Rates of monomer conversion

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... 

According to Reaction 1 the rate of monomer conversion is given as... 

The degenerative nature of propagation results in reformation of the same active species, but with monomer consumption and chain growth. Although the monomer s thermodynamic polymerizability is independent of the mechanism, the mechanism and structure of the active species determines the rate of monomer conversion. The structure of the active species involved in carbocationic polymerizations was discussed in Section II detailed information on the reactivities of model species was presented in Chapter 2, with the conclusion that covalent precursors do not react directly with alkenes, but must first ionize to sp2-hybridized carbenium ions. Only the resulting carbenium ions can add to double bonds. 

An attempt was nade to simulate the comidex tem of SAN graftii onto (UI)-EPTM initiated by benzoyl laroxide in benzene solution. The approach was based on the kinetic analysis of a reaction sdieme involvit 54 reaction steps which led to 26 differential equations for the variables of interest, i.e. grafting effidency and rates of monomers conversion. 

The polymerization rate, Rp, being the rate of monomer conversion, can be determined by measuring the decrease of the infrared absorption of the reactive group ... 

The experimental fact, that the monomer conversion takes place mainly inside the monomer swollen latex particles, is the justification for Equation 25.8 neglecting propagation in the continuous phase. Accordingly, the rate of emulsion polymerization can be approximated quite accurately by the rate of monomer conversion inside the polymer particles [12] ... 

Obviously, the rate of monomer conversion is important to know when designing a process and eqn [8] can be used for this purpose. Of course, as the polymerization proceeds, the monomer and initiator concentrations will be reduced and the overall rate will slow down and integrated versions of eqn [8] are used to predict the time course of a typical reaction. 

In the isoreactive regime, the rate of monomer addition is just enough to offset the rate of monomer conversion to polymer, and to keep the concentration in the reactor constant. This condition also leads to a constant instantaneous molecular weight as long as [R ] remains approximately constant because of slow initiator decomposition. 

The production rate is 2—4 t/h, depending on the feed rate, monomer concentration in the feed, and conversion. The conversion of isobutylene and isoprene typically ranges from 75—95% and 45—85%, respectively, depending on the grade of butyl mbber being produced. The composition and mol wt of the polymer formed depend on the concentration of the monomers in the reactor Hquid phase and the amount of chain transfer and terminating species present. The Hquid-phase composition is a function of the feed composition and the extent of monomer conversion. In practice, the principal operating variable is the flow rate of the initiator/coinitiator solution to the reactor residence time is normally 30—60 minutes. 

Figure 1 The typical tendencies for the variation of monomer conversion by the polymerization time and for the variation of polymerization rate by the monomer conversion in the ideal emulsion polymerization process.

All these effects increase the overall polymerization rate and decrease the degree of polymerization. The effect of polymerization temperature on the variation of monomer conversion with the polymerization time is exemplified in Fig. 8 for the emulsion polymerization of styrene. 

According to Equation 9 polymers with close to theoretical molecular weight distributions could be prepared even at very high conversions provided [M] and [I] remain constant throughout the polymerization. This condition can be fulfilled by continuously adding a mixed monomer/inifer feed at a sufficiently low constant rate to a coinitiator charge, making certain that the rate of monomer/inifer addition and that of monomer/inifer consumption are equal over the course of the polymerization. 

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. 

Butyllithium initiation of methylmethacrylate has been studied by Korotkov (55) and by Wiles and Bywater (118). Korotkov s scheme involves four reactions 1) attack of butyllithium on the vinyl double bond to produce an active centre, 2) attack of butyllithium at the ester group of the monomer to give inactive products, 3) chain propagation, and 4) chain termination by attack of the polymer anion on the monomer ester function. On the basis of this reaction scheme an expression could be derived for the rate of monomer consumption which is unfortunately too complex for use directly and requires drastic simplification. The final expression derived is therefore only valid for low conversions and slow termination, and if propagation is rapid compared to initiation. The mechanism does not explain the initial rapid uptake of monomer observed, nor the period of anomalous propagation often observed with this initiator. The assumption that kv > kt is hardly likely to be true even after allowance is made for the fact that the concentration of active species is much smaller than that of the added initiator. Butyllithium disappears almost instantaneously but propagation proceeds over periods from tens to hundreds of minutes. The rate constants finally derived therefore cannot be taken seriously (the estimated A is 2 x 105 that of k ) nor can the mechanism be regarded as confirmed. 

