Polymerization nonisothermal

This phenomenon can be observed in free radical polymerization (nonisothermal) due to the exothermic nature of the polymerization reaction. However, due to the gel effect, it is also observed in some isothermal free radical polymerizations in a CSTR [11-14]. Figure 5.2 shows the rate of polymerization plotted versus monomer conversion for the free radical solution polymerization of methly methacrylate. Unlike a more common reaction in which the rate of reaction falls monotonically with conversion, the rate of reaction rises with conversion due to the onset of the gel effect. Thus the system can be thought of as autocatalytic. At high conversions the polymerization... 

Tables IV and V contain appropriate balance equations for nonisothermal free-radical polymerizations and copolymerizations, which are seen to conform to equation 2k. Following the procedure outlined above, we obtain the CT s for homopolymerizations listed in Table VI. Corresponding CT s for copolymerizations can be. obtained in a similar way, and indeed the first and fourth listed in Table VII were. The remaining ones, however, were derived via an alternate route based upon the definitions in Table VI labeled "equivalent" together with approximate forms for pj, which were necessitated by application of the Semenov-type runaway analysis to copolymerizations, and which will subsequently be described. Some useful dimensionless parameters defined in terms of these CT s appear in Tables VIII, IX and X.

In order to get a quantitative idea of the magnitude of the effects of these temperature variations on molecular structure and morphology an experimental study was undertaken. Two types of polymerizations were conducted. One type was isothermal polymerization at fixed reaction time at a series of temperatures. The other type was a nonisothermal polymerization in the geometry of a RIM mold. Intrinsic viscosities, size exclusion chromotograms (gpc) and differential scanning calorimetry traces (dsc) were obtained for the various isothermal products and from spatially different sections of the nonisothermal products. Complete experimental details are given below. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

Figure 6 shows the temperature proflle that should be used with the initiator monomer system described in the caption to reduce the monomer concentration from 0.47 mol/L to 0.047 mol/L. The optimal nonisothermal policy consists of decreasing temperature from a temperature above the optimal isothermal temperature to one below it. The rate of polymerization could be increased, as expected, by an initially higher temperature, but the temperature must be decreased to avoid depletion of initiator and depolymerization. However, the amount of time saved by this policy does not seem to be significant in comparison to the isothermal policy for this case. 

A closer look at the nonisothermal and isothermal policy results reveals some additional interesting features with regard to optimization. As mentioned earlier, isothermal policies were determined by two factors. One was the M, value and the other was the dead end polymerization caused by depletion of initiator. It was also observed that the minimum time from a nonisothermal policy was considerably less than the minimum time due to the isothermal policy whenever H>, was the controlling factor in the isothermal policy when the isothermal policy was controlled by initiator depletion, a nonisothermal policy did not show significant improvement in minimum time relative to the isothermal one. 

In this paper we formulated and solved the time optimal problem for a batch reactor in its final stage for isothermal and nonisothermal policies. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and optimum time was studied. It was shown that the optimum isothermal policy was influenced by two factors the equilibrium monomer concentration, and the dead end polymerization caused by the depletion of the initiator. When values determine optimum temperature, a faster initiator or higher initiator concentration should be used to reduce reaction time. 

Comparison of isothermal and nonisothermal policies revealed some interesting features of the polymer system. When M , values determine the isothermal policy, a nonisothermal operation reduces the minimum time compared to isothermal operation (by about 15%). However, when dead-end polymerization influences isothermal operation, a nonisothermal operation does not offer significant improvement. 

J. Hamer, T. Akramov, and W. Ray. The dynamic behavior of continuous polymerization reactors II, nonisothermal solution homopolymerization and copolymerization in a CSTR. Chem. Eng. Sci., 36 1897-1914, 1981. 

The question of choosing a PFTR or a CSTR will occur throughout this book. From the preceding arguments it is clear that the PFTR usuaUy requires a smaller reactor volume for a given conversion, but even here the CSTR may be preferred because it may have lower material cost (pipe is more expensive than a pot). We will later see other situations where a CSTR is clearly preferred, for example, in some situations to maximize reaction selectivity, in most nonisothermal reactors, and in polymerization processes where plugging a tube with overpolymerized solid polymer could be disastrous. 

There are many interesting problems in which complex chemistry in nonisothermal reactors interact to produce complex and important behavior. As examples, the autocatalytic reaction, A — B, r = kC/ Cg, in a nonisothermal reactor can lead to some quite complicated properties, and polymerization and combustion processes in nonisothermal reactors must be considered very carefully in designing these reactors. These are the subjects of Chapters 10 and 11. 

In building mathematical models of product formation in a mold it is possible to treat a polymeric material as motionless (or quasi-solid), because the viscosity grows very rapidly with the formation of a linear or network polymer thus, hydrodynamic phenomena can be neglected. In this situation, the polymerization process itself becomes the most important factor, and it is worth noting that the process occurs in nonisothermal conditions. 

Parallel-Plate, Nonisothermal Newtonian Drag Flow with Temperature-depen-dent Viscosity (a) Review the approximate linear perturbation solution given in Example 1.2-2 in R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1, Wiley, New York, 1977. (b) Review an exact analytical solution in B. Martin, Int. J. Non-Newtonian Mech., 2, 285-301 (1967). 

