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!! Importance of Particle AdhesionImportance of Particle Adhesion!! History of Particle AdhesionHistory of Particle Adhesion!! Method of measurement of AdhesionMethod of measurement of Adhesion!! Adhesion Induced DeformationAdhesion Induced Deformation!! JKR and nonJKR and non--JKR TheoryJKR Theory!! Role of Electrostatic ForcesRole of Electrostatic Forces!! ConclusionsConclusions

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Books:

D. S. Rimai and D. J. Quesnel, Fundamentals of Particle Adhesion, Global Press (available through the Adhesion Society at adhesion society.org) (2001).

D. J. Quesnel, D. S. Rimai, and L. H. Sharpe, Particle Adhesion: Applications and Advances, Taylor and Francis (2001)

D. S. Rimai and L. H. Sharpe, Advances in Particle Adhesion, Gordon and Breach Publishers (1996).

D. S. Rimai, L. P. DeMejo, and K. L. Mittal, Fundamentals of Adhesion and Interfaces, VSP Press (1995).

K. L. Mittal, Particles on Surfaces: Detection, Adhesion, and Removal, 1, 2 and 3, Plenum Press (1986), (1988), (1990), (1995).

A. Zimon, Adhesion of Dust and Powders, Consultants Bureau (1976).

T. B. Jones, Electromechanics of Particles, Cambridge University Press (1995).

J. Israelachvili, Intermolecular and Surface Forces, Academic Press (1992).

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ArticlesH. Krupp, Advan. Colloid Interface Sci. 1, 111 (1967).

K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London, Ser A 324, 301 (1971).

D. S. Rimai and L. P. DeMejo, Annu. Rev. Mater. Sci.26, 21 (1996).

D. S. Rimai and A. A. Busnaina, Particulate Science and Technology 13, 249 (1995).

B. Gady, D. Schleef, R. Reifenberger, D. S. Rimai, and L. P. DeMejo, Phys. Rev. B 53, 8065 (1996).

N. S. Goel and P. R. Spencer, Polym. Sci. Technol. 9B, 763 (1975).

D. Maugis and H. M. Pollock, Acta Metall. 32, 1323 (1984).

L. N. Rogers and J. Reed, J. Phys. D 17, 677 (1984).

K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc. London Ser. A 324, 301 (1971).

B. V. Derjaguin, V. M. Muller, and Yu. P. Toporov, J. Colloid Interface Sci. 53, 314 (1975).

D. Tabor, J. Colloid Interface Sci. 58, 2 (1977).

V. M. Muller, V. S. Yushchenko, and B. V. Derjaguin, J. Colloid Interface Sci. 77, 91 (1980).

D. J. Quesnel, D. S. Rimai, and L. P. DeMejo, J. Adhesion 51, 49 (1995).

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Articles

Soltani, M. and Ahmadi, G., On Particle Adhesion and Removal Mechanisms in Turbulent Flows, J. Adhesion Science Technology, J. Adhesion Science Technology Vol. 7, 763-785 (1994).

Soltani, M. and Ahmadi, G., On Particle Removal Mechanisms Under Base Acceleration, J. Adhesion Vol. 44, 161-175 (1994).

Soltani, M., Ahmadi, G., Bayer, R.G. and Gaynes, M.A., Particle Detachment Mechanisms from Rough Surfaces Under Base Acceleration, J. Adhesion Science Technology Vol. 9, 453-473 (1995).

Soltani, M. and Ahmadi, G., Direct Numerical Simulation of Particle Entrainment in Turbulent Channel Flow, Physics Fluid A Vol. 7 647-657(1995).

Soltani, M. and Ahmadi, G., Particle Detachment from Rough Surfaces in Turbulent Flows, J. Adhesion Vol. 51, 87-103 (1995).

Soltani, M. and Ahmadi, G., Detachment of Rough Particles with Electrostatic Attraction From Surfaces in Turbulent Flows, J. Adhesion Sci. Technol., Vol. 13, pp. 325-355 (1999).

