR theory and all the equations of Hertz theory have been found to apply extremely well for molecularly smooth surfaces.

For example, Fs = -3πRγ has been found to be correct within about 25% for a variety of surfaces in vapors or liquids and to be independent of the elastic modulus and contact area of the contacting curved surfaces

– Asperities as small as 1-2nm can significantly lower the actual adhesion forces from the predicted values. A serious practical limitation to the Hertz and JKR theory

– Just as in the case of a liquid droplet advancing or receding on a surface, a growing (advancing) and contracting (receding) contact area between two solid surfaces can also have different values for W or γ.

– The notion that even the simplest adhesion process may not always be reversible, but involves energy dissipation, has profound effects for understanding many adhesion phenomena and also provides a link between adhesion and friction.

15.6 Effect of capillary condensation on adhesion

– The mechanical and adhesive properties of many substances are very sensitive to the presence of even trace amounts of vapors in the atmosphere. (by solid-gas surface energy change or capillary condensation)

– Liquids that wet or have a small contact angle on surfaces will spontaneously condense from vapor into cracks and pores as bulk liquid. capillary condensation

The Kelvin equation :

where rk is the Kelvin radius, V is the molar volume of liquid, psat is the saturation vapor pressure for planar liquid-vapor interface.

)/ln( sat21

21

ppRT

Vr

rr

rrk

At initial equilibrium, μ(l) = μ(g) and P(l) = p(g) = p*

And from consideration of Gibbs free energy, N·dμ = V·dp,

dμ(l) = Vmolar(l)·dp(l) and dμ(g) = Vmolar(g)·dp(g)

From ideal gas law Vm(g) = RT / p(g),

Applying dP on liquid,

Integrating both sides,

)()(

)( gdpgp

RTgd

)()(

)()()( m gdpgp

RTgddPlVld

PlVp

pRT

gp

gdpRTdPlV

p

p

Pp

p

)(*

ln)(

)()( m*

*

*

m

RT

PlV

p

p )(exp

*m

The effect of a liquid condensate on the adhesion force between a macroscopic sphere and a surface

< Laplace pressure method >

cos2)90sin(2

2

11

11

1

2

11

rrd

rRdPxF

rxrP

90-

cos4 RF

Additional liquid surface tension contribution F 2πxγ is negligible except for θ 90°

Consider how the total surface free energy of the system Wtot changes with separation D.

And,

From the constraint of constant liquid volume,

Maximum attraction occurs at D = 0, where

< Surface free energy method >

)smallfor(constant)cos()(2

termssmallersurfaces)other romconstant(f)()sin(2

L2

SVSL2

tot

R

RW

dD

dR

dD

dWF

cos4 L2tot

4/4/2/

)cos2()cos1)(3/(

sin)sin()()sin(

4322434322

232222

0

22

RDRRRDR

RdRDR

RdRdDRV

theorem)Chordby2

,small(for2 R

d

)/1(

cos4

)/2(

1

02

L

33222

dD

RF

DRdD

d

dD

dR

dD

dDRR

dD

dV

cos4 Lmax RF

Adding the direct solid-solid contact adhesion force inside the liquid annulus,

– Since γS > γSV the adhesion force should always be less in a vapor than in vacuum. Anyway, the adhesion force in air may increase with relative humidityif γSV1(moist air) > γSV2(dry air).

– Often γLcosθ greatly exceeds γSL, whence the adhesion force is determined solely by the surface energy of the liquid.

– F = 4πRγLcosθ holds good for saturated vapors as well as for low relative pressure (~0.2) vapors corresponding to meniscus radii of only ~ 0.5 nm(about the size of molecule), except for water(r1 > 2 nm needed).

– Since real particle surfaces are often rough, their adhesion in vapor is not always given by the equation above.

– Capillary condensation also occurs in solvents containing water, and it can lead to a dramatic increase in the adhesion of hydrophilic colloidal particles. trace amount of water can have a dramatic effect on colloidal stability used in industrial separation and extraction process

– If the contact angle exceeds 90°, a vapor cavity should ‘capillary condense’ between the two surfaces, again resulting in an adhesive force.

SVSLL 4)cos(4 RRF )cos( 132312

Summary

– Definition of surface energy. Surface energy = surface tension

– Work of adhesion, interfacial energy (between hydrocarbons and water)

– Surface energies of small clusters

– Contact angles and wetting films

– Contact angle hysteresis. Origins of hysteresis in contact angle and adhesion energies

– Adhesion force between solid particles :Derjaguin approximationHertz theoryJKR theory

– Effect of capillary condensation on adhesion between solid particlesCapillary condensationThe Kelvin equationThe Young-Laplace equationLaplace pressure methodSurface free energy method