Stiffening Transition in Semiflexible Cyclic Macromolecules

Benková, Zuzana; Cifra, Peter

doi:10.1002/mats.201000047

Cited by 8 publications

(21 citation statements)

References 38 publications

(47 reference statements)

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“…For this root we also have t 1 = cos(2π/N), which corresponds to an angle of 2π/N between neighboring bonds of a regular polygon of N sides. We note that envisaging a planar rigid polygonal structure as limiting case is also in line with recent simulation results on semiflexible rings, 18,19 in which with growing stiffness a flattening of the rings to a quite planar shape was observed.…”

Section: A the Limiting Case T → X −supporting

confidence: 87%

Maximum entropy principle applied to semiflexible ring polymers

Dolgushev

Berezovska

Blumen

2011

The Journal of Chemical Physics

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Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation.

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Section: A the Limiting Case T → X −supporting

confidence: 87%

Maximum entropy principle applied to semiflexible ring polymers

Dolgushev

Berezovska

Blumen

2011

The Journal of Chemical Physics

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“…Abreu and Escobedo obtained using a configurational‐bias Monte Carlo method for polymers in the good solvent condition a value of g = 0.62 for the ring‐shaped case and g = 0.46 for the theta‐shaped case. However, those values may not be conclusive because their value of g = 0.62 for ring‐shaped polymers was larger than those usually reported by others . Uehara et al studied the radius of gyration of caged polymers without excluded volume interactions by a quaternionic method for generating random polygons and random walks, and they found that the ratio of 〈 S 2 〉( f , N )/〈 S 2 〉( f = 2, N ) increases monotonically with respect to the number of bridges f , and approaches a constant value of about 1.3 for large f .…”

Section: Introductionmentioning

confidence: 93%

“…At the present time, there is no general agreement on the value of g for ring‐shaped polymers in good solvent. There have been extensive studies on this issue by theory, experiments, and computer simulations in the literature . Most reported values fell in the range of 0.52–0.62, all larger than the ideal chain value of 0.5.…”

Section: Introductionmentioning

confidence: 98%

“…There have been extensive studies on this issue by theory, experiments, and computer simulations in the literature. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Most reported values fell in the range of 0.52-0.62, all larger than the ideal chain value of 0.5. Studies on the θ-shaped, δ-graph, or higher f cases are scarce.…”

Section: Introductionmentioning

confidence: 99%

“…However, those values may not be conclusive because their value of g = 0.62 for ring-shaped polymers was larger than those usually reported by others. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] Uehara et al [ 12 ] studied the radius of gyration of caged polymers without excluded volume interactions by a quaternionic method for generating random polygons and random walks, and they found that the ratio of 〈 S 2 〉( f , N )/〈 S 2 〉( f = 2, N ) increases monotonically with respect to the number of bridges f , and approaches a constant value of about 1.3 for large f . In terms of the g -parameter, the results of Uehara et al correspond to an expression of g = c / f , where the numerical coeffi cient c ranges from 1 (for f = 2) to an upper bound of about 1.3 for large f .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Radius of Gyration, Mean Span, and Geometric Shrinking Factors of Bridged Polycyclic Ring Polymers

Zhu

Wang

et al. 2016

Macromol. Theory Simul.

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This study concerns the equilibrium geometric properties of a family of cyclic chains, referred to as the “bridged polycyclic rings,” which have f flexible subchains bridging two common branch points. By increasing the number of bridges, f, this family encompasses the usual linear chain (f = 1), monocyclic ring (f = 2), bicyclic θ‐shaped polymer (f = 3), and multicyclic rings with increasing topological complexity. Results of their radius of gyration, mean span, and, consequently, geometric shrinking factors (also known as the g‐factors) are obtained by three approaches—the Gaussian chain theory, simulations based on the Kremer–Grest bead‐spring model, and a Flory‐type mean‐field approach. Using the confinement analysis from bulk structures method, the equilibrium partition coefficients (K) of several of those cyclic excluded volume chains in a cylindrical pore with inert surfaces are obtained, and the results fall onto a common curve on a graph of K versus the polymer‐to‐pore size ratio, using the mean span as the representative polymer size, in the range of K relevant to polymer separation in size exclusion chromatography (SEC) experiments. Applications of the results in predicting the SEC retention volume of such bridged polycyclic ring polymers are discussed in the framework of the equilibrium partition theory.

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Piston Compression of Semiflexible Ring Polymers in Channels

Cifra

Bleha

2021

Macro Theory & Simulations

Self Cite

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Molecular simulations in nanochannels are used to explore the compression elasticity of ring polymers of stiffness (persistence length) similar to DNA. By combination with the parallel data for linear polymers, the effect of chain topology on their compression behavior is assessed. The results show that the ring polymers are much less bendable at longitudinal compression than the linear analogs. The chain span of linear polymers is continuously reduced at compression, whereas in ring polymers, an abrupt decrease of the span is observed. The simulation data elucidate this phenomenon as the buckling of a ring polymer into the double‐folded hairpin. The shrinking ratio of sizes of the ring and linear chains shows a complex behavior much differing from the existing reports. The force–displacement functions for chains of both topologies at moderate confinement are very well accounted for by the mean‐field Flory scheme. The theory predicts the difference in the mechanical stiffness of the ring and linear polymers in qualitative agreement with the simulation data. These findings are relevant to the compression behavior of semiflexible ring polymers under spatial constraints such as in nanofluidic experiments, disordered media, or cellular environment.

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Stiffening Transition in Semiflexible Cyclic Macromolecules

Cited by 8 publications

References 38 publications

Maximum entropy principle applied to semiflexible ring polymers

Maximum entropy principle applied to semiflexible ring polymers

Radius of Gyration, Mean Span, and Geometric Shrinking Factors of Bridged Polycyclic Ring Polymers

Piston Compression of Semiflexible Ring Polymers in Channels

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