MOLECULE-PLANAR SURFACE INTERACTIONS-Motivation : Molecular Origins of BiocompatibilityCOLLOIDS : DEFINITION AND APPLICATIONSDERIVATION OF SPHERE-PLANAR SURFACE POTENTIALSPHERE-PLANAR SURFACE VDW INTERACTION AND HAMAKER CONSTANTANALYTICAL FORMULAS FOR VDW INTERACTIONS FOR OTHER GEOMETRIESCOLLOIDAL STABILITY : OTHER LONG RANGE FORCESCOLLOIDAL STABILITY: EFFECT ON DISPERSION3.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSEILECTURE 11: COLLOIDS AND INTERPARTICLE POTENTIALSOutline :LAST LECTURE : MOLECULE- PLANAR SURFACE INTERACTIONS....................................................2COLLOIDS : DEFINITIONS AND APPLICATIONS ...................................................................................3 DERIVATION OF SPHERE-PLANAR SURFACE POTENTIAL .................................................................4SPHERE-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 stabilityReadings: "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-DMSEMOLECULE-PLANAR SURFACE INTERACTIONS -Motivation : Molecular Origins of Biocompatibility-Calculation of the Net Potential for Interacting Bodies; Volume Integration Method; procedures and assumptions1) Choose the mathematical form of the interatomic/ionic/molecular potential, w(r) (e.g. assume an arbitrary power law : -nw(r)= -Ar)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 body4) 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, 5) Constant material properties :  and A are constant over the volume of the body→volume integration : ����W(D)= w(r) dVrGeometry : z = direction perpendicular to the sample surfaceD (nm) = normal molecule-surface separation distancex (nm) = direction parallel to sample surface = circular ring radius (m)A = infinitesimal cross-sectional area (m2) = dx dzV = ring volume (m3)= 2x (dxdz)N = # of atoms within the ring = 2x) dx dz = number density of atoms in the material constituting the surface (atoms/m3)r = distance from molecule to differential area( ) ( )p rrMOL-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( ) ( )�=�p rp rp rMOL-SFCn-3MOL-SFC3MOL-SFC4-2 AW(D) = n - 2 n - 3 D- ALondon Dispersion Interactions n = 6 ; W(D) = 6DW(D) - AF(D) = D 2D23.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSECOLLOIDS : DEFINITION AND APPLICATIONS Colloid; Definition : Particles that possess atleast one dimension 10 nm -1 m, usuallydispersed in a fluid medium, called a "colloidalsuspension" (e.g. smoke, paint, cosmetics, fog,dust, milk, blood, pharmaceutical powders)→contact area between particles and the dispersingmedium is large→interparticle surface forcesdetermine macroscopic behavior"Colloidal Inks"- highly concentrated, stable,dispersed colloidal suspension with appropriateviscoelastic properties so that it can flow through anozzle attached to a robotic set-up used to print3D structures. After the ink exits from the nozzle, itwill "set" via a fluid-to-gel transition induced by avariety of stimuli such as drying, pH, ionicstrength, or solvent quality. This involves theconcept of"percolation"- criticalvolume fraction abovewhich the system iscapable of sustaininga stress, continuouspathway throughentire material→processes final andmechanicalproperties tailoredby interparticlesurface 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-DMSEDERIVATION OF SPHERE-PLANAR SURFACE POTENTIAL , Vp pr p r p22 22Chord 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 spherePotential of each atom/moleculewith all atoms / molecules of planarsurface(D ) (2R )+ -�1 442 4 431 4 442 4 4 43r pp rz=2RSPHERE-SFC MOL-SFCz=0MOL-SFCn-3W(D) = W(D) z z zdz -2 AW(D) = n - 2 n - 3 DW(D( ) ( )( ) ( )( ) ( )2 2n 32 2n 32 2(2R )(D )2R(D )R-�--++��p rp rp rz=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 integral-2 A zdzW(D) = n - 2 n - 3 z-4 AW(D) =n - 2 n - 3 (n - 4)(n - 5)2 2DR6Dp rn-5- A n = 6 (VDW)=43.052 Nanomechanics of Materials and Biomaterials Thursday 03/15/07 Prof. C. Ortiz, MIT-DMSESPHERE-PLANAR SURFACE VDW INTERACTION AND HAMAKER CONSTANT2 26 3 1MOL SFC SPHERE SFC2