Response index

It is seen that, for a truly linear detector, the response index (a) will be unity and the experimentally determined value of (a) will be an accurate measure of the proximity of the response to strict linearity. It is also clear that (a) could be used to correct for any non-linearity that might occur in the detector and thus improve the accuracy of an analysis. 

The curves relating detector output to solute concentration for detectors having different response indexes are shown in figure 2. 

It is seen that errors in the smaller component can be as great as 12.5% (1.25% absolute) when the response index is 0.94. Yet on examining the curve for a response index of 0.94 in figure 2 the non-linearity is scarcely apparent. When the response index is 1.05 the error is 9.5% (0.95% absolute) and again the poor linearity is not obvious in figure 2. As already stated, to obtain accurate results without employing a correction factor, the response index should lie between 0.98 and 1.02. Most LC detectors can be designed to meet this linearity criteria. 

I spent a lot of time wrestling with that one. One day, I recalled an ingenious way of combining measurements developed by two researchers, Drs. Pincus and Hoagland, while studying hormonal function in schizophrenic patients. No single measure set schizophrenics apart from normal patients, so they cooked up a kind of statistical stew, using lymphocyte counts and potassium levels instead of carrots and potatoes. They called it the TRI (Total Response Index). 

By using a number of different changes they created a weighted index that they called the Total Response Index (TRI), finding it to be more useful than any single measure as a reflection of overall response magnitude. 

For the purpose of illustrating how the composite risk index in Equation 6.6 would be used to classify a hypothetical waste, it is helpful to simplify Equations 6.4 and 6.5. This is done by assuming that the summation over all responses (index r) has been calculated, that only one waste classification boundary represented by the index j is being considered (i.e., the boundary between exempt and low-hazard waste, based on a negligible risk, or the boundary between low-hazard and high-hazard waste, based on an acceptable risk), and that the modifying factor (F) is unity. Further, the calculated dose in the numerator of the risk index is denoted by D and the allowable dose in the denominator is denoted by L. Then, the composite risk index for all hazardous substances in the waste, expressed in the form of Equation 6.6, can be written as ... 

This method for defining detector linearity is perfectly satisfactory and ensures a minimum linearity from the detector and consequently an acceptable quantitative accuracy. However, the specification is significantly looser than that given above and there is no means of correcting for any non-linearity that may exist as there is no correction factor given that is equivalent to the response index. It is strongly advised that the response index of all detectors (CiC and LC)... 

There are two methods that can be used to measure the response index of a detector, the incremental method of measurement and the logarithmic dilution method of measurement. The former requires no special apparatus but the latter requires a log-dilution vessel which fortunately is relatively easy to fabricate. 

Thus the slope of the Log/Log curve will give the value of the response index (r). If the detector is truly linear, r = 1 i.e. the slope of the curve will be sin 7r/4 =1). Alternatively, if suitable software is available, the data can be curved fitted to a power function and the value of (r) extracted from the results. The same data can be employed to determine the linear range as defined by the ASTM E19 committee. In this case, however, a linear plot of detector output against solute concentration at the peak maximum should be used and the point where the line deviates from 45° by 5% determines the limit of the linear dynamic range. 

Thus if the logarithm of the detector output is plotted against time, then for a truly linear detector, a straight line will be produced having a slope (-QA )- If the detector has a response index of (r) and the... 

Thus, the response index can be easily determined. However the accuracy of the measurement will depend on the flow rate remaining constant throughout the calibration, and consequently for a GC detector a precision flow controller must be employed and for an LC detector, a good quality solvent pump. Manufacturers do not usually provide the response indices for their detectors and so it is left to the analysts to measure it for themselves. 

The Response Index - (r) - The response index of detector is a measure of its linearity and for a truly linear detector would take the value of unity. In practice the value of (r) should lie between 0.98 and 1.02. If (r) is known, quantitative results can be corrected for any nonlinearity. 

Linear Dynamic Range - (D ) - The linear dynamic range of a detector is that concentration range over which the detector response is linear within defined response index limits. It is also dimensionless and is taken as the ratio of the concentration at which the response index falls outside its defined limits, to the minimum detectable concentration or sensitivity. The linear dynamic range is important when the components of a mixture being analyzed cover a wide concentration range. 

