Polymerization steady state characteristics

Let us consider the steady state characteristics of continuous emulsion polymerization of styrene in the first stage reactor. The steady state value of the number of polymer particles formed in the first stage reactor can be calculated using the following equations. From Eqs. (1) and (2), we have ... 

Thus, it is obvious that the dynamic and steady-state characteristics of a polymeric melt would be equivalent when appriiately shifted by an amount c relative to each other. In order to determine the shift factor c, the procedure suggested by Spriggs [108] needs to be followed, namely, of superinqx>sing the plot of nCWrio versus cV on die plot of n ( >y versus >. For exanqde, a value of c s has been found [112] to correlate the dynamic and steady-state viscoelastic data of a particular grade of linear low-density polyethylene (LLDPE) over a wide range of shear rate and frequency. 

Thus, it is obvious that the dynamic and steady-state characteristics of a polymeric melt could be equivalent when appropriately shifted by an amount c relative to each other. Note that only in the case of e = —1 and hence c = 1 does the Spriggs model predict a correlation at -y = to. 

In summary, then, polymerization of ATP-actin under conditions of sonication displays two characteristic deviations from the simple law described by equation (4), which is only valid for reversible polymerization. These are (a) overshoot polymerization kinetics, and (b) the steady-state amount of polymer formed decreases, or the steady-state monomer concentration increases, with the number of filaments. These two features are the direct consequence of ATP hydrolysis accompanying the polymerization of ATP-actin, as will be explained now. 

The key problems in a polymerization CSTR are the determination and characterization of micro- and macromixing, and the possibility of multiple steady states due to the exothermic nature of the reactions. Recent studies of CSTRs for bulk or solution free-radical polymerization indicate the possibility of multiple steady states due to the large heat evolution and difficult heat transfer that are characteristic of the reactors. Furthermore, even in simple solution polymerization (for example, in methyl methacrylate polymerization in ethyl acetate solvent), autocatalytic kinetics can lead to runaway conditions even with perfect temperature control for certain combinations of solvent concentration and reactor residence time. In practice, the heat evolution can be an additional source of autocatalytic behavior. 

Emulsion polymerization is usually carried out isothermally in batch or continuous stirred-tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small ( 0.5 fim) polymer particles, which are the locus of the reaction, are suspended in a continuous aqueous medium. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. In industrial practice, such a reactor often shows sustained oscillations. Solid-catalyzed olefin polymerization in a slurry batch reactor is a classic example of a slurry reactor where the solid particles change size and characteristics with time during the reaction process. 

This can be explained by the fact that the flow in the CCTVFR became closer to plug flow as the Taylor number was dropped closer to. Therefore, the steady-state particle number and the steady-state monomer conversion could be arbitrarily varied by simply varying the rotational speed of the inner cylinder. Moreover, no oscillations were observed, and the rotational speed of the inner cylinder could be kept low, so that the possibility of shear-induced coagulation could be decreased. Therefore, a CCTVFR with these characteristics is considered to be highly suitable as a pre-reactor for a continuous emulsion polymerization process. In the case of the continuous emulsion polymerization of VAc carried out with the same CCTVFR, however, the situation was quite different [365]. Oscillations in monomer conversion were observed, and almost no appreciable increase in steady-state monomer conversion occurred even when the rotational speed of the inner cylinder was decreased to a value close to. Why the kinetic behavior with VAc is so different to that with St cannot be explained at present. 

An approach similar to that taken by Nomura and Harada was used by Samer to quantify the effects of droplet nucleation on emulsion polymerization kinetics in a CSTR. In their simplified analysis, it was assumed that radical capture by particles and droplets is proportional to the ratio of particle and droplet diameters. This assumption is reliable at low to moderate residence times, when polymer particles still closely resemble monomer droplets with respect to composition and surface characteristics. For predominant droplet nucleation, the maximum particle generation is limited by the concentration of monomer droplets in the feed. In Fig. 11 the steady state particle generation is given as a function of the residence time and temperature. Nucleation efficiency is defined as the number of particles divided by the number of droplets in the... 

Dreyfuss and Dreyfuss (13) showed that the cationic polymerization of cyclic ethers has the characteristics of a "living" polymerization, in that there appears to be a lack of termination except through reaction of the cationic growing chain end with impurities and that eventually a steady state is attained where the living polymer is in equilibrium with its monomer. 

