Conversion-time plots

For each data set examined, the onset of the gel effect (which is the initial value for the integration of the differential equations) was taken at the point where there is a departure from linearity in the conversion-time plot. While a good argument can be made ( ) for using another definition of the onset of the gel effect, the data available did not allow for a more detailed approach. 

Secondary alcohols react at much higher rates than primary alcohols having similar molecular dimensions. Conversion/time plots for several secondary alcohols are reported in Fig 20. 

Preparation and Properties of High-Molecular-Weight Poly (propylene oxide). Figure 4 shows a typical conversion-time plot for polymerization of propylene oxide by a hexacyanometalate salt complex catalyst. This reaction is characterized by an initial period during which almost no conversion occurs, followed by a period of rapid polymerization. The initial period, termed the induction period, is highly... 

Determination of Enantiomeric Purity from a Conversion-Time Plot... 

Equation (5) or (5b) is the highly important deduction of Harkins-Smith-Ewart theory. Its validity has been fully confirmed for many cases of polymerization (19). Furthermore, although it is difficult to determine the nvimber of particles, Np, accurately (19) this simple relationship has been used to determine the absolute value of the rate constant, kp, satisfactorily for the polymerization of butadiene and isoprene by Smith (20) and by Morton et al.(21). Conditions where the rate of polymerization is not proportional to the number of particles are where Trommsdorff s effect (22-24) or Gordon s unsteady state (25) principles apply. However, the existence of linear portions of the conversion-time plots proves the absence of these principles in this system. 

From these three polymerizations, the conversion-time plots are shown in Figure 11. Obviously, the rates of polymerization in these three test runs were not the same, the one at r = 0.207 is higher than... 

Figure 6.10 Conversion-time plots for the polymerization of methyl methacrylate in benzene at 50° C. The labeled curves are for the indicated monomer concentrations. (After Ref. 49.)...

Figure 6.12 Comparison of conversion-time plots for normal, inhibited, and retarded free-radical polymerization. Curve 1 normal polymerization curve 2 inhibition curve 3 retardation curve 4 inhibition followed by retardation.

Figure 1. Conversion-time plots for the hydrolysis of 2-nitroacetanilide in MeOH H20 (1 1) with activated (o) and non activated (A) HY zeolite (Si/Al=30) (2 g/mmol).

Figure 3 compares the conversion-time plots for the hydrolysis of 2-nitroacetanilide over zeolites with different pore structures (HY, HBeta and HMOR) and different framework Si/Al ratios. 

Figure 6.10 Conversion-time plots for the polymerization of methyl methacrylate in benzene at 50°C. The labeled curves are for the indicated monomer concentrations. In the present case, at monomer concentrations less than about 40 wt% the rate (slope of conversion vs. time) is approximately as anticipated from the ideal kinetic scheme, but deviation (rate acceleration) occurs at higher monomer concentrations. (Adapted from Schulz and Haborth, 1948.)...

Figure 6.11 Comparison of conversion-time plots for normal, inhibited, and retarded free-radical polymerization. Curve 1 normal polymerization in the absence of inhibitor/retarder. Curve 2 inhibition polymerization is completely stopped by inhibitor during the initial induction period, but at the end of this period with the inhibitor having been completely consumed, polymerization proceeds at the same rate as in normal polymerization (curve 1). Curve 3 retardation a retarder reduces the polymerization rate without showing an induction period. Curve 4 inhibition followed by retardation (After Ghosh, 1990).

Figure 4.13. The principles of integral and differential reactors as shown by a conversion/time plot (C/t), and the transfer of the corresponding concentration data to its position along the length of a continuous tubular reactor. (From Moser and Lafferty, 1976.)...

Figure 2.3.8 shows conversion-time plot for polymerization of styrene in ether (15 wt% styrene charge) at 80°C, using V-65 as initiator. The time axis was based on the number of initiator half-lives. From the product literature of Wake Chemical Co., initiator half-lives at 60 and 80°C were calculated to be equal to 200 and 20 min, respectively. It was noted from Figs. 2.3.8 and 2.3.9 that the slowdown period at 80°C corresponded to conversion values of 12.4% and a number-average MW of... 

Fig. 2.3.5 Conversion-time plot for polymerization of styrene in ether at 80 C. Sttirting reactor composition is 14 g/135 g/0.222 g for styrene/etherA -501 (Replotted with permission from Wang etal., 1999)...

Fig. 2.3.17 Conversion-time plots for batch polymerization of methacryUc add in water with different levels of initiator (V-50) at 90°C. The starting compositions are given in the plots (Replotted with permission from Wang et al., 1999)...

