Chain length, distribution, simulation kinetics

The first set of simulations has been performed using a constant value of kt. In this specific case all radicals thus exhibit the exact same probability for termination irrespective of their chain length. Broadening processes that lead to a certain dispersity in the radical chain-length distribution can by definition not influence the kinetics of such a system. These simulations are therefore not meant to test equation 3.8 but rather to show the ease and... 

Fig. 3.20 Simulation of polymerisation within a dropiet at a diffusion coefficient Z = 10 " m /s radial profiles of number and mass average of the polymer s chain length distribution upper plot kinetics according to the basic equations in Table 3.1, whereas below the modified schcane for propagation and termination has been applied in the lower row the literature model of mrunent...

In calculations the moments can be treated as concentrations. Kinetic simulation of radical polymerization to evaluate dispcrsitics typically involves evaluation of the moments rather than the complete distribution. This method of moments is accurate as long as the kinetics are independent of chain length. 

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] ... 

The first simulations with chain-length dependent termination rate coefficients were performed assuming no transfer to monomer and again only radical formation as a result of the laser pulse. The only physical process that can now undermine the assumption of a monodisperse radical distribution is the well known Poisson broadening of propagation reaction (initiator decomposition was assumed to be instantaneous). As already mentioned above, this effect can be tested very simply as by using a set of differential equations to describe the kinetics of this system, a Poisson distribution of these processes is automatically introduced [34, 38], This broadening process was thus actually already present in the previous set of simulations, but was not reflected in the kinetics because of the constant value of kt that was used in those calculations. 

The first assumptions that should be mentioned are those that were previously used in the time-resolved method. It is again assumed that the radical monodispersity hypothesis holds and that the simple relation between chain length and time (equation 3.27) is valid. Poisson distribution and chain transfer to monomer are thus ignored in this kinetic analysis. Again computer simulations will be used to test the validity of these assumptions. 

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