Sumer and Sitti

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Rolling and Spinning Friction Characterization of Fine

Particles using Lateral Force Microscopy based Contact

Pushing

BILSAY SUMER and METIN SITTI

Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA

ABSTRACT. Here, we have utilized Lateral Force Microscopy (LFM) based mechanical pushing of

micro/nano-objects to study adhesion and friction characterization at the micro/nanoscale. Con-

tinuum micro/nano-friction models for particle rolling, spinning and sliding cases are discussed for

general particle-substrate interfaces. A rolling resistance model using the Double-Hertz model is

devoloped for such general interfaces. Using the friction models, the effect of work of adhesion,

effective Youngs modulus, and contact radius at the particle-substrate interface are studied in de-

tail. Combining friction models with experimental particle pushing vertical and lateral force data,

the critical frictional interface parameters such as critical rolling distance and the interfacial shear

strength are measured for a polystyrene particle and glass substrate interface. Results show that

the critical rolling distance varies with the particle radius, and it is measured to be 42 nm , 84 nm ,

and 128 nm on average for 5 m, 10 m, and 15 m radius particles, respectively. Next, using the

particle spinning experimental data, the interfacial shear strength of the particle-substrate interface

is measured as 9-15 MPa .

KEYWORDS. Lateral Force Microscopy; micro/nanotribology; micro/nanoscale contact mechanics;

particle friction. Corresponding author, [email protected]

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1 Introduction

The physical understanding of different types of particle motions, such as sliding, rolling, stick-

slip and spinning, is indispensable since the mode of motion of particles determines the energy

loss and wear in the contacting surfaces. Numerous researchers have studied these motions in

the micro/nanoscale, such as particle attachment and detachment from surfaces [1], aggregation

and dispersion of powders [2], and micro/nano-manipulation operations to achieve two- or three-

dimensional micro/nanoelectromechanical systems [3,4]. Among the possible particle motions, quite

a few works have addressed the object-substrate rolling and spinning friction characterization in

the micro/nanoscale, resulting in a need for more theoretical and experimental work. For example,

using an atomic force microscopy (AFM) probe and by observing the motion change of carbonnanotubes (CNTs) from sliding-rotating mode to stick-roll mode, the friction anisotropy of CNTs on

graphite surface was explained [5]. Using a needle shaped tool under a scanning electron microscope

(SEM) or a piezoresistive AFM cantilever in ambient environment, different motion behaviors of

spherical objects were characterized [6,7]. Utilizing a non-contact adhesion measurement, based on

the previous theoretical work of Dominik and Tielens [8], for the rst time, the existence of rolling

moment of resistance of an adhesion bond between a microsphere and at surface was experimentally

demonstrated [9].

This paper focuses on the theoretical and experimental determination of rolling and spinning

friction (resistance) of micro/nanoparticles. If an adhesive elastic spherical particle is brought into

contact with an elastic half-plane, there would be a nite adhesional circular contact area that

can be determined by using continuum elastic theories. However, when an external disturbance,

such as a lateral point force or moment, is applied at the center of the sphere to start the rolling

motion, the contact area changes from the static contact condition and takes an elongated shape

where the rolling contact area is not circular anymore as observed with glass ball experiments on

a polyurethane surface [10] or polydimethylsiloxane (PDMS) hemispheres on a silicon wafer [11] in

the macrodomain. The adhesional contact zone responses to the perturbation such that front side

is adhering and back side is peeling, resulting in a pressure distribution that is asymmetric about

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the instantaneous center of rotation. Therefore, theoretical analysis of the rolling contact for the 3D

case (sphere) does not lead to an analytical solution due to the nonuniform contact area extension

in contrast to a two dimensional case (cylinder), where an implicit equation is derived describing

the rolling contact area and resistance [12]. Dominik and Tielens [8] proposed an approximateanalytical model to calculate the pressure distribution and resistance moment associated with the

rolling motion. However, their method can only be applied to certain material combinations where

the pressure distribution inside the contact area obeys the Johnson-Kendall-Roberts (JKR) model

and was not experimentally veried. If a lateral point force or moment is applied with some distance

from the center of the sphere, spinning motion of the particle is realized. Spinning motion is the

least investigated among the motion types although the slip mechanism is very similar to sliding

motion.

The ultimate goal of the presented work is to build a reliable method that leads to knowledge

about the mechanical and tribological properties of micro/nanoscale particles. A quasi-static model

of micro/nanoparticle behavior during manipulation is developed and used to explain the experi-

mental results. Previous work of Dominik and Tielens [8] is extended such that a cohesive zone

solution for the rolling moment of resistance has been found by adding the effects of adhesion using

a continuum elastic model, and possible particle motions such as sliding, rolling and rotation in mi-

cro/nanoscale are described by showing several mode diagrams. Mode diagrams have enhanced the

understanding of the manipulation and characterization procedure at the micro/nanoscale. In the

experiments, 5, 10 and 15 m radius polystyrene (PS) microparticles have been pushed laterally on

a glass substrate and the friction forces are recorded while observing the possible particle motions

and the resistance to rolling and spinning motions are reported.

The organization of the paper is as follows. In Section 2, the kinematics of the transverse

pushing of the micro/nanoparticles is investigated and the critical forces to initiate each motion of

the particle are determined using the equilibrium equations. In Section 3, micro/nanoscale friction

models for rolling, sliding and spinning motion modes of a particle pushed on a at substrate are

discussed. Here, the upper limits of the resistances for each motion are found for different effective

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Youngs moduli and work of adhesion cases for varying lateral pushing forces. In Section 4, LFM

based contact pushing experiments for different sizes of PS microparticles on a glass substrate are

reported and these experimental data are used to quantify the particle-substrate friction parameters

such as critical rolling resistance and shear strength. Finally, conclusions and future directions arereported in Section 5.

