Rate for polymerization

In a batch reactor, the relative monomer concentrations will change with time because the two monomers react at different rates. For polymerizations with a short chain life, the change in monomer concentration results in a copolymer composition distribution where polymer molecules formed early in the batch will have a different composition from molecules formed late in the batch. For living polymers, the drift in monomer composition causes a corresponding change down the growing chain. This phenomenon can be used advantageously to produce tapered block copolymers. 

The rates of polymerization (Table 3.15) can, in the first instance, be ascribed to the reduced termination rate for polymeric as compared to low-molar-mass radicals, an effect which operates here from the start of the reaction. 

For each initiator there is a useful temperature range for which the initiator decomposition rate constant, kd, will produce radicals at suitable rates for polymerization. The initiation rate is usually controlled by the decomposition rate of the initiator, which depends directly on its concentration (first-order reaction). The temperature window can be enlarged by the use of catalysts such as a tertiary amine (Eq. (2.80)), or an organometallic compound in a redox reaction (Eqs (2.81) and (2.82)). 

Figure 22.6 Variation of viscosity as a function of shear rate for polymeric melts.

Barnes and co-workers have studied mixed-monolayer systems [278,281,283,284] and found some striking nonidealities. Mixed films of octadecanol and cholesterol, for example, show little evaporation resistance if only 10% cholesterol is present [278] apparently due to an uneven granular microstructure in films with cholesterol [284]. Another study of cellulose decanoate films showed no correlation between holes in the monolayer and permeation rate [285]. Polymerized surfactants make relatively poor water evaporation retarders when compared to octadecanol [286]. There are problems in obtaining reproducible values for r [287] due to impurities in the monolayer material or in the spreading solvent. 

Graphically test whether these data indicate catalyzed or uncatalyzed conditions and evaluate the rate constant for polymerization at 270°C. Propose a name for the polymer. 

Figure 6.2 Acceleration of the polymerization rate for methyl methacrylate at the concentrations shown in benzene at 50 C. [Reprinted from G. V. Schulz and G. Haborth, Makromol. Chem. 1 106 (1948).]...

Figure 6.3 shows some data which constitute a test of Eq. (6.26). In Fig. 6.3a, Rp and [M] are plotted on a log-log scale for a constant level of redox initiator. The slope of this line, which indicates the order of the polymerization with respect to monomer, is unity, showing that the polymerization of methyl methacrylate is first order in monomer. Figure 6.3b is a similar plot of the initial rate of polymerization—which essentially maintains the monomer at constant con-centration—versus initiator concentration for several different monomer-initiator combinations. Each of the lines has a slope of indicating a half-order dependence on [I] as predicted by Eq. (6.26).

Using typical activation energies out of Tables 6.2-6.4, estimate the percent change in the rate of polymerization with a 1°C change in temperature at 50°C for thermally initiated and photinitiated polymerization. 

Finally we recognize that a 1°C temperature variation can be approximated as dT and that (dRp/Rp) X 100 gives the approximate percent change in the rate of polymerization. Taking average values of E from the appropriate tables, we obtain E j = 145, E = 16.8, and Ep = 24.9 kJ mol . For thermally initiated polymerization... 

Note that the initiator decomposition makes the largest contribution to E therefore photoinitiated processes display a considerably lower temperature dependence for the rate of polymerization. 

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

When results are compared for polymerization experiments carried out at different frequencies of blinking, it is found that the rate depends on that frequency. To see how this comes about, we must examine the variation of radical concentration under non-stationary-state conditions. This consideration dictates the choice of photoinitiated polymerization, since in the latter it is almost possible to turn on or off—with the blink of a light—the source of free radicals. The qualifying almost in the previous sentence is actually the focus of our attention, since a short but finite amount of time is required for the radical concentration to reach [M-] and a short but finite amount of time is required for it to drop back to zero after the light goes out. 

If the light source is switched on and off and held for long periods of equal duration in either light or darkness, then the radical concentration in the system will consist of an alternation between the situation described in Figs. 6.5a and b. Because we have specified that the duration of each phase is long, the net behavior is essentially a series of plateaus in which the illumination is either Iq or zero and the radical concentration is either [M], or zero, with brief transitions in between. This is illustrated in Fig. 6.5c. The concentration of radicals is consistent with Iq, but is present only half of the time hence the rate of polymerization is only half what it would be for the same illumination operating continuously. 

Thus if we were to compare the rate of polymerization with intermittent illumination relative to that with continuous illumination, but under otherwise identical conditions, we would observe the following limits for equal periods of light and dark ... 

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

We shall consider these points below. The mechanism for cationic polymerization continues to include initiation, propagation, transfer, and termination steps, and the rate of polymerization and the kinetic chain length are the principal quantities of interest. 

Applying the Arrhenius equation to Eq. (6.116) shows that the apparent activation energy for the overall rate of polymerization is given by... 

In a series of experiments at 60 C, the rate of polymerization of styrene agitated in water containing persulfate initiator was measuredt for different concentrations of sodium dodecyl sulfate emulsifier. The following results were obtained ... 

C with AIBN and measured the initial rates of polymerization for the ... 

Rate of polymerization. The rate of polymerization for homogeneous systems closely resembles anionic polymerization. For heterogeneous systems the concentration of alkylated transition metal sites on the surface appears in the rate law. The latter depends on the particle size of the solid catalyst and may be complicated by sites of various degrees of activity. There is sometimes an inverse relationship between the degree of stereoregularity produced by a catalyst and the rate at which polymerization occurs. 

