Initiation rate constants free radical polymerizations

A case classically associated with radical chain polymerization for which a (pseudo)steady state is assumed for the concentration of active centers this condition is attained when the termination rate equals the initiation rate (the free-radical concentration is kept at a very low value due to the high value of the specific rate constant of the termination step). The propagation rate, is very much faster than the termination rate, so that long chains are produced from the beginning of the polymerization. For linear chains, the polydispersity of the polymer fraction varies between 1.5 and 2. 

In relation to the mechanism of polymerization, the cobalt octabromo derivative (7b) is also an effective initiator for controlled free-radical polymerization of acrylic esters, where the apparent first-order rate constant of propagation (kapp) at 50 °C is more than 30 times larger than kapp using 7a under identical conditions. This is due to a higher concentration of radicals resulting from greater dissociation of the dormant organocobalt species. 

Lewis and Volpert continue the discussion of the isothermal form of frontal polymerization in Chapter 5. Isothermal frontal polymerization is also a localized reaction zone that propagates but because of the autoacceleration of the rate of free-radical polymerization with conversion. A seed of poly(methyl methacrylate) is placed in contact with a solution of a peroxide or nitrile initiator, and a front propagates from the seed. The monomer diffuses into the seed, creating a viscous zone in which the rate of polymerization is faster than in the bulk solution. The result is a front that propagates but not with a constant velocity because the reaction is proceeding in the bulk solution at a slower rate. This process is used to create gradient refractive index materials by adding the appropriate dopant. 

Free-radical polymerization processes are used to produce virtually all commercial methacrylic polymers. Usually free-radical initiators (qv) such as azo compounds or peroxides are used to initiate the polymerizations. Photochemical and radiation-initiated polymerizations are also well known. At a constant temperature, the initial rate of the bulk or solution radical polymerization of methacrylic 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 methacrylic monomers initiated with 2,2 -azobisisobutyronitrile [78-67-1] (AIBN) have been deterrnined and are shown in Table 8. 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

Addition of phosphonyl radicals onto alkenes or alkynes has been known since the sixties [14]. Nevertheless, because of the interest in organic synthesis and in the initiation of free radical polymerizations [15], the modes of generation of phosphonyl radicals [16] and their addition rate constants onto alkenes [9,12,17] has continued to be intensively studied over the last decade. Narasaka et al. [18] and Romakhin et al. [19] showed that phosphonyl radicals, generated either in the presence of manganese salts or anodically, add to alkenes with good yields. 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

The initiator must produce free radicals at a reasonably constant rate during the polymerization process. 

The above example gives us an idea of the difficulties in stating a rigorous kinetic model for the free-radical polymerization of formulations containing polyfunctional monomers. An example of efforts to introduce a mechanistic analysis for this kind of reaction, is the case of (meth)acrylate polymerizations, where Bowman and Peppas (1991) coupled free-volume derived expressions for diffusion-controlled kp and kt values to expressions describing the time-dependent evolution of the free volume. Further work expanded this initial analysis to take into account different possible elemental steps of the kinetic scheme (Anseth and Bowman, 1992/93 Kurdikar and Peppas, 1994 Scott and Peppas, 1999). The analysis of these mechanistic models is beyond our scope. Instead, one example of models that capture the main concepts of a rigorous description, but include phenomenological equations to account for the variation of specific rate constants with conversion, will be discussed. 

In contrast, recent kinetic investigation of the polymerization of spacerless G2 dendron-substi-tuted styrene and methylmethacrylate, respectively, in solution lead to the unexpected conclusion that above a certain critical monomer concentration a strong increase in the rate of the free radical polymerization is observed [21]. The results can be explained by self-organization of the growing polymer chain to a spherical or columnar superstructure in solution, depending on the degree of polymerization (DP, Fig. 2). The rate constants and low initiator efficiency lead one to conclude that the self-assembled... 

Table 5. Reduction potentials ( red), excited triplet (singlet for NTAB and CTAB) energies, free energy changes (AGet) and quenching rate constants (A q, measured for n-butyltriphenylborate anion) of the light absorbing molecules used as initiators of free-radical polymerization.

The steps in free-radical polymerization reaction and the corte- spending rate laws are summarized in Table 7-3. For the polymexiza-tion of styrene at 80°C initiated by 2,2-azobkisobutyromtrile the rate constants are... 

A free-radical polymerization is carried out in a CSTR with an average residence time of 240 min. The reaction is first order to monomer M and half order to initiator I, and the pseudo-first-order rate constant for the monomer reaction is 2.3 x 10 min when the initiator concentration is 0.01 M. The decomposition rate constant for initiator is 4.1 x 10 min. ... 

Note that Equation 7.21 predicts that rate of polymer formation in free-radical polymerization is first order in monomer concentration and half order in initiator concentration. This assumes, of course, that the initiator efficiency is independent of monomer concentration. This is not strictly valid. In fact, in practice Equation 7.21 is valid only at the initial stage of reaction its validity beyond lOto 15% requires experimental verification. Abundant experimental evidence has confirmed the predicted proportionality between the rate of polymerization and the square root of initiator concentration at low extents of reaction (Figure 7.2). If the initiator efficiency, f, is independent of the monomer concentration, then Equation 7.21 predicts that the quantity Rp/[I] [M] should be constant. In several instances, this ratio has indeed been found to show only a small decrease even over a wide range of dilution, indicating an initiator efficiency that is independent of dilution. This confirmation of first-order kinetics with respect to the monomer concentration suggests an efficiency of utilization of primary radicals, f, near unity. Even where the kinetics indicate a decrease in f with dilution, the decreases have been invariably small. For undiluted monomers, efficiencies near unity are not impossible. 

Consider the free-radical polymerization of methyl methacrylate in toluene solution at 77°C, initiated by AIBN. When the initial monomer concentration was 2.07 M and the initial AIBN concentration was 2 X 10 M, the initial rate of polymerization was determined to be Vp = 2.49 X 10" M min. a. Determine the initial rate of initiation, Vj, and kj(k by considering that the rate constant for the decomposition of AIBN at 77°C is k = 5.7 X 10 min, and that virtually all radicals are capable of initiating chains. 

Additional well-defined side-chain liquid crystalline polymers should be synthesized by controlled polymerizations of mesogen-ic acrylates (anionic or free radical polymerizations), styrenes (anionic, cationic or free radical), vinyl pyridines (anionic), various heterocyclic monomers (anionic, cationic and metalloporphyrin-initiated), cyclobutenes (ROMP), and 7-oxanorbornenes and 7-oxanorbornadienes (ROMP). Ideally, the kinetics of these living polymerizations will be determined by measuring the individual rate constants for termination and... 

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