2 Method

To characterize the frictional properties of a ne particle moving on a at and smooth substrate, an

LFM based lateral particle pushing method is proposed with a protocol such that: 1) Using top-view

optical microscope or AFM tapping mode scanning based images, the particle location is determined

precisely; 2) The AFM probe tip is located above the at substrate with a height equal to the radius

of the particle ( R), and substrate moved with a constant speed V along a line parallel to the y-axis

as illustrated in Figure 1, which passes through the particle center with or without an offset ( x0 ); 3)

Due to this substrate motion, the particle is pushed parallel to the y-axis for a prescribed distance,

and probe vertical bending and torsional twisting angle ( ) are measured simultaneously. During

lateral particle pushing, AFM tip is assumed to be in contact with the particle at all times, and theresulting tip-particle and particle-substrate interaction forces are shown in Figure 2. The objective

is to extract the particle-substrate frictional parameters depending on the particle motion mode,

which could be sliding, rolling, stick-slip, or spinning (rotation). Here, spinning is possible if the

particle is pushed along a line that has a non-zero offset ( x0 ) value with the particle centerline.

Figure 1:

The friction of possible particle motion modes will be modeled using continuum micro/nanoscale

friction models, and experimental lateral and vertical force measurements during particle pushing

will be used to quantify the relevant frictional parameters. Approximate analytical models used for

motion modes will be derived depending on the lateral pushing force, x0 , and the tip, particle and

substrate geometrical and material properties. The substrate and the object surfaces are assumed

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to be very smooth to neglect roughness effects, and the particle-substrate contact mechanics is

assumed to be elastic assuming small and reversible deformations.

Figure 2:

To extract the particle-substrate friction force from the LFM measurements, forces in Figure

2 are solved using a quasi-static dynamic behavior assuming a very slow constant pushing speed.

Taking a rectangular cross section AFM cantilever probe geometry with width ( w), thickness ( t) and

length ( l), where the tip is at the very end of the probe with a height of h, quasi-static equilibrium

force equations can be given as

F t = F 2y + F 2z = tan 1 (F y/F z)

f t = F t cos( )N t = F t sin ( )f s = F t sin

N s = F t cos (1)

where F t is the reaction force at the tip, which is dened in terms of torsional ( F y) and normal

forces (F z) of the AFM cantilever, subscripts s and t denote the substrate and the AFM probe tip,

respectively, f t and f s are the frictional forces and N t and N s are the normal reaction forces at

the tip-particle and particle-substrate interfaces, respectively, is the loading angle, and is the

contact angle between the tip and the particle.

During pushing, particle and tip could stick, slide, stick-slip, roll, or spin. Conditions for suchmotions are derived using (1). The particle could slide on the substrate if

f s > s As (2)

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and the tip could slide on the particle if

f t > t At (3)

where s and t are the shear strengths and As and At are the contact areas for the particle-

substrate and the tip-particle interfaces, respectively, and the sliding friction is assumed as directly

proportional to the area of adhesional contact assuming negligible normal force, single asperity

contact and wearless interfacial sliding. Next, the particle could roll if

(f s + f t ) R > M max,s + M max,t (4)

or it could spin for a non-zero x0 (x0

(0, R]) and

F yx0 > max,s + max,t (5)

where M max,s and M max,t are the maximum rolling resistances and max,s and max,t are the max-

imum spinning resistances at the tip-particle and particle-substrate interfaces, respectively. The

physical interpretation of these resistances will be discussed in detail in the subsequent sections.

Solving (1) using above conditions gives the critical lateral pushing force conditions for particlesliding, tip sliding, particle rolling, and particle spinning, respectively as follows:

F t Assin

F t At

cos( )F t

M max,s + M max,tR (sin ( ) + sin )

F t max,s + max,tx0 sin (6)

In the schematic given in Figure 2, and with = = / 2 taken from now on, the vertical F z

force effect on the particle and the tip friction behavior becomes negligible. Thus, F t = F y will

be assumed in the friction models, but the friction of the tip-particle interface is included in the

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experiment section. When F y exceeds any of the above critical forces, the corresponding motion

behavior is observed. Multiple motion modes can also occur such as sliding with rolling, and rolling

with spinning, if any of the above conditions are obeyed simultaneously.

3 Friction Models

3.1 Rolling Friction Modeling

Assuming pure rolling of an adhesive elastic spherical particle on a rigid half-plane without sliding,

the aim of this section is to nd a general expression for the upper limit of the resistance of rolling

moment. The maximum rolling resistance moment is the critical moment that should be exceeded tostart the irreversible rolling process. For a sphere with a radius R on a at and smooth substrate, the

maximum rolling moment resistances in (6) are modeled using continuum elastic contact mechanics

models. Many aerosol ne particle works [13,14] have used an approximate rolling moment resistance

model such as

M max = F pa (7)

where M max is the maximum rolling resistance, F p is the pull-off force, and a is the equilibrium

contact radius. For a compliant and adhesional interface, the JKR model gives F p = 1 .5RW ,

where W is the interfacial work of adhesion. However, this model can be used as a rst-order

approximation and does not necessarily capture the physics of the problem, since the rolling force

is expected to be much smaller than the detachment force (pull-off force) and the detachment force

never acts at the equilibrium contact area.

More accurate particle rolling resistance models were also developed by calculating the approx-

imate analytical pressure distributions at the rolling interface using the JKR model [8], which is

only accurate for highly adhesional and compliant interface cases, such that :

M max 6RW (8)

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where is the critical rolling distance ( a) and is the interatomic distance [15]. Criticalrolling distance can be dened as the displacement of the sphere that may roll on the surface before

irreversible rearrangement in the contact area occurs.

