photo-acoustics research laboratory dynamics of microspherical adhesive particles on vibrating...

Photo-Acoustics Research Laboratory

Dynamics of Microspherical Adhesive Particles on Vibrating SubstratesÇetin Çetinkaya

Photo-Acoustics Research LaboratoryDept. of Mechanical and Aeronautical Engineering

Center for Advanced Materials ProcessingClarkson University, CAMP 241 Box 5725, Potsdam, NY 13699-5725

[email protected] (315) 268-6514 Fax: (315) 268-6695

http://clarkson.edu/mae/faculty_pages/cetinkaya.html

October 2, 2012

Seminar Abstract:

Dispersive adhesion (intermolecular Van der Waals) forces often become a dominant effect in nano- and micro-length scales as surface (e.g. electrostatic and hydrodynamic) and volume proportional (e.g. inertia) forces rapidly diminish. Decreased mechanical stiffness at these length-scales further increases the significance of adhesion. In this seminar, the focus will be on the work-of-adhesion characterization of micrometer-scale spherical particles. Following a review of the status of the theories, a non-contact characterization method will be introduced. The current method is based on the resonance frequency measurement of a spherical particle making a rocking motion on a flat surface. In the reported experiments, rocking motion is excited by a short acoustic pulse generated either by an air-coupled acoustic transducer or a contact ultrasonic transducer attached to the substrate. Elastic deformation of the particle at the contact zone and surface energy provide the required restitution force for oscillations and the angular inertia of the particle with respect to its contact point is the inertia effect. The transient response of the micro-particle is acquired with a fiber optic vibrometer, and the resonance frequency of the motion is extracted from the frequency spectrum of the acquired waveform. The resonance frequency is related to the work-of-adhesion of the particle-substrate system. The nonlinear coupling effect between modes of vibration will also be introduced. Particular applications of the presented experimental characterization approach in pharmaceutics and xerography (electrophotography) will be discussed in detail. Potential applications of the approach to biological systems and future research directions will also be discussed.

1

mailto:[email protected]

https://mymail.clarkson.edu/exchweb/bin/redir.asp?URL=http://clarkson.edu/mae/faculty_pages/cetinkaya.html










Dynamics of Microspherical Adhesive Particles on

Vibrating Substrates

Mechanical and Industrial EngineeringUniversity of Illinois at Chicago2:00-3:15, October 2, 2012

Çetin ÇetinkayaDept. of Mechanical and Aeronautical Engineering

Clarkson UniversityPotsdam, New York 13699-5725

[email protected] (315) 268-6514

NSF (Award #: 1066877)


Seminar Outline• Introduction

Length-scale argument

Toner in copying/printing and pharmaceutical particles

• Adhesion models for spherical particles on flat surfaces

1-D models: JKR, DMT, etc.

2-D model: rocking motion

• Approach: Ultrasonic base and air-coupled acoustics

• Lateral pushing experiments

• Effects of nanoparticles on toner adhesion

• Nonlinear interactions between vibrational modes

• Conclusions and remarks

3


Introduction: Why Study Particle Adhesion?

• Adhesion is a significant effect, especially at nano/micro-length scales, since body (e.g. inertia) and surface forces (e.g. charge, hydrodynamic) diminish faster than adhesion.

• Micro-scale particles are involved in a wide spectrum of industrial processes and natural phenomena: Toner, pharmaceutical particles, biological cells, etc.

• Methods to make particles with narrow distributions are today available and utilized. narrow distributions increase process and end-product predictability. Near-perfect spherical particles exhibit strong adhesion.

4


Pharmaceutical Particles

• Adhesion properties of pharmaceutical particles affect:Macroscopic/bulk mechanical/adhesion propertiesPowder transfer and handlingFlowability of powdersPowder mixing/blending uniformityGranulationCompaction

• In resulting tablets, these parameters play roles in:Compaction propertiesMechanical propertiesDissolution rates/profilesContent uniformityMass density distributionPhysical stabilityMechanical integrity

5


Toner and the Xerographic Industry

Dr. Scott M. Silence, Consumables Development and Manufacturing Group Xerox Corp., June 4, 2007

Toner is a critical material for the xerographic industry: Its design impacts, energy, cost, environment, etc.

