Fig. 3.

Single molecule trajectories of ring polymers show large conformational fluctuations. Transient fractional extension of ring DNA polymers in semidilute unentangled linear solutions with concentrations of 0.1 c^* at a Wi = 0.9, b Wi = 1.4, and c Wi = 2.3, and background linear chain concentration of 1.0 c^* at d Wi = 1.5, and e)Wi = 3.0. Individual single molecule trajectories are shown in gray lines and ensemble averaged trajectories are shown in a black line. A characteristic individual single molecule trajectory is highlighted in blue line. Molecular ensembles consist of n = 24, n = 25, and n = 33 molecules, respectively for Wi = 0.9, 1.4, and 2.3 at 0.1 c^*, and n = 38 for both Wi = 1.5 and Wi = 3.0 at 1.0 c^*. The dashed line indicates the time at which the step strain input is stopped. f Magnitude of ring polymer conformational fluctuations as a function of Wi, plotted as average fractional fluctuation values, such that average chain extension fluctuations 〈δ〉 are normalized by the contour length of ring polymers L_circ and linear polymers L, respectively. Data for ring polymers in dilute solution, 0.025 c^* linear semidilute solution, 0.1 c^* linear semidilute solution, and 1.0 c^* linear semidilute solution are denoted as dark cyan right triangle, dark red diamond, red up triangle, and magenta down triangle, respectively. Data for 1.0 c^* linear polymers (black circle) are taken from prior work³³. Error bars represent standard deviation. Source Data are provided as a Source Data file