will, of course, become separated, maybe as depicted by the broken line. The
bridging by calcium ions can readily occur for adsorbed protein layers, if the
calcium ion activity is sufficiently large, say>5 millimolar. The casein
micelles mentioned in the previous section also aggregate in such a situation.
We finish this section with an important conclusion, which is that
considerablehysteresiscan occur in the force–distance or the free energy–
distance curves between approach and moving apart of two particles.
Classical DLVO theory proceeds from the assumption that the interaction
force is at equilibrium under all conditions, but this is mostly not the case if
polymers are involved. The shape of a curve as depicted in Figure 12.9 will
also depend on the rate at which the particles are moved.
FIGURE12.9 Force needed (F) to bring two particles to a distancehif the particles
are covered by negatively charged polymer layers and the solvent contains divalent
cations. The scales are only meant to indicate an order of magnitude. The dotted line
is conjectural.