Influence of Attached Polymers

Colloidal dispersions can be very well stabilized by polymers attached to the particle surfaces [17]. Here we consider polymer chains that are in a good solvent . This means that the chains are swollen and repel each other. As two colloidal particles, protected with attached polymers, approach each other the local osmotic pressure increases dramatically due to steric hindrance of the polymer chains on both particles. This competition between the chains for the same volume leads to a repulsive interaction, as was realized already by Fischer [42]. 

Polymers can be attached to surfaces for instance as mushrooms, brushes or as adsorbed chains, see Fig. 1.3. In case of mushrooms and brushes the 

The first positive term on the right-hand side represents the osmotic repulsion between the brushes and the second negative term originates from the elastic energy gain upon retraction of chains (less stretching). The repulsion dominates the interaction for h Sb- As will become clear in Sect 2.1, the pressure yields the interaction potential between two plates from which also the interaction between two spheres can be derived. 

In Fig. 1.4 we qualitatively sketch the effect of adding a polymer brush to two (uncharged) colloidal spheres subject to Van der Waals attraction. Commonly, one assumes the total interaction is the sum of all pair interactions  

So in Fig. 1.4 the total interaction potential is W,oi = Wvdw + hrmh- Without the anchored polymer chains the particles would coagulate spontaneously, since the 

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