# Background

### Fundamentals

In Learning Module 1, we have discussed the mechanics of transport in capillary electrophoresis. Another important consideration is zone broadening, or separation efficiency. In the simplest sense, this is a measure of how skinny a peak is in a separation. A method with high separation efficiency will have smaller band spreading, or peak width. Since separation peaks are ideally Gaussian, peak width is defined by σ, or variance of the Gaussian function used to fit the separation peak. The quantitative descriptor of efficiency is theoretical plates, N, which is related to analyte migration time, and the variance in migration time, σt2, of the Gaussian fit (equation 2.1). You will find other variations of this equation that include width at half height or width of base rather than variance. If you are using Igor Pro, software, the program will report migration time and variance in seconds, and you should use equation 2.1 to calculate theoretical plate count. In an ideal case, the only source of zone broadening is the longitudinal diffusion. In reality, Joule heating may introduce convective flow, and analyte may adsorb to the capillary surface. The detection cell may be a source of variance, for example if the capillary is connected to the detection cell in such a way to allow the analyte band to spread. A key factor in capillary electrophoresis is the band spreading introduced in the sample introduction. For example, if a sample plug is particularly large (for example, 10% of the capillary length), upon separation, the detected analyte peak will generally be larger than the injected plug.

$N = \dfrac{t^2}{σ_t^2} \tag{equation 2.1}$

### Sample Introduction

Sample introduction is generally achieved with pressure, voltage, or siphoning. Pressure-assisted injections involve the application of reproducible pressures in the range of 0.5-5 p.s.i. Gravity-based injections involve raising the injection end of the capillary, immersed in a sample vial, higher than the detection end to promote siphoning. Voltage based injections introduce sample differentially depending of sample mobility. Thus, cations will preferentially load onto a capillary as compared to neutral compounds or anions. A successful injection introduces a small analyte plug in a reproducible manner. Reproducibility is achieved with electronic timing.

### Basic Protocol

Sample introduction in capillary electrophoresis system requires knowledge of the performance, standard operation procedures and a working knowledge of the figures of merit to quantitatively assess whether the injection technique is adequate. Most users learn what is important through experience. To streamline this process, we have outlined a systematic evaluation of different conditions for pressure-assisted injections. The researcher will record migration time and peak width for triplicate runs obtained at various pressure and injection durations. It is important that all other parameters remain the same (capillary dimensions, analyte, buffer, separation voltage...). In doing this, the researcher can effectively gauge the effect of changing either injection pressure or duration. Ultimately, this exercise will assist new researchers in documenting strategies for sample introduction.

### Application

Capillary electrophoresis is frequently employed for quantitative analysis. Reproducible and efficient injections are important for quantitation. The researcher will devise a protocol for quantitative analysis, for example, using a 3-point standard calibration curve. The final exercise of this learning module is a lab practical. A colleague or mentor will provide a sample containing analyte above the limit of quantification. The user will then implement the strategies she/he has devised and determine the analyte concentration as a means of assessing her/his lab skills.