Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2437
Title: Loose, flat knots in collapsed polymers
Authors: Orlandini, E
Stella, AL
VANDERZANDE, Carlo 
Issue Date: 2004
Publisher: KLUWER ACADEMIC/PLENUM PUBL
Source: JOURNAL OF STATISTICAL PHYSICS, 115(1-2). p. 681-700
Abstract: We consider single ring polymers which are confined on a plane but maintain a fixed three-dimensional knotted topology. The equilibrium statistics of such systems is studied on the basis of a model on square lattice in which the configurations are represented by N-step polygons with a number of self-intersections restricted to the minimum compatible with the topology. This allows to define the size, s, of the flat knots and to study their localization properties. Due to the presence of both excluded volume and attractive interactions, the model undergoes a theta transition. Accurate Monte Carlo results show that, while in the high temperature swollen regime both prime and composite knot components are localized ([s](N) similar to N-t, with t = 0), in the low temperature, compact phase they are fully delocalized (t = 1). Right at the theta transition weak localization prevails (t = 0.44 +/- 0.02). Part of the results can be interpreted by taking into account a dominance of figure eight shapes for the coarse grained knotted polymer configurations, and by applying the scaling theory of polymer networks of fixed topology. In particular t = 3/7 can be conjectured as an exact exponent characterizing the weak knot localization at the theta point.
Notes: Univ Padua, Dipartimento Fis, INFM, I-35131 Padua, Italy. Univ Padua, Sez INFN, I-35131 Padua, Italy. Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium. Katholieke Univ Leuven, Inst Theoret Fys, B-3001 Heverlee, Belgium.Orlandini, E, Univ Padua, Dipartimento Fis, INFM, I-35131 Padua, Italy.attilio.stella@pd.infn.it
Keywords: knots; polymers; Monte Carlo
Document URI: http://hdl.handle.net/1942/2437
ISSN: 0022-4715
e-ISSN: 1572-9613
DOI: 10.1023/B:JOSS.0000019820.70798.ed
ISI #: 000220250600029
Category: A1
Type: Journal Contribution
Validations: ecoom 2005
Appears in Collections:Research publications

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