Isothermal runs

The pressure profiles obtained from isothermal runs at five different temperatures using this method are shown in Figure 2. It can be observed that in general, the pressure rise is fairly linear for most of the duration of the experiments so that a zero-order approximation may be used to fit the data. This linearity was found to hold even after 5 days for the 175 °C isotherm, reaching a pressure level of approximately 300 psia (this was the longest duration of all the experiments). In the case of the 225 °C isotherm, the pressure accumulation finally levels off at approximately 1100 psia after one day. 

This relationship can be used to calculate rate constant k at any time f of the isothermal run. This is illustrated by the following example. 

Figure 5.4-63. Nitration isothermal runs in reaction calorimeter (adapted from Hoppe and Grob, 1990).

Faster analysis (a factor of three to five for temperature-programmed, up to a factor of 10 for isothermal runs)... 

Comparison of chemiluminescence isothermal runs with oxygen uptake and DSC measurements has been at the centre of interest since practical industrial applications of the chemiluminescence method were attempted. It is a fact that the best comparison may be achieved when studying polymers that give a distinct induction time of oxidation typical for autoaccelerating curves of a stepwise developing oxidation. This is the particular case of polyolefins, polydienes and polyamides. The theoretical justification for the search of a mutual relationship between the oxidation runs found by the various methods follows directly from the kinetic analysis of the Bolland-Gee scheme of polymer oxidation. 

Transition Region Considerations. The conductance of a binary system can be approached from the values of conductivity of the pure electrolyte one follows the variation of conductance as one adds water or other second component to the pure electrolyte. The same approach is useful for other electrochemical properties as well the e.m. f. and the anodic behaviour of light, active metals, for instance. The structure of water in this "transition region" (TR), and therefore its reactions, can be expected to be quite different from its structure and reactions, in dilute aqueous solutions. (The same is true in relation to other non-conducting solvents.) The molecular structure of any liquid can be assumed to be close to that of the crystals from which it is derived. The narrower is the temperature gap between the liquid and the solidus curve, the closer are the structures of liquid and solid. In the composition regions between the pure water and a eutectic point the structure of the liquid is basically like that of water between eutectic and the pure salt or its hydrates the structure is basically that of these compounds. At the eutectic point, the conductance-isotherm runs through a maximum and the viscosity-isotherm breaks. Examples are shown in (125). 

Figure 4.7 Log (oe"(co) versus log(viscosity) for the TGDDM epoxy-based on four isothermal runs...

Figure 4.7 shows the correlation between the viscosity and the ionic mobility based on isothermal runs for this system as monitored by the value of e" (5 kHz). A representative calibration curve relating the FDEMS sensor output to degree of cure is shown in Figure 4.8. Unlike viscosity, separate calibration curves for different temperatures must be generated from the isothermal runs because they are temperature dependent.

Clear indications of the induction period and of an increase in the reaction rate after copolymerization has started were found for isothermal runs by DSC measurements by Peyser and Bascom 941 even for melt copolymerization. According to the copolymerization mechanism, the induction period is interpreted as a gradual increase in the concentration of active centres45,52 and is identical with the time for reaching the maximum on the conductivity curves57). An induction period has also been established by other measurements 39,40>73.90.95), where it is often considered as an imprecision in the determination of the monomer concentration, mixing effect, temperature establishement, or it is not considered at all. 

The powder samples of polymer were also subjected to isothermal runs under vacuum for 30 minutes in the same temperature range, showing no appreciable differences in color development. 

From Eqs (5.18) (5.21), it is obvious that for any couple of values of conversion and temperature, the rate of consumption of epoxy groups, (dx/ dt), will depend on the particular value of a . And this, in turn, depends on the particular cure schedule e.g., for a particular couple (x,T), a different value of a will result from isothermal runs or from runs at constant heating rate that intercept the particular point (x,T). Therefore, Eq. (5.1) has no general validity for this case. 

