Conversion time dependence

A closer examination of the different solutions shows that the conversion-time dependence for a second order stoichiometric reaction performed in a PFTR is identical with a first order reaction conducted in a CSTR. This can be explained by the different mixing patterns of the PFTR and the CSTR. 

I explained in Chapter 4 that there are two types of ADC -the Wilkinson and the Successive Approximation. In this chapter. Section 4.6.6, I discussed the choice of ADC in a general manner. Clearly, for high count rate situations the choice is easy - the faster the better Simplicity would suggest a Successive Approximation ADC, with its fixed conversion (dead) time, rather than the Wilkinson, with a conversion time dependent on pulse height. However, if the average gamma-ray energy were to fall in, or below, channel 360, even a 450 MHz Wilkinson ADC would... 

Gorbunova and co-workers [35] studied the cure kinetics of a phenol-urethane composition by DMTA and DSC and compared the results obtained by these techniques. Equations were derived to relate the viscosity and the degree of conversion. Time dependence of the conversion was described by a second-order equation in all cases, although the coefficients of this equation are different for DSC and dynamic mechanical measurements. 

In a nonactivated polymerization, which is an order of magnitude slower from the outset, the polymerization of PD runs as a heterogeneous process, with its conversion-time dependences being linear at least up to 50% conversion (formal zero-order kinetics) [106]. The high values of molar mass that are attained in this way confirm a low concentration of the growth centers. The polymers prepared by nonactivated polymerization contain no labile structures, which otherwise arise from side reactions [107], and also show a better thermal stability than those synthesized by activated polymerization [108] this should be true also for the CL polymerization. 

The transmission coefficient Cl (Qj,t), considering transient (broadband) sources, is time-dependent and therefore accounts for the possible pulse deformation in the refraction process. It also takes account of the quantity actually computed in the solid (displacement, velocity potential,...) and the possible mode-conversion into shear waves and is given by... 

The elongation of a stretched fiber is best described as a combination of instantaneous extension and a time-dependent extension or creep. This viscoelastic behavior is common to many textile fibers, including acetate. Conversely, recovery of viscoelastic fibers is typically described as a combination of immediate elastic recovery, delayed recovery, and permanent set or secondary creep. The permanent set is the residual extension that is not recoverable. These three components of recovery for acetate are given in Table 1 (4). The elastic recovery of acetate fibers alone and in blends has also been reported (5). In textile processing strains of more than 10% are avoided in order to produce a fabric of acceptable dimensional or shape stabiUty. 

In the genuine low-temperature chemical conversion, which implies the incoherent tunneling regime, the time dependence of the reactant and product concentrations is detected in one way or another. From these kinetic data the rate constant is inferred. An example of such a case is the important in biology tautomerization of free-base porphyrines (H2P) and phtalocyanins (H2PC), involving transfer of two hydrogen atoms between equivalent positions in the square formed by four N atoms inside a planar 16-member heterocycle (fig. 42). 

The rate of formation of radicals will depend on a number of features, including the concentration of initiator, temperature and the presence of other agents. Since subsequent stages of polymer growth occur almost instantaneously it is the relative slowness of this stage which causes the overall conversion times in most polymerisations to be at least 30 minutes and sometimes much longer. 

Space time ST is equal to the residence time in a plug flow reactor only if the volumetric flowrate remains constant throughout the reactor. The residence time depends on the change in the flowrate through the reactor, as well as V/u. The change in u depends on the variation in temperature, pressure, and the number of moles. The concept of SV with conversions in the design of a plug flow reactor is discussed later in this chapter. 

The chemistry in this case is the irreversible conversion of A to B, which follows simple, linear kinetics. When we write the time-dependent mass balances for this system we have ... 

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

Calculation of kinetic parameters - In the experiments carried out in the single autoclave the H2 pressure was not maintained and the consumption of H2 controlled the conversion of AcOBu, which could be described by pseudo-first order rate constant. In the activity tests performed in SPR16 the conversion of AcOBu increased linearly up to ca. 50 % with reaction time. Initial reaction rates were calculated from AcOBu conversion vs. reaction time dependence, the initial concentration of substrate and the amount of catalyst or the amount of promoters in 1 g of catalyst. 

