The topological effect on the Mechanical properties of polymer knots

Yani Zhao; Franco Ferrari

Home/Archive/arXiv

arXiv · 1512.04081

The topological effect on the Mechanical properties of polymer knots

Yani Zhao·Franco Ferrari

View original source ↗Read source document ↗Export metadata ↓

Abstract

The mechanical properties of polymer knots under stretching in a bad or good solvent are investigated by applying a given force $F$ to a point of the knot while keeping another point fixed. The Monte Carlo sampling of the polymer conformations on a simple cubic lattice is performed using a variant of the Wang-Landau algorithm. The results of the calculations of the specific energy, specific heat capacity and gyration radius for several knot topologies show a general trend in the behavior of short polymer knots with lengths up to seventy lattice units. At low tensile force $F$, knots can be found either in a compact or an extended phase, depending if the temperature is low or high. At any temperature, with increasing values of the force $F$, a polymer knot undergoes a phase transition to a stretched state. This transition is characterized by a strong peak in the heat capacity. There is also a minor peak, which corresponds to a transition occurring at low temperatures when the conformations of polymers in the stretched phase become swollen with increasing temperatures. It is also shown that the behavior of short polymer rings is strongly influenced by topological effects. The limitations in the number of accessible energy states due to topological constraints is particularly evident in knots of small size and such that their minimum number of crossing according to the Rolfsen knot table is high. An example is provided by a cinquefoil knot $5_1$ with a length of only fifty lattice units. The thermal and mechanical properties of knots that can be represented with diagrams having the same minimum number of crossings, are very similar. The size effects on the behavior of polymer knots have been analyzed too. Surprisingly, it is found that topological effects fade out very fast with increasing polymer length.

Explore related subjects

cond-mat.soft cond-mat.stat-mech

Keep this discovery

BibTeX RIS

Yani Zhao, Franco Ferrari. 2015-12-13. The topological effect on the Mechanical properties of polymer knots. https://arxiv.org/abs/1512.04081

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Slow Dynamics and the Geometry of Jammed Packings

Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the $p$-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the $p$-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The $p$-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.

cond-mat.soft↗

arXiv2026

A Phase-Field Study of Desiccation Crack Pattern Maturation under Drying-Wetting Cycles

The characteristic intersection angle of the desiccation crack relaxes from near \ang{90} toward \ang{120} under repeated drying--wetting cycles. However, the theoretical understanding of this relaxation is insufficient, especially the modeling of the drying--wetting cycles. Here we introduce a phase-field model of desiccation fracture, extending the model proposed in previous studies by adding crack healing and a scar effect left by past cracks. By repeating drying--wetting cycles in a finite element simulation, we find that the angle distribution develops a growing peak near \ang{120} as the cycle number increases, consistent with experiments. The standard deviation of the intersection angle from \ang{120} relaxes exponentially with a characteristic time of about 2.85 cycles. These results are consistent with experiments, except that the characteristic time is slightly smaller than the experimental value. Crack energy dominates the total energy and also relaxes exponentially with nearly the same characteristic cycle as the angle relaxation. This decay is driven mainly by a shortening of the effective crack length rather than a change in effective fracture toughness.

cond-mat.soft↗

arXiv2026

Kinetics of ferritin crystal formation and melting in acoustically levitated droplets

Understanding protein crystallization pathways is essential for controlling crystallization in structural biology, materials science, and pharmaceutical applications. Classical nucleation theory does not fully capture crystallization processes for several proteins, including ferritin. Here, we combine acoustic levitation with small- and wide-angle X-ray scattering (SAXS and WAXS) to monitor ferritin crystallization in evaporating aqueous polyethylene glycol (PEG) solutions. Acoustic levitation rapidly drives the droplets through a broad range of protein and polymer concentrations, enabling time-resolved measurements of crystallization during evaporation. The scattering data show that ferritin crystals form during evaporation and subsequently lose their crystalline order upon further dehydration. Varying the PEG molecular weight switches between distinct crystallization pathways: one dominated by attractive protein-protein interactions and another dominated by repulsive interactions and excluded-volume effects. Furthermore, we find that lower molecular weight PEG (1000 g/mol) suppresses the dehydration-induced loss of crystalline order observed for higher molecular weight PEG (6000 g/mol), providing a simple strategy for improving protein crystal stability.

cond-mat.soft↗