Page 136 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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

364 Electrophoresis

Solvent, solute A solvent is chemically identified as the solvating the free ion and the energies of interaction of the
substance present in considerable excess in a mixture, intact molecule with the solvent. It is clear in chemical
while the solute is that present in minor quantities. thermodynamics that these differences can be discussed
through chemical potentials of the two states, but ab initio
calculations of these processes are not possible.
ELECTROPHORESIS is the movement of charged par- The experimental basis for these laws of conduction of
ticles when suspended or dissolved in a polar liquid and solutions involved the measurement of conductivity of a
the mixture is placed in an electric field. This generally solution by applying Ohm’s law to the electrical measure-
excludes the movement of charged particles in gases, al- ments. From these experiments Kohlrausch showed that at
though with modifications the basic concepts could be infinite dilution each ion contributed a definite amount to
applied to these suspensions. Although the procedure is the conductivity irrespective of the nature of the other ion.
more widely known for studying biological molecules and In order to explain these phenomena it became necessary
colloidal particles, the underlying principles were discov- to introduce the concept of electrochemical equivalences
ered during early research on the electrical conduction of showing that the conductance of a solution is the product
solutions of inorganic salts. For most purposes the move- of the number of ion in the solution, the charge carried by
ment of the ion is translational and carried out under the each ion, and the velocity or their mobilities u ± .
influence of a constant electric field. Movement in an os- Quantitative relationships were developed between the
cillating electric field could be included within the gen- current i carried through the solution by C + gram moles of
eral term “electrophoresis”; at high frequencies, however, a univalent anion and the mobilities observed in an electric
the molecular motions of dipoles must be included, and field E:
here quantum treatments are more relevant, so these are
i + = u + C + E. (1)
not considered to be electrophoretic phenomena. For this
reason little is mentioned in this article on the effects of The equivalent expression for the cation is the same as Eq.
oscillating fields on charged ions. It is also implicit in (1), and so the total current i is
the considerations of electrophoresis that the particles or
macroions are insulators and that the internal arrange- i = i + + i − = (u + C + + u − C − )E, (2)
ments of ions in molecules are not affected by external
which can be compared directly with Ohm’s law as used
fields.
to define resistance,
E = 1/k, (3)
I. UNDERLYING THEORY where k is the conductance, hence, k = u + C + + u − C −
and the conductance is proportional to the velocities of the
A. Background ions. The quantity of positive electricity carried in one di-
rection by the cations is proportional to u + and C + , while
When a constant electric field is applied across a column of
that in the other direction by the anions is proportional
water, current flows and gases evolve at the electrodes—
to u − and C − . This makes it possible to define a coeffi-
hydrogen at the cathode and oxygen at the anode. This
cient that proportionates the current passed between the
phenomenon is known as electrolysis and was discovered
individual ions. This is called a transference or transport
by M. Faraday in 1832. He provided quantitative laws
number:
to relate the amount of chemical decomposition with the
number of coulombs passed. It is in recognition of his T + = C + u +
work that the primary electrochemical constant is called C + u + + C − u −
the faraday. It was not until much later that the source of and
the decomposition was discovered, since the understand-
C − u −
ing of this phenomenon required the knowledge that salts T + = . (4)
can dissociate into ions when dissolved in a polar sol- C + u + + C − u −
vent, a concept first appreciated by S. Arrhenius in 1887. Here, T ± is dimensionless, but C ± u ± has dimensions
−3
2
The dissociation of salts into ions is now universally ac- mol · A · sec · liters , making this equivalent to the num-
cepted, and the fact that dissolving a salt in water causes ber of molar coulombs required to sweep out a unit volume
the spontaneous dissociation of a molecule into one or per second or number of faradays required to sweep out a
more cations (positively charged) and anions (negatively unit volume per second.
charged) is never questioned. The driving force for this In general, the parameter measured in electrophoresis
dissociation arises from the differences in energy between is the velocity of the ion, which is done by identifying