Until now, all lessons in this course have focused on chromatographic techniques. However, other powerful separation methods exist, including capillary electrophoresis (CE). This lesson introduces the fundamental principles of CE, a high-efficiency technique that separates ionic and ionogenic species based on their migration in an electric field. Students will explore how analytes move in response to an electric field, how heat is generated and managed, and why CE is particularly well-suited to small and complex ionic molecules.
Learning Goals #
After this lesson you should be able to
Explain the principle of electrophoresis and how ionic species migrate under the influence of an electric field.
Describe the types of analytes suitable for capillary electrophoresis.
Discuss the generation of current and power in CE and the significance of Joule heating.
Define electrophoretic mobility and describe the factors that influence it.
Explain the origin and implications of electro-osmotic flow in CE.
READ MODULE 5.1
ONLY THE INTRODUCTION UNTIL (and excluding) SECTION 5.1.1
1. Introduction #
1.1. Principle of electrophoresis #
In chromatography analyte molecules or ions spend periods of time in the mobile phase, during which they migrate through the column (or across a TLC plate), and periods in the stationary phase, during which migration is paused. This was covered in Lesson 1.
Figure 1. Schematic illustration of the principle of electrophoresis. In this figure, electrophoresis occurs inside a capillary, but it can also be conducted in other formats.
The situation is different when analye ions migrate under the influence of an electric field (see picture). Analyte cations migrate towards the negative cathode, whereas analyte anions migrate towards the positive anode. Different species can be separated with high resolution, if their migration velocities are sufficiently different. This is the principle of electrophoresis and it is illustrated by the separation of amino acids in the electropherogram shown in Figure 2. This was obtained using the capillary version of the technique (capillary electrophoresis) that provides a high separation efficiency (narrow peaks).
Figure 2. Example of an electropherogram displaying the separation of different amino acids by capillary electrophoresis (CE). Based on data from [1].
1.2. Applications of CE #
It follows from the above that the applications field of capillary electrophoresis (CE) is limited to ionic (permanent ions) or ionogenic (ionizable) analytes.
EXERCISE 1
Which of the following classes of analytes do you think capillary electrophoresis (CE) is applicable to?
This is correct! Capillary electrophoresis is applicable to a large number of classes of analytes.
This is not correct. Try again! Hint: A very large number of classes are applicable!
It turns out that CE does have a broad range of applications. For mixtures of small anions it offers unique solutions (see electropherogram below; I.S.= internal standard). Small inorganic cations can be analysed with atomic-spectroscopy techniques (AAS, ICP, etc.), but CE allows ammonium (and tetramethyl ammonium, etc.) to be included in the set of analytes and allows speciation of ions (e.g. Fe2+ vs. Fe3+).
Figure 3. Separation of small (A) anions, and (B) inorganic cations by capillary electrophoresis. I.S. denotes as internal standard. Based on data from [2].
Many metabolites are ionic or ionogenic, as are small-molecule drugs. The latter are predominantly weak bases that can be protonated. Occasionally, they are (dissociatable) acids. Nucleotides have phosphate groups (see picture) and amino acids, peptides and proteins are amphoteric compounds. All these classes of analytes are amenable with CE.
Arne Tiselius (1902-1971, Sweden)
Arne Wilhelm Kaurin Tiselius performed his doctoral studies on the “moving-boundary” method, which later became known as zone electrophoresis. He was fascinated by the study of proteins in biological samples, including human serum. He was awarded the Nobel Prize in Chemistry in 1948, at the age of 46. In 1919, Tiselius spoke words that seem remarkably true more than 100 years later: “We live in a world where, unfortunately, the distinction between true and false appears to become increasingly blurred by manipulation of facts, by exploitation of uncritical minds, and by the pollution of the language.”.
2. Current and Power #
2.1. Electric field #
Electrophoretic separations are driven by voltage and not by pressure (in fact, any pressure differences, e.g. due to having the buffer vials at different heights) should be avoided. Electrophoretic mobility (in a particular buffer) is an intrinsic property of the analyte ions.
