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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

From Electronic Structure to Ion Transport: Photoelectron Spectroscopy and Molecular Dynamics Simulations Reveal the Role of Anions in Lithium Battery Electrolytes

Electrolyte anions are pivotal for lithium battery performance, yet their fundamental electronic structural properties are not well understood. In this work, we employ a combination of negative-ion photoelectron spectroscopy (NIPES), ab initio calculations, and molecular dynamics (MD) simulations to investigate the electronic structures of three representative electrolyte anions. This multiscale approach enables us to elucidate how their intrinsic electronic properties govern anion–solvent interactions in gas-phase clusters, as well as lithium-ion (Li + ) solvation structures and ion transport behavior in the condensed phase. NIPES reveals that difluoro(oxalato)borate (DFOB – ), bis(fluorosulfonyl)imide (FSI – ), and bis(oxalato)borate (BOB – ) all exhibit high electron binding energies, with vertical/adiabatic detachment energies increasing from DFOB – (6.09/5.70 eV) to FSI – (6.80/6.10 eV) to BOB – (6.82/6.40 eV), correlating with enhanced oxidation stability. Ab initio calculations reveal that DFOB – /FSI – –solvent complexes bind Li + ∼ 10 kcal/mol stronger than BOB – series, aligning with the strength of a Li + –anion model. DFOB – exhibits pronounced charge localization on both oxygen and fluorine atoms, enabling their involvement in Li + coordination. In contrast, fluorine atoms in FSI – are largely electron-depleted and remain excluded from direct Li + binding. MD simulations further demonstrate that LiDFOB and LiFSI systems exhibit Li + diffusion coefficients three and five times higher than those of LiBOB across four common solvents. Notably, LiFSI salt in acetonitrile (AN) exhibits the fastest Li + diffusion among 12 electrolyte systems, highlighting the synergistic effect of FSI – and AN in promoting ion mobility. In conclusion, these findings provide a molecular-level understanding of the critical roles of anion and its microsolvation in optimizing Li + diffusion dynamics, once again emphasizing the positioning of FSI – and DFOB – as prime candidates for next-generation electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2022

Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi’s golden rule rate

Under vibrational strong coupling (VSC), the formation of molecular polaritons may significantly modify the photo-induced or thermal properties of molecules. In an effort to understand these intriguing modifications, both experimental and theoretical studies have focused on the ultrafast dynamics of vibrational polaritons. Here, following our recent work [Li et al., J. Chem. Phys. 154, 094124 (2021)], we systematically study the mechanism of polariton relaxation for liquid CO 2 under a weak external pumping. Classical cavity molecular dynamics (CavMD) simulations confirm that polariton relaxation results from the combined effects of (i) cavity loss through the photonic component and (ii) dephasing of the bright-mode component to vibrational dark modes as mediated by intermolecular interactions. The latter polaritonic dephasing rate is proportional to the product of the weight of the bright mode in the polariton wave function and the spectral overlap between the polariton and dark modes. Both these factors are sensitive to parameters such as the Rabi splitting and cavity mode detuning. Compared to a Fermi’s golden rule calculation based on a tight-binding harmonic model, CavMD yields a similar parameter dependence for the upper polariton relaxation lifetime but sometimes a modest disagreement for the lower polariton. We suggest that this disagreement results from polariton-enhanced molecular nonlinear absorption due to molecular anharmonicity, which is not included in our analytical model. Finally, we also summarize recent progress on probing nonreactive VSC dynamics with CavMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Iron surface corrosion in supercritical CO2 at atomic scale investigated by molecular dynamics simulations

