! Features of van ! Features of van der der Waals Waals Force Force ! Sphere Near a Plane ! Sphere Near a Plane ! Cylinder near a Flat Plate ! Cylinder near a Flat Plate ! Interfaces ! Interfaces ! Hamaker ! Hamaker Constants Constants ! Hamaker ! Hamaker Constants for Dissimilar Constants for Dissimilar Materials Materials ME 437/537 Ahmadi ME 437/537 Ahmadi d Interaction Energy Interaction Energy ! Generally Attractive ! Generally Attractive z ! Short Range ! Short Range A 1 1 x z φ = − + + x = [ 2 ln ] + + 12 x 1 x 1 x d ! Origin in Atomic Dipole ! Origin in Atomic Dipole Range of Application A=Hamaker Const. Range of Application A=Hamaker Const. Ad Ad z < z → φ ≈ − ~ 0 . 2 d 0 12 kT 12 z ME 437/537 Ahmadi ME 437/537 Ahmadi 1
van der Surface Added Drag/Lift Basset × 8 × 8 Particle Surface F 10 N F F 10 N ν Waals Tension Mass ν ν F ν (air) (water) πµ 3 dU πµ 3 dU d dV Diameter µ πγ ρ ρ 3 f 2 2 2 F ν ~ A F ~ 2 d F ~ d F ~ d V d V Poly- Poly- 1.2-1.8 70-100 0.2 12 123 2 am D 12 z st F ~ dt d (µm) o B ν styrene stynne t × − − 5 10 − × 18 × − 0.2 8 9 10 10 − 15 3 10 12 4 10 Si Si 13.6-14.4 800-850 7 410 × − − − 10 − 13 2 × × 10 − 4 15 4 10 Cu Cu 17 1000 9.8 580 7 10 9 10 3 10 × − 10 − 10 − 11 Ag Ag 18 1060 15.5 910 20 − − 8 4 10 × × 12 6 3 3 10 9 10 o U = z = 1 m / s 4 A o F v ME 437/537 Ahmadi ME 437/537 Ahmadi van der Surface Added Drag/Lift Basset Waals Tension Mass Sphere Near Sphere Near d a Surface a Surface d dV Diameter ρ µ πγ ρ f 2 2 2 F ν ~ A 3 F ~ d V d V F ~ 2 d F ~ d 123 2 am D 12 z st F ~ dt d (µm) o B ν t z o − × 9 × − × − 10 − 0.2 2 10 16 10 12 8 10 8 10 × − 10 − 8 10 2 10 2 × − × − 13 8 8 10 8 10 − − 10 − × × A d 20 7 − × 6 8 2 10 10 8 10 F = 8 10 132 2 12 z o F v ME 437/537 Ahmadi ME 437/537 Ahmadi 2
Cylinder Near Cylinder Near Planar Surfaces Planar Surfaces a Surface a Surface d z o A F z o = 132 π 3 area 6 z 0 A φ = 132 Surface Energy Surface Energy 1 / 2 π F A d 2 12 z = 132 0 2 length 16 z 0 ME 437/537 Ahmadi ME 437/537 Ahmadi − 20 A / 10 J Materials Vacuum Water Two Materials Two Materials Polystyrene 7.9 1.3 2 A A = 11 22 ≈ A A A A + 12 A A 12 11 22 Gold 40 30 11 22 Silver 50 40 Three Materials Three Materials Al 2 O 3 16.75 4.44 = + − − A A A A A 132 12 33 13 23 Copper 40 30 − 2 ( A A ) = + − = − 11 33 2 Water 4.0 - A A A 2 A ~ ( A A ) 131 11 33 13 + 11 33 A A 11 33 ME 437/537 Ahmadi ME 437/537 Ahmadi 3
ω h ( eV ) 131 R + Combinations Water Polystyrene d d = + 1 2 R s 2 Au-Cu 6.41 5.93 d 1 s d 2 Au-Diamond 6.11 5.45 Au-Si 5.32 4.70 Au-Ge 6.50 5.93 + d d Au-MgO 1.99 1.25 − 2 1 2 2 R ( ) A d d / 2 d d / 2 2 Φ = − + + [ 1 2 1 2 ln ] + − − d d d d d d 6 − − − 2 2 2 2 2 2 1 2 1 2 1 2 R ( ) R ( ) R ( ) 2 2 2 ME 437/537 Ahmadi ME 437/537 Ahmadi = + For Equal For Equal ! ! van van der der Waals Waals force is very large force is very large = = r d s d d d Sizes 1 2 Sizes at short distances at short distances ! Short range force ! Short range force 2 2 2 A d d d Φ = − + + − [ ln( 1 )] − 2 2 2 2 6 2 r 2 ( r d ) r ! Can be computed for particles, ! Can be computed for particles, cylinders and plane interfaces cylinders and plane interfaces = + − ≈ − A A A A ( A A ) 121 11 22 12 11 22 ME 437/537 Ahmadi ME 437/537 Ahmadi 4
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