Derejaguin approximation

It is therefore of interest to estimate the dependence of the attractive interaction, b d,T) on the sphere size. For relatively short-range interactions between spheres, the attractive interaction per sphere can be approximately obtained from the interaction between two flat plates. As we now show, this approximation results in an effective attraction between spheres that increases linearly with the sphere radius. Once the interaction energy per sphere is known, the virial coefficient can be calculated from Eq. (7.4) and the stability of the system to phase separation is related to the magnitude of this coefficient. Thus, the general plan is to (i) find the effective interaction between two flat plates, (ii) relate this interaction energy to an interaction between spheres via the Derejaguin approximation, (iii) calculate the virial coefficient for the spheres in order to assess the stability of the single-phase colloidal dispersion. 

We first consider the balance of interactions for flat plates. Once this interaction is understood, the interaction between two spheres can be obtained within the Derejaguin approximation the virial coefficient and hence the stability of the system to phase separation can then be determined. 

As before, we consider the interaction of two flat plates coated by grafted polymeric layers. Once the interaction between the two flat surfaces is known, the Derejaguin approximation and virial expansion can be used to determine the stability of the spherical colloidal dispersion as described previously. 

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