Question

Plot the force between two 20 nm diameter spherical alumina particles as a function of distance. The Hamaker constant for alumina is 140*10-21 J.

if you show me the data of the plot that would be great

Answer 1

The van der Waals force between two spheres of same radii is (from a general equation):

F = - AR² / [(2R)x6d²]

    = -AR/(12d²)

if d<<R

where:

A is the Hamaker constant (140x10^-21 J)

R is the sphere radius

d is the distance between surfaces of the spheres

Note: 1nm = 1x10^-9m

Use a Excel file to do calculations.

	A(J)	R(m)	d(m)	F(N)
1	1.40E-19	2.00E-08	2.00E-10	-5.83333E-09
2			8E-10	-3.64583E-10
3			1.2E-09	-1.62037E-10
4			1.6E-09	-9.11458E-11
5			2E-09	-5.83333E-11
6			2.4E-09	-4.05093E-11
7			2.8E-09	-2.97619E-11
8			3.2E-09	-2.27865E-11
9			3.6E-09	-1.80041E-11
10			4E-09	-1.45833E-11
11			4.4E-09	-1.20523E-11
12			4.8E-09	-1.01273E-11
13			5.2E-09	-8.62919E-12
14			5.6E-09	-7.44048E-12
15			6E-09	-6.48148E-12
16			6.4E-09	-5.69661E-12
17			6.8E-09	-5.04614E-12
18			7.2E-09	-4.50103E-12
19			7.6E-09	-4.0397E-12
20			8E-09	-3.64583E-12
21			8.4E-09	-3.30688E-12
22			8.8E-09	-3.01309E-12
23			9.2E-09	-2.75677E-12
24			9.6E-09	-2.53183E-12
25			1E-08	-2.33333E-12
26			1.04E-08	-2.1573E-12
27			1.08E-08	-2.00046E-12
28			1.12E-08	-1.86012E-12
29			1.16E-08	-1.73405E-12
30			1.2E-08	-1.62037E-12
31			1.24E-08	-1.51752E-12
32			1.28E-08	-1.42415E-12
33			1.32E-08	-1.33915E-12
34			1.36E-08	-1.26153E-12
35			1.4E-08	-1.19048E-12
36			1.44E-08	-1.12526E-12
37			1.48E-08	-1.06525E-12
38			1.52E-08	-1.00993E-12
39			1.56E-08	-9.58799E-13
40			1.6E-08	-9.11458E-13
41			1.64E-08	-8.67539E-13
42			1.68E-08	-8.2672E-13
43			1.72E-08	-7.88715E-13
44			1.76E-08	-7.53271E-13
45			1.8E-08	-7.20165E-13
46			1.84E-08	-6.89193E-13
47			1.88E-08	-6.60178E-13
48			1.92E-08	-6.32957E-13
49			1.96E-08	-6.07386E-13
50			2E-08	-5.83333E-13

You may see a decreasing repulsive force. For higher distances you have to use a more complex equation.