Conversion-time relations

In copolymerization, control of the copolym composiricm can be obtained when applying monomer addition profiles. These monomer addition profiles either can be based on the direct translation of on-line measurements to monomer addition steps (controlled ccxnposiritxi reactor) or the profiles can be predicted by emulsion copolymoization models on a conversion basis. The required conversion-time relation is then obtained by on-line measurements. 

When the rate of the process is determined both by chemical kinetics and transport phenomena, the necessary mathematical model becomes quite complicated, and the necessary parameters may be difficult to determine. It may be safer to take a more empiricd appoach, and measure the degree of conversion as a function of time, in a laboratory batch reactor, for well defined conditions. One will probably find that the apparent reaction order is betweeen 0 and 1. The results may be expressed as a conversion/time relation, that can be substituted in eq. (7.13b). Together with eq. (7.14) one finds a differential equation that can be solved numerically, or simply graphically. 

For the chemical reaction and product layer diffusion controlling regimes conversion-time relations for the unreacted core model simplifies Kinetics controlling ... 

Analytical expressions were reported for the average conversion-time relations for the pore diftusion and kinetics controlling regimes. 

The time-scale of this haem conversion is related to the antioxidant status of the LDL and that of the erythrocyte lysate. The incorporation of lipid-soluble antioxidants, such as tocopherol and butylated hydroxy-toluene (BHT) at specific time points during the LDL-erythrocyte interaction, prolongs the lag phase to oxidation, eliminates the oxy to ferryl conversion of the haemoglobin and delays the oxidative modification of the LDL. 

We also correlated the elastic modulus (G ) with the extent of reaction by combining data obtained from rheology and FTIR. We found that the elastic modulus did not show an appreciable increase until a short time before the gel point of the sample had been reached. However, in the vicinity of the gel point and beyond, the elastic modulus increased significantly with conversion. Information relating modulus to extent of reaction, which plays a critical role in the application of these systems, can therefore be readily obtained using our approach. 

For an isothermal spherical particle (at the surrounding bulk-gas temperature) of species B reacting with gaseous species A as in Example 9-1, derive the time (f)-conversion (/B) relation from the SCM for each of the following three cases individually, and show that additivity of the three results for t agrees with the overall result reached in Example 9- 1 ... 

Two models developed in Chapter 9 to describe the kinetics of such reactions are the shrinking-core model (SCM) and the shrinking-particle model (SPM). The SCM applies to particles of constant size during reaction, and we use it for illustrative purposes in this chapter. The results for three shapes of single solid particle are summarized in Table 9.1 in the form of the integrated time (t conversion (/B) relation, where B is the solid reactant in model reaction 9.1-1 ... 

Figure 5. Proportion of conversation time devoted to different topics. The data are average values from three separate studies (two conducted in university canteens, one in public places). Social topics include anything concerned with personal relationships, personal experiences and arrangemenst for future social activities. The category politics includes all topics relating to religion, ethics and morals as well as politics. Source Dunbat et al. submitted.

Yagi et al. (1951) roasted pyrrhotite (iron sulfide) particles dispersed in asbestos fibers and found that the time for complete conversion was related to particle size as follows ... 

Figure 1 shows the conversion in relation to time. The uncatalyzed reaction has a conversion of 99% after 25 hours the catalyzed reaction reached the same stage after 8 hours. The third curve shows the reaction course of a batch which, after having been esterified uith a solid catalyst for one hour, continued after removal of the catalyst. This followed a course similar to that of the catalyzed reaction. 

Figure 18. Relations between rank of coal (volatile matter), temperature, and time of coalification (after Karweil (12)) (Z is a conversion factor relating volatile matter to coal rank)...

Starch conversion in a fixed time relates linearly to the enzyme concentration. 

Eq.(25) is derived from Eq.(lO). It can.therefore be concluded that we are now predictable the variation of the value of n and hence monomer conversion versus time relation with satisfactory accuracy as long as the observed number of polymer p u ticles is used. 

Fig. 20 Compar Ison of observed conversion vs. time relation with that of approximate calculation.

In the case of alkyl vinyl ethers [27, 30] reaction rates were again high and the same experimental technique was used. However, the initiation reaction did not appear to be as fast as that in the polymerization of Al-vinylcarbazole, and the conversion/time data showed evidence of an initial acceleration to a maximum rate of polymerization, particularly in runs carried out at —25°C. The mechanism of initiation was assumed to involve direct addition of the initiating carbonium ion to the double bond of the monomer, in the light of related evidence from similar reaction in the presence of strong nucleophiles [80, 81]. At 0°C there was also an indication of a contribution from a termination reaction. Polymer yields were always in excess of 75%, however, and the termination process was neglected in the kinetic analysis. The simple scheme envisaged is ki... 

With these assumptions two different conversion-time curves are associated. It is easily derived that for the case of assumption 1, the number of particles and therefore the rate increase in proportion to the square of the reaction time, provided [M] is constant (3). At the conversion. C, where the micelles have just disappeared, all particles contain a growing polymer radical and the rate is double the equilibrium rate given by Equation 9. The rate after Cj decays exponentially to the equilibrium value. If assumption 2 holds, the rate increases according to a complex function of reaction time. In Figure 3, examples are given of conversion-time curves which seem to correspond to the theoretical relations derived on the basis of either assumption. The usual course of the reaction is probably intermediate between the two types and may in addition be modified by changes in the monomer concentration in the particles during this period of transition from micelle to particle. 

Once the indomethacin forms are available, seeding a crystallization batch with the desired form will usually result in the isolation of that form. When excess solid Form II and Form III, either individually or as a mixture, are stirred (agitated, equilibrated) in most solvents and for sufficient time, they convert to the more stable Form I. The time to conversion is roughly related to solubility conversion time is faster for the solvents with higher indomethacin solubility. In water (Table 3-1), where the solubility is relatively low. Form n and Form III of indomethacin did not convert even after 24 hours of stirring. 

Figures 7.15-7.18 show how reactor capacity (i.e., maximum productivity, g product/g enzyme/min) is affected by operational parameters. Enzyme and substrate concentration appear to affect reactor capacity to a large extent (Figures 7.15 and 7.16) especially at lower enzyme concentrations. Effects of permeate flux and reactor volume on conversion are related to each other by means of substrate residence time in the reaction vessel. Ingreasing residence time, that is increasing reactor volume or lowering fluxes, results in higher conversions at the expense of lower capacities (Figures 7.17 and 7.18).

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