Steady state rates, polymerization

D. Influence of the Operating Conditions on the Polymerization Steady-State Rate. 

Amount of a-TiCk. In Fig. 15 the polymerization rate, obtained at constant pressure of olefin with different amount of a-TiCh, is plotted vs. time. The steady-state rate is found to be proportional to the amount of a-TiCU present in the reaction system (Fig. 16), in agreement with the heterogeneous nature of the catalysis (30, 33). 

Polymerization Temperaiure. Apparent Activation Energy Based on the Steady-State Rate. The rates observed at different temperatures, referred... 

A kinetic model for the particle growth stage for continuous-addition emulsion polymerization has been proposed (35). Below the monomer saturation point, the steady-state rate of polymerization, depends on the rate of monomer addition, R, according to the following reciprocal relationship ... 

In this chapter we discuss four topics the pseudo-steady-state hypothesis, polymerization, enzymes, and bioreactors. The pseudo-steady-state hypothesis (PSSH) plays an important role in developing nonelementary rate laws. Consequently, we will first discuss the fundamentals of the PSSH, followed by its use of polymerization reactions and enzymatic reactions. Because enzymes are involved in all living organisms, we close the chapter with a discussion on bioreactions and reactors. 

Price and Akkapeddi [22] note that their value for the rate of EO polymerization in HMPT is about 40-fold less than that reported for DMSO by Bawn et al. [20]. Price and Akkapeddi point out that Bawn et al. report initial rates rather than steady state rates. However, they suggest that the more important reason for the difference in rate is the large difference in catalyst concentration. The higher concentration used by Price and Akkapeddi would lead to greater association of alkoxides and to lower rate coefficients. 

In the case of bulk monomers, it is easy to calculate the rate of initiation from the G values, the dqse rate, and the physical constants of the monomer. If the k /k values are known foi- the monomer in question at the temperatBre used, the rates of initiation can be calculated from the observed steady state rates of polymerization. Thus for the simplest case. 

Using the above type of experimental setup for propylene polymerization with TiCls-AlEts in n-heptane, the rate of polymerization was measured [5] at different speeds of stirring and constant propylene pressure. The results obtained indicated that there were two different steady-state rate curves for the stirring speeds of 400 and 600 rpm. In each case, a steady bulk monomer concentration was reached in about 3-4 hours. Show how the overall process at steady state can be modelled to show dependence of the polymerization rate on stirring speed and to enable determination of both the mass transfer rate constant and polymerization rate constant from rate measurements at different stirring speeds. 

According to the analysis and consideration detailed above for photoinitiated polymerization, it may now be concluded thatT or [M ] can be varied by varying the frequency of blinking. Under otherwise comparable conditions, the average rate (Rp) at different flashing conditions with the same 7q is related to the steady-state rate (Rp)s as... 

Rate of polymerization In chain polymerization, the rate at which the monomer (M), of concentration [M], is converted to polymer, —d[M]/df. Since the rate of propagation occurs hundreds of times more frequently than initiation, rates of polymerization and propagation are the same and the symbol J p is used for both. For a steady state chain polymerization reaction, J p is defined by the following equation... 

The steady-state rate of radical polymerization (RP) is given by... 

Thus defined, k replaces in Equation (1), which otherwise remains an exact expression for steady-state rate. For this reason k is a tremendously important quantity its variations directly dictate, through Equation (1), variations in rate of polymerization. This is why CLDT can be said to shape RP kinetics. 

At high conversion, the growth of viscosity hinders the termination by radical-radical reactions, but it has less effect on the propagation reaction, because diffusion of small monomer molecules is not so much affected by viscosity. Hence, both the rate of polymerization and the molecular weight of the polymer show an increase, there is auto acceleration at high conversion. This effect is known as gel-effect or Tommsdorf-effect, which is usually accompanied by a sudden rise of temperature (Swallow 1973). Such effect was observed in many systems, for instance in the y-ray induced steady-state bulk polymerization of methyl methacrylate (Luthjens et al. 2001). 

It is interposed between the system and the source of light to cause periodic interruption of the light. The cut out portion determines the value r. (For example, a rotating sector with 1 3 opening corresponds to r = 3.) The blinking frequency as well as t and f are determined by the speed of sector rotation. The polymerization rate is conveniently determined by dilatometric technique (p. 321). The rate measured with the rotating sector present is the average polymerization rate (Rp) while that measured without the sector present is the steady-state rate of polymerization Rp)s-... 

In contrast, the rate law for the nearly steady-state rate (interval II, conversion 5 to 50%) of polymerization in emulsion (2,47-50) is... 

Table 4. Steady-state Rate Constants, Initiator Distributions, Monomer and Polymer Impregnation Results, and Effect of Ground Leather on Polymerization Rate... 

Redox initiation is often used in polymerizations in aqueous systems. Thus H2O2 and Fe " " ion can be used to initiate the polymerization of acrylamide in water. Derive an expression for the steady-state rate of polymerization in this case ... 

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