19 Chromatograms and Separation Efficiency*
Analytes are separated in a chromatography experiment because they have different partition coefficients—equilibrium constants (K) for the concentrations of analyte, A, between the stationary and mobile phases (Eqn. 19.1).
(Eqn. 19.1) [latex]K = \frac{[A]_{stat}}{[A]_{mob}}[/latex]
All analytes move along the length of the chromatography column at the same speed when in the mobile phase, and stop moving when associated with the stationary phase. Analytes that spend more time associated with the stationary phase thus take longer to elute, or, in other words, are retained for a greater time. The retention time of an analyte is proportional to its partition coefficient.
A chromatogram is a plot of signal versus time. Sample injection occurs at time zero and the signal is from a detector placed at the end of a chromatography column. When analytes have sufficiently different partition coefficients, a chromatogram shows a series of resolved peaks that do not overlap with one another. However, when the partition coefficients for two or more analytes are very similar, full separation may not occur and the peaks on a chromatogram will overlap.
Band Broadening
Hypothetically, a sufficiently long column should be able to resolve two analytes, no matter how small the difference in their partition coefficients. In practice, diffusion imposes a penalty for greater time on a column: the bands (i.e. peaks) of analyte broaden over time, which may result in loss of resolution and/or loss of signal. As a consequence, the efficiency of a separation depends on both the retention time and the peak width. Rate theory for chromatography includes a parameter called the number of theoretical plates, N, defined for an analyte of interest. N is the preferred metric for comparing separation efficiency between different columns or methods. Its value increases as the retention time increases and as the peak width decreases. A related metric is the plate height, H. Unlike N, the value of H is independent of column length. Smaller values of H are preferred.
The van Deemter equation (Eqn. 19.2) models the plate height as a function of the flow rate, v, of the mobile phase, where A, B, and C are coefficients that depend on multiple factors.
(Eqn. 19.2) [latex]H = A + \frac{B}{v} + Cv[/latex]
The A term is a function of the size, shape, uniformity, and general quality of the packing of stationary phase particles. It accounts for the possibility of multiple paths of different length through the packed particles (a.k.a. eddy diffusion). The B term accounts for diffusion along the concentration gradient from the band of analyte (a.k.a. longitudinal diffusion). The C term accounts for the rates of mass transfer between the stationary and mobile phases. Competing effects between these terms results in a local minimum in a plot of H versus mobile phase flow rate, albeit that recent advances have made H less sensitive to flow rate.
General Elution Problem
The general elution problem is that satisfactory conditions for the separation of both weakly-retained and strongly-retained analytes are difficult to obtain. When the weakly-retained analytes are well separated, the strongly-retained analytes are broadened too much. When the strongly-retained analytes are separated with sharp peaks, the weakly-retained analytes are not resolved.
The above problem is addressed by changing the conditions over the course of the separation. In liquid chromatography, gradient elution is the most common approach. It takes the form of sequential or gradual changes in the solvent composition of the mobile phase over time. In gas chromatography, the most common approach is changes in temperature over time. In both cases, the general preference of analytes for the mobile phase is increased over time. Weakly-retained analytes are separated under conditions that promote interactions with the stationary phase, then the elution of strongly-retained analytes is sped up by conditions that reduce interactions with the stationary phase. This approach helps obtain sharp and resolved peaks for all analytes.
Connections
- Gradient elution is a method of changing the partition coefficient (Ch. #) on the fly.
- It is useful to conceptualize the number of theoretical plates as the number of times a partition equilibrium (Ch. #) is established along the length of the column (in reality, true equilibrium is never established due to the constant elution).
- Although many figures of merit and other metrics of performance are more favourable when their value is larger, the plate height, like a limit of detection (Ch. #) is more favourable when a smaller value.
Post-Reading Questions
- Does band broadening from the A, B, and C terms in the van Deemter equation get smaller, stay constant, or get larger from increases in mobile phase flow rate?
- Will an analyte with a larger partition coefficient have a shorter or longer retention time?
- What happens to the efficiency of the separation when the A, B, and C terms increase in magnitude in the van Deemter equation? Answer separately for each term.
- Based on the van Deemter equation, sketch the expected trends in plate height versus flow rate for each of the A, B, and C terms. Make a separate sketch for each term, then for the combined effect of all three terms.
- When using a C18 column, should a gradient elution be programmed to gradually transition the mobile phase from water to acetonitrile, or from acetonitrile to water?
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:
- Sketch a chromatogram and label the migration time, a peak for a less-retained analyte, and a peak for a more-retained analyte.
- Quantitatively relate partition coefficient with capacity factor and retention time.
- Qualitative and quantitatively describe the resolution between two chromatogram peaks.
- Relate the number of theoretical plates and plate height to separation efficiency.
- Describe the phenomena that contribute to the A, B, and C terms in the van Deemter equation.
- Propose a gradient elution method for a given type of chromatography, including examples of mobile phases.