MEMS Devices for Force Sensing in Biology
Transcript of MEMS Devices for Force Sensing in Biology
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MEMS Devices for Force Sensing in Biology
Thomas KennyDepartment of Mechanical Engineering
Stanford [email protected]://mems.stanford.edu
PASI on MEMS6/21/04
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● MEMS devices may be good for many things.
● A large fraction of MEMS sensors detect signals by detecting physical force. Often these forces are very small
● There are some interesting scientific applications for miniature, sensitive force sensors, especially in Biology.
Theme
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Some Definitions
● MEMS : Micro Electro Mechanical Systems
● Micromachining : The use of IC Fab tools to make micromechanical structures
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Why are MEMS Interesting?
Technological Applicationsinertial, automotive, optical, biochemical
Interesting Fundamentalssmall forces, novel interactions, science Measurement opportunities
Science Opportunitiesnew materials, design and performanceimplications, little quality work done
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MEMS Devices in Bewildering Variety have been demonstrated on the surfaces of wafers.
Variety!
Frank, Pisano, UC Berkeley Rao, Aimi, MacDonaldUCSB
Gulvin, et.al Xerox Wilson
Chui, et.al, IBM Almaden
Carter, Kang, White, Duwel, Draper Labs
All from Proceedings, Hilton Head ‘04
Pourkamali, Ayazi, Ga. Tech
Li, et.al, MIT
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Commercial Piezoresistive Pressure Sensor
Doped Silicon Strain Gauges for Diaphragm Strain Detection.
MEMS Force Measurement Example
Lucas Novasensor
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Lucas Novasensor
Model NP301
● Range : 5 PSI -> 100 kPa● Accuracy : 0.5% FullScale ● Diaphragm Area : 0.5 mm x 0.5 mm● Full Scale Force is 25 mN, Specified Errors
correspond to 100 µN. ● The RMS noise is less than 10 nN/√Hz.
Force in a Silicon Pressure Sensor
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How Small is a nanoNewton?
Examples (in 1g)
● A drop of water weighs 10 µN● The Si diaphragm of the Novasensor
Pressure sensor weight about 50 nN● An eyelash weighs 100 nN● Polysilicon micromachined structures
can weigh about 1 nN
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Forces get smaller● For Pressure Sensors, F ~ Area = L2
● For Inertial Sensors, F ~ Volume = L3
Transducers Lose Sensitivity● Capacitors scale as Area = L2
● Optical, Piezoelectric, Piezoresistive also lose sensitivity as size is reduced
These trends oppose miniaturization
Scaling Issues for Force Sensors
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Noise generally does not improve with miniaturization
● Electrical Noise will probably be the same.
● Energy Fluctuations (kBT) will result in larger errors.
Thermomechanical noise scales as 1/√m
● Some 1/f noise becomes more significant
Increased surface/volume
Scaling Issues for Force Sensors
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ADXL202 Example
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ADXL202 Example
● This Accelerometer has the following Fundamental Parameters :
Structural Thickness = ~ 2 µm
Mass = ~ 1 x 10-10 kg
Suspension Stiffness = ~ 1 N/m
Resonant Frequency = ~ 10 kHz
Detectable Acceleration = 0.5 mg/
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ADXL202 Example
● This Accelerometer has the following Fundamental Parameters :
Structural Thickness = ~ 2 µm
Mass = ~ 1 x 10-10 kg
Suspension Stiffness = ~ 1 N/m
Resonant Frequency = ~ 10 kHz
Detectable Acceleration = 0.5 mg/
Detectable Displacement = 0.005Å/
Detectable Force = 0.5 pN//
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Thermal fluctuations in micromechanical systems exert a noise force, which cannot be distinguished from inertial forces.
● The minimum detectable acceleration from thermal noise is
Thermodynamics in Accelerometers
An =
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Thermal fluctuations in micromechanical systems exert a noise force, which cannot be distinguished from inertial forces.
● The minimum detectable acceleration from thermal noise is
Thermodynamics in Accelerometers
An =
ωo = 10 kHz, m = 0.1 µgm, Q = 0.7
An = 0.3 mg/
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Driving
Rotation input
Sensing output
MEMS gyros operate by detection of Coriolis Forces applied to moving masses F = mω x v
Force Sensing in Gyroscopes
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MEMS gyros operate by detection of Coriolis Forces applied to moving masses F = mω x v
Need large amplitude, high-frequency oscillation for large signals.
