Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2409.10974

Mapping self-avoiding walk on obstacle-ridden lattice onto chelation of heavy metal ions: Monte Carlo study

V. Blavatska·Ja. Ilnytskyi·E. Lähderanta
View original source ↗Read source document ↗Export metadata ↓

Abstract

Self-avoiding walk (SAW) represents linear polymer chain on a large scale, neglecting its chemical details and emphasizing the role of its conformational statistics. The role of the latter is important in formation of agglomerates and complexes involving polymers and organic or inorganic particles, such as polymer-stabilized colloidal suspensions, microemulsions, or micellar solutions. When such particles can be adsorbed on a polymer of considerably larger dimensions than themselves, this setup may represent chelation of heavy metal ions by polymeric chelants. We consider the SAW of the length $N$ on a cubic lattice ridden by randomly distributed obstacles of the concentration $p$ interpreted as ions. The SAW monomers can bind to the obstacles with variable binding energy $\varepsilon$ mimicking formation of the chelation bond. Pruned-enriched Rosenbluth method (PERM) Monte Carlo (MC) algorithm is applied to simulate system behaviour. We focus on several relevant properties related to the chelation efficiency and strength, as functions of the variables set $\{p,N,\varepsilon\}$. The results are interpreted in terms of conformational freedom, excluded volume effects and loop formation for the SAW, and the tendencies being predicted are in agreement with some experimental data.

Explore related subjects

cond-mat.softcond-mat.dis-nn

Keep this discovery

BibTeXRIS

V. Blavatska, Ja. Ilnytskyi, E. Lähderanta. 2024-09-17. Mapping self-avoiding walk on obstacle-ridden lattice onto chelation of heavy metal ions: Monte Carlo study. https://doi.org/10.1103/physreve.110.064503

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↗