x r
0
x
van der Waals attractive interactions;
attraction potential : V A
attraction potential between spherical particles:
A: Hamaker constant (attraction parameter)
x 12
r (x) A
V
A= −
2 S
A
2 γ
x π 12 (x) A
V = − ≈
attraction potential between plate-like particles:
A: Hamaker constant (attraction parameter)
Hamaker constants of various materials
Hamaker constants of various materials
per object per object
( 11 33 ) 2
13 33
11 313
131 A A A 2 A A A
A ≈ ≈ + − ≈ −
( 11 33 )( 22 33 )
132 A A A A
A ≈ − −
232 131
132
A A
A ≈
22 11
12
A A
A ≈
Combination of Hamaker constants
A
132: particle(1)-particle(2) interaction through medium (3)
A
12: particle(1)-particle(2)
interaction in vacuum
The stability of a colloidal disperse system is strongly dependent on the attractive pair potential, VA, between the dispersed particles.
VA is determined by the geometric arrangement, G, of the particles (e.g. lamella-lamella;
sphere-sphere; sphere-lamella; etc. interactions, independently of the chemical composition),
and the Hamaker constant, A, of the overall system (which depends on the chemical composition of the constituting species, but is independent of the
geometrc arrangement). Formally:
VA = A × G
The Hamaker constant A of the overall system originates from a combination of the individual Hamaker constants, Ai, of the dispersion medium and that of the dispersed particles. It can be derived from the summation of the der Waals dispersion forces between the constituting species (dispersion medium; dispersed particles).
van der Waals attractions in colloidal disperse systems
G: geometric arrangement
Dependence of the van der Waals pair potential V
Abetween two colliding particles on the overall Hamaker constant ”A” of the system
V A, van derWaalsinteraction energy(kT)
two spherical particles, R=4µm
surface separation, x (nm), of two interacting particles