Soltani, M., Ahmadi, G. and Hart, S. C., Electrostatic Effects on Resuspension of Rigid-Link Fibers in Turbulent Flows, Colloids Surfaces, Vol. 165, pp. 189-208 (2000).

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Technologically importantTechnologically importantA. Semiconductor fabricationA. Semiconductor fabrication

B. ElectrophotographyB. Electrophotography

C. PharmaceuticalsC. Pharmaceuticals

D. PaintD. Paint

E. AgricultureE. Agriculture

F. Aeronautics and spaceF. Aeronautics and space

G. Etc.G. Etc.

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Fundamentally ImportantFundamentally Important

A. Avoids confounding interactions A. Avoids confounding interactions (gravity, applied loads, etc.)(gravity, applied loads, etc.)

B. Allows thermodynamic parameters such B. Allows thermodynamic parameters such as work of adhesion to be determined.as work of adhesion to be determined.

C. Allows present understanding of C. Allows present understanding of adhesion to be tested.adhesion to be tested.

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Particles are attracted to substrates (or Particles are attracted to substrates (or other other particles) via certain types of particles) via certain types of interactions. These interactions. These interactions create interactions create stresses between the stresses between the materials. These materials. These stresses, in turn, create strains stresses, in turn, create strains that may that may be be large or small, elastic or plastic.large or small, elastic or plastic.

Only by understanding both the Only by understanding both the interactions interactions and theand the mechanical mechanical response of the response of the materials to these materials to these interactions can adhesion interactions can adhesion be understood.be understood.

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This presentation will focus on particle This presentation will focus on particle adhesion. However, just as the JKR adhesion. However, just as the JKR theory describes adhesion between theory describes adhesion between macroscopic bodies, the concepts macroscopic bodies, the concepts presented presented can be readily generalized to other can be readily generalized to other situations.situations.

The JKR model is the underlying theory on The JKR model is the underlying theory on which most of our present understanding of which most of our present understanding of adhesion is based. adhesion is based.

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Hertz (circa 1890): Proposed that a rigid indenter, Hertz (circa 1890): Proposed that a rigid indenter, acting under a compressive load P, would cause a acting under a compressive load P, would cause a deformation of radius deformation of radius aa in a substrate having a in a substrate having a YoungYoung’’s modulus s modulus EE and a Poisson ratio and a Poisson ratio νν given by given by

1930s: 1930s: DerjaguinDerjaguin and Bradley independently and Bradley independently proposed proposed the concept of adhesionthe concept of adhesion--induced induced deformations between deformations between particles and substrates. particles and substrates. DerjaguinDerjaguin assumed that the assumed that the adhesionadhesion--induced contact radius can be calculated induced contact radius can be calculated from from HertzianHertzian theory.theory.

( )E4

RP13a2

3 ν−=

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1937: Hamaker proposes that surface forces 1937: Hamaker proposes that surface forces were related to the density of atoms in the were related to the density of atoms in the particle and substrate, particle and substrate, nnPP and and nnSS, respectively. , respectively. Hamaker further proposed that the interaction Hamaker further proposed that the interaction parameter parameter AA (commonly referred to as the (commonly referred to as the Hamaker constant) was related to London Hamaker constant) was related to London dispersion forces bydispersion forces by

The load The load PP is then given byis then given by

λπ SP2 nnA =

206 z

RAP =

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By combining this result with the By combining this result with the HertzianHertzianindenter model, one sees that the indenter model, one sees that the DerjaguinDerjaguinmodel relates the contact radius to the model relates the contact radius to the particle radius byparticle radius by

( ) 220

23

81 R

zAa ν−

=

4

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1956: 1956: LifshitzLifshitz proposes a model relating the London proposes a model relating the London dispersion forces (i.e. the major component of van dispersion forces (i.e. the major component of van derderWaals interactions in most systems) to the generation Waals interactions in most systems) to the generation of electromagnetic waves caused by instantaneous of electromagnetic waves caused by instantaneous dipole fluctuations. Surface forces are shown to have dipole fluctuations. Surface forces are shown to have an effective range, rather than being contact forces.an effective range, rather than being contact forces.

