Detector response distributions

V. Copolvmerization Kinetics. Qassical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon whkh to derive nations which would reflect detector response for a GPC separation based upon properties other than molecular weight. The distributions can then serve as c bration standards analagous to the use of molecular weight standards. 

The ELSD is not plagued with the problem of baseline shift and is significantly more sensitive however it presents other disadvantages, such as the strong non-linearity of the detector response and the possibility of interference from non-volatile compounds in the sample matrix [87]. The HPLC method using traditionally reversed-phase solvents and a hybrid column/pre-column has demonstrated the separation of ethoxylated homologues of broadly distributed linear AEOs... 

Wavelength dependence of detector response can also be compensated by using a fluorescent screen in front of the photocell or photomultiplier. This screen acts as a quantum counter. A concentrated solution of Rhodamin B in glycerol (3g per litre) or fluorescein in 0.01N NajCO, has been used for this purpose. Quantum counters work on the principle that whatever be the wavelength of radiation incident on the screen, if completely absorbed, the photodetector sees only the wavelength distribution of fluorescence from the dye. It requires that the fluorescence yield of the counter material be independent of wavelength of excitation and therefore that its emission intensity is directly proportional to the incident intensity. 

On-line measurements of the sulfur content of atmospheric aerosols have been made by removing gaseous sulfur species from the aerosol and then analyzing the particles for sulfur with a flame photometric detector (24) or by using an electrostatic precipitator to chop the aerosol particles from the gas so that the sulfur content could be measured by the difference in flame photometric detector response with and without particles present. These and similar methods could be extended to the analysis of size-classified samples to provide on-line size-resolved aerosol composition data, although the analytical methods would have to be extremely sensitive to achieve the size resolution possible in size distribution analysis. 

The ELS detector was previously also referred to as a mass detector, pointing to the fact that the response is (mainly) determined by the mass of the sample rather than by its chemical structure. Van der Meeren et al., though, demonstrated that the ELSD calibration curves of phospholipid classes were also dependent on the fatty acid composition (52). The dependence on the fatty acid composition is, however, completely different in nature and much less pronounced than for UV detection. The reason for this behavior is to be found in the partial resolution of molecular species, even during normal-phase chromatography. Thus, the peak shape depends not only on the chromatographic system but also on the fatty acid composition and molecular species distribution of the PL sample (47). Because it was shown before, based on both theoretical considerations and practical experiments, that the ELS detector response is generally inversely proportional to peak width (62,104), it follows that the molecular species distribution of the PL standards used should be similar to the sample components to be quantified. It was shown that up to 20% error may be induced if an inappropriate standard is used (52). 

Figure 2. Particle size distribution of a commercially available polybutadiene latex calculated using different detector response functions.

FIGURE 11.6 UV and ICP-MS-based Sd-FFF fractogram of a colloidal (0.2 to 0.8 Urn) fraction detector responses versus time (a) particle size distribution (UV response) and element-based size distribution for Mn and U (b) and element ratios for Mn/Si and U/Si (c). 

Figure 3 Spectral power distributions of the two cool white lamps available overlaid with detector response curve. Source. Courtesy of Dr. R. Levin, Osram Sylvania.

If the cross section is slowly varying in energy and angle with respect to the detector response functions, and the detector efficiency depends only on Ei fi and not on r, and the energy distribution of the incident electrons is independent of r, then using (2.19) we have... 

In many cases, the number of species occurring simultaneously in a synthetic polymer is so large, that it is not possible to separate them from one another. Hence the chromatogram obtained for a polymer by SEC seldom resembles the typical high efficiency separations obtained for small molecules by interactive chromatography (reversed-phase, etc.). However, the chromatogram of detector response versus retention volume, is a measure of the molecular size distribution, which can provide a vast amount of information on the polymer (Figure 9.5). 

The dependences of the retention ratio R on the size of the fractionated species (molar mass for the macromolecules or particle diameter for the particulate matter) are presented for various polarization FFF methods in the entry Field-Flow Fractionation Fundamentals. The raw, digitized fractogram, which is a record of the detector response as a function of the retention volume, is represented by a differential distribution function h(y). i can be processed to obtain a series of the height values hi corresponding to the retention volumes as shown in Fig. 1. Subsequently, the retention volumes are converted into the retention ratios Rf. 

As can be seen from Eq. (2), the observed intrinsic viscosity for each slice is proportional to the ratio of two detectors responses. It follows that detector noise, which is an irreducible component of the measurement process, introduces noise in the intrinsic viscosity that depends on this ratio. However, two detectors have different sensitivities at the tails of polymer distribution the concentration detector is less sensitive to the high-molecular-weight end and the viscometer is less sensitive to the opposite end. Thus, the noise increases dramatically on both tails of the distribution, where the ratio (2) does not produce physically meaningful values. For example, the logarithm of intrinsic viscosity computed from the slice ratios (2) sometimes does not increase monotonically with molecular weight (i.e., with decreasing elution volume V) even for the flexible coillike polymers (curves 2 in Fig. 1). 

The time at which a peak appears in the detector response is called the retention time of the solute it is the time it takes a given solute to travel the length of the column. For a Gaussian peak distribution, the retention time corresponds to the peak center. Mathematically, the retention time of component i is simply... 

To deduce a particle size distribution, the detector response must be deconvoluted by means of a simulation calculation. The scattering particles are assumed to be spherical in shape, and the data are subjected to one of three different computational methods. One system uses the unimodal model-dependent method, which begins with the assumption of a model (such as log normal) for the size distribution. The detector response expected for this distribution is simulated, and then the model parameters are optimized by minimizing the sum of squared deviations from the measured and the simulated detector responses. The model parameters are finally used to modify the originally chosen size distribution, and it is this modified distribution that is presented to the analyst as the final result. 

A second approach uses the unimodal model-independent method, which begins with the assumption that the size distribution consists of a finite number of fixed size classes. The detector response expected for this distribution is simulated, and then the weight fractions in each size class are optimized through a minimization of the sum of squared deviations from the measured and simulated detector responses. The third system uses the multimodal model-independent method. For this, diffraction patterns for known size distributions are simulated, random noise is superimposed on the patterns, and then the expected element responses for the detector configuration are calculated. The patterns are inverted by the same minimization algorithm, and these inverted patterns are compared with known distributions to check for qualitative correctness. 

Further progress in experimental techniques will allow lifetime measurements in neutral and singly ionized atoms to be extended to even shorter wavelengths and lifetimes. Any free neutral and singly ionized atom can be produced in a lasergenerated plasma. For short-lived states, the pump-probe technique allows to overcome the problems with detector response time. A distributed feedback laser pumped by picosecond pulses from a mode-locked NdrYAG laser can serve as a light source. 

In radiation measurements, folding means to obtain the shape of the measured spectrum when the source and the detector response are known. Several examples of folding using a Gaussian distribution as the response function are presented next. 

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