Abstract
We provide numerical support for a long-standing prediction of universal scaling of winding angle distributions. Simulations of interacting self-avoiding walks show that the winding angle distribution for N-step walks is compatible with the theoretical prediction of a Gaussian with a variance growing asymptotically as C log N, with C = 2 in the swollen phase (previously verified), and C = 24/7 at the θ-point. At low temperatures weaker evidence demonstrates compatibility with the same scaling and a value of C = 4 in the collapsed phase, also as theoretically predicted.
Highlights
Polymers in a dilute solution can be either swollen or collapsed, or at an intermediate critical point, the so-called θ-point, depending on the quality of the solvent [1]
An N -step chain has O(log N ) segments and a law-of-large-numbers argument implies that the winding angle distribution becomes Gaussian with variance proportional to log N
We note that there have been simulations of interacting self-avoiding walks up to length N = 300 [9], suggesting that the results at the θ-point and in the collapsed phase are more consistent with a stretched exponential of the type exp(−|θ|α/C log N ) with α ≈ 1.5
Summary
Polymers in a dilute solution can be either swollen or collapsed, or at an intermediate critical point, the so-called θ-point, depending on the quality of the solvent [1].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