Understanding the corrosion behavior of steels in supercritical carbon dioxide (S-CO2) is essential for ensuring the safe application of S-CO2 as a heat-transfer fluid in high-temperature energy systems, including advanced nuclear reactors. In this work, molecular dynamics (MD) simulations using ReaxFF potential are performed to explore the atomic-scale corrosion mechanisms of body-centered cubic iron (BCC-Fe) in S-CO2. The results show that CO2 molecules in S-CO2 decompose at the Fe surface, generating free C and O atoms that form Fe-C and Fe-O bonds and subsequently produce oxides and carbides. Concurrently, Fe atoms dissolve from the surface and diffuse into the S-CO2 region, resulting in interdiffusion of Fe, C and O atoms at the interface. The corrosion-layer thickness calculations show that high pressure and temperature induced by S-CO2 have stronger effects than surface orientation on the corrosion process. In addition, surface Fe atoms undergo substantial displacement under S-CO2 exposure, further accelerating corrosion. When a radiation-induced void is introduced near the Fe surface, the corrosion is enhanced. The void-matrix interface expands the reaction surface area and simultaneously induces corrosion reactions inside the bulk, resulting in a deeper penetration of C and O and thicker corrosion layers. All these results indicate that high-temperature, high-pressure and radiation-induced voids can seriously affect the corrosion of Fe in S-CO2, and must be considered to better use S-CO2 in nuclear facilities.

Li, Wenhua↗
DOE OSTI2022

Predicting initial dissolution rates using structural features from molecular dynamics simulations

Predicting chemical durability of glass materials is important for various applications from daily life such as drink glass and kitchen ware to advanced technologies such as nuclear waste disposal and biomedicine. In this work, we explored prediction of initial dissolution rate through structural features from molecular dynamics (MD) simulations for a wide range of glass compositions (total 28) including borosilicate and aluminosilicate glasses, ZrO 2 -containing and V 2 O 5 -containing boroaluminosilicate glasses. The initial dissolution rates (r 0 ) measured experimentally at 90 °C with varying solution conditions were correlated with structural features (e.g., polyhedral linkages and non-bridging oxygen species) obtained from MD simulations, either from this study or from literature. Since hydrolysis of the glass network through breaking of the network former linkages (e.g., Si-O-Si, Si-O-Al, etc.) is a critical step of network glass dissolution, the statistics of these linkages obtained from MD were correlated to r0 through linear regression, where the coefficient of determination (R 2 ) and root mean square error are found to be 0.949 and 0.681, respectively. This model was compared and discussed with existing models developed by various approaches including machine learning, the kinetic rate equation, topological constraint theory, and other descriptors from MD simulations. The discussion provides insights on future model improvements to predict glass dissolution. In addition, the impact of V 2 O 5 on the glass dissolution was examined in detail, implicating that the impact is not the same across all glass compositions and test conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ab initio study of the structure and properties of amorphous silicon hydride from accelerated molecular dynamics simulations

This paper presents a large-scale ab initio simulation study of amorphous silicon hydride (a-Si 1-x H x ) with an emphasis on the structure and properties of the material across a range of hydrogen concentration by combining accelerated molecular dynamics (MD) simulations with first-principles density-functional calculations. The accelerated MD scheme relied on classical metadynamics, which enabled the development of 2500+ high-quality structural models of a-Si 1-x H x , with system sizes ranging from 150 to 6000 atoms and hydrogen concentrations vary from 6 to 20 at. %. The resulting amorphous networks were found to be completely free from any coordination defects and that they all exhibited a pristine band-gap in their electronic spectrum. The microstructural properties of hydrogen distributions were examined with an emphasis on the presence of isolated and clustered environments of hydrogen atoms. The results were compared with experimental data obtained from X-ray diffraction, infrared spectroscopy and nuclear magnetic resonance studies.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Ab initio study of the structure and properties of amorphous silicon hydride from accelerated molecular dynamics simulations

