Isoelectric Points with Respect To Electrolyte Concentration

4 ISOELECTRIC POINTS WITH RESPECT TO ELECTROLYTE CONCENTRATION 

Equations (16.10)-(16.12) show that owing to the factor exp( — the contri- 

It immediately follows from the existence of isoelectric points that if the two interacting membranes have different isoelectric points, then the interaction force alters its sign at these isoelectric points (note that the interaction force between membranes with the same isoelectric point does not change its sign). 

An example is given in Fig. 16.2, which shows the interaction force between two membranes, each consisting of with two sublayers, in a monovalent symmetrical electrolyte solution as a function of the electrolyte concentration. Here membranes 1 and 2 have different isoelectric points. It is seen that the interaction force is positive (i.e., repulsive) at concentrations less than 0.07 M and higher than 0.18 M and negative (i.e., attractive) between 0.07 and 0.18M, corresponding to the isoelectric points at 0.07 M for membrane 1 and 0.18 M for membrane 2. Membranes consisting of more than two layers may exhibit more than one isoelectric point. The 

FIGURE 16.2 Electrostatic force P between two ion-penetrable membranes, each consisting of two layers, immersed in a monovalent symmetrical electrolyte solution as a function of the electrol3de concentration n (M). The Donnan potentials at n = 0.1 M in the respective 

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