Termination, chain length dependent radical polymerization kinetics

Subject headings polymerization / radical reactions / reaction kinetics / termination chain-length dependence... 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

Computational Aspects of Free Radical Polymerization Kinetics with Chain Length Dependent Termination... 

Recently, a model to evaluate the CLD and the polymerization rate in RAFT polymerizations in bulk at high conversion has been developed. In the model, the presence of intermediate radicals and diffusion limitations for all involved reactions have been accounted for. Then, not only the rate constant of bimolecular termination but also that of RAFT addition are supposed to be conversion and chain-length-dependent. In particular, the kinetic rate constants of these two bimolecular reactions have been evaluated according to the following general expression ... 

Autoacceleration, where the rate of polymerization increases with conversion in isothermal conditions, is observed in both thermal- and photoinitiated free-radical polymerizations because the termination mechanisms are the same for both. As the chains grow longer, it becomes more difficult for the active centers to diffuse and imdergo bimolecular termination thus, termination frequency decreases and active centers at the chain ends can become trapped. In cases where termination is controlled by diffusion, the pseudo-steady-state assumption is no longer valid and chain length dependent termination (CLDT) may occur (67). As is discussed for chain cross-linking photopolymerizations below, more complicated kinetic treatments must then be considered, including unsteady-state kinetics. 

Equation 56 indicates a first-order dependence of the rate of polymerization on the monomer concentration and a square-root dependence on the concentration of the initiator. These dependencies have been confirmed for the example of many polymerizing systems. It should be pointed out that deviations from equation 56 (such as chain-length-dependent rate coefficients or primary radical termination) are manifest in a change in the exponents associated with the initiator and monomer concentrations (386,387). The rate of polymerization will scale with a weaker than square-root dependence on [I] and a stronger than hnear dependence on [M]. Extreme dilution of monomer can also change the exponents of monomer and initiator concentration. Equation 56 is easily integrated to yield an expression which directly correlates the monomer conversion with the observed kinetic rate coefficient obs-... 

The discussion of the rate of bimolecular termination has, up to now, been mainly of a qualitative nature. The scaling of average or macroscopic kt values with viscosity, solvent effects and coil dimensions were discussed without much attention for the chain-length dependence of this process. This dependence originates from the simple fact that free-radical termination is a diffusion-controlled process. Consequently, the overall mobility of polymer chains and/or polymer chain ends determine the overall rate of radical loss in a polymerizing system. As small chains are known to be much more mobile than large ones, the chain length of radicals can be expected to have a profound effect on the termination kinetics. 

Also the group of Olaj have performed quite a number of simulation studies, mainly on the kinetics of PLP. In a recent series of papers [172-174, 230] they have used a simulation method based on an iterative procedure [239-241]. The time interval is divided in small, equal intervals, each of duration kp [M]. The radical profile is then converged until a pseudo-steady-state profile is obtained, from which relevant kinetic data can then be calculated such as the rate of polymerization and / or the MWD. Olaj et al. [172-174, 230] used these kinetic data to explore the possibilities of recovering chain-length dependent termination rate coefficients from PLP experiments. In their simulations they compared the exact value of (which can be calculated in a simulation, but is not experimentally accessible) with the value of that they obtained from analyzing output data of their simulations, which are experimentally accessible parameters. In the case of using MWD data [172], the second moment of this distribution, according to [242-244] ... 

In this thesis the chain-length dependence of termination reactions during free-radical polymerization has been investigated. Interest in the kinetic parameters describing this process, primarily arises from the profound effect that termination reactions have on the overall kinetics of polymerization processes, on the MWD of the final product and therefore also on the final product properties. 

Smith GB, Russell GT, Yin M, Heuts JPA. The effects of chain length dependent propagation and termination on the kinetics of free-radical polymerization at low chain lengths. Eur Polym J 2005 41 225-230. 

Eqs. (26) and (27) apply irrespective of the nature of the initiation process it is required merely that the propagation and termination processes be of the second order. They emphasize the very general inverse dependence of the kinetic chain length on the radical concentration and therefore on the rate of polymerization. The kinetic chain length may be calculated from the ratios k /kt as given in Table XI and the rate of polymerization. Thus, for pure styrene at 60°C... 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

Different kinds of approach have recently appeared in a number of important studies, incorporating into the kinetic relations changes in kt with chain length. They start from the empirical functional dependence of the rate constant of bimolecular termination on the degree of polymerization of the reacting radicals... 

The kinetic chain length is thus inversely dependent on the radical concentration [Eq. (6.123)] or the polymerization rate [Eq. (6.124)]. This is of great practical significance as it shows that any attempt to increase the rate of polymerization by increasing the radical concentration will be only at the expense of producing smaller size polymer molecules. Equations (6.123) and (6.124) are applicable for all cases of bimolecular termination irrespective of the exact mechanism (combination or disproportionation) and also irrespective of the nature of the initiation process. Thus, for any monomer the Idnetic chain length will be Independent of whether the polymerization is initiated by thermal, redox, or photochemical means, or of the initiator used, if the [M ] or Rp is the same. 

Figure 4 shows the dependence of the time to failure on the rate of bimolecular radical termination which is directly related to diffusion of the polymeric segments in the solid matrix. Again, the log-log plot is linear with a positive slope and this time, again less than unity. Increased diffusion shortens the kinetic chain length and increases the time to failure. 

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