Single calibration curves

An external standardization allows a related series of samples to be analyzed using a single calibration curve. This is an important advantage in laboratories where many samples are to be analyzed or when the need for a rapid throughput of samples is critical. Not surprisingly, many of the most commonly encountered quantitative analytical methods are based on an external standardization. 

Figure 9.17 Plot of log [i ]M versus retention volume for various polymers, showing how different systems are represented by a single calibration curve when data are represented in this manner. The polymers used include linear and branched polystyrene, poly(methyl methacrylate), poly(vinyl chloride), poly(phenyl siloxane), polybutadiene, and branched, block, and graft copolymers of styrene and methyl methacrylate. [From Z. Grubisec, P. Rempp, and H. Benoit, Polym. Lett. 5 753 (1967), used with permission of Wiley.]...

On addition of polyethylene oxide of M.W. 300,000 at a concentration of 0.025 g liter , it is seen that a single calibration curve is obtained, independent of NaCl concentration. (It should be noted, however, that at very low NaCl concentration, less than about 0.005 M, the curve still appears at lower elution voliames). This curve is not linear but does exhibit fairly good resolution. It is likely that the effect of polyethylene oxide... 

The effect of pH in the range studied is completely eliminated by addition of 300,000 MW polyethylene oxide with "collapse" of the data onto a single calibration curve. This competitive adsorption effect will be discussed more fully in section 4. 

In the presence of polyethylene oxide MW 300,000 at a concentration of 0.025 g liter , variations in pH and ionic strength have no effect on elution volumes and a single calibration curve is obtained as shown in Figure 4 and Table II. This behavior presumably also results from modification of the glass surface by the polyethylene oxide surfactant, but in this case charge effects appear to be completely suppressed and the effective pore diameter and volume reduced. Such an interpretation is also in accord with the fact that the elution voliomes are lower with polyethylene oxide than with Tergitol, since Tergitol is a much smaller molecule than the polyethylene oxide. 

It was shown that the logarithm of the product of intrinsic viscosity and molecular weight of polymers of different chemical and stereochemical composition, configuration, or molecular weight is linearly related to the elution volume.81 A plot of log (r) M) vs. elution volume provides a single calibration curve, useful for samples of similar composition, and is termed a universal... 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

Figure 2.14 Molecular weight calibration curves for porous silica microsphere columns. Chromatography conditions column, 10 X 0.78 cm mobile phase, tetrahydrofuran, 22°C flow rate, 2.5 ml/min detection, UV absorbance at 254 nm sample, 25 pi solutions of polystyrene standards, (a) Four individual columns showing four different calibration ranges (b) four columns in series with two distinct pore sizes (60,60,750,750A), providing a single calibration curve with a broader molecular weight range than the individual columns. (Adapted from Ref. 54 with permission.)...

When only a single element is to be determined and its concentration range is narrow, the matrix composition is essentially constant and so are the effects of matrix absorption and enhancement. The analytical problem is then reduced to the preparation of a single calibration curve, which is often linear. Figure 15-9 shows an example, for analysis in the parts-per-million (ppm) range. In this particular case, the background, represented by the intercept on the ordinate, is very high. 

Larew, L.A. Johnson, D.C. Quantitation of chro-matographically separated maltooligosaccharides with a single calibration curve using a postcolumn enzyme reactor and pulsed amperometric detection. Anal. Chem. 1988, 60, 1867-1872. 

Of particular concern was whether the density-distance relationship would vary with the angle from the axis of the cylindrical detector. As it turned out, an empirical center of the crystal near its geometrical center could be found such that the angular dependence was virtually eliminated (Lin, 1981). Thus, a single calibration curve that relates intensity to distance can be established for each detector. 

Table II. Limits of Detection and Effects on Overall Precisions for Six Elements When Using Single Calibration Curves and Curves Prepared Daily...

Consider a typical procedure such as the spectrophotometrlc determination of an analyte in groundwater samples. Quite likely, a single calibration curve will be used to cover a concentration range that extends from below the regulatory limit (hopefully) to some elevated concentration far removed from the limit. In this situation, a DL can be based on confidence limits (CL) around the calibration curve (7-14). The DL estimate produced in this fashion can then reflect the combined uncertainties in sample analysis and calibration. 

For many commercial polymers the columns cannot be calibrated because well-characterized standards are unavailable. The situation is further complicated for branched polymers or copolymers, for which there is no single calibration curve relating elution volume to molecular weight (1). 

Qearly no single calibration curve would work because the high temperature peak reflects the shape of the LLDPE component TREF curve as well as the amount of the LLDPE component present. The shape of the valley region as well as that of the second peak are also dependent on the detail curve shape of the LLDPE component. 

Maibusch, R., Kuss, H. M., Coedo, A. G., and Dorado,T. (1999). Spark ablation inductively coupled plasma mass spectrometry analysis of nrinor and trace elements in low and high alloy steels using single calibration curves./.j4na/./4r. Spectrom. 14(8), 1155. 

This is in contrast to concentration calibration curves, for which standard and sample solutions should differ in composition as little as possible. This completely unproblematic use of a single calibration curve is counterbalanced by the difficulty of precisely determining the individual activity coefficients of a particular type of ion in the standard solutions. Here again, one starts with concentrations, available by accurately weighing a certain amount of some salt of the corresponding measured ion. All methods for calculating the individual activity coefficients are only approximations. Thus one must use sufficiently accurate values experimentally determined by an independent method, and these are available only for a few ions (see Appendix). When this same problem arose in very precise pH measurements, the value of the activity coefficient of a dilute chloride solution was internationally agreed upon [54]. This lead to the operational definition of pH and to the well-defined pH values of a few standard buffer materials. 

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