SINGLE MOLECULE ELASTICITY OF TITIN (AFM) & DNA (OPTICAL TWEEZERS) - Structure and physiological role of Titin (Rief, et al. CHEMPHYSCHEM 2002, 3, 255-261)→sawtooth force profilesINTRODUCTION TO NANOINDENTATION NANOINDENTATION : INDENTER GEOMETRIESNANOINDENTATION : TYPES OF DEFORMATION OLIVER-PHARR ANALYSIS: GEOMETRIC SET-UP Linear Elastic, Isotropic, Continuum Contact Mechanics Theory (Oliver and Pharr, 1992 JMR, 7(6) 1564) : Geometry set-up and definitions of geometric parameters : assumes "sink-in"OLIVER-PHARR ANALYSIS : MATHEMATICAL FORMULATION (Oliver and Pharr, 1992 JMR, 7(6) 1564) APPENDIX : DETAILED GEOMETRY OF INDENTERS 1 APPENDIX : DETAILED GEOMETRY OF INDENTERS 2 APPENDIX : DETAILED GEOMETRY OF INDENTERS 3 (Do Kyung Kim, KAIST) APPENDIX : BERKOVICH GEOMETRY CALCULATION OF CONTACT AREA APPENDIX : OLIVER-PHARR CITATIONS APPENDIX : NANOINDENTATION INSTRUMENTATION3.052 Nanomechanics of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 22: THEORETICAL ASPECTS OF NANOINDENTATION Outline : REVIEW LECTURE #21 : EXPERIMENTAL SINGLE MACROMOLECULE ELASTICITY........................ 2 NANOINDENTATION .............................................................................................................................3-7 Introduction ............................................................................................................................. 3 Indenter Geometries................................................................................................................ 4 Types of Deformation .............................................................................................................. 5 Oliver-Pharr Analysis : Geometric Set-Up .............................................................................. 6 Oliver-Pharr Analysis :Mathematical Formulation.................................................................... 7 APPENDIX............................................................................................................................................8-13 Detailed Geometry of Indenters..........................................................................................8-10 Berkovich Contact Area......................................................................................................... 11 Oliver-Pharr Citations ............................................................................................................ 12 Nanoindentor Instruments ..................................................................................................... 13 Objectives: To understand general theoretical formulations for reducing material properties from nanoindentation experiments Readings: Course Reader Documents 45 (one of the most cited papers in Materials Science)-46, Additional Historical Ref (posted on stellar's Supplementary Materials) : Sneddon 1965 Int. J. Engng. 3, 47-57. 13.052 Nanomechanics of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE SINGLE MOLECULE ELASTICITY OF TITIN (AFM) & DNA (OPTICAL TWEEZERS) - Structure and physiological role of Titin (Rief, et al. CHEMPHYSCHEM 2002, 3, 255-261)→sawtooth force profiles Force (pN)Distance (μm)inextensible WLCB-formLcontourextensible WLCoverstretching transitionΒ-form S-formstretchedS-formLcontourI.II.III.IV.Biological Relevance of Overstretching Transition? Ability to switch between different structures is critical to the processes of transcription, replication, condensaton, e.g. the base pairs are much more exposed in S-DNA than normal DNA, the transition may be biologically significant for accessing information contained in the DNA code (Bustamante, et al. Science 1999, 271, 795) I. low stretched behaves like WLC (p ≈ 50 nm under physiological conditions, much larger than most polymers ~ 1nm, hence much smaller forces, need optical tweezers) II. intermediate stretches -some extensibility as apparent by finite slope beyond Lcontour (B-form) III. At 65 pN ~ 0.06 nN, reversible strain-induced conformational transition; chain "yields" and stretches out almost 2× its native B-form contour length at relatively constant force (plateau in force region) -All of hydrogen bonding and binding between 2 strands is still in tact, tilting of base pairs, tightened helix, reduction in diameter "overstretching transition" IV. entropic elasticity of S-form V. can't see here - if you go to high enough stretches, separation between strains (mechanical "melting") 23.052 Nanomechanics of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE INTRODUCTION TO NANOINDENTATION Definition : Controlled compression and decompression of a probe tip into a sample surface while measuring force (load, P) versus indentation displacement or depth, h (nm-scale) continuously → probe tip is relatively rigid compared to the sample → can measure mechanical properties (e.g. modulus, hardness) on areas nm-μm scale; e.g. thin films and small volume structures → called "nano" since the indentation depth is of nanometer scale, however lateral contact areas and forces can be > nanoscale -multiaxial deformation Pmaxhmaxainitial surfaceindentersurface profile at PmaxAFM-based Indentation Tip-Sample Indentation Depth or Separation Distance, D (nm)Force, F (nN)00adhesionsurface forcescontact forcesjump-to-contactloadingunloading -e.g. silicon or silicon nitride indenter probe on a cantilever force transducer -cantilever oriented at an angle to the surface (~11°) -indenter geometries, e.g. pyramidal (less well defined) -load range ~ nN-mN, smaller contact radii ~ 10s of nm Instrumented or Depth-Sensing Indentation (DSI) Load, PIndentation Depth, hPmaxhmaxloadingunloadingLoad, PIndentation Depth, hPmaxhmaxloadingunloading (Hysitron, Micromaterials, Appendix→extension of conventional hardness testing to smaller length scale) - diamond indenter - indenter oriented perpendicular to the surface - variable indenter geometries; Berkovich, cube corner, etc. - load range ~ μN-mN, larger contact radii ~ μm 33.052 Nanomechanics of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE NANOINDENTATION : INDENTER GEOMETRIES AFM-Based Indentation Side and back viewFront view120º33º29º~18 μm~18 μm56º18º18º33º33º~9 μm~9 μmBottom viewab29º~10 μm50