LAST TIME : WHAT IS NANOMECHANICS?→subset of the field of nanotechnology, involving nN-scale forces or nm-scale displacements (nano=1●10-9) HOW CAN WE MEASURE SUCH TINY FORCES? EXAMPLE OF A FORCE TRANSDUCER- Microfabricated Cantilever Beams With Nanosized Probe Tips3.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE I LECTURE 2 : THE FORCE TRANSDUCER Outline : LAST TIME : WHAT IS NANOMECHANICS.............................................................................................. 2 HOW CAN WE MEASURE SUCH TINY FORCES?.................................................................................. 3 EXAMPLE OF A FORCE TRANSDUCER ................................................................................................. 4 Microfabricated cantilever beams with nanosized probe tips.................................................................. 5 Attachments to nanosized probe tips...................................................................................................... 6 CANTILEVER BEAM THEORY ................................................................................................................. 7 LIMIT OF FORCE DETECTION : THERMAL OSCILLATIONS ................................................................. 8BIOSENSORS ........................................................................................................................................... 9 Objectives: To understand the basic principles of how high resolution force transducers function, their physical limitations, and applications. Readings: Course Reader Documents 6-8 Multimedia : Listen to IntroductoryPodcast mp3 at : http://web.mit.edu/cortiz/www/Nanonewton.html 13.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE LAST TIME : WHAT IS NANOMECHANICS?→subset of the field of nanotechnology, involving nN-scale forces or nm-scale displacements (nano=1●10-9) 1. Noncontact : High Resolution Force Spectroscopy, surface forces measurement (e.g. electrostatics, van der Waals forces, etc.) 2. Contact : Nanoindentation, single cell tensile testing (e.g. elasticity, plasticity, → dislocations) etc. interaction force, F(r) (nN)Interaction distance, (r) (nm)interaction force, F(r) (nN)Interaction distance, (r) (nm) 0.5 μm0.5 μm8 μm 0.9 μmc-axis The study of forces, motions, energies, and deformations : much of 3.032 was continuum mechanics 23.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE HOW CAN WE MEASURE SUCH TINY FORCES? i.e. nN (=1•10-9 N), even pN (=1•10-12 N) ! → typical engineering structures are Newtons Separation distance ~ nmInteraction force ~ nN Force Transducer- sensor device that responds to an external force where you can output and record that response Transducer Calibration - determine the relationship between the externally applied force and output signal to automatically convert to a force 1) high sensitivity and 2) small in dimensions, fine probe (~ nm) δsample ● Typically a spring (not conventional!) which deflects in response to a external force, δ= transducer (spring displacement), know the elastic properties (stiffness) of the spring (i.e. Hooke's Law) you can convert into force, F. F= kδ 33.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE EXAMPLE OF A FORCE TRANSDUCER- Microfabricated Cantilever Beams With Nanosized Probe Tips Typical Values :b= 150 μmθ=35oL=200 μmL1=150 μmt =0.6 μmd = 18 mm top viewL1bdd2θLt2θbcantileverprobe tipside viewtop viewL1bdd2θLt2θbcantileverprobe tipside view The Millipede Vettiger, et al. IBM J. Res. Develop. 44 3 2000 323 Potential Applications : 1) thermomechanical data storage in thin polymer media -High throughput 2) imaging/characterization 3) nanolithography 4) atomic and molecule manipulations 43.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE ATTACHMENTS TO NANOSIZED PROBES AT THE END OF MICROFABRICATED CANTILEVERS Single Cell Dictyostelium Discoideum (Benoit, et al. Nature Cell. Bio 2000, 2 (6), 313.) Colloid : Seog, Ortiz/ Grodzinsky Labs 2001 E. Coli Bacteria Ong, et al. Langmuir 1999, 15, 2719. Nanotube Tips : Yenilmez, et al. Applied Phys. Lett.. 80, 12 2002 2225 Nanotube Tips (Biomolecule Functionalized) : Wong et al. Nature 1998, 394 (6688), 52. 53.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE CANTILEVER BEAM THEORY 0Lxδ(max) 63.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE CANTILEVER BEAM THEORY (CONT'D) 0Lxδ(max) 73.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE LIMIT OF FORCE DETECTION : THERMAL OSCILLATIONS cantileverδ In the absence of any externally applied forces [e.g. far away from the cantilever surface], a high resolution force tranducer will oscillate at its natural resonant frequency (maximum displacement of the amplitude of the oscillations) due to a non-zero thermal energy, kBT (room temperature)= 4.1 ● 10-21 J → the system can be modeled as a driven, damped harmonic oscillator. These oscillations are the background noise in the nanomechanical experiment and are given by the following equation : ()()1/21/4⎛⎞ρ⎜⎟⎝⎠1/2min BwF= 1.007t E k TblQ Fs=-kδ(t)forced oscillation :Fa(t)=Fmcos(ω’t-φ)oscillatingFd=-βδ’(t)δο−δm+δmFο−Fm+FmmFs=-kδ(t)forced oscillation :Fa(t)=Fmcos(ω’t-φ)oscillatingFd=-βδ’(t)δο−δm+δmFο−Fm+Fmm 83.052 Nanomechanics of Materials and Biomaterials Thursday 02/08/06 Prof. C. Ortiz, MIT-DMSE FORCE RANGE FOR VARIOUS NANOMECHANICAL INSTRUMENTS micropipette aspirationmicroneedlesnanoindentationoptical & magnetic tweezerssurface forces apparatus10-1510-14 10-13 10-1210-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3fN pN nN μNmNatomic force microscopy / high resolution force spectroscopybiomembrane force
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