Tatiana Birshtein | Saint Petersburg State University (original) (raw)
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Papers by Tatiana Birshtein
Polymer Science Series A, 2008
ABSTRACT The structure of polymer and polyelectrolyte stars in solution was studied by means of j... more ABSTRACT The structure of polymer and polyelectrolyte stars in solution was studied by means of joint analysis of the results of analytical consideration, allowing for nonlocal effects, and numerical simulation based on the Scheutjens-Fleer self-consistent field approach. A limitation of the theoretical treatment is the assumption that all ends of polymer chains are fixed onto the external surface and its benefit is the possibility of obtaining compact and interpretable results. The Scheutjens-Fleer approach makes it possible to study conformations without introduction of additional limitations. The combination of analytical methods and direct numerical calculation turns out to be especially informative.
Macromolecular Chemistry and Physics, 2002
Macromolecular Theory and Simulations, 2000
ABSTRACT We studied a polymer brush composed of homodisperse end-grafted chains in a binary A-B s... more ABSTRACT We studied a polymer brush composed of homodisperse end-grafted chains in a binary A-B solvent mixture by means of numerical self-consistent-field calculations. The focus is on the case that the solvents have a solubility gap in the bulk phase behavior, and we investigated the system near the bulk binodal. We assume that both solvents are good solvents for the polymer: the monomers of the chains have amphiphilic properties. When the minority solvent B is the better solvent, it is possible to find a preferential uptake of the solvent B. This solvent uptake can either occur in a continuous manner or in a first-order transition. From a wetting perspective, such a stepwise increase in B uptake may be identified as a prewetting step. In this case, however, the step is not necessarily caused by specific interactions with the solid substrate, but it results from an instability in the structure of the polymer brush at intermediate compositions of A and B in the brush. It is not always true that at coexistence the substrate is completely wet by the minority solvent, even when there is a prewetting step. We examine the post-transition solvent uptake up to and beyond the bulk binodal (in the case of partial wetting). The numerical SCF results complement a recent analysis of the same problem by a model of the Alexander-de Gennes type. Both in the numerical and in the analytical models, it is observed that the first-order phase transition is unusual: the polymer chains absorb the better solvent and then suddenly collapse to a very dense sublayer when there is only a small amount of the wetting component.
Macromolecular …, 2010
We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long... more We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force the globule unfolds ...
…, 2010
Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons... more Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons) are studied by means of Scheutjens− Fleer self-consistent field (SF-SCF) modeling and scaling analysis. Limiting cases of minimal and maximal possible losses of ...
Macromolecular …, 1994
Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type AB with antisymmetr... more Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type AB with antisymmetric composition (polymer P1 with A: B= 3: 1 (w/w) and polymer P2 with A: B= 1: 3 (w/w)) and their binary mixture were studied by small-angle X-ray scattering (SAXS) ...
…, 2009
We present results of numerical self-consistent field (SCF) calculations for the equilibrium mech... more We present results of numerical self-consistent field (SCF) calculations for the equilibrium mechanical unfolding of a globule formed by a single flexible polymer chain collapsed in a poor solvent. In accordance with earlier scaling theory and stochastic dynamics ...
Polymers
By using the numerical lattice Scheutjens–Fleer self-consistent field (SF-SCF) method we have stu... more By using the numerical lattice Scheutjens–Fleer self-consistent field (SF-SCF) method we have studied the effect of the restricted flexibility of grafted chains on the structure and mutual interaction of two opposing planar conventional and A-type dipolar brushes. Brushes are immersed in the solvent consisting of chains similar to the grafted ones. The increase of the chain rigidity enhances the segregation of grafted chains in a A-type dipolar brush into two populations: backfolded chains with terminal monomers near the grafting surface and chains with the ends at the brush periphery. The fraction of backfolded chains grows by an increase of the Kuhn segment length. It is shown that two opposite A-type dipolar brushes from semi-rigid chains are attracted to each other at short distances. The attraction becomes more pronounced and begins at larger distances for more rigid chains with the same brush characteristics: polymerization degree, grafting density, and dipole moments of monom...
