2017 
Armao, J. J., Nyrkova, I., Fuks, G., Osypenko, A., Maaloum, M., Moulin, E., et al. (2017). Anisotropic SelfAssembly of Supramolecular Polymers and Plasmonic Nanoparticles at the Liquid Liquid Interface. J. Am. Chem. Soc., 139(6), 2345–2350.
Abstract: The study of supramolecular polymers in the bulk, in diluted solution, and at the solid liquid interface has recently become a major topic of interest, going from fundamental aspects to applications in materials science. However, examples of supramolecular polymers at the liquid liquid interface are mostly unexplored. Here, we describe the supramolecular polymerization of triarylamine molecules and their lighttriggered organization at a chloroform water interface. The resulting interfacial nematic layer of these 1D supramolecular polymers is further used as a template for the precise alignment of spherical gold nanoparticles coming from the water phase. These hybrid thin films are spontaneously formed in a single process, without chemical prefunctionalization of the metallic nanoparticles, and their ordering is improved by centrifugation. The resulting polymer chains and strings of nanoparticles can be coaligned with high anisotropy over very large distances. By using a combination of experimental and theoretical investigations, we decipher the full sequence of this oriented selfassembly process. In such a highly anisotropic configuration, electron energy loss spectroscopy reveals that the selfassembled nanoparticles behave as plasmonic waveguides.


Ruscher, C., Semenov, A. N., Baschnagel, J., & Farago, J. (2017). Anomalous sound attenuation in Voronoi liquid. J. Chem. Phys., 146(14), 15 pp.
Abstract: The physics of simple fluids in the hydrodynamic limit and notably the connection between the proper microscopic scales and the macroscopic hydrodynamical description are nowadays well understood. In particular, the three peak shape of the dynamical structure factor S(k, omega) is a universal feature, as well as the kdependence of the peak position (proportional to/k) and width proportional to k(2), the latter accounting for the sound attenuation rate. In this paper, we present a theoretical model of monodisperse fluid, whose interactions are defined via the Voronoi tessellations of the configurations [called the Voronoi liquid and first studied in Ruscher et al., Europhys. Lett. 112, 66003 (2015)], which displays at low temperatures a marked violation of the universal features of S(k,omega) with a sound attenuation rate only proportional to k. This anomalous behaviour, which apparently violates the basic symmetries of the liquid state, is traced back to the existence of a time scale which is both short enough for the viscoelastic features of the liquid to impact the relaxational dynamics and however long enough for the momentum diffusion to be substantially slower than the sound propagation on that characteristic time. Published by AIP Publishing.


Semenov, A. N., & Subbotin, A. V. (2017). Phase Separation Kinetics in Unentangled Polymer Solutions Under HighRate Extension. J. Polym. Sci. Pt. BPolym. Phys., 55(7), 623–637.
Abstract: Phase separation processes following highrate extension in unentangled polymer solutions are studied theoretically. The flowinduced demixing is associated with the coilstretch transition predicted in highmolecularweight polymer solutions at highenough Weissenberg numbers. The developed meanfield theory is valid in the dilute/semidilute solution regime, where the stretched coils overlap strongly. We elucidate and discuss the main kinetic stages of the polymer/solvent separation process including (i) growth of concentration fluctuations and formation of oriented protofibrils by anisotropic spinodal decomposition; (ii) development of welldefined highly oriented and stiff fibrils forming an anisotropic network (crosslinked fiber); (iii) microphase separation and lateral collapse of the network yielding dense oriented fiber. These novel predictions are in qualitative agreement with the experimental data. (C) 2017 Wiley Periodicals, Inc.
Keywords: extension; fibers; phase separation; orientation


2016 
Subbotin, A. V., & Semenov, A. N. (2016). Adsorption of flexible polyelectrolytes on charged surfaces. Soft Matter, 12(32), 6771–6787.
Abstract: Adsorption of weakly charged polyelectrolyte (PE) chains from dilute solution on an oppositely charged surface is studied using the selfconsistent meanfield approach. The structure of the adsorbed polymer layer and its excess charge are analyzed in the most important asymptotic and intermediate regimes both analytically and numerically. Different regimes of surface charge compensation by PE chains including partial and full charge inversion are identified and discussed in terms of physical parameters like the magnitude of specific shortrange interactions of PE segments with the surface, solvent quality and ionic strength. The effect of excludedvolume monomer interactions is considered quantitatively both in the marginally good and poor solvent regimes.


Subbotin, A. V., & Semenov, A. N. (2016). Phase separation in dilute polymer solutions at highrate extension. Journal of Polymer Science Part BPolymer Physics, 54(11), 1066–1073.
Abstract: In this article the demixing instability and phase segregation in unentangled polymer solutions of semiflexible chains at highrate uniaxial extension above the coil to stretched coil transition was studied. Orientation of the stretched chains was described in terms of an effective potential field. Based on the free energy analysis it was shown that the flowinduced orientation of polymer segments could drastically reduce the energy of their steric repulsion. As a result attraction between the chains gain more importance, and this effect lead to the demixing process and eventual segregation of polymer from the solvent if the strain rate exceeds some critical value. A meanfield theory was developed to study this flowinduced phase separation effect. The phase diagrams of the system showing the spinodal and binodal transitions at different extension rates were calculated and discussed. (c) 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 10661073


2015 
Semenov, A. N. (2015). Thermodynamic nature of vitrification in a 1D model of a structural glass former. Journal of Chemical Physics, 143(4).
Abstract: We propose a new spinglass model with no positional quenched disorder which is regarded as a coarsegrained model of a structural glassformer. The model is analyzed in the 1D case when the number N of states of a primary cell is large. For N. 8, the model exhibits a sharp freezing transition of the thermodynamic origin. It is shown both analytically and numerically that the glass transition is accompanied by a significant growth of a static length scale. pointing to the structural (equilibrium) nature of dynamical slowdown effects in supercooled liquids. (C) 2015 AIP Publishing LLC.


Semenov, A. N., & Shvets, A. A. (2015). Theory of colloid depletion stabilization by unattached and adsorbed polymers. Soft Matter, 11(45), 8863–8878.
Abstract: The polymerinduced forces between colloidal particles in a semidilute or concentrated polymer solution are considered theoretically. This study is focussed on the case of partially adsorbing colloidal surfaces involving some attractive centers able to trap polymer segments. In the presence of free polymers the particles are covered by selfassembled fluffy layers whose structure is elucidated. It is shown that the freepolymerinduced interaction between the particles is repulsive at distances exceeding the polymer correlation length, and that this depletion repulsion can be strongly enhanced due to the presence of fluffy layers. This enhanced depletion stabilization mechanism (which works in tandem with a more shortrange steric repulsion of fluffy layers) can serve on its own to stabilize colloidal dispersions. More generally, we identify three main polymerinduced interaction mechanisms: depletion repulsion, depletion attraction, and steric repulsion. Their competition is analyzed both numerically and analytically based on an asymptotically rigorous meanfield theory. It is shown that colloid stabilization can be achieved by simply increasing the molecular weight of polymer additives, or by changing their concentration.


Subbotin, A. V., & Semenov, A. N. (2015). Electrohydrodynamics of a ConeJet Flow at a High Relative Permittivity. Jetp Letters, 102(12), 815–820.
Abstract: We have proposed a new solution of the electrohydrodynamic equations describing a novel conejet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative permittivity and using the slender body approximation, the conejet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager's principle of maximum entropy production. Three different regimes of the conejet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the conejet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge, and electric field of the jet.


Subbotin, A. V., & Semenov, A. N. (2015). Electrohydrodynamics of conejet flow at high relative dielectric permittivity. Pis'ma v Zhurnal eksperimental'noi i teoreticheskoi fiziki, 102(1112), 932–937.
Abstract: In this paper we propose a new solution of the electrohydrodynamic equations describing a novel conejet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative dielectric permittivity and using the slender body approximation, the conejet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager's principle of maximum entropy production. Three different regimes of the conejet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the conejet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge and electric field of the jet.


Subbotin, A. V., & Semenov, A. N. (2015). Electrohydrodynamics of stationary conejet streaming. Proceedings of the Royal Society aMathematical Physical and Engineering Sciences, 471(2182).
Abstract: We discover novel types of stationary conejet steams emitting from a nozzle of a syringe loaded with a conductive liquid. The predicted conejetflow geometries are based on the analysis of the electrohydrodynamic equations including the surface current. The electric field and the flow velocity field inside the cone are calculated. It is shown that the electric current along the conical stream depends on the cone angle. The stable values of this angle are obtained based on the Onsager's principle of maximum entropy production. The characteristics of the jet that emits from the conical tip are also studied. The obtained results are relevant both for the electrospraying and electrospinning processes.