Example : Robert Bosch Automotive Skid Control Gyro
Force Sensing in Gyroscopes
Structural Thickness ~ 12 µm Mass ~ 3 x 10-9 kg
Suspension Stiffness ~ 0.5 N/m Resonant Frequency ~ 2 kHz
Amplitude of Oscillation ~50 µm Velocity ~ 0.6 m/s
Detected Rotation ~ 0.1 deg/sec
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MEMS gyros operate by detection of Coriolis Forces applied to moving masses F = mω x v
Need large amplitude, high-frequency oscillation for large signals.
Example : Robert Bosch Automotive Skid Control Gyro
Force Sensing in Gyroscopes
Structural Thickness ~ 12 µm Mass ~ 3 x 10-9 kg
Suspension Stiffness ~ 0.5 N/m Resonant Frequency ~ 2 kHz
Amplitude of Oscillation ~50 µm Velocity ~ 0.6 m/s
Detected Rotation ~ 0.1 deg/sec Detected Force ~ 4 pN
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Thermal fluctuations in micromechanical systems exert a noise force, which cannot be distinguished from Coriolis forces.
From this, we clearly see that maximizing amplitude and frequency are important, and that maximizing Q is also important.
The Bosch Skid-Control Gyro is also operating very close to thermodynamic limits
Thermodynamics in Gyroscopes
F.Ayazi and K.Najafi, JMEMS 10,169 (2001).
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Force Sensing Cantilevers
● In AFM, cantilevers are used to detect surface topography by measuring nN forces.
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Piezoresistive Cantilevers
● In AFM, piezoresistive cantilevers are used for measurement of 100 pN forces near surfaces
● Important when Optical methods are inconvenient● Sensitivity scales as 1/t^3, so reductions in
thickness are very important to pursue
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Thinner Piezoresistive Cantilevers
Thin piezolever examples
● 1 µm thick -> 20 pN/√Hz » (Chui, APL’96)
● 0.35 µm thick -> 1 pN/√Hz » (Reid, Transducers’97)
Issue : Avoiding Diffusion of Doped Si Strain Gauge
throughout Cantilever Thickness during High-Temperature
Steps in Processing. Very hard as devices are thinner than 1 µm.
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Ultrathin Epi-Doped Cantilevers
-2
-1
0
1
2
-5
0
5
0 0.2 0.4 0.6 0.8 1Time (s)
-10
0
10
-50
0
50
Force (pN)
Voltage (uV)
Cantilever response to Applied Load(1 Hz to 1.2 kHz bandwidth)
44µm x 350 µ m
97 nm thick
500 fN resolution(10 Hz to 1 kHz)
8 fN/√Hz at 1 kHz
J. A. Harley et al, “High Sensitivity Piezoresistive Cantilevers under 1000Å Thick”, Appl. Phys. Lett., Vol 75, No. 2, pp. 289-291, 1999
V F(pN)
Strain gauge formed by epitaxial growth of 30 nm doped layer
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Ultrathin n-type Piezoresistive Cantilevers
• N-type piezos have higher sensitivity and lower noise.• Epi-Si, plasma etching process allows fabrication
Yiching Liang
Cantilever noise measurement
120 fN resolution(10 Hz to 1 kHz)
1.6 fN/√Hz at 1 kHz
Y. Liang, S-W Ueng, T.W. Kenny, “Performance Characteristics of Ultra-Thin n-Type Piezoresistive Cantilevers”, Proceedings Transducers ’01, Munich Germany, p. 998 (2001).
2 0 µµ
8 µm x 144 µm
70 nm thick
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With Rugar, Mamin, Stipe, Yannoni, Botkin : IBM Almaden
Example Problem : MRFM
• Force detection of magnetic resonance should enable atomic resolution, 3-D, chemically selective imaging.• Magnetic forces from individual atoms are very small.
T.D. Stowe, et.al. “attoNewton Force Detection using Ultrathin Silicon Cantilevers”, Appl. Phys. Lett. 71, 288-290 (1997).
aa
UltrathinCantileverMagneticFilmAtom underMagnetic Resonance Force Noise
3.6 aN
Electrostatic test signal
36 aN
B=0.4 Hz
Tim Stowe, Kevin Yasumura, Anu Tewary
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Ultrathin Cantilever
● thickness (t) 600 Å● temperature 5 K● pressure 10-6 Torr
● f0=ωo/2 : π 1.7 kHz
● Q 6,700● k: 6x10-6 N/m● Fmin 0.820 aN/ Hz√
50 µmT.D. Stowe, et.al. “attoNewton Force Detection using Ultrathin Silicon Cantilevers”, Appl. Phys. Lett. 71, 288-290 (1997).
