Elena Govorun | Lomonosov Moscow State University (original) (raw)
Papers by Elena Govorun
Polymer Science, Series A, 2020
A relaxation model for the structure ripening under annealing of a microphase-separated polymer f... more A relaxation model for the structure ripening under annealing of a microphase-separated polymer film has been developed. Equations have been derived that describe the appearance and annihilation of defects in the kinetically controlled mode based on the experimental data on the hexagonal structure evolution. Using that equations, the time dependences of the defect-free area size have been analyzed. It has been found that the predominance of the defect annihilation upon their triple contact leads to the power-law dependence of the orientation correlation length ξ or ~ t 1/4 , which is observed experimentally at high annealing temperatures. A more detailed analysis of the evolution of two types of defects (dislocations and disclinations) shows that this dependence can also be realized in a model that takes into account the annihilation of disclination pairs and quadruples providing that dislocations influence this process. The results demonstrate that macrokinetic models can describe structural rearrangements in block copolymer films.
Comptes Rendus Chimie, 2006
Interchain interactions affect both reactivity and mobility of macromolecules and hence influence... more Interchain interactions affect both reactivity and mobility of macromolecules and hence influence such processes as interdiffusion and phase separation. Three types of reactions in polymer blends proceeding without participation of low molecular reagents and leading to different kinds of copolymers are considered. For polymeranalogous reaction leading to statistical copolymers, the evolution of the blend structure under concerted action of the
Polymer, 2018
The morphological diagrams of H-graft-P macromolecules in poor solvent were evaluated by means of... more The morphological diagrams of H-graft-P macromolecules in poor solvent were evaluated by means of molecular dynamics simulations and analytical theory. The Diagrams contain regions of spherical solid, onion-like and vesicle particles, domains of elongated (disc-like, torus, and worm-like) structures, and the area with necklace and coil conformations. The diversity of different morphologies is a result of surface activity of monomer units leading to formation of surface-rich structures and outward orientation of polar groups at the surface. The shape depends on the macromolecule length, solvent quality and monomer unit characteristics. The Diagrams were constructed basing on the visual analysis and on the calculations of shape factors and aggregation numbers, and evaluated by the original analytical theory, where the interplay of bulk and surface effects determines the globule shape.
Langmuir, 2017
The properties of surfaces with grafted macromolecules are determined by a fine structure of the ... more The properties of surfaces with grafted macromolecules are determined by a fine structure of the macromolecular layer, whereas the mixtures of macromolecules with surfactants are very rich in structure types. Using the scaling mean-field theory, we consider the self-assembly in polymer brushes into various patterns induced by interactions with low-molecular surfactants. The interaction energies of the parts of a surfactant molecule with the polymer units are assumed to be greatly different. With increasing the grafting density, the formation of lamellae perpendicular to the grafting plane, continuous layer with oblong or round pores, or homogeneous brush is predicted. The driving force of the pattern formation is a gain in the interaction energy of surfactant molecules oriented at the lateral surfaces of lamellae or pores. The process of pore formation in a homogeneous brush caused by a temperature change at definite grafting densities is described as the first-order phase transition. It is accompanied by a step-wise extension of the brush and by orientational ordering of surfactant molecules. The transitions between the other patterns are of the second order. The thickness of lamellae and the distance between pores are approximately twice the surfactant molecule size except for the extremely high grafting densities. The diagrams of brush patterns are presented and discussed.
Polymer Reviews, 2019
Amphiphilic monomer units contain both hydrophobic and hydrophilic groups. They are characterized... more Amphiphilic monomer units contain both hydrophobic and hydrophilic groups. They are characterized by affinity and antagonism simultaneously to both polar and nonpolar solvents, tend to settle themselves at solvent interfaces rather than in the bulk of the solvent and, thus, possess effective surface activity. For this reason, in selective solvents the macromolecules with amphiphilic monomer units self-assemble to complex morphologies with enlarged surface which could be similar to those formed by low-molecular surfactants, lipids and amphiphilic diblock-copolymers. In literature, macromolecules with amphiphilic monomer units are also referred to as polymer amphiphiles. When they consist of identical amphiphilic monomer units, they are called amphiphilic homopolymers. The article aims to review the macromolecular self-assembly driven by amphiphilicity of monomer units containing both solvophobic and solvophilic (hydrophobic and hydrophilic) groups. The particular attention is paid to the situation when such macromolecules assemble into the hollow and vesicle-like particles being especially prospective for different applications. We present the current state of experimental, computational and analytical research in this field and reveal the conditions favoring the formation of vesicles with thin (mono-, bi-or multilayer) membranes.