General conclusions about relative rates of monomer loss are probably valid at low conversion (<20%) before true network conditions are established. 

The conversion-time curves appear to be very similar to the shape typical of emulsion polymerization, i.e., an S-shaped curve is attributed to the autoacceleration caused by the gel effect (Smith-Ewart 3 kinetics, n>>l). The rate of polymerization-conversion dependence is described by a curve with two rate maxima. The decrease in the rate after passing through the first maximum is ascribed to the decrease of the monomer concentration in particles. Particle nucleation ends between 40 and 60% conversion, beyond the second rate maximum. This is explained by the presence of coemulsifier which stabilizes the monomer droplets against diffusive degradation. 

Fig. 4. Dependence of monomer conversion (open symbols) and the rate of polymerization (closed symbols) in the emulsifier-free emulsion polymerization of PEO-VB macromonomers on reaction time and the PEO-VB type [85]. Recipe [PEO-VB] =0.045 mol dm-3, [AVA]=0.45xl0-3 mol dm"3,60 °C. In water Cr(EO)38-C7-VB (O, ), Cr-(EO)25-VB (A,A)...

In traditional liquid solvents, the polymerization reaction rates are often limited by the local increase in viscosity during the process, as this lowers the mass transfer rate of the monomer to the reaction site. A lower viscosity and a higher diffusion coefficient in SCFs each contribute to overcome this limitation, however, allowing the polymerization rate to be significant up to high value of monomer conversion. 

The most common continuous emulsion polymerization systems require isothermal reaction conditions and provide for conversion control through manipulation of initiator feed rates. Typically, as shown in Figure 1, flow rates of monomer, water, and emulsifier solutions into the first reactor of the series are controlled at levels prescribed by the particular recipe being made and reaction temperature is controlled by changing the temperature of the coolant in the reactor jacket. Manipulation of the initiator feed rate to the reactor is then used to control reaction rate and, subsequently, exit conversion. An aspect of this control strategy which has not been considered in the literature is the complication presented by the apparent dead-time which exists between the point of addition of initiator and the point where conversion is measured. In many systems this dead-time is of the order of several hours, presenting a problem which conventional control systems are incapable of solving. This apparent dead-time often encountered in initiation of polymerization. 

The analytical predictor, as well as the other dead-time compensation techniques, requires a mathematical model of the process for implementation. The block diagram of the analytical predictor control strategy, applied to the problem of conversion control in an emulsion polymerization, is illustrated in Figure 2(a). In this application, the current measured values of monomer conversion and initiator feed rate are input into the mathematical model which then calculates the value of conversion T units of time in the future assuming no changes in initiator flow or reactor conditions occur during this time. 

In the terpolymerization of styrene, 2-ethylhexyl acrylate, and glycidyl acrylate a continuous-addition type of technique was used, and attempts were made to achieve maximum conversions. Relationships were sought between molecular weights, molecular weight distributions, reaction temperature, initiator concentration, half-life of the initiator, and rate of monomer-initiator addition. The molecular weights of the products depended strongly upon reaction temperature and on the rate of initiator decomposition. Narrower molecular weight distributions resulted from the use of initiators with shorter half-lives. 

In contrast, transfer reactions may not be detected by following the monomer conversion if the rate of reinitiation is comparable to that of propagation. In this case, transfer is detected by a nonlinear dependence of the polymer molecular weight as a function of monomer conversion or polymer yield (Fig. 3) termination does not affect the number of chains... 

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