Distributed Parameter Models Both non-Newtonian and shear-thinning properties of polymeric melts in particular, as well as the nonisothermal nature of the flow, significantly affect the melt extmsion process. Moreover, the non-Newtonian and nonisothermal effects interact and reinforce each other. We analyzed the non-Newtonian effect in the simple case of unidirectional parallel plate flow in Example 3.6 where Fig.E 3.6c plots flow rate versus the pressure gradient, illustrating the effect of the shear-dependent viscosity on flow rate using a Power Law model fluid. These curves are equivalent to screw characteristic curves with the cross-channel flow neglected. The Newtonian straight lines are replaced with S-shaped curves. 

From a process simulation point of view, in addition to impingement mixing, there are two main problems (a) nonisothermal and transient flow with chemical reaction, prevalent during the filling stage of the process, and (b) conductive heat transfer with heat generation due to the polymerization reaction. We discuss these two problems next, using the case of... 

The rational design of a reaction system to produce a desired polymer is more feasible today by virtue of mathematical tools which permit one to predict product distribution as affected by reactor type and conditions. New analytical tools such as gel permeation chromatography are beginning to be used to check technical predictions and to aid in defining molecular parameters as they affect product properties. The vast majority of work concerns bulk or solution polymerization in isothermal batch or continuous stirred tank reactors. There is a clear need to develop techniques to permit fuller application of reaction engineering to realistic nonisothermal systems, emulsion systems, and systems at high conversion found industrially. A mathematical framework is also needed which will start with carefully planned experimental data and efficiently indicate a polymerization mechanism and statistical estimates of kinetic constants rather than vice-versa. 

The mathematical complexity involved with temperature variations has limited most of the studies cited in this paper to the isothermal case. Since few commercial polymerization reactor systems can or should operate isothermally, there is a clear need to develop techniques to permit fuller application of reaction engineering to nonisothermal systems. In polymerizations as in simpler reactions, changes in temperature or temperature profile can have larger effects on rate and distribution than even reactor type. 

Butala et al. [43] applied optimization techniques to styrene polymerization initiated by BPO (dibenzoyl peroxide, 1 h half-life time, 91°C) and TBPB (tert-butyl perbenzoate, 1 h half-life time, 124°C). As mentioned before, the batch time can be minimized by using nonisothermal temperature profiles. Three independent runs with different optimization policies were performed. The detailed control policies are listed in Table 5.1. 

There are many ways to fabricate and model viscoelastic polymeric materials [22-32]. Fabrication often involves nonlinear flows that are spatially inhomogeneous, nonisothermal, and temporally complex. The flows also may involve material phase changes, and/or a wide range (1-5 decades) of strains and strain rates. Rheology is often the bridge between resin design and fabrication performance, and remains an active area of research [22]. 

Theonly important current application of tubular reactors in polymer syntheses is in the production of high pressure, low density polyethylene. In tubular processes, the newer reactors typically have inside diameters about 2.5 cm and lengths of the order of I km. Ethylene, a free-radical initiator, and a chain transfer agent are injected at the tube inlet and sometimes downstream as well. The high heat of polymerization causes nonisothermal conditions with the temperature increasing towards the tube center and away from the inlet. A typical axial temperature profile peaks some distance down the tube where the bulk of the initiator has been consumed. The reactors are operated at 200-300°C and 2000-3000 atm pressure. 

A continuous emulsion polymerization is characterized by (i) the continual addition of monpmer, surfactant, and initiator to the reaction vessel and (ii) the withdrawal of a steady stream of reactor fiuid. Several such reaction vessels may be set up in series with one another so that the effluent from the first feeds the second, etc. Any species in such a system remains in the reaction vessel for a finite time, termed the residence time. Such reactor vessels may be either completely or incompletely mixed and operate under either isothermal or nonisothermal conditions. The incompletely mixed, nonisothermal reactor is characterized by the existence of spatial concentration and temperature gradients in the reactor. 

The function of the chelator is to complex the ferrous ion and thus limit the concentration of free iron. Redox systems appear very versatile, permitting polymerization at ambient temperatures and the possibility of control of the rate of radical initiation versus polymerization time. This would thus permit control of heal generation and the minimization of reaction time. The use of the redox system ammonium persulfate (2 mmol) together with sodium pyrosulfite (Na S Oj 2.5 mmol) together with copper sulfate (0.002 mmol) buffered with sodium bicarbonate in I liter of water form an effective redox system for vinyl acetate emulsion polymerization. The reaction was started at 25 C and run nonisothermally to 70 C. The time to almost complete conversion was 30 min (Warson, 1976 and Edelhauser, 1975). 

A method has been proposed to calculate the MWD in the course of nonisothermal polymerization. The importance of this method lies in reducing the initial kinetic equations to a partial differential equation... 

The nonisothermal polymerization process in a tubular reactor at laminar flow is investigated in141 Experimental data on the polymerization of styrene under these conditions are presented in142). 

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