1967: 1967: KruppKrupp proposes adhesionproposes adhesion--induced plastic induced plastic deformations. He proposed that the adhesiondeformations. He proposed that the adhesion--induced stresses between a particle and a substrate induced stresses between a particle and a substrate could exceed the yield strength of at least one of the could exceed the yield strength of at least one of the contacting materials.contacting materials.

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Circa 1969: David Tabor approaches Ken Circa 1969: David Tabor approaches Ken Johnson about a rather perplexing student Johnson about a rather perplexing student Tabor has that does not seem to believe Hertz.Tabor has that does not seem to believe Hertz.

1971: The JKR (Johnson, Kendall, and Roberts) 1971: The JKR (Johnson, Kendall, and Roberts) theory of adhesion is published. This theory theory of adhesion is published. This theory recognized that both tensile and compressive recognized that both tensile and compressive interactions contribute to the total contact interactions contribute to the total contact radius. JKR model is derived using contact radius. JKR model is derived using contact mechanics. It assumes that there are no longmechanics. It assumes that there are no long--range interactions.range interactions.

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1975: 1975: DerjaguinDerjaguin, Muller, and , Muller, and ToporovToporovgeneralize the original generalize the original DerjaguinDerjaguin model of model of adhesion to include tensile interactions. This is adhesion to include tensile interactions. This is the DMT theory. the DMT theory.

1977: Tabor highlights differences in 1977: Tabor highlights differences in assumptions and predictions between JKR and assumptions and predictions between JKR and DMT theories. Also shows that, as long as the DMT theories. Also shows that, as long as the meniscus height is large compared to the range meniscus height is large compared to the range of surface forces, the JKR assumption of no of surface forces, the JKR assumption of no longlong--range interactions is valid.range interactions is valid.

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1980: Muller, 1980: Muller, YushchenkoYushchenko, and , and DerjaguinDerjaguin(MYD) propose a general model that purports (MYD) propose a general model that purports that both the JKR and DMT theories are subsets that both the JKR and DMT theories are subsets of the MYD model. They further divide the of the MYD model. They further divide the universe between small particle, high modulus, universe between small particle, high modulus, low surface energy systems (DMT) and larger low surface energy systems (DMT) and larger particle, lower modulus, higher surface energy particle, lower modulus, higher surface energy (JKR systems). (JKR systems).

1984: 1984: MaugisMaugis and Pollock generalize the JKR and Pollock generalize the JKR theory to include adhesiontheory to include adhesion--induced plastic induced plastic

deformations.deformations.

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1. Centrifugation1. Centrifugation

A. Better on large (R>20 A. Better on large (R>20 µµm)m)

B. SlowB. Slow

C. Well established techniqueC. Well established technique

D. Minimal interactionsD. Minimal interactions

E. Good statisticsE. Good statistics

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2. Electrostatic Detachment2. Electrostatic Detachment

A. Medium to large particles (R>5 A. Medium to large particles (R>5 µµm)m)

B. Interaction with electric fieldB. Interaction with electric field

C. Good statisticsC. Good statistics

3. Hydrodynamic Detachment3. Hydrodynamic Detachment

A. Small particles (R<0.5 A. Small particles (R<0.5 µµm)m)

B. Good statisticsB. Good statistics

C. Introduces a fluidC. Introduces a fluid

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4. Atomic Force Techniques4. Atomic Force Techniques

A. Measures attractive as well as A. Measures attractive as well as removal forceremoval force

B. Can exert precise loads on particlesB. Can exert precise loads on particles

C. Short and variable time scalesC. Short and variable time scales

D. Can distinguish force mechanismsD. Can distinguish force mechanisms

E. Poor statisticsE. Poor statistics

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5. Contact Area Technique5. Contact Area Technique

