Analytical calibration curves

VanArendonk, M. D., and Skogerboe, R. K., Correlation Coefficients for Evaluation of Analytical Calibration Curves, Anal. Chem. 53, 1981, 2349-2350. 

The first photoelectric fhiorimeter was described by Jette and West in 1928. The instrument, which used two photoemissive cells, was employed for studying the quantitative effects of electrolytes upon the fluorescence of a series of substances, including quinine sulfate [5], In 1935, Cohen provides a review of the first photoelectric fluorimeters developed until then and describes his own apparatus using a very simple scheme. With the latter he obtained a typical analytical calibration curve, thus confirming the findings of Desha [33], The sensitivity of these photoelectric instruments was limited, and as a result utilization of the photomultiplier tube, invented by Zworykin and Rajchman in 1939 [34], was an important step forward in the development of suitable and more sensitive fluorometers. The pulse fhiorimeter, which can be used for direct measurements of fluorescence decay times and polarization, was developed around 1950, and was initiated by the commercialization of an adequate photomultiplier [35]. 

Does it decrease the reliability of the analytical calibration curve ... 

The stability of enzyme electrodes is difficult to define because an enzyme can lose some of its activity. Deterioration of immobilized enzyme in the potentiometric electrodes can be seen by three changes in the response characteristics (a) with age the upper limit will decrease (e.g., from 10-2 to 10 3 moll-1), (b) the slope of the analytical (calibration) curve of potential vs. log [analyte] decrease from 59.2 mV per decade (Nernstian response) to lower value, and (c) the response time of the biosensor will become longer as the enzyme ages [59]. The overall lifetime of the biosensor depends on the frequency with which the biosensor is used and the stability depends on the type of entrapment used, the concentration of enzyme in the tissue or crude extract, the optimum conditions of enzyme, the leaching out of loosely bound cofactor from the active site, a cofactor that is needed for the enzymatic activity and the stability of the base sensor. 

Finally, consideration must be given to the availability of pure reference compounds from which to construct analytical calibration curves. Some compounds (such as phenolic acids) may be purchased commercially, but for others (such as benzoxazinoids) it will be necessary to first isolate and purify them from recognized natural sources described in the literature12 or to synthesise them.11... 

Standard curve Relationship between the analytical response and known concentrations of standard analyte = calibration curve = dose-response curve... 

Inductively coupled plasma-atomic emission spectrometry was investigated for simultaneous multielement determinations in human urine. Emission intensities of constant, added amounts of internal reference elements were used to compensate for variations in nebulization efficiency. Spectral background and stray-light contributions were measured, and their effects were eliminated with a minicomputer-con-trolled background correction scheme. Analyte concentrations were determined by the method of additions and by reference to analytical calibration curves. Internal reference and background correction techniques provided significant improvements in accuracy. However, with the simple sample preparation procedure that was used, lack of sufficient detecting power prevented quantitative determination of normal levels of many trace elements in urine. 

Figures 8 and 9, on the other hand, show typical analytical calibration curves for the same sample materials when the net intensity ratio (net analyte line intensity/net internal reference line intensity) was used as the measure of response. In this case, the cmrves exhibited a considerably smaller range of slopes for the various urine samples and were in much better agreement with the data for the reference solutions.

Figure 6, Analytical calibration curves for iron in 1% NaCl reference solutions (O) and in the dilute (D), normal (N)y and concentrated (C) urine samples. See Table IV, The analysis wavelength was 261,2 nm.

Figure 8. Analytical calibration curves for iron as in Figure 6, Here, however, the analyte responses are in terms of the ratio of the net intensity of the analytical line (Fe 261,1 nm) to the net intensity of an internal reference element line (Y 371.0 nm). Although they are shown in the figure, the data points for the dilute, normal, and concentrated urine samples are not readily distinguishable.

Figure 9. Analytical calibration curves for cadmium as in Figure 8...

Figure 10, Analytical calibration curves for chromium as in Figures 8 and 9, but with gallium as the internal reference element. The analytical line was Cr(II) 205,6 nm the intenml reference line was Ga 294,4 nm.

Figure 11, Analytical calibration curves for zinc in urine with yttrium as the internal reference element. The analytical and internal reference line wavelengths were 213,9 and 371.0 nm, respectively. (X) Additions to the urine samples, (O) additions to the 1% NaCl reference soltuions.

