3.052 Nanomechanics of Materials and Biomaterials Thursday 03/08/07 Prof. C. Ortiz, MIT-DMSE

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1 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE I LECTURE 9: QUANTITATIVE ASPECTS INTRA- AND INTERMOLECULAR FORCES Outline : LAST LECTURE : INTRODUCTION TO INTRA- and INTERMOLECULAR FORCES... BRIDGING TE GAP BETWEEN LENGT SCALES... 3 INTRA- AND INTERMOLECULAR POTENTIALS Review of Geneal Equations and LJ Potential... 4 Foms fo Diffeent Inteactions... 5 istoy and Pespectives... 6 Example : Chage -Dipole Inteaction... 7 Moe Complex Potentials and Additivity... 8 Binding Stengths and Equilibium Bond Lengths... 9 Objectives: To establish a quantitative famewok fo inta- and intemolecula foces Readings: Couse Reade documents 18-0, G. Malescio, "Intemolecula potentials- past, pesent, and futue" Natue Mateials, Multimedia : epain Biosenso Podcast; Monitoing of hepain and its low-molecula-weight analogs by silicon field effect, Nebojsa M. Milovic, Jonathan R. Beh, Michel Godin, Chih-Sheng Johnson ou, Kistofo R. Paye, Aathi Chandasekaan, Pete R. Russo, Ram Sasisekhaan, and Scott R. Manalis PNAS 006, 103, 36,

2 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE LAST LECTURE : INTRODUCTION TO INTRA- AND INTERMOLECULAR FORCES (within individual molecules) (between individual molecules) no eal physical diffeence -Definitions : Inteaction (moe geneal), foce (push o pull), bond (the attaction between atoms in a molecule o cystalline stuctue) all inta- and intemolecula foces ae electostatic in oigin key to life on eath (e.g. wate, cell membanes, potein folding, etc.), also mateials science (what holds matte togethe?). -stength measued elative to the themal enegy (oom tempeatue) : k B T= J : "ule" -Classifications; pimay o chemical, seconday o physical, and "special" -Biological systems and bottom-up self-assembly is based on the balance and inteplay of inta- and intemolecula foces. -Noncovalent inteactions allow fo dynamic systems, i.e. beaking evesible efoming bonds doesn't equie much enegy)/individually weak, foces ae cumulative stable in paallel. -Specific types of inta- and intemolecula foces; ionic, pola (e.g. -bonds), polaization, London dispesion, hydophobic (CR document 17) -Two examples (biological and synthetic) : noncovalent inteactions in folded poteins (human seum albumin) and selfassembling peptide amphiphiles (i.e. how chemical stuctue was designed ) Image emoved due to copyight estictions. Self assembly of peptide amphiphile molecule into a cylindical micelle. See Figue 1c in atgeink, et al. Science, 001 hieachical levels of potein stuctue-"native" and "denatued" atgeink, et al. Science, 001 See Review of Definitions fo Inte- and Inta-molecula foces

3 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE BRIDGING TE GAP BETWEEN LENGT SCALES -A typical inte- atomic, ionic, o intamolecula potential (e.g. LJ potential) 0.0 foce, f() (nn) Inteatomic o Intemolecula Sepaation Distance, (nm) A typical intesuface o intepaticle foce vs. sepaation distance cuve epulsive egime attactive egime 0 Tip-Sample Sepaation Distance, D (nm) k c Foce, F (nn) w() o U() f() (one atom, ion, o molecule) -1st step is to assume a mathematical fom of the potential W(D) F(D) (net inteaction between lage bodies, i.e. assemblies of atoms, ions, o molecules) D 3

4 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE REVIEW OF GENERAL EQUATIONS AND LENNARD JONES (LJ) POTENTIAL Inteatomic Potential o Bond Enegy (J o kbt) : -A B m n (1) -du() Inteatomic (Bond) Foce (nn): F() = = k()d () d -d U() df() Inteatomic (Bond) Stiffness (nn/nm) : k() = = (3) d d (nm)= inteatomic sepaation distance U() o w()= U attactive()+u epulsive()= + = - F()d A,B,m,n = constants detemined by the type of inteaction k -3 B = Boltzmann's constant = J/K T = absolute tempeatue (K) U ( m = 6, n = 1) = + =4E LJ LJ 7 -A B 6 1-6A 1B 13 F ( m=6, n=1) = + (5) B 1 6 σ σ - (4) E B = "binding enegy" o "bond dissociation enegy"; o depth of potential well s= distance at which U( s ) exhibits and inflection point, F( s )= minimum= FRUPTURE e = equilibium bond length = distance at which U( e )= minimum, F( e )= 0 =σ = distance at which U( )= 0, F( )= o o o w () (kbt) inteaction foce (nn) inteaction distance (nm) net o inteaction enegy (kj) A= Jm 6 B= Jm 1 epulsive E B e attactive -0.8 (nm)... Asymmetic o anhamonic potential, plotted in in...units of k B T s 4