A. Good statisticsA. Good statistics

B. Forces not directly measured.B. Forces not directly measured.

C. Equilibrium measurementC. Equilibrium measurement

D. Need spherical particlesD. Need spherical particles

E. Wide range of particle sizesE. Wide range of particle sizes

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6. 6. NanoindentorNanoindentor

A. Easy to interpret measurementsA. Easy to interpret measurements

B. Readily repeatableB. Readily repeatable

C. Simulation of particle adhesion C. Simulation of particle adhesion rather than actual rather than actual

measurement.measurement.G. AhmadiME 437/537

7. 7. IsraelachviliIsraelachvili Surface Force ApparatusSurface Force Apparatus

A. Uses crossed cylinders rather A. Uses crossed cylinders rather than particlesthan particles

B. Cylinders can be coated with B. Cylinders can be coated with materials of interestmaterials of interest

C. Simulation of particle adhesion C. Simulation of particle adhesion

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There is a total energy There is a total energy UUTT of a system, where of a system, where

wherewhere

UUEE is the elastically stored energyis the elastically stored energy

UUMM is the mechanical energy associated is the mechanical energy associated with the applied load.with the applied load.

UUSS is the total surface energy = wis the total surface energy = wAAππaa22

SMET UUUU ++=

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The JKR equation is given by:The JKR equation is given by:

( )[ ]{ }2/12AAA

3 Rw3PRw6Rw3PKRa π+π+π+=

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1.1. The deformations are elastic.The deformations are elastic.

2.2. The contact radius is small The contact radius is small compared to the particle radius.compared to the particle radius.

3.3. All interactions are localized to All interactions are localized to within the contact region, within the contact region, i.e.i.e.there are no longthere are no long--range range interactions.interactions.

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High elastic High elastic modulus spherical modulus spherical particles on particles on elastomeric elastomeric substrates.substrates.

Polystyrene on Polyurethane

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Polystyrene particles on a silicon wafer

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R0.5 (µm0.5)0 1 2

Con

ntac

t Rad

ius

(mic

rons

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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Burnham, Colton, and Pollock (Phys. Burnham, Colton, and Pollock (Phys. Rev. Rev. LettLett. 69, 144 (1992)) measured . 69, 144 (1992)) measured the attractive force between an AFM the attractive force between an AFM cantilever tip and a flat graphite cantilever tip and a flat graphite surface. They reported that the range surface. They reported that the range of attractive forces was too great to be of attractive forces was too great to be explained in terms of van explained in terms of van derder Waals Waals forces. forces.

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Horn and Smith (Nature 366, 442 (1993); Horn and Smith (Nature 366, 442 (1993); Science 256, 362 (1992); J. Electrostatics Science 256, 362 (1992); J. Electrostatics 26, 291 (1991)) reported an increase in 26, 291 (1991)) reported an increase in detachment force between two flat silica detachment force between two flat silica substrates, one of which had been coated substrates, one of which had been coated with with dimethyethoxysilanedimethyethoxysilane. The increase in . The increase in adhesion was associated with a transfer of adhesion was associated with a transfer of charge from one material to the other.charge from one material to the other.

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Dickinson (see, for example, Dickinson (see, for example, Fundamentals of Adhesion and Fundamentals of Adhesion and InterfacesInterfaces, Rimai, DeMejo, and Mittal , Rimai, DeMejo, and Mittal (eds.), pp. 179(eds.), pp. 179--204 (1995) reported the 204 (1995) reported the emission of charged particles generated emission of charged particles generated upon the fracture of a material upon the fracture of a material (fractoemissions).(fractoemissions).

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Van Van derder Waals forces are electrodynamic and are Waals forces are electrodynamic and are expected to be short range. Under certain expected to be short range. Under certain circumstances they may contribute significantly to circumstances they may contribute significantly to adhesion.adhesion.