This again emphasizes the need for an improved procedure for defining detector specifications. The linear dynamic range of the electron capture detector is again ill-defined by many manufacturers. In the DC mode the linear dynamic range is usually relatively small, perhaps two orders of magnitude, with the response index lying... 

The sensitivity should be given as that solute concentration that produces a signal equivalent to twice the noise. Such data allows a rational comparison between detectors. The linear dynamic range is also not precisely clear from the original publication but appears to be at least three orders of magnitude for a response index of (r) where 0.97 < r < 1.03, but this is an estimate from the data published. The... 

The out-of-balance signal caused by the presence of sample vapor in contact with the sensor is amplified and fed to a recorder or computer data acquisition system. For maximum sensitivity hydrogen should be used as the carrier gas, but to reduce fire hazards, helium can be used with very little compromise in sensitivity. The sensitivity of the katherometer is only about 10 g/ml (probably the least sensitive of all GC detectors) and has a linear dynamic range of about 500 (the response index being between 0.98 and 1.02). Although the least glamorous, this detector can be used in most GC analyses that utilize packed columns and where there is no limitation in sample availability. The device is simple, reliable, and rugged and, as already stated, relatively inexpensive. 

The detector was claimed to be moderately linear over a dynamic range of three orders of magnitude but values for the response index are not known. It is also not clear whether the associated electronics contained signal modifying circuitry or not. The disadvantages of this detector included erosion of the electrodes due to "spluttering", contamination of the electrodes from sample decomposition and the need for a well-controlled vacuum system. 

As a result of limited sensitivity and restricted linear dynamic range, the refractive index detector is often a "choice of last resort" and is used for those applications where, for one reason or another, all other detectors are inappropriate or impractical. However, the detector has one particular area of application for which it is unique and that is in the separation and analysis of polymers. In general, for those polymers that contain more than six monomer units, the refractive index is directly proportional to the concentration of the polymer and is practically independent of the molecular weight. Thus, a quantitative analysis of a polymer mixture can be obtained by the simple normalization of the peak areas in the chromatogram, there being no need for the use of individual response factors. The sensitivity of most RI detectors will be about 1 x 10 g/ml and the linear dynamic range around 1 x 10 to 2 X 10 4 g/ml with the response index (r) lying between 0.97 and 1.03. 

The response index for a series of compounds of different chemical types ranged from 0.96 to 1.04. The response of the detector was found to be proportional to the carbon content of the solutes tested, which would be expected. However, due to the limited number of compounds that were tested this relationship should be assumed only with caution. A chromatogram of blood lipids obtained by incremental gradient elution and monitored by the modified detector is shown in... 

The detector response index has been featured as a means of defining linearity, but it can also be used to take into account any non-linearity that is present and appropriately modify the peak height or peak area calculations and thus improve quantitative accuracy. An example of two peaks constructed from Gaussian functions using response factors of 0.95 and 1.05 are shown in figure 5. Such values were considered to be outside those which would be acceptable for a detector to be defined as linear. 

A) is the linearity constant, and (r) is the numerical value of the response index. 

Now if the response index (r) is not unity, which will be the case for virtually all practical detectors, then the value of (r) should be taken into account in the expressions used to obtain quantitative results. Consider firstly the computer integration of the area. The area is calculated by summing all the signals from the detector over the period of the peak. Now, if (r l) then, from equation (2), the area that will incorporate the non-linearity will be... 

Thus, the concentration of any (or all) of the components present in the mixture can be determined, providing they are adequately separated from one another. It is interesting to note that if the maximum accuracy and precision is required, and the data is to be corrected for a response index that is other than unity, either peak heights must be used or the chromatogram must be processed manually. For repeat analyses of the same type of mixture, the operating conditions can be maintained constant and, as there is no extreme change in sample composition, the response factors will usually need to be determined only once a day. 

Assuming the first instance that the response index of the detector is unity, if the (p)th solute in the mixture is at a concentration of (Cp, ) in the sample and (Cp(,t,) in the standard solution, then... 

If the value or the response index, (r), is not unity, then the corrected area and height must be used. Thus again assuming... 

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