The Differential Detector

The differential form of the Gaussian function has already been discussed and is sigmoid in shape with a positive maximum at the first point of inflexion of the Gaussian curve and a minimum at the second point of inflexion. If the peaks are completely resolved in the normal chromatogram, then they can be clearly and unambiguously identifiable in their differential form. If, however, the peaks are not completely resolved, then the differential curve of the unresolved peaks are confused and extremely difficult to interpret and for this reason the differential form of the Gaussian function is rarely used. Nonetheless, if the elution profile of the solutes are not Gaussian in form, the differential detector can be extremely useful. 

As probes must be manufactured individually for each different tube type, the probe development is an important factor for the economic use of the method. The classical procedure of probe development is a combination of experience and experiment. The new probe design is based on the experience with already manufactured probes. For an evaluation of the new design the probe must be manufactured. If the probe design is complicated, for example due to dual exciter coil arrangement or segmented differential detector coil systems, the costs of the development can be very high. Therefore a method for the pre-calculation of the probe performance is extremely useful. 

The basis of chromatography is in the differential migration of chemicals injected into a column. The carrier fluid takes the solutes through the bed used for elution (mobile phase). The bed is the stationary phase. Based on mobility, the retention-time detectors identify the fast and slow-moving molecules. Based on internal or external standards with defined concentration, all unknown molecules are calculated in a developed method by software. GC columns are installed in an oven which operates at a specified temperature. A diagram of an oven with GC column is shown in Figure 7.16. 

The fringes contrasts are subject to degradation resulting from dissymmetry in the interferometer. The optical fields to be mixed are characterized by a broadband spectrum so that differential dispersion may induce a variation of the differential phase over the spectrum. Detectors are sensitive to the superposition of the different spectral contributions. If differential dispersion shifts the fringes patterns for the different frequency, the global interferogramme is blurred and the contrast decreases. Fig. 5 shows corresponding experimental results. 

Optical parametric oscillator (OPO, see 20) is the real equivalent to the radio frequency shifter however OPO can be replaced by a simple addition of a local oscillator (e.g. laser) through a beam splitter. Multiplication takes place at the level of detectors. For sake of S5mimetry, detectors can be placed at both output of the beam splitter, the intermediate frequency is then the output of the differential amplifier. 

The second most widely used detector in HPLC is the differential refractometer (RI). Being a bulk property detector, the RI responds to all substances. As noted in Table 3 the detection limits are several orders of magnitude higher than obtained with the UV detector. Thus, one turns to the RI detector in those cases in which substances are non-UV active, e.g. lipids, prostaglandins. In addition, the RI detector finds use in preparative scale operation. Finally, relative to the UV detector, the RI is significantly more temperature and flow sensitive and cannot be used in gradient elution. 

Detection is also frequently a key issue in polymer analysis, so much so that a section below is devoted to detectors. Only two detectors, the ultra-violet-visible spectrophotometer (UV-VIS) and the differential refractive index (DRI), are commonly in use as concentration-sensitive detectors in GPC. Many of the common polymer solvents absorb in the UV, so UV detection is the exception rather than the rule. Refractive index detectors have improved markedly in the last decade, but the limit of detection remains a common problem. Also, it is quite common that one component may have a positive RI response, while a second has a zero or negative response. This can be particularly problematic in co-polymer analysis. Although such problems can often be solved by changing or blending solvents, a third detector, the evaporative light-scattering detector, has found some favor. 

The output signal of concentration-sensitive detectors is proportional to the concentration or weight of polymer in the column eluent. Examples of this type include the differential refractometer and the ultraviolet-visible spectrophotometer. Infrared and fluorescence detectors are used infrequently. None of the detectors described above is truly universal i.e., the response of these detectors varies with the chemical species, and, in case of the DRI, response is also a function of the chromatographic eluent.156 Recently, an... 

Haney, M. A., The differential viscometer. II. On-line viscosity detector for size-exclusion chromatography, /. Appl. Polym. Sci., 30, 3037, 1985. 

In the above-described measurement, which we call the absolute method, all pumps have equal speeds (rpm) owing to interconnection to the same drive-shaft. In order to express, if required, a deviation registered for the analyte concentration, one must calibrate with a standard by varying its rpm (B) with respect to that of the titrant (A) a B/A rpm ratio greater than unity means a proportionally lower concentration and vice versa. In general, the absolute method serves to control a sample stream with nearly constant analyte concentration as a sensor one uses not only electroanalytical but often also optical detectors. However, with considerably varying analyte concentrations the differential method is more attractive its principle is that in the set-up in Fig. 5.15 and with the sensor adjusted to a fixed and most sensitive set-point, the rpm of the sample stream (C) is varied with respect to that of the titrant (A) by a feedback control (see Fig. 5.3a) from the sensor via a regulator towards the... 

The impedance can be measured in two ways. Figure 5.23 shows an impedance bridge adapted for measuring the electrode impedance in a potentiostatic circuit. This device yields results that can be evaluated up to a frequency of 30 kHz. It is also useful for measuring the differential capacity of the electrode (Section 4.4). A phase-sensitive detector provides better results and yields (mostly automatically) the current amplitude and the phase angle directly without compensation. 

This is the differential definition of the absolute intensity. The total absolute intensity can be deduced by integration from Eq. (7.19) and Eq. (7.20) for any normal transmission geometry. Geometries are discriminated by the shape and size of the irradiated volume, the image of the primary beam in the registration plane17 of the detector, and the dimensions of the detector elements18. 

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