Function of Conversion

Having expressed some useful parameters in terms of reactivity ratios through the use of conditional probabilities, we are now going to consider a few examples, to give you a feel for what happens in a copolymerization. Actually, we are going to consider just one example and you are going to do the rest. 

Before getting to that, there is something important you should realize about batch copolymerizations, by which we mean a reaction where monomer is not being continuously introduced. The copolymer composition and the parameters that measure the departure from randomness and things like run number can change considerably with conversion. In other words, the type of copolymer that you get at the beginning of the reaction can be very different to what you get near the end, when most of the monomer has been used up. 

Conversion in this case is defined as the fraction of total monomer that has been used 

Choose an interval of conversion where a specified amount of total monomer is used up (e.g., 1%). 

Assume that [A] and [B] are constant over this interval. 

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Testing of Painted Products. The enhancement of paint adhesion is one of the principal functions of conversion coating (20—22). A group of tests based on product deformation is used to test the painted product. The appHance and cod-coating industries use the mandrel bend, the cross-hatch adhesion test, and the direct and reverse impact tests. Adhesion after a water soak is judged using a cross-hatch test performed on the exposed surface. 

Many researchers have correlated the overall decomposition as an nxh. order reaction, with most paraffins following the first order and most olefins following a higher order. In general, isoparaffin rate constants are lower than normal paraffin rate constants. The rate constants are somewhat dependent on conversion due to inhibition effects that is, the rate constant often decreases with increasing conversion, and the order of conversion is not affected. This has been explained by considering the formation of aHyl radicals (38). To predict the product distribution, yields are often correlated as a function of conversion or other severity parameters (39). 

For a given catalyst and feedstock, catalytic coke yield is a direct function of conversion. However, an optimum riser temperature will minimize coke yield. For a typical cat cracker, this temperature is... 

Catalytic coke is a byproduct of the cracking of FCC feed to lighter products. Its yield is a function of conversion, catalyst type, and hydrocarbon/catalyst residence time in the reactor. 

EPR methods that allow a more direct determination of kv have been developed. These enable absolute radical concentrations to be determined as a function of conversion. With especially sensitive instrumentation, this can be done by direct measurement/57 160 An alternative method, applicable at high conversions, involves trapping the propagating species in a frozen matrix361 362 by rapid cooling of the sample to liquid nitrogen temperatures. 

Data on the rate of consumption of the inhibitor as a function of conversion may also be used to obtain kjkp(sq. 31) ... 

The remaining problem in the model development is to estimate the decrease in kp as a function of conversion. As the reaction proceeds beyond the point of chain entanglement, a critical conversion is reached where the propagation reaction becomes diffusion controlled and kp begins to fall with further increase in polymer concentration. At the critical conversion, one may write... 

Heat transfer can, of course, be increased by increasing the agitator speed. An increase in speed by 10 will increase the relative heat transfer by 10. The relative power input, however, will increase by 10In viscous systems, therefore, one rapidly reaches the speed of maximum net heat removal beyond which the power input into the batch increases faster than the rate of heat removal out of the batch. In polymerization systems, the practical optimum will be significantly below this speed. The relative decrease in heat transfer coefficient for anchor and turbine agitated systems is shown in Fig. 9 as a function of conversion in polystyrene this was calculated from the previous viscosity relationships. Note that the relative heat transfer coefficient falls off less rapidly with the anchor than with the turbine. The relative heat transfer coefficient falls off very little for the anchor at low Reynolds numbers however, this means a relatively small decrease in ah already low heat transfer coefficient in the laminar region. In the regions where a turbine is effective,... 

Similarly, Garcia-Rubio and Hamielec (17) conducted bulk polymerizations of acrylonitrile at various temperatures and initiator levels in glass ampoules. Their plots of the rate of polymerization as a function of conversion are typical of the extensive radical occlusion in this very glassy polymer. 

Now let s discuss the pressure computations. The observed reactor pressure is a sum of the partial pressures of nitrogen and the styrene monomer vapor. The vapor pressure of the styrene vapor is an increasing function of temperature and decreasing function of conversion. This is explained by the Flory-Huggins relationship ( ). 

Figure L Solution of kinetic equations for molecjdar weight and LCB development in bulk VAc polymerization. Ms, Mw, and Bs are plotted as a function of conversion. Model predictions Cm = 2.0 X Cp = 3.0 X i0 K == 1.0.

For esterification with an equimolar initial mixture of reactants, the mole fractions of the components in the reaction mixture are the following functions of conversion ... 

Figure 34.7a and b. EG and organic acid selectivity as a function of conversion with different supports. 

