Objective: Utilize the electrical triple-layer model to calculate the surface charge density and zeta potential on a silica surface in contact with an aqueous electrolyte made of KCl, whose pH is adjusted by either KOH or HCl.
The following surface chemical reactions occur when a silica surface is in contact with an aqueous solution:
In the above, ka1, ka2, and km are, respectively, the equilibrium reaction constants for the above reactions, and they can be expressed as
In the above, [x] represents the concentration of species x on the surface. For example, [H+ ] and [K+ ] represent the concentrations of the ions H+ and K+ on the surface, and they are obtained by the Boltzmann distribution with [K+ ]B and [H+ ]B being the bulk concentration of K+ and H+ ions:
The total site density of the functional group on the silica surface is
Other related constants are listed in the following table:
For given salt concentration KCl and pH, one can determine by solving equations (12), (13), and (14) with Matlab solve( ). The 1st column and 2nd column in the file, data.txt, represent the concentration of KCl (i.e., CKCl in the SI unit mol/m3 ) and the measured (in the SI unit of V) from the experiments available from the literature at pH=6.5
(1) Using of solve () to determine for CKCl varying from 0.1 mol/m³ to 10³ mol/m³ . Use the following command to create the log spaced vector for CKCl, logspace(-1, 3, 50). In the same figure plot versus CKCl (solid line), versus CKCl (dashed line), and versus CKCl (dashdotted line). Use semilogx() to change the x-axis as the log scale. (Use initial guess of -0.1V, – 0.08V, -0.05V for )
(2) Use textread( ) to read the experimental data from data.txt into matlab. In the same figure obtained from the above step plot the experimentally measured (the 2nd column) versus CKCl (the 1st column) using circles. One expects the predictions (dash-dotted line) agree well with the experimental data (circles).