The liquid phase between the electrodes is commonly referred to as background electrolyte (BGE) or simply “buffer” (not as mobile phase, because there is no flow if only electrophoretic effects are in play). Because buffers are conductive, applying a voltage (V in volts, V) leads to an electrical current (I, in amperes, A), described by Ohm’s law (I=V/R, where R, in Ohm, \Omega, is the resistance of the BGE between the electrodes), which in turn leads to the production of heat. The power (P in Watt, W) is described by Joule’s law (P=I^2 \cdot R or simply P=I\cdot V).
Figure 4. Separation of peptides by capillary electrophoresis.
2.2. Heat #
In an electrophoretic cell the produced heat causes differences in temperature, which in turn produces differences in liquid density, resulting in convective movement of the liquid. Such convections jeopardize electrophoretic separations and they need to be minimized.
In the history of electrophoresis convective flows were counteracted by stabilizing media, such as paper strips (paper electrophoresis) or gels (gel electrophoresis). An alternative approach is to use very narrow electrophoretic channels (capillary electrophoresis, CE). CE allows effective heat dissipation and very efficient, fast separations at high voltages. An example is the separation of a tryptic digest of b-galactosidase shown in Figure 4.
3. Instrumentation #
The basic instrumentation for CE is shown below. Common internal diameters of the fused-silica capillaries used are between 50 and 100 µm; capillary length (from injection to detection 150 to 500 mm); voltages 10 to 30 kV. UV spectroscopy s the most common detection principle. There are two common injection methods, which are fundamentally different. In pneumatic injection, the BGE reservoir at the capillary inlet is replaced by a sample vial and a pressure difference is applied for a short period of time. In electrokinetic injection a voltage is applied instead of a pressure pulse. Pneumatic injection results in the non-selective injection of the entire sample, whereas electrokinetic injection leads to the selective injection of ionic analytes
Figure 5. Simplified schematic of an instrument used for capillary electrophoresis.
READ SECTION 5.1.1
Basic Theory of CE
4. Migration of ions in an electric field #
4.1. Electrophoretic mobility #
An ion i moves through the BGE with a migration velocity v_i given by
Equation 5.3: v_i=\mu_i \cdot E = \frac{\mu_i \cdot \Delta V}{L}
where \mu_i is defined as the electrophoretic mobility of the ion, E is the field strength, V the applied voltage and L the total length of the capillary. A steady-state, constant ion velocity is achieved when the electrical force exerted on the ion (F_{\text{el}}=z_i \cdot E), where [latez]z_i[/latex] is the charge of the ion, is equal to the viscous counterforce (Stokes’ law, F_{\text{visc}}=6\pi \cdot \eta \cdot r_i \cdot v_i), where \eta is the viscosity of the solution, r_i the radius of the ion. Setting F_{\text{el}}=F_{\text{visc}} results in
Equation 5.4: \mu_i=\frac{v_i}{E}=\frac{z_i}{6 \pi \cdot \eta \cdot r_i}
showing the electrophoretic mobility to depend on the charge-to-size ratio of the analyte particle (z_i/r_i) and on the viscosity of the solution.
Figure 6. Forces (large, dark-blue arrows) applied to an analyte cation as it migrates towards the negative cathode in an electrophoretic system as indicated by the pink arrow. The small light-blue arrows pointing to the left indicate a retardation effect caused by the net negative charge of the diffuse ion cloud (light blue) surrounding the analyte cation.
EXERCISE 2
Why do H⁺ (or H₃O⁺) and OH⁻ ions exhibit exceptionally high electrophoretic mobilities in aqueous solution?
This is correct!
This is not correct. Try again!
Try to explain why Li+ has a lower mobility than electrophoretic mobility than Na+.
This is correct!
Unfortunately, this is not correct. Try again! Look carefully at the equations for migration time.
For weak ions, the effective mobility (\mu_{\text{eff}}) is determined by the mobility of the ion and the fraction (\alpha) of the molecules that are ionized, i.e.