The journal of physical chemistry. B, Jan 11, 2014
By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generat... more By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generation dendrimer with attached terminal chemically different oligomeric segments is studied theoretically. It is demonstrated that an incompatibility of terminal segments with inner dendrimer units leads to formation of a "hollow" core with reduced polymer density in the dendrimer center. This effect is enhanced with a deterioration in the solvent quality for terminal segments. This observation is in accordance with experimental results and molecular dynamics simulation data for an analogous system. It is established that the main factor determining the hollow core formation is the segregation between inner and terminal units because the main driving force for the effect is the localization of the terminal segments at the dendrimer periphery. The influence of structural parameters of dendrimer such as the number of generations and length of the terminal chain on this effect is als...
Macromolecular Symposia, 2015
ABSTRACT A planar polymer brush of arm-grafted polymer stars subjected to external deformation is... more ABSTRACT A planar polymer brush of arm-grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean-field model of the star brush that takes into account segregation of the brush-forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a “two-step” shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens-Fleer numerical self-consistent field (SF-SCF) approach for free (non-deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF- SCF approach and the developed mean-field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two-population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation.
Macromolecules, 1998
Interaction of brushes oriented face-to-face under compression and subsequent extension is invest... more Interaction of brushes oriented face-to-face under compression and subsequent extension is investigated theoretically. Brushes formed by mesogenic chains with induced stiffness in the liquidcrystalline (LC) state are considered. It is shown that the contact between LC brushes composed of long folds of grafted chains (FLC structure) leads to interpenetration of brushes and to formation of a combined structure. The brushes remain combined under the extension of this structure.
![Research paper thumbnail of Coil-globule type transitions in polymers. 2. Theory of coil-globule transition in linear macromolecules [Erratum to document cited in CA114(22):208164m]](https://attachments.academia-assets.com/66917350/thumbnails/1.jpg)
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Macromolecules, 1976
ABSTRACT
Macromolecular Theory and Simulations, 2001
ABSTRACT An analog of the Alexander-De Gennes box model is used for the theoretical investigation... more ABSTRACT An analog of the Alexander-De Gennes box model is used for the theoretical investigation of an external deformation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory-Huggins parameter χAB = 3.5). The thermodynamics of a polymer in the solvents A and B is described by parameters χA and χB, χA > χB. The brush behavior under deformation is investigated with regard to solvent composition and polymer-solvent interactions. It is shown that in a pre-binodal range of the solvent composition ΦB < ΦB0 in the bulk (here ΦB0 is a binodal value) there is such a value of ΦB = Φ B* that deformation does not affect solvent composition inside the brush. This invariant quantity Φ B*, being a function of only thermodynamic parameters, is independent of the brush characteristics, such as grafting density. It is shown that two types of the first-order phase transitions can arise in the system considered: a compositional phase transition induced by a change in the solvent composition in the bulk, and a deformational phase transition caused by an external deformation of the brush. The value of Φ B* defines a borderline concentration of the admixture in the bulk; the brush behavior in the ranges 00 ⪇ ΦB ⪇ Φ B* and Φ B* ⪇ ΦB < ΦB0 are different. If no compositional phase transition occurs in the system, the deformational phase transition should arise under stretching at Φ B* ⪇ ΦB. If the compositional phase transition exists, it is realized in the range ΦB < Φ B* and causes the deformational phase transition in this concentration range, not only under stretching, but also under compression. Microphase segregation inside the brush is demonstrated for both phase transitions despite overestimation of the brush homogeneity in the box model.
