Measurement time constant

Another use of Eq. (5.3) is that by measuring tD and and computing A via Eq. (4.19) one can estimate the catalyst surface area NG. Alternatively this also can be done by comparing the parameter 2FNG/I with the experimentally measured time constant t via Eq. (4.32). 

Experiment with the influence of different values of the measurement time constants, Xc iwid T v, Plot all the temperatures to compare the results. 

The considerations so far rely on constant heating power, and the way how this power is applied to the microhotplate does not play a role. In fact, a monolithically integrated control circuitry does not apply constant power but acts as an adjustable current source. Moreover, for measuring the thermal time constant experimentally, either a rectangular voltage or rectangular current pulse is applied. Analyzing the dynamic temperature response of the system leads to a measured time constant, which... 

The deviation between the time constants for membrane heating and cooling was measured as well (Eq. (3.37)). The heater of a single microhotplate was driven with a rectangular-shape current pulse. The pulse amplitude was adjusted to produce a temperature rise of 50 °C. In this case the measured time constant for cooling was... 

Figure 2 X-ray diffraction patterns of (A) the exposed front surfaee and (B) the shielded back surface of a P2O7-ACP/R 2 eomposite slab molded in a Teflon holder and suspended in a HEPES-buffered saline solution for 167 h at 37°C. The relative intensity (RI) values for (A) ranged from 230 to 570 counts/sec and for (B) from 90 to 800 counts/sec. The standard uncertainty of these values is 1/(3/ /)where 3 is the measurement time constant (in seconds).

The time constants of pressure and differential pressure measurements are on the order of 0.1 seconds. Temperature measurement time constants are usually between 1 and 10 seconds. Composition measurements (analyzers) are even slower, varying from 5 seconds to 10 minutes. 

Table 5-5. Measured Time Constants for the Non-deuterated Clusters as a Function of Vibrational Energy"...

Table 5-6. Effect of Dueteration on Measured Time Constants for n = 3 as a Function of Vibrational Energy...

C. F. Bernasconi, Relaxation Kinetics, Academic Press, New York, 1976. This standard textbook discusses comprehensively the linearization of rate laws for a wide variety of reaction sequences as well as experimental methods of measuring time constants. ... 

Secondary electron transfer from Ha" to Qa also speeds up with decreasing temperature in Rb. sphaeroides reaction centres, the measured time constant decreasing from approximately 230ps at room temperature to lOOps at 80K (Kirmaier et al., 1985a). Below 80K, the rate of the reaction is independent of temperature. In contrast, the rate of this reaction in the Rps. viridis reaction centre is independent of temperature between 295 and 5K (Kirmaier and Holten, 1988). Possible explanations for the temperature dependence of this reaction have been discussed, and it has been pointed out that the acceleration of this reaction seen in Rb. sphaeroides reaction centres between 295 and 80K cannot be taken as evidence that X equals flAG for this reaction (Parson, 1996 Warshel et al., 1989 Gunner and Dutton, 1989 Kirmaier et al., 1988 Kirmaier et al., 1985a). In particular, it has been shown that the temperature dependence of the rate of electron... 

Fig. 48. DLTS measurement time constant t (inverse of rate window) versus the inverse temperature of the peak in the electron emission spectrum at that r for a typical sample. The activation energy of 0.94 eV is the slope of the raw data without the 2kT correction (see text). The circles are from DLTS spectra the triangles are calculated from directly recorded capacitance transients.

The relaxation trace of the complexation reaction of Ni with pyridine-2-azo-p-dimethylaniline (PADA), shown in Fig. 2, was achieved by applying the SF mode. The measured time constant is in good agreement with the literature (3). 

We developed earlier in (39) the relationship between free and trapped carrier density when the system rests at equilibrium. Equation (69) has a different meaning in that it states that equilibrium will be maintained for any time variation during kinetic measurements. Equation (69) is termed the quasistatic approximation and it was introduced to account for the properties of measured time constants in DSC [51 ]. 

The fundamental rate constants will (almost) always be denoted by the symbol k, with subscripts to indicate different rate constants for example it is common to use and to indicate the forward and backward steps of an individual transition, or to use kg for the rate of the transition from the ith state to the yth state. As the reader will have noticed, the latter form is used in this volume. An equilibrium constant, the ratio of two rate constants, will normally be denoted by an upper case K, with suitable subscripts. The measured time constants, t, will be quoted with a subscript where necessary. The relation between k, t and k, the eigenvalues of the matrix of rate constants, was discussed in section 2.1 and will be illustrated in sections 4.2 and 5.1. 

The most straigthforward reaction model containing four intermediates is the linear sequential one. In this case each measured time constant gives directly the decay time of one intermediate. Thus only the order of the intermediates in the reaction scheme requires further informations. We have discussed the two possible arrangements of the 0.9ps- and the 3.5ps kinetlc as well as a branched reaction scheme elsewhere /6,7/. Here we present the specific case where the 3.5ps kinetic precedes the 0.9ps-kinetic. The main purpose is to show that the absorption data can really decide between a scheme with four intermediate states of well defined time constants (model I) and one with only three intermediates... 

Unfortunately, this simple treatment is rarely valid in practice, since the D value of most detectors varies with the modulation frequency, /, of the radiation being measured (see Chapter 6). With pyroelectric detectors, D varies approximately thus if the speed of the moving mirror is halved while keeping the measurement time constant, the SNR will increase. Conversely, D of most quantum detectors usually increases as / increases up to some maximum value ( 1 kHz for photoconductive MCT detectors). It then remains approximately constant as the modulation frequency is increased, and Anally drops off at frequencies above 1 MHz. Since it is rare that interferometers are operated at scan speeds that modulate the incident radiation at frequencies greater than 1 MHz, operating at high scan speeds when an MCT detector is employed is usually beneficial. 

A common factor of both diffusion weighting and MTC can on the one hand be a highly desirable effect but can on the other hand be an artefact of other measurements, affecting, for example, the accuracy of measured time constants if not carefully monitored. 

An increase in a filter lime in a Progranunable Logic Controller (PLC) or a Distributed Control System (DCS) or a damping setting in a transmitter will add a measurement time constant, which contributes to loop dead time and hence, loop period. 

Zhu et al. have studied the effects of cations in the electrolyte on hole transport times ( ) and lifetimes (ih) in C343-sensitised NiO, prepared form Ni(OH)2 colloids, using small-modulation transient photocurrent and photovoltage measurements.Figure 3.72 shows the measured time constants plotted against /sc-... 

In principle, two relaxation-time constants in the impedance spectrum can always be expected—rotational-diffusion (orientation) relaxation time x, and chemical-reaction relaxation time x j. In practice, if rotational diffusion is faster than reaction, the measured time constant x will be practically equal to x,. If the chemical step is faster than rotational diffusion, a distinct second relaxation occurs at higher frequencies than those of rotational diffusion. 

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