22 Electrophoresis and Electroosmosis*
Electrophoresis
Electrophoresis refers to the solution-phase migration of charged species in an electric field. This electric field is created by applying a potential (i.e. voltage) across two metal electrodes located at different points in an electrolyte solution. Cations migrate toward the cathode (negatively charged electrode) while anions migrate toward the anode (positively charged electrode). Applied voltages range from many tens of volts up to tens of kilovolts, depending on the distance between the electrodes and the desired field strength. Electric field strengths are measured with units of V cm–1.
The migration rate, v, of a charged species is Eqn. 22.1, where µ is the electrophoretic mobility and E is the electric field strength.
(Eqn. 22.1) [latex]v = µE[/latex]
The electrophoretic mobility combines a drag force (i.e. frictional term), f, and an accelerating force from the net charge, q, as µ = q/f. Stokes’ Law estimates f = 6πηr for a small ion in electrolyte solution, where η is the viscosity of the solution and r is the hydrodynamic radius of the ion. Ions with a higher magnitude of charge thus have greater electrophoretic mobility. For ions with the same charge, the electrophoretic mobility increases in magnitude as the hydrodynamic radius decreases.
Electroosmosis
At macroscopic scales, electrophoresis is the dominant form of voltage-induced mass transport. At microscopic scales, electroosmosis becomes important.
Electroosmosis most famously occurs in silica capillaries or in fluidic channels with glass surfaces. Silanol (–Si–OH) groups at silica and glass surfaces are weak acids and ionize (–Si–O–) in aqueous solution across a wide range of pH, resulting in a negative surface charge. This charge attracts hydrated counter ions, such as Na+ (aq), to the surface. When these counter ions migrate by electrophoresis, they drag water molecules along with them. The result is the net flow of water toward the cathode, which also transports neutral molecules. The velocity of the electroosmotic flow depends on the magnitude of the applied electric field, the charge density on the silica or glass surface, and the ionic strength of the solution.
Net Migration
In experiments, dissolved molecules and ions migrate under the combined effects of electrophoresis and electroosmotic flow (EOF). Apparent mobilities for chemical species are the sums of their individual electrophoretic mobilities and the system electroosmotic mobility. Under most conditions at microscopic scales, electroosmosis dominates such that anions still have net motion toward the cathode. Cations migrate the fastest under the synergistic effects of electrophoresis and electroosmosis, neutral species migrate at the rate of electroosmosis, and anions migrate most slowly due to the opposing effects of electrophoresis and electroosmosis. Thus, more highly charged cations migrate faster whereas more highly charged anions migrate more slowly.
Connections
- The charging current in voltammetric methods (Ch. 17) arises from the electrophoretic migration of ions.
- Electrophoresis is similar to voltammetry in that a voltage is applied across a sample, but also opposite: in voltammetry (Ch. 16), the charging current is a side effect and redox reactions are of interest; in electrophoresis, redox reactions (e.g. reduction and oxidation of water at opposite electrodes) are side effects and the migration of ions is of interest.
- Electric fields driving the movement of ions is also important to the operation of analyzers for mass spectrometry (Ch. 27).
Post-Reading Questions
- For a consistent distance between the anode and cathode, how does the electrophoretic migration rate change when the applied voltage is increased?
- Will EOF occur in a plastic (e.g. polyethylene terephthalate) capillary?
- How can heating of the solution be reduced in an electrophoresis experiment?
Topic Learning Objectives
The chapter is a primer for the following learning objectives, which will be covered in lecture and/or with additional assigned reading:
- Understand how the electrophoretic force, the drag force, and EOF result in a constant migration velocity for an ion.
- Understand the role for supporting electrolyte and the origin Joule heating.
- Understand the molecular origin of the EOF.
- Draw a diagram of the flow profile for EOF versus pressure-driven flow.
- Predict the relative migration rates for a set of molecules.