External linear calibration

Standardizing the Method Equations 10.32 and 10.33 show that the intensity of fluorescent or phosphorescent emission is proportional to the concentration of the photoluminescent species, provided that the absorbance of radiation from the excitation source (A = ebC) is less than approximately 0.01. Quantitative methods are usually standardized using a set of external standards. Calibration curves are linear over as much as four to six orders of magnitude for fluorescence and two to four orders of magnitude for phosphorescence. Calibration curves become nonlinear for high concentrations of the photoluminescent species at which the intensity of emission is given by equation 10.31. Nonlinearity also may be observed at low concentrations due to the presence of fluorescent or phosphorescent contaminants. As discussed earlier, the quantum efficiency for emission is sensitive to temperature and sample matrix, both of which must be controlled if external standards are to be used. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. 

External standard method (linear calibration curve of peak areas)... 

The amounts of EMA and HEMA (derivatized as MEMA) are determined based upon external standard calibration. A nonweighted linear least-squares estimate of... 

The amount of NIPA is determined based upon external standard calibration. A non-weighted linear least-squares estimate of the calibration curve is used to calculate the amount of NIPA in the unknowns. The response of any given sample must not exceed the response of the most concentrated standard. If this occurs, dilution of the sample will be necessary. 

The concentration of the analyte in the injected sample is determined based on the height or area of the analyte peak and interpolation of the internal or external standard linear calibration curve according to the following equation ... 

Case 3. Linearity demonstrated from 50% of the ICH reporting limit to 150% of the shelf life specification of a related substance, and a significant y-intercept is observed (Figure 3.8). Due to the significant -intercept, a single-point calibration (e.g., high-low or one-point external standard calibration) is not suitable. In this case, multiple-point external standard calibration is the most appropriate. See Section 3.3.3 for more discussion of the significant y-intercept. 

Prerequisites for the Calibration Types. It depends on the design of the analytical procedure as to which regression parameters are meaningful and which results are acceptable. In other words, the model to be used for quantitation must be justified. For a singlepoint calibration (external standardization), a linear function, zero intercept, and the homogeneity of variances are required. The prerequisites for a linear multiple-point calibration are a linear function and in case of an unweighted calibration also the homogeneity of variances. A non-linear calibration requires only a continuous function. With respect to the 100%... 

Fig.l Linear calibration plot for external standard method. 

The standard addition method is commonly used in quantitative analysis with ion-sensitive electrodes and in atomic absorption spectroscopy. In TLC this method was used by Klaus 92). Linear calibration with R(m=o)=o must also apply for this method. However, there is no advantage compared with the external standard method even worse there is a loss in precision by error propagation. The attainable precision is not satisfactory and only in the order of 3-5 %, compared to 0.3-0.5 % using the internal standard method 93). 

Frequently, quantitative analyses are based on external-standard calibration (see Section 8C-2). In atomic absorption, departures from linearity are encountered more often than in molecular absorption. Thus, analyses should never be based on the... 

The LAS in soils was quantified through the use of a standard sample of a LAS (C10-C14) as an external standard. Calibration plots were constracted from measurements of peak areas versus known weights of the reference LAS. Both fluorescence and UV detection resulted in linear plots for 0-0.75 ug and 0-2 ug LAS injected respectively and with correlation coefficients (R ) greater than 0.99. The individual LAS homologues were shown to have similar molar responses for fluorescence detection as was found previously for the UV system (Matthijs and De Henau 1987 Kikuchi et al 1986). 

Figure 5.10. Typical calibration curve using external standardization (linear calibration through origin). Note that the slope of the curve is equal to the response factor of the analyte.

The methods of quantitation and the criteria for precise and accurate determination for LC are similar to those used in GC, though there are a number of important differences. External standard calibration—i.e. where the detector response to a solution of known concentration is measured and then a calibration curve is constructed—is the recommended method for quantitation in LC. It is imperative that the linearity of detector response is confirmed over the concentration range of interest with standards prepared in a matrix similar to the sample. Table 6.2 details detector characteristics. The increased precision obtained compared to GC is attributable to the... 

The criteria for acceptable linearity of least squares fit and zero intercept when plotting ratios of analyte to internal standard areas vs. concentration are similar to the case for external standard calibrations described earlier. More than one IS can be used, both for calculating RRTs to compensate for retention time variations as well as the RRFs for improving quantitation. The variations that a quantitation IS can compensate for depend upon the point at which it is introduced in the analysis. If it is put into the final extract prior to injection on the chromatograph, it can correct for concentration variations due to evaporative volume changes, variations in injection volume, and variations in detector response. This is called an injection internal standard. If the internal standard is put into the initial sample, and into calibration standards prepared in an equivalent matrix, it can additionally correct for variations in recovery during the sample preparation process. This is called a method internal standard. Combined use of separate compounds for each purpose can aid in determining the causes of peak area variability. 

Fig. 1 Linear calibration plot for external standard method. SI, S2, and S3 external standards for calibration U unknown sample.

Dobney et al. [88] have examined different sets of in-house polycarbonate standards (containing a selection of elements such as Ti, Sb, Cr, Co, Al, Ni, Na) to assess the feasibility of using external standard calibration and grid ablation for (bulk) quantification in LA-ICP-MS. Acceptable linear calibration... 

Calibration standards of the 18 elanents and a calibration blank were prepared from multielement standards in 2% NaCl + 1% HNO3, using an external linear-through-zero calibration graph. A different blank (1% HNO3) was subtracted from all samples due to the fact that some contaminations were present in 2% NaCl. Concentrations of the six multielement standards were 25, 50,100, 500,1000, and 5000 ppt. 

The purity of a sample of K3Fe(CN)6 was determined using linear-potential scan hydrodynamic voltammetry at a glassy carbon electrode using the method of external standards. The following data were obtained for a set of calibration standards. 

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