{'fraction_non_alphanumeric': 0.02641232575201761, 'fraction_numerical': 0.004402054292002935, 'mean_word_length': 4.683333333333334, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The theta-temperature depression caused by topological effect in ring polymers studied by Monte Carlo simulation.

We studied equilibrium conformations of linear and ring polymers in dilute solutions over the wide range of segment number N of up to 2048 with Monte Carlo simulation, and evaluated N dependence of the radii of gyration, R(g), of chains. The polymer molecules treated in this study are assumed to be composed of beads and bonds, and they are put in a three-dimensional face-centered cubic (FCC) lattice. The values of Flory's critical exponent, ν, for linear and ring polymers were estimated from the N dependence of R(g), and the temperatures at which ν reach 1/2 were obtained. Here we define those as Θ-temperatures in this report. The simulation result shows that the Θ-temperature for ring polymers is evidently lower than that of the linear polymers, and the origin of the Θ-temperature depression is discussed. Since R(g) of a ring polymer is smaller than that for a linear polymer at the same N and temperature, the segment density for a ring polymer is increased by the topological effect and the repulsive force between segments of a ring polymer at the Θ-temperature for a linear polymer is stronger. Thus, the origin of the Θ-temperature depression for ring polymers is the repulsive force emphasized by the topological effect of rings.