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● Antibody-Antigen Binding (100 pN)» Lee and Colton, 1994
● Cellular Adhesion (5-100 pN)» Adams, Chen, Smith and Nelson (1998)
● Actin-Myosin Mechanical Behavior (10 pN-10nN)» Finer, Simmons and Spudich (1994)
● Protein Folding (0.1-100 pN)» Powers, Daburesse, Noller (1993)
● Insect Biomechanics (nN-mN)» Full, Federle (1993)
● Small Animal Locomotion/Adhesion (nN-mN)» Autumn, Full
Many current topics in Biology are related to measurements of forces
Biology Force Measurement Opportunities
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Cadherin Molecule Background
● Cadherins - A model system» Used to hold sheets of cells, such as
skin, together.
» Important for development of an organism from fertilized egg to multicellular individual.
» Defects in cadherins lead to cancer.
● Diverse family of molecules» N-cadherin, E-cadherin, K-cadherin, etc.
» Many types of interactions to study.
» Adhesion contrast for different pairings expected
● Have been cloned, which allows for mutational studies.
● Single-molecule interactions are expected to be 10-200 pN.
(Nelson, et. al., 1998).
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Cadherins - Background
● A transmembrane protein» Two functionally significant domains -
Extracellular and cytoplasmic
» Extracellular domain has five repeats
» Distal four domains contain Ca++ binding sites
Structure of the Cadherin/Catenin complex
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● Dimer then binds to another cadherin dimer in a homophilic reaction
» A weak interaction (<< 1 nN)
» Clustering or other cooperative phenomena are thought to be involved
– May take a zipper form.
– Stronger bonds are thought to form through clustering (Yap, et. al. 1997)
– Interactions with the cytoskeleton strengthen bonds (Adams and Nelson, 1998)
Extracellular Domain provides adhesion
•Only the N-terminal domain is involved in cell-cell adhesion•Dimerizes with adjacent cadherin on the same cell
Dimeric structure of cadherin, shown in
a diagram of the zipper model.
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Whole-Cell Force measurements
● Laminar flow to assay adhesion based on resistance of cells to detachment from capillaries coated with purified E-cadherin (Yap, et. al., 1997).
» Cell adhesion rates
● Adhesion rates of cells subject to centrifugation
(Yap, et. al., 1997).
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Mechanical Properties of Molecules
Interaction Forces near 100 pN expected. Many complications (underwater operation,surface chemistry issues)
MEMS Adhesion Measurement
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Bead Attachment
● Pre-prepared 2 µm Polystyrene Bead with neutravadin/biotin coating
● Manual attachment to cantilever prior to AFM experiment.
Robert Rudnitsky
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Cover-slip Length (Å)NHS-SS-Biotin 24.3
NHS-SS-Biotin
Cadherins are “tethered” to a slide via a chain of other molecules
Robert Rudnitsky
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Cover-slip Length (Å)NHS-SS-Biotin 24.3NeutrAvidin 20 to 29.5
Cadherins are “tethered” to a slide via a chain of other molecules
Biotin-Avidin complex. Biotin binding pocket indicted. PDB ID: 2AVI
Robert Rudnitsky
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Cover-slip Length (Å)NHS-SS-Biotin 24.3NeutrAvidin 20 to 29.5Biotinylated Protein A 22+30
The Protein A-Fc complex, Binding sites indicted. PDB ID: 1FC2
Cadherins are “tethered” to a slide via a chain of other molecules
Robert Rudnitsky
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Cover-slip Length (Å)NHS-SS-Biotin 24.3NeutrAvidin 20 to 29.5Biotinylated Protein A 22+30Fc-E-Cadherin 30 to 40
+192.5 to 250Sub-total 318.8 to 395.8
Cadherins are “tethered” to a slide via a chain of other molecules
C-Cadherin Ectodomain from Boggon T.J., (PDB ID: 1L3W)
Robert Rudnitsky
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Cover-slip Length (Å)NHS-SS-Biotin 24.3NeutrAvidin 20 to 29.5Biotinylated Protein A 22+30Fc-E-Cadherin 30 to 40
+192.5 to 250Sub-total 318.8 to 395.8
Bead 294.5 to 371.5
Total 613.3 to 767.3
Cadherins are “tethered” to a slide via a chain of other molecules
Robert Rudnitsky
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Unanswered questions remain
What is the actual binding force?