The work described in this paper uses the resistance moment derivation method in [8] andthe Double-Hertz (DH) model to derive an analytical rolling resistance model for general particle-

substrate interface cases. Maugis [16] utilized a Dugdale potential to match the Lennard-Jones

potential where a constant adhesional stress acts over a nite radius where there is no real contact.

The Maugis-Dugdale (MD) model is widely accepted and used in micro/nanoscale contact mechanics

problems requiring a transition model. Greenwood and Johnson [17] presented an alternative to

the MD model called the DH model. In the DH model, the difference between two Hertz pressure

distributions is utilized where adhesive tensile stresses act inside and outside the contact area and

compressive stresses act only inside. An advantage of this model over the MD model is that the

shape of the gap outside the contact is described by elementary functions; hence, unlike in the MD

model, no elliptical integrals are involved. Also, the adhesive pressure distribution given by the

DH model includes only elementary functions that simplify the integral calculation in the rolling

resistance whereas the MD model includes inverse trigonometric functions, which should be solved

numerically. Therefore, the DH model is used in this work to derive an analytical expression for the

rolling resistance moment for general particle-substrate interfaces. In the DH model, the pressure

distribution is given by the combination of Hertz pressures along the contact axis ( r ) for an intimate

contact radius ( a) with the adhesional tensile stresses in the radius of ( c) as

P 1 (r ) = 0c2 r

2

c2 a21 / 2

a2 r

2

c2 a21 / 2

r < a (9)

P 2 (r ) = 0c2 r

2

c2 a21 / 2

a < r < c (10)

where 0 is dened as the maximum adhesional stress and is given in terms of the work of adhesion

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(W ) and the interatomic distance ( ) at the closest point as

0 =16

93W

(11)

However, there is no direct relationship between the normal load ( F z) and the real and adhesional

contact radii ( a and c) in the DH model unlike the JKR model. Two closed-form equations should

be solved iteratively in order to nd ( a) and ( c) for a given normal load. Dening a parameter

(m = c/a ) between two contact radii, the equations are given in dimensionless form as [17]

a (m2 1)1 / 2 +

2

a 2 3(m + 1)

(m 1)(m + 2)= 0

F z 23 a 3

3 a 2 (m2 + m + 1) m 1m + 1

1 / 2 = 0 (12)

The dimensionless numbers that appear in the above equations are dened as

a =a

(R2 W/K )1 / 3

c =c

(R2 W/K )1 / 3

F

z =F

z(R2 W/K )1 / 3

= oR

K 2 W

1 / 3(13)

where K = [(1 21 )/E 1 + (1

22 )/E 2 ]

1 represents the equivalent elastic modulus between the

particle and the substrate; E 1 and E 2 are the Youngs moduli, 1 and 2 are the Poissons ratios

for the particle and the substrate, respectively; and is the Tabor number [18] that represents the

ratio of the elastic displacement of the surfaces at pull-off to the effective range of surface forces.Using the simulation parameters given in Table 1, the DH, MD and JKR models are compared in

Figure 3 according to the variations of the dimensionless real and adhesional contact radii ( a and

c ) to in case of a zero normal load. The solution of a for the MD and the DH models match

very close to each other for the full range of , while the DH solution of c gives small discrepancy

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with the MD solution for intermediate and low values. Both the DH and MD solutions approach

the JKR solution for large values.

Table 1:

Figure 3:

Using the DH model based solution, asymmetric rolling contact geometry in Figure 4(a) is

divided into two contact areas as shown in Figure 4(b) similar to [8] where the leading part is

increased by a value and trailing part is decreased by the same amount and the leading and

trailing edges are assumed to be in the symmetric pressure distribution during the initiation of

rolling motion. The shifted distance is called as critical rolling displacement which can be dened

as a distance of sphere that may roll before irreversible rearrangement in the contact area occurs.

The four radii during the initiation of the rolling motion are dened as a + , c + , a , and c.Moment calculations associated with only one of the contact radii are given below, since others can

be derived in the same way. The moment due to the shift of the left contact area for the real contact

radius a + is given as:

M rl = 3 / 2

/ 2 a +

0xP 1 (r, a + )dA =

8 k 20a2 R (a + )4 (14)

where innitesimal area dA and x can be rewritten as dA = rdrd and x = r cos in polar

coordinates. Here, is the indentation depth and is given in terms of arbitrary parameter ( k)

such as:

=(1 k)a

2

kc2

R

(15)

Figure 4:

By calculating the other three radii rolling moment resistances and adding them up, the total

maximum rolling moment resistance is computed as

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M max = M rl + M al + M rr + M ar =8 k 20a2 R [(a + )4 (c + )4 (a )4 + ( c )4 ] (16)

where subscripts rl , al , rr , and ar represent the real contact radius of the left contact area, the

adhesional contact radius of left contact area, the real contact radius of the right contact area, and

the adhesional contact radius of the right contact area given in Figure 4(b), respectively. Conducting

a polynomial expansion and simplifying the equation by assuming 8 3 a and 83 c terms as negligible,

the total maximum rolling moment resistance ( M max ) and related critical tangential force ( F roll )

can be approximated as

M max W0(a3 c

3 )c2 a2

F roll W0

R(a3 c

3 )c2 a2

(17)

The DH transition model given above is compared with the Dominik and Tielens model in (8) in

Figure 5 using the simulation parameters in Table 1. In the limiting case, where the Tabor numberis larger than 5, both models converge to each other, which shows the validity of the approximation.

For a Tabor number lower than 5, the JKR solution overestimates F roll , showing that the cohesive

zone is responsible for reducing the energy release rate during the rolling motion.

Figure 5:

3.2 Sliding and Spinning Friction Modeling

By applying a lateral point force with = / 2, the particle can slide depending on the applied

normal and lateral forces and adhesion at the particle-substrate interface. Assuming a single asperity

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contact, sliding friction changes with the real contact area [19,20] such as

F slide = A (18)

where A = a 2 is the contact area, is the interfacial shear strength, and a is the real contact

radius. a is computed using the DH model in this work. Assuming a pure sliding case, microslip is

not considered, which could occur in the static friction phase.

