1. Materials and Biomaterials INTERPARTICLE AND INTERSURFACE FORCES II
3.052 Nanomechanics of
Materials and Biomaterials
LECTURE # 11 :
INTERPARTICLE AND INTERSURFACE FORCES II
Prof. Christine Ortiz
DMSE, RM
Phone : (617)
WWW :

2. Interparticle and Intersurface Forces :
Review : Lecture #10
Interparticle and Intersurface Forces :
I. Net Interaction Free Energy or Potential : W(D) (J or kBT)
assumptions : (1) w(r)=-A/rn (2) “pairwise additivity”
W(D)MOL-SFC =-2pAr/(n-2)(n-3)Dn-3
W(D)SPHERE-SFC =-4p2Ar2R/(n-2)(n-3)(n-4)(n-5)Dn-5 (D<<R)
=-8p2Ar2R3/3(n-2)(n-3)Dn-3 (D>>R)
W(D)SPHERE-SPHERE =-2p2Ar2R/(n-2)(n-3)(n-4)(n-5)Dn-5 (D<<R)
(*equal radii) ~1/Dn (D>>R)
W(D)planes/unit area =-2pAr2/(n-2)(n-3)(n-4)Dn-4
net interaction force (N): F(r)=-dW(D)/dD = k(r)dr
net interaction stiffness(N/m) : k(r)=-d2 W(D)/dD2 = dF(r)/dr
II. Contrasts Between Interatomic / Intermolecular Interactions and Interactions Between Bodies :
Interactions between bodies :
1. are much longer range (i.e. decay much more slowly with D)
2. are size-dependent
3. are geometry-dependent
III. Comparison with Experimental Data : retardation effects
IV. Derjaguin Approximations : F(D)sphere-surface=2pRW(D)planes (D>>R)
F(D)sphere-sphere=2pR1R2/(R1+R2)W(D)planes (D>>R)
F(D)crossed-cylinders=2pR1R2/(sinq)W(D)planes (D>>R)

3. Contrasts Between Interatomic / Intermolecular Interactions and Interactions Between Bodies

4. Interaction Potential Between a Sphere and a Flat Surfacez
z=2R
WSPHERE-SFC(D)=WMOL-SFC(D+z)(rp(2R-z)zdz)
where : WMOL-SFC(D+z)=(-A2pr)/[(n-2)(n-3)(D+z)n-3]
WSPHERE-SFC(D)=
-A2pr/(n-2)(n-3)(D+z)n-3 (rp(2R-z)zdz)
-A2p2r2/(n-2)(n-3) (2R-z)z/(D+z)n-3dz
for D,z<<R
WSPHERE-SFC(D)=-A4p2r2R/(n-2)(n-3)(n-4)(n-5)Dn-5
Dispersion VDW (n=6):
WSPHERE-SFC(D)=-Ap2r2R/6D
z=2R
2R-z
z=0
sphere
z=R R x x
z=2R dz
planar
surface z
D+z
z=0
z=0 ' D
z=2R
z=0
CHORD THEORUM :
x2=(2R-z)z (*p. 143 Israelachvili)
area=px2
volume=px2dz
# of atoms=rpx2dz= rp(2R-z)zdz

5. Interaction Potential Between a Sphere and a Flat Surfacez
z=2R
WSPHERE-SFC(D)=
-A4p2r2R/(n-2)(n-3)(n-4)(n-5)Dn-5
Dispersion VDW (n=6):
WSPHERE-SFC(D)=-Ap2r2R/6D
2R-z
sphere
z=R R x x dz
planar
surface z
D+z
z=0 ' D
CHORD THEORUM :
x2=(2R-z)z (*p. 143 Israelachvili)
area=px2
volume=px2dz
# of atoms=rpx2dz= rp(2R-z)zdz

6. The Hamaker Constant

7. Experimental Measurement of Van der Waals Interactions
(*Israelachivili, page 197)

8. Retardation Effects in Dispersion Interactions

9. Derjaguin Approximations

10. Derjaguin Approximations