Высокомолекулярные соединения

Серия C

ВЫСОКОМОЛЕКУЛЯРНЫЕ СОЕДИНЕНИЯ, Серия C, 2013, том 55, № 7, с. 805-807

RECENT DEVELOPMENTS IN COMPUTER MODELING OF POLYMER SYSTEMS

DOI: 10.7868/S0507547513070106

A great variety of complex fluids like solutions and melts of linear and branched polymers, gels, supramo-lecular structures, formed from amphiphilic molecules, vesicles, membranes, liquid crystals, and colloidal suspensions, etc., are nowadays generally referred to as soft matter. Soft matter plays the most prominent role today in numerous aspects of our everyday life. It is generally considered as providing the very basis of emerging novel materials. Soft matter is expected to essentially determine the progress in the near future. The importance of soft matter systems for various branches of technology, biology, and medicine, along with a number of intellectual challenges related to the understanding and interpretation of processes in soft matter, have in turn prompted an outburst of research in this area during the last few decades. A central and ever increasing role in the relevant scientific investigations is thereby played by various methods of computer modeling. Indeed, computer simulations of polymers have proved indispensable as a research tool in the field. While a plethora of new knowledge about polymer-related properties and processes is supplied by ongoing computational studies, the very methods used by scientists in computer simulations are constantly being developed and excelled in both their efficiency and outreach. Therefore, this special issue of Polymer Science Series C was initiated as an effort to make our readers familiar with the latest insights and concepts in the field of computer modeling of polymer systems.

Strong emphasis in this special issue is put on the modeling and properties of semiflexible macromole-cules, owing to their significance both in view of technological applications as well as from the standpoint of basic science. Liquid crystalline polymers, for instance, offer attractive possibilities for the development of new functional materials by combining the properties of low molecular weight liquid crystals with those of macromolecular compounds. Moreover, semirigidity plays an important role among biopolymers, as, e.g., in DNA, where variable rigidity and chirality provide cell stability. Considerable insight regarding the impact of semiflexibility in polymers has

been gained only recently, which prompted us to put some emphasis on such aspects in this special issue.

The topic is introduced by the opening review article of V. Ivanov, J. Martemyanova, A. Rodionova, and M. Stukan, who provide a survey of some modern simulational methods such as the method of expanded ensembles, of entropic sampling, or the Wang-Landau algorithm, employed in various studies of semiflexible polymer solutions. As an example, the impact of semirigidity on the intramolecular orientation and spatial ordering of a single chain segment in the bulk and close to an adsorbing surface is illustrated by a series of own investigations of these authors. The important case of nematic ordering in semidilute polymer solutions in the bulk and in a thin film, as well as the corresponding phase diagrams, are considered, too, along with an overview of other promising studies on semiflexible polymers.

Single-chain phase diagrams for three specific models (flexible and semiflexible homopolymer chains, and flexible AB heteropolymers, comprised of alternating square-well and hard-sphere monomers) are presented as derived from the Wang-Landau study by M. Taylor, W. Paul, and K. Binder. While the polymers reside in an expanded coil state at high temperature, they are found to undergo a series of collapse and/or freezing transitions with decreasing temperature. This contribution provides a number of important details on the implementation of the Wang-Landau algorithm, the underlying Monte Carlo move set, and the subsequent thermodynamic and structural analysis required to characterize phase behavior.

Interestingly, the persistent length of macromole-cules as one of their basic characteristics describing local stiffness appears difficult to extract from the physical properties of polymers. H.-P. Hsu, W. Paul, and K. Binder elucidate the problem on the ground of extended Monte Carlo simulations using the prune-enriched Rosenbluth method for self-avoiding walks (with lengths of up to 50000!) and bottle-brush polymers described by the Bond Fluctuation method on a lattice. It is argued, inter alia, that the intuitively appealing Kratky-Porod worm-like model may lead to

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quite misleading results and that a unique choice for a well defined persistent length as a measure of intrinsic chain stiffness does not emerge. The authors offer a rather detailed consideration of the problem that is designed to help experimentalists with a proper interpretation of their data on semiflexible polymers.