The adhesion performance of toner plays a key role in determining the image quality of the prints and copies.

Development

SN

S N

3. Toner must develop latent image on photoreceptor

Fusing

5. Toner must melt into paper

Cleaning

6. Toner must be removed from photoreceptor

Paper

Transfer4. Toner must move from photoreceptor to paper

PhotoreceptorSubstrate

Charging

Exposure

2

1

3

4

5

6

6

Photo-Acoustics Research Laboratory 7

CouplingGel

PiezoelectricTransducer

SiO2 Substrate

Output Signal

InterferometerHead

Excitation Pulse

PSLParticle

Experiment: Micro-particles on a Vibrating Substrate


Oscillatory Dynamics of Single Particles on Surfaces

3/2

0

( , , ) 6 ( ) ( )R A

aM a W r r sin

a

Rocking (In-Plane) MotionAxial (Out-of-Plane) Motion

33/2( ) 6R A

K aF a a W K

r

θ

δe

Substrate

O′O

δe

Substrate

K. L. Johnson, K. Kendall and A.D. Roberts, Proc. R. Soc. of London. A. 324, 301 (1971).C. Dominik and A. Tielens, Philos. Mag. A 72, 783 (1995). 8

23/202

(1 ( ) )3

aa

r a


Instrumentation Diagram of Experimental Set-up

Fiber Interferometer

Vibrometer Controller

Digitizing Oscilloscope

Video Monitor

Pulser /ReceiverUnit

Laser Probe

Transducer

Computer/ Video Card

Trigger

CCD Camera

Objective Lens

Particles

Silicon Substrate

9


Adhesion Theories: Dynamics of Particles on Surface

Linearized Axial Motion (JKR)

Natural Frequency:

Linearized Rocking Motion

Natural Frequency:*

* 2

6 ( )

( )A

On

W r r

I m r

WA is the work-of-adhesion

K is the stiffness of adhesion bondr is the mass density of the particler is the radius of the particle

WA is the work-of-adhesionr is the mass density of the particle is the mass moment of inertia of the particler is the radius of the particle

Note: It is independent of the elastic properties of the particle and substrate materials.Dominik C. and Tielens A.G.G.M., Philosophical Magazine A, 72, No.3, 783-803, 1995.

For a PSL spherical particle (D = 21.4 mm) on Si substrate, the linearized axial and rocking motion resonance frequencies are calculated:

Axial Resonance Frequency: 1.98 MHz Rocking Resonance Frequency: 38.57 kHz

1.98 MHz >> 38.57 kHz

2 21/3

3 2

327( )

20 4A

n

W K r

r

2 1 0 1 2 3 4 2

1

0

1

2

n m

PN

Hertz Model

OI

10

F

δ


M. D. M. Peri and C. Cetinkaya, J.of Colloid and Interface Science, Vol. 288, 2005.M. D. M. Peri and C. Cetinkaya, Philosophical Magazine A, Vol. 85, No. 13, 2005.

50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 1000

1

2

3

4

5

6

7

8x 10

-6

Freq (kHz)

(am

plitu

de)

Multiplication Factor (4.33)-P1 75kHz 400V

Wafer

Particle

0 50 100 150 200 250 300 350 400

-6

-4

-2

0

2

4

6

Time (sec)

Dis

pla

cem

ent(

nm

)

P1 75kHz 400V

Observation: Air-Coupled Pulse of Rocking Motion

Particle Diameter (PSL on Si) 21 mm

Air-coupled excitation (central freq): 75 kHz

Rocking frequency (approximated): 72.4 kHz

Measured rocking amplitude: θmax~ 0.06 deg

Measured rocking frequency: 76.5 kHz

Measured work-of-adhesion: 26.16 mJ/m2The first non-contact experimental demonstration of the existence of rolling resistance and its characterization.