For a perfect crystal, the theoretical shear strength is approximated as a constant value of

G/ 30 [21], which is shown to be the case for defect-free nanoscale contacts in the AFM experiments

[19], where G = 2G1 G2 / (G1 + G2 ) is the effective shear modulus given in terms of the shear moduli

(G1 , G2 ) of the particle and the substrate, respectively, dened as Gi = E i / [2(1 + i)]. However,

surface force apparatus (SFA) experiments, which have typically micrometer scale contact areas,

give again constant but much smaller than the AFM experiments, i.e. = G/ 1290. This shows

that the shear strength is scale dependent, which has been investigated using a micromechanical

dislocation model [22]. A single-dislocation-assisted (SDA) slip model is proposed for a wide range

of contact radii from 10 nm to 10 m. Although no experimental evidence is presented so far, the

proposed theory lls the gap between the AFM and SFA experiments, and establishes the frictional

stress as a varying function of contact size. According to the SDA slip model, for very small contact

radii (a < 20 nm ), is taken as G/ 43 using the previous AFM experimental results [19]. When

the contact size increases, shear stress is decreased until a second constant region is encountered,

where levels to G/ 1290 when a is larger than around 40 m as observed in SFA experiments [20].

Therefore, the rst region is the result of concurrent slip without the aid of dislocation motion; the

second region is the result of SDA slip; and the third region is the result of multiple-dislocation-

cooperated (MDC) slip. Thus, , which is a function of a, can be dened as

(a) =

G/ 43 a < 20 nm

G10N (a/b )M 20 nm < a < 40 m

G/ 1290 a > 40 m

(19)

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where M = tan 1 [(G/ 43 G/ 1290)/ (8104 b 28b)], N = 28b, and b = 0 .5 nm is the Burgers

vector [23].

In the pure spinning motion case, there would be a relative shear motion between the particle

and the substrate as in the case of sliding motion. However, particle rotates about its own centerwithout a real displacement in contrast to sliding motion. Therefore, the slip mechanism discussed

above is valid, and the maximum spinning moment resistance and lateral force required to spin the

particle for a given x0 value can be written as

max =a

0 2r 2 (a)dr =23

(a)a3

F spin =23x0 (a)a

3

(20)

where F spin is the critical lateral force to spin the particle ( max = F spin x0 ).

3.3 Mode Diagrams

In this section, rolling, sliding and spinning friction models are used to create mode diagrams

showing the regions of possible motion of a micro/nanoparticle for given lateral pushing forces ( F y),

effective Youngs moduli (K ), and interfacial work of adhesion ( W ). Here, it is assumed that a

lateral point force, F y , is applied at the mid-plane of a sphere ( = = / 2) with a negligible

normal force component. Thus, F t = F y is taken from now on, where the friction between the

AFM probe tip and particle is assumed to be negligible. This is a reasonable assumption since

the order of magnitude for the tip-particle interface friction values is far smaller than the values of

the particle-substrate interface. The simulation parameters are given in Table 1 for a polystyrene

particle and a smooth glass substrate interface case since the experiments were conducted for these

materials. When the total force F y obeys the condition F y > F roll , F y > F slide , or F y > F spin , the

particle rolls, slides, or spins, respectively. If more than one conditions is fullled simultaneously,

the particle would show all of those motion behaviors such as rolling with sliding and spinning with

rolling.

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The diagram in Figure 6 shows the possible motion modes of a polystyrene particle for different

critical rolling distance assumptions where < < a. In the plots, the lower and upper limits of

the critical rolling distance, i.e., = and = a, respectively, are taken to set a minimum and

maximum value for the rolling resistances, respectively. For each gure, there is a minimum lateralforce required to push the particle, otherwise the particle sticks to the surface. For this particular

conguration of the polystyrene particle and glass substrate, pure rolling is the most dominant

mode of motion and there are only small regions that are shown in Figure 6(c) where the particle

starts to slide rst before rolling with increasing F y.

Figure 6:

Rolling and sliding could be observed simultaneously, if F y is higher than both F roll and F slide

critical force limits. However, if F y is applied with an offset x0 to the mid-plane of the particle and

F y > F spin , the particle would also spin (rotate). In the extreme cases, where x0 = R and = ,

rolling is the rst motion mode for a low F y following a combined spinning and rolling motion as

seen in Figure 6. If F y is increased further, the particle can roll, rotate and slide simultaneously

leading to a very complicated motion. However, in the extreme cases where x0 = R and = a, rst

the spinning motion occurs, followed by rolling and sliding motions with higher F y .Similarly, the effect of the interface properties, such as work of adhesion ( W ) and equivalent

elastic modulus ( K ) on the motion of any particle on any at and smooth surface are investigated

by keeping the radius of the particle xed and varying the other parameters. K is varied from 5 GPa

to 100 GPa, while W is varied from 0.01 J/m 2 to 1 J/m 2 . In Figure 7, x0 = 0 and = a are taken,

and the critical lateral forces required to roll and slide a particle are plotted in 3D for four different

particle radii. Sliding motion is observed rst for nanoparticles with about 100 nm diameter with

W > 0.35 J/m 2 for any K . For stiff nanoparticles with W < 0.35 J/m 2 , rolling is observed rst.

On the other hand, for much larger microparticles (e.g., R = 15 m), rolling dominates the initial

motion at low lateral forces; only for highly adhesional ( W > 0.3 J/m 2 ) and relatively soft ( K < 60

GPa) interfaces, sliding happens rst.

