Curve, conversion

Stoicescu and Dimonie103 studied the polymerization of 2-vinylfuran with iodine in methylene chloride between 20 and 50 °C. The time-conversion curves were not analysed for internal orders but external orders with respect to catalyst and monomer were both unity. Together with an overall activation energy of 2.5 kcal/mole for the polymerization process, these were the only data obtained. Observations about the low DP s of the products, their dark colour, their lack of bound iodine and the presence of furan rings in the oligomers, inferred by infrared spectra (not reported), completed the experimental evidence. The authors proposed a linear, vinylic structure for the polymer, and a true cationic mechanism for its formation and discussed the occurrence of an initial charge-transfer complex on the... 

The radical chain mechanism of the sulfochlorination is very similar to that of the chlorination. Accordingly, in normal cases the regioselectivities of the sulfochlorination and the chlorination are equal. For example, (-1) substituents decrease the reactivities of the adjacent C-H bond. This influence can even be observed at the y position. Thus, the consecutive second sulfochlorination affords no geminal or vicinal disulfochlorides in the product. Where there are differences between the regioselectivities of sulfochlorination and chlorination (as in the case of isoalkanes), it is because under the conditions of sulfochlorination, chlorination also takes place to a considerable extent. Figure 6 shows the main components of a sulfochlorination mixture. Today the kinetics and the regioselectivity of the sulfochlorination of /z-alkanes are so well known that the kinetic modeling of the concentration-conversion curves is possible for all partners of the reaction [12]. 

The initial rate of polymerization was determined from the initial slopes of time-conversion curves (Fig. 1) using f-BuX/Me3 Al/MeCl systems at -40 °C. This... 

Fig. 7. Calculated time/conversion curves and experimental data points in the anionic polymerization of MMA (C0 = 0.1 mol/1) initiated by methyl-a-lithioisobutyate (C0 = 0.05 mol/1) at 25 °C in THF (Products higher than the tetramer are omitted) (A. H. E. Muller, L. Lochmann, J. Trekoval, Ref.S0))...

The previously outlined mechanistic scheme, postulating reversible propagation and cyclization, was simplified by neglecting the de-cyclization because in the very short time of the studied reaction the extent of de-cyclization is negligible. The rate constants appearing in the appropriate differential equations were computer adjusted until the calculated conversion curves, shown in Fig. 7, fit the experimental points. The results seem to be reliable inspite of the stiffness of the differential equations. 

Only a few quantitative data are available on copolymerization of methacrylates. Direct determination of the cross-propagation constants is readily achieved in living polymer systems whenever the absorption spectra of the two propagating species are different. Unfortunately, this is not the case in the methacrylate series. A new approach to this problem was developed by Muller 43). A mixture of two monomers is copolymerized, the reaction is interrupted at various times, and the concentrations of the residual monomers are determined as functions of time. The pertinent differential equations include 4 constants ku, k12, k21, and k22. Since kn and k22 were independently determined, the remaining cross-propagation constants are obtained by computer fitting the experimental conversion curves to the calculated ones. 

The kinetics of propagation of this cyclic barium salt is described in their following paper 83). The conversion curves are sigmoidal indicating, as anticipated, the accelera-... 

One of the calculation results for the bulk copolyroerization of methyl methacrylate and ethylene glycol dimethacrylate at 70 C is shown in Figure 4. Parameters used for these calculations are shown in Table 1. An empirical correlation of kinetic parameters which accounts for diffusion controlled reactions was estimated from the time-conversion curve which is shown in Figure 5. This kind of correlation is necessary even when one uses statistical methods after Flory and others in order to evaluate the primary chain length drift. 

Figure 9-4. Sites of feedback inhibition in a branched biosynthetic pathway. Si-Sj are intermediates in the biosynthesis of end products A-D. Straight arrows represent enzymes catalyzing the indicated conversions. Curved arrows represent feedback loops and indicate sites of feedback inhibition by specific end products.

Figure 2a reveals that the conversion of RBr increases with increasing the amount of water up to the amount of water being 3 mL, then it declines. Note that the sharp increase of the conversion curves is due to the fast difiusion of RBr from the organic phase to the catalyst-rich liquid phase where only part of RBr reacts with QOAc. 

The desired product is P, while S is an unwanted by-product. The reaction is carried out in a solution for which the physical properties are independent of temperature and composition. Both reactions are of first-order kinetics with the parameters given in Table 5.3-2 the specific heat of the reaction mixture, c, is 4 kJ kg K , and the density, p, is 1000 kg m . The initial concentration of /I is cao = 1 mol litre and the initial temperature is To = 295 K. The coolant temperature is 345 K for the first period of 1 h, and then it is decreased to 295 K for the subsequent period of 0.5 h. Figs. 5.3-13 and 5.3-14 show temperature and conversion curves for the 63 and 6,300 litres batch reactors, which are typical sizes of pilot and full-scale plants. The overall heat-transfer coefficient was assumed to be 500 W m K. The two reactors behaved very different. The yield of P in a large-scale reactor is significantly lower than that in a pilot scale 1.2 mol % and 38.5 mol %, respectively. Because conversions were commensurate in both reactors, the selectivity of the process in the large reactor was also much lower. 

