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Aliev M.A.,Institute of Biochemical Physics | Kuzminyh N.Y.,Institute of Biochemical Physics
Physica A: Statistical Mechanics and its Applications | Year: 2011

A two or more chemically different homopolymers attached to a single junction point form a macromolecule of miktoarm star copolymer. The model of such copolymer composed of an arbitrary number of types of homopolymer arms is considered. The lengths distributions of arms are assumed to be arbitrary, provided that average length of an each arm is long enough. The algorithm is suggested to find the contributions into the Landau free energy of this copolymer melt which are necessary to obtain a phase diagram in weak segregation regime. Using this algorithm the contributions are found up to the fourth order. The phase diagrams have been constructed for the simple model of AB 2 copolymer melt whose macromolecules consist of polydisperse A-block and two monodisperse B-blocks. © 2011 Elsevier B.V. All rights reserved.


Aliev M.A.,Institute of Biochemical Physics
Modern Physics Letters B | Year: 2015

The analytical expressions have been obtained to describe the dependence of spinodal curve at which isotropic state of polydisperse melt of semiflexible diblock copolymer becomes unstable with respect to formation of nematic state on the polydispersity indices of the blocks, parameters of anisotropic interactions, and flexibility of blocks. The flexibility of blocks is taken into account within discrete worm-like chain model, lengths of blocks are assumed to be distributed by the Schulz-Zimm distribution. It is shown that increase of degree of polydispersity of blocks yields the increase of nematic spinodal temperature. © 2015 World Scientific Publishing Company.


Zabrodin A.,Institute of Biochemical Physics
Journal of Geometry and Physics | Year: 2011

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ℓ and -ℓ-1 are constructed using the technique of intertwining vectors for elliptic L-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W-operators) serve as building blocks for the elliptic R-matrix which intertwines tensor product of two L-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang-Baxter equation for this R-matrix follows from simpler equations of the star-triangle type for the W-operators. A natural graphic representation of the objects and equations involved in the construction is used. © 2011 Elsevier B.V.


Aliev M.A.,Institute of Biochemical Physics
Molecular Physics | Year: 2016

The isotropic-to-nematic phase transition in a melt of semi-flexible homopolymers with length polydispersity have been considered within the Landau–de Gennes approach. The number of monomer units in chain is assumed to be a random variable distributed by the Schulz–Zimm distribution; the stiffness of macromolecules has been taken into account within discrete worm-like chain model. It was found that increase of polydispersity yields the increase of the temperature of the isotropic–nematic transition. © 2016 Taylor & Francis


Aliev M.A.,Institute of Biochemical Physics | Kuzminyh N.Y.,Institute of Biochemical Physics
Journal of Chemical Physics | Year: 2015

The stability limits of the isotropic state of melt of rod-rod AB polydisperse diblock copolymer have been studied within weak segregation theory. The number of units in A block is assumed to be a random variable distributed by the Schulz-Zimm distribution. Inspection of the spinodal curves shows that the copolymer melt with polydisperse rigid blocks is less stable with respect to formation of the nematic and microphase separated states than the monodisperse melt. The values of ratios between strengths of isotropic and anisotropic interactions in the system strongly influences the forms of isotropic-nematic boundary curves. © 2015 AIP Publishing LLC.


Aliev M.A.,Institute of Biochemical Physics | Yu Kuzminykh N.,Institute of Biochemical Physics
International Journal of Modern Physics B | Year: 2013

The phase behavior of the polydisperse An+1Bn multigraft copolymer melt is considered in a framework of weak segregation theory. The phase diagrams of melt are constructed within first harmonics approximation for two special cases: (i) lengths of backbone subchains between successive grafting points in each macromolecule are distributed according to the Schultz-Zimm distribution whereas lengths of side chains are fixed and (ii) both lengths of backbone subchains and side chains are distributed according to the same Schultz-Zimm distribution. The regions of stability of LAM, HEX and BCC mesophases in phase diagrams deform considerably as compared with the case of monodisperse graft copolymer. For both the cases the mean field phase diagrams indicate that order-disorder transition temperature grows as polydispersity index increases. © 2013 World Scientific Publishing Company.