In Figure 34.7a ethylene glycol (EG) selectivity is shown as a function of conversion for the same reactions discussed previously. Note that all of the highest selectivities to the two-carbon byproduct occurred on alternative supports. 

Equation 27 can be numerically integrated along the conversion trajectory to obtain the Initiator concentration as function of time. Therefore, calculation of t, 6 and C together with the values of M, Rp, rw and rn from the equations In Table II allows the estimation of the ratios (ktc/kp1), (kx/kp) and the efficiency as functions of conversion. Figure 3 shows the efficiency as function of conversion. Figure 4 shows the variation of the rate constants and efficiencies normalized to their initial values. The values for the ratio (ktc/kpl)/(ktc/kpl)o reported by Hui (18) are also shown for comparison. From the definition of efficiency it is possible to derive an equation for the instantaneous loading of initiator fragments,... 

None of the models, theoretical or empirical, proposed in the literature to account for the change in efficiency as function of conversion, can describe the behaviour observed. 

The total concentration of polymer chains Q attached to zirconium atoms was also determined as a function of conversion. A typical result obtained is shown in Fig. 17. It is evident from this data that Q increases in a linear way with conversion. It has been shown, however, that the rate of polym-... 

Fig. 17. The polymerization of styrene by Zr(benzyl)4. Measurements of the total number of polymer chains Q, attached to zirconium atoms as a function of conversion. [M]o = 3.0 M, [C]o = 0.03 M. Temperature 30°C. Solvent toluene W).

Figure 6.8. Concentration of rhodium in the organic phase as a function of conversion during the hydroformylation of 1-octene catalysed by Rh/ [P(4-C6H4C6Fi3)3].[41]...

The plot in Fig. 6 depicts the response of both Mn and MJMn as a function of conversion for a realistic case of fast reversible chain shuttling, with Ca° = Ca = 50 and Aeq = 200. In the fast reversible chain transfer regime, these reactions have some... 

Fig. 8 Effect of A on M IM as a function of conversion for semi-reversible chain transfer, in... 

The rate of polymerization in the dark, i.e., when the initiation is stopped, was used to uncouple the kinetic constants for termination and propagation. By performing these after-effect experiments (13-15) at various stages in the reaction, the kinetic constants for bimolecular carbon-carbon termination and propagation were characterized as a function of conversion. 

Figure 6. Estimated carbon radical concnetrations as a function of conversion for DMPA-initiated HEMA polymerization with and without TED present.

An equimolal mixture of octenes and hydrogen is fed to a fluidized bed of catalyst at 2 atm. Find the required weight of catalyst per unit of feed, Wc/F0, as a function of conversion in (a) plug flow (b) a completely mixed bed. 

Fig. 16 Concentration of decalin and product groups as a function of conversion over H-Beta (filled), HY (open), and H-Mordenite (half-filled). CP = cracking products ROP = ring opening products HP = heavy products. Adapted from refs. 44 and 45. 

Fig. 15.15 Cinnamyl alcohol selectivity as a function of conversion in the selective hydrogenation of cinnamaldehyde over differently supported Ru catalysts. Reactions conditions as listed in Tab. 15.4. Data compiled from literature [120,122,123,126], HSAG high-surface area graphite AC activated carbon.

Figure 3. Theoretical open-circuit potential as a function of conversion to total oxidation of hydrogen, methane, and n-butane at 973 K.

Disposing the Flory-Huggins modified equation, including the free entropy of mixing per total volume, AS , as a function of conversion and the enthalpy term expressed with the interaction parameter [66-68,72] ... 

Fig. 4. Vectorial representation of solubility parameters used to calculate the free enthalpy of mixing as a function of conversion, q...

The length of d (q) can then be calculated as a function of conversion according to... 

Similar to the derivation of schematic phase diagrams showing an UCST or LCSTbehavior, as shown in the previous section, it is now possible to plot a schematic phase diagram as a function of conversion, q, such as shown in Fig. 5. The binodal and spinodal curves are obtained by interconnecting all the coexisting points and inflection points of the AG -curves as a function of q similar to the procedure described in [67-69]. 

Based on Eq. (27) it is now possible to reconstruct free energy curves as a function of conversion for any polymer-solvent system discussed above. Plotted in Fig. 12 are the results of AG as a function of conversion for the 2,6-dimethyl-4-heptanone based system. These results clearly show the theoretically predicted change in curvature which is accompanied with the development of a curve having two minima and two inflection points [52,53,63,68]. 

Fig. 12. Free energy curves for 2,6-dimethyl-4-heptanone modified epoxies calculated with the solubility parameter approach at a constant temperature (315 K) as a function of conversion...

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