Igor Erukhimovich

Non-centrosymmetric superlattices in block copolymer blends

Materials with a macroscopic electric polarization display a variety of useful properties, such as piezo- and pyroelectricity and second-order nonlinear optical activity. Macroscopic polarization results when dipolar molecules are orientated in the same direction, or when ions are organized in a non-centrosymmetric crystal structure. Centrosymmetric molecules have no dipole moment and so cannot generate a macroscopic polarization. Non-centrosymmetry in amorphous materials can be engineered by depositing particular sequences of layers on top of each other, or by applying external fields (generally electric) to orientate the molecules. Here we report the formation of a non-centrosymmetric structure in an amorphous material through spontaneous self-assembly. Block copolymers are known to form ordered structures at the microscale owing to segregation of the different blocks, . We show that a mixture of a ternary triblock copolymer and a binary diblock copolymer will organize itself into a non-centrosymmetric layered structure in which the layers are occupied by different blocks. The structure is periodic with a length scale of around 60 nm.

On lyotropic behavior of molecular bottle-brushes : A Monte Carlo computer simulation study

A three dimensional continuous space Monte Carlo computer simulation study is presented to discuss the extension of flexible, linear polymer chains due to the presence of equally flexible side chains. We consider the enhancement of the persistence length of bottle-brush structures in an athermal solution due to steric interactions between the side chains. The largest structure studied consists of a backbone of 100 beads with 50 side chains of 20 beads each. The persistence length λ is evaluated in two different ways using the radius of gyration of the backbone and the bond angle correlation function, respectively. A correct description of the backbone conformations is shown to require at least two characteristic lengths. At a small length scale the backbone behaves flexible; the extension occurs at a larger length scale. There is a strong indication that the ratio between the persistence length and the diameter, which is the determining factor for lyotropic behavior of conventional semiflexible chains, le...

Phase equilibria and charge fractionation in polydisperse polyelectrolyte solutions

A new type of phase separation in the polyelectrolyte solutions consisting of several types of charged macromolecules differing in their degree of ionization is predicted via a general thermodynamic consideration. We show that even a small difference in the degree of ionization of otherwise equivalent components results in their spatial separation occurring upon decreasing the temperature much earlier than precipitation of the components from the solution. Some implications of charge fractionation in biological processes are discussed.

Localization transition of random copolymers at interfaces

The presence of copolymers at interfaces between two immiscible fluids is crucial to such processes as emulsion stabilization, wetting, microemulsion formation and reinforcement of polymer-polymer interfaces [1]- [10]. For oilwater interfaces, the polymers that are used in these applications are amphiphilic in nature. While one component is soluble in the oil phase, the other component is soluble in water. The difference in solubilities drives the copolymers to adsorb at the interface between the two phases. The localized copolymers can stabilize the interface in the sense that they significantly reduce the surface tension. The study of random copolymers has been motivated in recent years by relevance of these materials for both biological and technological applications. Moreover, the properties of these simple random systems may be important in understanding of much more complex systems such as proteins [11]- [13]. It is well-known that adsorption of long polymer chains on surfaces or interfaces is related to the bound state problem of a Quantum Mechanical (QM) particle in a potential well [14]. The Green’s function G(r, r ′ ;s,s ′ ) of a @

Nonconventional morphologies in two-length scale block copolymer systems beyond the weak segregation theory

The order-disorder and order-order transitions (ODT and OOT) in the linear multiblock copolymers with two-length scale architecture A(fmN)(B(N2)A(N2))(n)B((1-f)mN) are studied under intermediate cooling below the ODT critical point where a nonconventional sequence of the OOTs was predicted previously [Smirnova et al., J. Chem. Phys. 124, 054907 (2006)] within the weak segregation theory (WST). To describe the ordered morphologies appearing in block copolymers (BCs) under cooling, we use the pseudospectral version of the self-consistent field theory (SCFT) with some modifications providing a good convergence speed and a high precision of the solution due to using the Ng iterations [J. Chem. Phys. 61, 2680 (1974)] and a reasonable choice of the predefined symmetries of the computation cell as well as initial guess for the iterations. The WST predicted sequence of the phase transitions is found to hold if the tails of the BCs under consideration are symmetric enough (mid R:0.5-fmid R:</=0.05); the quantitative agreement between the WST and SCFT phase diagrams is reasonable in a narrow (both in f and chi=chiN) region close to the critical point, though. For mid R:0.5-fmid R:>0.05, a large region of the face-centered cubic phase stability is found (up to our knowledge, first within the SCFT framework) inside of the body-centered cubic phase stability region. Occurrence of the two-dimensional and three-dimensional phases with the micelles formed, unlike the conventional diblock copolymers, by the longer (rather than shorter) tails, and its relationship to the BC architecture is first described in detail. The calculated spectra of the ordered phases show that nonmonotonous temperature dependence of the secondary peak scattering intensities accompanied by their vanishing and reappearance is rather a rule than exception.