This paper presents a large-scale ab initio simulation study of amorphous silicon hydride (a-Si 1-x H x ) with an emphasis on the structure and properties of the material across a range of hydrogen concentration by combining accelerated molecular dynamics (MD) simulations with first-principles density-functional calculations. The accelerated MD scheme relied on classical metadynamics, which enabled the development of 2600+ high-quality structural models of a-Si 1-x H x , with system sizes ranging from 150 to 6,000 atoms and hydrogen concentrations vary from 6 to 20 at. %. The resulting amorphous networks were found to be completely free from any coordination defects and that they all exhibited a pristine band-gap in their electronic spectrum. The microstructural properties of hydrogen distributions were examined with great emphasis on the presence of isolated and clustered environments of hydrogen atoms. The results were compared with a suite of experimental data obtained from x-ray diffraction, infrared spectroscopy, spectroscopic ellipsometry and nuclear magnetic resonance studies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Stability of Calcium Ion Battery Electrolytes: Predictions from Ab Initio Molecular Dynamics Simulations

Multivalent batteries, such as magnesium-ion, calcium-ion, and zinc-ion batteries, have attracted significant attention as next-generation electrochemical energy storage devices to complement conventional lithium-ion batteries (LIBs). Among them, calcium-ion batteries (CIBs) are the least explored due to the difficult reversible Ca deposition-dissolution. In this work, we examined the stability of four different Ca salts with weakly coordinating anions and three different solvents commonly employed in existing battery technologies to identify suitable candidates for CIBs. By employing Born-Oppenheimer molecular dynamics (BOMD) simulations on salt-Ca and solvent-Ca interfaces, we find that the tetraglyme solvent and carborane salt are promising candidates for CIBs. Due to the strong reducing nature of the calcium surface, the other salts and solvents readily decompose. Further, we explain the microscopic mechanisms of salt/solvent decomposition on the Ca surface using time-dependent projected density of states, time-dependent charge-transfer plots, and climbing-image nudged elastic band calculations. Collectively, this work presents the first mechanistic assessment of the dynamical stability of candidate salts and solvents on a Ca surface using BOMD simulations, and provides a predictive path toward designing stable electrolytes for CIBs.

Born-Oppenheimer molecular dynamics↗
DOE OSTI2020

Nonadiabatic molecular dynamics simulation of C2H22+ in a strong laser field*

We investigate the alignment dependence of the strong laser dissociation dynamics of molecule C 2 H 2 2 + in the frame of real-time and real-space time-dependent density function theory coupled with nonadiabatic quantum molecular dynamics (TDDFT-MD) simulation. This work is based on a recent experiment study “ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene” [Wolter et al , Science 354 , 308–312 (2016)]. Our simulations are in excellent agreement with the experimental data and the analysis confirms that the alignment dependence of the proton dissociation dynamics comes from the electron response of the driving laser pulse. Our results validate the ability of the TDDFT-MD method to reveal the underlying mechanism of experimentally observed and control molecular dissociation dynamics.

Physics↗
DOE OSTI2024

Shock compression of crystalline TeO 2 to the high-pressure fluid regime: Insights from ab initio molecular dynamics simulations

The shock response of fully-dense and porous crystalline tellurium dioxide (TeO 2 ⁠) to the high-pressure and high-temperature fluid regime was investigated within the framework of density functional theory with Mermin’s generalization to finite temperatures. The principal and porous shock Hugoniot curves were predicted from canonical ab initio molecular dynamics (AIMD) simulations, with the phase space sampled along isotherms up to 80 000 K, for densities ranging from ρ = 3 to 17 g/cm 3 . The polymorphs investigated are α-TeO 2 paratellurite (⁠P4 1 2 1 2), TeO 2 cotunnite (⁠Pnma⁠), and TeO 2 post-cotunnite (⁠P2 1 /m⁠). Based on the discontinuity found in the calculated U s – u p slope of TeO 2 post-cotunnite at a shock velocity of U s ≃ 8.35km/s and a particle velocity of u p ≃ 3.64 km/s, the shock melting temperature and pressure are predicted to be ≃ 6500 K and ≃ 170 GPa. Results from the AIMD simulations are in line with the static compression data of TeO 2 paratellurite and cotunnite, and with the recent shock Hugoniot data for single-crystal α- TeO 2 for pressures up to 85 GPa, obtained using the inclined-mirror method and the velocity interferometer system for any reflector combined with powder gun and two-stage light-gas gun.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

