Osmotic pressure charged particles

It is important to note that the concept of osmotic pressure is more general than suggested by the above experiment. In particular, one does not have to invoke the presence of a membrane (or even a concentration difference) to define osmotic pressure. The osmotic pressure, being a property of a solution, always exists and serves to counteract the tendency of the chemical potentials to equalize. It is not important how the differences in the chemical potential come about. The differences may arise due to other factors such as an electric field or gravity. For example, we see in Chapter 11 (Section 11.7a) how osmotic pressure plays a major role in giving rise to repulsion between electrical double layers here, the variation of the concentration in the electrical double layers arises from the electrostatic interaction between a charged surface and the ions in the solution. In Chapter 13 (Section 13.6b.3), we provide another example of the role of differences in osmotic pressures of a polymer solution in giving rise to an effective attractive force between colloidal particles suspended in the solution. 

How are we to understand this odd result The answer is easy when we remember that osmotic pressure counts solute particles. The macroion cannot pass through the semiperme-able membrane. In the absence of added salt, its counterions will not pass through the membrane either since the electroneutrality of the solution must be maintained. Therefore the equilibrium pressure is that associated with z + 1) particles. Failure to consider the presence of the counterions will lead to the interpretation of a low molecular weight for the colloid. As we already saw, the presence of increasing amounts of salt leads to a leveling off of the ion concentrations on the two sides of the membrane. The effect of the charge on the macroion is essentially swamped out with increasing electrolyte. 

So far P is only an integration constant. As we see later it has a physical meaning P corresponds to the pressure in the gap. The first term describes the osmotic pressure caused by the increased number of particles (ions) in the gap. The second term, sometimes called the Maxwell stress term, corresponds to the electrostatic force caused by the electric field of one surface which affects charges on the other surface and vice versa. 

Clearly, the results of osmotic pressure measurements on solutions of charged colloidal particles, such as proteins, will be invalid unless precautions are taken either to eliminate or to correct for this Donnan effect. Working at the isoelectric pH of the protein will eliminate the Donnan effect but will probably introduce new errors due to coagulation of the protein. Working with a moderately large salt concentration and a small protein concentration will make the... 

The osmotic pressure between two flat surfaces can be derived within the Poisson-Boltzmann approximation. The PB equation was originally developed to describe ion distributions outside a large charged surface. However, there are extended PB equations where polymers have been included [32]. The expression for the osmotic pressure given below is valid in the absence of polymers. In the PB equation the correlations between ions are neglected, which means that Pei is identically zero. Furthermore, the ions are normally treated as point particles which means that the collision term disappears. Thus for symmetric systems only two terms remain, the kinetic pressure and the bulk pressure. The net pressure can be written as... 

Many solute properties are intertwined with those of the ubiquitous solvent, water. For example, the osmotic pressure term in the chemical potential of water is due mainly to the decrease of the water activity caused by solutes (RT In aw = —V ri Eq. 2.7). The movement of water through the soil to a root and then to its xylem can influence the entry of dissolved nutrients, and the subsequent distribution of these nutrients throughout the plant depends on water movement in the xylem (and the phloem in some cases). In contrast to water, however, solute molecules can carry a net positive or negative electrical charge. For such charged particles, the electrical term must be included in their chemical potential. This leads to a consideration of electrical phenomena in general and an interpretation of the electrical potential differences across membranes in particular. Whether an observed ionic flux of some species into or out of a cell can be accounted for by the passive process of diffusion depends on the differences in both the concentration of that species and the electrical potential between the inside and the outside of the cell. Ions can also be actively transported across membranes, in which case metabolic energy is involved. 

If, further, the particle is charged, the particle charge and electrolyte ions (mainly counterions) form an electrical double layer around the particle, as shown in Chapter 1. The osmotic pressure becomes... 

When two charged colloidal particles approach each other, their electrical double layers overlap so that the concentration of counterions in the region between the particles increases, resulting in electrostatic forces between them (Fig. 8.2). There are two methods for calculating the potential energy of the double-layer interaction between two charged colloidal particles [1,2] In the first method, one directly calculates the interaction force P from the excess osmotic pressure tensor All and... 

FIGURE 8.1 Electrical double layer around a charged particle exert the excess osmotic pressure AH and the Maxwell stress T on the particle. 

In the plane of symmetry between the parallel double layers, a charged particle experiences no electric force since the electric field is zero. The charged particle (say ion) concentration at this plane, however, is in excess of that in the bulk, so there is an excess pressure (osmotic pressure) at this plane compared with the bulk, which tends to push the surfaces apart. 

As with electrokinetic phenomena, the existence of negative adsorption implies the existence of an electrified interface. The behavior of this interface toward charged particles can always be investigated with the help of a particular molecular model, such as DDL theory, but it is useful to see how much information can be obtained without a detailed model, in keeping wih the spirit of the previous sections in this chapter. Consider, for example, the application of thermodynamics to the prototypical two-chamber (experiment on negative adsorption. If the very small osmotic pressure created by the suspended soil clay is neglected, the activity of any electrolyte in the two chambers is the same in both the suspension and the supernatant solution ... 

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