Linear range

An analytical method vahdation study should include demonstration of the accuracy, precision, specificity, limits of detection and quantitation, linearity, range, and interferences. Additionally, peak resolution, peak tailing, and analyte recovery are important, especially in the case of chromatographic methods (37,38). 

The response of the immobilized enzyme electrode can be made independent of the enzyme concentration by using a large excess of enzyme at the electrode surface. The electrode response is limited by the mass transport of the substrate. Using an excess of enzyme often results in longer electrode lifetimes, increased linear range, reduced susceptibiUty to pH, temperature, and interfering species (58,59). At low enzyme concentrations the electrode response is governed by the kinetics of the enzyme reaction. 

A simple ealibration eurve based on distilled water is suitable for tungsten determination (linearity range is 1-50 mg/dm of W), no interferenee from Fe, Co, Cr, Ni was found. The aeeuraey of the method is eonfirmedby analysis of eertified referenee materials of high alloy steels and niekel based alloys (in range of 0.3 to 15 % W). The analyzed values are agreeing well with the eertified values. 

Metrology and contamination analysis in particular have been decisive factors for profitable semiconductor production [4.47]. Semiconductor applications of TXRF go back to the late nineteen-eighties and were introduced by Eichinger et al. [4.48, 4.49]. Because of its high sensitivity, wide linear range, facile spectrum deconvolution, and... 

Type MDL (gs1) Linear range Temp, limit (°C) Features... 

We take intensity I to mean x-ray quanta per second measured by a detector. An instantaneous detector measures / directly that is, the detector gives a reading always proportional to intensity over the linear range of the detector. The reading could appear on an ammeter after suitable amplification. 

Electrolytic tin plate is ideal for an intercomparison of the three methods, not only because of its great importance, but also because the value of a for tin is near 400, which corresponds to a relatively large linear range (Equation 6-9). Such an intercomparison was carried out10 with satisfactory results on standard samples on which the tin thickness was established by a chemical method. 

The advantages of controlled-potential techniques include high sensitivity, selectivity towards electroactive species, a wide linear range, portable and low-cost instrumentation, speciation capability, and a wide range of electrodes that allow assays of unusual environments. Several properties of these techniques are summarized in Table 1-1. Extremely low (nanomolar) detection limits can be achieved with very small sample volumes (5-20 pi), thus allowing the determination of analyte amounts of 10 13 to 10 15 mol on a routine basis. Improved selectivity may be achieved via the coupling of controlled-potential schemes with chromatographic or optical procedures. 

The equipment required for direct potentiometric measurements includes an ion-selective electrode (ISE), a reference electrode, and a potential-measuring device (a pH/millivolt meter that can read 0.2mV or better) (Figure 5-1). Conventional voltmeters cannot be used because only very small currents are allowed to be drawn. The ion-selective electrode is an indicator electrode capable of selectively measuring the activity of a particular ionic species. Such electrodes exhibit a fast response and a wide linear range, are not affected by color or turbidity, are not... 

The measured potential is thus a linear function of pH an extremely wide (10-14 decades) linear range is obtained, with calibration plots yielding a slope of 59 mV per pH unit. The overall mechanism of the response is complex. The selective response is attributed to the ion-exchange properties of the glass surface, and in particular the replacement of sodium ions associated with the silicate groups in the glass by protons ... 

How would you extend the linear range of calibration plots based on the use of enzyme electrodes ... 

Use equations to explain why and how an increase in the sensitivity of an enzyme electrode is often coupled to a narrower linear range. 

There are a number of properties of a detector that determine whether they may be used for a particular analysis, with the most important being (a) the noise obtained during the analysis, (b) its limit of detection, (c) its linear range, and (d) its dynamic range. The last three are directly associated with the analyte being determined. 

The linear range (see Figure 2.6) is defined as that range for which the analytical signal is directly proportional to the amount of analyte present. 

When the linear range is exceeded, the introduction of more analyte continues to produce an increase in response but no longer is this directly proportional to the amount of analyte present. This is referred to as the dynamic range of the detector (see Figure 2.6). At the limit of the dynamic range, the detector is said to be saturated and the introduction of further analyte produces no further increase in response. 

Figure 2.6 Detector response curve showing (a) ideal behaviour, (b) real behaviour, (c) its linear range, (d) its dynamic range, (e) the noise level, and (f) the limit of detection at three times the noise level.

Other features of an analytical method that should be borne in mind are its linear range, which should be as large as possible to allow samples containing a wide range of analyte concentrations to be analysed without further manipulation, and its precision and accuracy. Method development and validation require all of these parameters to be studied and assessed quantitatively. 

The upper limit to the linear range was 5000 ngml, hut at concentrations >1000 ngml carry-over from the autosampler was observed. This could be reduced by extensive washing. 

Burrell and Hurtubise (.32) investigated calibration curves extended well beyond the normal linear range for RTF and RTF of benzoCf)quino-line adsorbed on a silica gel chromatoplate under neutral and acidic conditions. As the benzoCf)quinoline concentration increased, the RTF curves leveled off, whereas the RTF curves passed through a maximum and then decreased. The extended calibration curves along with fluorescence and phosphorescence spectra and phosphorescence lifetimes for benzoCf)quinoline revealed differences in the RTF and RTF phenomena. For example, it was determined that RTF could arise from molecules adsorbed on the surface and in multilayers of molecules, whereas phosphorescence was only generated from molecules adsorbed on the surface of the chromatoplate and not in the multilayers. ... 

Transverse moving head of four-quadrant position detectors (Fig. 2), precise measuring lateral displacement which corresponds to lateral voltage F/ when it varies at the linear range of 10 V, thus we can compute the rotated angle a of the reflection ray ... 

Thus, one can be far from the ideal world often assumed by statisticians tidy models, theoretical distribution functions, and independent, essentially uncorrupted measured values with just a bit of measurement noise superimposed. Furthermore, because of the costs associated with obtaining and analyzing samples, small sample numbers are the rule. On the other hand, linear ranges upwards of 1 100 and relative standard deviations of usually 2% and less compensate for the lack of data points. 

The RSD is small in the middle and large near the ends of the linear range, as in photometry. 

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