2014 
Farago, J., Semenov, A., Frey, S., & Baschnagel, J. (2014). New conserved structural fields for supercooled liquids. European Physical Journal E, 37(6).
Abstract: By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2point density correlation functions. One of these fields is scalar and associated with the volume of the Voronoi cell, whereas the other one, termed the “geometric polarisation”, is vectorial and related to the local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glassforming liquid. We show that the geometric polarisation is statically correlated to the force field, but contrary to it develops a plateau regime when the temperature is lowered. This different relaxation is related to the cage effect in glassforming liquids, which prevents a complete relaxation of the shape of the cage around particle on intermediate time scales.


Nyrkova, I., Moulin, E., Armao, J. J., Maaloum, M., Heinrich, B., Rawiso, M., et al. (2014). Supramolecular SelfAssembly and Radical Kinetics in Conducting SelfReplicating Nanowires. Acs Nano, 8(10), 10111–10124.
Abstract: By using a combination of experimental and theoretical tools, we elucidate unique physical characteristics of supramolecular triarylamine nanowires (STANWs), their packed structure, as well as the entire kinetics of the associated radicalcontrolled supramolecular polymerization process. AFM, smallangle Xray scattering, and allatomic computer modeling reveal the twocolumnar “snowflake” internal structure of the fibers involving the pstacking of triarylamines with alternating handedness. The polymerization process and the kinetics of triarylammonium radicals formation and decay are studied by UVvis spectroscopy, nuclear magnetic resonance and electronic paramagnetic resonance. We fully describe these experimental data with theoretical models demonstrating that the supramolecular selfassembly starts by the production of radicals that are required for nucleation of doublecolumnar fibrils followed by their growth in doublestrand filaments. We also elucidate nontrivial kinetics of this selfassembly process revealing sigmoid time dependency and complex selfreplicating behavior. The hierarchical approach and other ideas proposed here provide a general tool to study kinetics in a large number of selfassembling fibrillar systems.


Semenov, A. N. (2014). Longrange correlation effects in directional living polymers. Soft Matter, 10(47), 9534–9561.
Abstract: The statistics of (equilibrium) living polymers including both linear chains and rings are considered theoretically. Particular attention is addressed to directional polymers characterized by an arrow along the backbone defined by its chemical structure. Thermodynamic and correlation properties of living polymers are studied both in the meanfield and in the critical scaling regimes. It is shown that living polymers with no rings, classical living polymers with rings, and directional living polymers with rings form three distinct classes characterized by different critical exponents and qualitatively different longrange correlation functions.


2013 
Semenov, A. N., & Meyer, H. (2013). Anomalous diffusion in polymer monolayers. Soft Matter, 9(16), 4249–4272.
Abstract: The tagged chain dynamics in strictly twodimensional (2D) polymer melts (where the chains are collapsed to dense spots) is considered both theoretically and by computer simulations. It is shown that the chain relaxation time in such systems scales as t(m) proportional to Nalpha with alpha approximate to 1.73 (N is the number of monomer units per chain). An extended transient regime of anomalous subdiffusion is identified at t less than or similar to t(m) where the chain centreofmass (CM) velocity autocorrelation function (VAF) scales as C(t) proportional to N(0)t(1.42). This anomalous dynamics is accounted for by the effect of the viscoelastic hydrodynamic interactions (VHI). The developed quantitative theory of the VHIcontrolled chain dynamics is in good agreement, with no parameter adjustment, with the extensive simulation data. The dynamics of polymer monolayers with frictional contact to the supporting surface is considered as well. It is shown that an external (Langevin) friction gamma leads to the asymptotic regime C(t) f proportional to (N gamma)(1.37)t(0.84) that crosses over to N(0)t(1.42) at longer t. We also present a detailed analysis of other important factors controlling the 2D chain diffusion: finite boxsize, inertial and finite compressibility effects.


Shvets, A. A., & Semenov, A. N. (2013). Effective interactions between solid particles mediated by free polymer in solution. Journal of Chemical Physics, 139(5).
Abstract: Effective potentials of interaction between solid nonadsorbing surfaces in semidilute or concentrated polymer solutions are calculated using two approaches: the numerical selfconsistentfield theory (SCFT) and the analytical theory generalizing the groundstate dominance approximation by taking into account the finite chainlength (chainend) effects (GSDE). A good agreement between the two approaches is demonstrated within the natural region of validity of the asymptotically exact GSDE theory. It is shown that in most cases the interaction potentials involve the shortrange depletion attraction which is replaced by the polymermediated repulsion at longer separations ranging from roughly 10 xi to 3R(g) (xi is the concentration correlation length and Rg is the polymer coil gyration radius). For a given polymer concentration and molecular weight the highest repulsion energy barrier, Um, is predicted for xi/Rg similar to 0.2 and in the thetasolvent conditions. The fluctuationinduced (antiCasimir) polymermediated repulsion forces are analyzed as well. It is shown that the overall polymermediated repulsion energy between naked spherical particles of radius Rc = 200 nm is typically not enough for their kinetic stabilization. There are, however, a few special cases where colloidal stability can be imparted by free polymers only. (C) 2013 AIP Publishing LLC.


2012 
Farago, J., Meyer, H., Baschnagel, J., & Semenov, A. N. (2012). Hydrodynamic and viscoelastic effects in polymer diffusion. Journal Of PhysicsCondensed Matter, 24(28), 284105.
Abstract: We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Theta solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Theta solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the centerofmass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).


Farago, J., Meyer, H., Baschnagel, J., & Semenov, A. N. (2012). Modecoupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions. Physical Review E, 85(5), 051807.
Abstract: A modecoupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the densitybased MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the centerofmass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail alphaN(1/2)t(3/2) for the c. m. VAF. The case of nonmomentumconserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first N(1)t(5/4) (as in the dMCT approach), then N(1/2)t(3/2). Both the amplitude and the duration of the first t(5/4) stage crucially depend on the Langevin friction parameter gamma. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c. m. mean square displacement widely observed in numerical and experimental works.


Farago, J., Semenov, A. N., Meyer, H., Wittmer, J. P., Johner, A., & Baschnagel, J. (2012). Modecoupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations. Physical Review E, 85(5), 051806.
Abstract: We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a densitybased modecoupling theory (dMCT) using the MoriZwanzig approach and projecting the fluctuating force onto pairdensity fluctuation modes. The effect of dynamical density fluctuations on the centerofmass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c. m. velocity autocorrelation function (c. m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t(1) and the Rouse relaxation time t(N). We obtain an analytical expression for the c. m. VAF in terms of molecular parameters. In particular, the c. m. VAF scales as N(1)t(5/4) (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted t(5/4) dependence of the c. m. VAF is supported by data of nonmomentumconserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].


Lazutin, A. A., Semenov, A. N., & Vasilevskaya, V. V. (2012). Polyelectrolyte Complexes Consisting of Macromolecules With Varied Stiffness: Computer Simulation. Macromolecular Theory And Simulations, 21(5), 328–339.
Abstract: Monte Carlo simulations are employed in order to analyze the structure of polyelectrolyte complexes consisting of two identical but oppositely charged macroions with varying chain stiffness. It is shown that two complex structures can arise depending on the stiffness of the constituent chains. Stiff chains are organized into a ladder structure in which chains are located parallel to each other and monomeric units are arranged into ionic pairs according to their position in the chain. Flexible chains form a globular scrambledegg structure with a disordered position of monomer units. The conformational transition between the two structures proceeds as a phase transition.
Keywords: interpolymer complexes; ladder and scrambledegg structures; microstructures; Monte Carlo simulations


Meyer, H., & Semenov, A. N. (2012). Anomalous Dynamics in 2D Polymer Melts. Physical Review Letters, 109(24).
Abstract: The dynamics in polymer monolayers where chains are strongly confined and adopt 2D conformations are drastically different to those in the bulk. It is shown that viscoelastic hydrodynamic interactions play a major role defining the anomalous chain diffusion properties in such systems where chains cannot cross each other. We developed a quantitative analytical theory of polymer subdiffusion in 2D systems revealing a complex behavior controlled by a delicate interplay of inertial, viscoelastic hydrodynamic interactions, finiteboxsize and frictional effects. The theory is fully supported by extensive momentumconserving and Langevin moleculardynamics simulation data explaining the highly cooperative character of 2D polymer motions. DOI: 10.1103/PhysRevLett.109.248304


