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STATISTICAL PHYSICS OF MACROMOLECULES Polymers are long molecular chains, and most specific and interesting properties of polymer systems are connected with the fact that, in the course of thermal motion, these chains bend occasionally and adopt a variety of conformations. Conformational properties of polymers are studied theoretically by the methods of classical statistical physics; the corresponding field of science is called statistical physics of macromolecules. This field provides theoretical background for physical chemistry of polymers and for molecular biophysics, since most important molecules in biological systems are biopolymers (DNA, proteins, etc.). We are doing research in several fields of the statistical physics of macromolecules. For instance, polyelectrolytes are charged macromolecules, and peculiar properties of polyelectrolyte systems emerge from the interplay of long-range Coulomb and short-range Van-der-Vaals forces. We are studying the specific effects that take place in the solutions, melts, and gels of charged macromolecules. For example, polyelectrolyte gels swollen in a solvent exhibit a very sharp conformational transition when the solvent quality becomes poorer (gel collapse): the volume of the gel can undergo a thousand-fold jumpwise change. We are developing the theory of transitions of this type and investigating various accompanying phenomena. Another interesting effect is the compatibility enhancement in polymer mixtures if the chains contain some small fraction of charged links. We have shown that such polyelectrolyte mixtures can exhibit the so-called microphase separation transition, with the formation of regular microdomains rich with one or another component. The microphase separation transition in various polymer systems is another field of our research. Until recent years this transition was associated mainly with block-copolymer systems with incompatible blocks: since blocks are connected into one chain, they cannot separate macroscopically; thus microdomain structure is formed. However, it was shown recently that the microphase separation can take place in other polymer systems, such as polyelectrolyte mixtures (see above), interpenetrating polymer networks, and random copolymers. We have shown that even in ordinary polymer blends, when nothing prevents the separation into macroscopic phases, the formation of microdomains is still possible if the system is not far from the glass transition temperature. Another direction of our studies is the multiplet structure in ionomers, i.e., polymers that would be potentially charged in a polar medium, but in the nonpolar environment, the counterions are condensed on polymer chains forming ion pairs. These ion pairs strongly attract each other due to the dipole-dipole interactions, and the formation of the resulting multiplet structure can be regarded as microphase separation. The theory of liquid-crystalline polymers is the traditional topic of our studies. We developed the first theory of spontaneous orientational ordering in the solutions of polymer chains with partial flexibility, and now we are dealing with more complex systems such as liquid-crystalline polyelectrolytes and orientationally ordered gels. Dynamic properties of concentrated polymer solutions are very complicated because polymer chains are highly entangled with each other. The key notion is that of topological restrictions for a motion of a given chain imposed by surrounding chains. Usually the effect of topological restrictions is modeled by the "tube" constraint: polymer chains can move only in a snake-like fashion along the tube (reptation), while perpendicular motion is forbidden due to topological restrictions. We are studying the effect of topological restrictions from a more fundamental point of view, without introducing crude approximations, such as "tube" constraints. Among other topics of our research are polymer-colloid interactions, penetration of polymers through membranes, gel electrophoresis of DNA, and theory of polymer absorption. |
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