An equation for the over-all rate of polymerization, which would explain the experimentally observed data and would take into account kinetic terms for all individual reaction steps, would be extremely involved and unwieldy. Fqrtunately, it is possible to make one simplifying assumption which leads directly to an expression relating known quantities, for instance, the concentration of monomer in a solution at the start of the reaction, to measurable characteristics, like the over-all rate. This assumption postulates the presence of a steady state during a certain stage of the polymerization reaction. 

Analysis of the kinetics of CRP reactions is more complex than for conventional radical polymerizations consequently, a detailed derivation of the basic equations will not be given here. The fundamental activation-deactivation pseudoequilibria that control the living characteristics of the various CRPs have been outlined in Equation 3.31 to Equation 3.33, and if the steady state is to be achieved rapidly, then the rates of activation and deactivation must be considerably larger than the rates of the initiation and termination reactions. In successful CRP reactions, the time taken to reach the equilibrium steady state is estimated to be in the range 1 to 100 ms. 

We have already mentioned several effects that are connected with the polymeric nature of the layer. It is evident tliat all the charge transport processes listed are affected by the physicochemical properties of the polymer. Therefore, we also must deal with the properties of the polymer layer if we wish to understand the electrochemical behavior of these systems. The elucidation of the stracture and properties of polymer (polyelectrolyte) layers as well as the changes in their morphology caused by the potential and potential-induced processes and by other parameters (e.g., temperature, electrolyte composition) set an entirely new task for electrochemists. Owing to the long relaxation times that are characteristic of polymeric systems, the equilibrium or steady-state situation is often not reached within the time allowed for the experiment. 

Owing to the long relaxation times characteristic of polymeric systems, the equilihrium or steady-state situation often has not been reached within the timescale of the experiment. Figure 9 shows the changes of the resistance of polyanihne... 

Subsequent generations of electrocatalytically active systems use deposited three-dimensional chemical microstructures, these are the polymer modified electrodes. These multilayer polymeric structures contain redox-active groups. Typical examples of the latter include redox polymers, electronically conducting polymers, and ionomer films loaded with redox-active species or loaded ionomers. Much emphasis is placed on these second-generation systems their operational characteristics under steady-state conditions are elucidated mainly by Andrieux and Saveant and Albery and Hillman. The fundamental characteristic of these second-generation polymer-based electrocatalytic systems is that their electrochemically active centres contained within the polymer matrix exhibit a dual purpose. They must be efficient electron transporters (the layer must have reasonable electronic or redox conductivity) as well as display i.e., good inherent electrocatalytic activity. 

As sketched in Figure 8.8b, the SECM tip electrogenerates a redox species that is transported to the substrate through the polymeric film. The measurement of a redox cycling or feedback allows for the quantification of the permeation of the redox species within the membrane. Steady-state measurements such as those obtained from these approach curves, ij - d, for example, presented in Figure 8.11, have been proposed. A complete theoretical analysis of the approach curve shape depending on the membrane characteristics (permeation and thickness) has been described. For thin membrane layers of thickness e, the approach curves follow the first-order approximation, and when fitted by Equations 8.3 to 8.5, an effective heterogeneous rate constant k ff = PDp/e is obtained from which the permeability of the electroactive species PDp ensues. 

With a continuous source of new radicals in the system, an equilibrium is achieved instantaneously between radical generation and consumption, such that Rinit = Rurm- This characteristic, proven to be true for almost all FRP conditions [6], is a result of the fast dynamics of radical reactions compared to that of the overall polymerization system. Often referred to as radical stationarity or the quasi-steady-state assumption (QSSA), it leads to the well-known analytical expression for total radical concentration [Eq. (9)]. 

The use of the new system at ambient pressure and at moderate temperatures allows to follow the reaction kinetics by analysing the concentration of educts and products as a function of time. Batch experiments showed that there is a marked induction period of slow reaction progress (Fig. 18.6) [22, 60, 63]. The systems exhibit the characteristics of an auto-catalytic reaction. Addition of new monomer up to the original starting concentration during the conversion of the monomer does not result in a new induction period but shortly after completion of the reaction the system answers to another addition of monomer with a new induction period [14, 64]. In steady state experiments the polymerization was proceeding over days with constant reaction rate, i. e. without decrease of the catalyst s activity. The re-... 

This set of equations gives the possibility to calculate the dynamic behavior of a CSTR and, what is more important, the characteristics of the steady state. In contrast to free radical polymerization where multiple steady states and even oscillating regimes can exist owing to the second-order chain termination reaction and the gel effect [54], Eqs. (3.22) and (3.23) have only one stationary solution. Hereinafter, steady-state parameters of the MWD are discussed. 

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