Chain initiation absolute rate

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

Cyclohexyl xanthate has been used as a model compound for mechanistic studies [43]. From laser flash photolysis experiments the absolute rate constant of the reaction with (TMS)3Si has been measured (see Table 4.3). From a competition experiment between cyclohexyl xanthate and -octyl bromide, xanthate was ca 2 times more reactive than the primary alkyl bromide instead of ca 50 as expected from the rate constants reported in Tables 4.1 and 4.3. This result suggests that the addition of silyl radical to thiocarbonyl moiety is reversible. The mechanism of xanthate reduction is depicted in Scheme 4.3 (TMS)3Si radicals, initially generated by small amounts of AIBN, attack the thiocarbonyl moiety to form in a reversible manner a radical intermediate that undergoes (3-scission to form alkyl radicals. Hydrogen abstraction from the silane gives the alkane and (TMS)3Si radical, thus completing the cycle of this chain reaction. 

Furimsky E, Howard JA, Selwyn J (1980) Absolute rate constants for hydrocarbon autoxidation. 28. A low temperature kinetic electron spin resonance study of the self- reactions of isopropylperoxy and related secondary alkylperoxy radicals in solution. Can J Chem 58 677-680 Gebicki JM, Allen AO (1969) Relationship between critical micelle concentration and rate of radiolysis of aqueous sodium linolenate. J Phys Chem 73 2443-2445 Gebicki JM, Bielski BHJ (1981) Comparison of the capacities of the perhydroxyl and the superoxide radicals to initiate chain oxidation of linoleic acid. J Am Chem Soc 103 7020-7022 Gilbert BC, Holmes RGG, Laue HAH, Norman ROC (1976) Electron spin resonance studies, part L. Reactions of alkoxyl radicals generated from alkylhydroperoxidesand titanium(lll) ion in aqueous solution. J Chem Soc Perkin Trans 2 1047-1052... 

V, volumetric rate of the initiation of a chain reaction p. volumetric rate of the propagation of a chain reaction Va)A- absolute rate of a reaction with respect to component N... 

Fig. 14.9 Snapshots of a system of twenty 100 carbon atom long polyethylene chains deformed at 300 K. The initial slab at the top rapidly deforms with the applied stress in the x dimension of the slab, roughly doubling in the first 500 ps to / — 2.64 (second image from the top) then the rate of deformation is slower and doubles again in 1500ps to X — 5.15 (third image from the top). Beyond this point the cell deforms even more slowly to reach a final deformation of X = 6.28 (bottom image). In absolute values, the initial cell of dimensions 1.88 x 5.32 x 5.32 nm deforms to 11.8 x 2.23 x 1.96nm. [Reprinted by permission from M. C. Levine, N. Waheed, and G. C. Rutledge, Molecular Dynamics Simulation of Orientation and Crystallization of Polyethylene during Uniaxial Extension, Polymer, 44, 1771-1779, (2003).]...

Derivation. The Bodenstein approximation of a quasi-stationary free-radical population allows the absolute values of the initiation and termination rates to be equated. With terminating chain transfer first-order in free radicals and monomer ... 

Equation 17 can then be plotted as a linear function of rate versus initiator concentration to yield k and k Kg. Furthermore, if Kg is determined, for example, from conducxivity measurements, then the absolute value of k is also available. A number of such measurements have been taken and yield rate constant values for various monomers (mainly styrenes and dienes) and various counterions and solvents (3 ). In general these data indicate that, although the free anions are only present in very small proportion (Kg lO ), they are responsible for most of the chain propagation because their rate constants (kp 10 -10 M sec ) are several orders greater than those of the ion pairs (k 10 M sec ). Hence, Reaction 14 seems to represent an adequate picture of the anionic mechanism in these systems. 

Peracchia et al. [36] had reported that for the PEGylated copolymer the entrapment of PEG chains within the particle core seems to be more pronounced when acetone is used as solvent instead of THF actually the structure of the PEG chain seemed to be influenced by the formation process, and in particular by its rate, that decreases, moving from solvent-displacement with water and acetone, to solvent-displacement with water and tetrahydrofuran. The different coverage of the nanoparticle by PEG chains, obtained in different operating conditions, may explain the lower absolute value of Zeta potential obtained using THF at any initial polymer concentration, and eventually also the values observed at low concentration in acetone lower than in the higher concentration range [70,96,106]. 

While Equation 1.35, in combination with Equation 1.32, can give the number-average degree of polymerization, it is important not to ignore the role of the transfer reactions. Even in the case where transfer to initiator and solvent is nonexistent (presumably by careful initiator choice and a solvent-free polymerization), transfer to monomer can never be avoided entirely. Another way to approach the problem is to consider the simplest definition of dp, that is, the total number of polymerized monomers units divided by one-half the number of chain ends. Here, it is worth considering the number of chain ends produced by each of the processes [17]. Neither propagation nor termination by combination produce any chain ends (n=0), while both initiation and termination by disproportionation produce one chain end ( =1), and transfer reactions actually create two chain ends (n=2). The steady-state approximation again allows the absolute number of each of these processes to be substituted by the overall rate of each ... 

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