Journal of Physics: Condensed Matter
Thermoresponsive polymers are usually characterized by a locally amphiphilic chain structure and ... more Thermoresponsive polymers are usually characterized by a locally amphiphilic chain structure and their self-assembly in solution is controlled, in particular, by the surface activity of the monomer units or side chains. We theoretically study the condensed state of a single diblock copolymer molecule consisting of a hydrophobic block and amphiphilic block with hydrophobic groups in the backbone and pendant polar groups. The equilibrium parameters of the polymer globules of different shapes are determined using the mean-field approach to determine the most favorable structure. Morphological diagrams of condensed macromolecules are presented depending on the chain length, amphiphilic block fraction, interaction parameters, and pendant volume and length. The diagrams are compared with those of a copolymer molecule with the same fraction of amphiphilic monomer units which are regularly distributed along the chain. The diblock copolymer molecule is found to form a single spherical or fla...
Conformation-dependent design of polymer sequences can be considered as a tool to control macromo... more Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling, the probability distributions of block length k being calculated. The problem is similar to that of gambler’s ruin and first passage time in probability theory but the consideration is generalized to 3D and the domains of different shapes are considered. In any domain, the probability distribution can be described by the asymptote ∼k −3/2 at moderate values of k if the s...
The Journal of Chemical Physics
Microphase separation in random multiblock copolymers is studied with mean-field theory assuming ... more Microphase separation in random multiblock copolymers is studied with mean-field theory assuming that long blocks of a copolymer are strongly segregated, whereas short blocks are able to penetrate into "alien" domains and exchange between the domains and interfacial layer. A bidisperse copolymer with blocks of only two sizes (long and short) is considered as a model of multiblock copolymers with high polydispersity in the block size. Short blocks of the copolymer play an important role in microphase separation. First, their penetration into the "alien" domains leads to the formation of joint long blocks in their own domains. Second, short blocks localized at the interface considerably change the interfacial tension. The possibility of penetration of short blocks into the "alien" domains is controlled by the product χN sh (χ is the Flory-Huggins interaction parameter, N sh is the short block length). At not very large χN sh , the domain size is larger than that for a regular copolymer consisting of the same long blocks as in the considered random copolymer. At a fixed mean block size, the domain size grows with an increase in the block size dispersity, the rate of the growth being dependent of the more detailed parameters of the block size distribution.
Soft Matter
Amphiphilic polymer blocks can envelop the domains of major non-amphiphilic blocks in diblock cop... more Amphiphilic polymer blocks can envelop the domains of major non-amphiphilic blocks in diblock copolymer melts: a theoretical study.
Polymer Science, Series A
Polymer Science, Series C
The European Physical Journal E - Soft Matter, 2004
A new modification of evolutionary approach to sequence design of copolymers has been proposed. A... more A new modification of evolutionary approach to sequence design of copolymers has been proposed. A model of step-by-step evolution of a two-letter (HP) copolymer sequence has been studied by means of a coarse-grained Monte Carlo algorithm. The conditions for accepting a change in the primary sequence depend on the spatial conformation of HP-copolymer chain. This leads to a coupling between sequence and conformation and to formation of protein-like conformations and primary sequences (for some values of parameters of the model) independently of initial sequence and/or conformation. Simple theory describing these computer simulation observations is developed.
The European Physical Journal E Soft Matter, Dec 1, 2006
The compositional relaxation in random copolymer systems on a macroscopic scale is considered in ... more The compositional relaxation in random copolymer systems on a macroscopic scale is considered in theory. A set of diffusion equations is derived that describes the motion of chains of different composition and then converted into coupled equations for statistical moments of the compositional distribution. Several ways to solve the closure problem for these equations are discussed. The simplest is the situation when the shape of the transient compositional distribution can be predicted a priori, for example, a bimodal distribution is kept during interdiffusion of two copolymers that are not very close in composition. For a general case, it is shown that the cumulant-neglect closure based on the truncation of high-order cumulants is an effective method to get an approximate solution in terms of the time-dependent local mean composition and its dispersion. This method is applied to non-homogeneous compatible polymer systems, such as a random copolymer AB of a composition varying in space, a bilayer of Bernoullian copolymers AB of different composition, and a bilayer of homopolymers A and B, in which an autocatalytic polymer-analogous reaction A → B takes place, with possibility of the neighbor group effect. It is found that the interdiffusion can lead to a substantial broadening of the local compositional distribution, which, in turn, accelerates the system dynamics and promotes chemical reactions.
