SYMBOLS AND DEFINITIONS PARAMETER NAME SYMBOL FORMULA DEFINITION - - an , , or radical that has gained or lost one or more - - any process by which an electrically neutral atom or molecule is converted into an electrically charged atom or molecule counterion - - oppositely charged free ion in relative to surface coion - - free ion in solution with same sign charge as solution - solution containing free , salt solution material - - an insulating material or a very poor conductor of , when are placed in an electric , practically no current flows in them because, unlike , they have no loosely bound, or free, electrons that may drift through the material electrical field E E=F/q region around an , q, in which an electric , F, is exerted (/meter) on another charge electrical potential ψ (or Ф, E=∂ψ/∂ the amount of needed to move a unit charge from a reference point to depending (Ф is in ) a specific point against an on the text) ε (C2J-1m-1) a universal electric constant which is a generalized, or large-scale, description of electric behavior that does not specify detailed features on the atomic dimension. It is a measure of the relative effectiveness of that substance as an electrical or the extent of reduction of electric fields and consequently reduced strength of electrostatic interactions in a medium. -12 dielectric permittivity of εο 8.854 ●10 Also known as the dielectric permittivity of free free space C2J-1m-1 static dielectric constant DC ε dielectric permittivity of a substance normalized by dielectric permittivity of ε = relative dielectric s (unitless) free vacuum εs ε permittivity o specific inductive capacity

1 dielectric constant of free The perfect electrical insulator is a vacuum, which has a DC of 1.00000. By εV ε o εV= =1 vacuum ε comparison, air has a DC of 1.00059, almost the same as a vacuum, and o water has a DC value of 78.2. A. polyelectrolyte − − polymer with ionizable groups along its chain, carries fixed charge ionomer Electrical migration Electrical force an ion feels in solution in response to the electrical field present. Electroquasistatic ∂ Negligible time-varying magnetic fields are present and therefore an electrical (µH) ≈ 0 ∂t potential can be defined. (This is usually true unless you are standing in an MRI machine, for example.) Η () Field produced by either a or by current flows. ’s constant F 96,500 Amount of charge in one of electrons. C/mole Universal Gas Constant R 8.314 It is defined in terms of the (kB) and Avogadro’s . -1. -1 J mole K number (NA): R = NAkB Debye length κ−1 (nm) Characteristic length of electrostatic interactions Other handy In Cartesian Coordinates: references: ∇.Ε ∂E ∂E ∂E = x + y + z of E ∂x ∂y ∂z

Ex, Ey, and Ez are the x, y, and z components of the E vector (divergence takes a vector and makes a ) ∇Φ of ∂Φ ∂Φ ∂Φ = iˆ + iˆ + iˆ Φ x ∂x y ∂y z ∂z the iˆ ’s are the unit directional vectors (gradient takes a scalar and makes a vector) ∇2Φ Laplacian of ∂ 2 Φ ∂ 2 Φ ∂ 2 Φ = + + Φ (div grad ∂x 2 ∂y 2 ∂z 2 Φ)

2 pKa The pKa of an acid is the pH at which it is half dissociated, where [A-] = [HA] For the ionization of a weak acid, HA ↔ H+ + A- The apparent equilibrium constant K is [ H + ][A−] K = [ HA] The pKa is then defined as pKa = -log K = log (1/K)