Microphase separation in random multiblock copolymers.

Microphase separation in random multiblock copolymers is studied with the mean-field theory assuming that long blocks of a copolymer are strongly segregated, whereas short blocks are able to penetrate into "alien" domains and exchange between the domains and interfacial layer. A bidisperse copolymer with blocks of only two sizes (long and short) is considered as a model of multiblock copolymers with high polydispersity in the block size. Short blocks of the copolymer play an important role in the microphase separation. First, their penetration into the "alien" domains leads to the formation of joint long blocks in their own domains. Second, short blocks localized at the interface considerably change the interfacial tension. The possibility of penetration of short blocks into the "alien" domains is controlled by the product χNsh (χ is the Flory-Huggins interaction parameter and Nsh is the short block length). At not very large χNsh, the domain size is larger than that for a regular copolymer consisting of the same long blocks as in the considered random copolymer. At a fixed mean block size, the domain size grows with an increase in the block size dispersity, the rate of the growth being dependent of the more detailed parameters of the block size distribution.

Multiblock copolymers prepared by patterned modification: Analytical theory and computer simulations.

We describe a special type of multiblock copolymers which are synthesized by a hypothetic procedure of the modification of monomer units in a polymer melt according to a certain geometrical criterion. In particular, we explore the case of lamellar-like structures: the sequence statistics of the resulting multiblock copolymers is described and their ability to self-assemble is studied. It is found that the block-size distribution P(k) for such random copolymers contains a large fraction of short blocks with the asymptotic dependence ∼k(-3/2), where k is the block size. A characteristic feature of such multiblock copolymers is their extremely high block-size polydispersity with the polydispersity index being proportional to the space period of the modification. The morphological behavior of such copolymers is simulated by means of dissipative particle dynamics. A stable self-assembled lamellar structure is observed, but the domain size appears to be sufficiently larger than the initial pattern period.

New strategy to create ultra-thin surface layer of grafted amphiphilic macromolecules.

It was found first that macromolecules made of amphiphilic monomer units could form spontaneously an ultra-thin layer on the surface which the macromolecules are grafted to. The width of such layer is about double size of monomer unit consisting of hydrophilic A (repulsive) and hydrophobic (attractive) B beads. The hydrophilic A beads are connected in a polymer chain while hydrophobic B beads are attached to A beads of the backbone as side groups. Three characteristic regimes are distinguished. At low grafting density, the macromolecules form ultra-thin micelles of the shape changing with decrease of distance d between grafting points as following: circular micelles-prolonged micelles-inverse micelles-homogeneous bilayer. Those micelles have approximately constant height and specific top-down A-BB-A structure. At higher grafting density, the micelles start to appear above the single bilayer of amphiphilic macromolecules. The thickness of grafted layer in these cases is different in different regions of grafting surface. Only at rather high density of grafting, the height of macromolecular layer becomes uniform over the whole grafting surface. The study was performed by computer modeling experiments and confirmed in framework of analytical theory.

Microphase separation in polymer solutions containing surfactants.

A microphase separation in solutions containing a polymer and a mixture of two solvents, one of which consists of amphiphilic molecules (surfactant), is considered theoretically in the weak-segregation regime. A surfactant molecule is described as a dimer consisting of hydrophobic and polar parts. The energy gain due to the orientation of surfactant molecules can lead to the appearance of non-homogeneities in the solution, where density fluctuations cause the orientational ordering of surfactant molecules. The difference in the interaction energies of hydrophobic and polar groups of a surfactant with solvent is considered as a main reason for orienting surfactant molecules. The free energy is calculated for various morphologies (lamellar, cylindrical hexagonal, spherical particles arranged at different cubic lattices). The phase diagrams are presented. With worsening the solvent quality, the transitions from disordered to a macro-separated state at low polymer and surfactant concentrations or to a body-centered-cubic, then hexagonal, and then lamellar structure at high polymer and surfactant concentrations are predicted. The amphiphilicity degree of surfactant molecules should exceed a certain critical value to make a microstructure formation possible. The period of the lamellar microstructure decreases with increasing the surfactant and polymer concentrations.

Diffusion-induced growth of compositional heterogeneity in polymer blends containing random copolymers.

The compositional relaxation in random copolymer systems on a macroscopic scale is considered in theory. A set of diffusion equations is derived that describes the motion of chains of different composition and then converted into coupled equations for statistical moments of the compositional distribution. Several ways to solve the closure problem for these equations are discussed. The simplest is the situation when the shape of the transient compositional distribution can be predicted a priori, for example, a bimodal distribution is kept during interdiffusion of two copolymers that are not very close in composition. For a general case, it is shown that the cumulant-neglect closure based on the truncation of high-order cumulants is an effective method to get an approximate solution in terms of the time-dependent local mean composition and its dispersion. This method is applied to non-homogeneous compatible polymer systems, such as a random copolymer AB of a composition varying in space, a bilayer of Bernoullian copolymers AB of different composition, and a bilayer of homopolymers A and B, in which an autocatalytic polymer-analogous reaction A --> B takes place, with possibility of the neighbor group effect. It is found that the interdiffusion can lead to a substantial broadening of the local compositional distribution, which, in turn, accelerates the system dynamics and promotes chemical reactions.

Conformation-dependent sequence design: evolutionary approach.

A new modification of evolutionary approach to sequence design of copolymers has been proposed. A model of step-by-step evolution of a two-letter ( HP) copolymer sequence has been studied by means of a coarse-grained Monte Carlo algorithm. The conditions for accepting a change in the primary sequence depend on the spatial conformation of HP-copolymer chain. This leads to a coupling between sequence and conformation and to formation of protein-like conformations and primary sequences (for some values of parameters of the model) independently of initial sequence and/or conformation. Simple theory describing these computer simulation observations is developed.

Stability of dense hydrophobic-polar copolymer globules: regular, random and designed sequences.

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 mean-field 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 H-units: regular HP-sequences (P-units separated by equal H-blocks), random copolymers (uncorrelated positions of P-units, i.e. Flory distribution of H-block lengths), proteinlike (PL) sequences (designed sequences involving both long H-blocks dominating by total mass, and short blocks dominating by number). We showed that PL-globules are more stable (lower free energy) and are characterized by a higher temperature of the coil-to-globule transition when compared with the other sequences mentioned above. We also considered HP-H-copolymers 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.

Primary sequences of proteinlike copolymers: Levy-flight-type long-range correlations.

We consider the statistical properties of primary sequences of two-letter HP copolymers (H for hydrophobic and P for polar) designed to have water soluble globular conformations with H monomers shielded from water inside the shell of P monomers. We show, both by computer simulations and by exact analytical calculation, that for large globules and flexible polymers such sequences exhibit long-range correlations which can be described by Levy-flight statistics.