The Journal of Chemical Physics
ABSTRACT
Polymer Science Series A
The problem of growth of a single spherical particle of the disperse phase under the phase separa... more The problem of growth of a single spherical particle of the disperse phase under the phase separation conditions in a homopolymer A-homopolymer B-diblock copolymer AB blend was considered. The particle growth was assumed to proceed in a finite-size region by diffusion of chains dissolved in the continuous phase. An equation for the time variation of the particle radius was obtained under the assumption that the copolymer chains captured by the particle growing from the homogeneous blend are uniformly distributed over the particle surface. The stabilizing effect of the diblock copolymer was studied numerically. The effect of finite size of the system on the particle growth was considered. It was shown that the particle must lose spherical shape when a certain size is attained.
Polymer Science Series A
A new approach was developed to the theory of polymer-analogous transformations in a compositiona... more A new approach was developed to the theory of polymer-analogous transformations in a compositionally inhomogeneous polymer blend. Diffusion equations describing the evolution of blend composition were derived for an arbitrary distribution of units in the chains of a copolymer produced in the course of reaction. The calculation of the free energy of the blend was shown to be much simplified by using information entropy. As an example, an expression for the free energy was obtained in terms of variables describing a distribution of triads of various types in the reacting chains.
Polymer Science Series A
The competition of spinodal decomposition and interchain exchange reaction in a melt of a Markov ... more The competition of spinodal decomposition and interchain exchange reaction in a melt of a Markov multiblock AB copolymer is theoretically studied. The stability region of the homogeneous system state is determined depending on the blockiness parameter, which changes in the course of the reaction. Within the random phase approximation, equations for the structural factor are derived; they describe the linear stage of the spinodal decomposition. The compatibilizing effect of the exchange reaction is studied via numerical solution of these equations. The region of unstable fluctuations is found to be narrowed during the reaction as (const − t)^1/2, whereas the characteristic inhomogeneity size increases as ~ exp(const t). As is shown, the polydispersity of the chain length significantly delays phase separation in the polymer blend even in the absence of a chemical reaction.
Polymer Science, Series A, 2020
A relaxation model for the structure ripening under annealing of a microphase-separated polymer f... more A relaxation model for the structure ripening under annealing of a microphase-separated polymer film has been developed. Equations have been derived that describe the appearance and annihilation of defects in the kinetically controlled mode based on the experimental data on the hexagonal structure evolution. Using that equations, the time dependences of the defect-free area size have been analyzed. It has been found that the predominance of the defect annihilation upon their triple contact leads to the power-law dependence of the orientation correlation length ξ or ~ t 1/4 , which is observed experimentally at high annealing temperatures. A more detailed analysis of the evolution of two types of defects (dislocations and disclinations) shows that this dependence can also be realized in a model that takes into account the annihilation of disclination pairs and quadruples providing that dislocations influence this process. The results demonstrate that macrokinetic models can describe structural rearrangements in block copolymer films.
Comptes Rendus Chimie, 2006
Interchain interactions affect both reactivity and mobility of macromolecules and hence influence... more Interchain interactions affect both reactivity and mobility of macromolecules and hence influence such processes as interdiffusion and phase separation. Three types of reactions in polymer blends proceeding without participation of low molecular reagents and leading to different kinds of copolymers are considered. For polymeranalogous reaction leading to statistical copolymers, the evolution of the blend structure under concerted action of the
Polymer, 2018
The morphological diagrams of H-graft-P macromolecules in poor solvent were evaluated by means of... more The morphological diagrams of H-graft-P macromolecules in poor solvent were evaluated by means of molecular dynamics simulations and analytical theory. The Diagrams contain regions of spherical solid, onion-like and vesicle particles, domains of elongated (disc-like, torus, and worm-like) structures, and the area with necklace and coil conformations. The diversity of different morphologies is a result of surface activity of monomer units leading to formation of surface-rich structures and outward orientation of polar groups at the surface. The shape depends on the macromolecule length, solvent quality and monomer unit characteristics. The Diagrams were constructed basing on the visual analysis and on the calculations of shape factors and aggregation numbers, and evaluated by the original analytical theory, where the interplay of bulk and surface effects determines the globule shape.
