Measurements and Models

1 The Basic Measurements

The basic measurements made by an analyst on a chromatogram for purposes of quantitation are shown in Figure 1.1; they comprise all the 'Y's and 'X's of the trace, the voltages and times, their combinations, repetitions and trends. There are no other measurements to be made, but much analytical information can be derived from these measurements.

These quantities are obtained by integrators, lab computers or data processors – the names are used synonymously throughout this book. The integrator is the only window into the chromatograph to show what is happening. It is both measuring device and diagnostic tool.

Regulatory pressures from Good Laboratory Practice (GLP), Good Manufacturing Practice (GMP), IS0 9000 and bodies such as the US Food and Drug Administration (FDA) put increasing demands on the quality and credibility of analytical results. It is the aim of this book to show analysts how to use integrators to provide good quality results – provided that the chromatography is up to it.

Measurements and Their Use

Integrator measurements serve three analytical purposes:

(1) solute identification and quantitation;

(2) diagnostics, trouble-shooting and system measurement;

(3) results assessment and trend analysis;

and, increasingly, one corporate finance purpose for monitoring:

(4) performance measurement and lab resource utilization.

2 Quantitation

Peak Area and Peak Height

Solute quantity is measured from peak areas and/or heights. In a controlled analysis, peak area is the true measure of solute quantity if the solute elutes intact and is detected linearly. It can be shown to be so theoretically for peaks with or without a known shape, and experimentally by plots of area against solute quantity.

Peak height is an alternative measure of solute quantity. There is no theoretical proof of this unless a specific peak shape such as Gaussian is assumed, but experimentally it is easy to show that plots based on height and quantity are also linear over a usable though smaller range (Figure 1.2), even for peaks that are not particularly symmetrical as long as their shapes do not change. Peak height is an easier measurement to make and has advantages for the measurement of small overlapping peaks, but it ignores most of the data contained in the detector signal.

The choice of which is best to use in practice is discussed at the end of Chapter 2. Area is the normal choice when signal-to-noise ratio (SIN) is large because height is susceptible to peak asymmetry while area is not, and the linear dynamic range for area measurement is greater than for height. When signal-to -noise ratio is small, height is preferred because errors of baseline placement affect height less than area.

Peak 'Volume'

The ability of the photo diode array detector (DAD) to measure peaks over a range of wavelengths allows a third measure of solute quantity: peak 'volume'. Here, all the peak areas measured at the wavelengths to which the analyte species responds are added together to create a three-dimensional measure (time, amplitude, wavelength). It is proposed that this measure is better because it contains more data and more information. For this to be true, background noise must be proportional to analyte signal otherwise the signal-to-noise ratio degrades away from λ max and the benefits of the extra information become compromised by its lower quality. The usual case is that noise has origins independent of the solute signal and does degrade the signal.

Peak volume would be better than area or height if the signal-to-noise ratio is good at all measurements but this may be hard to achieve. With current diode array detectors and current integration software, peak area (measured at λmax) remains the safest measure of solute quantity, especially for trace peaks.

Retention Time and Solute Identity

Once solutes in a mixture have been identified, they are subsequently recognized on a daily basis by their retention times. Integrators assign peak names and response factors to peaks which elute inside a specified time window. If another peak elutes at that time it also will be recognized as the expected peak; if two peaks co-elute they will not be uniquely identified. If retention time varies with sample size due to increasing peak asymmetry, it is quite possible for incorrect identification to be made when a peak crosses from one window into the next. When this happens, the integrator will assign the wrong name, response factor and standard concentration to that peak, and these errors will continue into the final report.

Integrators can measure relative retention time, i.e. the peak retention time compared with the retention time of a standard peak. Experimental variations cancel but the errors of both measurements add together so that relative retention times are more accurate but less precise than absolute retention time. There is also the usual problem of finding a suitable standard.

To an integrator, retention time is the elapsed time from the moment of injection until the peak maximum emerges, which includes the gas or solvent hold-up time. The retention time of asymmetric peaks does not coincide with the centre of gravity of the peak. Separation of the observed retention time tR (mode), from the peak centre of gravity (mean) is one measure of asymmetry (see also: First Moment and Equation 40).

The mean retention has not achieved any common use in the analytical laboratory. It is difficult to measure manually but integrators which sample the peak signal at a fixed frequency could, with a simple addition to their software, measure it very easily. Its theoretical value lies in the separation of tR and tmean being equal to the Exponentially Modified Gaussian (EMG) time constant τ (Figure 1.3).

Column Hold-up Time

The journey time of a molecule or atom of mobile phase from the beginning to the end of the column is called the column hold-up time. Since the mobile phase is the propellant of a chromatograph, no solute can emerge before this time has elapsed. The hold-up time is the shortest retention time possible, it is also equal to the total residence time of a solute in the mobile phase as it traverses the column.

Integrators measure the column hold-up time as the retention time of an unretained solute. Knowing this time allows the analyst to optimize mobile phase flow rate to achieve maximum column performance.

3 Diagnostics and System Suitability Tests

Most of the instrument checks that an analyst makes before injection to assess instrument readiness can be made automatically by standard integrator routines, or by a software program running in the integrator. Absence of noise and a stable baseline in the correct place (near zero millivolts) are accepted indications that a chromatograph is ready for sample injection. Tests on peak shape, size and resolution indicate whether...