Transient experiments

Consideration of the time dependence of relaxation phenomena adds additional complications. The value of a measured modulus or compliance will very definitely depend on the exact manner in which the experiment is carried out. 

As an example, consider the following experiments. First, a polymer is subjected to a constant uniaxial stress cr for one hour this perturbation results in some measurable strain, say e(l hour). In a second experiment, however, an identical sample is subjected to sufficient stress to result in the same strain s (1 hour) immediately upon application of the stress. Then the stress is decreased so that the strain remains constant at s (1 hour). The value of the stress after 1 hour in the second experiment is defined as j2- In general, j1 and r2 will not be the same, the stress cr2 associated with the constant strain experiment being lower. However, since the strains are the same, the two modulus values 

The corresponding experiment in extension results in the tensile creep compliance D(t) defined by 

Similarly, a shear stress relaxation experiment would measure G(t), the shear stress relaxation modulus 

Equations of the form of (2-3) and (2-6) relating moduli and compliances are no longer applicable to our new time-dependent functions, since 

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The latter may be fiirther subdivided into transient experiments, in which the current and potential vary with time in a non-repetitive fashion steady-state experiments, in which a unique interrelation between current and potential is generated, a relation that does not involve time or frequency and in which the steady-state current achieved is independent of the method adopted and periodic experiments, in which current and potential vary periodically with time at some imposed frequency. 

Each of these models will be examined in subsequent sections as devices for describing specific transient experiments. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

A second source of difficulty is caused by the unavoidable empty space in recycle reactors. This limits their usefulness in some studies. Homogeneous reactions in the empty gas volume may interfere with heterogeneous catalytic measurements. Transient experiments could reveal much more information on various steps in the reaction mechanism but material in the empty space can obscure sharp changes. 

Figure 12.5. Ethylene oxidation on Pt finely dispersed on Au supported on YSZ.7 Effect of the current 1 on x 1, where x is the time constant measured during a galvanostatic transient experiment with I as the applied current x is obtained by fitting either r/r0=exp(-t/x) or l-exp(-t/x) to the experimental data depending on the sign of the current and whether the reaction is electrophilic or electrophobic, (a) Positive values of I for electrophilic (squares, T=371°C, pO2=18.0 kPa, Pc2H4=0-6 kPa) and electrophobic behavior (circle, T=421°C, p02=l 4.8 kPa, Pc2H4 CU kPa) (b) negative currents, electrophilic behavior (T=421°C, p02=14.8 kPa, pC2H4=0.1 kPa. Reprints with permission from Academic Press.

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = but the dependence on Sc is weak for... 

Transient experiments with inert tracers are used to determine residence time distributions. In real systems, they will be actual experiments. In theoretical studies, the experiments are mathematical and are applied to a d5mamic model of the system. 

This study presents kinetic data obtained with a microreactor set-up both at atmospheric pressure and at high pressures up to 50 bar as a function of temperature and of the partial pressures from which power-law expressions and apparent activation energies are derived. An additional microreactor set-up equipped with a calibrated mass spectrometer was used for the isotopic exchange reaction (DER) N2 + N2 = 2 N2 and the transient kinetic experiments. The transient experiments comprised the temperature-programmed desorption (TPD) of N2 and H2. Furthermore, the interaction of N2 with Ru surfaces was monitored by means of temperature-programmed adsorption (TPA) using a dilute mixture of N2 in He. The kinetic data set is intended to serve as basis for a detailed microkinetic analysis of NH3 synthesis kinetics [10] following the concepts by Dumesic et al. [11]. 

Table 4 summarizes the rate constants kj - Aj exp(-Ej / RT) for the forward and the reverse reaction derived from our microkinetic analysis of the steady-state and transient experiments with the three catalysts, i.e. Cs-Ru/MgO, Ru/MgO, and Ru/AlaOs catalyst [24]. 

Analysis of the dynamics of SCR catalysts is also very important. It has been shown that surface heterogeneity must be considered to describe transient kinetics of NH3 adsorption-desorption and that the rate of NO conversion does not depend on the ammonia surface coverage above a critical value [79], There is probably a reservoir of adsorbed species which may migrate during the catalytic reaction to the active vanadium sites. It was also noted in these studies that ammonia desorption is a much slower process than ammonia adsorption, the rate of the latter being comparable to that of the surface reaction. In the S02 oxidation on the same catalysts, it was also noted in transient experiments [80] that the build up/depletion of sulphates at the catalyst surface is rate controlling in S02 oxidation. 

This chapter reports the results from transient experiments (mainly, TPD or TPSR) coupled with on-line analysis of reaction mixture at the outlet of a well-stirred reactor. It means that the gas composition detected at the outlet of the reactor is in contact with the catalyst inside the reactor. Catalytic runs in isothermal conditions were also proceeded in order to avoid strong adsorptions of reactants or intermediates. 

