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Encyclopedia of Physical Science and Technology En005H-218 June 15, 2001 20:33

Electrophoresis 367

With respect to the physical factors influencing the sta-
bility and shapes of boundaries in electrophoresis, it is ap-
parent that all ions in the solution are moving toward their
oppositely charged electrodes. Naturally, various physical
properties are employed to detect and identify the ions
(e.g., pH indicators could be used to study the movement
+
of H and absorption of ultraviolet light for proteins or nu-
cleic acids). The question arises, however, as to how many
boundaries would form when a solution of ions were elec-
trophoresed. As a result of the work of Longsworth and
Dole it is possible to define for any system the number of
boundaries. Their work shows that for most purposes in a
system containing n ions there will occur a maximum of
n − 1 boundaries. If there are p anions and q cations, then
q − 1 boundaries move toward the cathode, p − 1 bound-
aries move toward the anode, and one stationary boundary
FIGURE 2 Equilibration of ions across a boundary (a) containing
the macrocation M and two small gegenions A and C . forms. A stationary boundary does not necessarily mean
+

that no ions are being transported. It means that there are
no visible indications of this transport. Hence, a station-
the solution means that concentrations of individual ions
ary boundary will form if the transport number of the ion
are not equal across a boundary containing a macroion.
is the same on both sides of an interface, which means
This inequality is called the Donnan phenomenon (after
the ion moves at the same velocity on both sides or the
an Irish electrophysiologist who first discussed it). It can
concentrations are equal across the interface [Eq. (4)]. In
be explained using the system given in Fig. 2, where a
the case of proteins the greater proportion of the charge of
macrocation is present on only one side of the boundary.
the ion arises from dissociation of the exposed side chains
Thus, at equilibrium there occur the following equalities
of the condensed amino acids, so the total charge is de-
(brackets indicate chemical activities, which in dilute so-
termined by the relative amount of dissociation of these
lutions equal concentrations):
groups, which in turn is controlled by the pH of the so-
+
−
+
Phase 1: [M ] + [C ] = [A ], lution. Thus, for all zwitterions there is a pH where the
(10) total charge is zero (isoelectric point) and the molecule
+
−
Phase 2: [C ] = [A ].
has zero mobility. At this point it is possible to produce
At equilibrium the chemical potential of the solvent in a stationary boundary that does not transport ions, but
+ +
phase 1 must equal that in phase 2 while [C ] 1 < [C ] 2 this is different from a stationary boundary induced by
+
and [A ] 1 > [A ] 2 , so the effect is an intrinsic instability the electrochemical effects described by the Kohlrausch
−
at a free boundary. If this boundary were formed across regulating function. Producing the stationary boundary by
a physical membrane permeable to A and C but not isoelectric focusing is discussed in Section III.B.
+
−
+
M , an electrical potential and osmotic pressure would
exist across the membrane. This hydrostatic pressure can-
C. Origin of Molecular and Particulate Charge
not occur in free-solution boundaries. Clearly, the extent
of the instability is considerably reduced if the molar con- Equation (6) is a general expression for movement of a
centrations of the gegenions are high relative to that of the single charged particle in an electric field, and it is possible
macroion. This condition is normally employed in elec- to relate the charge to other molecular parameters. It can
trophoresis of macroions. It should be mentioned that the be shown from irreversible thermodynamics that the flow
generation of an osmotic pressure across a membrane sep- of a mole of ions (J) in a system is described by Eq. (11):
arating phase 1 and phase 2 is normal for all molecules
whether they are neutral or charged. The effect of these J = L 0 E + L i (∂u i /∂x), (11)
instabilities is to produce a rapid radjustment of concen- i
trations of ions immediately after a boundary is formed, where E is the electric field strength, (∂u i /∂x) is the force
making the sum of electrochemical and chemical poten- caused by concentration gradients of any ionic or neu-
tials equal across the boundary. It is to reduce these dis- tral species in the solution [for many purposes this mass
turbances in free-solution electrophoresis with macroions transport is expressed by the diffusion, Eq. (8)], and L 0
that the solvent is dialyzed to equilibrium against the so- and L i are phenomenological coefficients. The latter are
lution before an experiment is begun. defined by molecular parameters and composition of the