Macromolecular Chemistry and Physics, 1994
Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type A-B with antisymmet... more Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type A-B with antisymmetric composition (polymer PI with A : B = 3 : 1 (w/w) and polymer P2 with A : B = 1 : 3 (w/w)) and their binary mixture were studied by small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) in order to determine the microphase structure. The cylindrical microstructure is confirmed for both copolymers, whereas, in the mixture, both techniques have unambiguously shown that a regular lamellar structure is obtained at the polymer-polymer composition P1 : P2 = 1 : 1 (ratio of the numbers of chains). Qualitatively, the same results are obtained for corresponding systems simulated by the cooperative motion algorithm (CMA). Direct observations of the structure as well as the cooperative structure factors determined in the strong segregation limit for the simulated systems indicated lamellar structures in the blend of composition P1 :P2 = 1 : 1, in contrast to the microfibrillar morphology of the copolymers. The simulation additionally indicated a polymer-polymer microseparation. The experimental and simulation results are compared with theoretical predictions based on the self consistent field theory.
Biopolymers, 1976
ABSTRACT
Biopolymers, 1979
ABSTRACT The general method of obtaining the partition function and thermodynamic characteristics... more ABSTRACT The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.
Biophysical Chemistry, 1974
ABSTRACT
Macromolecular Theory and Simulations, 2004
A novel Brownian dynamics method has been developed to simulate the properties of polymer brushes... more A novel Brownian dynamics method has been developed to simulate the properties of polymer brushes under shear. Simulations of 100 chains with a chain length of 100 segments have been carried out for a range of shear rates. Compared to previous methods there is a substantial saving in computational time as the self-consistent molecular field method has been chosen to calculate the volume interactions between polymer segments. An important criterion for observing significant deformations of the brush is that the chains must be stretched to beyond the Gaussian threshold. Density profiles and end segment distribution functions for the grafted chains have been determined and show a collapse of the brush under shear in a way similar to that in which a brush contracts in a poor solvent. In particular, the free ends of the chains become concentrated in a narrow region at the periphery of the brush. The number of chains that are affected by shear has also been calculated and shows that there is a progressive transmission of shear into the brush. † Institute of Macromolecular Compounds, Russian Academy of Sciences, 31 Bolshoi pr.,
Polymer Science Series A, 2008
ABSTRACT The structure of polymer and polyelectrolyte stars in solution was studied by means of j... more ABSTRACT The structure of polymer and polyelectrolyte stars in solution was studied by means of joint analysis of the results of analytical consideration, allowing for nonlocal effects, and numerical simulation based on the Scheutjens-Fleer self-consistent field approach. A limitation of the theoretical treatment is the assumption that all ends of polymer chains are fixed onto the external surface and its benefit is the possibility of obtaining compact and interpretable results. The Scheutjens-Fleer approach makes it possible to study conformations without introduction of additional limitations. The combination of analytical methods and direct numerical calculation turns out to be especially informative.
Macromolecular Chemistry and Physics, 2002
Macromolecular Theory and Simulations, 2000
ABSTRACT We studied a polymer brush composed of homodisperse end-grafted chains in a binary A-B s... more ABSTRACT We studied a polymer brush composed of homodisperse end-grafted chains in a binary A-B solvent mixture by means of numerical self-consistent-field calculations. The focus is on the case that the solvents have a solubility gap in the bulk phase behavior, and we investigated the system near the bulk binodal. We assume that both solvents are good solvents for the polymer: the monomers of the chains have amphiphilic properties. When the minority solvent B is the better solvent, it is possible to find a preferential uptake of the solvent B. This solvent uptake can either occur in a continuous manner or in a first-order transition. From a wetting perspective, such a stepwise increase in B uptake may be identified as a prewetting step. In this case, however, the step is not necessarily caused by specific interactions with the solid substrate, but it results from an instability in the structure of the polymer brush at intermediate compositions of A and B in the brush. It is not always true that at coexistence the substrate is completely wet by the minority solvent, even when there is a prewetting step. We examine the post-transition solvent uptake up to and beyond the bulk binodal (in the case of partial wetting). The numerical SCF results complement a recent analysis of the same problem by a model of the Alexander-de Gennes type. Both in the numerical and in the analytical models, it is observed that the first-order phase transition is unusual: the polymer chains absorb the better solvent and then suddenly collapse to a very dense sublayer when there is only a small amount of the wetting component.
