Kinetic chain length instantaneous

The instantaneous degree of polymerization gives a measure of the instantaneous kinetic chain length. It may be written as the ratio of the rate of propagation to the rate of production of dead chains by various mechanisms ... 

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.

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... 

Under these assumptions, the expressions for rate of polymerization (J p), kinetic chain length (A, the average number of monomer units on a living chain) and instantaneous number average degree of polymerization (DP)," , the average number of monomer units on a dead polymer chain formed at an instant in time) are written as... 

The data are from a free radical polymerization of butyl acrylate (BA) in butyl acetate. When fractional monomer conversion reached 0.4, an extra amount of azobisisobutyro-nitrile (AIBN) initiator was added (initiator boost). Its effect can be immediately seen in the rapid drop of as the quasi-steady state approximation (QSS A) predicts for kinetic chain length (e.g., see Chapters 1 and 5) which is the molecular weight of chains being produced at any instant in a free radical reactions. It is proportional to the concentration of monomer to that of initiator. Hence, the addition of initiator causes the instantaneous chain length, and hence to fall. 

The molar mass can be addressed using the kinetic chain length concept for free radical polymerization the instantaneous number average chain length, is given in the QSSA for the aforementioned conditions... 

Note that the kinetic chain length is controlled by the extent of chain transfer. Also note that this is the instantaneous... 

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... 

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,... 

Kinetic approaches represent realistic and comprehensive description of the mechanism of network formation. Under this approach, reaction rates are proportional to the concentration of unreacted functional groups involved in a specific reaction times an associated proportionality constant (the kinetic rate constant). This method can be applied to the examination of different reactor types. It is based on population balances derived from a reaction scheme. An infinite set of mass balance equations will result, one for each polymer chain length present in the reaction system. This leads to ordinary differential or algebraic equations, depending on the reactor type under consideration. This set of equations must be solved to obtain the desired information on polymer distribution, and thus instantaneous and accumulated chain polymer properties can be calculated. In the introductory paragraphs of Section... 

How is the chain length estimated If we define the instantaneous chain length as the ratio between the rate of propagation and rate of termination, we reach an expression for the kinetic degree of polymerization, DP, (equivalent to the number of mers in the chain) as follows ... 

The attractiveness and major advantage of using pulsed lasers in kinetic studies is a result of the short duration of the laser pulse (typically 10 to 20 ns). Opposed to more conventional methods such as rotating sector and spatially intermittent polymerization, the initiation period can now be considered to be instantaneous on the time scale of propagation. As a consequence, all radicals formed in one laser pulse are of approximately the same chain length at any moment in time, which greatly simplifies the kinetic scheme. It is this quality of laser-induced experiments that leads to the reliability of the PLP method to determine kp values (in conjunction with an accurate MWD determination). 

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. 

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