Cospectral polymers: Differentiation via semiflexibility

Abstract

We consider polymer structures which are known in the mathematical literature as "cospectral." Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations.

Semiflexibility Highlights the Polymers' Topology: Monte Carlo Studies

“…This is qualitatively confirmed by our simulation results on the smallest tree-like cospectral pair. [18] Discrete semiflexible rings provide another example of analytical results obtainable through MEP. [5,6] It turns out that in the rigid limit, besides solutions pertaining to unknotted rings, one obtains other solutions related to knotted rings.…”

“…Our recent mathematical-analytical study [18] shows that when the polymers are semiflexible one can distinguish between cospectral structures. This is qualitatively confirmed by our simulation results on the smallest tree-like cospectral pair.…”

“…While recent analytical extensions of the generalized Gaussian structures picture (GGS) [1] to the case of semiflexible branched polymers [2][3][4][5] and rings [5,6] give qualitative clues to the behavior of polymers, numerical simulation techniques allow to investigate the role of the excluded volume and thus provide a more realistic approach. For this we present here a simulation study of different topological structures by means of the bond fluctuation model (BFM), [7,8] which allows to account both for branching and/or presence of loops and also for semiflexible behavior.…”

“…We compare the simulation data with the theoretical predictions based on the extended GGS approach [2][3][4] and on the maximum-entropy principle (MEP). [5,6] Now, a theoretical approach which was recently shown to be very well suitable for the description of semiflexible tree-like polymers (STPs) as well as of semiflexible rings is the MEP. [9,10] Being initially applied to semiflexible chains in a discrete [11] and in a continuous [12] framework, it was implemented to STPs [2] and generalized to semiflexible rings.…”

“…[9,10] Being initially applied to semiflexible chains in a discrete [11] and in a continuous [12] framework, it was implemented to STPs [2] and generalized to semiflexible rings. [5,6] An important feature of the MEP method is that it introduces constraints only on adjacent bonds. Moreover, the treatment of STPs with MEP was shown to be equivalent, and hence an alternative, to the recently developed approach for STPs [2] done in the spirit of Bixon and Zwanzig.…”