Higher-Order Sensors

The concept of order applies across the analytical field (recall the discussion of kinetics in Chapter 2). Order is also applied in classifying chemical sensors. When only one physical parameter constitutes the output of the sensor and is correlated with concentration, we call it a first-order sensor. An example is optical sensing of a component at one fixed wavelength. The concentration of the unknown sample is then obtained from the calibration curve (Fig. 10.1a) against absorbance, or by a standard addition method. For nonlinear sensors it is possible to use a linearization function /. 

For example, the output of a glass electrode (in mV) plotted against the antilog of activity of hydrogen ion yields a linear pH scale. It is the simplest form of performing analysis. This simplicity comes with a price, however. If the sample is contaminated by an unknown impurity, or if the response function 91 changes for whatever reason, an undetectable error accrues. Therefore, the first-order analysis relies on the invariability of the experimental conditions. 

The analogy between spectrophotometric analysis and chemical sensing at multiple wavelengths leads to an even stronger case of third-order analysis. When the spectrum is recorded at the output of a chromatographic column, the components are resolved according to their chromatographic retention times, Ir. The response (Fig. 10.1c) can be shown as 

In this case, multiple species can be quantified and the baseline drift can be mathematically corrected. The third-order sensors thus belong to the category 

It is always possible to reduce the order of an analytical technique. This is indicated in Fig. 10.1c by two primed, dashed lines. A good example is GC-MS, where the MS is operated in total ion count mode, only as a chromatographic detector. 

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Raw signals from chemical sensors are rarely suitable for direct multivariate analysis. Some form of signal conditioning is always necessary before the input matrix is composed. Examples of preprocessing techniques used in the static and in the dynamic mode of multicomponent analysis are summarized in Table 10.1. They can be used as such or in combination. In higher-order sensors, where different transduction modes are used, the homogeneity of the input matrix is important. Thus, the matrix must contain data that are comparable in dimensions and that are commensurate. 

Li, E. Wang, X. Zhang, C., Fiber optic temperature sensor based on interference of selective higher order modes, Appl. Phys. Lett. 2006, 89, 091119... 

The hypothesis of a normal distribution is a strong limitation that should be always kept in mind when PCA is used. In electronic nose experiments, samples are usually extracted from more than one class, and it is not always that the totality of measurements results in a normally distributed data set. Nonetheless, PCA is frequently used to analyze electronic nose data. Due to the high correlation normally shown by electronic nose sensors, PCA allows a visual display of electronic nose data in either 2D or 3D plots. Higher order methods were proposed and studied to solve pattern recognition problems in other application fields. It is worth mentioning here the Independent Component Analysis (ICA) that has been applied successfully in image and sound analysis problems [18]. Recently ICA was also applied to process electronic nose data results as a powerful pre-processor of data [19]. 

This modeling approach can be applied to different types of chemical sensors, particularly to the study of their dynamic behavior. We have seen the first hint of this approach in Thermal Sensors (Table 3.1). It is related to the operations performed by now-largely extinct analog computers, which were well suited for solving complex systems of higher order and partial differential equations. 

Let us illustrate the benefits of higher order on a concrete analytical example measurements of concentration of Mg2+ with an ISE and with an optical sensor. After linearization of the potentiometric signal, the two experiments can be displayed as a bilinear plot (Fig. 10.2). Contained in this plot is an unusual sample point S, which clearly falls out of the linear correlation because it lies outside the statistically acceptable 3a noise level. This outlier is an indication of the presence of an interferant. Its presence is clearly identified in this bilinear plot from combined ISE and optical measurement, although it would be undetected in a first-order sensor alone. 

J. Smulko, J. Ederth, L.B. Kish, P. Heszler, C.G. Granqvist, "Higher-Order Spectra in Nanoparticle Gas Sensors", Fluctuation and Noise Letters 4 (2004) L597-L603. 

J.M. Smulko, L.B. Kish, Higher-Order Statistics for Fluctuation-Enhanced Gas-Sensing , Sensors and Materials 16 (2004) 291-299. 

The sensor response to DMMP vapor exposure (without any added dopant) is shown in Fig. 25. A percentage-response of approximately 2.1% was obtained, and the response time was 2 s [20]. This response is attributed to the leaking of the higher-order modes through the modified cladding of the fiber, due to the increased conductivity in polypyrrole film due to DMMP absorption. 

The SIM technique uses the intensity infomiation in two dimensions (2D), which can enhance the sensor detection sensitivity. The intensity distribution in 2D is the function of the optical excitation and the boundary conditions of the optical fiber, whereby changing the boundary conditions results in intensity modulation in 2D [36]. It is known that in SIM technique applications, higher-order modes are excited by off-axis illumination of the optical fiber [16, 38]. Those modes have more interactions with the core/cladding interface therefore, they are more sensitive to changes in the refractive index of the cladding material. 

The FM of the MSOF fiber excites several higher-order modes in the tapered region, while the second tapered region acts as a spatial filter for the intermodal interference. An 8 nm Pd thin film deposited in a vacuum chamber on the LPG formed the sensor. Its responses to different concentrations of H2 in nitrogen are shown in Fig. 17a, b, which summarizes the dependence of the intensity changes on the H2 concentration. The response time of the sensor to reach a 0.9 level of transmission change was found to be about 10 s. 

The fractional power in the cladding increases with mode number and capillary length. Thus, for sensor application, excitation of higher-order leaky modes leads to direct illumination of the immobilized fluorophores on the surface. 

Higher-order chemical sensing can alleviate some inherent problems of chemical sensors. For example, a sensor array can mathematically correct for systematic drift. It also provides cross selectivity for elimination of interference. 

Some examples of static output signals are shown in Figure 3.6 a besides an ideal linear (proportional) behavior, real sensors often show inverse-proportional, exponential, parabolic, higher-order polynomial, or much more complicated dependencies. For reasons of simplicity, our considerations below refer to linear behavior. 

Note-. While marine algae may use iodine for self-defense, herbivores and higher-order predators furfher down the ecosystem may use dietary iodine as a surrogate sensor for overall availabilify of ecosysfem resources. 

Horton B. E., Percies B. D., Tan E. L., and Ong K. G. 2009. A wireless, passive pH sensor based on magnetic higher-order harmonic fields. Sensor Letters 7 599-604. 

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