Molecular weight distribution in free-radical polymerization

Clay, P.A. Gilbert, R.G. Molecular weight distributions in free-radical polymerizations. I. Model development and implications for data interpretation. Macromolecules 1995, 28 (2), 552-569. 

In Chapter 9, we mentioned that the use of microreactors leads to a significant improvement in the control of the molecular-weight distribution in free radical polymerization by virtue of superior heat-transfer efficiency.Free-radical polymerization reactions are usually highly exothermic, so precise temperature control is essential to carry out these reactions in a highly controlled manner. Thus, from an industrial viewpoint, a major concern with free-radical polymerization is the controllability of the reaction temperature. Temperature control often arises as a serious problem during the scale-up of a bench process to industrial production. In this section, we will discuss the numbering-up of microreactors to increase production volumes in radical polymerization in industry. 

Stockmayer, W.H.J., 1945. Distribution of chain lengths and compositions in copolymers. Chem. Phys. 13,199-207. Tobita, H., 1993. Molecular weight distribution in free radical polymerization with long-chain branching. J. Polym. Sci. B Polym. Phys. 31, 1363-1371. 

Clay PA, Gilbert RG Molecular weight distributions in free-radical polymerizations , manuscript in preparation... 

Hamielec AE, Hodgins JW, Tebbens K. Polymer reactors and molecular weight distribution, 2. Free radical polymerization in a batch reactor. Aiche J 1967 13 1087-1091. 

In summary, since the lifetime of a growing polymer chain is equal to its residence time in the reactor, the effect of the residence time distribution causes extreme broadening of the molecular weight distribution during step-growth polymerization in a CSTR. The constancy of the polymerization environment, which acted to narrow the distribution in free radical polymerization, has an insignificant effect in step-growth polymerization. 

They are discrete transforms and can therefore operate directly on the separate equations for each species, reducing them to one expression. Nonlinear terms arising from condensation polymerization can be handled and, with some difficulty, so can realistic terminations in free radical polymerization. They are a special case of the generating functions and can be used readily to calculate directly the moments of the distribution, and thus, average molecular weights and dispersion index, etc. Abraham (2) provided a short table of Z-transforms and showed their use with stepwise addition. 

The absence of termination during a living polymerization leads to a very narrow molecular-weight distribution with polydispersities as low as 1.06. By comparison, polydispersities above 2 and as high as 20 are typical in free radical polymerization. 

Crowley, T.J. Choi, K.Y. Discrete optimal control of molecular weight distribution in a batch free radical polymerization process. Ind. Eng. Chem. Res. 1997, 36, 3676-3684. 

Ttp 4 Chain microstructure and propagation reactions. Propagation reactions are mainly responsible for the development of polymer chain microstructure (and control chain composition and sequence length distribution in copolymerizations). In free radical polymerization, the stereoregularity of a high molecular weight homopolymer chain depends on polymerization temperature almost exclusively. It is usually independent of initiator type and monomer concentration. Calculations on stereoregularity... 

Veregin, R.P.N., Odell, P.G., Michalak, L.M., and Georges, M.K., 1996, Molecular Weight Distributions in Nitroxide-Mediated Living Free Radical Polymerization Kinetics of the Slow Equilibria between Growing and Dormant Chains, Macromolecides, 29 3346... 

Vinylidene fluoride (b.p. — 84°C) is free-radically polymerized in suspension or emulsion at 10-300 bar and 10-150°C. Suspension-polymerized material contains less branching and consequently a narrower molecular-weight distribution than the emulsion-polymerized material. For this reason, the suspension-polymerized material has higher crystallinity, greater mechanical strength, and better chemical stability. Materials from both polymerization methods contain a considerable proportion of head-to-head linkages. 

Figure 4. Miscibility of polystyrene standards with narrow molecular weight distribution in n-butane as a function of molecular weight and polymer concentration (left), and the weight and number average molecular weights of polystyrene obtained from free-radical polymerization of styrene in n-butane using t-butyl peroxide aa initiator (right) at 160 C. [ 1 MPa = 10 bar].

Quantum chemistry is particularly useful for studying complex processes such as free-radical polymerization (see Radical Polymerization). In free-radical polymerization, a variety of competing reactions occur and the observable quantities that are accessible by experiment (such as the overall reaction rate, the overall molecular weight distribution of the polymer, and the overall monomer, polymer, and radical concentrations) are a complicated function of the rates of these individual steps. In order to infer the rates of individual reactions from such measurable quantities, one has to assume both a kinetic mechanism and often some additional empirical parameters. Not surprisingly then, depending upon the assumptions, enormous discrepancies in the so-called measured values can sometimes arise. Quantum chemistry is able to address this problem by providing direct access to the rates and thermochemistry of the individual steps in the process, without recourse to such model-based assumptions. 

Radical Addition to C=C Bonds. Radical addition to C=C bonds are of importance for free-radical polymerization as this reaction forms the propagation step, and thus influences the reaction rate and molecular weight distribution in both conventional and controlled free-radical polymerization, and the copolymer composition and sequence distribution in free-radical copolymerization. Numerous studies have examined the applicability of high level theoretical methods for stud5dng radical addition to C=C bonds in small radical systems (32,33,37,93,94). The most recent study (37) included W1 barriers and enthalpies, and geometries and frequencies at the CCSD(T)/6-31 lG(d,p) level of theory, and is the highest level study to date. The main conclusions from this study, and (where still relevant) the previous lower level studies, are outlined below. 

It can thus be easily inferred that chain transfer may alter the properties of the pol5uneric product in an undesirable way, or—in contrast—may be used advantageously to specifically reduce the molecular weights obtained in a specific polymerization process or to introduce specific end groups. The first case discussed above (which refers to the kinetic concept of chain transfer) is assumed for the derivation of the Mayo equation, which is frequently used to derive chain transfer rate coefficients. This specific case does not alter the overall rate of the polymerization system, because it does not change the overall free radical concentration, but rather influences the molecular weight distribution. 

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