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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 6 (1998), S. 101-110 
    ISSN: 1434-6036
    Keywords: PACS. 61.41.+e Polymers, elastomers, and plastics[:AND:] 87.15.-v Molecular biophysics - 64.70.-p Specific phase transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte-Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to . In this article, we take (resp. ( )) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the along the chain, with periodicity 2p. The simulations are done for various chain lengths N, in d=2 (square lattice) and d=3 (cubic lattice). There is a critical value p c (d,N) of the periodicity, which distinguishes between different low temperature structures. For p 〉p c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p 〈p c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, and to illustrate the physics of the various phase transitions. A tentative variational approach is also presented.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 85 (1996), S. 103-130 
    ISSN: 1572-9613
    Keywords: Ribbon ; topological entanglement ; knot ; link ; satellite knot ; writhe ; double-stranded polymer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as √n, and similar results hold for the twist and writhe.
    Type of Medium: Electronic Resource
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