● Does the binding force scale linearly with density?
● What are the forces for heterophilic interactions?
● How does the cadherin molecules’ structure affect binding?
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500 400 200 100
Cantilever Approaches
Force (N
)
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Snap Down
Force (N
)
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Contact
Force (N
)
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Distance (nm)
Force (N
)
Cantilever retracts
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Distance (nm)
Force (N
)
Cantilever retracts and Deflects
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Distance (nm)
Force (N
)
Unbinding Force F = - k x
Adhesion forces can be detected by measuring the cantilever’s deflection.
AFM Measurements can produce Force-Distance Curves
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500 400 200 100
Retracts
Distance (nm)
Force (N
)
Unbinding Force F = - k x
Adhesion forces can be detected by measuring the cantilever’s deflection.
AFM Measurements can produce Force-Distance Curves
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Single and multiple adhesions are observed
Position (nm)0 100 200 300 400 500
-100
0
100
For
ce (
pN)
Position (nm)0 100 200 300 400 500
-100
0
100
For
ce (
pN)
Surface
With protein interactions the unbinding location is retarded off the surface. In the absence of protein interactions, unbinding takes place at the surface
Unbinding Event
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Force probability distributions show evidence of multiple binding events
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
0
1
2
3
4
5
6x 1012 LAST Unbinding events force dist (Normalized) -- 200 ? γ/µλ ΦχΕχαδ ιν Ρινγερσ 1.8 µΜ [Χα++]
Φορχε (Ν)
Νορµαλιζεδ ∆ιστριβυτιον
● Force increment of
~ 20 pN● Peaks at:
» 18-21 pN
» 41-43 pN
» 59-61
» 81-83 pN
perhaps indicating
single, double, triples
and quadruple
unbinding events.
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Ongoing Work
● Does the binding force scale linearly with density?
● What are the forces for heterophilic interactions?
● How does the cadherin molecules’ structure affect binding?
● Is there a measureable time interval for the binding interaction?
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● Small Animal/Insect Locomotion» There are many examples of small animals which are
remarkably agile yet simple and relatively unintelligent.
More Biology Force Measurement Examples
Blaberus discoidalis, Death-HeadCockroaches, Female and Male
Michael Bartsch, Mark Cutkosky, Walter Federle, Bob Full
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● Man-Made Robot Locomotion» There are many examples of man-made robots which are very
sophisticated and expensive, yet rather clumsy and fragile.
More Biology Force Measurement Examples
Mars Pathfinder Rover, JPL, 1999
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Day 59» The rover partway down
“Half Dome”
Day 64» The rover has
completed its descent from “Half Dome”
Day 66» Rover driving forward
after backing up to analyze rocks
Man-Made Robot Locomotion
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Robotic Cockroaches?
● Biomimetic robots mimic morphology or function observed in nature● Cockroaches identified as a model system for legged robots● Biomechanical measurements yield lessons for robot design
Sprawlita - Sean Bailey & Jonathan Clark, Stanford Biomimetics
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Ground Reaction Force Measurement
● Ground reaction forces show» How animal propels and stabilizes
itself
» Distribution of body weight during various phases of locomotion
» How the animal deals with obstacles and perturbations
» Transmission of muscle forces and torques through the skeleton or exoskeleton
● Our Goal: to measure both in-plane and normal ground reaction force components
Fx
Fy
Fz
z
y
x
Insect Leg GroundReaction Forces
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Scaling & Comparative Biomechanics
Cavagna – 1975, Full – 1989
Human:2 Legs
Dog:4 Legs
Roach:6 Legs
Crab:8 Legs
Spring-Loaded Inverted Pendulum model is a generally applicable
single-leg model for organisms of all sizes:ELEPHANT to COCKROACH
Grasso – 1998
Empirical Results: Human Walking
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Early Cockroach Data
Mesothoracic Leg Forces
ull, R.J., Blickhan, R., Ting, L.H., “Leg Design in Hexapedal Runners.” J. Experimental Biology 158, 369-390. 1991.
