Mathematical Description of the Kinetics of the Heterophase Macromolecular Reaction of Hydrazidation of Grafted Polyglycidyl Methacrylate

Abstract

Hydrazidation of a grafted copolymer of polycaproamide and polyglycidyl methacrylate was mathematically modeled by solving the diffusion equation with a boundary condition in the form of a flow.At present, an important role in the environment protection is played by sorption-active polymeric materials, including those in the fibrous form [1,2]. However, only two kinds of chemisorption fibers are manufactured industrially (TsM-A2 and Mtilon-1) and the VION-KN fiber is produced at a pilot plant. Other types of fibrous chemisorbents are manufactured as one-time pilot batches. Of fundamental importance for the functioning of modern industrial processes used to manufacture chemisorption fibers is mathematical modeling, which makes it possible to create reliable systems for the control techniques being developed. In this context, the aim of this study was to construct a mathematical model of the heterophase macromolecular reaction in which a special class of branched polymers-grafted copolymers of polycaproamide (PCA) and polyglycidyl methacrylate (PGMA), undergoes hydrazidation, in order to solve the problem of optimization of the process for production of fibrous chemisorption materials with predictable sorption properties.Among the known ways to obtain chemisorption fibers, the method based on the graft polymerization and chemical transformation in the polymer chains is the most promising [3]. This is because modification of a finished fiber is a simpler technological process, compared with that in which fibrous chemisorbents are obtained by synthesis of copolymers with functionally active groups and then fibers are formed. Owing to the distribution of sorption-active groups in the surface layers of the fiber, the sorbent has good mechanical properties and the highly developed specific surface area provides high rates of mass-exchange processes. The wide diversity of forms of fibrous sorption materials enables their efficient technological implementation in sorption processes [4].Previously, the modified quasi-stationary method (MQM) has been used for mathematical analysis of the occurring processes in studying the fundamental aspects of the kinetics of polymer-analogous transformations of grafted PGMA under the action of sulfur-containing compounds (thiourea and potassium thiocyanate) [5] and diamines (ethylenediamine and hexamethyldiamine) [6]. As this method is based on a simple summation of the kinetic and diffusion resistances, it can only be regarded as a simplified mathematical model, whose disagreement with the experiment may be as wide as 15% [7]. Therefore, a more precise mathematical kinetic model derived by analytical solution of the equation of isotropic diffusion [8] was adopted in the present study.The interaction between the oxirane groups of a grafted PCA3PGMA copolymer and hydrazine hydrate underlies the method for production of the POLAN-OG chemisorption fiber having a high sorption capacity and good sorption kinetics [9]. The macrokinetics of this interaction was described by solving the equation...

Sorptive polymers based on modified fibers

“…The principles for regulating the preparation processes of chemically sorptive fibers were formulated based on mathematical modeling of the macrokinetics of chemical reactions in grafted polymer chains using a modified quasisteady-state method and a solution of the differential equation for isotropic diffusion with a boundary condition in the form of a flux [16,17]. Analytical equations enabling the synthesis of sorptive polybases to be predicted were found.…”

Modified polymeric materials, some fundamental and applied aspects

“…Mathematical modeling of the macrokinetics of the chemical processes (quasi-steady-state, modified quasisteady-state, and solution of the exact diffusion equation with a boundary condition in the form of a flux) has been carried out [5]. The principles controlling the preparation of actively absorbent fibers, the process technology, and the technical regulatory documentation that were required to organize the production of actively absorbent fibers based on grafted copolymers and that were proven experimentally could be developed.…”