Radii of Gyration of Ring-Shaped Polystyrenes with High Purity in Dilute Solutions.

Abstract

Ring polystyrenes (PSs) were synthesized by anionic polymerization technique and purified with preparative size-exclusion chromatography (SEC). Seven ring PSs with their weight-average molecular weight (M w ) ranging from 17k to 570k were prepared and they were confirmed to have high purities all over 96% by liquid chromatography at the chromatographic critical condition (LCCC) analyses. Their radii of gyration (R g s) were determined in benzene-d 6 as a good solvent and in cyclohexane-d 12 or cyclohexane-h 12 as Θ solvents by small-angle neutron scattering (SANS) or light scattering (LS). It has been found that R g s of ring polymers are scaled with M w as R g ∝M w 0.60 in a good solvent and as R g ∝M w 0.53 in Θ solvents. Moreover it was confirmed that g factors, R g 2 (Ring) /R g 2 (Linear) , obtained in Θ solvents are meaningfully larger than theoretically predicted values owing to the topological effect stored in ring molecules.

Marked difference in conformational fluctuation between giant DNA molecules in circular and linear forms

“…The statistical average, or mean value, of the radius of gyration has been theoretically deduced for various polymer architectures. [13][14][15] These theoretical results have been verified by experiments [16][17][18][19][20] and by simulations. 21,22 On the other hand, much less attention has been paid to deviation/fluctuation of the radius of gyration.…”

“…When we approximate Eq. (19) with the Gaussian distribution (namely, a quadratic expression), the mean value and the standard deviation take the following form:…”

Influence of the Solvent Quality on Ring Polymer Dimensions

“…As such, no precipitation or appreciable collapsing is to be expected. The same temperature was used in ref 26. We note, however, that a systematic study of the isotope effect the θ -decrement upon cyclization as well as the presence of knots 7,52 and its molecular weight dependence, although interesting, has not been pursued at this stage as it was not within the scope of the present investigation.…”

Interactions of complex polymers with nanoporous substrate

“…[50][51][52][53][54] Rings can be either knotted or unknotted and they cannot interconvert between different topologies without bond breaking and reformation. As a result, theoretical studies of rings using the Gaussian chain model suffer from the inability to account for these topological constraints.…”

“…It was shown that, even in the absence of excluded volume interactions, the size of rings do not scale with chain length N n with n = 0.5 as predicted by the Gaussian chain model, instead the exponent n 4 0.5 for rings. 50,53,54 Interestingly, Li et al 55 recently showed that while the conformational properties of unknotted rings differ from Gaussian chain rings, the confinement free energy of unknotted rings by a non-adsorptive slit follows the same scaling law as that of Gaussian chain rings.…”