Macromolecular …, 2010
We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long... more We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force the globule unfolds ...
…, 2010
Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons... more Equilibrium structural properties of polymer brushes formed by dendritic polymer chains (dendrons) are studied by means of Scheutjens− Fleer self-consistent field (SF-SCF) modeling and scaling analysis. Limiting cases of minimal and maximal possible losses of ...
Macromolecular …, 1994
Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type AB with antisymmetr... more Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type AB with antisymmetric composition (polymer P1 with A: B= 3: 1 (w/w) and polymer P2 with A: B= 1: 3 (w/w)) and their binary mixture were studied by small-angle X-ray scattering (SAXS) ...
…, 2009
We present results of numerical self-consistent field (SCF) calculations for the equilibrium mech... more We present results of numerical self-consistent field (SCF) calculations for the equilibrium mechanical unfolding of a globule formed by a single flexible polymer chain collapsed in a poor solvent. In accordance with earlier scaling theory and stochastic dynamics ...
Polymers
By using the numerical lattice Scheutjens–Fleer self-consistent field (SF-SCF) method we have stu... more By using the numerical lattice Scheutjens–Fleer self-consistent field (SF-SCF) method we have studied the effect of the restricted flexibility of grafted chains on the structure and mutual interaction of two opposing planar conventional and A-type dipolar brushes. Brushes are immersed in the solvent consisting of chains similar to the grafted ones. The increase of the chain rigidity enhances the segregation of grafted chains in a A-type dipolar brush into two populations: backfolded chains with terminal monomers near the grafting surface and chains with the ends at the brush periphery. The fraction of backfolded chains grows by an increase of the Kuhn segment length. It is shown that two opposite A-type dipolar brushes from semi-rigid chains are attracted to each other at short distances. The attraction becomes more pronounced and begins at larger distances for more rigid chains with the same brush characteristics: polymerization degree, grafting density, and dipole moments of monom...
The journal of physical chemistry. B, Jan 11, 2014
By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generat... more By using the Scheutjens-Fleer self-consistent field approach, the structure of the fourth-generation dendrimer with attached terminal chemically different oligomeric segments is studied theoretically. It is demonstrated that an incompatibility of terminal segments with inner dendrimer units leads to formation of a "hollow" core with reduced polymer density in the dendrimer center. This effect is enhanced with a deterioration in the solvent quality for terminal segments. This observation is in accordance with experimental results and molecular dynamics simulation data for an analogous system. It is established that the main factor determining the hollow core formation is the segregation between inner and terminal units because the main driving force for the effect is the localization of the terminal segments at the dendrimer periphery. The influence of structural parameters of dendrimer such as the number of generations and length of the terminal chain on this effect is als...
Macromolecular Symposia, 2015
ABSTRACT A planar polymer brush of arm-grafted polymer stars subjected to external deformation is... more ABSTRACT A planar polymer brush of arm-grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean-field model of the star brush that takes into account segregation of the brush-forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a “two-step” shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens-Fleer numerical self-consistent field (SF-SCF) approach for free (non-deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF- SCF approach and the developed mean-field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two-population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation.
Macromolecules, 1998
Interaction of brushes oriented face-to-face under compression and subsequent extension is invest... more Interaction of brushes oriented face-to-face under compression and subsequent extension is investigated theoretically. Brushes formed by mesogenic chains with induced stiffness in the liquidcrystalline (LC) state are considered. It is shown that the contact between LC brushes composed of long folds of grafted chains (FLC structure) leads to interpenetration of brushes and to formation of a combined structure. The brushes remain combined under the extension of this structure.