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Sensor Geometry & Features
Michael Bartsch
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Normal
Transverse
Axial
Flexure Design
• Normal Load Mid-flexure and
edge piezoresistors strained equally
• Transverse Load Edge piezo strain
due to bending
Mid-flexure resistor lies along neutral axis
Michael Bartsch
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Flexure Design
Normal
Transverse
Axial
• Normal Load Mid-flexure and
edge piezoresistors strained equally
• Transverse Load Edge piezo strain
due to bending
Mid-flexure resistor lies along neutral axis
Michael Bartsch
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P. americana Front Leg Forces
● Dual peak in normal forces observed in other larger organisms, not previously observed for roaches.
● Possibly indicates flexing of “thigh muscles” in mid-stride
● Lateral forces consistent with clockwise leg twist followed by ccw.
● Many more sets of data to analyze, each illustrating different details- 1
- 0 . 5
0
0 . 5
1
0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 1 0 . 1 2 0 . 1 4
T i m e ( s )
Flexure Lateral Force (mN)
B o t t o m L e f t
B o t t o m R ig h t
T o p R I g h t
-1 2-1 0
-8-6-4
-2
02
0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 0 .1 0 .1 2 0 .1 4
T im e (s)
Flexure Normal Force (mN)
B ottom Left
B ottom R ig h t
T op R ig h t
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Ant Front & Rear Leg Forces
• Average flexure and piezo sensitivity: 670V/N unamplified
• Min theoretical resolution on a 3kHz bandwidth: 14nN
• Visible chart features- Spike at initial claw
contact w. sensor- Dual peak in front
leg force- Rear leg drag
TL
BL
TR
BR
- 5 0
- 4 0
- 3 0
- 2 0
- 1 0
0
1 0
2 0
0 0 . 0 5 0 . 1 0 . 1 5 0 . 2 0 . 2 5
T i m e ( s )
Flexure Force (
N)
B o t t o m R i g h t F l e x u r e
T o p R i g h t
B o t t o m L e f t
T o p L e f t
F r o n t L e gS t e p
R e a r L e gS t e p
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Cockroach Carpenter Ant Fruit FlyBlaberus Camponotus Drosophila
discoidalis modici melanogaster
Animal
Length 5cm 10mm 2mm
Animal
Weight 30mN
Sensor
ElementArea
Maximum
Expected 300mNForceMinimum
Resolvable 10nN
RequiredSensitivity 1V/N 100V/N 10000V/N(0.1mV/Res.)MinimumMechanical 300Hz 1kHz 3kHzBandwidth
350µN 3µN
(5mm)2 (1mm)2 (200µm)2
3.5mN 30µN
100µN 1µNForce (Typ/50)
Estimated Measurement Requirements
Camponotusmodici
1cm
Drosophilamelanogaster
1mm
Sens
or P
erfo
rman
ceIn
sect
Blaberus discoidalis
Michael Bartsch, Bob Full
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Macroscopic Adhesion
● Geckos are known for their remarkable wall-climbing ability.
● Mechanism for adhesion is not well established.
● Microscopic structures are responsible for adhesion.
● Understanding can lead to inspirations for new artificial dry adhesive.
Tokay gecko
K. Autumn, Y. Liang, W.P. Chan, T. Hsieh, R. Fearing, T.W. Kenny, and R. Full
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● In fact, Geckos use NANOTECHNOLOGY for their adhesion capabilities
K. Autumn, Y. Liang, W.P. Chan, T. Hsieh, R. Fearing, T.W. Kenny, and R. Full
Macroscopic Adhesion
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January 21, 2000 - President Clinton announces $500M initiative on “nanotechnology”
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1 cm
Foot of a Gecko
Tokay Gecko
(Autumn, 2000)
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1 cm
Foot of a gecko
Array of Setae
75 µm(Autumn, 2000)
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75 µm
Array of setae
An Isolated Seta
20 µm(Autumn, 2000)
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Spatula-Shaped Tips
1 µm
20 µm
An isolated hair
(Autumn, 2000)
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(a)
1 cm
(a) the foot of a Tokay gecko
(c) an isolated seta (~φ5µm)
(c)
20 µm
(b) an array of tiny hair (setae)
(b)
75 µm
(d) spatula-shaped tips (~φ0.2µm)
(d)
1 µm
Structure of a Gecko Foot
Setae: [Ruibal, 1965]
~106 setae per animal Material: keratin ~100-1000 spatula-
shaped tips per seta
Kellar Autumn
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Adhesion Hypothesis
F ≈ 800nN/spatula ≈ 200µN /seta
Dense arrays of “spatulae” deform to match topology of opposing surface.
