A Monte Carlo study of the second virial coefficient of semiflexible ring polymers

• Published in: Polymer journal Vol. 42; no. 9; pp. 735 - 744
• Main Authors: Ida, Daichi, Nakatomi, Daisuke, Yoshizaki, Takenao
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01-09-2010; Nature Publishing Group
• Subjects: 639/301/923/1028; 639/705/531; Applied sciences; Bending; Biomaterials; Bioorganic Chemistry; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Computer simulation; Cyclohexane; Exact sciences and technology; Knots; Mathematical models; Monte Carlo methods; Organic polymers; original-article; Physicochemistry of polymers; Polymer Sciences; Properties and characterization; Shape; Solution and gel properties; Surfaces and Interfaces; Thin Films; Virial coefficients; second virial coefficient; semiflexible ring polymer; topological interaction; MC simulation; Monte Carlo method; Chemical solution; Computer simulation; Semiflexible chain; Cyclic polymer; Second virial coefficient; Theoretical study
• ISSN: 0032-3896; 1349-0540
• DOI: 10.1038/pj.2010.61

A Monte Carlo (MC) study was made of the second virial coefficient
A
2
of the ideal Kratky–Porod (KP) worm-like ring using a model composed of infinitely thin bonds with harmonic bending energy between successive bonds. Two kinds of statistical ensembles were generated: one composed of configurations of all kinds of knots with the Boltzmann weight, called the mixed ensemble, and the other composed of only those of the trivial knot, called the trivial-knot ensemble. The effective volume
V
E
excluded to one ring by the presence of another, resulting only from a topological interaction, and also the mean-square radius of gyration 〈
S
2
〉 were evaluated for each ensemble. The dimensionless quantity
λV
E
/
L
2
proportional to
A
2
was found to be a function only of the reduced total contour length
λL
, as in the case of
λ
〈
S
2
〉/
L
, where
λ
−1
is the stiffness parameter of the KP ring and
L
is its total contour length. The quantity
λV
E
/
L
2
first increased and then decreased after passing through a maximum at
λL
≃5, as
λL
was increased. A comparison with literature data for ring atactic polystyrene in cyclohexane at Θ shows that the present MC results may qualitatively explain the behavior of the data.
The effective volume
V
E
excluded to a Kratky–Porod (KP) worm-like ring by the presence of another, resulting only from a topological interaction, was evaluated by Monte Carlo simulations. The quantity
λV
E
/
L
2
proportional to the second virial coefficient
A
2
was shown to be a function only of
λL
with
λ
−1
the stiffness parameter of the KP ring and
L
its total contour length.