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The zeta potential is an important and readily measurable indicator of the stability of colloidal dispersions. The magnitude of the zeta potential indicates the degree of electrostatic repulsion between adjacent, similarly charged particles in a dispersion. For molecules and particles that are small enough, a high zeta potential will confer ...
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The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
where ε r is the dielectric constant of the dispersion medium, ε 0 is the permittivity of free space (C 2 N −1 m −2), η is dynamic viscosity of the dispersion medium (Pa s), and ζ is zeta potential (i.e., the electrokinetic potential of the slipping plane in the double layer, units mV or V).
For example, from Fe 2+ + 2 e − ⇌ Fe(s) (–0.44 V), the energy to form one neutral atom of Fe(s) from one Fe 2+ ion and two electrons is 2 × 0.44 eV = 0.88 eV, or 84 907 J/(mol e −). That value is also the standard formation energy (∆ G f °) for an Fe 2+ ion, since e − and Fe( s ) both have zero formation energy.
In 1923, Peter Debye and Erich Hückel reported the first successful theory for the distribution of charges in ionic solutions. [7] The framework of linearized Debye–Hückel theory subsequently was applied to colloidal dispersions by S. Levine and G. P. Dube [8] [9] who found that charged colloidal particles should experience a strong medium-range repulsion and a weaker long-range attraction.
Of primary importance in the analysis of stability in particle suspensions is the value of the zeta potential exhibited by suspended solids. This parameter indicates the magnitude of interparticle electrostatic repulsion and is commonly analyzed to determine how the use of adsorbates and pH modification affect particle repulsion and suspension ...
Zeta potential titration is a titration of heterogeneous systems, for example colloids and emulsions. Solids in such systems have very high surface area. This type of titration is used to study the zeta potential of these surfaces under different conditions. Details of zeta potential definition and measuring techniques can be found in the ...