Intensity, I, of electromagnetic radiation The power per unit solid angle often used synonymously with radiant power, P. Intercept, b, of a regression line The y value in a regression line when the x value is zero in an analytical calibration curve, the hypothetical value of the analytical signal when the concentration of analyte is zero. 

Instrument response may be linearly or nonlinearly related to the analyte concentration. Calibration is accomplished by preparing a series of standard solutions of the analyte at known concentrations and me uring the instrument response to each of these (usually after treating them in the same manner as the samples) to prepare an analytical calibration curve of response versus concentration. The concentration of an unknown is then determined from the response, using the calibration curve. With modem computer-controlled instruments, this is often done electronically or digitally, and direct readout of concentration is obtained. 

Table 17.3 lists some representative detection limits of various elements by atomic absorption and flame emission spectrometry. We should distinguish here between the sensitivity and detection limits in atomic absorption. The former term is frequently used in the atomic absorption literature. Sensitivity is defined as the concentration required to give 1% absorption (0.0044 A). It is a measure of the slope of the analytical calibration curve and says nothing of the signal-to-noise ratio (S/N). Detection limit is generally defined as the concentration required to give a signal equal to three times the standard deviation of the baseline (blank)— see Chapter 3. 

The power supply to the hollow cathode source is modulated and an ac detection system is used. This arrangement prevents any radiation from the flame or resonance detector from producing an output signal. Random noise is less troublesome than in a conventional spectrophotometer. The resonance detector must, of course, produce a cloud of atomic vapor of the same element being aspirated into the flame. The hollow cathode source also must emit resonance lines of the same element. Analytical calibration curves closely parallel those obtained with conventional atomic absorption systems and sensitivities and detection limits are similar. 

If difficulty is encountered in drawing the analytical calibration curve by the free-hand technique, use the method of least squares . 

To get reliable quantization of triterpenoid saponins in extract solution, calibration curves for each target analyte must be generated, due to different signal responses. For determination of triterpenoid saponins in complex matrix with good accuracy and precision [25, 31], selection of internal standard (IS) is key. The ideal IS would be chemically similar to the target analytes. Calibration curve is constructed using the peak area ratios of analyte to IS versus the concentration of analyte. 

Freedom from interelement effects is also a characteristic of ICP excitation, so that an analytical calibration for the determination of a rare earth will usually be valid for any complex mixture of rare earths if there is no spectral line interference. Two examples of this freedom can be seen in figs. 37D.7 and 37D.8, which show analytical calibration curves for the determination of Y in complex... 

The most fundamental approach for quantitative analysis involves the use of a conventional analytical calibration curve. This curve establishes a functional relationship between the ion current of the analyte and known concentrations of carefully prepared calibration standards. For dilute solution analysis, these standards usually consist of gravimetrically prepared aqueous dilutions of high-purity metal salts. These compounds should be either nitrate or oxide salts. Chloride salts should be avoided whenever possible to prevent the possibility of molecular ion interferences (see chapter on interferences). An alternate approach is to use commercially available calibration standard solutions that have been obtained fix>m a trusted source. After dilution, the standards are preserved with high-purity nitric acid to prevent precipitation or adsorption of the trace analyte species onto the interior walls of the sample holding container. 

Another correction approach that is somewhat more straightforward is to compensate for polyatomic molecular spectral overlap interferences on trace element analyses is by making a correction in the concentration domain. This correction is accomplished by measuring the equivalent analyte concentration of the interference in the absence of the analyte (i.e., C aiyte 0).This measurement is made for a known concentration in the sample of the interfering component of the molecular ion. Typically, a standard solution (known concentration) of the interferent, with no analyte present, is measured under the same conditions as the calibration and analysis of the analyte element. The apparent analyte concentration for this interfering molecular ion is computed from the analyte calibration curve (or regression function). An interferent correction constant (K) is calculated by the following equation ... 

Sensitivity in the context of quantitative analysis is the ability to measure small differences in concentration of an analyte species. Sensitivity is usually defined as the slope of the analytical calibration curve (plot of ion current as a function of concentration) divided by the precision (expressed as standard deviation of the ion current) of an intermediate concentration calibration standard (see Figure 7.2).The equation to compute sensitivity is as follows ... 

---