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Additional info for Polyelectrolytes
The ordinate of Fig. J 3b gives the degree of dissociation of counter ions which is related to the average concentration outside. The activity coefficient of co u n ter ions must be smaller t han this ordinate. Many experimental data support the theoretical results obtained. It has often been observed t hat po lyvalen t counter ions are strongly and co m pletely bound by macroions in po lyelectrolyte solutions (/6). The replace ment of bound monovalent counter ions by polyvalent ones has been frequently observed as well.
25 DISTRIBUTION OF COUNTER IONS occupied by the apparent volume of the macroions and the region outside of this volume. The chemical potent ial is the sum of energy and entropy terms. The contribution of the ent ropy is expressed as kTx In (con centration), and the difference in the entropy between the two phases contains the term kTx In (volume ratio). For a long cylinder having a uniform charge density, the coulomb potential around the cylinder is expressed as a logarithmic function of the distance.
The number of free counter ions, Il*jz, can not exceed nlz2 Q, which is i nversely proportional to the square of the valence. ns their condensation takes place at a lower density of charges and a smaller number of free counter ions. The critical value of the charge density is determined by the balance between the entropy and energy difference of bound and free counter ions. In the two-phase approximation, counter ion condensation is not influenced by the valence of each char ged group on the macroion at a given value of the charge dcnsity as long as charged groups can be repre sented by a uni form charge density along the cylinder.