Polymerization kinetics free radical, chain length dependent

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... 

Equation (P6.44.23) shows that the distribution function for the degree of polymerization of polymer formed by a free-radical chain mechanism, in which chain transfer is absent, depends only on the kinetic chain length and the ratio of disproportionation to coupling. The plot of vs. x according to Eq. (P6.44.23) gives the... 

The Importance of Chain-Length Dependent Kinetics in Free-Radical Polymerization A Preliminary Guide... 

Based on an analysis of kinetic data on small radical additions and the first few propagation steps in free-radical polymerization, backed up by theoretical investigations of the propagation rate coefficient, we proposed the empirical formula given by Eq. 8 for the description of the chain-length dependence of the propagation rate coeffi-... 

In this paper we examined the effect of CLDP on kinetics in low-conversion free-radical polymerization. We have shown that although the chain length dependence of the individual fej, does not extend beyond for common systems, a significant macroscopic effect may be observed in systems with DPa up to 100. This observation leads us to draw some preliminary conclusions regarding CLDP (a) it should probably not be ignored in living radical polymerizations with low DPa ( 0>... 

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. 

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. 

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. 

In conclusion it can be said that the MWD method is capable of determining the chain-length dependence of kt model-independently. This method has been validated theoretically and, as long as the number MWD can be determined and scaled correctly, the method is robust and reliable. In this thesis, the first model-independent results have been reported for a set of three acrylates. These results will enable a better description of the overall kinetics of free-radical polymerizations and better predictions of the resulting MWDs and polymer properties. It is sincerely hoped that this method and lines of thought presented will find continuation in future scientific work by others in this field of great scientific interest and practical importance. 

Heuts JPA, Russell GT. The nature of the chain-length dependence of the propagation rate coefficient and its effect on the kinetics of free-radical polymerization. 1. SmaU-molecule studies. Eur Polym J 2006 42 3-20. 

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. 

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... 

A polymer may be formed by hundreds, thousands, or even tens of thousands of monomeric units. This material can also be present in natural form, for example, cellulose and rubber. The characteristics of these macromolecules depend on the monomer, chain length, and composition of the mixture. The mechanism and kinetics have been presented. We present the free radical polymerization of styrene (solution polymerization) as an example. 

Elimination of [R ] by means of equation 54 leads to an expression for the kinetic chain length v that shows the dependence of the different kinetic parameters. One important characteristic of the free radical polymerization is hereby well illustrated The sizes of the macromolecules produced are inversely proportional to the square root of initiator concentration. Increasing the initiator concentration leads to smaller size polymer molecules. 

In free radical addition polymerization the distribution of molar mass depends upon the mechanism of termination. The simplest case to consider is when the mechanism is through disproportionation and is equal to the kinetic chain length v. In this case the chain grows and terminates at the length to which it had grown. At this point it is necessary to define a new... 

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