Langmuir, 2017
The properties of surfaces with grafted macromolecules are determined by a fine structure of the ... more The properties of surfaces with grafted macromolecules are determined by a fine structure of the macromolecular layer, whereas the mixtures of macromolecules with surfactants are very rich in structure types. Using the scaling mean-field theory, we consider the self-assembly in polymer brushes into various patterns induced by interactions with low-molecular surfactants. The interaction energies of the parts of a surfactant molecule with the polymer units are assumed to be greatly different. With increasing the grafting density, the formation of lamellae perpendicular to the grafting plane, continuous layer with oblong or round pores, or homogeneous brush is predicted. The driving force of the pattern formation is a gain in the interaction energy of surfactant molecules oriented at the lateral surfaces of lamellae or pores. The process of pore formation in a homogeneous brush caused by a temperature change at definite grafting densities is described as the first-order phase transition. It is accompanied by a step-wise extension of the brush and by orientational ordering of surfactant molecules. The transitions between the other patterns are of the second order. The thickness of lamellae and the distance between pores are approximately twice the surfactant molecule size except for the extremely high grafting densities. The diagrams of brush patterns are presented and discussed.
Polymer Reviews, 2019
Amphiphilic monomer units contain both hydrophobic and hydrophilic groups. They are characterized... more Amphiphilic monomer units contain both hydrophobic and hydrophilic groups. They are characterized by affinity and antagonism simultaneously to both polar and nonpolar solvents, tend to settle themselves at solvent interfaces rather than in the bulk of the solvent and, thus, possess effective surface activity. For this reason, in selective solvents the macromolecules with amphiphilic monomer units self-assemble to complex morphologies with enlarged surface which could be similar to those formed by low-molecular surfactants, lipids and amphiphilic diblock-copolymers. In literature, macromolecules with amphiphilic monomer units are also referred to as polymer amphiphiles. When they consist of identical amphiphilic monomer units, they are called amphiphilic homopolymers. The article aims to review the macromolecular self-assembly driven by amphiphilicity of monomer units containing both solvophobic and solvophilic (hydrophobic and hydrophilic) groups. The particular attention is paid to the situation when such macromolecules assemble into the hollow and vesicle-like particles being especially prospective for different applications. We present the current state of experimental, computational and analytical research in this field and reveal the conditions favoring the formation of vesicles with thin (mono-, bi-or multilayer) membranes.
Journal of Physics: Condensed Matter
Thermoresponsive polymers are usually characterized by a locally amphiphilic chain structure and ... more Thermoresponsive polymers are usually characterized by a locally amphiphilic chain structure and their self-assembly in solution is controlled, in particular, by the surface activity of the monomer units or side chains. We theoretically study the condensed state of a single diblock copolymer molecule consisting of a hydrophobic block and amphiphilic block with hydrophobic groups in the backbone and pendant polar groups. The equilibrium parameters of the polymer globules of different shapes are determined using the mean-field approach to determine the most favorable structure. Morphological diagrams of condensed macromolecules are presented depending on the chain length, amphiphilic block fraction, interaction parameters, and pendant volume and length. The diagrams are compared with those of a copolymer molecule with the same fraction of amphiphilic monomer units which are regularly distributed along the chain. The diblock copolymer molecule is found to form a single spherical or fla...
Conformation-dependent design of polymer sequences can be considered as a tool to control macromo... more Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with the spatial positions of the monomer units. The geometrical patterns of lamellae, hexagonally packed cylinders, and balls arranged in a body-centered cubic lattice are considered as typical microphase-separated morphologies of block copolymers. Random trajectories of polymer chains are described by the diffusion-type equations and, in parallel, simulated in the computer modeling, the probability distributions of block length k being calculated. The problem is similar to that of gambler’s ruin and first passage time in probability theory but the consideration is generalized to 3D and the domains of different shapes are considered. In any domain, the probability distribution can be described by the asymptote ∼k −3/2 at moderate values of k if the s...
The Journal of Chemical Physics
Microphase separation in random multiblock copolymers is studied with mean-field theory assuming ... more Microphase separation in random multiblock copolymers is studied with mean-field theory assuming that long blocks of a copolymer are strongly segregated, whereas short blocks are able to penetrate into "alien" domains and exchange between the domains and interfacial layer. A bidisperse copolymer with blocks of only two sizes (long and short) is considered as a model of multiblock copolymers with high polydispersity in the block size. Short blocks of the copolymer play an important role in microphase separation. First, their penetration into the "alien" domains leads to the formation of joint long blocks in their own domains. Second, short blocks localized at the interface considerably change the interfacial tension. The possibility of penetration of short blocks into the "alien" domains is controlled by the product χN sh (χ is the Flory-Huggins interaction parameter, N sh is the short block length). At not very large χN sh , the domain size is larger than that for a regular copolymer consisting of the same long blocks as in the considered random copolymer. At a fixed mean block size, the domain size grows with an increase in the block size dispersity, the rate of the growth being dependent of the more detailed parameters of the block size distribution.