Subbotin, A. V., & Semenov, A. N. (2012). Aggregation effects in solutions of model oligopeptides and other amphiphilic polymers. Polymer Science Series C, 54(1), 36–47.
Abstract: The problems of the aggregation behavior of amphiphilic macromolecules in solution are discussed. The cases of electrically neutral and polyelectrolyte chains are examined. The effect of chain parameters, interaction parameters, and external factorstemperature, solvent quality, medium pH, and solution ionic strengthon the structure and stability of the aggregates is analyzed. As examples, two systems are selected: (i) a solution of model oligopeptides with different chain architectures that contain hydrophobic alanine and negatively charged polar aspartic acid and (ii) a solution of HP copolymers in which hydrophobic (H) groups are located in the backbone and polar (P) side groups have a rigid bond to the backbone. The micelles formed by the oligopeptides are thermodynamically stabilized after the addition of a univalent salt; in addition, the effect heavily depends on the pH of a medium and the size of the added cations. For the second system, the regions of stability of aggregates of different geometries are determined and the corresponding phase diagram is constructed as a function of the surface tension and bending modulus of the surface of the aggregate. The problems related to the kinetics of coalescence of the aggregates are discussed.


2011 
Farago, J., Meyer, H., & Semenov, A. N. (2011). Anomalous Diffusion of a Polymer Chain in an Unentangled Melt. Physical Review Letters, 107(17).
Abstract: Contrary to common belief, hydrodynamic interactions in polymer melts are not screened beyond the monomer length and are important in transient regimes. We show that viscoelastic hydrodynamic interactions (VHIs) lead to anomalous dynamics of a tagged chain in an unentangled melt at t


Semenov, A. N., & Nyrkova, I. A. (2011). Endgrowth/evaporation living polymerization kinetics revisited. Journal of Chemical Physics, 134(11).
Abstract: Endgrowth/evaporation kinetics in living polymer systems with “associationready” free unimers (no initiator) is considered theoretically. The study is focused on the systems with long chains (typical aggregation number N >> 1) at long times. A closed system of continuous equations is derived and is applied to study the kinetics of the chain length distribution (CLD) following a jump of a parameter (Tjump) inducing a change of the equilibrium mean chain length from N(0) to N. The continuous approach is asymptotically exact for t >> t(1), where t(1) is the dimer dissociation time. It yields a number of essentially new analytical results concerning the CLD kinetics in some representative regimes. In particular, we obtained the asymptotically exact CLD response (for N >> 1) to a weak Tjump (epsilon = N(0)/N – 1


2010 
Nyrkova, I. A., & Semenov, A. N. (2010). Twisted surfactant structures: an advanced theoretical model. Soft Matter, 6(3), 501–516.
Abstract: We analyze twisted membrane structures of chiral surfactants in the framework of the equilibrium theoretical approach based on a continuous elastic model. It is shown that both the surfactant ribbon width and its twist pitch can be defined by equilibrium factors, including the chiral elastic energy. We show however that the theoretically predicted dependencies of the ribbon geometrical parameters on the enantiomeric excess (ee) obtained for the unilamellar liquid membrane model are in partial, but qualitative disagreement with experimental data. The surfactant membrane model is then generalized in two directions: (i) we consider also multilamellar ribbons (of many bilayers), (ii) we allowed for the crystalline (Lbeta) state of the bilayers. The multibilayer crystalline structure of selfassembling twisted ribbons is consistent with recent results of Xray and other experimental studies on gemini surfactants, and, simultaneously, the theory developed for such ribbons yields the eedependencies of the twisted ribbon width and pitch that are in reasonable agreement with the data based on TEM images.


Semenov, A. N. (2010). BondVector Correlation Functions in Dense Polymer Systems. Macromolecules, 43(21), 9139–9154.
Abstract: It is wellknown that homopolymer chains do not exactly follow the Gaussian statistics even in the melt state. In particular, orientations of two bonds l(1) and of the same chain in a concentrated polymer system are always correlated even when they are separated by a long segment of s >> 1 units: <(l) under bar (1) . (l) under bar (2)>(s) = C(s) similar to l/s(3/2). It is important to know how these orientational correlations are distributed in space, i.e. how <(l) under bar (1) . (l) under bar (2)> depends on the distance (r) under bar between the bonds.(1) An unexpected feature is revealed in the present paper: it is shown that the distancedependent bondvector correlation function K(r) = <(l) under bar (1) . (l) under bar (2)>(r) is extremely sensitive to the definition of r. Depending on the definition, K(r) for r >> b (b is the monomer size) can be either significantly lower, or significantly higher than the positionaveraged correlator C(s) with s similar to r(2)/b(2) corresponding to a given distance r. We propose an “invariant” definition of the intrachain orientational correlation function and show that it is related to the formfactor of a single chain. A quantitative link between the orientational and positional correlations in polymer melts is thus discovered. We also have found a quantitative relationship between the intrachain and interchain correlation functions. It is shown that the interchain orientational correlation function (for bonds of different chains) is longrange and follows the l/r(4) scaling law in the case of infinite chains.


Semenov, A. N., & Subbotin, A. V. (2010). Theory of SelfAssembling Structures of Model Oligopeptides. Macromolecules, 43(7), 3487–3501.
Abstract: Aggregation and micelle formation in dilute solutions of amphiphilic oligopeptides (Ala(nH) Asp(nP)) is considered theoretically. It is shown that the peptides can selfassemble forming micelles of different morphologies in the regime where Asp units are negatively charged. The micelles are stable thermodynamically if a sufficient amount of monovalent salt is added (the “salting in” effect). The thermodynamic stability of the micelles also strongly depends on pH and on the size delta of added cations. The micelles get destabilized as their surface charge (due to Asp units) decreases at low pH or low ionic strength Iinfinity. A larger cation size delta also results in aggregation (precipitation) of the micelles. The aggregation process can be kinetically arrested clue to electrostatic repulsion even in the regime of weakly charged Asp units. The kinetically defined size R of the aggregates strongly depends on the effective peptide/water interfacial tension gamma and on the Debye length r(D): R decreases as either gamma or r(D) is increased.


2009 
Nyrkova, I. A., & Semenov, A. N. (2009). Theory of chiral recognition in DNA condensation. Soft Matter, 5(5), 979–989.
Abstract: Collapse of long chiral Amacromolecules assisted by a chiral Badditive (where B associates with A) is considered theoretically. Based on a simple model we demonstrate that the compaction activity of B molecules can strongly depend on the sense of their chirality. The theory is applied to the DNA compaction in the presence of conformationally rigid divalent enantiomeric cations (SS and RR enantiomers).(1) It is shown that both chiral isomers of the dications adsorb well on the DNA surface, but the SS and RRbinding energies are different, reflecting their unequal stereocomplementarities (the 'boltandnut' effect). Unexpectedly, we find that the compaction activity of less strongly bound SS dication is significantly higher than that of its RR enantiomer. Moreover, the RR molecules tend to replace the SS enantiomers adsorbed on the DNA, so that SS compaction ability is significantly reduced in the presence of RR isomers. The theory thus provides a basis for explanation of recently observed dramatic stereoisomeric selectivity and antagonistic effects in DNA compaction.(1) The revealed chiral discrimination effects may serve as selection mechanisms leading to natural homochirality.


Semenov, A. N. (2009). Theory of Cluster Formation in Homopolymer Melts. Macromolecules, 42(17), 6761–6776.
Abstract: A physical mechanism of micelle formation in homopolymer systems is elucidated. The mechanism is applicable in particular to melts of stereoisomeric polymers, for example, polystyrene. It is hinged on aggregation and crystallization of occasional atypical stereoregular fragments of mostly irregular (atactic) polymer chains. Phase diagrams involving the regimes of lamellar, tapelike, and disklike semicrystalline micelles are obtained and discussed. The possible relevance of the theory to the puzzling anomalous cluster phenomena observed in homopolymer melts (lowfrequency solidlike rheological behavior; lowq excess light scatteringFischer cluster modes) is discussed as well.