All-Atom Molecular Dynamics Simulations of Cationic Polyelectrolyte Brushes in the Presence of Halide Counterions

Understanding the response of the charged polyelectrolyte (PE) brushes and brush-supported water and ions to the changes in the nature of screening counterions is significant in developing strategies for utilizing PE brushes in various applications. In this paper, we employ all-atom molecular dynamics (MD) simulations for studying the behavior of cationic [poly(2-(methacryloyloxy)ethyl) trimethylammonium] (PMETA) brushes and brush-supported water and ions in the presence of different halide (X: I – , Br – , Cl – , and F – ) screening counterions. We find that despite the F– ion having the largest charge density, the extent of binding of the counterions on the PMETAX brushes varies as I – > Br – > Cl – > F – , leading to PMETAX brush height being least with I– counterions and greatest with F – counterions. This trend in the binding of the halide ions matches the previous experimental result and can be explained by identifying the chaotropic nature of the I – and Br – ions that promote a disruption of water structure and a more favorable binding of the ions to the polymer chains. Such a binding trend also ensures that the order of the water molecules around the PMETAX chains or the counterions as well as the number of water–water hydrogen bonds inside the brush layer increases in the following order of the counterion-specific PMETAX brushes: F – > Cl – > Br – > I – . Furthermore, halide-ion-PMETAX-chain binding takes place via both interchain and intrachain bridging: intrachain bridging dominates for the case of counterions that show enhanced binding (I – and Br – ), while interchain bridging is more favored for the case of counterions that show weakened binding (F – and Cl – ). Also, a greater degree of intrachain bridging leads to greater compressibility and flexibility of the brush layer. Lastly, we show that the mobility of the halide ions follows a nonmonotonic trend with the charge density: the mobility decreases as I – < Br – < Cl – (as their binding to the PMETAX chains varies as I – > Br – > Cl – ), but the mobility of F – ions is in between that of I – and Br – ions. We argue that the strongly attached hydration layer and the ensuing friction inside the brush layer lead to such a reduced mobility of the F – ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Evaluation of Physical Security Risk for Potential Implementation of FLEX using Dynamic Simulation Methods

The requirements for United States nuclear power plants to maintain a large onsite physical security force contribute to their large operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability Program Physical Security Pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. This pathway will analyze and minimize the conservatisms built into current security postures in order to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within this pathway has successfully developed a dynamic force-on-force (FOF) modeling framework using various computer simulation tools and integrated them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This document provides an overview of lessons learned in applying a dynamic computational framework that links results from a commercially available FOF simulation tool, a commercially available thermal-hydraulic tool, and EMRALD to an operating commercial nuclear power plant. This process of including plant procedures and multiple analysis results is being called Modeling and Analysis for Safety Security using Dynamic EMRALD Framework. Previous reports described how a user could integrate their plant-specific FOF models with the dynamic simulation tool EMRALD, model operator actions, integrate with probabilistic risk assessment tools, such as Computer Aided Fault Tree Analysis System or Systems Analysis Programs for Hands-on Integrated Reliability Evaluations, and with thermal-hydraulic tools, such as RELAP-5. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report documents the results of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. The purpose of this study was to verify that results achieved using generic models are similar to actual plant results and to refine our guidance of the use of the framework. Such an assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants. NOTE: The work performed in this report is based on a generic EMRALD model with actual plant data used for the analysis. However, only the generic model and general results of the analysis are in the report. No plant’s sensitive information is discussed in this report. The discussion shows examples of insights that can be obtained from the MASS-DEF methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Validating continuum theory for Cottrell atmosphere solute drag by molecular dynamics simulations

When a dislocation moves through a field of mobile solute atoms, solutes segregate to the dislocation and form Cottrell atmospheres which exert solute drag forces. Over the last 70 years, continuum theory has been used extensively to estimate these drag forces and their dependence on the dislocation velocity, however few prior works have validated the accuracy of continuum theories. Here, in this work, molecular dynamics (MD) simulations of dislocation motion in face-centered cubic Ni containing interstitial H atoms were performed in order to test the accuracy of continuum theory predictions. Our results demonstrate that continuum theory provides an accurate estimate of the solute drag force for velocities below the critical velocity at which the solute drag force is maximized. Above the critical velocity, continuum theory systematically deviates from MD. Additional analysis reveals that this deviation results from the multi-valued and unstable nature of solute drag under load control, and also from the transition to random solute drag which occurs at high velocities.

