Sedimentation Equilibrium of Mixtures of Charged Colloids

observe higher densities, where excluded volume becomes important.4.6.2 The influence of the saltIn all sections the salt concentration is chosen to be either ρ s = 3µM, orρ s =< 0.1nM. The first value is a very convenient concentration to showinteresting phenomena like the ’colloidal Brazil nut effect’ (4.3), the layeringof components, linear profiles and many other phenomena discussed sofar. The latter concentration(s), ρ s < 0.1nM, shows the effects somewhatstronger, but cannot easily be realised in experiments since e.g. water alreadyhas a minimum concentration of 0.1µM of ions. It is chosen however,to imitate a system of colloids in the presence of counter-ions only, as oftenused in simulations or in anorganic solvents.Two examples will show an effect we already knew from theory. By increasedsalt concentrations the density distributions collapse, while the electric fielddisappears, see figure 4.12. As well, the segregation disappears, as shownfor a binary system in figure 4.13. While decreasing the salt concentrationthe mean heights of the components tend to a constant. This constant isdetermined by the system height H. The mean hight of component i in thehigh salt limit is equal to the gravitational length h i = L i , as it should be(equal to a barometric distribution). The region where ρ s < 1 2 Z2 ρ, wherenon-barometric profiles are expected, is below ρ s < 3 · 10mM.4.6.3 The layer widthThis section is a consideration of the layer width of the profiles, i.e. thelength or height over which the colloids of a certain species extend. It will bedenoted by ξ i . Most arguments will be qualitative, since an exact knowledgeof ξ i requires analytical solutions for the density profiles or, equivalently, thepotential. Most attention will be paid to the so-called linear regimes, i.e.where Z −1 ≪ y ≪ 1, with y = Zρ/2ρ s (see equations (3.7)).The width of the regime where the density profiles decay linearly decreaseswith the number of components, as could already be seen by comparingmonodisperse with binary suspensions. If one proceeds to add components,these linear regimes disappear at a certain point, due to entropy. The numberof components that can be added until the linear profiles break down, dependson the height of the suspension and the mass per charge of the components.This loose argument cannot be made rigorous, though from a physical point ofview this can still be understood: as explained, layering occurs at sufficientlow salt concentrations. As an effect of the layering, the lower colloidalcomponents are compressed by the weight of the higher components (see31