Length, instantaneous chain

Figures 1-4 show that when polymerizations were carried out at low concentrations of initiator and/or at low temperatures, the agreement between the model predictions and the experimental data is not so good. This is due to the fact that under those reaction conditions where R is low a large kinetic chain length is expected. When this is so, chain transfer to monomer becomes a reaction to be taken into account, since it markedly influences the chain length of the polymer being formed. A decrease in the instantaneous degree of polymerization, due to chain transfer to monomer, will reduce the concentration of the entangled radicals and, consequently, a decrease in the rate of polymerization is expected.

Example 13.5 Determine the instantaneous distributions of chain lengths by number and weight before and after termination by combination. Apply the quasi-steady and equal reactivity assumptions to a batch polymerization with free-radical kinetics and chemical initiation. 

Assume that this is the controlling resistance so that U=h. A kinetic model is needed for Rp and for the instantaneous values of and Iw The computer program in Appendix 13 includes values for physical properties and an expression for the polymerization kinetics. Cumulative values for the chain lengths are calculated as a function of position down the tube using... 

Many conformations were sampled by the usual MC procedure. The result is of course that there is no preferred orientation of the molecule. Each conformation can, however, be characterised by an instantaneous main axis this is the average direction of the chain. Then this axis is defined as a director . This director is used to subsequently determine the orientational order parameter along the chain. The order is obviously low at the chain ends, and relatively high in the middle of the chain. It was found that the order profile going from the centre of the molecules towards the tails fell off very similarly to corresponding chains (with half the chain length) in the bilayer membrane. As an example, we reproduce here the results for saturated acyl chains, in Figure 10. The conclusion is that the order of the chains found for acyl tails in the bilayer is dominated by intramolecular interactions. The intermolecular interactions due to the presence of other chains that are densely packed around such a chain,... 

The termination process occurs instantaneously via entrant free radicals of (near) zero molecular weight. These radicals do not perturb significantly the distribution of chain lengths in converting growing chains to dead polymer. Indeed, termination in this instance is equivalent to chain transfer, which gives an identical value for the polydispersity index. 

The addition of amines and ethers to alkyllithium compounds profoundly affects polymerization of such species. Amines and ethers alter the association of RLi compounds and change the course of the polymerization and its kinetics. Also, the presence of small amounts of such impurities as water, alcohols, or a-acetylenes, influences the kinetic chain length. The chain-termination reaction with such acidic protons is almost instantaneous. However, there are certain types of protons, such as a-aromatic, secondary amine, and /3-acetylenic, that are not acidic enough to react immediately but will undergo transmetalation during the course of a polymerization reaction. This results in termination or chain transfer of the polymer chain, and limits the realization of polymers of... 

Holroyd and Noyes69 have some difficulty in explaining how the chain length of the reaction was increased by ketene at constant absorbed intensity. If other reactions of hydroxyl or hydroperoxy radicals were introduced that were chain ending then, by competition with reactions (155) and (157), dependence on ketone concentration might be increased. They did not suggest the probability that the decomposition of methylene peroxy radicals would be second order and not instantaneous, i.e.,... 

Even when all prerequisites are fulfilled, solution of eqn. (68) only yields the degree of polymerization of the instantaneously produced polymer. In the stationary state, of course, the ratio of the growth and termination rates does not change. If the ratio [XT]/[M] also remains essentially unchanged, a polymer with equal mean chain length is formed in the course of the whole stationary period. When [XT]/ [M] increases, the degree of polymerization... 

Fig. 12 Instantaneous chain length distribution on a number and weight basis, where dead chains are formed by disproportionation termination. The value of n is increased by decreasing the bimolecular termination rate...

On the other hand, however, it is not straightforward to calculate the MWDs for intermediate cases using the conventional approach. A notable advantage of using an MC simulation technique is that it can be applied to virtually any type of emulsion polymerization, and can account for the chain-length-dependent bimolecular termination reactions in a straightforward manner [265]. Sample simulation results for instantaneous MWDs were shown [265] that were obtained using parameters for styrene polymerization that were reported by Russell [289]. 

When the bimolecular terminations are highly diffusion controlled, the termination reactions are dominated by interactions between radicals with short and long chain lengths even in bulk polymerization, and the MWD of the longer polymer radicals tends to follow the most probable distribution [287, 292]. Under such conditions, oligomeric chains that can be observed only in the number fraction distribution may be formed via disproportionation termination irrespective of particle size. Figure 13 shows the effect of particle size on the instantaneous chain length distribution where the bimolecular terminations are from disproportionation [265]. 

Fig. 13 Effect of particle size on the instantaneous chain length distribution, where bimolecular terminations are chain-length dependent and are by disproportionation...

A simple alternative method was proposed by Gilbert et al. [296, 297] to determine the chain transfer constants based on the chain length distribution (CLD). If the dominant chain termination mechanism is chain transfer to monomer, the instantaneous numerical MWD (the number fraction distribution) is given by ... 

Fig. 15. The effect of retarder addition on the instantaneous [RCO3 ] concentration at 25 % reaction for oxidations with different chain lengths but a common value for the unretarded maximum rate [9]. A, CH3CHO values for and 4 ordinate 4 X scale [RCO3 ] for XH = 0 is 2.08 X 10 mole. . B, C2H5CHO values for and...

To simplify the subsequent treatments, we make the following five assumptions (i) polymer particles contain at most one radical, (ii) a radical with no longer than s monomer units can desorb from and enter into the particles with the same rate irrespective of chain length, (iii) instantaneous termination occurs when another radical enters the particle already containing a radical, (iv) no distinction is made between radicals with or without an initiator fragment on its end, and (v) water-phase reactions such as propagation, termination, and transfer i an be neglected from a kinetic point of view, as shown in Section II,A, Under these assumptions, the rate coefiident for radical desorption from the particles is derived with both deterministic and stochastic approaches,... 

Reaction of a molecule that is activated with an initiator to form a free radical. This free radical, when reacting with a normal molecule creates a new free radical, causing a full fledged chain reaction. This process creates, from a monomer, a long chain polymer instantaneously. No intermediate chain length polymers are present. This process is also called vinyl polymerization. 

Consider the reactions (8.24) to (8.27) for this polymerization. If the usual assumption is made that kp is independent of chain length and also that the initiation step [Eq. (8.24)] is instantaneous, application of the law of mass action gives the following set of rate equations ... 

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