Dislocations↗
DOE OSTI2020

Predicting Small Molecule Transfer Free Energies by Combining Molecular Dynamics Simulations and Deep Learning

Accurately predicting small molecule partitioning and hydrophobicity is critical in the drug discovery process. There are many heterogeneous chemical environments within a cell and entire human body. For example, drugs must be able to cross the hydrophobic cellular membrane to reach their intracellular targets, and hydrophobicity is an important driving force for drug–protein binding. Atomistic molecular dynamics (MD) simulations are routinely used to calculate free energies of small molecules binding to proteins, crossing lipid membranes, and solvation but are computationally expensive. Machine learning (ML) and empirical methods are also used throughout drug discovery but rely on experimental data, limiting the domain of applicability. We present atomistic MD simulations calculating 15,000 small molecule free energies of transfer from water to cyclohexane. This large data set is used to train ML models that predict the free energies of transfer. We show that a spatial graph neural network model achieves the highest accuracy, followed closely by a 3D-convolutional neural network, and shallow learning based on the chemical fingerprint is significantly less accurate. A mean absolute error of ~4 kJ/mol compared to the MD calculations was achieved for our best ML model. We also show that including data from the MD simulation improves the predictions, tests the transferability of each model to a diverse set of molecules, and show multitask learning improves the predictions. This work provides insight into the hydrophobicity of small molecules and ML cheminformatics modeling, and our data set will be useful for designing and testing future ML cheminformatics methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Machine-Learned Force Field for Molecular Dynamics Simulations of Nonequilibrium Ammonia Synthesis on Iron Catalysts

Ammonia (NH 3 ) is one of the most important industrial chemicals. The conventional NH 3 synthesis method-the Haber–Bosch process-converts atmospheric nitrogen (N 2 ) into NH 3 using H 2 with an iron (Fe) catalyst. However, this process requires high pressures (100–200 atm) and temperatures (700–800 K) near thermal equilibrium. Recently, Fe-based nanocatalysts have been reported to produce promising NH 3 yields under atmospheric pressures and temperature-modulated nonequilibrium conditions. Understanding the mechanism of nonequilibrium catalysis with programmed temperature variation could help to optimize this fully electrified and less energy-intensive process. Although reactive molecular dynamics (RMD) simulations can be a useful tool to model nonequilibrium catalytic processes, they require the development of accurate force fields (i.e., interatomic potentials). Here, we present a machine-learned (ML) force field within the Deep Potential MD (DPMD) framework, trained using periodic density functional theory (DFT) calculations, to model NH 3 synthesis on Fe catalysts with various surface adsorbates such as *N, *H, *N 2 , *H 2 , *NH, *NH 2 , and *NH 3 . Here, we generated the DFT data from static models of elementary reactions on the most stable (110) surface of body-centered cubic Fe, which then were augmented by data from constant number of particles–volume–temperature (NVT) DFT-MD trajectories at various temperatures. Finally, we utilized the fully optimized ML force field to investigate reaction dynamics at an Fe(110) surface at linearly increasing temperatures using NVT-DPMD simulations. Our simulations indicate that pulsed temperature ramping could prove favorable for NH3 synthesis. For example, we conducted ramping under multiple sets of conditions: (i) from 900 to 1200 K over periods of 0.1–0.3 ns for Fe surfaces precovered with N or NH along with H; and (ii) from 300 to 600 K over 0.1–0.3 ns for Fe surfaces precovered with NH 3 . While our simulations so far are limited to short time scales (very rapid heating), these observations shed light on the mechanism of the high NH 3 synthesis rate achieved in a novel temperature-modulated nonequilibrium catalytic reactor using pulsed heating and cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Probing the Core–Shell Organization of Nanoconfined Methane in Cylindrical Silica Pores Using In Situ Small-Angle Neutron Scattering and Molecular Dynamics Simulations

