Conversion, steady-state polymerization

Frequently function R can be written as a single term having the simple form of equation 1. For Instance, with the aid of the long chain approximation (LCA) and the quasi-steady state approximation ((JSSA), the rate of monomer conversion, I.e., the rate of polymerization, for many chain-addition polymerizations can be written as... 

Continuous Polymerizations As previously mentioned, fifteen continuous polymerizations in the tubular reactor were performed at different flow rates (i.e. (Nj g) ) with twelve runs using identical formulations and three runs having different emulsifier and initiator concentrations. A summary of the experimental runs is presented in Table IV and the styrene conversion vs reaction time data are presented graphically in Figures 7 to 9. It is important to note that the measurements of pressure and temperature profiles, flow rate and the latex properties indicated that steady state operation was reached after a period corresponding to twice the residence time in the tubular reactor. This agrees with Ghosh s results ). 

There are many interesting reports in the literature where computer simulations have been used to examine not only idealized cases but have also been used in an attempt to explain segregation and viscosity effect in unperturbed polymerization reactors (6). Some experimental work has been reported (7, 8). It is obvious, however, that although there is some change in the MWD with conversion in the batch and tubular reactor cases and that broadening of the MWD occurs as a result of imperfect mixing, there is no effective means available for controlling the MWD of the polymer from unperturbed or steady-state reactors. 

N h is zero at the start of interval I, since h — Q.N decreases, h increases, and the product N h increases with time during interval I. At the start of interval II, N has reached its steady-state value N. h may or may not reach an absolutely constant value. Behavior D in interval II usually involves a steady-state h value, while behavior E usually involves a slow increase in h with conversion, h will remain approximately constant or increase in interval III although a decrease will occur if the initiation rate decreases sharply on exhaustion of the initiator concentration. Most texts show Eq. 4-5 for the polymerization rate instead of the more general Eq. 4-4. Equation 4-5 applies to intervals II and III where only polymer particles exist (no micelles). It is during intervals II and III that the overwhelming percent of monomer conversion to polymer takes place. In the remainder of Sec. 4-2, the discussions will be concerned only with these intervals. 

According to Bodenstein, for a chain reaction in the steady state, the number of radicals formed and disappearing in a given time must be the same. This applies to most addition polymerizations, at least in the region of low conversion. Under these conditions v, and v, may be equated ... 

These kinetic results have led to a variety of interpretations. Magat and associates have proposed kinetic schemes based on the idea that a steady state does not exist and that only small (primary) radicals can terminate polymer chains (52, 93). Bamford and Jenkins have criticized this concept of emulsion-type polymerization (77). They point out that if the source of initiation were removed no more small radicals would be formed and polymerization should continue indefinitely. They cite a photosensitized reaction at 60° in which the light was shut off at about 15% conversion, whereupon the rate fell to one-half of its original value in 60 seconds. Bamford and Jenkins point also to evidence from the fast reaction that argues against emphasis on termination between polymer radicals and small radicals. 

The validity of the non-steady state assumption is shown in Figure 1, where the molecular weight of the copolymerization mixture increases with conversion at the beginning of copolymerization. The long lived radical is observed from the ESR spectrum in Figure 2, measured at room temperature for polymerization in toluene this agrees with the S02 radical similar to the norbomene-S02 system (16). 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

The lag between density cell response and reactor events were considerably less for this example and the figures ignore any correction. After establishing a "steady state" response to the monomer feed (about 160 minutes into the reaction), the incremental increase of the feed rate is seen not to alter the overall fractional conversion since the rate of polymerization increases to parallel the monomer feed rate. At the end of this set of data the rate is 2-3 times that observed earlier before the feed. 

The available data from emulsion polymerization systems have been obtained almost exclusively through manual, off-line analysis of monomer conversion, emulsifier concentration, particle size, molecular weight, etc. For batch systems this results in a large expenditure of time in order to sample with sufficient frequency to accurately observe the system kinetics. In continuous systems a large number of samples are required to observe interesting system dynamics such as multiple steady states or limit cycles. In addition, feedback control of any process variable other than temperature or pressure is impossible without specialized on-line sensors. This note describes the initial stages of development of two such sensors, (one for the monitoring of reactor conversion and the other for the continuous measurement of surface tension), and their implementation as part of a computer data acquisition system for the emulsion polymerization of methyl methacrylate. 