5 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE FORMS OF INTERATOMIC / INTERMOLECULAR POTENTIALS Type of inteaction Schematic Inteaction Enegy, w() covalent, metallic -, chage-chage Cu Complicated, shot ange Cu + Q 1 Q QQ 1-1 w()= (Coulomb Enegy) u θ Q 4πε chage-dipole fixed dipole Qucosθ - u Q w()= - 4πε feely otating dipole Qu -4 w()= - φ ( ) dipole-dipole 6 4πε o kbt u 1 θ 1 θ u u u [ cosθ1cosθ sinθ1sin θ cos φ] w()= - fixed dipole 4πε o u u 1 u -6 w()= - feely otating dipoles 3( 4πε ) o kbt (Keesom Enegy) chage-induced dipole Q Q -4 w()= - ( ) 4πε dipole-induced dipole u θ u u ( 1+3cos θ) -6 w()= - ( ) 4πε fixed dipole feely otating dipole u -6 w()= - (Debye Enegy) induced dipole-induced dipole ( 4πε ) 3hν -6 O w()= - (London Dispesion) hydogen bond 4( 4πε o ) Complicated, shot ange, w() ~ - O O O 1-3 w() = inteaction fee enegy (J), Q = electic chage (C), u = electic dipole moment (C m), = electic polaizability (C m J -1 ), = distance between inteacting atoms o molecules (m), k B = Boltzmann's constant = J K -1, T = absolute tempeatue (K), h = Planck's constant = J s, ν = electonic absoption (ionization) fequency (s -1 ), ε o =dielectic pemittivity of fee space = C J -1 m -1. The foce is obtained by diffeentiating the enegy, w(), with espect to the distance,. (*Adapted fom Isaelachvili, Intemolecula and Suface Foces 199) 5

6 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE INTERMOLECULAR POTENTIALS: ISTORY AND PERSPECTIVE A eally inteesting aticle : "Intemolecula Potentials- past, pesent, futue" Gianpieto Malescio Natue Mateials 003,, Isaac Newton (1704) : Attaction between atoms -Roge Joseph Boscovich (1745) - 1st foce-distance cuve (qualitative) -Guiseppe Belli (1814) : fom expeimental data concluded ~1/ n -Maxwell, Van de Waals, Debye, London : - quantum mechanics/ coespondence with classical electostatics, inteactions between the electons and nuclei foming the molecules calculation equies solving the Schödinge equation fo a system of inteacting paticles. The enegy associated with the electonic motion is the potential enegy fo the motion of the nuclei, and can be egaded as the intemolecula (effective) inteaction potential. 6

7 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE SAMPLE POTENTIAL : CARGE - FIXED DIPOLE INTERACTION Qucosθ - w()= - (1) 4πε = chage-dipole sepaation distance (nm) u= electic dipole moment = ql (Cm) q= chage of dipole (C) l = sepaation distance between dipole chages(m) Q= chage of the ion (C) θ = dipole angle elative to hoizontal Chage Q=ze dipole moment = ql l/ +q θ 5 x W() (J) 0 +e +q -q θ (nm) 0.4 kt at 300 K -q l/ x Figue by MIT OCW. (*Fom Isaelachvili, Intemolecula and Suface Foces 199) 7

8 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE MORE COMPLEX POTENTIALS : ADDITIVITY w() VDW = w() oient + w() induced + w() dispesion (1) -u -6-6 Keesom Enegy : Feely otating dipole-feely otating dipole inteaction : w() oient = = C oient () 3kT(4πε o ) -u -6-6 Debye Enegy : Feely otating dipole- nonpola (induced dipole) inteaction : w() induced = = C induced (3) (4πε o ) -3hν -6-6 Dispesion Enegy : Induced dipole-induced dipole : w() dispesion = = C dispesion (4) 4(4πε o ) Biomolecula Adhesion : -contolled by bonds between molecula ligands and cell suface eceptos which exhibit the lock-n-key pinciple (e.g. biotin-steptavidin) complex, multiatomic, elatively weak fomed by an assembly of multiple, weak noncovalent inteactions (e.g. -bonding, coulombic, van de Waals, hydophilic / hydophobic, electostatic) complementay, steically-contained geometic consideations specificity Two images emoved due to copyight estictions. Coutesy of Bill Ross. Used with pemission. See Gubmülle, et al, Science 1996 (* and 8

9 3.05 Nanomechanics of Mateials and Biomateials Thusday 03/08/07 Pof. C. Otiz, MIT-DMSE BINDING STRENGT AND EQUILIBRIUM BOND LENGTS Inteaction Stength, kj/mol Stength, k B T dispesion hydophobic dipole-induced dipole TERMAL.5 1 ENERGY dipole-dipole 5 ion-ion bond lipid in bilaye 5 10 (hydophobic) cabohydate-lselection 6 5 biotin-avidin single covalent, C-C double covalent, C=C tiple covalent, C C Inteaction Inteaction Distance (nm) dispesion 0.35 hydophobic bonding 0.3 ion-ion 0.5 covalent Mateial metals ceamics and glasses semiconductos diamond wate inet gases solid salt cystals alkanes, hydocabons, flouocabons, amphiphiles in wate polymes/poteins Inteaction metallic covalent / ionic covalent / ionic covalent covalent, -bonding dispesion ionic hydophobic potentially alldepending on chemical stuctue 9