Chapter 2
Derjaguin, Landau [13], Verwey and Overbeek [14], based on the long range
London-van der Waals attractive forces and repulsive electrostatic forces between
two close spheres.
The universal attractive forces, known as van der Waals forces, arise from
spontaneous electric and magnetic polarizations, giving a fluctuating
electromagnetic field within the media in the gap between them [1].
Fortwo spheres with radii R1 and R2 and center-center separation distance H,
the interaction energy is:
2R↑R2 +________2R^R2________+ Jn ⅞2 + 2(Λ1 +R2)h [2 4]
h2+ 2(Rl + R2)h h2 + 2(Rl + R2)h + 4RlR2 h2 + 2(Ri + R2)h + 4RlR2 ∖ '
Here h = H - R1 - R2 is the minimum distance between the two approaching
surfaces. If R1 = R2 = R, Eq. [2.4] becomes:
TT a∖ 2r2 2r2 d2 1 H2+4Rh 1 roκl
Ua —--— --1— -----------R + In— ---------— [2.5]
6μ2+47M h +4ΛΛ + 4Λ1Λ2 H2 + 4Rh + 4R2
If h«R, Eq. [2.5] can be simplified as:
ÀR
Ua=~- [2.6]
λ 12h
In these expressions, A is the so-called Hamaker constant. Eq. [2.4] was
derived for spheres in vacuum. For similar materials, spheres of material 1
suspended in another medium of material 2, A is now the effective Hamaker
constant, usually calculated as:
12
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