Zabrodin A.,Institute of Biochemical Physics
Complex Analysis and Operator Theory | Year: 2010

The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms of free fermionic operators. This representation provides an explicit identification of the partition function with a tau-function of the 2D Toda lattice hierarchy. Its dispersionless (quasiclassical) limit yields the tau-function for analytic curves encoding the integrable structure of the inverse potential problem and parametric conformal maps. A similar fermionic realization of partition functions for grand canonical ensembles of 2D Coulomb charges in the presence of an ideal conductor is also suggested. Their representation as Fredholm determinants is given and their relation to integrable hierarchies, growth problems and conformal maps is discussed. © 2010 Birkhäuser / Springer Basel AG.


Aliev M.A.,Institute of Biochemical Physics | Kuzminyh N.Yu.,Institute of Biochemical Physics | Ugolkova E.A.,RAS Institute of Chemistry
Physica A: Statistical Mechanics and its Applications | Year: 2013

The stability limits of the homogeneous state of melts of rod-coil RC, RC2, and CRC polydisperse block copolymers have been investigated in the framework of the weak segregation theory. It was assumed that the number of units in either the rod-like R or the flexible C block is a random variable distributed by the Schulz-Zimm distribution. Inspection of the spinodal curves shows that the copolymer melts with polydisperse rigid blocks are less stable with respect to formation of the nematic state than melts with the monodisperse ones. If flexible C blocks are polydisperse the homogeneous state of a rod-coil melt is less stable against microphase separation than the homogeneous state of monodisperse melt of the same architecture. © 2013 Elsevier B.V. All rights reserved.


Tsvetkov N.A.,Korea Advanced Institute of Science and Technology | Larina L.L.,Korea Advanced Institute of Science and Technology | Shevaleevskiy O.,Institute of Biochemical Physics | Al-Ammar E.A.,King Saud University | Ahn B.T.,Korea Advanced Institute of Science and Technology
Progress in Photovoltaics: Research and Applications | Year: 2012

A barrier layer of undoped TiO 2 was deposited on the Nb-doped TiO 2 electrode to suppress the recombination at the Nb-doped TiO 2/dye-electrolyte interface for highly efficient dye-sensitized solar cells (DSCs). The Nb content in TiO 2 was varied in a range of 0.7-3.5 mol% to modify the TiO 2 energy-band structure. Nb-doped TiO 2/dye interfaces were characterized by a combination of ultraviolet photoemission spectroscopy and optical absorption spectroscopy measurements, allowing the determination of the conduction band minimum (CBM) of the TiO 2 electrode and the lowest unoccupied molecular orbital of the N719 dye. The lowering of TiO 2 CBM by Nb doping induced the increase in short-circuit current of DSCs. However, open-circuit voltage and fill factor are decreased, and this result was ascribed to the enhanced recombination at the Nb-doped TiO 2/dye-electrolyte interface. The effect of doping on charge transport in DSCs was analyzed using electrochemical impedance spectroscopy. We have shown that by introducing of TiO 2 barrier layer, the Nb doping content, which results in DSC highest efficiency, can be increased because of the suppression of the dopant-induced recombination. The energy conversion efficiency of the solar cells increased from 7.8% to 9.0% when undoped TiO 2 electrode is replaced with electrode doped with 2.7 mol% of Nb because of the improvement of the electron injection and collection efficiencies. The correlation between the electronic structure of the TiO 2 electrode, charge transfer characteristics, and photovoltaic parameters of DSCs is discussed. Copyright © 2012 John Wiley & Sons, Ltd.


PubMed | Institute of Biochemical Physics and RAS Institute of Chemistry
Type: Journal Article | Journal: The Journal of chemical physics | Year: 2016

The phase behavior of a monodisperse melt of polymer molecules consisting of two rod-like segments joined at an angle has been inspected within the Landau theory of phase transitions. The interactions between monomer units were assumed to be of the Maier-Saupe form. The Landau-de Gennes expansion of the free energy of the melt has been obtained up to the sixth order in powers of the nematic order parameter, the coefficients of this expansion have been calculated from the microscopic model of polymer molecule. The phase diagram contains the regions of stability of isotropic, prolate uniaxial, oblate uniaxial, and biaxial nematic phases. The isotropic-uniaxial nematic and uniaxial-biaxial nematic transitions are of the first and second order, respectively. We found two Landau points in the phase diagram at which continuous transition from biaxial nematic state to isotropic phase occurs.

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