2008 
Maresov, E. A., & Semenov, A. N. (2008). Mesoglobule Morphologies of Amphiphilic Polymers. Macromolecules, 41(23), 9439–9457.
Abstract: A statistical theory of finitesized aggregates and domain structures in dilute solutions of amphiphilic macromolecules (homopolymers or copolymers) is developed. A minimalist model involving, essentially, two types of chemical groups (insoluble H and soluble P) is studied in the regime where polymer tends to phase separate, forming rather dense amorphous particles with low Surface energy. The surface tension and the elastic bending moduli of the polymer/solvent interface are obtained and are related to the molecular parameters. The Gaussian modulus kappa(G) is predicted to be negative; typically vertical bar kappa(G)vertical bar is smaller than the mean bending modulus kappa(2). It is shown that the condensed polymer phase can remain dense, homogeneous, and stable with respect to microphase separation even as the surface tension decreases down to zero (or below it). Stable large aggregates of welldefined size are predicted in this regime. The size of aggregates and their shape depend on surface tension gamma, the spontaneous bending modulus kappa(1), and the ratio kappa(G)/kappa(2). We show that bicontinuous morphologies (rather than colloidally stable polymer mesoglobules) are thermodynamically favorable for small vertical bar kappa(G vertical bar). We present a quantitative argument showing that the gyroid structure is more favorable than other bicontinuous morphologies (primitive cubic and double diamond). The gammakappa(1) phase diagrams showing the regions of stability of different morphologies are obtained. Two types of spherical rnesoglobules are predicted, namely equilibrium and metastable globules whose sizes are shown to be essentially different: they depend on kappa(1) in qualitatively different ways. Recent experimental data on mesoglobule formation in solutions of thermosensitive amphiphilic polymers are discussed in the theoretical light.


Nunez, E., Clark, C. G., Cheng, W., Best, A., Floudas, G., Semenov, A. N., et al. (2008). Thermodynamic, structural, and nanomechanical properties of a fluorous biphasic material. Journal Of Physical Chemistry B, 112(21), 6542–6549.
Abstract: The dynamics of the amphiphilic semifluorinated F(CF2)(12)(CH2)(12)H (F12H12) alkane that undergoes two condensed phase transitions have been investigated by Brillouin light spectroscopy, shear rheometry, small(SAXS) and wideangle (WAXS) Xray scattering, and thermodynamic PVT measurements. The solid (I)solid (II) transition (T,) is marked by a stronger temperature dependence of the sound velocity in phase II and by a 2 orders of magnitude drop of the shear modulus. Between the T, and the melting transition (Tm), the presence of two phonons implies a coexistence of solid (II) and amorphous (liquid) regions in the submicrometer range at thermal equilibrium as revealed by the SAXS pattern of a single reflection superimposed on a very broad amorphous halo. This intriguing finding of a transient, very slow (over 10 h) solid/liquid coexistence within phase II is rationalized by a twostage mechanism for melting of the smectic phase (II) of F12H12. A refinement of the known packing motifs for the two solidstate structures is proposed.


Semenov, A. N. (2008). Theory of Colloid Stabilization in Semidilute Polymer Solutions. Macromolecules, 41(6), 2243–2249.
Abstract: A universal asymptotically exact theoretical approach elucidating the origin of the depletion stabilization phenomenon is developed. The theory predicts that colloidal particles in a semidilute polymer solution may be kinetically stabilized by a longrange polymerinduced repulsion. It is shown that the repulsion is due to a depletion of chain ends in the middle of the slit between solid surfaces. A nonmonotonic concentration dependence of the stabilization effect is predicted. The theory is generalized to account for surface attraction of chain ends and for polydispersity of the chains. The stabilization is enhanced for more rigid and less polydisperse chains and for the case of reversible endadsorption.


2007 
Beckrich, P., Johner, A., Semenov, A. N., Obukhov, S. P., Benoit, H., & Wittmer, J. P. (2007). Intramolecular form factor in dense polymer systems: Systematic deviations from the Debye formula. Macromolecules, 40(10), 3805–3814.
Abstract: We discuss theoretically and numerically the intramolecular form factor F(q) in dense polymer systems. Following Flory's ideality hypothesis, chains in the melt adopt Gaussian configurations, and their form factor is supposed to be given by Debye's formula. At striking variance to this, we obtain noticeable ( up to 20%) nonmonotonic deviations which can be traced back to the incompressibility of dense polymer solutions beyond a local scale. The Kratky plot (q2F(q) vs wave vector q) does not exhibit the plateau expected for Gaussian chains in the intermediate q range. One rather finds a significant decrease according to the correction delta( F1( q))) q3/32F that only depends on the concentration F of the solution, but neither on the persistence length or the interaction strength. The nonanalyticity of the above q3 correction is linked to the existence of longrange correlations for collective density fluctuations that survive screening. Finitechain size effects are found to decay with chain length N as 1//N.


Nyrkova, I. A., & Semenov, A. N. (2007). Correlation effects in dynamics of living polymers. Europhysics Lett., 79(6), 66007.
Abstract: Theoretically studying the dynamics of entangled living polymers which can reversibly break and recombine, we find a number of diffusioncontrolled regimes of essentially nonexponential stress relaxation. This behavior is in contrast to predictions of the classical theory of Cates and its more recent generalizations. The nonexponential relaxation is due to strong correlations between chain scissions and recombinations: multiple selfrecombinations are much more frequent than recombinations with other chains and are resulting in fast release of topological constraints (entanglement tube coarsening). The strong renormalization effect of correlations on the lifetime of a living chain (the time period tau(b) until the chain breaks and one of its fragments recombines with another chain) is also elucidated. We show that the correlation effects defining the dynamics are controlled by the activation energy for chain recombination and by the chain rigidity. Copyright (C) EPLA, 2007.


Nyrkova, I. A., & Semenov, A. N. (2007). Dynamic scattering of semirigid macromolecules. Physical Review E, 76(1), 011802.
Abstract: The polarized (VV) and depolarized (VH) dynamic light scattering functions of dilute solutions of semirigid macromolecules are calculated assuming that the scattering wave vector q_ is high compared to the chain Kuhn segment l: ql > 1. The terminal relaxation rate is Gamma proportional to q(8/3). Dynamics of both uniaxial and biaxial wormlike macromolecules (filaments) are considered. Biaxial macromolecules are characterized by two persistence lengths proportional to elastic constants for bending in two perpendicular directions (easy and hard bending). We showed that biaxiality may result in a significant broadening of the relaxation spectrum. A nonmonotonous q dependence of the depolarized scattering intensity is predicted. Analyzing the shorttime behavior of the dynamic structure factor for t < 1/Gamma, we show that it is characterized by two additional characteristic times: t(perpendicular to)proportional to q(4) and t(parallel to)proportional to q(8) reflecting the transverse and the longitudinal dynamics of polymer chains. The longitudinal motions (along the chain contour) increase the initial relaxation rate of the structure factor by a factor of 2. The longitudinal contribution to the dynamic structure factor is significant even for t > t(parallel to).


Nyrkova, I. A., & Semenov, A. N. (2007). Nonlinear scission/recombination kinetics of living polymerization. European Physical Journal E, 24(2), 167–183.
Abstract: Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor sigma < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for sigma << 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (onedimensional association). The kinetic model involves i) the unimer activation step (a transition to an assemblycompetent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0, with initial concentration of unimers M greater than or similar to M* (M* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M* << M << M*/sigma the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t(1), t(2), t(3) and t*; 2) there are transient regimes (t(1) less than or similar to t less than or similar to t(3)) when the molecularweight distribution is strongly nonexponential; 3) the chain scissions are negligible at times shorter than t(2). The chain growth is autoaccelerated for t(1) less than or similar to t less than or similar to t(2): the cutoff chain length (= polymerization degree < n >(w) N1 proportional to t(2) in this regime. 4) For t (2) < t < t (3) the length distribution is characterized by essentially 2 nonlinear modes; the shorter cutoff length N1 is decreasing with time in this regime, while the length scale N2 of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t*, shows a sharp maximum in the vicinity of M*; the effective exponent partial derivative ln 1/t*/partial derivative ln M is as high as similar to sigma(1/3) just above M*.


