Molecular Interactions and Power Laws

To understand the origin of the attraction between colloidal particles, it is necessary to back off a bit and consider the interactions between individual molecules. Macroscopic interactions — as we shall call the interactions between colloids since these particles are large compared to atomic dimensions —are the summation of the pairwise interactions of the constituent molecules in the individual particles. Therefore we begin by examining the interactions between a pair of isolated molecules. 

Our primary interest in this section is to discuss the functional form that relates potential energy to the distance of separation for various types of interactions. For many interactions an inverse power dependence on the separation describes the potential energy. Several examples of this are shown in Table 10.1. The main point to be observed now is that the value of the exponent in the inverse power dependence on the separation differs widely for the various types of interactions. An immediate consequence of this is that the range of the interactions is quite different also. 

COS 0 47re0x2 ix = dipole moment, d = angle between line of centers and axis of dipole length of dipole small compared to x (sign depends on z and orientation) Coulomb 2 

2 2 2 3 A fksTx6 Free rotation of dipoles (always negative) Keesom 6 

It is those functions with an inverse sixth-power dependence on the separation that are our main concern in this chapter. Those power laws with exponents greater or less than 6 are included in Table 10.1 mainly to emphasize the point that many types of interactions exist and that these are governed by different relationships. The interactions listed are by no means complete Interactions of quadrupoles, octapoles, and so on might also be included, as well as those due to magnetic moments however, all of these are less important than the interactions listed. Let us now examine Table 10.1 in greater detail. 

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