2 (1 cos )r


A

rigidrigid

W

rf

4

4512

2/3

A

neckneck

W

rf

14

4512

2/3

*2

kF k x x

r 2* / rkk

0cI k 0 5

1 5

2 16

kf

r

23 50

64

5k f r

*2

/ ( / 2) 4

( / 2)

F M D Mk

x D D

6/*kWA

Natural Frequencies and Rolling Stiffness

26 AM W r

Rolling Moment Resistance:

Lateral Pushing: Rigid Rolling:

Rocking w.r.t. the neck

Rigid Particle-Substrate


Lateral Pushing Experiments: AFM Tip Set-up

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 500 1000 1500 2000 2500 3000 3500 4000

x (nm)

F (

nN

)

56.1

44.3

50.8

26.1

25.3

31.9

33.4

36.9

D = 31.9mm PVP particle Tipless AFM cantilever probe

W. Ding, A. Howard, M. D. M. Peri, C. Cetinkaya, Philosophical Magazine, Vol. 87, Issue 36 pp. 5685 – 5696, 2007.W. Ding, H. Zhang and C. Cetinkaya, Journal of Adhesion, Vol. 84, No. 12, pp. 996-1006, 2008.I. Akseli, M. Miraskari, H. Zhang, W. Ding, and C. Cetinkaya, Non-Contact Rolling Bond Stiffness Characterization of Polyvinylpyrrolidone (PVP) Particles, Journal of Adhesion Science and Technology (Invited), 25, 4-5, 407-434, 2011

The first work in determining the critical rolling angle


• During tablet manufacturing, essential excipients associated with sticking problems are binders and lubricants. PVP’s surface adhesion characteristics affect numerous pharmaceutical unit operations such as granulation, blending, and lubrication/compaction.

• A non-toxic synthetic polymer since it is not absorbed through the gastrointestinal tract or mucous membranes.

• PVP (a typical binder) is water-soluble. It has been known for its superior ability to modify adhesion properties. Commonly used biomaterials in pharmaceutical formulations.

• Other applications: disintegrant, suspending agent, coating agent, tablet binder, and hydrophilizing biomaterial

• Particle size distribution: 20-60 µm.

Adhesion of PVP Particles


Poly(vinyl) Pyrrolidone (PVP) Microspherical Particles

20mm

Particle mean diameter: 20mm-60mm Trench width: 4mm-10mm Trench depth: 1mm

15


0 20 40 60 80 100 120 140 160 180 200-8

-6

-4

-2

0

2

4

6

Time (sec)

Dis

plac

emen

t(nm

)

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

-6

Freq (kHz)

Am

plitu

de (a

.u.)

Resonance Frequencies: PVP on Silicon, D = 26.4 mm


0 20 40 60 80 100 120 140 160 180 2000

1

2

3

4

5

6

7x 10

-7

Freq (kHz)

Am

plitu

de (a

.u.)

0 20 40 60 80 100 120 140 160 180 200-7

-6

-5

-4

-3

-2

-1

0

1

2

3

Time (sec)

Dis

plac

emen

t(nm

)

D = 55.8 mm


0 20 40 60 80 100 120 140 160 180 2000

0.5

1

1.5

2

2.5

3

3.5

4x 10

-7

Freq (kHz)

Am

plitu

de (a

.u.)

0 20 40 60 80 100 120 140 160 180 200-20

-15

-10

-5

0

5

10

15

20

Time (sec)

Dis

plac

emen

t(nm

)

D = 51.5 mm


Resonance Frequencies of the PVP-Silicon Systems

PVP Particle D = 36.3mm PVP Particle D = 34.6mm

0 20 40 60 80 100 120 140 160 180 200-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (sec)

Dis

pla

ce

me

nt(

nm

)

0 25 50 75 100 125 150 175 200 225 2500

0.3

0.6

0.9

1.2

1.5x 10

-7

Freq (kHz)

Am

plit

ud

e (

a.u

.)

