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Monte Carlo Simulation Studies of the Size and Shape of Ring Polymers
Author(s) -
Zifferer Gerhard,
Preusser Werner
Publication year - 2001
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/1521-3919(20010601)10:5<397::aid-mats397>3.0.co;2-x
Subject(s) - ring (chemistry) , chain (unit) , monte carlo method , polymer , scaling , work (physics) , statistical physics , mathematics , bond length , materials science , molecule , physics , chemistry , thermodynamics , geometry , quantum mechanics , composite material , statistics , organic chemistry
The present work gives a comparison between the properties of athermal ring polymers and those of linear chains. Based on bond fluctuation (BF) and pivot algorithm (PIV) for the construction of molecules, a new algorithm was developed, which proved most efficient due to large acceptance fractions and small (integral) auto‐correlation times of global properties, in addition having the advantage of a large set of different bond vectors. While the topological state of ring polymers remains unchanged by exclusive use of BF, knotted structures (which were identified with the help of Alexander polynomials) can by formed and removed by the use of PIV. In accordance with previous work, it turned out that the probability of unknotted rings (in principle) exponentially decreases with an increasing number of segments, however, so slowly that the appearance of knotted structures (ca. 0.1% for N = 512) is a rare event in the range of chain‐lengths evaluated ( N = 32 – 8192). The chain‐length dependence of global quantities of ring polymers are described by the use of scaling relations with proper short chain corrections, in analogy to linear chains. The instantaneous shape of ring polymers is more symmetric than that of linear chains. Local quantities, i.e., mean squared bond lengths and mean bond angles are the same for both systems, at least in the limit of an infinite number of segments.