When x0 = R, the spinning behavior of a particle with R = 5 m is investigated in Figure 8

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Figure 7:

together with the sliding and rolling motions. For the whole range of W and K parameters, the

spinning resistance is much lower than the two other motions. Thus, spinning is observed rst for

microparticles in general. However, when x0 0, spinning resistance can become the same asor larger than the rolling and sliding resistances; thus rolling with spinning and rolling with both

spinning and sliding could be possible at a critical x0 .

Figure 8:

4 Experiments

4.1 Sample Preparation

Plain glass microslides (Fisher Scientic, Pittsburgh, PA, USA) were used as substrates. They

were kept approximately 5 minutes in acetone, methanol and deionized (DI) water lled cups in an

ultrasonic bath cleaner in the given sequence. They were dried using a nitrogen gun. By using a

micropipette, a monodispersed polystyrene particle dispersion (Alfa Aesar, Ward Hill, MA, USA)

diluted with DI water were scattered on a glass slide randomly with a low density, which uses the

surface tension based particle self-assembly during water evaporation and dried in air.

4.2 Experimental Conditions

Experiments were conducted in ambient conditions. Ambient environmental parameters such as

temperature and humidity were measured as 19 C 0

and 3032%, respectively. Polystyrene particleswere selected since they are highly hydrophobic [24]. Thus, the water meniscus layer is not expected

to form between the tip-particle and the particle-substrate interfaces. The material of the AFM

probe tip was silicon. Since there is always a natural oxide layer with a nanometer scale thickness in

ambient conditions for silicon, tip-particle and particle-substrate interfaces have the same physical

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and chemical properties. Measured from the AFM images, root mean square (rms) roughness the

glass slides was around 0.17 nm , suggesting that roughness effect on the friction forces could be

neglected. The effect of wear on friction was also neglected. It was assumed that the natures of

the friction between the tip and the particle, and also between the particle and the substrate werepredominantly adhesional due to the smooth surfaces and low normal forces. Finally, particles

were pushed with the same constant velocity (0.1 m/s ) in all experiments. Recent observations

indicate that dry friction increases with increased velocity [25], and the frictional properties of

a micro/nanoparticle heavily depend on the velocity. At high velocities, dynamic effects such as

inertial and damping forces should be taken into account whereas at very low speeds stick-slip

behavior of the particle is observed. Therefore, the substrate moves with a constant and low speed

that satises the quasi-static assumption in the force models.

4.3 Experimental Setup

An AFM system (Autoprobe CP-II; Veeco, Santa Barbara, CA, USA) with a top-view optical

microscope imaging system was used to monitor and manipulate the particles. In this system, the

AFM probe was xed and the substrate was moved with a constant speed. A 25 m diameter

polystyrene particle attached AFM probe (Novascan, Ames, IA, USA) with a stiffness of 7.75 N/m

was used to measure W between a glass and silicon oxide interface experimentally as approximately

0.1 J/m 2 from the pull-off force measurements. For stable particle manipulation, a tapping mode

AFM probe (ATEC-NC; Nanosensors , Neuchatel, Switzerland) with a stiffness of around 45 N/m

and a tip radius of less than 10 nm was used. This probe has a tetrahedral tip that protrudes from

the very end of the probe, which enables direct top-view imaging of the AFM probe tip. During

contact pushing experiments, the AFM was operated in constant height mode where the forcefeedback control was disabled, and the normal and lateral forces were recorded during the particle

pushing operation. Here, the substrate alignment is critical. To take care of possible alignment

errors, contact height of at least three points on the glass substrate were measured through the

AFM force-distance curves to calibrate the alignment of the substrate with respect to the xyz piezo

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scanner motion axes.

The dimensions of the AFM cantilever were measured from the scanning electron microscope

(SEM) images where its length, width and tip height were measured as 151 .9 m, 45.1 m and 17.2

m, respectively. Since it was difficult to measure the cantilever thickness from SEM images, thenormal bending stiffness of the probe were calibrated using the Saders method [26] as 46.3 N/m

for measuring the vertical bending forces. Moreover, lateral force measurements require calibration

of the torsional stiffness of the AFM probe and lateral deection sensitivity which are detailed in

the Appendix.

4.4 Experimental Results

LFM based contact pushing of polystyrene microparticles with radii of 5, 10 and 15 m was per-

formed to measure the critical rolling and spinning forces. These diameters of particles were selected

to enable top-view optical microscope imaging in real-time while pushing the particles where the

Autoprobe CP-II optical microscope imaging resolution is limited to image only this size of diam-

eters reliably. In addition to the top-view optical microscope images, lateral and vertical forces on

the AFM probe during particle pushing were recorded to compute the critical frictional parameters.

As a rst step, the critical rolling distances of polystyrene microparticles with 5 m, 10 m and

15 m radii are characterized and sample lateral forces during rolling motion are given in Figure

9(a). A set of 15 pure rolling based pushing measurements were conducted using the same particles

for the three radii. Using these vertical ( F z) and lateral ( F y) experimental pushing force data and

the proposed maximum rolling resistance model in (17), values were computed for the three radii

as 42.2 5.9 nm , 83.5 6.3 nm and 128.5 13.6 nm , respectively. The resulting rolling andspinning resistance values, in terms of lateral force values, are presented in Table 2. These valuesare observed to be in the expected range of < < a. From these measurements, pull-off forces

and contact radii for the three radii are computed as 2 .4 N , 4.7 N and 7.1 N and 0.21 m, 0.33

m, and 0.43 m, respectively, using the DH model discussed before. As expected, the rolling force

is much smaller than the detachment force and the critical rolling distance value is in the range of

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a5 ,

a3 for the given polystyrene-glass interface and as the particle radius increases the critical

rolling distance approaches the real contact radius ( a). Apart from the visual feedback observed

during the motion, sliding experiments were done using the PS attached AFM probes in order to

prove that these experiments were the result of pure rolling motion of the spheres. The experimentalprocedure is detailed in the Appendix. The forces recorded in the sliding experiments were much

higher than the forces recorded during the rolling experiments proving that rolling experiments were

the result of the pure rolling motion of the spheres.