The fraction can be calculated if the \text{p}K_{\text{a}} value(s) of the analyte and the pH of the BGE are known. Effective mobilities of various species are illustrated in the figure below.
Figure 7. Schematic illustration of the change in mobility with pH for acidic, basic, amphoteric and proteinaceous compounds.
EXERCISE 3
What is the net charge of amino acids in a background electrolyte (BGE) with pH = 2?
Correct! At pH 2, amino acids typically carry a net positive charge due to protonation of both functional groups.
Protonation does not always lead to a net zero charge. Also note that at low pH, the carboxyl group is protonated, not deprotonated.
Why do different amino acids have different electrophoretic mobilities at pH = 2, even though they carry the same charge?
Correct! Small variations in size and solvation result in different charge-to-size ratios.
At pH 2, most amino acids are fully protonated.
Electrophoretic migration is slowed down by retardation and relaxation effects. The retardation is an extra viscous drag caused by the diffuse cloud of BGE ions around the analyte cation. Because this cloud has an excess charge that is opposite to that of the analyte ion, it is pulled in the opposite direction. Because the cloud is disturbed, this causes a rearrangement of the solvation shell (relaxation). The diffuse ion cloud contracts when the ionic strength of the BGE (I) increases. As a rough guidline, electrophoretic mobility decreases roughly in proportion with \sqrt{I} as aresult of retardation and relaxation effects.
READ SECTION 5.1.2
Electro-osmotic flow
4.2. Electro-osmotic flow (EOF) #
When the pH increases above about a value of 2, the silanol groups at the inner wall of the fused-silica capillary increasingly deprotonate and the wall becomes negatively charged. This is compensated by an electrical double layer with an excess positive charge. If an electric field is applied this double layer is pulled towards the negative electrode, causing an electro-osmotic flow (EOF). This is illustrated in the figure below.
Figure 8. Schematic explanation of the concept of the electro-osmotic flow (EOF).
The EOF reaches its maximum around pH = 7 and it decreases with increasing ionic strength of the BGE. The EOF is affected by the condition of the surface. It will be reduced if components from the sample are adsorbed on the surface or if ions from the sample or the BGE exchange with protons of the silanols. If the this happened the capillary may be reconditioned by washing with acid and organic solvents.
The apparent mobility of analyte i is the sum of their electrophoretic mobility and the mobility of BGE due to the EOF, i.e.
Equation 5.8: \mu_{\text{app},i}=\mu_{\text{EOF}}+\mu_i
For anions the electrophoretic mobility is in the opposite direction of that of cations and the EOF, meaning that their mobility is effectively subtracted from the EOF. If the EOF exceeds the electrophoretic mobilities of the anions, all analytes move in the same direction, so that cations and anions can be analysed in a single run, as illustrated in the figure below.
Figure 9. Constructed electropherogram, showing cations (pink) migrate faster to the detector than neutrals (white), while anions (light blue) move slower.
Concluding remarks #
Capillary electrophoresis offers a powerful alternative to chromatographic methods for the separation of ionic and ionogenic analytes. Its high efficiency stems from the absence of a stationary phase and the use of an electric field instead of pressure-driven flow. This lesson introduced the principles underlying CE, the types of analytes it can separate, and how instrumental and physicochemical parameters, such as electrophoretic mobility and electro-osmotic flow, govern separation performance. These foundational concepts will be expanded upon in subsequent lessons.
References #
[1] Q. Zhu, N. Zhang, M. Gong, Rapid amino acid analysis of beers using flow-gated
capillary electrophoresis coupled with side-by-side calibration, Anal. Methods, 2017, 9, 4520, DOI: 10.1039/c7ay01267e
M.A. Travassos Lemos, R.J. Cassella, D. Pereira de Jesus, A simple analytical method for determining inorganic anions and formate in virgin olive oils by capillary electrophoresis with capacitively coupled contactless conductivity detection, Food Control, 2015, 57, 327-332, DOI: 10.1016/j.foodcont.2015.04.026
