An earlier (pragmatic) theory for calculating the interparticle interaction energy between two sterically-stabilised particles, in the presence of free polymer and solvent, is extended to take account of the possible compression of the attached polymer chains by the free polymer chains, as observed in neutron scattering experiments. This theory is compared with a recent approach based on the Scheutjens-Fleer model of polymers at interfaces. Both theories account well for the depletion flocculation observed when the added free polymer is of the same type as the attached polymer, that is, in this case when polystyrene (PS) is added to dispersions of silica particles, carrying terminally-anchored polystyrene chains, in toluene. However, subtle deficiencies are revealed in the pragmatic theory when the added polymer is different from the attached polymer. For example, when polydimethylsiloxane (PDMS) is added to the same dispersions, a type of incipient flocculation occurs at high PDMS volume fractions. This is related to the basic incompatibility of PS and PDMS. It is shown that an additional term, namely a displacement interaction term, must be included in the pragmatic theory this accounts for the free energy change associated with displacement of free coils, from overlap with the attached chains, into bulk solution. Similarly, when polyvinylmethylether (PVME) is added to the dispersions, bridging flocculation, is observed at very low PVME volume fractions. The pragmatic theory does not account for this. Depletion flocculation occurs in the same systems at much higher PVME volume fractions.
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