Usually, free-radical initiators such as azo compounds or peroxides are used to initiate the polymerization of acrylic monomers. Photochemical (72—74) and radiation-initiated (75) polymerizations are also well known. At a constant temperature, the initial rate of the bulk or solution radical polymerization of acrylic monomers is first order with respect to monomer concentration and one-half order with respect to the initiator concentration. Rate data for polymerization of several common acrylic monomers initiated with 2,2 -azobisisobutyronittile (AIBN) [78-67-1] have been determined and are shown in Table 6. The table also includes heats of polymerization and volume percent shrinkage data. 

Chain transfer is an important consideration in solution polymerizations. Chain transfer to solvent may reduce the rate of polymerization as well as the molecular weight of the polymer. Other chain-transfer reactions may iatroduce dye sites, branching, chromophoric groups, and stmctural defects which reduce thermal stabiUty. Many of the solvents used for acrylonitrile polymerization are very active in chain transfer. DMAC and DME have chain-transfer constants of 4.95-5.1 x lO " and 2.7-2.8 x lO " respectively, very high when compared to a value of only 0.05 x lO " for acrylonitrile itself DMSO (0.1-0.8 X lO " ) and aqueous zinc chloride (0.006 x lO " ), in contrast, have relatively low transfer constants hence, the relative desirabiUty of these two solvents over the former. DME, however, is used by several acryhc fiber producers as a solvent for solution polymerization. 

When initiator is first added the reaction medium remains clear while particles 10 to 20 nm in diameter are formed. As the reaction proceeds the particle size increases, giving the reaction medium a white milky appearance. When a thermal initiator, such as AIBN or benzoyl peroxide, is used the reaction is autocatalytic. This contrasts sharply with normal homogeneous polymerizations in which the rate of polymerization decreases monotonicaHy with time. Studies show that three propagation reactions occur simultaneously to account for the anomalous auto acceleration (17). These are chain growth in the continuous monomer phase chain growth of radicals that have precipitated from solution onto the particle surface and chain growth of radicals within the polymer particles (13,18). 

The monomer recovery process may vary ia commercial practice. A less desirable sequence is to filter or centrifuge the slurry to recover the polymer and then pass the filtrate through a conventional distillation tower to recover the unreacted monomer. The need for monomer recovery may be minimized by usiag two-stage filtration with filtrate recycle after the first stage. Nonvolatile monomers, such as sodium styrene sulfonate, can be partially recovered ia this manner. This often makes process control more difficult because some reaction by-products can affect the rate of polymerization and often the composition may vary. When recycle is used it is often done to control discharges iato the environment rather than to reduce monomer losses. 

The limiting oxygen index of Tefzel as measured by the candle test (ASTM D2863) is 30%. Tefzel is rated 94 V-0 by Underwriters Laboratories, Inc., in their burning test classification for polymeric materials. As a fuel, it has a comparatively low rating. Its heat of combustion is 13.7 MJ/kg (32,500 kcal/kg) compared to 14.9 MJ /kg (35,000 kcal/kg) for poly(vinyHdene fluoride) and 46.5 MJ /kg (110,000 kcal/kg) for polyethylene. 

Adsorption systems employing molecular sieves are available for feed gases having low acid gas concentrations. Another option is based on the use of polymeric, semipermeable membranes which rely on the higher solubiHties and diffusion rates of carbon dioxide and hydrogen sulfide in the polymeric material relative to methane for membrane selectivity and separation of the various constituents. Membrane units have been designed that are effective at small and medium flow rates for the bulk removal of carbon dioxide. 

AlkyUithium compounds are primarily used as initiators for polymerizations of styrenes and dienes (52). These initiators are too reactive for alkyl methacrylates and vinylpyridines. / -ButyUithium [109-72-8] is used commercially to initiate anionic homopolymerization and copolymerization of butadiene, isoprene, and styrene with linear and branched stmctures. Because of the high degree of association (hexameric), -butyIUthium-initiated polymerizations are often effected at elevated temperatures (>50° C) to increase the rate of initiation relative to propagation and thus to obtain polymers with narrower molecular weight distributions (53). Hydrocarbon solutions of this initiator are quite stable at room temperature for extended periods of time the rate of decomposition per month is 0.06% at 20°C (39). 

Aromatic radical anions, such as lithium naphthalene or sodium naphthalene, are efficient difunctional initiators (eqs. 6,7) (3,20,64). However, the necessity of using polar solvents for their formation and use limits their utility for diene polymerization, since the unique abiUty of lithium to provide high 1,4-polydiene microstmcture is lost in polar media (1,33,34,57,63,64). Consequentiy, a significant research challenge has been to discover a hydrocarbon-soluble dilithium initiator which would initiate the polymerization of styrene and diene monomers to form monomodal a, CO-dianionic polymers at rates which are faster or comparable to the rates of polymerization, ie, to form narrow molecular weight distribution polymers (61,65,66). 

During Stages II and III the average concentration of radicals within the particle determines the rate of polymerization. To solve for n, the fate of a given radical was balanced across the possible adsorption, desorption, and termination events. Initially a solution was provided for three physically limiting cases. Subsequentiy, n was solved for expHcitiy without limitation using a generating function to solve the Smith-Ewart recursion formula (29). This analysis for the case of very slow rates of radical desorption was improved on (30), and later radical readsorption was accounted for and the Smith-Ewart recursion formula solved via the method of continuous fractions (31). 

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