Semenov, A., Charlot, A., AuzelyVelty, R., & Rinaudo, M. (2007). Rheological properties of binary associating polymers. Rheologica Acta, 46(5), 541–568.
Abstract: Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of BA and BC associating polymers with 1: 1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of BA and BC; ( 2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; ( 3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly nonMaxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = betacyclodextrin, B=either chitosan or hyaluronan) including similar behavior of G' and G '' in a wide frequency range, strong temperature dependence of the characteristic frequency omega(x), and an extremely strong effect of added free stickers (fC) on the dynamics.


Subbotin, A. V., & Semenov, A. N. (2007). Spatial selforganization of comb macromolecules. Polymer Science Series A, 49(12), 1328–1357.
Abstract: The properties and the selfassembly of single comb macromolecules in solution were studied. The elastic properties of a polymer chain with a high density of side chains forming a cylindrical brush were discussed, in particular, its persistence length was calculated. The cases of brushes with flexible and rigid side chains, as well as brushes with two types of incompatible side segments, were considered. It was shown that brushes with rodlike dangling chains have a higher rigidity. In addition, a comb macromolecule with the hydrophobic main chain and hydrophilic side chains was considered. Such a macromolecules in a selective solvent forms a globule with the hydrophobic core and a soluble shell. The specific feature of the globule is its ability to acquire nonspherical spatial forms. Problems related to the stability and transformation of globule shape are discussed in detail.


Wittmer, J. P., Beckrich, P., Johner, A., Semenov, A. N., Obukhov, S. P., Meyer, H., et al. (2007). Why polymer chains in a melt are not random walks. Europhysics Lett., 77(5), 56003.
Abstract: A cornerstone of modern polymer physics is the “Flory ideality hypothesis” which states that a chain in a polymer melt adopts “ideal” randomwalklike conformations. Here we revisit theoretically and numerically this pivotal assumption and demonstrate that there are noticeable deviations from ideality. The deviations come from the interplay of chain connectivity and the incompressibility of the melt, leading to an effective repulsion between chain segments of all sizes s. The amplitude of this repulsion increases with decreasing s where chain segments become more and more swollen. We illustrate this swelling by an analysis of the form factor F(q), i.e. the scattered intensity at wave vector q resulting from intramolecular interferences of a chain. A “Kratky plot” of q(2)F( q) vs. q does not exhibit the plateau for intermediate wave vectors characteristic of ideal chains. One rather finds a conspicuous depression of the plateau, delta(F1(q))=vertical bar q vertical bar(3)/32 rho, which increases with q and only depends on the monomer density rho. Copyright (c) EPLA, 2007


2006 
Angerman, H. J., Johner, A., & Semenov, A. N. (2006). Microphase separation in thin block copolymer films: A weak segregation meanfield approach. Macromolecules, 39(18), 6210–6220.
Abstract: In this paper, we consider thin films of AB block copolymer melts confined between two parallel plates. The plates are identical and may have a preference for one of the monomer types over the other. The system is characterized by four parameters: the FloryHuggins chiparameter accounting for the repulsion between the A monomers and the B monomers, the fraction f of A monomers in the block copolymer molecules, the film thickness d, and a parameter h quantifying the preference of the plates for the monomers of type A. In certain regions of parameter space, the film will be microphase separated. Various structures have been observed experimentally, each of them characterized by a certain symmetry, orientation, and periodicity. We study the system theoretically using the weak segregation approximation to mean field theory. The theory is phenomenological in the sense that in the Landau expansion of the free energy the third and fourth order vertexes are approximated by constants, while the second order vertex is approximated by a quadratic function of the wave vector. As a consequence, the details of the architecture are not taken into account, and within the scope of the theory, our results apply equally well for multiblock copolymers and triblock copolymers, though the mapping from the rescaled parameters to the physical parameters would be a bit different. We restrict our analysis to the region of the parameter space where the interaction strength chi is close to its spinodal value Os, the composition f is close to the critical composition, the plate preference h is small, and the film thickness d is close to a small multiple of the natural periodicity L0 = 2 pi/q(0) (the first three conditions define the weak segregation regime). We will present our results in the form of phase diagrams in which Delta similar to vertical bar(d/nL(0) – 1)/epsilon vertical bar is placed along the horizontal axis, and T similar to (chi – chi(s))/epsilon(2) is placed along the vertical axis, where epsilon is a measure for the composition asymmetry (f – 0.5). We present a series of such phase diagrams for increasing values of the rescaled parameter H = h epsilon(3). We find that if Delta is small, corresponding to films whose thickness is commensurate with the bulk periodicity, parallel orientations of the structures are favored over perpendicular orientations. We also predict that on increasing the value of the parameter H, the region of stability of the bcc phase shrinks.


Jarkova, E., Johner, A., Maresov, E. A., & Semenov, A. N. (2006). Globules of annealed amphiphilic copolymers: Surface structure and interactions. European Physical Journal E, 21(4), 371–386.
Abstract: A meanfield theory of globules of random amphiphilic copolymers in selective solvents is developed for the case of an annealed copolymer sequence: each unit can be in one of two states, H (insoluble) or P (soluble or less insoluble). The study is focussed on the regime when H and P units tend to form long blocks, and when P units dominate in the dilute phase, but are rare in the globule core. A firstorder coiltoglobule transition is predicted at some T = Tcg. The globule core density at the transition point increases as the affinity of P units to the solvent, (epsilon) over tilde, is increased. Two collapse transitions, coil > “loose” globule and “loose” globule > “dense” globule, are predicted if (epsilon) over tilde is high enough and P units are marginally soluble or weakly insoluble. H and P concentration profiles near the globule surface are obtained and analyzed in detail. It is shown that the surface excess of P units rises as (epsilon) over tilde is increased. The surface tension decreases in parallel. Considering the interaction between close enough surfaces of two globules, we show that they always attract each other at a complete equilibrium. It is pointed out, however, that such equilibrium may be difficult to reach, so that partially equilibrium structures (defined by the condition that a chain forming one globule does not penetrate into the core of the other globule) are relevant. It is shown that at such partial equilibrium the interaction is repulsive, so the globules may be stabilized from aggregation. The strongest repulsion is predicted at the coiltoglobule transition point Tcg: the repulsion force decreases with the distance between the surfaces according to a power law. In the general case (apart from Tcg) the force vs. distance decay becomes exponential; the decay length xi diverges as T > Tcg. The developed theory explains certain anomalous properties observed for globules of amphiphilic homopolymers.


Semenov, A. N. (2006). Dynamics of associating polymers with random structure. Europhysics Lett., 76(6), 1116–1122.
Abstract: Solution dynamics of associating polymer chains with many (N >> 1) randomly distributed strongly interacting groups (stickers) are considered theoretically. The stickers tend to associate pairwise, and the polymer backbone is semirigid and soluble. It is shown that there exists a finite concentration range where the polymers form a reversible network with a virtually frozen structure: in this regime both the stress relaxation time and the viscosity exponentially increase with N and with c.


Semenov, A. N. (2006). Micelle formation in statistical copolymers. Physical Review E, 73(4).
Abstract: Formation of microdomain structures in concentrated systems of irregular (stochastic) copolymers with weak composition asymmetry (epsilon < 1) is considered theoretically. The study is focused on the weak segregation regime for infinitely long copolymer chains near the disordertoorder transition. It is shown that the transition occurs below the spinodal (at chi(0)<chi(*)) and that it results in the formation of micelles rather than in a superposition pattern of a few harmonic composition waves. The micelle size is inversely proportional to Delta chi=chichi(0). For small Delta chi the micelles are like large nearly uniform droplets with “reflected” composition, epsilon. As Delta chi increases the micelle composition profile develops oscillations. A firstorder transition from sphericalwave micelles to micelles with internal bcc structure is predicted at chi/chi(*)1 proportional to epsilon(2). Interaction of micelles is also considered. It is shown that micelles always tend to form a fcc superlattice. The micellization in the weak segregation regime is controlled by the socalled nonlocal free energy. The classical fourth order (in composition parameter A) approximation for this energy is significantly generalized in the regime of low volume fraction of micelles. It is shown that the nonlocal energy strongly (exponentially) increases with A near and above a certain critical value A similar or equal to A(*).


