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Detailed basic definitions of electrochemical quantities are being developed by the Commission on Electrochemistry26. Meanwhile the present appendix employs the names and symbols recommended in the Manual, and defines other quantities and concepts which have special relevance to colloid and surface chemistry.

Electrochemical double-layer. The electrical state of a surface depends on the spatial distribution of free (electronic or ionic) charges in its neighbourhood. This distribution is usually idealized as an electrochemical double-layer. Similar double-layers may also exist around micelles of association colloids or around polyelectrolyte molecules. Current views of electrical double-layers are based on a physical model in which one layer of the double-layer is envisaged as a fixed charge or surface charge attached to the particle or solid surface, while the other layer is distributed more or less diffusely in the liquid in contact with the particle. This layer contains an excess of counterions, opposite in sign to the fixed charge, and usually a deficit of co-ions of the same sign as the fixed charge. Counter and co-ions in immediate contact with the surface are said to be located in the Stern layer, and form with the fixed charge a molecular capacitor. Ions farther away from the surface form the diffuse layer or Gouy layer.

The fixed surface charge density is denoted by $ {\sigma}^0$; that in the Stern layer by $ {\sigma}^i$ and that in the Gouy layer by $ {\sigma}^d$27. In a system which is electroneutral, $ {\sigma}^o+{\sigma}^i+{\sigma}^d = 0$. The individual values attributed to the various charge densities depend on the precise definition adopted for surface charge.

A surface or a particle carrying no net fixed charge is said to be at the point of zero charge (abbreviation p.z.c.). The precise identification of this condition depends on the definition adopted for surface charge.

The electrical potential at the inner boundary of the Gouy layer is $ {\psi}^d$28$ ^,$29.

The differential capacitance of the electrical double-layer per unit area $ = {\partial}{\sigma}/{\partial}{\psi}=C_$dl30: the quantities held constant in this differentiation must be specified.

The integral capacitance of the electrical double layer per unit area $ ={\sigma}/{\psi}=K_$dl31.

A surface showing no electro-osmosis (see below) or a particle showing no electrophoresis is said to be at the isoelectric point (i.e.p.)32.

A macro-ion of a polyampholyte (in particular a protein) is said to be isoelectric if it exhibits no electrophoresis. It is isoionic if besides the polyampholyte and H$ ^+$ or OH$ ^-$ ions (in general ions of the solvent) no other ions are present in the system.

Potential determining ions are those species of ions which by virtue of their equilibrium distribution between the two phases (or by their equilibrium with electrons in one of the phases) determine the difference in Galvani potential between these phases. They are often, but not always, identical with the ions which stabilize a colloidal suspension formed from these phases, and which are sometimes called peptizing ions33.

(Effective) thickness of the (diffuse electrical) double-layer = length characterizing the decrease with distance of the potential in the double layer = characteristic Debye length in the corresponding electrolyte solution $ =

$\displaystyle 1/{\kappa}=[{\epsilon}_r{\epsilon}_0RT/(F^2{\sum}_ic_iz^2_i)]^\frac{1}{2}$ (rationalized four-quantity system)$\displaystyle ;$

$\displaystyle 1/{\kappa}=[{\epsilon}_rRT/(4{\pi}F^2{\sum}_ic_iz^2_i)]^\frac{1}{2}$ (three-quantity electrostatic system)$\displaystyle ;\footnotemark $

where $ {\epsilon}$ = static permittivity $ = {\epsilon}_r{\epsilon}_0$; $ {\epsilon}_r=$ relative static permittivity of solution; $ {\epsilon}_0 =$ permittivity of vacuum; $ R =$ gas constant; $ T=$ thermodynamic temperature; $ F =$ Faraday constant; $ c_i =$ concentration of species $ i$; $ z_i =$ ionic charge on species $ i$.

Donnan equilibrium is the equilibrium characterized by an unequal distribution of diffusible ions between two ionic solutions (one or both of the solutions may be gelled) separated by a membrane which is impermeable to at least one of the ionic species present, e.g. because they are too large to pass through the pores of the membrane. The membrane may be replaced by other kinds of restraint, such as gelation, the field of gravity, etc., which prevent some ionic components from moving from one phase to the other, but allows other components to do so.

Donnan emf (Donnan potential), $ E_D$, is the potential difference at zero electric current between two identical salt bridges, usually saturated KCl bridges (conveniently measured by linking them to two identical electrodes) inserted into the two solutions in Donnan equilibrium.

Membrane emf: (membrane potential), $ E_m$, is the potential difference between two saturated KCl bridges inserted into two solutions separated by a membrane. The solutions need not be in equilibrium with one another and need not contain any colloidal material.

Suspension effect (Pallmann effect, or Wiegner effect), $ E_s$, is the Donnan emf between a suspension and its equilibrium liquid.

The relationships between these measured emf's and the behaviour of the membrane are complicated by a number of factors.

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