In his interdisciplinary contribution, motivated essentially by biophysics, A. Bhattacharya explores the translocation dynamics of a driven semiflexible polymer chain through a nanopore in a cell membrane. It is demonstrated that growing polymer rigidity leads to an increase of the characteristic translocation time. The scaling of the latter with chain length can be described by the same power law as for flexible polymers, provided one uses for the scaling power an effective value of the Flory exponent which takes into account the respective degree of polymer stiffness. A qualitative physical explanation for the dependence of various quantities on chain stiffness is suggested by extending the Sakaue tension propagation theory to a semiflexible chain.

An interesting and little explored aspect in this vein concerns the interaction of stiff and soft building units in macromolecules and, most notably, the ensuing impact on structural properties and phase behavior. Thus, S. Dolezel, S. Behringer, and F. Schmid present a new coarse-grained model system, designed as a tool for investigating the phase behavior of rod-coil block copolymer systems on mesoscopic length scales. The model captures the relevant physics by providing packing of rods through hard core interactions, in addition, the conformational freedom of flexible coils is explicitly taken into account, as is the energetic repulsion between coils and rods. The proposed conversion of interactions to density fields leads to an efficient numerical treatment within a Monte Carlo simulation and is thus particularly suited to investigate how en-tropic and energetic contributions of coils alter ordering effects of rods at different packing fractions.

In two separate contributions, Yu. Kriksin, P. Kha-latur, and A. Khokhlov examine the ordering in a mixture of flexible and rigid diblock copolymers by means of the self-consistent field modeling approach. Self-organization of both constituents into a network in the course of microphase separation is demonstrated to produce a stable hexagonal structure with different types of ordering determined by the stiff blocks. The resulting anisotropy appears potentially promising for applications in optics. By extending the approach to three dimensions and increasing both spatial resolution and system size, the authors find new phases upon variation of temperature, especially, a new transition to a hexagonally arranged columnar morphology that possesses macroscopic chirality arising as a result of spontaneous symmetry breaking in the system of achiral rod-coil copolymers.

In a slightly different aspect, namely, that of microphase separation under geometric constraints, the phase behavior of a melt of diblock copolymers in con-

finement is described by C. Gross and W. Paul using a new soft-quadrumer model where the interactions with the container walls are obtained by systematic coarse-graining of chemically realistic potentials. By means of Monte Carlo simulation these authors demonstrate the nucleation of a new lamella in the center of a thin film and the subsequent reorientation transition of the lamellar phase.

Somewhat related to the aforementioned approach, A. Teplukhin suggests a simplified procedure for modeling the internal degrees of freedom as, e.g., the bond lengths, twisting-, and bending angles in polymers, by means of an efficient Monte Carlo method. It is shown that the conventional Metropolis procedure, which takes into account the respective energy contributions, can be reduced to regular checks on whether these angles correspond to the standard values for concrete types of atoms.

Monte Carlo simulations using entropic sampling are a valuable alternative to traditional methods. In the entropic sampling algorithms, instead of sampling the Boltzmann distribution of the system as in the Metropolis procedure, one estimates the configurational density of states and then directly derives from it all thermodynamic properties such as conformational energy, heat capacity, entropy, and free energy. This very efficient approach combined with the WangLandau scheme is used by P. Vorontsov-Velyaminov, A. Yurchenko, M. Antyukhova, I. Silantyeva, and

A. Antipina for studying the thermodynamic and structural properties of several lattice and continuous polymer models, including the models of star-like polymers, neutral and charged chains which interact with each other or with flat surfaces.

Another topic of application-motivated high scientific interest and intensive research activity at present is that of branched macromolecules whose conforma-tional properties and monomer distribution differ considerably from those of linear polymers and has been controversially discussed in the literature. In their review article, J. Klos and J.-U. Sommer give an overview of the state-of-the-art knowledge of physical properties of dendrimers, as seen from coarse-grained computer

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