There are longThere are long--range interactions that contribute range interactions that contribute to adhesion. These may be due to electrostatic to adhesion. These may be due to electrostatic interactions.interactions.

There is evidence that adhesion has longThere is evidence that adhesion has long--range range contributions. If this is correct, is the JKR theory, contributions. If this is correct, is the JKR theory, which is based on contact mechanics, appropriate?which is based on contact mechanics, appropriate?

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Consider a spherical toner particle of Consider a spherical toner particle of radiusradius

RR = 6 = 6 µµm and m and q/mq/m = 15 = 15 µµC/g. C/g.

⇒⇒ qq = 1.4 x 10= 1.4 x 10--1414 C.C.

⇒⇒ σσ = 3 x 10= 3 x 10--55 C/mC/m22..

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Van Der WaalsElectrostatic

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For a single, dielectric, spherical particle For a single, dielectric, spherical particle with a uniform charge distributionwith a uniform charge distribution

22

0

2

0Im 2

44

124

1⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=

RR

RqF σπ

επεπ

( )0

22222

0Im 4

41

εσπσπ

επRRF ==

FIm = 12 nNFIm = 12 nNG. AhmadiME 437/537

van van derder Waals Attraction:Waals Attraction:

FFVWVW = 625 = 625 nNnN

20

VW z6RAF =

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Define Define RRcritcrit by by FFVWVW = = FFImIm

If: If: AA = 10= 10--1919 J J zz00 = 4 = 4 ÅÅ

⇒⇒ RRcritcrit = 0.5 mm = 0.5 mm

For For RR < < RRcritcrit: van : van derder Waals dominatedWaals dominated

For For RR > > RRcritcrit: electrostatic dominated: electrostatic dominated

However: Both forces contribute to However: Both forces contribute to adhesion.adhesion.

220

0

6 σπε

zA

Rcrit =

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Schematic illustration of experimental setup. The Schematic illustration of experimental setup. The larger toner particles fix the size of the air gap larger toner particles fix the size of the air gap while the applied electric field cause the smaller while the applied electric field cause the smaller particle to transfer from the photoconductor (top) particle to transfer from the photoconductor (top) to the receiver (bottom). to the receiver (bottom).

SpacerParticle

ParticledD

Chrome cermet receiver

Photoconductor

12

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Toner Diameter (microns)0 2 4 6 8 10 12 14

Forc

e (n

N)

0

100

200

300

400

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Thus far, it would appear that the Thus far, it would appear that the JKR contact mechanics assumption JKR contact mechanics assumption is valid.is valid.

However, if electrostatic forces However, if electrostatic forces become more significant, longbecome more significant, long--range range interactions would have to be taken interactions would have to be taken into account.into account.

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220

0

6 σπε

zA

Rcrit =

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Increase the size of the particle.Increase the size of the particle. Electrostatic Electrostatic forces as forces as RR22 whereas van whereas van derder Waals forces Waals forces vary linearly with vary linearly with RR..

Increase the surfaceIncrease the surface--charge density.charge density. The The critical radius varies as 1/critical radius varies as 1/σσ22..

Decrease the surface energy/Hamaker Decrease the surface energy/Hamaker constant.constant. Examples include coating a surface Examples include coating a surface with Teflon or zinc stearate.with Teflon or zinc stearate.

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Add asperities to the particle.Add asperities to the particle. These serve as These serve as physical separations that reduce adhesion physical separations that reduce adhesion (Tabor and Fuller (Proc. R. Soc. (Tabor and Fuller (Proc. R. Soc. LondLond. A 345, . A 345, 327 (1975); Schaefer et al. J. Adhesion 327 (1975); Schaefer et al. J. Adhesion SciSci. . TechnolTechnol. 9, 1049 (1995)). 9, 1049 (1995))

Add neighboring particles having a similar Add neighboring particles having a similar charge.charge. ((GoelGoel and Spencer, in and Spencer, in Adhesion Adhesion Science and Technology Part BScience and Technology Part B, L. H. Lee , L. H. Lee (ed.)). (ed.)).

