Rate constants free radical propagation

The effect of pressure on the rate of free radical propagation reactions has been studied in homopolymerizations only for styrene. Since aV is negative for this reaction, the apphcation of pressure increases the propagation rate. Nicholson and Norrish (12) list the propagation rate constant for styrene as 72.5 liters-mole- —sec.- at atmospheric pressure and 30° C. This increases to 206 liters-mole —sec. at 2000 atm. and 400 hters-mole —sec. at 3000 atm. From these data it is possible to calculate the value of AV for the propagation step to be —13.3 cc. per mole. Walling and Pellon (16) report a value of —11.5 cc. per mole for the same reaction measured by a different technique. 

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. 

The effect of the medium on the rates and routes of liquid-phase oxidation reactions was investigated. The rate constants for chain propagation and termination upon dilution of methyl ethyl ketone with a nonpolar solvent—benzene— were shown to be consistent with the Kirkwood equation relating the constants for bimolecular reactions with the dielectric constant of the medium. The effect of solvents capable of forming hydrogen bonds with peroxy radicals appears to be more complicated. The rate constants for chain propagation and termination in aqueous methyl ethyl ketone solutions appear to be lower because of the lower reactivity of solvated R02. .. HOH radicals than of free RO radicals. The routes of oxidation reactions are a function of the competition between two R02 reaction routes. In the presence of water the reaction selectivity markedly increases, and acetic acid becomes the only oxidation product. 

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. 

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. 

The interpretation of the shock tube results is that during the induction period the branching chain reaction predominates until significant amounts of H2 and O2 have reacted and back reactions have become important. After the induction period, the concentration of free radical propagators go through a maximum and then slowly approach equilibrium values until the higher-order termination steps limit chain propagation, and the back reactions become important. All of the individual rate constants in the mechanism could be evaluated and are consistent with simple collision theory. 

We can estimate an upper limit for the autoxidation as follows. We assume that despite the fact that we do not observe any catalyzed CHP decomposition even after 120 hours at 65°C, we still decompose it at a rate of 1% over a period of 120 hours. Using this rate for radical production, the normal solution rate constants for the propagation and termination reactions and the formulae given in Ref. 10, we estimate the rate of CHP production to be 0.54 X 10 Ms The observed rate, 2.6 x 10 Ms l, is thus about 5 times larger then the upper limit of the estimated initiated free-radical rate. 

Rate constants for free radical propagation increase with decreasing polymer free radical resonance stabilization (Table 20-2). The activation energies, however, are more or less independent of the constitution. Consequently the rate constants are predominantly determined by the preexponential factors of the Arrhenius equation. In addition, they also depend on the viscosity of the reaction medium to a slight extent. 

To illustrate more clearly the nature of free radical polymerization, it is instructive to examine the values of the individual rate constants for the propagation and termination steps. A number of these rate constants have been deduced, generally using nonstationary-state measurements such as rotating sector techniques and emulsion polymerization [26]. Recently, the lUPAC Working Party on Modeling of kinetics and processes of polymerization has recommended the analysis of molecular weight distributions of polymers produced in pulsed-laser-initiated polymerization (PLP) to determine values of... 

To develop their model, Wen and McCormick adopted a number of simplifying assumptions. These are (1) initiation produces two equally reactive radicals, (2) chain transfer reactions are neglected, (3) the rate constants for radicals of different sizes are assumed identical, (4) the propagation rate constant kp, termination rate constant kp and the rate constant for radical trapping kb are all simple functions of free volume as shown below, and (5) there is no excess free volume. The material balance equations for the initiator, the functional group, the active radical, and the trapped radical concentrations... 

The parameter f is the initiator efficiency factor, is the initiator decomposition rate constant, is the propagation reaction rate constant, and [ST]a,o and [STlo are the initial monomer concentrations in microemulsion droplets and in the polymerization system, respectively. This kinetic model was based on the assiunption that (i) all the free radicals generated in the continuous aqueous... 

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. 

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

Olaj OF, Schnoll-Bitai I. Solvent effects on the rate constant of chain propagation in free radical polymerization. Monatsh Chem 1999 130 731-740. 

All the above schemes include, in essence, different variants of empirical linear equations in which the rate constants for chain propagation in the free radical polymerization are brought into correlation with thermodynamic (heat, Hammett constant (a), the change in the Gibbs energy in the equilibrium reaction) and kinetic (loga-ridims of the rate constants of the reference reaction and the reaction under study) characteristics of the addition reaction. 

Polymer propagation steps do not change the total radical concentration, so we recognize that the two opposing processes, initiation and termination, will eventually reach a point of balance. This condition is called the stationary state and is characterized by a constant concentration of free radicals. Under stationary-state conditions (subscript s) the rate of initiation equals the rate of termination. Using Eq. (6.2) for the rate of initiation (that is, two radicals produced per initiator molecule) and Eq. (6.14) for termination, we write... 

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

---