Semenov, A. N., GonzalezPerez, A., Krafft, M. P., & Legrand, J. F. (2006). Theory of surface micelles of semifluorinated alkanes. Langmuir, 22(21), 8703–8717.
Abstract: Surface structures of semifluorinated alkanes F(CF2)(n)(CH2)(m)H( referred to as FnHm) spread on the air/water interface are investigated theoretically. The study is focused on the disklike surface micelles that were recently identified by AFM and scattering techniques at sufficiently high surface concentrations. We show that (1) the micelles emerge as a result of liquid/liquid (rather than liquid/gas) phase separation in the Langmuir layer; (2) the micelles are islands of the higherdensity phase with roughly vertical orientation of FnHm molecules (Fparts extend toward air, Hparts toward water) and the matrix is the lower densityphase where the FnHm diblocks are nearly parallel to the water surface; (3) the micelles and the hexagonal structure they form are stabilized by the electrostatic interactions which are mainly due to the vertical dipole moments of the CF2CH2 bonds in the vertical phase; and (4) the electrostatic repulsive interactions can serve to suppress the micelle size polydispersity.


2005 
Khokhlov, A. R., Semenov, A. N., & Subbotin, A. V. (2005). Shape transformations of proteinlike copolymer globules. European Physical Journal E, 17(3), 283–306.
Abstract: Shapes of globules formed by amphiphilic multiblockcopolymers in a selective solvent are considered theoretically. We focus on copolymers consisting mostly of insoluble Hunits forming large core surrounded by a shell of soluble Pblocks. It is shown that the globule becomes nonspherical when the effective shell tension is low enough. The resultant shape depends on the shell bending energy: it is prolate if this energy is larger than the elastic energy of the core, and oblate in the opposite case. The central result is the prediction of the formation of a surface pattern of fingers accompanying or even preempting the shape transition mentioned above. We elucidate and discuss the following finger morphologies: 1) nearly spherical knob; 2) a necklace of spherical beads extending away from the surface; 3) mostly cylindrical fingers; 4) large thornlike fingers. The first 3 morphologies develop at equilibrium as the shell area increases (or, equivalently, the shell tension decreases). Considering the relevant kinetical aspects we show that formation of fingers is a nucleation and growth process, and that the energy of their equilibrium nucleation is likely to be high. Therefore, the finger formation may be delayed, and may actually occur in the regime where the plain spherical surface is metastable. It is the last morphology (thornlike fingers) that characterizes the metastable regimes when the finger formation is controlled by a high activation energy. The universal features of the above predictions inviting experimental tests are discussed.


Nyrkova, I. A., & Semenov, A. N. (2005). Multimerization: Closed or open association scenario? European Physical Journal E, 17(3), 327–337.
Abstract: We address the problem of classification of the type of association (multimerization) in solutions of identical unimers. Although the aggregation is still routinely characterized in terms of either “open association” or “closed association” models, neither of the two models can provide a fair description of many aggregation processes. We demonstrate that a realistic multimerization may show mixed basic features, i.e. simultaneously those typical of the classical open association and those typical of the classical closed association. In particular, we show that a living polymerization may seem to exhibit a critical micelle concentration (CMC), whereas the basic integral characteristics of a “closed” system with rather monodisperse micelles ((m(w)/m(n))(mic) = 1.02) may not imply a welldefined CMC. Therefore, a multimerization must be characterized by the detailed micelle size distribution that largely defines the equilibrium and dynamical properties of the system. To this end, we suggest a simple method of deriving the micelle size distribution c(m) (depending also on the total concentration of amphiphilic molecules) from the concentration dependence of just the mean aggregation number, m(w)(c). Our results thus invite a reconsideration of the basic methods used for interpretation of experimental data on micellization.


Nyrkova, I. A., & Semenov, A. N. (2005). On the theory of aggregation and micellization: PEOPVP copolymer in water. Faraday Discussions, 128, 113–127.
Abstract: We develop a theoretical approach to micellization of the PEOPVP blockcopolymer in water. This copolymer is a weak polyelectrolyte due to protonation of VP blocks. The theory accounts for nonlinear ion screening, and predicts strong position dependence of both ion concentration and the effective Debye length. We consider both the case when the local Debye length is small compared to the core radius and the case when it is large. We found that the effective (local) pH is not uniform even inside one micellar core, hence nonuniform protonation of the core with higher charge density near the surface. In many cases the core charge is concentrated in a relatively thin surface layer. Considering statistical weights of nonequilibrium micelles and their continuous evolution we show that kinetics of both formation and dissociation of typical blockcopolymer or surfactant micelles can be extremely slow. Thus micelle formation at the genuine (equilibrium) critical micelle concentration (c.m.c.) is totally suppressed (involves astronomical time scales) if the micelles are big enough. An 'apparent' critical micelle concentration (c.m.c.*) is introduced to account for this effect. The apparent c.m.c.* could be much higher than the genuine equilibrium c.m.c., i.e. a significant hysteresis is inherent in these systems. We also determine the ranges of metastability of micelles depending on the experimental timescales.


Nyrkova, I. A., & Semenov, A. N. (2005). On the theory of micellization kinetics. Macromolecular Theory And Simulations, 14(9), 569–585.
Abstract: We consider certain general features of aggregation (micellization) processes in solutions of amphiphilic molecules, in particular, blockcopolymers. We demonstrate that nonequilibrium effects can be very important for micellization. In particular, we show that micelle formation at the conventional (equilibrium) critical micelle concentration (CMC, c(c)) can be inhibited by high activation energy barriers. This is likely to be the case when the micelles are large. In this case an aggregation actually occurs at higher concentrations, above an apparent CMC, c(a). The concentration Ca can be much. higher than the equilibrium CMC. Hence significant hysteresis effects are inherent in amphiphilic systems since micelle formation and dissociation are activation processes. To further clarify this idea we consider relaxation of a micellar system after a, temperature jump (or a jump of another essential parameter) and discuss qualitatively different relaxation times corresponding to the relaxations of the micellar sizes and of the total number of micelles. We also discuss different kinetic pathways of micelle formation and relaxation and show that in certain cases the idealgas (combinatorial) contribution to the micelle free energy is significant for the kinetics.


Obukhov, S. P., & Semenov, A. N. (2005). Longrange interactions in polymer melts: The antiCasimir effect. Physical Review Letters, 95(3).
Abstract: It is well known that small neutral particles normally tend to aggregate due to the van der Waals forces. We discover a new universal longrange interaction between solid objects in polymer media that is directly opposite the van der Waals attraction. The new force could reverse the sign of the net interaction, possibly leading to the net repulsion. This universal repulsion comes from the subtracted soft fluctuation modes, which are not present in the real polymer system, but rather are in its ideal counterpart. The predicted effect has a deep relation to the classical Casimir interactions, providing an unusual example of fluctuationinduced repulsion instead of normal attraction. That is why it is referred to as the antiCasimir effect. We also find that the correlation function of monomer units in a concentrated solution of infinite polymer chains follows a powerlaw rather than an exponential decay at large distances.


Semenov, A. N., & Obukhov, S. P. (2005). Fluctuationinduced longrange interactions in polymer systems. Journal Of PhysicsCondensed Matter, 17(20), S1747–S1775.
Abstract: We discover a new universal longrange interaction between solid objects in polymer media. This polymerinduced interaction is directly opposite to the van der Waals attraction. The predicted effect is deeply related to the classical Casimir interactions, providing a unique example of universal fluctuationinduced repulsion rather than normal attraction. This universal repulsion comes from the subtracted soft fluctuation modes in the ideal counterpart of the real polymer system. The effect can also be interpreted in terms of subtracted (ghost) largescale polymer loops. We establish the general expressions for the energy of polymerinduced interactions for arbitrary solid particles in a concentrated polymer system. We find that the correlation function of the polymer density in a concentrated solution of very long chains follows a scaling law rather than an exponential decay at large distances. These novel universal longrange interactions can be of importance in various polymer systems. We discuss the ways to observe/simulate these fluctuationinduced effects.


2004 
Abramchuk, S. S., Semenov, A. N., & Khokhlov, A. R. (2004). Binary polymer mixtures in selective solvents: Interfacial structure. Macromolecular Theory And Simulations, 13(1), 64–72.
Abstract: The interaction of a large polymer droplet (formed by a poorly soluble polymer A) with a soluble polymer additive (polymer B) is investigated in the framework of a meanfield approach. We found that polymer B may tend to adsorb on the surface of the droplet even when it is immiscible with polymer A in the droplet and is soluble in the solvent surrounding the droplet. We calculated the concentration profiles of both polymers A and B near the interface and established conditions for polymer B accumulation at the interface. The dependencies of the surface tension and the interfacial excess of polymer B on its bulk concentration are also calculated. We found that even a very small amount of homopolymer B additive may result in a significant reduction of the interfacial tension (by a factor of 2). The effect is stronger if the additive is more flexible than the insoluble polymer.


