Effect of on conformational properties of uncharged polymer. (a) vs ; (b) vs ; (c) double logarithmic plot of vs .
Dependence of persistence length on for , 50 (◻), 150 (◇), and 3000 (▿), as calculated with Eq. (3.5). Filled symbols correspond to Eq. (3.4).
The shape factor vs for varying chain stiffness.
Radius of gyration, for a charged stiff polymer with , , and different . Monomer density .
For a chain of , , , and ; (a) vs [filled, Eq. (3.4); open, Eq. (3.5)]; (b) the shape factor vs .
Radius of gyration for a chain of length and some values of bending force constant ; monomer density . (a) ; (b) . Typical configurations are included for , , and at different .
Dependence of the degree of ionization on for different and values; the chain length and .
Dependence of degree of ionization on the polymer concentration. , , and . The corresponds to the overlapping concentration assuming that the chain is rodlike.
Snapshots of the formation of a toroid with one nucleus. , , , , and . (1)–(9) correspond to time steps 200, 1530, 1940, 4100, 5210, 5500, 6140, 8200, and 10 000, respectively.
Snapshots of formation of a toroid with multiple nuclei. , , , , and . (1)–(9) correspond to time steps 200, 1450, 1800, 2300, 3400, 3850, 3900, 3970, and 10 000, respectively.
Dynamic exchange between toroidal and folded-chain structures in a typical run, as seen in the trace of radius of gyration and Coulomb energy as a function of time. Total simulation time steps are . , , , , and .
The evolution of transitions among coil, folded-chain, and toroid states for a stiff chain of and for , , and . (1)–(9) correspond to time steps 200, 2160, 2900, 3080, 6100, 8100, 8200, 8300, and 10 000, respectively.
(a) Sketch of a toroid. (b) dependence of , , and R. , , and .
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