Flat Substrate Trenched Substrate

3 2

1 45

4A

n

W

r

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x 10-7

Freq (kHz)

Am

plitu

de (a

.u.)

0 20 40 60 80 100 120 140 160 180-12

-10

-8

-6

-4

-2

0

2

4

6

8

Time (sec)

Dis

plac

emen

t(nm

)

19


Lateral Pushing Experiments


• Adhesion measurement based on detachment is difficult

• Particle not glued to a cantilever• Detachment force is much larger

than rolling force

21

W. Ding, A. Howard, M.D.M. Peri, C. Cetinkaya, Philosophical Magazine, Vol. 87, Issue 36 pp. 5685 – 5696, 2007.W. Ding, H. Zhang and C. Cetinkaya, Journal of Adhesion, Vol. 84, No. 12 , pp. 996-1006, 2008.

Lateral Pushing Experiments: SEM Test Set-up


0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 500 1000 1500 2000 2500 3000 3500 4000

x (nm)

F (

nN

)

56.1

44.3

50.8

26.1

25.3

31.9

33.4

36.9

Spherical PVP Particles: Lateral Pushing-Translating

Optical microscope image of the pushing of a 31.9mm PVP particle with a tipless AFM cantilever probe.

22


Spherical PVP Particles: Table 1, 2 and 3

23


Materials: Nano-particle Coated Toner

• Bare Polymer Particles: Nominal diameters of 9.0 µm and 6.0 µm

• Polymer particles with 24 nm diameter silica nanoparticle coating: Nominal diameter of 6.0 m, and surface area coverage of 10%, 50% and 100%

• Polymer particles with 110 nm diameter silica nanoparticle coating: Nominal diameter of 6.0 m, and surface area coverage of 50% and 100%

24


Nano-Particle Coated Toner (Side View): 0% SAC

Bare polymer particle with smooth surfaceCoated with ~ 15 nm of Au for SEM imaging Diameter: ~ 5.6 µmSubstrate: Silicon

25


Specified surface area coverage (SAC): 10%

Nanoparticle diameter: 15~32 nm (average: ~24 nm)

Nanoparticle material: Silica

Substrate: Silicon

Nano-Particle Coated Toner (Side View): 10% SAC

26


Specified SAC : 50%



Substrate: Silicon

Nano-Particle Coated Toner (Top View): 50%

27


Specified SAC: 50%



Substrate: Silicon

Nano-Particle Coated Toner (Side View): 50%

28


Specified SAC: 100%



Substrate: Silicon

Nano-Particle Coated Toner (Top View): 100%

29


SAC: 100%



Substrate: Silicon

Nano-Particle Coated Toner (Side View): 100%

30


Force-Displacement (10% SAC)

Coated Toner: Pushing Results for 10% SACSAC: 10%

Toner/Nanoparticle diameter: 6μm/15~32 nm (average: ~24 nm)



31


SAC: 50% and 100%

Toner/Nanoparticle diameter: 6μm/15~32 nm (average: ~24 nm)




Coated Toner: Pushing Results for 50% and 100%

32


Nominal Diameter

(m)

Coating Nanoparticle

Size(nm)

Nanoparticle Surface Area

Coverage

Number of Particles Tested

Average Diameter

(m)

Average Pre-rolling Stiffness

(N/m)

Average Work-of-Adhesion(mJ/m2)

