First order sensor

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 /. 

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. 

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... 

The step change is close to the situation where the sensor is suddenly moved from one place to another having a different state of the measured quantity. The exponential change could, for example, be the temperature change of a heating coil or some other first-order system. Finally, the velocity fluctuations of room air can be approximated with a sine or cosine function. 

In an ideal first-order system, only one capacity causes a time lag between the measured quantity and the measurement result. Typically, an unshielded thermometer sensor behaves as a first-order system. If this sensor is rapidly moved from one place having temperature Tj to another place of temperature T2, the change in the measured quantity is close to an ideal step. In such cases, the sensor temperature indicated by the instrument has a time histoty as shown in Fig. 12.13. 

Continuing the above example, the inertial error obviously is the difference between the final temperature and the sensor temperature. From Eq. (12.15), the inertial error of a first-order system is... 

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. 

As described for stopped flow experiments above, all commercially available SPR systems work under (pseudo) first-order conditions as well. This is realized either by a large excess of free ligand (in the large volume of the cuvette) compared with a nanoliter volume of the sensor layer [156] or by continuous replacement of free ligand in a flow injection system (e.g.,BIAcore [157]). 

In the simplest case a 1 1 complex is formed between the host in solution and the guest immobilized on the surface. The response of the SPR sensor, R, is proportional to the concentration of the complex formed, and thus pseudo-first-order rate equations can be used to analyze the data.73 If no host is initially bound the function for R... 

The RI sensitivity, SKr, of the above sensor structure is given in Fig. 6.7. Whereas the sensitivity for the first-order mode increases monotonically with the increased wall thickness, the sensitivity for the second and third order modes oscillates significantly. In particular,, S Rr becomes nearly zero at certain regions that... 

Altitude Response. Pressure response is an issue that needs to be addressed for every instrument deployed on an aircraft. First, it must be decided how chemical abundances are to be reported. If standard practice is followed and they are reported as mixing ratios, then it must be determined whether the instrument is fundamentally a mass- or a concentration-depen-dent sensor, because this definition determines the first-order means by which instrument response is converted to mixing ratios as a function of pressure. In this context, a mass-sensitive detector is a device with an output signal that is a function of the mass flow of analyte molecules a concentration-sensitive detector is one in which the response is proportional to the absolute concentration, that is, molecules per cubic centimeter. 

In Figure 16-6 b, the interface at = 0 controls the reaction kinetics. If L denotes the interface conductivity coefficient, the rate of A uptake is given by L-A//a( = 0). For long times, the sensor registers a first order rate law E(t) e /T, r = (c°A-A )/(L-R T). This result is obtained for the linear geometry of Figure 16-6. In this context, we mention the a->P transformation of Ag2S as discussed in Sec-... 

A measuring instrument consists basically of a sensor and a transducer. The sensor transmits a signal x to the transducer every second and the transducer responds as a first-order system with a time constant of Ss and a steady-state gain of 2 units. The output yt of the transducer drives a transmitter which also approximates to first-order behaviour with a time constant of 4s and a steady-state gain of 5. 

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/ ... 

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. 

In order to simulate a realistic industrial reactor, some important assumptions on the actuator and the sensors have been done. Namely, a first-order linear dynamics,... 

Let p be the fraction of the channels (not voltage sensors) in the open state. For a first order process, p is the solution of the differential equation... 

Microdielectrometry was introduced as a research method in 1981 14 and became commercially available in 1983 20). The microdielectrometry instrumentation combines the pair of field-effect transistors on the sensor chip (see Sect. 2.2.3) with external electronics to measure the transfer function H(co) of Eq. (2-18). Because the transistors on the sensor chip function as the input amplifier to the meter, cable admittance and shielding problems are greatly reduced. In addition, the use of a charge measurement rather than the admittance measurement allows the measurements to be made at arbitrarily low frequencies. As a matter of practice, reaction rates in cure studies limits the lowest useful frequency to about 0.1 Hz however, pre-cure or post-cure studies can be made to as low as 0.005 Hz. Finally, the differential connection used for the two transistors provides first-order cancellation of the effects of temperature and pressure on the transistor operation. The devices can be used for cure measurements to 300 °C, and at pressures to 200 psi. 

If a plot of log [-dPddt] versus log[A] is a straight line, the slope of the line is the reaction order with respect to A. Figure 7.19 represents Mn2+ oxidation at pH 8.5 and p02 0.2 obtained by pH-stat technique. The technique utilizes a pH electrode as a sensor so that as OH is consumed (during Mn2+ oxidation), the instrument measures the rate of OH- consumption and activates the autoburete to replace the consumed OH-. It is assumed that for each OH- consumed, an equivalent amount of Mn2+ is oxidized. These pH-stat data clearly show that the first part of the oxidation of manganese is zero-order, whereas the second part is first-order. Keep in mind, however, that these particular reaction orders are strictly empirical and without necessarily any mechanistic meaning. 

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