LC
DETECTORS:
Craig A. Dorschel, Juris L. Ekmanis, James E. Oberholtzer, F. Vincent Warren, Jr., and Brian A. Bidlingmeyer Waters Chromatography Division of Millipore Corporation 34 Maple Street Milford, MA 01751
For accurate quantitation in LC, testing for detector linearity is of paramount importance. The relationship between the output signal of the detector and the concentration of the sample in the detector must be defined, and the characteristics of the detector response must be understood. Scientists expect the LC detector to give a response that is linear to concentration, and conventional calibration procedures often emphasize the fitting of straight lines to calibration data. It is easy to overlook the fact that modern LC detectors may be nonlinear or that system contributions may cause the detector response to become nonlinear. Neither situation is in itself a problem; however, failure to take note of nonlinearity or to use an appropriate method of data reduction can lead to serious inaccuracies in quantitative determinations. This article will examine the definition of linearity, describe procedures by which the linearity of a detector may 0003-2700/89/0361 -951 A/$01.50/0 © 1989 American Chemical Society
Evaluation and Practical Implications of Linearity
be evaluated, illustrate the practical implications of assumed linearity, and discuss appropriate ways of handling signals from nonlinear detectors so that quantitative analyses can be achieved. The procedures are then applied to two specific cases. The first example will be for the UV-vis photometric detector, the most popular detector for LC. Another commonly used detector, the differential refractive index detector, requires some special considerations that are described as part of the second example. Other LC detectors (e.g., fluorescence, electrochemical, conductivity) will not be discussed but can be evaluated according to the general procedures described here. Definition of linear range and dynamic range The terms linear range and dynamic range are widely used in descriptions of
linear range and dynamic range apply to two distinct concepts (1-5). In casual use, the two terms are often combined or used interchangeably. This can lead to considerable confusion. For example, one author, while stressing that the terms are not synonymous, refers to "dynamic range" and "linear dynamic range" (6). The latter term, if viewed alone, can blur the distinction between the concepts, and the simpler phrase linear range is preferable. The dynamic range of an LC detector is usually much broader than the linear range. It is defined by ASTM (1) as "that range of concentrations of the
INSTRUMENTATION detector performance. A clear understanding of these two terms is a necessity for the discussion that follows. This article follows usage adopted by the American Society for Testing and Materials (ASTM), in which the terms
test substance, over which a change in concentration produces a change in detector signal." (Note that the dynamic range may encompass both linear and nonlinear response behaviors.) The lower limit of the dynamic range is de-
ANALYTICAL CHEMISTRY, VOL. 6 1 , NO. 17, SEPTEMBER 1, 1989 · 951 A
American Chemical Society Announces
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INSTRUMENTATION fined as the concentration producing a detector output signal equal to a speci fied multiple of the detector's shortterm noise level (usually 2X). Shortterm noise is defined (1-5) as that por tion of the signal t h a t consists of random, periodic variations in the de tector signal having a frequency of 1 m i n - 1 or greater. The lower limit of the dynamic range has also been termed the "minimum detectability" (1-5). However, the focus of this article is on linearity rather than detectability, and the latter will not be discussed here in any detail. We note only that the limit ing concentrations for linearity and de tectability are not necessarily the same. The upper limit of the dynamic range is the concentration at the point where the slope of the curve obtained by plotting detector response as a func tion of concentration becomes zero. If the response curve never flattens to zero slope, the highest measured con centration is taken as the upper limit of the dynamic range. (Under ordinary circumstances, this would represent a full-scale response at the detector's least-sensitive setting.) Before defining the term linear range as it applies to an LC detector, it is first necessary to define a linear detector. A detector is linear when the relationship of the detector output signal to the con centration of the sample in the cell is rigorously described by a linear equa tion of the form R = SC + R0
whereR = detector response (signal output) S = sensitivity (or response fac tor) C = concentration Ro = response at zero concentra tion Note that the value for R is always measured relative to the baseline de tector output, either as part of the pro cess of area or height determination for a chromatographic peak or in the mea surements required for a static test. Because, by definition, the detector response must be zero for zero concen tration, the intercept, Ro, must equal zero for a linear detector. The equation then becomes R = SC
PHM89100
(2)
The slope of the line obtained by plot ting response as a function of concen tration (i.e., the response curve) is the constant S. For any point on this line, the value of S is obtained by dividing response by concentration: R/C = S
City, State, Zip
(1)
(3)
We therefore define a linear detector as
952 A · ANALYTICAL CHEMISTRY, VOL. 6 1 , NO. 17, SEPTEMBER 1, 1989
one for which the sensitivity (or re sponse factor) of the detector, and therefore the slope of the response curve, has a constant value at all con centrations. In practice, the linearity of a detector can be assessed by calculat ing R/C over a range of concentrations and observing whether the values thus obtained are in fact constant to within some defined limit. The linear range of a detector can now be defined as the range of concen trations over which the sensitivity (S) is constant to within a defined toler ance. The ASTM practices for evaluat ing GC detectors (1-5) employ this def inition and specify a tolerance of ±5%. Similar definitions are likely to be in cluded in ASTM practices for LC de tectors (7). Observed linear ranges may vary considerably among detector types, and even from unit to unit. Among commonly used chromatographic de tectors, the flame ionization detector used in GC has one of the broadest lin ear ranges. The sensitivity (R/C) for this detector has been reported to be constant over 6 to 7 orders of magni tude (2). The response of many detectors can be treated according to Equations 2 and 3, at least for a limited range of concentrations. For cases in which nonlinearity is found, a different mathe matical approach may be required. Later we will discuss an approach that can be applied to the case of an "al most-linear" detector. Experimental considerations To properly evaluate the detector in an LC system as a component, it is useful to isolate the detector from other sys tem components. For nondestructive, concentration-sensitive detectors such as the LC detectors discussed here, an off-line (static) test is appropriate be cause it allows the exact concentration of the test solution in the cell to be known at the time of measurement. With the detector disconnected from the LC system, test solutions may be introduced directly into the cell via a syringe, a pump, or another appropri ate device. Measurements are then tak en in a static mode (i.e., no flow through the detector cell). Note that a static test is inappropri ate for destructive detectors (e.g., elec trochemical detectors), which are less commonly used in LC. In cases for which a static test is inadvisable, some workers (8) have removed the LC col umn and have introduced the test solu tions directly into the flowing system. This approach may lead to erroneous conclusions regarding linearity unless care is taken to ensure that all system
10-1
X
(b) 2
Response (AU)
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10-3
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10-4
