The release of monovalent counterions by addition of divalent counterions in coulombic interaction system

Abstract

The additivity rule of counterion activity or osmotic pressure in rodlike polyelectrolyte solutions has been discussed on the basis of the Fokker-Planck and Poisson equations in relation to the fluctuation of counterion distribution. This new theory has concluded that the additivity rule of counterion activity is less applicable than that of osmotic pressure due to the electric expansion force acting on the free-volume surface resulting from the fluctuation of counterion distribution. The theory has introduced an approximate relation between the counterion activities in the mixture solution of divalent and monovalent counterions, such that Deltaa+ = DeltaC++ - Deltaa++, in which Deltaa+ represents the increase of activity of monovalent counter-ions resulting from the addition of divalent counterionsDeltaC++, (in molar) to the solution, and Deltaa++ means the increase of the divalent counterion activity (in molar) in this process. This relation has been experimentally examined for Na-PSS solutions in the process of Cu2+ ion addition by the use of Na+ and Cu2+ sensitive electrodes, and it has been turned out that the relation is established in the low charge state of polyion.