Figure 1A shows the conversion-ee dependencies in the enantioselective hydrogenation of 2,3-butanedione (BD). As shown that the introduction of quinuclidine (Q), as an AT A, significantly increased the ee values in the whole conversion range. Upon Q addition, first order rate constant k3 increased from 0.0102 to 0.0158 while k2 remained almost unchanged (0.0008 and 0.0005, respectively). After 4 hours reaction time, measurable amount of butanediols was found. The yields of butanediols were as follows in the absence of quinuclidine R,R=2.0%, S,S=1.7%, R,S=5.4%, in its presence R,R=2.3% S,S=1.2% R,S=3.7%. Figure IB shows the ee-conversion dependencies... 

Observed monomer concentrations are presented by Figure 2 as a function of cure time and temperature (see Equation 20). At high monomer conversions, the data appear to approach an asymptote. As the extent of network development within the resin advances, the rate of reaction diminishes. Molecular diffusion of macromolecules, initially, and of monomeric molecules, ultimately, becomes severely restricted, resulting in diffusion-controlled reactions (20). The material ultimately becomes a glass. Monomer concentration dynamics are no longer exponential decays. The rate constants become time dependent. For the cure at 60°C, monomer concentration can be described by an exponential function. 

Fig. 5 shows the time dependence of the solid-state ion exchange process. The process has pseudo first order kinetics in the investigated conversion range for both (i) the distribution and crystallinity loss of the CdCl2 salt and (ii) the formation of new Cd,H-Y phase. The rate constant obtained for the decay of... 

The enthalpy of copper at nitrogen temperature is H77K = 6 J/g, so the total entropy of the sphere will be about 6 x 106 J. The time needed to cool from 77 K down to 4K is of the order of 4h. The total helium consumption from room temperature to 4.2 K would be about 6001. The temperatures reached in a test run are reported in Table 16.2. The expected final sphere temperature is about 20 mK. A comparison of MiniGRAIL and Nautilus cool down is made in Table 16.2. The high power leak on the sphere has been attributed to a time-dependent heat leak caused by the ortho-para conversion (see Section 2.2) of molecular hydrogen present in the copper of the sphere (see Fig. 16.5) (the Nautilus bar instead is made by Al). A similar problem has been found in the cool down of the CUORICINO Frame (see Section 16.6). 

An example of activity developing with a Co catalyst is shown in Figure 9.9 (right). CO-conversion (respectively the yield of products) increases with time by a factor of about 10, from ca. 4% to ca. 55%.7,17 Figure 9.9 (left) shows the time dependence of FT with an iron catalyst. There are a strong initial carbon deposition (referring to iron carbide formation) and fast water gas shift reaction, and FT... 

The integrated form of the simple Michaelis-Menten kinetics (Eq. (8)), is most suitable to analyze the time-dependent progressive substrate conversion or the corresponding product formation. 

Fig. 3. Time dependence of the conversion of normal ethylene adsorbed on Pt(lll) to ethylidyne at four different temperatures.

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

This paper is about a reinterpretation of the cationic polymerizations of hydrocarbons (HC) and of alkyl vinyl ethers (VE) by ionizing radiations in bulk and in solution. It is shown first that for both classes of monomer, M, in bulk ([M] = niB) the propagation is unimolecular and not bimolecular as was believed previously. This view is in accord with the fact that for many systems the conversion, Y, depends rectilinearly on the reaction time up to high Y. The growth reaction is an isomerization of a 7t-complex, P +M, between the growing cation PB+ and the double bond of M. Therefore the polymerizations are of zero order with respect to m, with first-order rate constant k p]. The previously reported second-order rate constants kp+ are related to these by the equation... 

The same experiment can be carried out quantitatively. By taking into account radiationless processes, namely, internal conversion fcIC, intersystem crossing isc, and bimolecular quenching kQ[Q] with a quencher Q, the time-dependent concentrations of the donor D and the acceptor A in the excited singlet state Si, [Ds,] and [As,] can be expressed as follows ... 

H]-ethanolamine into PE was inhibited by C6-ceramide in a dose and time-dependent manner (b) delayed disappearance of label from CDP-choline and CDP-ethanolamine in pulse-chase experiments indicated impaired conversion of these CDP-metaboUtes to PC and PE by CPT and EPT, respectively (c) the activities of CPT and EPT are decreased upon C6-ceramide treatment (see Eigure 2 adapted from Bladergroen et al. 1999b). In contrast to BHK cells the activity of CT was not affected significantly in rat-2 fibroblasts by short-chain ceramides. 

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