BRIDGING THE GAP BETWEEN LENGTH SCALES MOLECULE-SURFACE INTERACTIONS : MOLECULAR ORIGINS OF BIOCOMPATIBILITY CALCULATION OF THE NET POTENTIAL FOR INTERACTING BODIES : VOLUME INTEGRATION METHOD : PROCEDURES AND ASSUMPTIONS \INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: GEOMETRYINTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: DERIVATION INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: DERIVATION INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: DERIVATION3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 1I LECTURE 10: MOLECULE-SURFACE INTERACTIONS Outline : LAST LECTURE : BRIDGING THE GAP BETWEEN LENGTH SCALES ................................................. 2 MOLECULE-SURFACE INTERACTIONS: MOLECULAR ORIGINS OF BIOCOMPATIBILITY................ 3 CALULATION OF THE NET POTENTIAL FOR INTERACTING BODIES .............................................4-8 Volume Integration Method : Procedures and Assumptions................................................ 4 Molecule-Surface Interactions...........................................................................................5-8 Geometry................................................................................................................ 5 Derivation 1 ............................................................................................................ 6 Derivation 2............................................................................................................. 7 Dispersion, London................................................................................................. 8 Objectives: To mathematically scale up intermolecular potentials to intersurface and interparticle potentials Readings: Course Reader documents 22 & 23, also reading posted on Supplementary Materials Section, Israelachvili, Chapter 10. Multimedia : Bonding and Protein Structure Demo (California Lutheran University), link on Stellar.3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 2BRIDGING THE GAP BETWEEN LENGTH SCALES -A typical inter- atomic, ionic, or intamolecular potential (e.g. LJ potential) -0.04-0.03-0.02-0.0100.010.020 0.2 0.4 0.6 0.8 1Interatomic or Intermolecular Separation Distance, r(nm)force, f(r) (nN) → A typical intersurface or interparticle force vs. separation distance curve Tip-Sample Separation Distance, D (nm)Force, F (nN)repulsiveregimeattractive regime0kc w(r) or U(r) → f(r) (one atom, ion, or molecule) -6w(r)= -Ar rr W(D) → F(D) (net interaction between larger bodies, i.e. assemblies of atoms, ions, or molecules) D3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 3MOLECULE-SURFACE INTERACTIONS : MOLECULAR ORIGINS OF BIOCOMPATIBILITY BLOOD PRESSURE+ATTRACTIVE FORCESdenaturesPLATELETS!http://www.rinshoken.or.jp/org/CR/photo-e.htmSolid-Liquid Interfaceblood plasma proteinsBLOOD FLOWBIOMATERIAL SURFACEBLOOD CLOT!-acute occlusive thrombosis- infection / inflammation- neointimal hyperplasiaD. Gregory http://medphoto.wellcome.ac.ukadsorbs BLOOD PRESSURE+ATTRACTIVE FORCESdenaturesdenaturesPLATELETS!http://www.rinshoken.or.jp/org/CR/photo-e.htmSolid-Liquid Interfaceblood plasma proteinsBLOOD FLOWBIOMATERIAL SURFACEBLOOD CLOT!-acute occlusive thrombosis- infection / inflammation- neointimal hyperplasiaD. Gregory http://medphoto.wellcome.ac.ukadsorbs3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 4CALCULATION OF THE NET POTENTIAL FOR INTERACTING BODIES : VOLUME INTEGRATION METHOD : PROCEDURES AND ASSUMPTIONS 1) Choose the mathematical form of the interatomic/ionic/molecular potential, w(r) (e.g. in this case we will use an arbitrary power law : nAw(r)= - r) 2) Set up the geometry of the particular interaction being derived (e.g. molecule-surface, particle-surface, particle-particle, etc.) 3) Assume "pairwise additivity"; i.e. the net interacion energy of a body is the sum of the individual interatomic/intermolecular interactions of the constituent atoms or molecules which make up that body 4) A solid continuum exists : the summation is replaced by an integration over the volumes of the interacting bodies assuming a number density of atoms/molecules/m3, ρ 5) Constant material properties : ρ and A are constant over the volume of the body ↓ volume integration •∫∫∫W(D)= w(r) dVρ3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 5\INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: GEOMETRY r=(z2+x2)1/2zplanar surface atom or moleculedxdzz=0z=Dx=0vxr=(z2+x2)1/2zplanar surface atom or moleculedxdzz=0z=Dx=0vxzplanar surface atom or moleculedxdxdzdzz=0z=Dx=0vx Geometry : z = direction perpendicular to the sample surface D (nm)= normal molecule-surface separation distance x (nm) = direction parallel to sample surface = circular ring radius (m) A = infinitesimal cross-sectional area (m2) = dx dz V = ring volume (m3)= 2πx (dxdz) N = # of atoms within the ring = ρ (2πx) dx dz ρ = number density of atoms in the material constituting the surface (atoms/m3) r = distance from molecule to differential area3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 6INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: DERIVATION r=(z2+x2)1/2zplanar surface atom or moleculedxdzz=0z=Dx=0vxr=(z2+x2)1/2zplanar surface atom or moleculedxdzz=0z=Dx=0vxzplanar surface atom or moleculedxdxdzdzz=0z=Dx=0vxnAw(r)= - (1)r Substitute (2) into (1) : 22r= z +x (2) ()/2n22Aw(r)= - (3)z+x Net Interaction Energy : •∫∫∫W(D)= w(r) dVρ N()∞∞∫∫  ρπpotential of number of moleculeseach molZ= x=Z=Dclxe0ue=W(D)= w(r) 2 x dz dx (4) substitute (1) → (2) ()()/2∞∞∫∫ρπZ= x=n22Z=D x=0AW(D)= - 2 x dzdx (5)z+x3.052 Nanomechanics of Materials and Biomaterials Tuesday 03/13/07 Prof. C. Ortiz, MIT-DMSE 7INTERACTION POTENTIAL BETWEEN AN ATOM / MOLECULAR AND SURFACE: DERIVATION r=(z2+x2)1/2zplanar surface atom or