Other authors observed the same inconsistent results for other epoxy-anhydride-tertiary amine systems. For example, Peyser and Bascom (1977) observed first-order kinetics under isothermal and dynamic conditions however, the activation energy for dynamic runs was E = 104.2 kJ mol-1, much larger than the value for isothermal runs, E = 58.6 kJ mol-1. 

This simple kinetic model predicts the presence of an induction period in isothermal runs, where (3 gets close to (3eq, followed by a first-order kinetics, as experimentally observed. 

Figure 5.4 Relative approach of the concentration of active species to the equilibrium value for isothermal runs, plotted as a function of conversion. (Riccardi et at., 1999 - Copyright 2001 - Reprinted by permission of John Wiley Sons, Inc.)...

The column flow, diameter and length are attractive parameters for shortening chromatographic runs. In comparison with steeper temperature profiles and isothermal runs at higher temperatures one has to remember that such procedures may lead to a more pronounced broadening of the peaks, which is acceptable as long as the total quality of the analysis does not suffer and the respective gain in speed of the separation is sufficient. 

Au number of input variables or constants Az number of isothermal runs... 

The detailed kinetic model has been used to simulate the behavior of the reactive system in MATLAB/SIMULINK by performing Az = 9 isothermal runs at different temperatures 7), equally spaced by 5°C from 7) = 60°C to Tg = 100°C. For... 

The more usual procedure for estimating % and Ta/ from experimental data taken at different temperatures consists in considering N/ distinct isothermal problems and estimating the relevant values of the rate constants then, from these data and the relationship (3.59) it is possible to estimate koi and a/ Nevertheless, since the law describing the temperature dependence of the rate constants is known, it is possible to estimate directly koi and E. To deal with 9 different isothermal runs, it is only necessary to repeat the integration 9 times for each computational step of the objective function in other words, the dimension Nz of the data can be eliminated by posing in series the 9 sets of data. 

A programmed run has been found to be highly effective in analyzing accelerants and is preferred over isothermal runs. 

Some major differences between the two runs can be seen and are typical of PTGC. For a homologous series, the retention times are logarithmic under isothermal conditions, as we saw in Chapter 6, and they are linear when programmed. The programmed run was begun at a lower temperature (50°C) than the one used for the isothermal run (150°C), which... 

For an isothermal run, the growth constant K may be evaluated by determining the initial and final weights of the seeds, the number of crystals, and the variation of supersaturation with time. Values of the growth constant obtained at several different temperatures may be used with Eq. (26) to predict nonisothermal operation. Palermo s work is in agreement with McCabe s (Ml) earlier work, for it is in essence an analysis limited to a single crystal size, rather than a distribution of sizes. 

A more careful examination of the feed rate data showed that, while It was true the benzene/propylene feed was pumped over the entire catalyst bed 1.3 times faster than during the Isothermal run (LWHSV adiabatic = 1.3 LUHSV Isothermal), the feed rate through the alkylation zone was much higher. A convenient way of expressing this rate was to determine how many grams of total feed passed through a unit (cm ) of catalyst surface area per hour. This rate was termed as superficial velocity and had g/cm -hr dimensions. the Isothermal reactor the superficial... 

Conversion data Itom an isothermal run at several flow rates were treated as in the previous section to obtain the observed psuedo—first-order rate constant. These were reported at various temperatures for the same catalyst sample (at the same deactivation level, since HDS does not deactivate the catalyst). All rate constants were evaluated per weight of fresh catalyst by using the deposition data of Table 2. Corrections were made to allow for concentration effects alone, Eqn. (9), and both concentration and diffusion effects, Eqn. (10), at all temperatures. The low—temperature asymptote was drawn using the obsl starting from the lowest temperature, until a statistically significant... 

Chromatography, we can reasonably ej ct the peak shapes to be gaussian. For an isothermal run, the mean retention time divided by the standard deviation will be a constant, while for a temperature programmed run, the peak parameters will be independent of retention time, and thus g(t,t ) g(t-t ). In this case Equation 9 becomes... 

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