9.0 N/A N/A 9 9.1 1.1 0.37 0.19 20 10

6.0 N/A N/A 8 6.0 0.4 0.43 0.17 23 9.1

6.0 24 10% 11 7.3 0.6 0.75 0.68 40 36

6.0 24 10% 7 7.3 0.7 0.095 0.031 5.0 1.7

6.0 24 50% 8 6.0 0.3 0.075 0.070 4.0 3.7

6.0 24 100% 6 6.3 0.5 0.020 0.015 1.1 0.78

0% 10% 50% 100%

Substrate Substrate

Collaborators: Dr. K. Law and Dr. S. Badesha, Xerox

Summary of Work-of-Adhesion Results


Two Possible Contact Models for Nanoparticles

Substrate Substrate

0% 10% 50% 100%

34


𝑀𝑅 (𝛿 , 𝜃)

�⃗�𝑠

𝜓

𝜓𝜃

𝛿(𝑡) 𝑶′

𝑩

Probe Laser Beam

PSL Particle

Substrate

Mathematical Modeling and Analysis: Nonlinear


Mathematical Modeling and Analysis: Nonlinear

• An adhesive spherical particle with a radius of r and a mass of m on a vibrating flat surface.

• The particle undergoes out-of-plane (δ) and in-plane (θ) motions.

2( ) cos( ) ( )( ) sin( )

( ) ( , ) ( ) ( cos( ) 2 ( )

sin( ) ( )( ))

R

O R

m F m Y r X

I M m r X

Y r

The equations of motion are simplified for its free vibrational motion:

2 2

2

( )

( ( ) ) (2 ( ) ) ( , ) 0

R

O R

m F m m r

I m r m r M

A. S. Vahdat, S. Azizi and C. Cetinkaya, “Nonlinear Dynamics of Adhesive Micro-spherical Particles on Vibrating Substrates”, submitted for publication in Journal of Adhesion Science and Technology, 2012.

36


Experimental Results and Observations

60 kHz reported before as rocking resonance frequency

The response of particle is transformed into frequency domain using FFT routine in order to understand the frequency contents of the response. For some particles there was no interesting/new observation in the spectral domain:

The total depression of the top of the particle is experimentally obtained: *( ) ( ( ) ) 2 (1 cos ( ))e t t r t

Transient response of adhesive particles vibrating on a ultrasonically excited flat substrate

δe

Substrate

θ

O′O

37



45.16 kHz82.70 kHz

Particle I

40.41 kHz

78.15 kHz

Substrate

θ

O′

O

In the spectral domain of depression of some particle, an interesting/new resonance frequency were observed.

Particle II

*( ) ( ( ) ) 2 (1 cos ( ))e t t r t

38



36.55 kHz

64.40 kHz

• In the spectral domains of some particles a frequency doubling phenomenon is observed in the rocking resonance frequency range.

• This phenomenon cannot be explained based on previously proposed in-plane and out-of-plane motions theories.

• So a coupled dynamic of particle motion should be studied to figure out the origin of frequency doubling.

Particle III

40.86 kHz

78.56 kHz

Particle IV

39


Mathematical Modeling and analysis

2( ( ) ) (2 ( ) ) ( , ) 0O RI m r m r M

In-plane dynamics is dominated by its linear terms and its harmonic response is approximated as:

( ) sin( )rt t

Θ: Amplitude of the rocking motion

:r Rocking resonance frequency

2 2( )Rm m F m r

2 2 2 2 2 21cos ( ) 1 cos(2 )

2r r r rm r mr t m r t

Double of rocking resonance frequency

The coupling between in-plane and out-of-plane vibrations is the source of the frequency doubling.

A. S. Vahdat, S. Azizi and C. Cetinkaya, “Doubling of Rocking Resonance Frequency of an Adhesive Microparticle Vibrating on a Surface”, accepted for publication in Applied Physics Letters, 2012.

40

24( )

cos ( ) 1 ( ( ) )2

tt O t

22

5OI m r


Mathematical Modeling and Analysis

0( ) sin( ) (...)rm t t

Explanation: The cosine function doubles its argument frequency, therefore in order to see both frequencies in the spectral domain the in-plane solution has to be modified as:

Conclusion: The inclined rocking motion of particle in a three-dimensional dynamic model implies the existence of whirling-like motion of particle.

