3'052 Nanomechanics of

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3.052 Nanomechanics of Materials and
Biomaterials
LECTURE 10 INTERPARTICLE AND
INTERSURFACEFORCES
Prof. Christine Ortiz DMSE, RM 13-4022 Phone
[phone] Email cortiz_at_mit.edu WWW
http//web.mit.edu/cortiz/www
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Interaction Strength
DEB
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Equilibrium Interaction Distance, re
re
re
r (nm)
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More Complicated Interaction Potentials
Grubmüller, et al, Science 1996 (http//www.mpi
bpc.gwdg.de/abteilungen/071/strept.html)
R. MERKEL, P. NASSOY, A. LEUNG, K. RITCHIE
E. EVANS, Nature 397, 50 - 53 (1999)
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BRIDGING THE GAP BETWEEN LENGTH SCALES
Force, F (nN)
kc
0
Surface Separation Distance, D (nm)
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BRIDGING THE GAP BETWEEN LENGTH SCALES
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Interaction Potential Between a Molecule and a
Planar Surface
z
atom or molecule
z0
v
r(z2x2)1/2
planar surface ratoms/m3
zD x0
x
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Interaction Potential Between a Molecule and a
Planar Surface
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Interaction Potential Between a Molecule and a
Planar Surface
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Contrasts Between Interatomic / Intermolecular
Interactions and Interactions Between Bodies
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Interaction Potential Between a Sphere and a Flat
Surface
z
z2R
WSPHERE-SFC(D)?WMOL-SFC(Dz)(rp(2R-z)zdz) where
WMOL-SFC(Dz)(-A2pr)/(n-2)(n-3)(Dz)n-3
WSPHERE-SFC(D) ?-A2pr/(n-2)(n-3)(Dz)n-3
(rp(2R-z)zdz) WSPHERE-SFC(D) -A2p2r2/(n-2)(n-3)
?(2R-z)z/(Dz)n-3dz for D,zltltR WSPHERE-SFC(D)-A4
p2r2R/(n-2)(n-3)(n-4)(n-5)Dn-5 Dispersion VDW
(n6) WSPHERE-SFC(D)-Ap2r2R/6D
z2R
2R-z
z0
sphere
zR
R
x
x
z2R
dz
planar surface
Dz
z
z0
z0
D
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z2R
z0
CHORD THEORUM x2(2R-z)z (p. 143
Israelachvili) areapx2 volumepx2dz of
atomsrpx2dz rp(2R-z)zdz
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Interaction Potential Between a Sphere and a Flat
Surface
z
z2R
WSPHERE-SFC(D) -A4p2r2R/(n-2)(n-3)(n-4)(n-5)Dn-5
Dispersion VDW (n6) WSPHERE-SFC(D)-Ap2r2R/6D
2R-z
sphere
zR
R
x
x
dz
planar surface
Dz
z
z0
D
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CHORD THEORUM x2(2R-z)z (p. 143
Israelachvili) areapx2 volumepx2dz of
atomsrpx2dz rp(2R-z)zdz
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Experimental Measurement of Van der Waals
Interactions (Israelachivili, page 197)