![Retardation Force](https://upload.wikimedia.org/wikipedia/commons/0/08/Retardation_Force.svg)
Electrophoresis, from Ancient Greek ἤλεκτρον (ḗlektron, "amber") and φόρησις (phórēsis, "the act of bearing"), is the motion of
dispersed particles
Dispersion may refer to:
Economics and finance
*Dispersion (finance), a measure for the statistical distribution of portfolio returns
*Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variatio ...
relative to a fluid under the influence of a spatially uniform
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
.
Electrophoresis of positively charged particles (
cation
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...
s) is sometimes called cataphoresis, while electrophoresis of negatively charged particles (anions) is sometimes called anaphoresis.
The
electrokinetic phenomenon of electrophoresis was observed for the first time in 1807 by Russian professors Peter Ivanovich Strakhov and Ferdinand Frederic Reuss at
Moscow University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
, who noticed that the application of a constant electric field caused
clay
Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4).
Clays develop plasticity when wet, due to a molecular film of water surrounding the clay par ...
particles dispersed in
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
to migrate. It is ultimately caused by the presence of a charged interface between the particle surface and the surrounding fluid. It is the basis for analytical techniques used in chemistry for separating molecules by size, charge, or binding affinity.
Electrophoresis is used in laboratories to separate
macromolecule
A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...
s based on size. The technique applies a negative charge so proteins move towards a positive charge. Electrophoresis is used extensively in
DNA,
RNA
Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
and
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
analysis.
History
Theory
Suspended particles have an
electric surface charge
Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge dis ...
, strongly affected by surface adsorbed species, on which an external electric field exerts an
electrostatic
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...
Coulomb force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
. According to the
double layer theory, all surface charges in fluids are screened by a
diffuse layer
A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
of ions, which has the same absolute charge but opposite sign with respect to that of the surface charge. The
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
also exerts a force on the ions in the diffuse layer which has direction opposite to that acting on the
surface charge
Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...
. This latter force is not actually applied to the particle, but to the
ions
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
in the diffuse layer located at some distance from the particle surface, and part of it is transferred all the way to the particle surface through
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
. This part of the force is also called electrophoretic retardation force, or ERF in short.
When the electric field is applied and the charged particle to be analyzed is at steady movement through the diffuse layer, the total resulting force is zero :
:
Considering the
drag on the moving particles due to the
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
of the dispersant, in the case of low
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
and moderate electric field strength ''E'', the
drift velocity
In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an a ...
of a dispersed particle ''v'' is simply proportional to the applied field, which leaves the electrophoretic
mobility
Mobility may refer to:
Social sciences and humanities
* Economic mobility, ability of individuals or families to improve their economic status
* Geographic mobility, the measure of how populations and goods move over time
* Mobilities, a contemp ...
μ
e defined as:
:
The most well known and widely used theory of electrophoresis was developed in 1903 by
Smoluchowski:
:
,
where ε
r is the
dielectric constant
The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...
of the
dispersion medium
Interface and colloid science is an interdisciplinary intersection of branches of chemistry, physics, nanoscience and other fields dealing with colloids, heterogeneous systems consisting of a mechanical mixture of particles between 1 nm ...
, ε
0 is the
permittivity of free space
Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...
(C² N
−1 m
−2), η is
dynamic viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...
of the dispersion medium (Pa s), and ζ is
zeta potential
Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface.
Zeta potential is a scientific term for electrokinetic potential in coll ...
(i.e., the
electrokinetic potential
Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface.
Zeta potential is a scientific term for electrokinetic potential in coll ...
of the
slipping plane
A double layer (DL, also called an electrical double layer, EDL) is a structure that appears on the surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The D ...
in the
double layer, units mV or V).
The Smoluchowski theory is very powerful because it works for
dispersed particles
Dispersion may refer to:
Economics and finance
*Dispersion (finance), a measure for the statistical distribution of portfolio returns
*Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variatio ...
of any
shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type.
A pl ...
at any
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
. It has limitations on its validity. For instance, it does not include
Debye length
In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
κ
−1 (units m). However, Debye length must be important for electrophoresis, as follows immediately from Figure 2,
"Illustration of electrophoresis retardation".
Increasing thickness of the double layer (DL) leads to removing the point of retardation force further from the particle surface. The thicker the DL, the smaller the retardation force must be.
Detailed theoretical analysis proved that the Smoluchowski theory is valid only for sufficiently thin DL, when particle radius ''a'' is much greater than the Debye length:
:
.
This model of "thin double layer" offers tremendous simplifications not only for electrophoresis theory but for many other electrokinetic theories. This model is valid for most
aqueous
An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be rep ...
systems, where the Debye length is usually only a few
nanometers
330px, Different lengths as in respect to the molecular scale.
The nanometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American and British English spelling differences#-re ...
. It only breaks for nano-colloids in solution with
ionic strength
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as ...
close to water.
The Smoluchowski theory also neglects the contributions from
surface conductivity
Surface conductivity is an additional conductivity of an electrolyte in the vicinity of the charged interfaces. Surface and volume conductivity of liquids correspond to the electrically driven motion of ions in an electric field. A layer of coun ...
. This is expressed in modern theory as condition of small
Dukhin number The Dukhin number () is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic effects, as well as to electrical conductivity and permittivity of fluid heterogeneous s ...
:
:
In the effort of expanding the range of validity of electrophoretic theories, the opposite asymptotic case was considered, when Debye length is larger than particle radius:
:
.
Under this condition of a "thick double layer",
Hückel predicted the following relation for electrophoretic mobility:
:
.
This model can be useful for some nanoparticles and non-polar fluids, where Debye length is much larger than in the usual cases.
There are several analytical theories that incorporate
surface conductivity
Surface conductivity is an additional conductivity of an electrolyte in the vicinity of the charged interfaces. Surface and volume conductivity of liquids correspond to the electrically driven motion of ions in an electric field. A layer of coun ...
and eliminate the restriction of a small Dukhin number, pioneered by Overbeek. and Booth. Modern, rigorous theories valid for any
Zeta potential
Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface.
Zeta potential is a scientific term for electrokinetic potential in coll ...
and often any ''aκ'' stem mostly from Dukhin–Semenikhin theory.
[Dukhin, S.S. and Semenikhin N.V. "Theory of double layer polarization and its effect on electrophoresis", Koll.Zhur. USSR, volume 32, page 366, 1970.]
In the thin double layer limit, these theories confirm the numerical solution to the problem provided by O'Brien and White.
For more modeling more complex scenarios, these simplifications become inaccurate, and the electric field must be modeled spatially, tracking it's magnitude and direction.
Poisson's equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with th ...
can be used to model this spatially-varying electric field. It's influence on fluid flow can be modeled with the Stokes Equation
, while transport of different ions can be modeled using the
Nernst–Planck equation
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect t ...
. This combined approach is referred to as the Poisson-Nernst-Planck-Stokes equations
. This approach has been validated the electrophoresis of particles
.
See also
References
Further reading
*
*
*
*
*
External links
List of relative mobilities
{{Authority control
Analytical chemistry
Colloidal chemistry
Electromagnetism