Table 2:

Figure 9:

In the experimental lateral force data analysis, we are interested in the critical force value (peak

value) that corresponds to a sharp drop in the data, which shows the initiation of the rolling motion.

If the AFM probe tip is withdrawn after this critical rolling distance, the force value is expected to

drop back to zero or a near-zero value. However, since the particle is forced to move continuously

on the surface after the motion starts, we hypothesize that the uctuations in the lateral force data

are related to the continuous peeling and adhering of trailing and leading edges in the contact area,respectively. Thus, the increase in the amplitude of the uctuations in the force data in Figure 9(a)

for larger particles could be due to the increased tip-particle contact area.

For the characterization of the spinning resistance, microparticles were pushed with different x0

values close to their radius values. For two different x0 values, spinning lateral forces are shown in

Figure 10 for a 10 m radius particle. As expected from (20), critical lateral force increases with

decreasing x0 . For characterizing the polystyrene particle and glass interface spinning resistance,

a set of 10 measurements with different x0 values were conducted for each particle radius using

the same particles. From these measurements, interfacial shear strength values were computed as

15.8 1.38 MPa , 11.4 0.27 MP a and 9.3 0.25 MP a for particles having 5 m, 10 m and 15m radii, respectively. Since G = 2 .71 GPa for the polystyrene-glass interface as given in Table

1, values were observed to be in the range of G/ 170 to G/ 290, which is in the intermediate

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regime in (19). Also, a values are hundreds of nanometers, which also match with the intermediate

regime condition for the contact radii in (19). Moreover, it was observed that as the contact size

of the particle was increased, the shear strength values were decreased showing the scaling effect as

predicted with the theory.

Figure 10:

The pushing point of AFM tip on the particle should be carefully aligned. Any misalignment

from the center mid-plane could cause a loss of contact at the particle-tip interface due to a complex

rolling with spinning motion of the particle. Such a particle contact loss sample behavior is displayed

in Figure 11. In this particular experiment, a 10 m diameter particle was pushed with a non-zero

mid-center offset value of 625 nm (x0 = 625 nm), which resulted in a rolling with spinning behavior.

Using the proposed models for a 5 m radius particle with x0 = 625 nm, the critical force values

to initiate rolling and spinning motions are computed to be very close to each other as 75.3 and

74.1 nN, respectively. Therefore, x0 = 0 and x0 = R should be applied for pure rolling and spinning

behaviors, respectively, to avoid a complex rolling with spinning motion. Identifying and modeling

such complex motions in the dynamic regime are particularly important for the particle micro/nano-

assembly applications, and it is a future work.

Figure 11:

5 Conclusion

A LFM based contact pushing method has been proposed to characterize the tribological properties

of micro/nanoscale particle and at substrate interfaces. Continuum micro/nano-friction models

for particle rolling, spinning and sliding cases have been devoloped for particle and at substrate

interfaces. Using these models, the effect of particle-substrate interface work of adhesion, effective

Youngs modulus, and contact radius have been studied. If the particle is pushed from the centerline

of the particle with no offset, mode diagrams show that microscale particles, in most of the cases,

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rst start to roll and then slide at higher lateral forces while nanoscale particles tend to start to

slide rst and then start to roll. By pushing particles with an offset of particle radius, it has been

shown that the spinning resistance is much smaller than the rolling resistance in most cases and the

sliding friction for microscale particles while it can get almost negligible at the nanoscale since itscales with a3 . These trends might change completely depending on the specic particle-substrate

case, though they can still be predicted precisely using the given friction models. Combining the

friction models with the experimental pushing vertical and lateral force data, the critical frictional

interface parameters, such as the critical rolling distance and the interfacial shear strength have been

measured for a polystyrene and glass interface case. The critical rolling distance changes with the

particle radius, and it has been measured to be 42 nm , 84 nm , and 128 nm on average for 5 m, 10

m, and 15 m radius particles, respectively. Next, using the particle spinning experimental data,

the interfacial shear strength of the particle-substrate interface has been measured as 9 15 MP a ,which matches with previous studies. This characterization method could be used to understand

and control the frictional behavior of micro/nanoparticles for 2D precision particle assembly (for

prototyping particle based micro/nanodevices and fabrication templates [27]), particle based solid

lubrication, particle removal, and aerosol applications.

Acknowledgement

This work is supported by the NSF CAREER award program ( IIS 0448042). The authors thankBurak Aksak for his help with AFM, Cagdas D. Onal for his valuable comments on modeling and

Afshin Tafazzoli for his early works.

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Appendix

A. Sliding Experiments

Besides the possible particle pushing modes such as sliding, rolling, rotation, sticking, stick-slipmotion, the sliding case is the most investigated one due to the unsophisticated measurement tech-

niques. Using conventional AFM probe tips or gluing a particle to the tipless AFM cantilever (colloid

probes), sliding shear strength of almost any material can be determined [28]. In the experiments,

PS attached AFM cantilever utilized which also used for the work of adhesion calculation. The

particle probe is forced to slide on the glass substrate with a negligible normal load while recording

the LFM voltage signal in friction loop. To derive friction loop, lateral force is plotted against the

lateral sample displacement as the piezoelectric stage moves perpendicular to the cantilever long

axis in a lateral direction, rst one way then the other, as shown in Figure 12. At the beginning of

each trace, the shearing force increases until the static friction force is overcome followed by a com-

plete sliding of the particle in the kinetic friction regime. After 10 successful sliding experiments,

the pure sliding force value is observed to be 1112 92 nN which is much higher than the rollingand spinning critical forces.

Figure 12:

B. Calibration Procedures

Several lateral force calibration methods have been proposed in the literature such as the optical

geometry method [29], static friction method [30], vertical lever method [31] and wedge method [32].

