Scanning Probe Acceleration Microscopy: Towards Real Time Reconstruction of Tip-Sample Forces in Tapping Mode AFM

8/7/2019 Scanning Probe Acceleration Microscopy: Towards Real Time Reconstruction of Tip-Sample Forces in Tapping Mode AFM

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PNAS, (2006), 103, 4813-4818

Appl.Phys.Lett., (2005), 87, 163120/1-163120/3

Scanning Probe Acceleration Microscopy:Towards Real Time Reconstruction of Tip-Sample Forces in Tapping Mode AFM

Tomek Kowalewski

Department of Chemistry

Carnegie Mellon University



Acknowledgements:

Justin Legleiter

Brian Cusick

Matthew Park

Funding:

NSF: CTS-0304568, DMR-9974457



E = 109 Pa



E = 108 Pa



E = 107 Pa





Plotting tapping force vs. cantilever deflection reveals that each tappingevent resembles closely the contact mode force curve.

The slope of these “mini force curves” depends in a familiar way on tehsample stiffness and dictates the width of the tapping pulse



0[ sin(2 )]eff o tip samo l p p em z bz k z D a f t F π −+ + − − =&& &

0

1[ ( sin(2 ))]o otip samp e

e

l p

ff

z bz kz k D a f t

m

F π −= − − + −&& &

Cantileveracceleration

These terms vary as exp( i ω op t)Tappingforce pulse

PNAS, (2006), 103, 4813-4818

Towards direct reconstruction of tip-sample force fromcantilever trajectory

Scanning Probe Acceleration Microscopy



S:N 105



S:N = 105

S:N = 104



S:N = 104

S:N 103



S:N = 103



S:N = 103



S:N = 10



1

1( ) ( ) ( )

N

rec oper

k y t y k ω δ ω ω

−

=

⎡ ⎤= ℑ −⎢ ⎥⎣ ⎦∑

PNAS, (2006), 103, 4813-4818

Harmonic Comb Filtering



1

1

( ) ( ) ( ) N

rec oper

k

y t y k ω δ ω ω −

=

⎡ ⎤= ℑ −⎢ ⎥

⎣ ⎦∑





Key To Modeling “Fluid Tapping” : LOW Q!

0 0 0[ sin( )]eff ext m z bz k z D a t F ω + + − − =&& &

26 / z HRF tipext −=

22 / 3 6 / )()3 /(4 DMT tip DMT tipeff ext a HR za RF −−= πκ

where

for z > a DMT

for z < a DMT

omQ

b

ω =

o

o

AQ

a

=



Appl.Phys.Lett., (2005), 87, 163120/1-163120/3

Simulated fluid tapping cantilever position



Fluid tapping cantilever trajectories



Appl.Phys.Lett., (2005), 87, 163120/1-163120/3

Simulated fluid tapping cantilever position



0 0 sin( ) y z D a t ω = − +Appl.Phys.Lett., (2005), 87, 163120/1-163120/3

Recall that optical lever measures cantilever deflection – not position!

Fluid Tapping Force-Curve



Experiment Simulation

Appl.Phys.Lett., (2005), 87, 163120/1-163120/3

Fluid Tapping Force-Curve



SPAM under water

PNAS, (2006), 103, 4813-4818



PNAS, (2006), 103, 4813-4818



⎥⎦⎤⎢

⎣⎡ ++−−= )]cos(

1)[sin(

10

2 t Q

t amky ybF m

y eff ext

eff

ω ω ω &&&

PNAS, (2006), 103, 4813-4818



⎥⎦⎤⎢

⎣⎡ ++−−= )]cos(1)[sin(1

0

2 t Q

t amky ybF m

y eff ext

eff

ω ω ω &&&



⎥⎦⎤⎢

⎣⎡ ++−−= )]cos(1)[sin(1

0

2 t Q

t amky ybF m

y eff ext

eff

ω ω ω &&&



⎥⎦⎤⎢

⎣⎡ ++−−= )]cos(1)[sin(1

0

2 t Q

t amky ybF m

y eff ext

eff

ω ω ω &&&

The effect of noise



The effect of noise

Harmonic Comb Filter



Harmonic Comb Filter

1

1

( ) ( ) ( )

N

rec oper

k

y t y k ω δ ω ω −

=

⎡ ⎤= ℑ −⎢ ⎥⎣ ⎦∑

Sliding window Fourier transform




PNAS, (2006), 103, 4813-4818





PNAS, (2006), 103, 4813-4818




g



Calibration curve



PNAS, (2006), 103, 4813-4818

Total brain lipid extract bilayers



p y



PNAS, (2006), 103, 4813-4818



PNAS, (2006), 103, 4813-4818

Conclusions:



Co c us o s

Documents

Scanning Probe Acceleration Microscopy: Towards Real Time Reconstruction of Tip-Sample Forces in Tapping Mode AFM