07: Intermolecular and surface forces
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1 Nanomanufacturing University of Michigan ME Winter : Intermolecular and surface forces February 3, 2010 John Hart hfp:// A.J. Hart 1
2 Announcements 2010 A.J. Hart 2
3 Recap: thermal proper>es Thermal energy in solids is carried by electrons and phonons Fourier s law (diffusive thermal transport) breaks down at small length scales and short Umes Like electrical conductance, there is a quantum unit of thermal conductance QuanUzed thermal conductance has been measured at VERY low temperatures in nanoscale structures, where the number of phonon modes is restricted BallisUc phonon transport occurs in sub- micron length CNTs Boundary scafering of phonons reduces thermal conducuvity and governs interface conductance this can be bad for contacts and good for thermoelectrics 2010 A.J. Hart 3
4 Course outline 0: IntroducUon to nanotechnology 1: ProperUes of nanostructures ( building blocks ) 2: InteracUons among nanostructures 3: Synthesis of nanostructures 4: Assembly of nanostructures and property scaling 5: Case studies and project presentauons Assignments: problem sets (4) exam (1), video assignment (1) project (1) 2010 A.J. Hart 4
5 2010 A.J. Hart 5
6 ~1 mm ~1 mm 2010 A.J. Hart 6
7 Pugno, J. Phys. Cond. MaF 19:395001, A.J. Hart 7
8 Today s agenda Origin of intermolecular and surface forces SummaUon of forces between solid bodies, based on pairwise interacuon potenuals CalculaUon of van der Waals forces and adhesion forces for regular geometries Methods of measuring surface forces Adhesion in nature 2010 A.J. Hart 8
9 Today s readings (ctools) Nominal: (on ctools) Israelachvili, excerpts from Intermolecular and Surface Forces Arzt et al., From micro to nano contacts in biological afachment devices Extras: (on ctools) Bishop et al., Nanoscale forces and their uses in self- assembly 2010 A.J. Hart 9
10 Forces hold the universe together Israelachvili A.J. Hart 10
11 Classifica>on of intermolecular forces Electrosta>c: Coulomb force between charges, and permanent dipole- dipole interacuons Polariza>on: Dipole moments induced in atoms by electric fields of nearby charges, and by permanent dipoles Quantum mechanical: give rise to chemical bonding Short- range: <1 nm (close to contact) Long- range: <100 nm Exponent on the force law is always > 3 (i.e., 1/r >3 ), else interacuon energy would increase for long distances and large bodies 2010 A.J. Hart 11
12 2010 A.J. Hart 12
13 Atomic, ionic, and molecular interac>ons Quantum mechanical (bonding) ElectrostaUc (charge- charge) PolarizaUon (charge- dipole, dipole- dipole) Israelachvili A.J. Hart 13
14 Quantum mechanical (exclusion) Israelachvili A.J. Hart 14
15 Defini>on of van der Waals (VDW) forces The afracuve or repulsive forces between molecular enuues (or between groups within the same molecular enuty) other than those due to bond formauon or to the electrostauc interacuon of ions (or ionic groups) with one another or with neutral molecules. The term includes: dipole dipole, dipole induced dipole and London (instantaneous induced dipole induced dipole) forces. The term is someumes used loosely for the totality of nonspecific a\rac>ve or repulsive intermolecular forces. Israelachvili; hfp://goldbook.iupac.org/v06597.html A.J. Hart 15
16 Lennard- Jones poten>al: neutral atoms or molecules repulsive - a\rac>ve Repulsive- afracuve balance = colloid stability hfp://en.wikipedia.org/wiki/lennard- Jones_potenUal 2010 A.J. Hart 16
17 Summing pairwise interac>ons Israelachvili A.J. Hart 17
18 2010 A.J. Hart 18
19 2010 A.J. Hart 19
20 2010 A.J. Hart 20
21 2010 A.J. Hart 21
22 2010 A.J. Hart 22
23 2010 A.J. Hart 23 Israelachvili. Sphere- plate (Langbein approxima>on) ( )( )( )( ) ) ( = n D n n n n R C D W ρ π D R C D W n 6 ) ( 6, 2 2 ρ π = =
24 Derjaguin approxima>on Israelachvili A.J. Hart 24
25 Derjaguin approxima>on F(Z), W(D) as derived for two planes D << (R1,R2) Applies to any force law Z = F ( D ) = 2πxdxf (Z ) Z =D x Z = D + z1 + z 2 = D R1 R2 1 1 dz = + xdx R1 R2 R1 R2 F ( D ) 2π f (Z )dz D R1 + R2 R1 R2 = 2π W ( D ) R1 + R2 Israelachvili A.J. Hart 25
26 Plane- plane versus sphere- sphere Equilibrium at points where force is zero (local minima of interacuon energy) Israelachvili A.J. Hart 26
27 VDW energies for regular geometries Israelachvili A.J. Hart 27
28 Hamaker constant How do we determine the pair potenual constant (C) for calculauons of total interacuon energy? 2010 A.J. Hart 28
29 Hamaker constants Israelachvili A.J. Hart 29
30 VDW- induced CNT deforma>on Hertel et al., Physical Review B 58(20):13870, A.J. Hart 30
31 MWNT telescoping bearings RelaxaUon Ume = nanoseconds VDW forces make this a constant- force spring Cumings, Science 289:602, A.J. Hart 31
32 Surface force apparatus (Israelachvili) Adjustment using interchangeable and variable- suffness springs Use opucal fringes to detect contact and measure separauon Calculate force knowing displacement and spring suffness SeparaUon controlled to 1 A Israelachvili A.J. Hart 32
33 Surface force apparatus (Israelachvili) Israelachvili A.J. Hart 33
34 (cap>ons for previous slides) Israelachvili A.J. Hart 34
35 Adhesion scaling in nature Artl et al., PNAS 100(19): , A.J. Hart 35
10: Electrosta7cs in solu7on
Nanomanufacturing University of Michigan ME599-002 Winter 2010 10: Electrosta7cs in solu7on February 15, 2010 John Hart ajohnh@umich.edu hdp://www.umich.edu/~ajohnh 2010 A.J. Hart 1 Announcements Video
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