Construction and investigation of the computer model of distribution of the composition of products from equilibrium condensation telomomerization
DOI:
https://doi.org/10.15587/1729-4061.2019.161858Keywords:
equilibrium condensation telomerization, nonlinear algebraic equations, computer simulation, composition of oligomersAbstract
Based on the mechanism of the course of polycondensation, we have built a scheme of reaction for the equilibrium condensation telomerization as a polycondensation process whose chain is disrupted by a monofunctional telogen chain. Given this scheme, we constructed the material balance equations for structural elements, which include an infinite number of terms. If a Flory principle about equal reactivity of terminal groups is fulfilled, the infinite sums represent geometric progressions with the same denominator. This makes it possible to collapse the process model into a closed system of four non-linear algebraic equations.
Our research into properties of the model that involved mathematical analysis and computer experiments has established the following:
– the distribution of telomerization products is a superposition of geometric distributions of base structural components with the same denominator of progression, but different magnitudes of starting concentrations. A Flory distribution for homopolycondensation can be considered as a special case of this distribution;
– the system of model’s equations can have up to 4 real roots. At a single solution to the system with a random selection of initial approximation, ~74 % of cases yield a false positive root. To verify the validity of the root, we have developed a criterion based on the magnitude of denominator in a converging geometric progression, and proposed a procedure of computer solution to the system, making it possible to find the true root;
– the model has been found to demonstrate regularities in the influence of reactants concentration on the composition of an equilibrium mixture at a constant concentration of the low-molecular by-side product of condensation. It is shown that when this concentration tends to zero the composition ceases to depend on the values for equilibrium constants.
The constructed model makes it possible to calculate a composition of the equilibrium mixture of oligomers depending on the ratio of monomer concentrations, telogen, and a low-molecular condensation product. That makes it useful in practice for preliminary quantifying the composition of equilibrium mixtures of oligomers when planning syntheses using a method of condensation telomerizationReferences
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Copyright (c) 2019 Serhei Kondratov, Yuliia Yevtushenko, Julia Kravchenko
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