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Localize charge to specific areas on Localize charge to specific areas on surface of the particle rather than surface of the particle rather than uniformly distributing it uniformly distributing it –– the sothe so--called called ““charged patch model.charged patch model.”” (D.A. (D.A. Hays, in Hays, in Fundamentals of Adhesion Fundamentals of Adhesion and Interfacesand Interfaces, D. S. Rimai, L. P. , D. S. Rimai, L. P. DeMejo, and K. L. Mittal (eds.))DeMejo, and K. L. Mittal (eds.))

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F neigh =40 nN

Neighbor Forces Acting on ParticleNeighbor Forces Acting on Particle

F elect = σ2 Ac / 2ε0

F = 40 nN

+ ++

- - -

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Assume that the particle charge is localized to a Assume that the particle charge is localized to a discreet section of the particlediscreet section of the particle

Electrostatic contribution to attractive force Electrostatic contribution to attractive force FFEEis given byis given by

AACC is the contact areais the contact area

σσ is the charge densityis the charge density0

C2

E 2AFε

σ=

14

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Note:Note: These particles are irregularlyThese particles are irregularly--shapedshaped

No silicaNo silica:: Particle radius = 4Particle radius = 4µµmm

WWAA = 0.05 J/m= 0.05 J/m22, q/m, q/m = 37 = 37 ++ 3 3 µµC/g, C/g, ρρ = 1.2 g/cm= 1.2 g/cm33

From JKR theory:From JKR theory:

Measured value:Measured value: FFSS = 970 = 970 nNnN

nN943Rw23F AS =π=

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2% Silica2% Silica:: Assume JKR contact radius = 196 nmAssume JKR contact radius = 196 nm

rrsilicasilica = 30 nm, = 30 nm, ρρsilicasilica = 1.75 g/cm= 1.75 g/cm33..

⇒⇒have about 10 silica particles within the contact have about 10 silica particles within the contact zone.zone.

Approximate JKR removal force byApproximate JKR removal force by

Measured: FMeasured: FSS’’ = 70 = 70 nNnN

nN39rw23nF AS =π=′

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⇒⇒ FFImIm = 20 = 20 –– 40 40 nNnN

( )20

2

Im24 R

qFεπ

α=

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Patch charge density limited by dielectric Patch charge density limited by dielectric strength of air.strength of air.

⇒⇒ FFEE ≈≈ 30 30 nNnN

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If the particle has sufficient If the particle has sufficient irregularity, irregularity, van van derder Waals forces, Waals forces, electrostatic electrostatic image forces, and image forces, and chargedcharged--patch forces patch forces all predict all predict about the same size force, about the same size force, which which is comparable to experimentally is comparable to experimentally determined detachment force.determined detachment force.

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For small, spherical particles, adhesion For small, spherical particles, adhesion appears to be dominated by van appears to be dominated by van derder Waals Waals interactions.interactions.

As the particles become bigger or more As the particles become bigger or more irregular, electrostatics become more irregular, electrostatics become more important.important.

van van derder Waals interactions can be reduced, Waals interactions can be reduced, even for small, spherical particles, to the even for small, spherical particles, to the point point where electrostatic forces can become where electrostatic forces can become dominant.dominant.

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The electric charge contribution increases The electric charge contribution increases with increasing charge and the presence of with increasing charge and the presence of

neighboring particles.neighboring particles.

These results hold for macroscopic systems These results hold for macroscopic systems as well as microscopic ones.as well as microscopic ones.

Electrostatic interactions are longElectrostatic interactions are long--range.range.

JKR theory should be extended to allow for JKR theory should be extended to allow for longlong--range interactionsrange interactions

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