Van der Waals forces, which were mentioned in the previous article, are important attractive forces at work within suspensions.  When all else fails, van der Waals forces will take over and cause flocculation.

Summation of Attraction by Atoms and Ions

Van der Waals forces are the summation of the attractive potentials between all atoms in one particle for all atoms in another particle.  Since each particle contains numerous atoms or ions, and since each atom or ion is attracted to each other atom or ion, in the absence of more powerful repulsive forces, adjacent particles will be attracted to one another.

Fundamentally, each atom and ion consists of a positively charged nucleus with numerous electrons (negative charges) spinning around it.  The center of charge of the positive nucleus remains in a relatively fixed position, while the center of charge of the electrons shifts slightly about that same position at high frequencies.  Through this mechanism, two ions or two atoms in close proximity will experience a net attractive force between them -- that is, between each positive nucleus and the negative electron cloud of the other ion or atom AND between each negative electron cloud and the positive nucleus of the other ion or atom.  Overall, the sum of this interaction is an attractive force, and this attractive force is known as the van der Waals force.

Always Present

Since the van der Waals force is created at the atomic level, it is always present.  How do you change it?  You can't.  How do you control it?  You can't.  How do you eliminate it?  You can't.  Van der Waals forces are always present.

BUT -- you can overpower it -- or mask it.  Most other interparticle forces (electrostatic and hydrophobic) that are present in suspensions are stronger than van der Waals forces.  When these other forces are present, they can cause particles to repel one another.  When this happens, it doesn't mean that the van der Waals forces have been turned off -- it means that they have been overpowered and are masked from view by interparticle repulsive forces. 

Short Range Forces

Van der Waals forces are especially short ranged, so they can even be partially masked by coating the particles with layers of polymeric additives.  A layer of a polyelectrolyte, for example, will hold particles apart (by the distance of one or two layers of additive which separate the particles.)  This is known as steric hindrance.  This adds to the distance over which van der Waals forces must act, and it reduces the magnitude of those attractive forces at the particles' surfaces.

Other Considerations

The equations for van der Waals forces and their several modifications are available in textbooks, such as Jim Funk's and my PPC textbook.  Without going through the details of all of the equations, I will try to summarize (in simple English) the interactions which must be taken into account.  Any of you who need to do the calculations can refer to the many available textbooks that contain the equations.

The three major interactions that combine to make up the van der Waals forces are: 

Keesom Dipole/Dipole Interaction:  When molecules which are dipoles come into close proximity, the net separation of their positive and negative charge centers affects the way the two molecules attract.  The interaction potential in this case is a function of the dipole moments of the two dipoles.

Debye Dipole/Induced Dipole Interaction:  When polarizable molecules come into close proximity, the interaction potential is a function of the dipole moment and the polarizability of each molecule. 

London Dispersion Forces:  This interaction potential takes into account the ionization potential of each molecule.

The total van der Waals interaction potential includes the sum of these three interaction potentials.  The total interaction potential is usually simplified to a summation of three terms (using one term each to describe the unique parts of each of the interaction potentials) divided by the separation distance to the 6^th power:

Hamaker's Contribution

Whereas the above equation and discussion applies to two molecules in close proximity, Hamaker and coworkers took into account all of the many atoms (ions) contained in each of two particles which are in close proximity to one another.  They simplified this to what we now known as the Hamaker constant.

                                                                A = π C ρ₁ ρ₂                                                                                  (2)

where                 A  =  the Hamaker Constant,
                          C  =  the sum of the three interaction potentials in Equation (1) above;
                                    i.e., [the value of the three terms in the square brackets],
                ρ₁ & ρ₂  =  the number of atoms per unit volume in each particle.

The total interparticle attractive energy (W) between two particles is then equal to:

                                            W  =  - (A R₁ R₂ ) / [ 6 r (R₁ + R₂) ]                                                                   (3)

where               A =  the Hamaker Constant,
             R₁ & R₂  =  particle radii, and
                          r = interparticle separation distance (IPS).    

For some typical ceramic powders, the Hamaker constant is 6-10 x 10^-20 J.  For water, it is 3.7-4.0 x 10^-20 J.

This is not the end of the story.  It becomes more and more complicated from here.  The practical information that I think needs to be known about van der Waals forces, however, is summed up in the last section.

Consequences of van der Waals Forces    

1.  Van der Waals forces are always present!

2.  Van der Waals forces are very weak attractive forces that only appear in the absence of other overpowering interparticle attractive or repulsive forces.

3.  Van der Waals forces function best when particles and/or molecules are particularly close together (10 nm or less.)  At larger separation distances, the magnitudes of van der Waals attractive forces drop off quickly.

4.  Sub-micron (colloidal) particles (which move very easily in suspension) are very susceptible to influence by van der Waals forces of attraction from other particles -- especially larger particles.

4.  Large particles produce relatively large (nevertheless weak) van der Waals forces.

5.  Meaningful attractive forces extend further from the surfaces of large particles than from small molecules.

6.  Small particles are more strongly attracted to the surfaces of large particles than to the surfaces of small particles.  In the absence of large particles (and other repulsive forces), small particles will nevertheless draw together.

Flocculation in Suspensions

In most cases within ceramic suspensions, flocculating conditions result by minimizing the magnitude of repulsive interparticle forces.  That is, in most cases, suspensions flocculate due to interparticle attractions by van der Waals forces.

Miscellany

Suggested topics for future issues of this E-zine .... Please continue to send your ideas or questions for future topics.  Thanks.  Until next time ...

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