Van-der-Waals Interaction Between Two Aggregates

The pair-contribution Vvdw, - can be further approximated with Eq. (3.23) by accounting for the retardation of the Hamaker coeflicient at large distances (Eq. (3.25)). 

According to Fig. 4.37, it is possible to locate the transition from the primary particle impact to the structure impact sth = 0.5 x Xp. This surface distance corresponds to an interaction energy of 0.0057 x A132 (Eq. (4.114)). Even for the relatively strong interacting system of titania particles in water ( 132,0 = 5.35 X 10 ° J), this is not more than 0.075 x ksF at room temperature. Hence, the primary particle approximation can be applied to all situations because the van-der-Waals energy has no physical relevance, i.e. it is exceeded by the thermal energy, when this approximation fails. 

In summary, the van-der-Waals interaction energy can be fairly well approximated by computing the interaction energy of the closest pair(s) of primary 

---