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The electrostatic potential energy, E pair, between a pair of ions of equal and opposite charge is: = where z = magnitude of charge on one ion e = elementary charge, 1.6022 × 10 −19 C ε 0 = permittivity of free space 4 π ε 0 = 1.112 × 10 −10 C 2 /(J·m)
The molar ionic strength, I, of a solution is a function of the concentration of all ions present in that solution. [3]= = where one half is because we are including both cations and anions, c i is the molar concentration of ion i (M, mol/L), z i is the charge number of that ion, and the sum is taken over all ions in the solution.
When a surface is immersed in a solution containing electrolytes, it develops a net surface charge.This is often because of ionic adsorption. Aqueous solutions universally contain positive and negative ions (cations and anions, respectively), which interact with partial charges on the surface, adsorbing to and thus ionizing the surface and creating a net surface charge. [9]
Ionic potential is the ratio of the electrical charge (z) to the radius (r) of an ion. [1]= = As such, this ratio is a measure of the charge density at the surface of the ion; usually the denser the charge, the stronger the bond formed by the ion with ions of opposite charge.
The electrical charge of the Na + and Cl − ion are assumed to be onefold positive and negative, respectively, z Na = 1 and z Cl = –1. The nearest neighbour distance amounts to half the lattice constant of the cubic unit cell r 0 = a 2 {\displaystyle r_{0}={\tfrac {a}{2}}} and the Madelung constants become
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The net charge of an ion is not zero because its total number of electrons is unequal to its total number of protons. A cation is a positively charged ion with fewer electrons than protons [2] (e.g. K + (potassium ion)) while an anion is a negatively charged ion with more electrons than protons. [3] (e.g. Cl-(chloride ion) and OH-(hydroxide ion)).
The Poisson–Boltzmann equation describes a model proposed independently by Louis Georges Gouy and David Leonard Chapman in 1910 and 1913, respectively. [3] In the Gouy-Chapman model, a charged solid comes into contact with an ionic solution, creating a layer of surface charges and counter-ions or double layer. [4]