Figure 2.3.17 shows conversion-time plots for polymerization of MAA in water at 90°C, for two starting compositions with different initiator (V-50) levels. This is contrasted with similar plots in Fig. 2.3.18, which is also at 90°C, but at two amounts of monomers. In Fig. 2.3.19, a lower proportion of initiator was used at the same reactor temperature compared to that used in Fig. 2.3.18. More plots (Figs. 2.3.19-2.3.21) show the adherence of the system to FRRPP behavior. Finally,...

Fig. 3.1.2 Conversion-time plots for S/AA formation from FRRPP (ether) and cyclohexane systems (Replotted with permission from Caneba et al., 2003)...

It is worth noting that after 120 min (four times VA-044 half-life), the conversion-time plot reached an asymptote. This may be due to termination of the... 

Fig. 3.2.3 Conversion-time plot for emulsion FRRPP of S in ether at 80°C and 70 psig...

Fig. 4.1.1 Conversion-time plots for batch polymerization of styrene in acetone with AIBN and V-501 initiators at 80°C and 70 psig. Starting compositions (weight basis) are indicated in the legend (Replotted with permission from Wang, 1997)...

The processes of reaction and diffusion occur at the same time in a variety of systems. These issues are particularly important in the formation of blend systems and are central issues in the performance property enhancement of such systems. A study of the competitive effects of the rates of the two processes can be easily carried out using FTIR microspectroscopy. The rate of diffusion can be monitored by the time evolution of the absorbance (concentration) profiles while the rate of reaction can be monitored as a time evolution of the reactant (or product) absorbance (concentration). Reaction of a random copolymer of styrene and maleic anhydride (SMA) with bis(amine)-terminated poly(tetrahydrofuran) (PTHF) is one such studied system [73]. Temperature was varied while studying the effects of two different PTHF molecular weights. The reaction rate constants were obtained from the initial slope of conversion-time plots. In addition, it was shown that the rate of diffusion was faster as diffusion of PTHF into the SMA phase occurred prior to the imide formation. The imide was formed in the SMA phase and quantitatively estimated. A corresponding decrease in the carbonyl stretching vibration of the maleic anhydride peak was seen. 

Figure 11.7 Conversion-time plot for polymerization of styrene in bulk at 90°C with only PSt-TEMPO adduct initiator in System I and with both PSt-TEMPO and r-butyl hydroperoxide initiators in System II...

Vyazovkin (1997, 2001) developed an enhanced isoconversional method that allows evaluation of an effective activation energy ( ) as a function of the extent of reaction (a). This methodology, often referred to as model-free kinetics (MFK), is described in Section 3.5. The MFK software allows calculations such as conversion-time plots at selected temperatures that can be compared with actual measured data. It also allows the calculation of DSC curves that can be compared with actual measured DSC curves to help validate the analyses. The same curves analyzed by ASTM kinetics may be evaluated by MFK kinetics, and the same guidance is given. MFK kinetics is very comprehensive in that it is applicable to the simplest as well as to the most complex cure reactions, provided that a baseline can be drawn between a clear beginning and a clear end of the reaction. But it should be pointed out that the software is provided only by Mettler Toledo and Perkin-Elmer. For other users it is possible to measure versus conversion by the ASTM method and generate a spreadsheet with the appropriate MFK equation [e.g., Eq. (3.31) in Chapter 3], to calculate conversion-time plots. 

Model-free kinetics software employs numerical integration methods to measure activation energy versus conversion from cure exotherms at three or more heating rates, or from isothermal data at three or more temperatures. In both cases a minimum of four runs is recommended. Predictions like conversion-time plots and calculated DSC curves are made using Eq. (3.31). An advanced version of MFK software allows analysis of data from arbitrary heating programs, such as combined ramp and isothermal. A drawback of the commercial software is that a discrete mathematical relationship is not produced that can be exported and incorporated into cure models. 

Isothermal TGA data are commonly analyzed in terms of the reaction models. The analysis starts by transforming mass-time to conversion-time plots. For transformation one can use Eq. (3.3) by replacing mr with m, which is the mass in a given moment of time. Figure 3.24 shows an a-t plot for the thermal... 

Figure 1. Conversion/Time Plot for Michael Adduct Homopolymerizations...

Fig. 4.2. Conversion-time plots for normal, retarded, and inhibited free-radical polymerizations. Retardation cases a and b are described in the text.

FIG. 4.13. A comparison between conversion time plots obtained by exact solution of the grain model equations and those obtained from the approximate equation (4.3.73)... 

---