Figure 5.46. A burst of warm feed at 310 K for the first 1400 seconds causes the system to shift into a higher temperature and higher conversion steady state. The fractional conversion curves A and C are for normal startup and B and D are for the startup with a warm feed period.

The FTS was conducted at varying temperatures (from 483 to 513 K) over approximately 50 h of reaction time in order to investigate the reaction kinetics achieved with the respective catalysts. A typical conversion curve using the Co/ HB catalyst as an example is shown in Figure 2.3. After a short settling phase (caused by the pore filling of liquid Fischer-Tropsch products) of only about 4 h, steady-state conditions were reached. In the observed synthesis period of 50 h no deactivation of the catalysts was detected. However, industrially relevant experiments over several weeks are still outstanding. 

Fig. 7. Time-conversion curves of thermally initiated emulsion polymerization of 1,4-DVB at 0.1 (I) 0.65 (II) and 0.85 (III) M SDS concentrations. Polymerization temperature = 90 °C water/monomer volume ratio = 12.5. [Reproduced from Ref.84 with permission,Hiithig Wepf Publ., Zug, Switzerland].

Andreev and coworkers—promoting effect of Cu addition on Fe-Cr shift catalysts, and Raney Cu/Zn catalysis described by an associative mechanism. Andreev and coworkers240 added promoters to traditional high temperature shift Fe-Cr catalyst, and found that Cu and Co moved the maximum in the CO conversion curve to lower temperatures. No explanation was provided for the effect. 

It is necessary now to find out whether my theoretical conclusion is supported by experimental evidence in fact, there are many results for bulk polymerizations that indicate a first-order growth reaction. The experimental support that I seek would be found in the shape of the curves relating the conversion, Y, to the total received dose of radiation or to the time at a constant dose-rate. If the polymerizations are of zero order with respect to m, the conversion curves will be rectilinear instead of concave to the dose (or time) axis. Rectilinear conversion curves are actually much more common than first-order type curves, and some instances of this behaviour are listed in Table 1. In example 8 of Table 1 the experimental points are actually on a straight line, but a curve has been drawn past them. 

The only studies on olefin polymerisations in methylene dichloride in which kp was deduced directly from the rate of reaction were carried out by Ledwith and his collaborators [9, 13] with extremely low concentrations of monomer and catalyst. They polymerised isobutyl vinyl ether and N-vinyl carbazole in a Biddulph-Plesch calorimeter with trityl or tropylium salts and obtained the first-order rate constants k1 from the conversion curves. Since different catalysts gave the same ratio of kx c they concluded that for each of them Xxr = c0 and hence identified with kp which must in fact be k p, as explained above. It seems unlikely that if several initiators give the same value of kp, they do so because they are all equally inefficient, and the inference that they do so because they are all 100% efficient, i.e., that for all of them x = c0, seems plausible - but it would be useful to have a direct check of this. 

A rate-constant, kx, was calculated from the first-order conversion curves, and this was related to what Plesch believed to be the kp+ by the conventional relation ... 

These authors (1968) reported on the polymerisation of isobutene in heptane by AlBr3 with an excess of TiCl4 at -14 °C. The conversion curves indicating a non-stationary... 

Towards the end of the polymerisations, the reactions tend towards first-order behaviour and thus we can make the reasonable assumption that [E] and [Pn+] are constant. With the further assumptions that [E] = [HClO4]0 k2 =k2and k2"=105 dm3 mol 1 s 1, [Pn+] can be calculated from the conversion curves in Figure 1 and is found to be of the order of 10"8 mol dm3 towards the end of the polymerisations. 

Poly(acrylic acid) is not soluble in its monomer and in the course of the bulk polymerization of acrylic acid the polymer separates as a fine powder. The conversion curves exhibit an initial auto-acceleration followed by a long pseudo-stationary process ( 3). This behaviour is very similar to that observed earlier in the bulk polymerization of acrylonitrile. The non-ideal kinetic relationships determined experimentally in the polymerization of these two monomers are summarized in Table I. It clearly appears that the kinetic features observed in both systems are strikingly similar. In addition, the poly(acrylic acid) formed in bulk over a fairly broad range of temperatures (20 to 76°C) exhibits a high degree of syndiotacticity and can be crystallized readily (3). 

A detailed investigation of the polymerization of this monomer in a series of solvents has shown, however, that the auto-accelerated character of the reaction is not related to the precipitation of the polymer. Thus, linear conversion curves and atactic polymers are obtained if the monomer is diluted in such nonassociating solvents as toluene, n-hexane, carbon tetrachloride and chloroform, in spite of the precipitation of the polymer, whereas, both auto-acceleration and syndiotacticity persist for fairly high dilutions in water, methanol and dioxane even under conditions where the reaction medium turns homogeneous (4). 

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