MOLECULE-PLANAR SURFACE INTERACTIONS -Motivation : Molecular Origins of Biocompatibility COLLOIDS : DEFINITION AND APPLICATIONS DERIVATION OF SPHERE-PLANAR SURFACE POTENTIAL SPHERE-PLANAR SURFACE VDW INTERACTION AND HAMAKER CONSTANT ANALYTICAL FORMULAS FOR VDW INTERACTIONS FOR OTHER GEOMETRIES COLLOIDAL STABILITY : OTHER LONG RANGE FORCES COLLOIDAL STABILITY: EFFECT ON DISPERSION3.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 11: COLLOIDS AND INTERPARTICLE POTENTIALS Outline : LAST LECTURE : MOLECULE- PLANAR SURFACE INTERACTIONS ................................................... 2 COLLOIDS : DEFINITIONS AND APPLICATIONS .................................................................................. 3 DERIVATION OF SPHERE-PLANAR SURFACE POTENTIAL ................................................................ 4 SPHERE-PLANAR SURFACE VDW INTERACTIONS AND HAMAKER CONSTANT ............................ 5 ANALYTICAL FORMULAS FOR VDW INTERACTIONS FOR OTHER GEOMETRIES ........................... 6 COLLOIDAL STABILITY ........................................................................................................................7-8 Other Long Range Forces........................................................................................................ 8 Effect on Dispersion................................................................................................................. 8 Objectives: To derive mathematically the sphere-surface potential and to understand other long-range interparticle forces and how they determine colloidal stability Readings: "Colloidal Processing of Ceramics", J. A. Lewis, J. Am. Ceram. Soc. 83 (10) 2341-59. 2000 (Posted on Stellar). Multimedia : Podcast : Briscoe, et al. Nature 2006 444, 191 - 194. It can wait until Spring Break if you want→won't be covered on exam, but will be on next pset which will be due a week or so after Spring break. MIDTERM: Everything up through today's lecture will be covered on exam. 13.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSE MOLECULE-PLANAR SURFACE INTERACTIONS -Motivation : Molecular Origins of Biocompatibility -Calculation 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. assume an arbitrary power law : ) -nw(r)= -Ar2) 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) dVρ 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 area ()()πρρMOL-SFCn-3-2 AW(D) = n-2 n-3 Dn= determined by the type of interaction; related to the range of the interactionA= molecular level parameter; related to strength of the interaction= atomic density ()()∂=∂πρπρπρMOL-SFCn-3MOL-SFC3MOL-SFC4-2 AW(D) = n-2 n-3 D-ALondon Dispersion Interactions n= 6 ; W(D) = 6DW(D) - AF(D) = D2D 23.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSE COLLOIDS : DEFINITION AND APPLICATIONS Colloid; Definition : Particles that possess at least one dimension 10 nm -1 μm, usually dispersed in a fluid medium, called a "colloidal suspension" (e.g. smoke, paint, cosmetics, fog, dust, milk, blood, pharmaceutical powders)→ contact area between particles and the dispersing medium is large→interparticle surface forces determine macroscopic behavior "Colloidal Inks"- highly concentrated, stable, dispersed colloidal suspension with appropriate viscoelastic properties so that it can flow through a nozzle attached to a robotic set-up used to print 3D structures. After the ink exits from the nozzle, it will "set" via a fluid-to-gel transition induced by a variety of stimuli such as drying, pH, ionic strength, or solvent quality. PercolationPercolation This involves the concept of "percolation"- critical volume fraction above which the system is capable of sustaining a stress, continuous pathway through entire material→ processes final and mechanical properties tailored by interparticle surface forces SEM images of 3D Periodic structures composed of colloidal "building blocks." New applications : -Tissue Engineering -Advanced Ceramics -High performance Composites (Smay, et al. Langmuir 2002, 18, 5429) 33.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSE DERIVATION OF SPHERE-PLANAR SURFACE POTENTIAL z=2Rplanar surface spherez=Rz=0dzzxxzDD+z'2R-zR,Vππρπ ρπ2222Chord Theorum = x = (2R - z)zArea = x olume = x dzN= number of atoms = x dz = (2R - z)zdz (*http://wintermute.chemie.uni-mainz.de/coll.html) ()()number of atoms in spherePowith all atoms / molecules of planarsurface-2 Atential of each atom/molecule(D ) (2R )+−∫  ρππρSPHERE-SFC MOL-SFCz=0MOL-SFCn-3W(D) = W(D) z z zdz W(D) = n-2 n-3 DW(D()()z=2R()()()()22n322n322(2R )(D )2R(D )R−∞−−++∫∫πρπρπρz=2RSPHERE-SFCz=0z=SPHERE-SFCz=0SPHERE-SFC-2 A z zdz)= n-2 n-3 zFor D << R, only small values of z contribute to the inte gral-2 A zdzW(D) = n-2 n-3 z-4 AW(D) =n-2 n-3