Macromolecules, 1976
ABSTRACT
Macromolecular Theory and Simulations, 2001
ABSTRACT An analog of the Alexander-De Gennes box model is used for the theoretical investigation... more ABSTRACT An analog of the Alexander-De Gennes box model is used for the theoretical investigation of an external deformation of polymer brushes in a mixture of two solvents. The basic solvent A and the admixture B are assumed to be highly incompatible (Flory-Huggins parameter χAB = 3.5). The thermodynamics of a polymer in the solvents A and B is described by parameters χA and χB, χA > χB. The brush behavior under deformation is investigated with regard to solvent composition and polymer-solvent interactions. It is shown that in a pre-binodal range of the solvent composition ΦB < ΦB0 in the bulk (here ΦB0 is a binodal value) there is such a value of ΦB = Φ B* that deformation does not affect solvent composition inside the brush. This invariant quantity Φ B*, being a function of only thermodynamic parameters, is independent of the brush characteristics, such as grafting density. It is shown that two types of the first-order phase transitions can arise in the system considered: a compositional phase transition induced by a change in the solvent composition in the bulk, and a deformational phase transition caused by an external deformation of the brush. The value of Φ B* defines a borderline concentration of the admixture in the bulk; the brush behavior in the ranges 00 ⪇ ΦB ⪇ Φ B* and Φ B* ⪇ ΦB < ΦB0 are different. If no compositional phase transition occurs in the system, the deformational phase transition should arise under stretching at Φ B* ⪇ ΦB. If the compositional phase transition exists, it is realized in the range ΦB < Φ B* and causes the deformational phase transition in this concentration range, not only under stretching, but also under compression. Microphase segregation inside the brush is demonstrated for both phase transitions despite overestimation of the brush homogeneity in the box model.
Macromolecular Chemistry and Physics, 1994
Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type A-B with antisymmet... more Two cylinder-forming polystyrene-block-polybutadiene block copolymers of type A-B with antisymmetric composition (polymer PI with A : B = 3 : 1 (w/w) and polymer P2 with A : B = 1 : 3 (w/w)) and their binary mixture were studied by small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) in order to determine the microphase structure. The cylindrical microstructure is confirmed for both copolymers, whereas, in the mixture, both techniques have unambiguously shown that a regular lamellar structure is obtained at the polymer-polymer composition P1 : P2 = 1 : 1 (ratio of the numbers of chains). Qualitatively, the same results are obtained for corresponding systems simulated by the cooperative motion algorithm (CMA). Direct observations of the structure as well as the cooperative structure factors determined in the strong segregation limit for the simulated systems indicated lamellar structures in the blend of composition P1 :P2 = 1 : 1, in contrast to the microfibrillar morphology of the copolymers. The simulation additionally indicated a polymer-polymer microseparation. The experimental and simulation results are compared with theoretical predictions based on the self consistent field theory.
Biopolymers, 1976
ABSTRACT
Biopolymers, 1979
ABSTRACT The general method of obtaining the partition function and thermodynamic characteristics... more ABSTRACT The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.
Biophysical Chemistry, 1974
ABSTRACT
Macromolecular Theory and Simulations, 2004
A novel Brownian dynamics method has been developed to simulate the properties of polymer brushes... more A novel Brownian dynamics method has been developed to simulate the properties of polymer brushes under shear. Simulations of 100 chains with a chain length of 100 segments have been carried out for a range of shear rates. Compared to previous methods there is a substantial saving in computational time as the self-consistent molecular field method has been chosen to calculate the volume interactions between polymer segments. An important criterion for observing significant deformations of the brush is that the chains must be stretched to beyond the Gaussian threshold. Density profiles and end segment distribution functions for the grafted chains have been determined and show a collapse of the brush under shear in a way similar to that in which a brush contracts in a poor solvent. In particular, the free ends of the chains become concentrated in a narrow region at the periphery of the brush. The number of chains that are affected by shear has also been calculated and shows that there is a progressive transmission of shear into the brush. † Institute of Macromolecular Compounds, Russian Academy of Sciences, 31 Bolshoi pr.,