# Difference between revisions of "Electrophoresis"

Written by Kevin Tian, AP 225, Fall 2011 --Ktian 20:06, 5 December 2011 (UTC)

Electrophoresis (EP) is an electrokinetic phenomenon that involves an interaction between the charges on a particle and a uniform electric field. The charges interacting with the electric field are in fact resulting from the formation of a double-layer of charge at the surface of specific particles in aqueous media. The effect itself can be a manifestation of apparent charge, as it does not require the particle have a net charge. The phenomenon should not be confused with Dielectrophoresis, which requires upon a spatially non-uniform electric field (EP does not though it will still work in the such conditions).

It is also possible for the EP effect to appear under AC field conditions, however this effect is limited to *very* low frequencies, as otherwise damping prevents the charges from moving fast enough for any forces to manifest themselves.

## Basic Concept

Figure 1: Taken from Wikimedia commons [1]. Image depicting the main forces involved in electrophoresis on an arbitrary particle.

The essential force is no different from that of an electrostatic force described by Coulomb's law. However the distinction is in the model used to describe the particles, namely the double-layer theory. As per said theory, it is believed that there is a 'core' that has a net surface charge. However this charge is screened by a diffuse layer of ions with the same magnitude but opposite sign of charge as the core surface charge.

If we were to then apply an electric field to this double-layer particle system in the context of an aqueous medium, we obtain the situation seen in Figure 1. We would have an electrostatic force (on the core surface charge) acting in one direction, and the frictional viscous force and EP Retardation forces (from the diffuse layer of ions) acting in the opposite direction. If the ions did not move, then this would result in a net zero force.

However since this diffuse layer of ions is mobile, the applied field sets it in motion. This motion creates a fluid flow parallel to the surface of the particle, generating shear stress on the particle via the fluid convection. The particles motion comes about in reaction to this shear stress.

## Basic Theory

Figure 2: Taken from Wikimedia commons [2]. Image illustrates the rationale behind the EP retardation force.

With this model in mind, the next step would be to quantitatively describe how particles move with a known electric field. By taking the force balance of the three forces and noting the expression for viscous drag and the electrical forces, one can obtain an expression for the electrophoretic mobility[3]:

$\mu_e = {{v}\over{E}}$.

Several theories have been put forth to describe the motion, with the most famous one being proposed by Marian Smoluchowski in 1903 [4] which yields the EP mobility as

$\mu_e={{\epsilon_m \zeta}\over{\eta}}$, where $\epsilon_m$ is the permitivity of the medium, $\zeta$ is the zeta potential and $\eta$ is the viscosity of the medium.

However though this theory is powerful (it applies to a particle of arbitrary shape and concentration) it is not widely applicable due to limited validity. Figure 2 illustrates one reason for this limited validity, namely the lack of including the Debye length in the theory. Since the Debye length describes the length scale over which electronic screening of an external field by mobile charges can actually occur, one notices that its omission is quite serious for general validity of the theory. If one increases the thickness of the double layer (mobile charges), it would follow that the retardation force weakens, yet this is not reflected in the Smoluchowski theory.

## Applications

Electrophoresis has been used in a variety of sorting techniques, where it may be desirable to sort a mixture of compounds, proteins and/or particles as according to their size and charge. Since those two parameters affect how strong the EP force on the particle is (on thus it's resulting velocity), simply performing EP on the entire sample will naturally separate the particles since the less charged and larger particles will move through a medium faster than the strongly-charged, smaller particles. Many examples of EP can be found in biology, a field where techniques such as Gel electrophoresis and Electroblotting have been extensively used with genetic material (DNA, RNA) and proteins.

## References

[4] von Smoluchowski, M. (1903). Bull. Int. Acad. Sci. Cracovie 184.