Semenov, A. N. (2004). Core/shell structures of proteinlike copolymers: Are finite aggregates thermodynamically stable? Macromolecules, 37(1), 226–237.
Abstract: We propose a theory of aggregation in solutions of amphiphilic copolymers consisting mostly of insoluble H (hydrophobic) units with a small fraction of soluble (P, polar) monomer units. When P units are arranged along the sequence in a periodic (regular) fashion, the resultant HP copolymers are essentially insoluble: they precipitate. The main result is that finite aggregates of HP copolymers can be made stable by an appropriate smart arrangement of the same number of soluble P units in the chemical sequence. An analytical approach yielding the thermodynamic quantities of Hcore/Pshell copolymer structures in the weak stretch limit is developed. We show that different types of copolymer aggregates and microdomain structures can be thermodynamically stable depending on the copolymer chemical sequence. The relationship between the blocklength distribution and copolymer aggregation is illustrated by a few phase diagrams. Copolymers that can form stable finite aggregates with Hcore/Pshell structure (including singlechain globules) are often referred to as the proteinlike copolymers. Thus, the present theory sheds a new light as to the essential features of proteinlike copolymer sequences.


Wittmer, J. P., Meyer, H., Baschnagel, J., Johner, A., Obukhov, S., Mattioni, L., et al. (2004). Long range bondbond correlations in dense polymer solutions. Phys Rev Lett, 93(14), 147801.
Abstract: The scaling of the bondbond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density rho via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense threedimensional solutions are found to decay with a power law P1(s) approximately s(omega) with omega=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) approximately g(omega(0))(s/g)(omega) with omega(0)=22nu=0.824 (nu=0.588 being Flory's exponent) is set by the number of monomers g(rho) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The powerlaw behavior is due to selfinteractions of chains caused by the chain connectivity and the incompressibility of the melt.


2003 
Govorun, E. N., Khokhlov, A. R., & Semenov, A. N. (2003). Stability of dense hydrophobicpolar copolymer globules: Regular, random and designed sequences. European Physical Journal E, 12(2), 255–264.
Abstract: Stability of dense globular structures formed by amphiphilic copolymers consisting of hydrophobic (insoluble) units and a small fraction of single polar (soluble) monomer units is considered in the meanfield approximation for different types of unit distributions along the chain. Polar (P) units are located in a relatively thin surface layer due to their strong repulsion from hydrophobic (H) monomer units. We compared globules formed by different copolymer sequences with the same gross numbers of P and Hunits: regular HPsequences (Punits separated by equal Hblocks), random copolymers (uncorrelated positions of Punits, i.e. Flory distribution of Hblock lengths), proteinlike (PL) sequences (designed sequences involving both long Hblocks dominating by total mass, and short blocks dominating by number). We showed that PLglobules are more stable (lower free energy) and are characterized by a higher temperature of the coiltoglobule transition when compared with the other sequences mentioned above. We also considered HPHcopolymers consisting of one long and many short hydrophobic blocks; we showed that it is these sequences that yield the dense globules corresponding to the lowest free energy.


Semenov, A. N., & Johner, A. (2003). Theoretical notes on dense polymers in two dimensions. European Physical Journal E, 12(3), 469–480.
Abstract: Two models of dense twodimensional (2d) polymers are considered: (1) when chain intersections in 2d are totally forbidden, and (2) when they are allowed to some extent. It is shown that both polymer chain statistics and dynamics are entirely different for the two models. In the first case studied by Duplantier in 1986 polymer chains are essentially segregated and are characterized by nonclassical gamma exponents. The contact line between segregated chains is fractal which leads to an unusual demixing behavior in 2d blends. In the second case (crossings are allowed) polymer coils are overlapping and show meanfield statistics with logarithmic corrections. The correlation function of concentration fluctuations in this system is predicted to exhibit a universal long range power tail (1/r(4)) which is due to nonmeanfield effects. The dynamical behavior of the two models is even more drastically different: The first model is characterized by a relatively fast dynamics with conformational relaxation time t(N)proportional toN(15/18) (i.e. t(N) is slightly shorter than the Rouse time proportional to N2). On the other hand an exponentially slow dynamics is predicted for model 2 (with 3d entanglements).


2002 
Johner, A., & Semenov, A. N. (2002). Commentary on “The polymer mat: Arrested rebound of a compressed polymer layer” by U. Raviv, T. Klein and T.A. Witten. European Physical Journal E, 9(5), 413–416.


Semenov, A. N. (2002). Adsorption of a semiflexible wormlike chain. European Physical Journal E, 9(4), 353–363.
Abstract: Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a selfsimilar monomer concentration profile c(x) similar to x(4/3) near the surface (when the distance to the surface x is much smaller than the chain persistence length l/2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2dimensional) trains of wormlike short loops (flat blobs) and coillike (3dimensional) loops forming a triplelayer structure: contact layer (x < Delta) of adsorbed fragments virtually laid on the surface, proximal layer (Delta < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Delta defines the range of monomer/surface attraction, Delta much less than l. The adsorption transition is continuous. However, its relative width DeltaT/T* is small (T* is the adsorption temperature, DeltaT is the relevant temperature interval): DeltaT/T* similar to (Delta/l)(4/3), i.e. a discontinuous transition in the limit Delta/l > 0.


2000 
Clement, F., Johner, A., Joanny, J. F., & Semenov, A. N. (2000). Stress relaxation in telechelic gels. 1. Sticker extraction. Macromolecules, 33(16), 6148–6158.
Abstract: We discuss the nonlinear rheology of telechelic gels formed by triblock copolymers with short hydrophobic end blocks (the stickers). In this first paper, we merely study the variation of the extraction time of a sticker from a hydrophobic aggregate with the chain tension. Using a model potential that binds the sticker/chain junction point to the aggregate/water interface, we explicitly show that the extraction time only depends on the chain tension at the junction point. The results are extended to more realistic potentials by heuristic arguments. At this level of description various effects (curvature of the aggregate, sticker flexibility, impenetrable aggregate constraint) can also be accounted for.


1997 
Nyrkova, I. A., Semenov, A. N., & Joanny, J. F. (1997). Highly anisotropic rigidity of ''ribbonLike'' polymers .2. Nematic phases in systems between two and three dimensions. Journal De Physique Ii, 7(6), 825–846.
Abstract: Various extensions of Onsager theory based on the second virial approximation are constructed in order to describe nematic Pphases in ribbon polymer solutions. If the average coil shape is anisotropic and the concentration is not too high, the coils can be considered as anisotropic solid objects and an ordinary expansion over the coil concentration can be performed. This first approach can be applied to study pancake nematic ordering. At higher concentrations and when the polymer chains are rather long, the polymer solution can be considered as a solution of short fragments connected into chains with a particular statistics reflecting the polymer structure with two rigidities: a similar virial expansion can be constructed. This last approach allows the consideration of the various symmetries of the nematic phases simultaneously. We also take into account the correlation correction to the mean field result which provides an essential additional angular dependence to the interaction free energy. Scaling arguments are applied in the case where the intracoil correlations are very strong, or if the coils interact as opaque objects. The methods developed here will be used in further publications to study liquid crystalline ordering in solutions of ribbon chains.


Nyrkova, I. A., Semenov, A. N., & Joanny, J. F. (1997). Highly anisotropic rigidity of ''ribbonlike'' polymers .3. Phase diagrams for solutions. Journal De Physique Ii, 7(6), 847–875.
Abstract: The behavior of solutions of polymer chains with anisotropic rigidity is considered theoretically. The diagrams of different scaling regimes and the phase diagrams for polymers with arbitrary contour length L, inplane rigidity l, and out of plane rigidity l(2) are obtained. Two new types of nematic structures in addition to ordinary nematic with ordering of tangent vectors are found for the regime of moderate second rigidity l(2) (l less than or equal to l(2) less than or equal to l(3)/d(2)): a pancake nematic (with ordering of the normals to the planes of main flexibility of the chains) and a biaxial nematic (when both tangent and normal vectors are ordered). We also found smectic A and smectic C phases in addition to three nematic phases. The scaling (modified blob) and meanfield with correlation corrections approaches are developed and used when appropriate. Order parameters, correlation radii and chain sizes are discussed for most of the regimes.


