Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1901.05575

Population dynamics of driven autocatalytic reactive mixtures

Hongbo Zhao·Martin Z. Bazant
View original source ↗Read source document ↗Export metadata ↓

Abstract

Motivated by the theory of reaction kinetics based on nonequilibrium thermodynamics and the linear stability of driven reaction-diffusion, we apply the Fokker-Planck equation to describe the population dynamics of an ensemble of reactive particles in contact with a chemical reservoir. We illustrate the effect of autocatalysis on the population dynamics by comparing systems with identical thermodynamics yet different reaction kinetics. The dynamic phase behavior of the system may be entirely different from what its thermodynamics may suggest. By defining phase separation for a particle ensemble to be when the probability distribution is bimodal, we find that thermodynamic phase separation may be suppressed by autoinhibitory reactions, while autocatalysis enhances phase separation and in some cases induce the ensemble that consists of thermodynamically single-phase systems to segregate into two distinct populations, which we term fictitious phase separation. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use method of characteristics and linearization to study the evolution of the standard deviation of concentration as well as the condition for phase separation, in good agreement with the full numerical solution. Applications are discussed to Li-ion batteries and {\it in situ} x-ray diffraction.

Explore related subjects

physics.chem-phcond-mat.mtrl-scicond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hongbo Zhao, Martin Z. Bazant. 2019-01-17. Population dynamics of driven autocatalytic reactive mixtures. https://doi.org/10.1103/physreve.100.012144

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

KEEP EXPLORING

Related papers

arXiv2026

Global approximations to the error function of real argument for vectorized computation

The error function of real argument can be approximated to a given uniform relative accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or also using the exponential function. The coefficients have been tabulated for up to 128-bit precision. Tests of a computer code implementation using the standard single- and double-precision floating-point arithmetic show good performance and vectorizability. Approximations to the complementary error function have also been found, including those where only additions, multiplications, and one division are needed to reach a uniform absolute accuracy.

physics.chem-ph↗
arXiv2026

From Heuristics to Machine Learning: The Performance Ceiling for Single-Ion Magnets and Its Electronic Origin

Machine learning (ML) is expected to speed up the discovery of single-ion magnets (SIMs), but does the structural information available before synthesis allow such predictions? For 1215 lanthanide complexes from the SIMDAVIS 1.2.1 database we compared three increasing levels of structural description: tabular features of the coordination site, continuous symmetry measures of the coordination polyhedron, and the complete 3D arrangement of atoms. All three converge to an accuracy near 76%, only slightly above the 71% of the single rule "predict SIM for Dy3+". To explain the failures, we combined multireference ab initio calculations with an inspection of the structures behind the high-confidence errors. The SIMs missed by the geometric models are field-induced relaxers whose ground Kramers doublets are prone to tunnelling, a property invisible to geometric descriptors. Many false positives contain several lanthanide centers or radicals, so their relaxation is collective and outside the single-ion picture. The electronic-structure and connectivity information needed to identify SIMs is therefore not accessible to geometric methods alone. Geometric models remain useful: restricting the screening to compounds with high prediction confidence raises the accuracy to 88% while retaining 48% of the dataset. Building on the analysis of the failures, we propose a strategy that combines simple filters for nuclearity and for radicals with ligand-field descriptors from ab initio calculations.

physics.chem-ph↗
arXiv2026

Composition-Dependent Self-Diffusion Coefficients in Liquid Mixtures from Hybrid Machine Learning

Self-diffusion coefficients are key descriptors of molecular mobility, yet experimental data remain scarce, highlighting the need for reliable prediction methods. In previous work, we introduced the hybrid Enhanced Stokes-Einstein (ESE) model, which advanced the state of the art in the physically consistent prediction of self-diffusion coefficients of solutes at infinite dilution in pure solvents by integrating the Stokes-Einstein equation with machine learning (ML). Here, we extend this approach to concentration-dependent self-diffusion coefficients and multicomponent solvents with HADES. This hybrid architecture leverages a deep-set neural network to connect pure-component and mixture prediction within a single framework. HADES predicts self-diffusion coefficients in liquid mixtures with any number of components at any composition and temperature. The only required inputs are SMILES-encoded molecular structures of the components and the pure-component viscosities, making the method broadly applicable. Trained and evaluated on a comprehensive dataset of 2526 data points for 600 systems, HADES significantly outperforms benchmark prediction methods. The trained model and its source code are fully disclosed, and the application is available via an interactive website https://ml-prop.mv.rptu.de/.

physics.chem-ph↗