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 #9 : QUANTITATIVE TREATMENT OF INTRA- AND INTERMOLECULAR FORCES

2. Review : Lecture #4 Experimental Aspects of Force Spectroscopy III : I. Comparison of high-resolution force spectroscopy techniques : atomic force microscopy (AFM), surface forces apparatus (SFA), optical tweezers (OT), biomembrane surface probe (BSP) II. Conversion of raw data in a high-resolution force spectroscopy experiment : sensor output, s  transducer displacement,   force, F z-piezo deflection, z  tip-sample separation distance, D III. Typical force spectroscopy data for a weak cantilever on stiff substrate (k sample >>k cantilever ) : APPROACH : (*sample and tip come together) A: tip and sample out of contact, no interaction, cantilever undeflected, zero force (set F=0) B/C: attractive interaction pulls tip down to surface and tip jumps to contact, cantilever exhibits mechanical instability D: contact, constant compliance regime, no sample indentation, tip and sample move in unison (  s/  z=1) RETRACT :(*sample and tip move apart) D: repulsive contact, constant compliance Regime, tip deflected up E: attractive force (adhesion) keep tip attached to surface, tip deflected down F: tip pulls off from surface, cantilever instability G: same as region A  s/m F=k  D=z  A B/C D D E F G A DD E F G Adhesive Interaction

3. Types of Intra- and Intermolecular Interactions in Different Materials

4. Biomolecular Adhesion controlled by bonds between molecular “ligands” and cell surface “receptors” which exhibit the “lock-n-key principle” (e.g. biotin-streptavidin) complex, multiatomic, relatively weak formed by an assembly of multiple, weak non-covalent interactions (e.g. H-bonding, coulombic, van der Waals, hydrophilic / hydrophobic, electrostatic) complementary, sterically-contrained geometric considerations specificity Grubmüller, et al, Science 1996 (*http://www.mpibpc.g wdg.de/abteilungen/ 071/strept.html) (*http://www.am ber.ucsf.edu/ambe r/tutorial/streptav idin/index.html)

5. BRIDGING THE GAP BETWEEN LENGTH SCALES r(nm) Tip-Sample Separation Distance, D (nm) Force, F (nN) 0 kckc

6. Characterizing an Individual Intra- and Intermolecular Interaction interaction force (electromagnetic in origin) (nN) interaction distance (nm) interaction energy (kJ/mol)

7. Characterizing an Individual Intra- and Intermolecular Interaction interaction force (electromagnetic in origin) (nN) interaction distance (nm) interaction energy (kJ/mol)

8. Steric Repulsion Interaction Potentials Soft RepulsionHard-Core Repulsion n=   Soft Repulsion B=10 -134 Jm 12 n=12 Due to overlap of negatively charged electron clouds (e.g. Pauli Exclusion principle) and (+) charged nuclei, quantum mechanical in origin; “short-range”, i.e. takes place over the order of distances of bond lengths ~0.1 nm

9. Attractive Interaction Potentials A=10 -77 Jm 6 m=6 London dispersion interaction longer range > ~1 nm A is a constant determined by the polarizability or ease of distortion of electron cloud

10. Net or Complete Interaction Potential : The Lennard-Jones or “6-12” Potential r(nm)

11. Interaction Strength EBEB

12. Equilibrium Interaction Distance, r e rere r (nm) rere r e ’>r e

13. Force Profile for The Lennard-Jones or “6-12” Potential r(nm) roro rere rsrs F rupture

14. More Complicated Interaction Potentials Grubmüller, et al, Science 1996 (*http://www.mpibpc.gwdg.de/abteilungen/071/strept.html) R. MERKEL*†, P. NASSOY*‡, A. LEUNG*, K. RITCHIE* & E. EVANS*§, Nature 397, 50 - 53 (1999)