Denton, P., Giroir-Fendler, A., Schuurman, Y. et al. (2001) A redox pathway for selective NOx reduction stationary and transient experiments performed on a supported Pt catalyst, Appl. Catal. A 220, 141. 

Near LST, the relaxation times become very long, and steady shear flow cannot be reached in the relatively short transient experiment. Large strains are the consequence for most reported data. 

The bulk of this review concerns transient experiments on heterogeneous catalysis at atmospheric pressure. After some comments on current methods for doing the experiments, the application of the method will be illustrated by two examples the oxidation of CO over Pt, and the hydrogenation of CO over Fe. 

Van Ho and Harriott (54) have done similar transient experiments on H2/CO over 10% Ni/Si02, and a result is shown in Fig. 23. Even though the bulk of the nickel is not carbided, the methane production rate rises from zero, as shown. 

A central point to be made in connection with Figures 1 and 2 is that a great deal of qualitative insight can be gained from relatively simple experiments. The results guide the selection of temperatures for steady-state and transient experiments which can be analyzed more quantitatively. 

The most sophisticated and incisive transient experiments are those derived from modulated molecular beam reactive scattering experiments. 

Recently, Shei-Kung Shi and John Schreifels in our laboratory (21) have done an interesting transient experiment involving the titration of adsorbed oxygen with hydrogen on Ru(001). The results indicate the caution with which Auger spectroscopy should be used to follow reactive chemisorbed oxygen concentrations. 

In order to analyze the adsorption behavior of carbon dioxide on silver it was necessary to understand the adsorption behavior of and its reactivity, because the adsorption of CO strongly relatedto the adsorbed oxygen species as will be described later. For this reason, the following transient experiments were purformed. 

Furthermore for the relevant adsorption steps CO-adsorption, H O-adsorption, CC -desorption, H -desorption, one concludes from the form of the transients that tne first three are not kinetical-ly controlled, as they are shock fronts and that Hj has no measurable sorption capacitance in presence of CO. The last conclusion has been also confirmed by independent experiments, i.e. strip-ping-off of adsorbed H by CO, and the transients in this case suggest that also the desorption, at least under the selected experimental conditions, is not kinetically controlled. Independent transient experiments showing that the CO2 sorption transients can have the form of shock wavefronts or simple wavefronts (see (7)) support the conclusion that CO2 sorption is not kinetically controlled it could be also shown that 1 0 can strip off... 

Figures 8a and 8b present the simulated current transients obtained from the self-affine fractal interfaces of r/ = 0.1 0.3 0.5 and r] = 1.0 2.0 4.0, respectively, embedded by the Euclidean two-dimensional space. It is well known that the current-time relation during the current transient experiment is expressed as the generalized Cottrell equation of Eqs. (16) and (24).154 So, the power exponent -a should have the value of - 0.75 for all the above self-affine fractal interfaces.

Polarization-transfer experiments which are based on a resonance condition, i.e. where a variable quantity in the experiment is matched to a parameter of the investigated spin system, can be carried out as a transient experiment or as an adiabatic experiment Figure 11.5 illustrates the differences between these two types of experiments. In a transient or sudden" experiment, the density operator is prepared in a state orthogonal to the effective polarization-transfer Hamiltonian (Fig. 11.5a). When the polarization-transfer Hamiltonian is switched on, the density operator starts precessing around the effective Hamiltonian, and usually maximum polarization transfer is reached after a 180° rotation. Since often the size of the effective Hamiltonian at the matching condition depends on... 

Channel techniques employ rectangular ducts through which the electrolyte flows. The electrode is embedded into the wall [33]. Under suitable geometrical conditions [2] a parabolic velocity profile develops. Potential-controlled steady state (diffusion limiting conditions) and transient experiments are possible [34]. Similar to the Levich equation at the RDE, the diffusion limiting current is... 

Temporal analysis of products (TAP) reactor systems enable fast transient experiments in the millisecond time regime and include mass spectrometer sampling ability. In a typical TAP experiment, sharp pulses shorter than 2 milliseconds, e.g. a Dirac Pulse, are used to study reactions of a catalyst in its working state and elucidate information on surface reactions. The TAP set-up uses quadrupole mass spectrometers without a separation capillary to provide fast quantitative analysis of the effluent. TAP experiments are considered the link between high vacuum molecular beam investigations and atmospheric pressure packed bed kinetic studies. The TAP reactor was developed by John T. Gleaves and co-workers at Monsanto in the mid 1980 s. The first version had the entire system under vacuum conditions and a schematic is shown in Fig. 3. The first review of TAP reactors systems was published in 1988. 

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