Determining the structure of nanoconfined fluids is essential for predicting the fate of these fluids in subsurface geologic formations with nanoporous features and for engineering novel nanoporous materials for storing compressed gases. In this study, we probe the structure of nanoconfined methane at pressures in the range of 15–100 bar using in situ small-angle neutron scattering (SANS) measurements and molecular dynamics (MD) simulations. The structure of methane is probed in MCM-41 and SBA-15 with cylindrical pores and diameters of 3.3 and 6.8 nm, respectively. In situ SANS measurements and MD simulations showed that the confined methane molecules are organized in a core–shell structure, with the shell arising from the adsorption of methane molecules on the silica surface. The shell thicknesses of the adsorbed deuterated methane (CD4) molecules in MCM-41 obtained by SANS measurements are 1.4 ± 0.5, 2.1 ± 0.1, 3.2 ± 0.8, 4.0 ± 0.3, and 6.0 ± 0.7 Å at equilibrated pressures of 15.6, 35.6, 55.5, 73.3, and 95.7 bar, respectively. The shell thicknesses of the adsorbed CD4 layer in SBA-15 pores are 2.7 ± 0.5, 4.3 ± 0.7, 6.6 ± 0.7, 10.2 ± 0.3, and 14.6 ± 0.8 Å at equilibrated pressures of 15.5, 32.7, 52.4, 70, and 99.5 bar, respectively. These experimental results are in close agreement with the results predicted from MD simulations. Adsorption of methane molecules on the silica surfaces is primarily driven by van der Waals interactions between the methane molecules and the hydroxyl groups on the silica surface, while electrostatic interactions play a minor role. In conclusion, the experimental and simulation approaches described in this study provide fundamental insights into the organization of confined gases using methane as a specific example in the context of compressed fluid storage in natural and engineered materials for adaptive energy use.

03 NATURAL GAS↗
DOE OSTI2020

Solvent-induced membrane stress in biofuel production: molecular insights from small-angle scattering and all-atom molecular dynamics simulations

The disruptive effect of organic solvents on microbial membranes represents a significant challenge to the economical production of green fuels and value-added chemicals from lignocellulosic feedstocks. One route to overcoming this challenge is to engineer microbes with membranes capable of resisting organic solvent stresses. In this regard, it is useful to understand the mechanisms by which organic solvents disrupt typical biomembranes. In this study, molecular dynamics (MD) simulation, complemented by small-angle X-ray and neutron scattering (SANS/SAXS), provide a molecular-scale view of the disruption of a microbial model membrane by 1-butanol and tetrahydrofuran (THF), two common water–organic cosolvent mixtures of importance in biofuel production. Solvent interactions at the interface between the head-group and fatty acid tail regions lead to more dramatic membrane changes than interactions solely at the head-groups or tails. Although both organic solvents are found to partition into the membrane, the depth of solvent penetration into the membrane is quite different. Specifically, 1-butanol localizes near the interface between the lipid heads and tails at low concentrations, but partitions into both the head and tail regions at high concentrations. In contrast, THF, overall, partitions less than 1-butanol and prefers the lipid tail regions. Importantly, the presence of 1-butanol near the head/tail interface introduces drastic membrane changes not seen with THF. The organic solvent interactions with the lipids lead to membrane thinning and fluidization, but more so for 1-butanol than for THF. These results suggest that an aim for the future engineering of robust membranes could be to design lipid head groups that reduce the accumulation of organic solvents at the head–tail interface and that rational designs need also be cognizant of the different solvent-specific mechanisms responsible for membrane disruption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