3.052 Nanomechanics of Materials and Biomaterials

3.052 Nanomechanics of Materials and Biomaterials

Prof. Christine OrtizDMSE, RM 13-4022

Phone : (617) 452-3084Email : cortiz@mit.edu

WWW : http://web.mit.edu/cortiz/www

LECTURE # 5 : EXPERIMENTAL ASPECTS OF

HIGH-RESOLUTION FORCE SPECTROSCOPY II

A Typical High-Resolution Force Spectroscopy

Technique : General Components

sample

I. high-resolution

force transducer

II. displacement

detection system

III. high-resolution

displacement control

computer• controls system

• performs data acquisition, display, and analysis

z

transducer displacement or deflection z displacement of sample normal to sample surface

REVIEW : LECTURE #2 :Experimental Aspects of High-Resolution Force

Spectroscopy I : The High-Resolution Force Transducer

• microfabricated cantilever beams and probe tips : deflect in response to an applied force (e.g. types, dimensions, attachments, material properties, cantilever beam theory)

• a force transducer or sensor can be represented by a linear elastic, Hookean spring :

F=k

=displacement at end of cantilever (m) we measure in force spectroscopy experimentF=external force applied to cantilever (N) we calculate from k=cantilever “spring constant” = 3EI/L3 (N/m) we know independentlyE=Young’s (elastic) modulus of cantilever material (Pa) I=moment of inertia of cross-sectional area (m4)L=cantilever length (m)

• force transducer sensitivity : kkeff

• force detection limits : thermal noise limitation (*model force transducer as a free, 1-D harmonic oscillator) :<Fm

2>1/2 = (k BTk ) <Fm 2>1/2~k

F

0

= k

F

F

How do we measure such small forces (i.e. nN or pN) ? High Resolution Force Sensor or Transducer that is : 1) soft and 2) small

Cantilever Beam TheoryF

0L

x

(max)

<0=0>0

surface forcesample surface

repulsive

attractive

restposition

(*NRL : http://stm2.nrl.navy.mil/how-afm/how-afm.html)

Example of a Force Transducer :The Cantilever Beam

Fundamental Limit of Force Detection

cantilever

Fs=-k(t)

forced oscillation :Fa(t)=Fmcos(’t-)

oscillating

Fd=-’(t)

m

m

F

Fm

Fm

m

Stiffness Requirements for a Force Transducer :

Force Sensitivity

F=k

Fs=kss

k

ks

FT=F=Fs

T=+s

sample surface

FT,T

Displacement Detection : Optical Lever (Beam) Deflection

Technique

sample

4-quadrantposition sensitive

photodiode

cantilever

laser beam

B

C D

VA+C-VB+D

VA+ B-VC+D

Lateral Force Microscopy

(LFM)

Normal Force Microscopy

(NFM)

A

probe tip

mirror

Displacement Detection : Optical Lever (Beam) Deflection

Technique4-quadrant

position sensitivephotodiode

cantilever

laser beam

probe tip

ZERO FORCE :mirror

=0

REPULSIVE FORCE :

ATTRACTIVE FORCE :

A BC D

>0

A BC D

A BC D

<0

Displacement Control :How can we move something one nanometer

at a time?

“Poling” of Piezoelectric Materials

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Advantages and Disadvantages of Piezoelectic Materials

Displacement Control :Piezoelectric Tube Scanners

voltageapplied

L

L+L

electrodes

connecting wires

d

+Y -X +X

D

D+D

polarization

x

yz

+Z

-Z

~

(*Digital Instruments “JV” PZT scanner)

Conversion of z-Displacement Data, z to

Tip-Sample Separation Distance, DIN-CONTACT :ZERO FORCE

OUT-OF-CONTACT :ATTRACTIVE FORCE

sample

piezo

D

z

sample

piezo

z

sample

piezo

IN-CONTACT :REPULSIVE

FORCE

Atomic Force Microscope (AFM)* :General Components and Their Functions

(*Binnig, G.; Quate, C. F.; Gerber, Ch. Phys. Rev. Lett. 1986, 56 (9), 930-933)

sample

sensor output F

position sensitive photodetector

mirrorlaser diode A BC D

10°-15°

cantilever

computer

piezoelectric scanner

probe tip

z

Surface Forces Apparatus :(*Israelachvili, J.N., et al. J. Chem. Soc. Faraday Trans. 1978, 74, 975.)

New surface forces apparatus (SFA Mk III) for measuring the forces between two molecularly smooth surfaces. Mk III employs four distance controls instead of three as in Mk II. The four

controls are: micrometer, differential micrometer ,different spring and piezoelectric tube. The mica surfaces are glued to cylindrical support disks of radius R and positioned in a crossed

cylinder geometry. The lower surface is mounted on a variable-stiffness double-cantilever force-measuring spring within the lower chamber and is connected to the upper (control) chamber via a

Teflon bellows.

(http://squid.ucsb.edu/~sfalab/mark-III.html)

Optical Tweezers(*Ashkin, et al. Phys. Rev. Lett.1985, 54, 1245.)

(*http://www.embl-heidelberg.de/CellBiophys/LocalProbes) (*http://atomsun.harvard.edu/~tweezer/2j.jpg)

objective lens

cover

slip

trapped

particle

~m

3D trappi

ng potenti

al

trappinglaser beam

Biomembrane Surface Probe(*R. MERKEL*†, P. NASSOY*‡, A. LEUNG*, K. RITCHIE* & E. EVANS*§ Nature 397, 50 - 53 (1999))

microsphere probe

force transducerpressurized glass pipet

Vertical Assembly- The epi-illuminated microscope images the nanoscale positional changes of the probe microsphere. Light from arc clamp D is made monochromatic though filter F1 and linearly polarized through polarizer P1. The light travels to objective E to reflect from the sample container and probe microsphere is recollected by the objective. An analyzer polarizer P2 enhances image contrast before imaging by camera C and digitization and analysis by computer A. Simultaneously computer A using feedback from the analyzed image controls the high voltage power supply B that drives piezo element F and hence controls the probe assembly position above the sample.

Typical Force Versus Distance Curveon a Stiff Substrate

RAW DATA

Tip-Sample Separation Distance, D (nm)

Forc

e,

F (

nN

)

adhesion

0

repulsiveregime

attractive regime

z-Piezo Deflection, z (nm)

Ph

oto

dio

de

Sen

sor

Ou

tpu

t, s

(V

) CONVERTED DATA

jump-to-contact

substrate compression no interaction

0 0

kc