Microphase separation in multiblock copolymer melts : Nonconventional morphologies and two-length-scale switching

The phase behavior of AfmN(BN2AN2)B(1-fmN) multiblock copolymer melts is studied within the weak segregation theory. The interplay between ordering on different length scales is shown to cause dramatic changes both in the ordered phase symmetry and periodicity upon small variation of the architectural parameters of the macromolecules. Phase diagrams are presented in the (f,chiN) plane (chi is the Flory-Huggins parameter) for various values of the architecture parameters n and m. Near the critical surface, i.e., for (f-0.5)2<<1, such nonconventional cubic phases as the face-centered cubic (FCC), simple cubic (SC), (double) gyroid, and the so-called BCC(2) (single gyroid) are found to be stable. The lamellar morphology is shown to be replaced by BCC2, FCC, or SC (depending on the structural parameters) as the most stable low-temperature phase.

Mesophase formation in two-component cylindrical bottlebrush polymers

When two types of side chains (A,B) are densely grafted to a (stiff) backbone and the resulting bottlebrush polymer is in a solution under poor solvent conditions, an incompatibility between A and B leads to microphase separation in the resulting cylindrical brush. The possible types of ordering are reminiscent of the ordering of block copolymers in cylindrical confinement. Starting from this analogy, Leiblers theory of microphase separation in block copolymer melts is generalized to derive a description of the system in the weak segregation limit. Also molecular dynamics simulation results of a corresponding coarse-grained bead-spring model are presented. Using side chain lengths up to N = 50 effective monomers, the ratio of the Lennard-Jones energy parameter between unlike monomers (ε(AB)) and monomers of the same kind (ε(AA) = ε(BB)) is varied. Various correlation functions are analyzed to study the conditions when (local) Janus-cylinder-type ordering and when (local) microphase separation in the direction along the cylinder axis occurs. Both the analytical theory and the simulations give evidence for short-range order due to a tendency toward microphase separation in the axial direction, with a wavelength proportional to the side chain gyration radius, irrespective of temperature and grafting density, for a wide range of these parameters.

Phase diagrams classification of thermoreversibly associating systems with due regard for mesoscopic cyclization effects

We consider systems of f-functional monomers Af, capable of thermoreversible associating with an equilibrium Arrhenius association constant k=g0 exp(−E/T). Effects of the parameters f, g0, and E on the global phase behavior of these systems are analyzed within two theoretical approaches differing in the way to allow for the presence of closed trails of labile bonds (cycles). Within the Flory approximation, which takes into account the trails closed at infinity only (i) sol–gel transition (emergence of the infinite cluster of labile bonds) is only a geometric transition; (ii) the phase diagrams with one, two, or three critical solution temperatures could exist; (iii) there are no diagrams with three phase coexistence temperatures (triple points). On the contrary, as consistent within our new mesoscopic cyclization (MsC) approach (i) the sol–gel transition is a genuine first order phase transition accompanied by a heat effect and phase separation; (ii) the phase diagrams are more varied and could possess tr...

TOWARDS A STATISTICAL THEORY OF ASSOCIATING TELECHELICS : EQUILIBRIUM MOLECULAR STRUCTURAL DISTRIBUTION AND ONE-CLUSTER STATIC SCATTERING

A rigorous statistical treatment of the system of associating telechelics with due regard for formation of complicated many-chains clusters is presented for the case when the active telechelic ends associate only in two (A2) and threefold (A3) aggregates. A diagram technique to describe the structure of these clusters and find the corresponding equilibrium molecular structural distribution is introduced and a regular procedure to calculate the average structural and scattering properties of the system is elaborated. A competition between forming of the tree- and looplike fragments and its influence on the critical concentration cg of gelation and structural characteristics of the system are analyzed in detail. The dependences of cg as well as the number- and weight-averaged degrees of associations both for the tree- and looplike fragments and the clusters as a whole are plotted as functions of the properly reduced number density of telechelics and the reduced equilibrium constant of the chemical reaction ...

Nonmonotonic incommensurability effects in lamellar-in-lamellar self-assembled multiblock copolymers

Using the self-consistent-field theory numerical procedure we find that the period D of the lamellar-in-lamellar morphology formed in symmetric multiblock copolymer melts A(mN/2)(B(N/2)A(N/2))(n)B(mN/2) at intermediate segregations changes nonmonotonically with an increase in the relative tail length m. Therewith D reveals, as a function of the Flory chi-parameter, a drastic change in the vicinity of the internal structure formation, which can be both a drop and a rise, depending on the value of m. It is argued that the unusual behavior found is a particular case of a rather general effect of the incommensurability between the two length scales that characterize the system under consideration.