This month in "GC Connections" John Hinshaw examines the anatomy of chromatographic peaks with attention to features that
help determine the suitability of individual chromatographs for a specific analysis task.
The human sense of shape and pattern recognition can discern subtle nuances among groups of visual cues that no computer system
can reproduce faithfully. Yet when it comes to measuring and evaluating chromatograms, analysts put a great deal of faith
into their computerized data handling systems. Over the course of one year a practicing chromatographer might look at 10,000
or more peaks. After some time an observer develops a finely tuned sense of what constitutes a good or bad peak shape, which
peaks will be detected and measured correctly by the data system, and an overall idea of how the observed peaks indicate the
instrumentation operational health. This sense is formalized in system suitability software that determines an array of chromatogram
metrics from test analyses and compares them to goals or minimum performance levels. These programs confirm the suitability
of individual chromatography systems to perform specific analytical tasks, often on a daily basis. Such software relies upon
accurate designation of target peaks and parameters when set up: Otherwise it is bound to perform poorly and can fail to find
Chromatographers who use data-handling or suitability software or who make such measurements themselves should have a thorough
understanding of the various metrics that are extracted from a chromatogram. Without this awareness they relinquish control
over the quality of their results — they are using a tool without a working knowledge of its functions and limitations.
This month's "GC Connections" examines the basic measurements of a peak's size and shape as used for purposes of assessing
and monitoring chromatographic separations over a period of time. The calculations presented here represent some of the most
commonly used metrics of this type. Other related calculations are found throughout various commercially available performance
monitoring systems as well as in individual laboratories' quality control (QC) and quality assurance (QA) procedures. This
column instalment is intended to aid in the general understanding of these calculations and it does not purport to present
computations that are any more or less appropriate than others.
Getting into Shape
As solutes enter and pass through a chromatography column and out to the detector they are subject to various processes that
modify the peaks' profiles as finally registered by a data system or chart recorder. Peaks must be constrained within certain
limits of retention time, width, and shape if minimum levels of peak resolution are to be maintained. By measuring their peak
shapes, chromatographers obtain information about the ability of their systems to perform a specific analysis as well as about
possible sources of peak shape distortion.
In an ideal chromatography system the separation process results in the normal Gaussian-shaped peak that is the basis for
many metrics. The Gaussian peak shape is a product of a statistical theoretical treatment of the solutes' transit through
a chromatography system. It represents a simple basis on which analysts can make a number of measurements by assuming that
it closely approximates their peak shapes. This assumption is justified by the random-walk and other theories of chromatography
that approximate the separation process as if it were the product of the bulk behaviour of large populations of solute molecules.
The randomness of the process results in a Gaussian peak elution profile. Additional effects, primarily extracolumn in nature,
act to modify the peak profile. Slow detector response speeds and broad injection profiles, relative to band spreading in
the column, are the two most common extracolumn effects.
Peak Width: A normal Gaussian distribution curve can be characterized by the fraction of its total area that lies within certain distances
from its midpoint. These distances are expressed in terms of multiples of the curve's standard deviation (σ), which is the
distance between the apex of the peak at its midpoint and the inflection points (Figure 1[c]). The inflection points lie on
either side of the peak's midpoint, where the slope of the curve reaches its maximum absolute value: They span a width (w
i) of 2σ from the left-hand point to the right-hand point. Approximately 68% of the area under a Gaussian curve lies between
the inflection points at ±1σ from its midpoint and 95.5% lies within ±2σ (Figure 1[b]). The extent of this distance, which
is defined as the peak width at base (w
b = 4σ), corresponds to the intersection points of lines drawn tangentially to the inflection points (Figure 1[d]). A distance
of ±4σ from the midpoint accounts for more than 99.95% of the area.
