1. 3.052 Nanomechanics of Materials and Biomaterials Prof. Christine Ortiz DMSE, RM 13-4022 Phone : (617) 452-3084 Email : cortiz@mit.edu WWW : http://web.mit.edu/cortiz/www LECTURE # 5 : EXPERIMENTAL ASPECTS OF HIGH-RESOLUTION FORCE SPECTROSCOPY II

2. 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

3. 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 experiment F=external force applied to cantilever (N)  we calculate from  k=cantilever “spring constant” = 3EI/L 3 (N/m)  we know independently E=Young’s (elastic) modulus of cantilever material (Pa) I=moment of inertia of cross-sectional area (m 4 ) L=cantilever length (m) force transducer sensitivity : k  k eff force detection limits : thermal noise limitation (*model force transducer as a free, 1-D harmonic oscillator) : 1/2 =  (k B Tk )  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

4. Cantilever Beam Theory F 0 L x   (max)

5.  <0  =0  >0 surface force sample surface repulsive attractive rest position (*NRL : http://stm2.nrl.navy.mil/how-afm/how-afm.html) Example of a Force Transducer : The Cantilever Beam

6. Fundamental Limit of Force Detection cantilever 

7. Stiffness Requirements for a Force Transducer : Force Sensitivity F=k  F s =k s  s k k s  FT=F=FsT=+sFT=F=FsT=+s sample surface FT,TFT,T

8. Displacement Detection : Optical Lever (Beam) Deflection Technique sample 4-quadrant position sensitive photodiode cantilever laser beam B CD V A+C -V B+D V A+ B -V C+D Lateral Force Microscopy (LFM) Normal Force Microscopy (NFM) A probe tip mirror

9. Displacement Detection : Optical Lever (Beam) Deflection Technique 4-quadrant position sensitive photodiode cantilever laser beam probe tip ZERO FORCE : mirror  =0 REPULSIVE FORCE :ATTRACTIVE FORCE : AB CD  >0 AB CD AB CD  <0

10. Displacement Control : How can we move something one nanometer at a time?

11. “Poling” of Piezoelectric Materials - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - +

12. Advantages and Disadvantages of Piezoelectic Materials

13. Displacement Control : Piezoelectric Tube Scanners voltage applied L L+  L electrodes connecting wires d +Y-X+X D D+  D polarization x y z +Z -Z ~ (*Digital Instruments “JV” PZT scanner)

14. Conversion of z-Displacement Data, z to Tip-Sample Separation Distance, D IN-CONTACT : ZERO FORCE OUT-OF-CONTACT : ATTRACTIVE FORCE sample piezo D  z sample piezo z  sample piezo IN-CONTACT : REPULSIVE FORCE

15. 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 mirror laser diode A B CD   10°-15° cantilever computer piezoelectric scanner probe tip z

16. 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)

17. 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 trapping potential trapping laser beam

18. 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.

19. Typical Force Versus Distance Curve on a Stiff Substrate RAW DATA Tip-Sample Separation Distance, D (nm) Force, F (nN) adhesion 0 repulsive regime attractive regime z-Piezo Deflection, z (nm) Photodiode Sensor Output, s (V) CONVERTED DATA jump-to-contact substrate compression no interaction 0 0 kckc