A small fraction actually are oriented to allow van der Waals adhesion.
If only ~2% of available spatulae is in real contact :
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Adhesive Development Opportunity
● Imagine an adhesive that can provide large attachment forces to all surfaces regardless of roughness, surface chemistry, or even moisture.
● Imagine that this adhesive can be easily cleaned after becoming dirty simply by pressing onto a clean surface a few times.
Goal - Identify the critical characteristics of the gecko adhesion structures, and explore ways to manufacture the same kinds of material.
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Our Gecko Measurement Plans
● Continue study of relationships between applied forces and adhesion force.
● Begin study of dynamics of adhesion.● Identify critical features that enable/enhance
adhesion.● Begin to try fabrication experiments and
measurements to develop an artificial adhesive.
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2-D Piezoresistive Force Sensing
[Ben Chui, 1997]
piezoresistive
conductiveVertical sensor
Lateral
sensor
45° ion implantation to embed piezoresistors on horizontal and vertical surfaces.
Forces resolved into 2 components
5 nN resolution, 5 kHz bandwidth
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Force Curve With Sliding
0 2 4 6 8 10-100
-50
0
50
100
150
200
Time (sec)
Sensor Output (µN)
Maximum Force
Typical Lateral Force Curve
Consistent measurements of adhesion near 200 µN
Maximum is reached through sliding of the setae across the surface
Sliding begins
Yiching Liang
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Does Moisture Help Adhesion?
61 1.42 41.3 Hydrophobic
70 1.10 40.4 Hydrophilic
Sample Sizeσ (µΝ)Mean (µΝ)Surface
• Surface water does not affect adhesion.
• Silicon oxide (hydrophilic)• Silicon (hydrophobic)
Yiching Liang, Su-Wen Ueng
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Preliminary Gecko Measurement Summary
● Adhesion Force consistent with vanderWaals effect.● Adhesion enhanced by sliding, regardless of speed.● Adhesion force mainly independent of humidity.● Adhesion effective underwater.● Adhesion not a strong function of surface
hydrophobicity.● Geckos walk through dirt - it normally takes about 5
steps for a gecko to recover adhesive capability after walking through graphite lubricant.
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Other Geckos
● Anoles setae are smaller and simpler.
» Easier to study and compare to theoretical values.
• Length: ~ 20-30 µm; density: ~ 106 setae/mm2.
• Each ends in a single tip.
anolis equestris
(Images by Kellar Autumn, Anne Peattie, and Juliann Chen)
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Other Natural Adhesive Examples
Assasin Bug - uses similar structures for manipulation
Photos by Kellar Autumn, Lewis + Clark College
QuickTimeª and aPhoto - JPEG decompressor
are needed to see this picture.
QuickTimeª and aPhoto - JPEG decompressor
are needed to see this picture.
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Overall Conclusions
● There are many opportunities for biological experiments with sensitive force measurements
● The applications range from opportunities for macro-scale bio-mimesis to the fundamental understanding of molecular biochemistry.
● It helps to be able to measure small forces, but there are many things that are very interesting at the larger scale.
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Acknowledgements
Colleagues:Dan RugarBarry StipeJohn MaminDave BotkinDoug ThomsonKoichi WagoHal JermanKellar AutumnBob FullJim SpudichJames NelsonMark CutkoskyMarkus Lutz
Students and Alumni : Aaron Partridge, Dr. T. Pfafman, Dr. K. Yasumura, J. Reynolds, J. Nerney, M. Bartsch, Dr. L. Zhang, O. Ajakaiye, R. Rudnitsky, Dr. A. Fitzgerald, Dr. J. Harley,Dr. J. Molho, Dr.Y. Liang, A. Herr, Dr. A. Barzilai, Dr. W. King, Dr. J. Grade, Dr. B. Chui, Dr. T. Stowe, Y. Hisunuma,Dr. E. Chow, A. Tewary, D. Laser, B. Pruitt
Funding from NSF, DARPA, Hertz Foundation, NSF Graduate Fellowship, NDSEG Fellowship, Terman Fellowship