The basic difficulty in the lateral force calibration is the high stiffness value in contrast to normalforce calibration causing a challenge to determine the lateral deection sensitivity. For example, in

the static friction method, friction loop is obtained experimentally by conducting lateral scanning of

the AFM cantilever on a hard substrate in LFM mode and the slope of the static friction is taken as

equal to the lateral sensitivity. While this approach may give satisfactory results for sphere attached

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probes (colloidal probes), in a typical AFM tip and substrate experiment, the contact stiffness of

the interface is comparable with the lateral stiffness of the cantilever. Although the contact stiffness

can be calculated using the continuum elastic theories and subtracted from the measured sensitivity,

this approach makes it an indirect method for the calibration. A new technique called diamagneticlateral force calibrator is proposed by Li et al. [33]. In this method, a pyrolytic graphite sheet

levitated by a strong magnetic eld is used as a reference spring to apply a known force on the AFM

cantilever-tip assembly and by recording the output signals the force constants can be obtained as

a system response. The basic advantage of this system is the cross-talk effect (coupling between

normal and lateral force signals) elimination and easy setup. In our setup, the lateral stiffness value

of the pyrolytic graphite sheet was found to be 34 .6 mN/m giving force constants of ll = 690.8

nN/V and nl = 122.8 nN/V for the AFM cantilever used in the rolling and spinning experiments.The force constants of particle attached probes were ll = 120.3 nN/V and nl = 11.8 nN/V .

References

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[4] M. Sitti and H. Hashimoto, IEEE/ASME Trans. Mechatronics 5 , 199-211 (2000).

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Superne, Nature 397 , 236238 (1999).

[6] S. Saito, H. T. Miyazaki, T. Sato, and K. Takahashi, J. Appl. Phys. 92 , 51405149 (2002).

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[8] C. Dominik and A. G. G. M. Tielens, Astrophys. J. 480 , 647673 (1997).

[9] M. D. Murthy Peri and C. Cetinkaya, Philosophical Magazine 85 , 13471357 (2005).

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[10] M. Barquins, D. Maugis, J. Blouet, and R. Courtel, Wear 51 , 378384 (1978).

[11] H. She and M. K. Chaudhury, Langmuir 16 , 622 -625 (2000).

[12] M. Barquins, J. Natural Rubber Res. 5 , 199-210 (1990).

[13] H. C. Wang, Aerosol Sci. Technol. 13 , 386393 (1990).

[14] M. Soltani and G. Ahmadi, J. Adhesion Sci. Technol. 8 , 763785 (1994).

[15] L. O. Heim, J. Blum, M. Preuss, and H. J. Butt, Phys. Rev. Letters 83 , 33283331 (1999).

[16] D. Maugis, J. Colloid Interface Sci. 150 , 243269 (1992).

[17] J. A. Greenwood and K. L. Johnson, J. Phys. D: Appl. Phys. 31 , 32793290 (1998).

[18] D. Tabor, J. Colloid Interface Sci. 58 , 213 (1977).

[19] R. W. Carpick, D. F. Ogletree, and M. Salmeron, Appl. Phys. Lett. 70 , 15481550 (1997).

[20] A. M Homola, J. Israelachvili, P. M. McGuiggan, and M. L. Gee, Wear 136 , 6583 (1990).

[21] A.H. Cottrell, Introduction to the Modern Theory of Metals. Institute of Metals , London

(1988).

[22] J. A. Hurtoda and K. S. Kim, Proc. R. Soc. Lond. A 455 , 33633384, (1999).

[23] K. L. Johnson, Proc. Instn. Mech. Engrs. 214 , 110 (2000).

[24] J. A. S. Cleaver and L. Looi, Powder Technol. 174 , 3437 (2007).

[25] H. Yoshizawa, C. Y. Lung, and J. Israelachvili, J. Phys. Chem. 97 , 41284140 (1993).

[26] J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Scient. Instrum. 70 , 39673969 (1999).

[27] A. Tafazzoli, C. M. Cheng, C. Pawashe, E. K. Sabo, L. Tron, M. Sitti, and P. R. LeDuc, J.

Mater. Res. 22 , 16011608 (2007).

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[28] E. Gnecco, R. Bennewitz, T. Gyalog, and E. Meyer, Wear 192 , 141150 (1996).

[29] E. Liu, B. Blanpain, and J. P. Celis, J. Phys. : Condensed Matter 13 , 619642 (2001).

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(2001).

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Instrum. 72 , 41644170 (2001).

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[33] Q. Li, K. S. Kim, and A. Rydberg, Rev. Scient. Instrum. 77 , 113 (2006).

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Table 1: Simulation parameters used in the contact mechanics analysis for a polystyrene (PS)particle and glass substrate interface.

Parameter Symbol Value Units ReferenceElastic Modulus (PS) E 1 3.80 GP a [34]

Elastic Modulus (Glass) E 2 73.40 GP a [35]Shear Modulus (PS) G1 1.42 GP a

Shear Modulus (Glass) G2 31.40 GP aPoissons Ratio (PS) 1 0.34 - [34]

Poissons Ratio (Glass) 2 0.17 - [35]Work of Adhesion W 0.1 J/m 2

Contact Angle / 2 rad.Loading Angle / 2 rad.

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Table 2: Experimental rolling and spinning resistance results for different radii ( R) particles.

R (m) F roll (nN ) (nm ) a F spin (nN ) (MP a ) b

5 78.2 14.1 42.2 5.9 64.2 5.1 15.8 1.3810 157.3 12.2 83.5 6.3 87.9 1.2 11.4 0.2715 254.2

25.3 128.5

13.6 105.2

1.4 9.3

0.25

a The critical rolling distance.b Interfacial shear strength.

