Ramp experiments

Let us assume that a viscoelastic material undergoes a shear strain that is a linear function of time. Let us assume further that the experiment is carried out in such conditions that the viscoelastic behavior is linear and the mechanical history is given by (7) 

Once steady-state conditions t - oo) are reached, one obtains 

By substituting this value of k into Eq. (5.52), the following relationship between the viscosity and the relaxation modulus is obtained  

This expression allows the determination of the viscosity at zero shear rate from the time dependence of the relaxation modulus. 

On the other hand, it is possible to relate the shear compliance function to the relaxation modulus by using the ramp experiment described above. Actually, Eqs. (5.35) and (5.52) lead to the expression 

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The Pt SiC catalyst (Fig. Ic) shows light-off around 220°C and NO reduction in the same temperature range as for the other catalysts. The NjO formation maximises around 235°C and is of similar magnitude as for the Pt/ZSM-5 catalyst. The NOj formation rate increases rapidly around this temperature and shows a maximum at 320°C. Adsorption of neither hydrocarbons nor NOx on the Pt SiC sample is obvious from Fig Ic. In Table 2 the NOx reduction efficiency and the selectivity towards N2 and N2O formation are summarised for the flow reactor experiments. Both the NOx reduction activity and the N2 selectivity of the Pt/SiC and Pt/ZSM-5 system appear to be similar, while Pt/Al203 shows a higher peak reduction value for the heating ramp experiments. 

When the three materials are tested under steady-state conditions, a different picture is obtained. The results of the NOx reduction activity and the N2 and N2O selectivity, under steady-state conditions, are included in Table 2. The maximum NOx reduction activity and the selectivity towards N2 for the Pt/Al203 system are lower than in the heating ramp experiment. Under steady-state cbnditions, the Pt/ZSM-5 system shows the highest overall NO reduction activity and a somewhat higher selectivity towards N compared with the heating ramp experiments. For Pt/SiC there are no significant differences between the two types of experiments. It was observed that also under steady-state the maximum NOx reduction coincides with almost complete CO2 conversion. 

The heating ramp experiments for Pt/SiC revealed no significant difference in NO reduction activity or N2 selectivity compared with the steady-state experiments (see Table 2). For Pt/Al203, on the other hand, both the activity for NO reduction and the N2 selectivity were significantly higher in the ramp experiments compared with the steady-state experiments. For Pt/ZSM-5 the activity was similar in the two cases whereas the N2 selectivity was higher in the steady-state experiments. This raises the question why the steady-state experiments and the heating ramp experiments are so different. 

Thermo-mechanical properties of the crosslinked EVA were measured using a Rheometric DMTA IV in a nitrogen atmosphere. Crosslinked EVA specimens were cut from the samples and mounted in the rectangular tension fixture. The typical sample dimensions were 10 mm long, 3.3 mm wide and 0.4 mm thick. During the dynamic temperamre ramp experiment, the heating rate was 7 °C/min and the frequency was 1 Hz. The static force was maintained at 20 % higher than the dynamic force. 

The drop of NO conversion exhibited by curve D at T > 200 °C in Fig. 9.4 is explained by depletion of surface nitrates in fact, in another similar experiment (not reported), wherein the catalyst had been pretreated with NO2 at 150 °C rather than at 60 °C, an earlier drop in the NO conversion was observed due to the reduced amount of nitrates stored at the higher temperature. Eventually, the match between curves D and A at T > 300 °C confirms the absence of any residual oxidizing agent (but NO) in the final part of the T-ramp experiment over the NO2 pretreated sample. 

Figure 9.6 shows that, on the contrary, when the same TPSR experiment was replicated with a step feed of NH3 instead of NO, no reaction was detected ammonia is thus unable to reduce the surface nitrates at 200 °C (as well as at lower temperatures, results not shown), which is apparently paradoxical, since NH3 is in principle a much better reducing agent than NO. Indeed, subsequent T-ramp experiments evidenced the reduction of surface nitrates by NH3, but only starting from T > 220 °C [21]. 

Notice that NO2 played no direct role in the redox cycle. Indeed, we have shown in [6] that in T-ramp experiments the rate of NO conversion at low T was essentially identical either when feeding NO -I- NH3 + NO2 to a clean V-catalyst, or when feeding NO + NH3 only to the V-catalyst presaturated with nitrates. 

In addition to these particular features of the soot combustion reactions, the reaction rate also depends on general variables, such as temperature for isothermal reactions and heating rate for ramp experiments, nature and partial pressure of gases in the stream, space velocity/residence time of gases in the solid bed, soot-to-catalyst ratio, and so on. 

Thermal stabihty of ceUs can be studied by linear programmed heating to cell failure, sometimes called the Thermal Ramp Experiment [14]. In one Thermal Ramp Experiment, cells were heated at a programmed heating rate (5 °C min is typical) from room temperature to 250 °C, at which temperature the ceU failed by initiating thermal runaway. 

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