Conformations Of Ring Polymers Research Articles

Conformations of ring polymers with excluded volume interactions

The influence of distance dependent excluded volume interactions (EVIs) on the conformational properties of ring polymers is investigated within the principles of Rouse–Zimm theory. This study characterizes the structural features, i.e., the mean square radius of gyration, static structure factor, scattering intensity, fractal dimensions, and the mean square intermonomer distances of ring polymers in dilute solutions. The excluded volume interactions between the nonbonded monomers are modeled by a harmonic potential, where the strength of these interactions is evaluated from Flory’s mean-field approach. The mean square radius of gyration of the rings with EVI follows a similar scaling relation as its linear analog with the degree of polymerization. Unlike linear polymers, the maximum in the Kratky plot of the static structure factor is observed as a result of an increased segment density due to the circularity constraint. EVI marks a structural transition from relatively compact conformation for the smaller rings to expanded conformations for larger ones. The fractal dimension of the rings with EVI lies between those of the random walk and the self-avoiding walk models of linear polymers in three dimensions. This theoretical model produces a relatively pronounced effect of EVI for larger rings. An understanding of the influence of EVI on conformations of the ring polymers at a single molecule level may be applied to various naturally existing cyclic biomolecules such as plasmids, cyclic proteins, and polysaccharides.

Multi-ring configurations and penetration of linear chains into rings on bonded ring systems and polycatenanes in linear chain matrices

Ring-linear blends composed of complexes bearing multiple rings are promising candidates for soft devices, and understanding the penetration of linear chains into rings is essential for enhancing their mechanical properties. Coarse-grained molecular dynamics simulations of ring-linear blends composed of bonded rings or polycatenanes bearing two or three rings were performed for revealing the conformations in blends. To investigate the relationship between the conformations of ring polymers and penetration of linear chains, we considered linear-rich systems with fring = 0.05 and 0.1, where fring is the fraction of ring complex. The number of linear chains penetrating rings (nP) was estimated from the Gauss linking number for all the pairs of ring polymers and linear chains. Dependence of penetration on the ring size was determined from the probability distributions of nP. Average nP (nP) of the systems with polycatenanes was slightly higher than those of the systems with bonded rings. For fring = 0.1, nP of the single ring was 3.41 when number of beads per a ring was Nring = 160. nP of the bonded two-ring system and poly-[2]-catenane with Nring = 80 was 2.60 and 2.87, respectively, while nP of the bonded three-ring system and poly-[3]-catenane with Nring = 80 was 3.63 and 3.87, respectively, which were slightly higher than that of the single ring with Nring = 160. Since the ring complexes had multiple chains penetrating even for low Nring, mechanical properties of the crosslinked ring-linear blend were expected to be controlled by the ring complexes instead of the single ring.

Conformation and dynamics of ring polymers under symmetric thin film confinement.

Understanding the structure and dynamics of polymers under confinement has been of widespread interest, and one class of polymers that have received comparatively little attention under confinement is that of ring polymers. The properties of non-concatenated ring polymers can also be important in biological fields because ring polymers have been proven to be a good model to study DNA organization in the cell nucleus. From our previous study, linear polymers in a cylindrically confined polymer melt were found to segregate from each other as a result of the strong correlation hole effect that is enhanced by the confining surfaces. By comparison, our subsequent study of linear polymers in confined thin films at similar levels of confinements found only the onset of segregation. In this study, we use molecular dynamics simulation to investigate the chain conformations and dynamics of ring polymers under planar (1D) confinement as a function of film thickness. Our results show that conformations of ring polymers are similar to the linear polymers under planar confinement, except that ring polymers are less compressed in the direction normal to the walls. While we find that the correlation hole effect is enhanced under confinement, it is not as pronounced as the linear polymers under 2D confinement. Finally, we show that chain dynamics far above Tg are primarily affected by the friction from walls based on the monomeric friction coefficient we get from the Rouse mode analysis.

Effect of Topology on the Conformations of Ring Polymers

The bond fluctuation method is used to simulate both non-concatenated entangled and interpenetrating melts of ring polymers. We find that the swelling of interpenetrating rings upon dilution follows the same laws as for linear chains. Knotting and linking probabilities of ring polymers in semi-dilute solution are analyzed using the HOMFLY polynomial. We find an exponential decay of the knotting probability of rings. The correlation length of the semi-dilute solution can be used to superimpose knotting data at different concentrations. A power law dependence $f_{n}\sim\phi R^{2}\sim\phi^{0.77}N$ for the average number $f_{n}$ of linked rings per ring at concentrations larger than the overlap volume fraction of rings $\phi^{*}$ is determined from the simulation data. The fraction of non-concatenated rings displays an exponential decay $P_{OO}\sim\exp(-f_{n})$, which indicates $f_{n}$ to provide the entropic effort for not forming concatenated conformations. Based upon this results we find four different regimes for the conformations of rings in melts that are separated by a critical lengths $N_{OO}$, $N_{C}$ and $N^{*}$. $N_{OO}$ describes the onset of the effect of non-concatenation below which topological effects are not important, $N_{C}$ is the cross-over between weak and strong compression of rings, and $N^{*}$ is defined by the cross-over from a non-concatenation contribution $f_{n}\sim\phi R^{2}$ to an overlap dominated concatenation contribution $f_{n}\sim\phi N^{1/2}$ at $N>N^{*}$. For $N_{OO}<N<N_{C}$, the scaling of ring sizes $R\sim N^{2/5}$ results from balancing non-concatenation with weak compression of rings. For $N_{C}<N<N^{*}$, non-concatenation and strong compression imply $R\sim N^{3/8}$. Our simulation data for non-interpenetrating rings up to $N=1024$ are in good agreement with the prediction for weakly compressed rings.

Conformation of Ring Polymers in 2D Constrained Environments

The combination of ring closure and spatial constraints has a fundamental effect on the statistics of semiflexible polymers such as DNA. However, studies of the interplay between circularity and constraints are scarce and single-molecule experimental data concerning polymer conformations are missing. By means of atomic force microscopy we probe the conformation of circular DNA molecules in two dimensions and in the concentrated regime (above the overlap concentration c*). Molecules in this regime experience a collapse, and their statistical properties agree very well with those of simulated vesicles under pressure. Some circular molecules also create confining regions in which other molecules are trapped. Thus we show further that spatially confined molecules fold into specific conformations close to those found for linear chains, and strongly dependent on the size of the confining box.

Some remarks about the conformation of ring polymers in the bulk and their potential study by small-angle neutron scattering

Some remarks about the conformation of ring polymers in the bulk and their potential study by small-angle neutron scattering

Conformation of ring polymers in computer simulated melts

Die Makromolekulare Chemie, Rapid CommunicationsVolume 9, Issue 9 p. 617-623 Article Conformation of ring polymers in computer simulated melts Stefan Geyler, Stefan Geyler Max-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanySearch for more papers by this authorTadeusz Pakula, Corresponding Author Tadeusz Pakula Max-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanyMax-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanySearch for more papers by this author Stefan Geyler, Stefan Geyler Max-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanySearch for more papers by this authorTadeusz Pakula, Corresponding Author Tadeusz Pakula Max-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanyMax-Planck-Institut für Polymerforschung, P.F. 3148, 6500 Mainz, West GermanySearch for more papers by this author First published: September 1988 https://doi.org/10.1002/marc.1988.030090904Citations: 31AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume9, Issue9September 1988Pages 617-623 RelatedInformation