A recent paper by Kiparissides, et al. (8) details a mathematical model for the continuous polymerization of vinyl acetate in a single CSTR. Operating conditions were shown to exist in which either steady-state operation or sustained conversion oscillations would occur for vinyl acetate. Experimental results for both cases were successfully simulated by their model. In addition, regulatory conversion control policies were considered in which both initiator feed rate and emulsifier feed rate were used as manipulated variables (Kiparissides (9)). The problem of conversion control in the operating region in which sustained conversion oscillations occur is one of significant commercial importance. Most commonly, however, a uniform concentration of emulsifier is required in the emulsion recipe and, hence, emulsifier flow rate cannot be used as a manipulated variable. 

Figure 2. Isothermal polymerization of methyl methacrylate in a CSTR (1 5). a. Predicted steady-state monomer conversion vs. reactor residence time for the solution polymerization of MMA in ethyl acetate at 86 °C. h. Steady-state and dynamic experiments for the isothermal solution polymerization of MMA in ethyl acetate (solvent fraction O.k) ( ) steady states,...

Emulsion Polymerization in a CSTR. 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 (. 5 Jim) polymer particles, which are the locus of reaction, are suspended in a continuous aqueous medium as shown in Figure 5. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. Gerrens and coworkers at BASF seem to be the first to report these phenomena both computationally and experimentally. Figure 6 (taken from ref. (253)) plots the autocatalytic behavior of the reaction rate for styrene polymerization vs. monomer conversion in the reactor. The intersection... 

The oxidation of propylene oxide on porous polycrystalline Ag films supported on stabilized zirconia was studied in a CSTR at temperatures between 240 and 400°C and atmospheric total pressure. The technique of solid electrolyte potentiometry (SEP) was used to monitor the chemical potential of oxygen adsorbed on the catalyst surface. The steady state kinetic and potentiometric results are consistent with a Langmuir-Hinshelwood mechanism. However over a wide range of temperature and gaseous composition both the reaction rate and the surface oxygen activity were found to exhibit self-sustained isothermal oscillations. The limit cycles can be understood assuming that adsorbed propylene oxide undergoes both oxidation to CO2 and H2O as well as conversion to an adsorbed polymeric residue. A dynamic model based on the above assumption explains qualitatively the experimental observations. 

The mathematical equations for this imperfectly mixed model consist of 12 differential equations similar to equations (l)-(4), four for each of the three CSTR s. At steady state, they reduce to 12 non-linear algebraic equations which are solved numerically in order to calculate the dependence of initiator consumption on polymerization temperature. An overall balance reveals that the monomer conversion and polymer production rate are still given by equations (5) and (8), while the initiator consumption is affected by the temperature and radicals distribution in the three CSTR s, so that equations (7) and (9) become much more complex. 

The use of the steady-state approximation is justified on the basis of two separate, independent observations. Firstly, after sufficient polymer has accumulated, the rate remains constant over an extended range of conversion (Figure 4). Secondly, Bengoughs measurements (10) of the non-steady-state kinetics of acrylonitrile polymerization show that a steady state is established within minutes, whereas the polymerization continues for hours. 

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. 

Steady-state conversions for VA and MMA polymerizations in a CSTR do not agree with reactor models based on Smith-Ewart Case II kinetics. This is not surprising since such a model does not consider many important phenomena. The particle-formation component of the Smith-Ewart Case II model is based on a simple mathematical relation which assumes that the rate of formation of new particles is proportional to the ratio of free (dissolved or in micelles) surfactant to total surfactant. This equation is based on the earlier concept of particle formation via free radical entry into micelles. 

Unsteady start-up behavior has been reported in some continuous reactors (14). In this work, the reactor was initially filled with water or partially polymerized latex, and the % conversion asymptotically approached a constant steady-state value, which required less than twice the residence time in the reactor. 

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