Function chain length dependence

As with the rate of polymerization, we see from Eq. (6.37) that the kinetic chain length depends on the monomer and initiator concentrations and on the constants for the three different kinds of kinetic processes that constitute the mechanism. When the initial monomer and initiator concentrations are used, Eq. (6.37) describes the initial polymer formed. The initial degree of polymerization is a measurable quantity, so Eq. (6.37) provides a second functional relationship, different from Eq. (6.26), between experimentally available quantities-n, [M], and [1]-and theoretically important parameters—kp, k, and k. Note that the mode of termination which establishes the connection between u and hj, and the value of f are both accessible through end group characterization. Thus we have a second equation with three unknowns one more and the evaluation of the individual kinetic constants from experimental results will be feasible. 

As described above, the arrangement of the various functional moieties was controlled spatially across the films at molecular dimensions in the form of LB films. In a series of folded type of sensitizer (S) and electron-donor (D) dyads in a previous work, however, the dyad molecules in the LB films can take many conformations due to flexibility of the longer alkyl chain of the dyads so that clear dependence of the photoinduced electron transfer rate on the alkyl chain length, i.e. S-D distance, was not observed [2], By this reason, we are studying the chain length dependence by using a series of linear type S-D dyads, in which the S and D moieties were linked by a single alkyl chain. In the closely packed LB films, the alkyl chain was considered to be extended and the distance between S and D to be... 

Freed et al. [42,43], among others [44,45] have performed RG perturbation calculations of conformational properties of star chains. The results are mainly valid for low functionality stars. A general conclusion of these calculations is that the EV dependence of the mean size can be expressed as the contribution of two terms. One of them contains much of the chain length dependence but does not depend on the polymer architecture. The other term changes with different architectures but varies weakly with EV. Kosmas et al. [5] have also performed similar perturbation calculations for combs with branching points of different functionalities (that they denoted as brushes). Ohno and Binder [46] also employed RG calculations to evaluate the form of the bead density and center-to-end distance distribution of stars in the bulk and adsorbed in a surface. These calculations are consistent with their scaling theory [27]. 

Expansion is considered for finite, regular polyethylene stars perturbed by the excluded volume effect. An RIS model is used for the chain statistics. The number of bonds in each branch ranges up to 10 240, and the functionality of the branch point ranges up to 20. The form of the calculation employed here provides a lower bound for the expansion. If the number, n, of bonds in the polymers is heid constant, expansion is found to decrease with increasing branch point functionality. Two factors dictate the manner in which finite stars approach the limiting behavior expected for very large stars, These two factors are the chain length dependence at small n of the characteristic ratio and of fa -a3) / n1/2. 

In MC simulation, any kinetic event can be accounted for, as long as the probability of each kinetic event is represented exphcitly. Chain length dependent kinetics can be accounted for in a straightforward manner if the functional form is provided. In conventional MC simulations of molecular build-up processes, the monomeric units are added to each growing polymer molecule one-by-one therefore, a multitude of random numbers and calculations are required to simulate the formation of each polymer molecule. To get around this problem, a new concept, the competition techniqueyV/as proposed in order to drastically reduce the amount of calculation required for the simulation [263,264]. 

Depend on the average chain length Depend on the polarity of the functional groups... 

For 27 (n = 3) and also for the lower homologue 29 (n = 2) another interesting pathway concerns the interaction of the silicenium centre with the nitrogen lone pair to generate 30, which dissociates further to the cyclic product 31 (reaction 28). The chain-length dependence of the formation of 30 as a function of n suggests that the cyclization step is quite sensitive to steric factors. 

The chain length dependence of termination rate constants (Section 5.2.1.4) should not be ignored when considering copolymerization kinetics. It has been pointed out that average chain lengths in copolymerization will be a function of the monomer feed composition especially in copolymerizations with disparate propagation rate constants. Factors determining the rate of copolymerizalion are not fully resolved and copolymerization kinetics remains a topic of discussion and an area in need of further study. 

A chain length-dependent partition coefficient for polymer chains between continuous and dispersed phase is considered. The same functional form proposed and experimentally validated by Kumar et al. for polystyrene is adopted [45]. A chain length dependence of the corresponding interphase mass transport coefficient is also accounted for. 

Tables 6 and 7 present as a function of termination and show that lo increases with increasing chain length dependent termination, i.e., CO is equal to 1.2,1.5 and 2.5 when Q in and (fin are equal to 0.16, 0.4 and 0.8, respectively. Additionally, when backbiting and virtual monomer reaction orders greater than one are accounted for, the method predicts cpout better than the method that considers only fast propagation (see Tables 2 and 3).

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