Free radical polymerizations rate constants

It is generally assumed that the temperature dependenee of free radical polymerization rate constants can be expressed using the well-known Arrhenius equation ... 

Rates of ionic polymerizations are by and large much faster than in free-radical processes. This is mainly because termination by mutual destruction of active centers occurs only in free-radical systems (Section 6.3.3). Macroions with the same charge will repel each other and concentrations of active centers can be much higher in ionic than in free-radical systems. Rate constants for ionic propagation reactions vary but some are higher than those in free-radical systems. This is particularly true in media where the ionic active center is free of its counterion. 

Gridnev AA, Ittel SD. Dependence of free-radical propagation rate constants on the degree of polymerization. Macromolecules 1996 29 5864-5874. 

It is noteworthy that a basic assumption made in the derivation of the free radical desorption rate constant is that the adsorbed layer of surfactant or stabilizer surrounding the particle does not act as a barrier against the molecular diffusion of free radicals out of the particle. Nevertheless, a significant reduction (one order of magnitude) in the free radical desorption rate constant can happen in the emulsion polymerization of styrene stabilized by a polymeric surfactant [42]. This can be attributed to the steric barrier established by the adsorbed polymeric surfactant molecules on the particle surface, which retards the desorption of free radicals out of the particle. Coen et al. [70] studied the reaction kinetics of the seeded emulsion polymerization of styrene. The polystyrene seed latex particles were stabilized by the anionic random copolymer of styrene and acrylic acid. For reference, the polystyrene seed latex particles stabilized by a conventional anionic surfactant were also included in this study. The electrosteric effect of the latex particle surface layer containing the polyelectrolyte is the greatly reduced rate of desorption of free radicals out of the particle as compared to the counterpart associated with a simple... 

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. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

It can be seen from equation (2) that when y 0 the model falls into the classical expression for the rate of conversion of free radical polymerization. Equation (la) shows that this will be the case whenever all macroradicals have the same high mobility (i.e., as n tends to infinity) or when both entangled and non-entangled radicals have the same termination rate constant (i.e. a is equal to unity). 

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... 

As done in Chapter 5, the effect of temperature can be determined using average activation of the various steps. Again, the rates of all single step reactions increase as the temperature increases but the overall result may be different for complex reactions. For free radical polymerizations the activation energies are generally of the order Ei>Ei E > El. Remembering that the description of the specific rate constant is... 

A list of some peroxo compounds that generate free radicals is given in Table 3.3, extensive information can be found in the literature. The initiators are selected according to their thermal half-lives to ensure that at the polymerization temperature they provide a source of free radicals. The rate equation for the thermal half-life is given by tj/2 = 0.693 kj, where kj is the rate constant for the thermal decomposition. In technical applications one often uses the tempera-... 

As mentioned in Section 9.3, Jackson (141) has obtained estimates of the chain-transfer coefficient of the growing radical with polymer in the free-radical polymerization of ethylene, C,p, by choosing the value so as to fit the MWD. As the polymerization conditions for the polymers mentioned in Table 10.1 are not disclosed, it is necessary to choose typical conditions 220° C and 2000 atm will be selected. Under these conditions Ctp, the ratio of the rate constant for attack on polymer (per monomer unit) to that for propagation, in a homogeneous phase, was found to be about 4.0 x 10 3. This is in good agreement with the known transfer coefficients for the lower alkanes (160), when allowance is made for the differences in pressure and temperature (100). The relation between Ctp and k is ... 

Stereocontrol of free radical polymerization is influenced by monomer constitution, solventy and temperature. Most polymerizations seem to follow at least a Markov first-order one-way mechanism. Ratios of the four possible rate constants ki/iy ki/8, k8/i, and k8/8 can be calculated from the experimentally accessible concentrations of configurational triads and diads. With increasing temperature, more heterotactic triads are formed at a syndiotactic radical whereas the monomer addition at an isotactic radical favors isotactic and not heterotactic triads. Compensation effects exist for the differences of activation enthalpies and activation entropies for each of the six possible combinations of modes of addition. The compensation temperature is independent of the mode of addition whereas the compensation enthalpies are not. 

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. 

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. Free-radical polymerizations tend to be highly exothermic. The following data are representative of the thermal (i.e., spontaneous) polymerization of styrene ... 

Once least squares values of the /3 s were obtained, it was desirable to extract from them as much information as possible about the original parameters. To do so, we make one further statement concerning the relations between the rate constants for mutual termination of polymeric radicals of different size. It has been shown (2) that termination rates in free radical polymerizations are determined by diffusion rates rather than chemical factors. The relative displacement of two radicals undergoing Brownian motion with diffusion coefficients D and D" also follows the laws of Brownian diffusion with diffusivity D = D -J- D" (11). It... 

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