Observation: If coupling between in-plane and out-of-plane vibrations causes the frequency doubling, then why sometimes we observe the doubled frequency only?

*( ) ( ( ) ) 2 (1 cos ( ))e t t r t

This term includes the double of the rocking resonance frequency

This term includes the rocking resonance frequency

0 (...) :This non-zero term attests that the rocking motion occurs around an inclined axis with respect to the substrate normal

41

24( )

cos ( ) 1 ( ( ) )2

tt O t

( ) sin( )rt t



θ0 = 3.1 mrad

θ0 = 5.1 mradθ0 = 6.5 mrad

0( ) sin( ) (...)rm t t

42

*( ) ( ( ) ) 2 (1 cos ( ))e t t r t

2( ( ) ) (2 ( ) ) ( , ) 0O RI m r m r M

2 2( )Rm m F m r



Simulation

Matching the simulations results to experimental ones to extract the work-of-adhesion and leaning angles:

43



Td = 0.50 μs

Tr = 22.14 μs

*( ) ( ( ) ) 2 (1 cos ( ))e t t r t

The out-of-plane, in-plane and total depression of particles can be extracted from the simulation as:

Te-r = 22.14 μsTe-d = 0.50 μs

Te-dr = 11.07 μs

44



Particle Particle Diameter

(μm)

Particle Density (kg/m3)

Approximated Leaning Angles (mrad)

Measured Work-of-Adhesion

(mJ/m2)

Expected Work-of-Adhesion

(Visser) (mJ/m2)

Particle I 21.4 1050 10.8 32.5 23.5

Particle II 21.4 1050 5.1 25.9 23.5

Particle III 21.4 1050 1.2 22 23.5

Particle IV 21.4 1050 1.0 26.5 23.5

Using experimentally obtained spectral response and simulations results, the work-of-adhesion and leaning angle values are extracted:

• No research work is available on the leaning angle approximations.

• The extracted work-of-adhesion values are in good agreement with the theoretically calculated one based on Hamaker constant.

J. Visser, Adv. Colloid Interface Sci. 3, 331 (1972).

45


MonolayerGraphene

PSL Particle

Si

SiO2

0.335nm

1248 nm

0.142 nm

Adhesion Energy of Monolayer Graphene on Silicon


• A unique method is introduced and demonstrated for work-of-adhesion characterization of particles in a non-contact and lateral pushing manner.

• Lateral pushing requires contact between the particle and tip. The tip is made rough to eliminate contact-adhesion related problems.

• Non-contact method is advantageous in micro-scale adhesion characterization since particle handling/manipulation is difficult.

• Multiple frequencies in non-contact method needs to be analyzed and understood. Experiments in trenches is designed to eliminate the problems associated with multiple-rolling planes and anisotropic adhesion properties.

• Coupling between in-plane and out-plane motions can be strongly nonlinear. This is observed and reported for a number of cases here.

• Future Directions: Effects of electric charges, Graphene adhesion (effects of nano-interfaces), and particle rolling in SAW.

47

Conclusions and Remarks


Acknowledgements

People:

Wei Ding (Professor)

M. Miraskari (Ph.D. candidate)

James Stephens (M.S. candidate)

Carson Smith (Honors student)

Ilgaz Akseli (Ph.D.)

Ivin Varghese (Ph.D.)

Christopher F. Libordi (M.S.)

Melissa E. Merrill (Undergrad R.A.)

Ganesh Subramanian (M.S.)

Liang Ban (Ph.D.)

Chen Li (Ph. D.)

Dr. Girindra N Mani (Post-doc)

Financial Support:

National Science Foundation

Xerox

Pfizer, Inc.

Wyeth Pharmaceuticals

Consortium for the Advancement of Manufacturing in Pharmaceuticals (CAMP)

OYSTAR USA

NYSERDA

Center for Advanced Materials Processing (CAMP)

Clarkson University

48

photo-acoustics research laboratory dynamics of microspherical adhesive particles on vibrating...

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