S. I. Kuchanov

Principles of the Quantitative Description of the Chemical Structure of Synthetic Polymers

A brief introduction to the statistical chemistry of polymers is provided and the potential applications of this approach for the mathematical modeling of some important processes of the synthesis of high molecular weight compounds are demonstrated. Proceeding from the consideration of the main peculiarities of synthetic polymers, the statistical characteristics of their chemical structure generally used for its quantitative description are indicated. The principle kinetic models of macromolecular reactions currently employed in polymer chemistry are considered. The advantages and disadvantages of different methods applied for the calculation of the composition and chemical structure of macromolecules are discussed. The results of invoking these methods in order to provide a quantitative description of the products of linear chain copolymerization and branched polycondensation are reported.

A correct account of the non-local terms in the Landau theory of phase transitions in polydisperse heteropolymers

The non-local terms previously disregarded in the Landau free energy expansion of a melt of polydisperse heteropolymers are shown to dramatically change the appearance of the phase diagram of a heteropolymer liquid.

Stochastic Branching Process for Description of Non-Random Irreversible Polycondensation

For the first time the possibility of the description of the products of non-random irreversible polycondensation by the theory of branching processes is rigorously substantiated. The formalism of this theory is shown to be efficient in finding any statistical characteristics not only of finite molecules but those of a polymer network as well. Exact equations are derived and their simplified forms are presented for networks being formed in the vicinity of the gel-point. Errors arising under the application of an approximation based on the traditional statistical approach are evaluated proceeding from the analysis of the numerical solutions of these equations.

Nonequilibrium Copolycondensation in Homogeneous Systems

Abstract Copolycondensation is a polycondensation of three or more monomers which under certain process conditions cannot be condensed by themselves. Some systems containing two condensable monomers, such as hydroxy or amino acids, are also thought to be copolycondensation polymers. Since the chains of copolycondensation copolymers contain two or more types of structural units, one can differentiate between them by their degree of polymerization, structure, and composition (microheterogeneity). In copolycondensation, as well as in copolymerization, it is important to relate quantitatively monomer activities and process conditions to the characteristics of the resulting copolymers. Even though this problem was solved 20 years ago [1, 2] in radical polymerization, systematic investigations of quantitative studies have only recently begun on copolycondensation polymers. This can probably be explained by the fact that at different stages of polycondensation investigation, largely equilibrium processes were st...

Copolymers with designed proteinlike sequences obtained by polymeranalogous transformations of homopolymer globules

In this paper we consider one of the ways to obtain HP-copolymers with specially designed “proteinlike” sequences such that in the dense globular conformation all the hydrophobic H-units form the core of this globule, while polar P-units constitute the envelope of this core. Namely, we assume that some low molecular reagent Z is added to the dilute solution of homopolymer H-globules and that it induces a polymeranalogous reaction H+Z→P. We present the full theoretical analysis of the macrokinetics of the corresponding chemical reaction and show that at a certain interrelation between the diffusion coefficient of the reagent Z and the constant of the chemical reaction it is possible to end up with a copolymer chain with proteinlike statistics in the sense described above. We analyze the statistical properties of the sequences in resulting copolymer chains for the general case. Also we consider the scattering properties and spinodal of the melts of these chains.

Statistical Thermodynamics of Copolymers and their Blends

Unlike homopolymers, heteropolymers consist of macromolecules comprising more than one type of elementary unit. Any sample of a synthetic heteropolymer represents a mixture of an enormous (practically infinite) number of different individual chemical compounds. Even at the same degree of polymerization l the molecules vary in chemical composition and structure, i.e. in the fractions of units of different types and in the pattern of their arrangement. The number of conceivable isomers grows exponentially with l and for actual polymers essentially exceeds the Avogadro number. This is why it is impossible in principle to characterize a sample of such a polymer by setting the concentrations of individual chemical compounds because the vast majority of them will be represented by no more than a single macromolecule. There is a fundamental difference between this situation and that of homopolymers, where the number of molecules with any l in a sample is large enough to provide an adequate macroscopic description in terms of concentrations of homologues (l-mers). Consequently, polydisperse homopolymers and their blends can be described using traditional thermodynamics, although with a nominally infinite number of components which are homologues. Such a consideration, in view of the argument outlined above, fails in the case of heteropolymers so that when developing a rigorous thermodynamic theory of their solutions, alloys, and blends it is necessary to use nontraditional approaches.

Application of iniferters for obtaining composition homogenous copolymers

SummaryAn original way of reducing composition heterogeneity has been proposed for copolymers obtained at high conversions. The main idea underlying this method consists in application as initiators of special compounds (iniferters) leading to alteration of the mechanism of polymer chain growth.

A mathematical problem of the theory of gelation

Current theory of gelation describes this process in terms of a set of nonlinear integral equations. In this article the uniqueness of nontrivial solutions of these equations within the unit functional hypercube has been proved. Besides, the convergence to this solution of iterations from an arbitrary point of the above hypercube has been established, which is of utmost importance for calculations of particular gelation processes.

Bifurcation analysis for the construction of a phase diagram of heteropolymer liquids

Rather general mean field theory of heteropolymer liquids developed earlier reduces the problem of the phase diagram construction to the determination of extremals of the free energy functional. These should be subsequently analyzed for their local and global stability. Tackling of this problem traditionally involves the examination of the behavior of the solutions of a set of nonlinear algebraic and partial differential equations at various values of the control parameters. Besides, the necessity arises here to construct in space of these parameters the lines where a polymer system loses the thermodynamic stability. To overcome mathematical difficulties encountered we employed a complex approach that combines analytical and numerical methods. A two-step procedure constitutes the essence of such an approach. First, the bifurcation analysis is invoked to find the asymptotics of the extremals in the vicinity of bifurcation points. Then these asymptotics are used as an initial approximation for the numerical...

Molecular theory of solutions and blends of heteropolymers. I. Thermodynamics of amorphous multicomponent polymer systems

On the basis of a variational principle a quantitative theory is developed enabling a thermodynamic description in terms of mean field approximation of heteropolymer mixtures of macromolecules with an arbitrary distribution for both degree of polymerization and composition. Rather simple general equations are derived to calculate compositions and volume fractions of spatially homogeneous macroscopic phases as well as to find the cloud-point curve, spinodal, and critical points. Potentialities of general theory are illustrated for copolymers synthesized by traditional methods.