Figure 1: Idealized chromatography peak. A normal Gaussian peak plotted as the departure from its midpoint in standard deviation
(σ) units. The signal amplitude is relative to the peak crest, which is equal to 1.0. (a) Peak width at half-height, wh; (b) peak width at base, wb; (c) peak width at the inflection points, wi; (d) lines drawn tangentially to the inflection points intersect the signal baseline at the base width of the peak. Adapted
from reference 1.
The width at half-height (w
h) is the most commonly used peak-width metric because it is the easiest to measure manually. The other width metrics are located
at fractional heights. The width at half-height is determined by measuring the height of the peak crest above the baseline,
dividing by two, and then measuring the span between the rising and falling sides of the peak where the signal crosses the
half-height points. The baseline of a peak is not located at the height at the base points (Figure 1[b]), but rather it is
the signal in the absence of any peaks. For single peaks the baseline can be constructed by a line that intersects the detector
signal at a distance greater than ±4σ on either side of the peak's midpoint. Unlike the widths at the inflection points and
at the base, the width at half-height of a normal Gaussian distribution is not an integral multiple of the standard deviation;
instead it equals 2.354σ.
The relationships among these peak-width measurements in terms of the width at half-height and sigma are:
Asymmetry: Only computer-generated Gaussian peak shapes (such as seen here) are perfectly symmetrical from front to back. Real chromatographic
peaks have some degree of asymmetry; their front and back halves are not the same shape. Extra-column dead volumes, peak mass
overloading, and reversible adsorption effects are some of the principal causes of peak asymmetry. Typically, excessive dead
volume as well as solute adsorption will cause peaks to tail, so that the back half is wider than the front, while overloading
the column with too much solute mass will create so-called fronting peak shapes that have a wider front part.
Analysts commonly use two different peak asymmetry metrics. First is the asymmetry factor (a), which is determined from the front (f) and back (b) peak widths at 20% of the peak height:
The second asymmetry metric is the tailing factor (TF), which uses the front and back widths at 5% of the peak height:
Figure 2 illustrates peak asymmetry measurements. The asymmetric peak shown here has the front and back widths at 10% and
5% height, asymmetry factor, and tailing factor shown in Table 1. For tailing peaks both factors will be greater than 1.0
and for fronting peaks they will be less than 1.0. In general, the asymmetry and tailing factors are similar in value as long
as the peak asymmetry is moderate (0.5 < a < 2.0). For peaks with a larger amount of tailing, the asymmetry factor tends to
be larger than the tailing factor, such as in this example, where the asymmetry factor a = 3.5 but the tailing factor is only 2.27. Thus, it is important to select and identify which peak asymmetry metric to use
for a particular application.
Figure 2: Measurements from an asymmetric chromatography peak. See text and Table 1 for explanation and asymmetry calculations.
Peak asymmetry metrics are useful when peak tailing is a concern. For example, in the analysis of carboxylic acids, phenols,
organic bases, or free amino acids by gas chromatography (GC), the polar nature of these solutes often produces marked peak
tailing. With extended use, columns may accumulate absorptive debris or experience a loss of surface deactivation that leads
to increased polar peak tailing and subsequent loss of resolution as well as compromised minimum detectable levels. By regularly
monitoring the asymmetry of these peaks, analysts can anticipate this kind of problem before it becomes serious and take steps
to remedy it.
Table 1: Asymmetry calculations from Figure 2.
Plates: The peak in Figure 1 is normalized to standard deviation units (σ), which are readily expressed in terms of the widths in
seconds at the inflection points, at half-height, or at base with the expressions in equations 1–3. However, measuring just
the peak width without also considering the time the peak took to be eluted removes the peak from the context of its column
passage. A peak with width at half-height equal to 2 s could be very good or very bad, depending on its elution time. Thus,
consideration of the peak width in the context of its retention time is important when measuring column quality.
To make meaningful comparisons from peak to peak or column to column, chromatographers can use the theoretical plate concept.
