Sergei Obukhov

Long range bond-bond correlations in dense polymer solutions

The scaling of the bond-bond 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 three-dimensional 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)=2-2nu=0.824 (nu=0.588 being Florys 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 power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.

The problem of directed percolation

A generalization of the percolation problem is proposed for disordered systems without a centre of inversion. Critical exponents are calculated in 5-ϵ dimensions. The structure of the infinite directed cluster is discussed.

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ξ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r≫ξ. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.

Configurational statistics of a disordered polymer chain

A problem of the configurational properties of a long flexible polymer chain with a quenched disorder is considered. The chain is assumed to be randomly constructed from monomers of two different kinds with different constants for the two-body interaction. Near the theta point, i.e. when the average interaction of monomers is small, the spatial correlation of the repulsive and attractive monomers of different kinds leads to an increase of effects of the disorder on large scales. There is also the competing effect of the repulsive three-body interaction which tends to screen the effects of disorder on large scales. For both effects the upper critical dimension is dc=3. A solution of the renormalisation group equation indicates that there always exists a critical scale at which the relative dispersion of sizes of polymers with different random sequences of monomers becomes of the order of unity. The magnitude of this critical scale depends strongly on the relation between the constant which characterises the dispersion of the two-body interaction B0 and the constant of the repulsive three-body interaction V0. If B0<3/32V0 at each physically attainable scale the effects of screening are prevalent and the dispersion of sizes of polymers with different sequences of monomers is small near the theta point. If the reverse inequality holds, the dispersion of sizes becomes of the order of unity near the theta point.

Melt of polymer rings: The decorated loop model

Melts of unconcatenated and unknotted polymer rings are a paradigm for soft matter ruled by topological interactions. We propose a description of a system of rings of length N as a collection of smaller polydisperse Gaussian loops, ranging from the entanglement length to the skeleton ring length , assembled in random trees. Individual rings in the melt are predicted to be marginally compact with a mean square radius of gyration . As a rule, simple power laws for asymptotically long rings come with sluggish crossovers. Experiments and computer simulations merely deal with crossover regimes typically extending to . The estimated crossover functions allow for a satisfactory fit of simulation data.

Non-ideality of polymer melts confined to nanotubes

Corrections to chain ideality have been demonstrated recently for polymer melts in the bulk and in ultrathin films. It has been shown that the effect of incomplete screening is stronger in the latter. We show here that the deviation from ideality is even stronger in thin capillaries. Describing the crossover from the free bulk to the confined regime as the radius of the capillary decreases below the typical coil radius we make connection to the so far disconnected work by Brochard and de Gennes (J. Phys. (Paris), Lett., 40 (1979) 399) predicting chain segregation in very thin capillaries. Due to the generalized Porod scattering of the segregated chains, the Kratky representation of the intrachain structure factor reveals a plateau for all regimes although the chains become swollen with increasing confinement.

Percolation in a system of randomly distributed sticks

Arguments are given that a full description of any realistic model of randomly distributed conducting sticks in an insulating matrix must incorporate the history of system preparation. Different regimes of composite formation produce different dependences of the percolation threshold value on the width-to-length ratio in : rho c approximately in 0, rho c approximately in 1 or even rho c approximately in 2.

Nanofluidity of a polymer melt: Breakdown of Poiseuille's flow model

Capillary rise of polymer in thin tubes ≈40 nm in diameter (comparable to the size of individual polymer molecule) shows anomalous molecular-weight dependence (Shin K. et al., Nat. Mater., 6 (2007) 961). We suggest that this dependence reveals breakdown of macroscopic hydrodynamics characterized by the bulk viscosity and propose a new microscopic mechanism for transport along a thin capillary based on the reptation model. The crossover capillary diameter from microscopic to macroscopic flow D*≈70 nm for 105 molecular-weight polyethylene and is proportional to the molecular weight. We discuss how a new transport mechanism might affect boundary conditions in a capillary when undulations of the walls prevent the slipage of the flow. We discuss the relevance of nonlinear effects and show, that they might be observed at the very onset of capillary rise flow.

Upper critical dimension of Kauffman cellular automata

Random Boolean networks on nearest-neighbour d-dimensional lattices are argued to belong to the universality class of directed percolation with quenched disorder in d+1 dimensions. Hansens computer simulations for d=4 are thus interpreted as being at the upper critical dimension.

The negative susceptibility of the n=0 vector model and polymer statistics

It is shown, that the negative susceptibility of the n=0 vector model does not imply unphysical characteristics for a related polymer system. In terms of the polymer system it corresponds to the narrowing of the distribution function of the total number of polymers in the solution with respect to the Poisson distribution.