Second order sensor

Fig. 10.1 (a) First-order chemical sensor in which absorbance is uniquely related to concentration by calibration curve, (b) Second-order sensor in which absorbance is shown as a function of wavelength X. Interferant is easily identified in the spectrum, (c) Third-order sensor yielding information in 3-D space. The red dashed line shows conversion of third-order sensor to second-order sensor when the value of response R is obtained at a fixed retention time/ ... 

Fig. 10.2 Bilinear plot obtained from second-order sensor. In this example, linearized ISE response is plotted against absorbance from fiberoptic sensor. Point S represents an outlier ...

When used in the time-invariant mode (i.e., in equilibrium), it is a first-order chemical sensor that can yield qualitative and quantitative information based on the LSER paradigm about composition of the vapor mixtures (Fig. 10.13). By acquiring the data in the transient regime, it becomes a second-order sensor and in addition to the composition, information about diffusion coefficients in different polymers is obtained. This is then the added value. It is possible only because the model describing the capacitance change included diffusion. In spite of the complexity of the response function, a good discrimination and quantification has been obtained. 

This excitement about second-order sensor calibration has led to a search by chemometric researchers to find equivalent instrumentation that gives rise to second-order data. The definition of second-order instruments is slowly solidifying and currently a foundation has been established to classify which techniques are true second-order devices. This definition of second-order instruments is simply two sensor arrays which are independent of each other. However, in order for the arrays to be independent, one of the arrays must modulate the sample s analyte concentrations. The best known instrument... 

For example, a temperature-measuring device, having its sensor placed in a protecting rube, is a system of second order. For such a system no single rime constant exists in the same way as a first-order system. The behavior of such a system is often given by a response time. Another concept is to give the apparent time constant t, which can be constructed by placing a line in the inflection point of the step response curve see Fig. 12.14. 

Lin Z., Booksh K.S., Burgess L.W., Kowalski B.R., A Second-Order Fiber Optic Heavy Metal Sensor Employing Second-Order Tensorial Calibration, Anal. Chem. 1994 66 2552-2560. 

The ambient temperature sensor in the IRT 3000 is a KTY type spreading resistance sensor. The resistance of the sensor can be written as a second order polynomial function... 

The discrete microhotplates were packaged and bonded in a DIL-28 package for temperature sensor cahbration. A Pt-lOO-temperature sensor was attached to the chip package in close vicinity to the sensors. The chips were then caHbrated in an oven at temperatures up to 325 °C with the help of the Pt-100 resistor. A second-order polynomial was extracted from the measurements for each temperature sensor providing the temperature coefficients i and a2. ... 

The tracking nonlinearity at high temperatures comes from the second-order coefficient of the polysilicon temperature sensor. 

Booksh, K., Henshaw, J.M., Burgess, L.W., and Kowalski, B.R., A second-order standard addition method with application to calibration of a kinetics-spectroscopic sensor for quantitation of trichloroethylene, J. Chemom., 9, 263-282, 1995. 

The second-order calibration example shown next is from the field of environmental analytical chemistry. A sensor was constructed to measure heavy metal ions in tap and lake water [Lin et al. 1994], The two heavy metal ions Pb2+ and Cd2+ are of special interest (the analytes) and there may be interferents from other metals, such as Co2+, Mn2+, Ni2+ and Zn2+. The principle of the sensor is described in detail in the original publication but repeated here briefly for illustration. The metal ions diffuse through a membrane and enter the sensor chamber upon which they form a colored complex with the metal indicator (4-(2-pyridylazo) resorcinol PAR) present in that chamber. Hence, the two modes (instrumental directions) of the sensor are the temporal mode related to the diffusion through the membrane, and the spectroscopic mode (visible spectroscopy from 380 to 700 nm). Selectivity in the temporal mode is obtained by differences in diffusion behavior of the metal ions (see Figure 10.22) and in the spectroscopic mode by spectral differences of the complexes formed. In the spectroscopic mode, second-derivative spectra are taken to enhance the selectivity (see Figure 10.23). The spectra were measured every 30 s with a resolution of 1 nm from 420 to 630 nm for a period of 37 min. This results in a data matrix of size 74 (times) x 210 (wavelengths) for each sample. 

Smilde AK, Tauler R, Henshaw JM, Burgess LW, Kowalski BR, Multicomponent determination of chlorinated hydrocarbons using a reaction-based chemical sensor. 3. Medium-rank second-order calibration with restricted Tucker models, Analytical Chemistry, 1994a, 66, 3345-3351. 

Figure 11.7 An illustration of the process used in two-dimensional sensor arrays with both GRAM and TLD. The left-hand side of the figure shows the two-dimensional response patterns used in calibration, and the right-hand side of the figure shows the resulting information from the second-order techniques. (Reprinted with permission from Elsevier Science BV.)...

Problems that arise in the first-order sensor arrays can exist in the second order as well. The primary problem is collinearity of response patterns. If two... 

Wang Y, Borgen O S, Kowalski B R, Gu M and Turecek F 1993 Advances in second order calibration J. Chemometr. 7 117-30 Lin Z and Burgess L W 1994 Chemically facilitated Donnan dialysis and its application in a fiber optic heavy metal sensor Anal. Chem. 66 2544-51 Lin Z, Booksh K S, Burgess L W and Kowalski B R 1994 Second order fiber optic heavy metal sensor employing second order tensorial calibration Anal. Chem. 66 2552-60... 

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