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microparticle

tip

substrate

y

z

x

p z

PhotodiodeLaser

V

Figure 1: Schematic of the LFM based particle lateral pushing and friction characterization setup:an AFM probe tip is used to push a micro/nanoparticle on a at and smooth substrate in lateraly direction while measuring the corresponding vertical and torsional probe deections. A reectedlight type optical microscope is used for the real-time top-view images of the probe tip and theparticle with a micrometer scale resolution.

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z

y

Microparticle

Substrate

y

zt

y f

s tt

s

s d

t

o x

Top view

Rolling

Rotation

Front view

Sliding

Fy F z

t+ s

Figure 2: Schematic of the tip-particle and particle-substrate interaction forces during the lateralparticle pushing operation with a constant speed of V . = = / 2 is taken to apply only a lateralpoint force on the particle during pushing in the friction modeling section. Particle can stick, slide,roll, spin, or stick-slip (Inset image shows the spinning case where the particle is pushed with anoffset x0 from the particle centerline.) depending on the lateral pushing force, x0 , particle size, andtip, particle and substrate material and interfacial adhesion properties.

0 1 2 3 4 50

2

4

6

8

10

12

14

Tabor number ( )

a *

, c

*

a* (DH)a* (MD)c* (DH)c* (MD)a*= c* (JKR)

Figure 3: The simulated variation of a and c with the Tabor number ( ) according to the DH,MD and JKR models in case of a zero normal load.

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R

a a

Cohesive ZoneOO

R

c c

Static Contact Pure Rolling Contact

F y

Front View

Top View

(a)

c+

a+

a-

c-

(b)

Figure 4: a) Top and front views of a sphere in static and rolling contact on a at surface. Thesphere is rotated in clockwise direction and elongated shape of the rolling contact with the criticalrolling distance ( ) is shown in the top view of the rolling contact schematic. The solid lines indicatethe edges of the real contact area and the dotted lines indicate the edges of the adhesional contactarea. b) Top view of the approximated shape of the rolling contact.

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0 1 2 3 4 5 6 7 8

0.4

0.5

0.6

0.7

0.8

0.9

1

F y

Transition ModelDominik and Tielens Model

Tabor number ( )

Figure 5: Comparison of the DH transition model (17) with the Dominik and Tielens model in [8]for a zero normal load where the DH solution is normalized by the JKR solution using the simulationparameters in Table 1.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

0.5

1

1.5

2

2.5

3

1 2 3 4

x 103

0

2

4

6

8

x 103

R ( m)

F y

( N )

SlidingRolling

R ( m)

F y

( N )

(a)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0

0.5

1

1.5

2

2.5

3

R ( m)

F y

( N )

SlidingRollingSpinning

0 1 2 3 4

0

1

2

3

x 103

R ( m)

F y

( N )

(b)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

R ( m)

F y

( N ) 0 0.01 0.02 0.03 0.04

0

0.005

0.01

0.015

0.02

R ( m)

F y

( N )

SlidingRolling

(c)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

R ( m)

F y

( N )

0 0 .0 1 0 . 02 0 .0 3 0 . 04 0 .0 5

5

0

5

10

15

20

x 103

R ( m)

F y

( N )

SlidingRollingSpinning

(d)

Figure 6: Simulated rolling, sliding, and spinning particle motion mode diagrams for various particleradii: a) The particle is pushed at the mid-plane ( = = / 2) and rolling occurs for the wholeregion where the critical distance is taken as the atomic distance ( = ). b) The particle is pushedwith some offset (xo = R) and spinning, sliding and rolling lines are shown ( = ). c) The criticaldistance is taken as the real contact radius ( = a) and rolling is the dominant part for the most of the region and transition occurs at about 200 nm and the motion of the particle is depicted in thegure being pushed from the mid-plane of the sphere. d) The critical distance is taken as the realcontact radius ( = a), and the motion of the particle is shown in the gure pushed with an offset(xo = R).

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(a) (b)

(c) (d)

Figure 7: 3D particle motion mode diagrams showing the possible regions of sliding and rollingmotions for a) 50 nm , b) 0.5 m, c) 5 m, and d) 15 m particle radii. K is the effective Youngsmoduli and W is the interfacial work of adhesion. Here, x0 = 0 and = a.

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(a)

(b)

Figure 8: a) A 3D particle motion mode diagram showing the possible regions of sliding, rollingand spinning motions for a particle with 5 m radius. K is the effective Youngs moduli and W isthe interfacial work of adhesion. Here, x0 = R. b) The spinning 3D critical lateral force diagram isshown for the same particle. 33


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0 5 10 15 20 25300

250

200

150

100

50

0

50

y-position ( m)

F y

( n N )

R = 5R = 10R = 15

mmm

(a)

(b)

Figure 9: a) Experimental lateral force data during rolling a 5 m, 10 m and 15 m radiuspolystyrene particle. (The AFM probe is xed and the substrate with the particle is moved with

a constant speed.) The particles are pushed approximately 10 m distance. b) Top-view opticalmicroscope images before (left image) and after (right image) the pushing operation for a 10 mradius particle to show the traveled distance.

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5 10 15 20 25120

100

80

60

40

20

0

20

y-position ( m)

F y

( n N )

xo

= 9.2 m

xo

= 8.5 m

Figure 10: The experimental spinning lateral force data for a 10 m radius particle for two differentoffset (x0 ) values.

0 5 10 15 20 25 30 35-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

y-position ( m)

Figure 11: Sample experimental lateral force data where the microparticle loses the contact withthe AFM probe tip due to a non-zero x0 value initially ( x0 = 625 nm).

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Static Friction Phase

Kinetic Friction Phase(Complete Sliding)

y-position (nm)

F y

( N )

Figure 12: Sample friction loop is shown for a PS particle attached probe while particle slides on aglass surface where the normal force is negligible.

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