Semenov, A. N., & Joanny, J. F. (1997). Formation of hairpins and band broadening in gel electrophoresis of DNA. Physical Review E, 55(1), 789–799.
Abstract: The dynamics of a long DNA molecule undergoing constantfield gel electrophoresis is considered theoretically on basis of the reptation theory. A generalized theoretical approach taking into account the possibility of a branched tube structure is presented. It is shown that in a wide range of electric fields a branched conformation is more stable than a linear conformation assumed by the standard biased reptation model. The process of nucleation of a branched structure from a linear structure is considered analytically in detail. The field dependencies of both longitudinal and transverse diffusion constants are discussed within the framework of the proposed twostates model. It is predicted that the longitudinal diffusion constant shows a sharp maximum in the weakfield regime.


Semenov, A. N., Joanny, J. F., Johner, A., & Avalos, J. B. (1997). Interaction between two adsorbing plates: The effect of polymer chain ends. Macromolecules, 30, 1479–1489.
Abstract: The interaction between two plates coated by adsorbed polymer layers is considered theoretically in the marginal solvent regime. A novel meanfield approach that takes into account the effect of chain ends is proposed. The approach generalizes the wellknown groundstate dominance theory. It is shown that the effect of polymer chain ends is important even if there is no specific interaction between the ends and the adsorbing plates. Both cases of polymer layers in equilibrium with a bulk dilute or semidilute solution and of fixed amount of polymer between the plates are considered. In all the cases the effect of polymer chain ends changes the interaction between the plates from an attraction to a repulsion if the plates are far enough from each other. This additional repulsive interaction can be qualitatively interpreted as being due to an idealgas pressure of chain ends.


1996 
Avalos, J. B., Joanny, J. F., Johner, A., & Semenov, A. N. (1996). Equilibrium interaction between adsorbed polymer layers. Europhysics Lett., 35(2), 97–102.
Abstract: We discuss the force between two surfaces coated with adsorbed polymer layers in thermodynamic equilibrium with a polymer solution. We use a meanfield theory that explicitly takes into account the loops and tails structure of the adsorbed polymer layers. The force has a nonmonotonic variation with distance: it is attractive at short distances where the loops dominate and where bridging is important and it is repulsive at large distances where the tails dominate.


Johner, A., Avalos, J. B., vanderLinden, C. C., Semenov, A. N., & Joanny, J. F. (1996). Adsorption of neutral polymers: Interpretation of the numerical selfconsistent field results. Macromolecules, 29(10), 3629–3638.
Abstract: We use results on polymer absorption obtained from a recent meanfield theory with two order parameters to interpret numerical results of the Scheutjens and Fleer approach. An extension of the analytical theory accounting for the local swelling of the polymer is also presented and discussed.


Nyrkova, I. A., Semenov, A. N., Joanny, J. F., & Khokhlov, A. R. (1996). Highly anisotropic rigidity of ''ribbonlike'' polymers .1. Chain conformation in dilute solutions. Journal De Physique Ii, 6(10), 1411–1428.
Abstract: We discuss the solution properties of polymers with a highly anisotropic rigidity which bend rather freely in a plane (the plane of main flexibility) and are extremely rigid in the direction perpendicular to this plane. Examples of these polymers are the ladder polymers recently synthesized or living polymers formed by the aggregation of peptide rodlike fragments. These polymers have a much higher out of plane persistence length l(2) than their inplane persistence length l. In the first paper of this series, we mostly investigate the conformation of single chains in solution (at extremely low concentrations). The conformation of an isolated chain with a highly anisotropic rigidity essentially depends on the dimensionless parameter Ohm = l(2)d(2)l(3) where d is the chain diameter. For small values of Ohm, (l(2) similar to l), the chain behaves as a standard semiflexible chain with isotropic rigidity. For large values of Ohm, (Ohm greater than or similar to 1), the chain adopts a onedimensional rodlike conformation at length scales smaller than l, an anisotropic disclike conformation at intermediate scales (corresponding to a contour length L such that l less than or similar to L less than or similar to l(2)) and a threedimensional swollen coil conformation at larger length scale. In the intermediate range of Ohm, l(2)/d(2) less than or similar to Ohm less than or similar to 1, the same three regimes are expected but the excluded volume interactions do not play any role in the disclike regime. At the end of the paper we discuss qualitatively the possible liquid crystalline phases (with nematic or smectic symmetry) which can emerge in these solutions at higher concentration.


Semenov, A. N., Avalos, J. B., Johner, A., & Joanny, J. F. (1996). Adsorption of polymer solutions onto a flat surface. Macromolecules, 29, 2179–2196.
Abstract: We present a theoretical description of polymer adsorption from solution which is based on a mean field approximation but which goes beyond the standard ground state dominance approximation. The properties of the adsorbed polymer chains are described by two coupled order parameters. This allows a description of the chains in terms of tails and loops. When the bulk solution is dilute, the adsorbed polymer layer has a double layer structure with an inner layer dominated by loops and an outer layer dominated by tails. Explicit asymptotic forms are found for the monomer concentration profile and for the crossover distance between the loops and tail regions. The precise concentration profile is obtained by a numerical solution of two coupled differential equations. One of the surprising results is that the total polymer adsorbed amount has a nonmonotonic variation with molecular weight and decreases for large values of the molecular weight. The concentration profiles are also determined when the bulk solution is semidilute or concentrated. At any bulk concentration, the monomer concentration has a nonmonotonic variation with the distance to the adsorbing wall and shows a minimum at a finite distance. This depletion effect can be significant in the vicinity of the crossover between dilute and semidilute solutions. All the results are in agreement with the existing numerical solutions of the complete mean field theory of polymer adsorption. Excluded volume correlations are taken into account by constructing scaling laws for polymers in a good solvent both in dilute and in semidilute solutions.


1995 
Semenov, A., & Joanny, J. (1995). Kinetics Of Adsorption Of Linear Homopolymers Onto Flat Surfaces – Rouse Dynamics. Journal De Physique Ii, 5(6), 859–876.
Abstract: The dynamic properties of unentangled adsorbed polymer layers are considered theoretically. The kinetics of penetration of a chain in an adsorbed layer is considered as a twostep process: entry corresponding to the attachment of the chain on the adsorbing surface and spreading on the surface. We discuss three types of experiments, the formation of an adsorbed layer, the desorption from an adsorbed layer and the exchange between an adsorbed layer and a bulk solution. The bottleneck for the adsorption of a new chain onto a solid wall (already covered by polymers) is the spreading stage corresponding to creation of G contacts with the wall with a total binding energy of order of kT. The desorption of a preadsorbed layer in contact with pure solvent is extremely slow and only a very small fraction of the adsorbed chains is expected to desorb within the experimental time scale. The exchange between labelled adsorbed chains and unlabelled chains in solution is slower than the formation of a saturated layer, but much faster than the desorption process. The molecular weight dependencies of the characteristic times of the three processes are predicted using the RouseZimm dynamics for the polymer chains.


Semenov, A., & Joanny, J. (1995). Structure Of Adsorbed Polymer Layers – Loops And Tails. Europhysics Lett., 29(4), 279–284.
Abstract: The structure of an adsorbed polymer layer in equilibrium with a dilute good solvent is considered theoretically. It is shown that under saturation conditions the tails of the polymer chains give an important contribution to the monomer density profile in the outer layer away from the wall: the tail contribution dominates over the loop contribution in the region alpha N0.5 < z < alpha Nnu, where z is the distance from the wall, alpha the link size, and nu the Flory exponent. The characteristic layer thickness is thus determined by the tail properties.


Semenov, A., Joanny, J., & Khokhlov, A. (1995). Associating Polymers – Equilibrium And Linear Viscoelasticity. Macromolecules, 28(4), 1066–1075.
Abstract: A theory for the equilibrium and dynamic properties of a solution of telechelic polymers in the limit of high aggregation number is presented. It is shown that (1) the micelles formed by telechelic chains (flowers) in a dilute solution strongly attract each other, (2) at some concentration phi* the flowers form a reversible gel where they are connected by multiple bridges, (3) the dynamics of individual micelles in the gel is governed by the bridge/loop exchange rate and by the effective barrier associated with the hopping of a micelle to a new position; this barrier is determined by the energy associated to a deformation/ compression of a micelle, (4) the viscosity is changing exponentially in the region phi > phi* (it is increasing in the vicinity of phi*); however, it can decrease (with phi) in a limited concentration range above phi*.

