We study the distribution function of the three dimensional wormlike chain with a fixed orientation of one chain end using the exact representation of the distribution function in terms of the Green's function of the quantum rigid rotator in a homogeneous external field. The transverse 1d distribution function of the free chain end displays a bimodal shape in the intermediate range of the chain lengths (1.3Lp, ..., 3.5Lp). We present also analytical results for short and long chains, which are in complete agreement with the results of previous studies obtained using different methods.PACS numbers: 05.40.-a, 36.20.-r, 61.41.+e
Electrical resistance of the elastomeric material polychloroprene filled with multiwalled carbon nanotubes (CNTs) dispersed by using an imidazolium based ionic liquid has been measured experimentally and calculated theoretically, as a function of the applied compression/decompression force F. Both experimental and theoretical results show that the electrical resistance R of the composite exhibits non-monotonic dependence on F. This observed non-monotonic dependence R(F) is explained by different mechanisms of conductivity that are specific to the respective domains of the magnitude of the compression/decompression force F. At small F, the observed decrease of conductivity with increasing F is found to be caused by the change of an average contact distance between CNTs. At higher F, the observed increase of R with increasing F is caused by the dependence of the per-particle surface area on F. The experimentally observed dependence R(F) is adequately described by the developed theory that relies on establishing the exact relation between the CNT network structure and the electrical response of the composite. Theoretical dependence between the conductivity of the composite and the applied stress is obtained using the percolation model of the electrical conductivity of CNT network that shows excellent quantitative agreement with the experimental results.
Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in the literature. An estimation of the configurational contribution to the total liquid's C(p) is presented. We also discuss the relation between the Kauzmann paradox and polymer semiflexibility.
Our study is based on the work of Stinchcombe [1974 J. Phys. C 7 179] and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi [1974 Phys. Rev. B 9 4575] for the regular lattice.
We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in the spirit of the previous Silberberg approach. The developed lattice theory incorporates the interaction between nearest-neighbor pairs of segments and finite chain length. The theory is completely mapped into the Scheutjens-Fleer theory in the limit of infinite coordination number.As a second part of the developed approach, we calculate the configurational entropy to investigate how the density structure of the semi-flexible polymers near the surface relates to possible reduction of glass transition temperature near nonabsorbing surface and enhancement near the strongly attractive surface.
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