Calibration curve, secondary

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

Noncompetitive ELISA methods are based on sandwich assays in which an excess supply of immobilized primary antibody, the capture antibody, quantitatively binds the antigen of interest and an enzyme-labeled secondary antibody is then allowed to react with the bound antigen forming a sandwich. A color reaction product produced by the enzyme is then used to measure the enzyme activity that is bound to the surface of the microtiter plate. Sandwich ELISA (noncompetitive) methods yield calibration curves in which enzyme activity increases with increasing free antigen concentration. 

Using the intrinsic viscosity data and the universal calibration curve( ) a secondary molecular weight calibration curve can be constructed for the polymer of interest as shown by the following equation ... 

This "secondary" molecular weight calibration curve was fit to a polynomial over the retention volume range of the sample. Then the molecular weight distribution statistics are calculated from this "secondary" calibration curve and the DRI trace of the sample under... 

Figure 10. "Secondary" Molecular Weight Calibration Curve for a PMMA Sample (Eastman 6041).

Figure 1. Illustrative method for constructing a secondary molecular weight calibration curve from an HDV calibration curve and intrinsic viscosity values of GPC polymer fractions...

Using the PMMA direct molecular weight calibration curve shown in Figure 4 and the Mark-Houwink parameters for PMMA in TFE shown in Equations 26 and 27, an HDV calibration curve can be constructed as described in the theory section. Then secondary molecular weight curves can be constructed for other polymers of interest by the methods discussed in the theory section as was done in Ref. 1, using the indirect PMMA molecular weight calibration curve. 

Limitations of the aluminum oxide sensor include (I) the sensor is a secondary measurement device and must periodically be culihraied to accommodate aging effects, hysteresis, and contamination and (2) sensors require separate calibration curves, which are typically nonlinear. 

Figure 26.3 presents the resulting calibration curve of the HRP-immunosensor for the amperometric detection of anti-CT. The values of the detection limit obtained (50 ng/ml) are similar to those obtained with optical fiber immunosensors, based on HRP-labeled secondary antibodies (160 ng/ml) [5-8]. 

Empirical Methods. The empirical methods use calibration standards to derive sensitivity factors that can be used to determine the unknown concentration of given elements in similar matrices [3. The sensitivity factors are derived from calibration curves that plot measured secondary ion intensities versus the known concentration of standards. Three types of sensitivity factors have been used the absolute sensitivity factor, the relative sensitivity factor, and the indexed relative elemental sensitivity factor. 

The ultimate development in the field of sample preparation is to eliminate it completely, that is, to make a chemical measurement directly without any sample pretreatment. This has been achieved with the application of chemometric near-infrared methods to direct analysis of pharmaceutical tablets and other pharmaceutical solids (74-77). Chemometrics is the use of mathematical and statistical correlation techniques to process instrumental data. Using these techniques, relatively raw analytical data can be converted to specific quantitative information. These methods have been most often used to treat near-infrared (NIR) data, but they can be applied to any instrumental measurement. Multiple linear regression or principal-component analysis is applied to direct absorbance spectra or to the mathematical derivatives of the spectra to define a calibration curve. These methods are considered secondary methods and must be calibrated using data from a primary method such as HPLC, and the calibration material must be manufactured using an equivalent process to the subject test material. However, once the calibration is done, it does not need to be repeated before each analysis. 

The relationship between concentration and secondary measurement is not always linear. Whether it is a straight line or a curved line that describes the calibration, an equation is needed to be able to predict concentrations for future samples. A quantitative calibration curve can also be used to calculate a number of important analytical properties (sensitivity, linearity, offset or baseline, detection limit [Currie 1995]). The calibration line would be... 

A specific reagent for the primary hydroxyl group determination is triphenylchloromethane [22], which has a very reactive chlorine atom and a bulky substituent (triphenylmethyl). Due to the high steric hindrance of triphenylchloromethane, a selective reaction with primary hydroxyl groups takes place. Unfortunately, the precision is not very high because the secondary hydroxyl groups react only to a very small extent (8-10%). In order to make it a more precise method, it is necessary that before the determination, a calibration curve should be done and the real primary hydroxyl content is corrected by the decrease in the quantity of secondary hydroxyl reacted. 

Fig. 2 Sensorgrams and calibration curve for different IL-8 concentrations in saliva supernatant premixed with lOmgmL of CM dextran sodium salt, a Sensorgrams corresponding to enhanced detection by secondary antibody for different IL-8 concentrations (5nM, 2nM, 1 nM, 500 pM, 250 pM, and OpM labeled as A, B, C, D, E, and F, respectively), b Calibration curve covering the IL-8 concentration range from 0 to 2 nM [26]...

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