Kinetic scheme of the synthesis of butadiene rubber on a modified lithium catalytic system taking into account its polycentricity

A mathematical simulation of the synthesis of butadiene rubber in a batch reactor under the action of an organolithium catalytic system in the presence of a modifier and with the addition of toluene to a solvent is carried out. A kinetic scheme of the process is proposed and the velocity constants of the elementary stages are determined on the basis of the developed model.


Introducing
One of the most characteristic differences between the processes of anionic and radical polymerization is that even when using initiators that seem to be individual (i.e. formally consisting of a single chemical substance), several forms of active centers (associated and non-associated molecules, solvates of ion pairs of different compositions, free ions, etc.), differing in their reactivity, can simultaneously be present in systems. This circumstance has a significant impact on the kinetics of polymerization processes and the molecular mass characteristics of the resulting polymers. Further, Li and Na (or a bimetallic complex) are designated-M t In the presence of a modifier, the polymerization of butadiene on an organolithium catalytic system is characterized by the first order of reaction according to the concentrations of the monomer and the catalyst and it proceeds without an induction period, so the initiation will be assumed to be instantaneous.
Calculations of molecular mass characteristics and subsequent comparison of the calculated curves with experimental data allow to identify the true mechanism of chain growth, in particular, to establish whether the process takes place at one or several types of active centres, to determine the role of exchange reactions and to estimate kinetic constants.
The next stage of the polymerization is the chain growth reaction (figure 2): An increase in the content of side vinyl groups in the polymer chain leads to the fact that the probability of transfer of chain to the polymer increases significantly. This leads to the formation of branched macromolecules, which has a positive effect on the physical and mechanical characteristics of the resulting rubber, such as viscosity and cold flowability, so it is important to include the chain transfer reaction to the polymer in the kinetic scheme (figure 3).  Figure 3. The chain transfer reaction to the polymer.
Toluene is introduced into the polymerization system to prevent gel formation. When toluene interacts with a "living" polymer chain in the presence of a modifier, a chain transfer reaction to toluene occurs: A) the actual transfer: P ~ CH 2 -CH = CH-CH 2 --Мt + + СH 3 k tТ P ~ CH 2 -CH = CH-CH 3 + СH 2 -Мt + B) the reinitiation: Also, to describe the process of polymerization of butadiene under the action of an organolithium catalytic system in the presence of a modifier, the transfer of a chain to a monomer was considered (figure 4).

Results
The following kinetic scheme is proposed for the mechanism of the polymerization of butadiene on an organolithium catalyst in the presence of a modifier:  Table 1. The kinetic scheme of the mechanism of the polymerization of butadiene on an organolithium catalyst in the presence of a modifier. I is the − initiator concentration, M is the −monomer concentration, S is the toluene concentration, k is the rate constants of the corresponding reactions, R(i, j, l) − is the concentration of macromolecules with i-active centers of the first type, j-active centers of the second type and  −monomeric links.

Stages
Reactions the initiation on the centers of the first type ) , on the centers of the second type the chain transfer to toluene (a) the actual transfer that occurs on the centers of the first type the transfer that occurs on the centers of the second type: the chain transfer to the monomer The exchange of active centers For the first time, the kinetic scheme of butadiene polymerization on a modified lithium-containing catalytic system includes chain transfer reactions to a monomer and a polymer.
According to the kinetic scheme, the system of equations describing the time change in the concentrations of monomer, toluene and growing chains, as well as the exchange of active centers for a periodic isothermal process will be as follows: where  is the molar fraction of active centers of the first type.
Equation (1)   The dependences of the average molecular weights on the conversion of the monomer are determined by the formulas (6): Where m0 is the molecular weight of the monomer link. During the identification, the objective function was selected: As a result of identification and in accordance with the literature data, it turned out that the chain growth reaction mainly occurs at the active centres of the first type. The reactions of chain growth, chain transfer to toluene, monomer and polymer are carried out on the active centres of the second type. Exchange reactions occur between the active centres.
The results of the studies of a process are presented in Figure 4-6. Figure 1 shows the dependence of the conversion on time at different temperatures. There is a regular increase in the slope of the conversion curve with an increase in the temperature of the experiment, which indicates a symmetric dependence of the effective growth constant on temperature.
The following figures show the dependence of the molecular weight characteristics on the conversion, calculated for a single-centre and two-centre model. As a result of the numerical experiment, it was obtained that the two-centre model most adequately describes the process under study in the presence of toluene and a modifier in a batch reactor. For calculations based on the single-center model, a software package was used that was previously developed to describe the process of synthesis of SRDN and SRDC, which took into account the chain transfers to the monomer and polymer.

Conclusion
A two-center mathematical model of the synthesis of butadiene rubber in a batch reactor in the presence of a modified organolithium catalytic system, complicated by chain transfer reactions and exchange reactions between active centers, has been developed. A kinetic scheme of the process is proposed and, based on the developed two-center model, the velocity constants of elementary stages for each type of active centers are determined. Using the method of the generating function, relations were obtained for calculating the moments of the molecular mass distribution of macromolecules by the degree of polymerization and by the number of active centers of each type.