These plates are entirely theoretical — no physical plates exist in the column. The term "plate" in this context comes from
industrial distillation columns. One way to produce fractions of higher purity is to add a series of internal metal plates
to the distillation column. Early in the development of the petroleum and related chemical industries, distillation columns
that gave a cleaner fractionation of mixtures were said to have high plate numbers and were deemed more efficient than columns
with lower plate numbers. This terminology was imported by petroleum chemists who become involved in chromatography.
For the purposes of this discussion the theoretical plate concept expresses the basic ability of a chromatographic column
to maintain solutes' distribution profiles as they pass through it. Peak widths upon elution from the column will always be
greater than at entry: Columns with greater theoretical plate numbers will broaden the solute bands less than columns with
fewer theoretical plates will.
The number of theoretical plates (N) relates the statistical standard deviation of a peak (σ) to the peak's elution time (t
As shown in equation 6, N can also be calculated from peak width measurements directly. Higher chromatographic theoretical plate numbers mean that
a peak will be narrower at a given retention time. As retention times increase, it follows that peaks with the same number
of theoretical plates will exhibit proportionately increasing widths as well. Figure 3 shows two symmetrical peaks, both with
50,000 area counts and 10,000 theoretical plates, which are eluted at 5 min and at 10 min; the second peak is twice as wide
as the first. The additional band spreading of the later peak also causes its height to decline in proportion.
In the context of asymmetrical peaks and peak tailing, theoretical plate number calculations that use the width at 10% of
the peak height may better reflect the greater overlap of tailing peaks. Since w
0.1 = 4.3σ, this theoretical plate calculation can be expressed as
Figure 3: Two peaks with identical theoretical plate numbers and area. Peak 1: Peak at 5.0 min with 10,000 plates and 50,000
µV-s area. Peak 2: Peak at 10.0 min with 10,000 plates and 50,000 µV-s area.
Chromatographers often use theoretical plate numbers as a basis for comparison of multiple columns of the same type. Taken
in the context of peak widths and retention times, plate number calculations provide an extra metric when qualifying replacement
columns in existing analyses as well as for ongoing separation quality control.
Plate Height: The number of theoretical plates depends directly on the length of a column. Longer columns of the same diameter and stationary
phase will yield more theoretical plates under the same operating conditions. Cutting pieces off a column will reduce the
total theoretical plate count. Due primarily to carrier-gas compressibility effects as well as to unequal coating characteristics
along the column length, this relationship is not truly linear: Half of a column will not have exactly half as many theoretical
plates as the original. To express the average performance of a column independently of its length, chromatographers often
use two additional metrics related to the number of theoretical plates.
The first of these is the length of column that corresponds to one theoretical plate. Termed the height equivalent to a theoretical
plate (h) or simply the plate height, this metric is equal to the length of a column (L) divided by N:
Here, the word height is also imported from distillation column technology and does not strictly apply to coiled chromatography
columns. An older name for this metric is height equivalent to a theoretical plate (HETP). The column length is expressed
in centimetres or millimetres for this calculation. If the column that produced the chromatogram in Figure 3 was 10 m (10,000
mm) long, then the two peaks each would have h = 1.0 mm. A related metric is the number of theoretical plates per metre of column length. If h = 1.0 mm, then N/L will be 1/(1 × 10-3) or 1000 theoretical plates/m.
It is important to understand that these three metrics related to theoretical plates (N, h, and N/L) all refer to the average broadening process that any one specific band of solutes undergoes as it transits the column. If
one peak exhibits 10,000 theoretical plates another peak next to it might measure 8000 or 12,000 plates because of differences
in the nature of the chemical interactions of different solutes with the column and stationary phase. In addition, the column
inherits the band shapes of solutes as they exit the inlet system and presents the eluted bands to the detector, so extracolumn
band-spreading effects arising in the inlet or detector system will be included in the observed peak shapes. Thus, peak width
and theoretical plate metrics reflect the overall system performance and not just the column alone.