Soft Matter
Amphiphilic polymer blocks can envelop the domains of major non-amphiphilic blocks in diblock cop... more Amphiphilic polymer blocks can envelop the domains of major non-amphiphilic blocks in diblock copolymer melts: a theoretical study.
Polymer Science, Series A
Polymer Science, Series C
The European Physical Journal E - Soft Matter, 2004
A new modification of evolutionary approach to sequence design of copolymers has been proposed. A... more A new modification of evolutionary approach to sequence design of copolymers has been proposed. A model of step-by-step evolution of a two-letter (HP) copolymer sequence has been studied by means of a coarse-grained Monte Carlo algorithm. The conditions for accepting a change in the primary sequence depend on the spatial conformation of HP-copolymer chain. This leads to a coupling between sequence and conformation and to formation of protein-like conformations and primary sequences (for some values of parameters of the model) independently of initial sequence and/or conformation. Simple theory describing these computer simulation observations is developed.
The European Physical Journal E Soft Matter, Dec 1, 2006
The compositional relaxation in random copolymer systems on a macroscopic scale is considered in ... more The compositional relaxation in random copolymer systems on a macroscopic scale is considered in theory. A set of diffusion equations is derived that describes the motion of chains of different composition and then converted into coupled equations for statistical moments of the compositional distribution. Several ways to solve the closure problem for these equations are discussed. The simplest is the situation when the shape of the transient compositional distribution can be predicted a priori, for example, a bimodal distribution is kept during interdiffusion of two copolymers that are not very close in composition. For a general case, it is shown that the cumulant-neglect closure based on the truncation of high-order cumulants is an effective method to get an approximate solution in terms of the time-dependent local mean composition and its dispersion. This method is applied to non-homogeneous compatible polymer systems, such as a random copolymer AB of a composition varying in space, a bilayer of Bernoullian copolymers AB of different composition, and a bilayer of homopolymers A and B, in which an autocatalytic polymer-analogous reaction A → B takes place, with possibility of the neighbor group effect. It is found that the interdiffusion can lead to a substantial broadening of the local compositional distribution, which, in turn, accelerates the system dynamics and promotes chemical reactions.
The Journal of Chemical Physics
ABSTRACT
Polymer Science Series A
The problem of growth of a single spherical particle of the disperse phase under the phase separa... more The problem of growth of a single spherical particle of the disperse phase under the phase separation conditions in a homopolymer A-homopolymer B-diblock copolymer AB blend was considered. The particle growth was assumed to proceed in a finite-size region by diffusion of chains dissolved in the continuous phase. An equation for the time variation of the particle radius was obtained under the assumption that the copolymer chains captured by the particle growing from the homogeneous blend are uniformly distributed over the particle surface. The stabilizing effect of the diblock copolymer was studied numerically. The effect of finite size of the system on the particle growth was considered. It was shown that the particle must lose spherical shape when a certain size is attained.
Polymer Science Series A
A new approach was developed to the theory of polymer-analogous transformations in a compositiona... more A new approach was developed to the theory of polymer-analogous transformations in a compositionally inhomogeneous polymer blend. Diffusion equations describing the evolution of blend composition were derived for an arbitrary distribution of units in the chains of a copolymer produced in the course of reaction. The calculation of the free energy of the blend was shown to be much simplified by using information entropy. As an example, an expression for the free energy was obtained in terms of variables describing a distribution of triads of various types in the reacting chains.
Polymer Science Series A
The competition of spinodal decomposition and interchain exchange reaction in a melt of a Markov ... more The competition of spinodal decomposition and interchain exchange reaction in a melt of a Markov multiblock AB copolymer is theoretically studied. The stability region of the homogeneous system state is determined depending on the blockiness parameter, which changes in the course of the reaction. Within the random phase approximation, equations for the structural factor are derived; they describe the linear stage of the spinodal decomposition. The compatibilizing effect of the exchange reaction is studied via numerical solution of these equations. The region of unstable fluctuations is found to be narrowed during the reaction as (const − t)^1/2, whereas the characteristic inhomogeneity size increases as ~ exp(const t). As is shown, the polydispersity of the chain length significantly delays phase separation in the polymer blend even in the absence of a chemical reaction.