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At least 415 records · Page 23

Bridging adsorption behavior of confined CH 4 -CO 2 binary mixtures across scales

An accurate understanding of the competitive adsorption of CH 4 -CO 2 binary mixtures in nano-confined systems is critical for engineering CO 2 storage in shale gas reservoirs. Due to difficulties in making reliable experimental observations in nano-scale, atomistic simulations (ASs), such as the Grand Canonical Monte Carlo (GCMC) method, provide a viable approach to studying the adsorption behavior of confined fluids. ASs are, however, limited in the size of the compositional domain due to the high computational cost. This work proposes a framework that combines AS and the lattice Boltzmann (LB) method to bridge the physics of confined fluids across scales. The Peng–Robinson equation of state (PR-EoS) produces fugacity coefficients, which serve as input for conducting multi-component GCMC simulations. These GCMC simulations explore the competitive adsorption behavior of CH 4 -CO 2 in nano-slits at various composition, pressure, and channel-width conditions. Both components generate adsorption layers with high densities near the walls with CO 2 preferentially adsorbing compared to CH 4 on the organic walls of carbon sheets. At the mesoscale, a pseudopotential model represents the intermolecular forces in multi-component, multiple-relaxation-time LB simulations. The LB simulations are in good agreement with the GCMC results, allowing us to obtain values for tunable LB parameters. We then extend the use of LB to simulate adsorption behavior in complex networks with nano-sized channels. The phase behavior and fluid properties in the complex geometries of nano-channels differ from nano-slits and bulk systems. Furthermore, the bridging of physics from GCMC (microscale) to LB (mesoscale) via the macroscale PR-EoS connects the adsorption behavior of binary systems across scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the “spectral gap optimization of order parameters (SGOOP)” approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation Study of High-Precision Characterization of MeV Electron Interactions for Advanced Nano-Imaging of Thick Biological Samples and Microchips

The resolution of a mega-electron-volt scanning transmission electron microscope (MeV-STEM) is primarily governed by the properties of the incident electron beam and angular broadening effects that occur within thick biological samples and microchips. A precise understanding and mitigation of these constraints require detailed knowledge of beam emittance, aberrations in the STEM column optics, and energy-dependent elastic and inelastic critical angles of the materials being examined. This simulation study proposes a standardized experimental framework for comprehensively assessing beam intensity, divergence, and size at the sample exit. This framework aims to characterize electron-sample interactions, reconcile discrepancies among analytical models, and validate Monte Carlo (MC) simulations for enhanced predictive accuracy. Our numerical findings demonstrate that precise measurements of these parameters, especially angular broadening, are not only feasible but also essential for optimizing imaging resolution in thick biological samples and microchips. By utilizing an electron source with minimal emittance and tailored beam characteristics, along with amorphous ice and silicon samples as biological proxies and microchip materials, this research seeks to optimize electron beam energy by focusing on parameters to improve the resolution in MeV-STEM/TEM. This optimization is particularly crucial for in situ imaging of thick biological samples and for examining microchip defects with nanometer resolutions. Our ultimate goal is to develop a comprehensive mapping of the minimum electron energy required to achieve a nanoscale resolution, taking into account variations in sample thickness, composition, and imaging mode.

36 MATERIALS SCIENCE↗

Cylinder Test

In 1941 G.I. Taylor proposed the cylinder test as an experiment to determine the properties of explosive products. The test consists of a hollow metal cylinder containing an unreacted cylindrical charge of explosives. The charge is detonated at one end of the cylinder and, as the detonation wave propagates, the product gas expands behind it. As the product gas is produced, the pressure acting on the metal increases and begins to push the walls outward. Consider the time at which the detonation wave has reached the halfway point between the two ends of the cylinder. In front of the wave nothing has changed and the metal tube has the same initial radius. Behind the wave, the radius of the tube has expanded. The farther behind the wave a section of tube is, the larger its radius has become. The longer the wall is exposed to the pressurized gas, the more it expands, so that the radius is largest where the detonation was initiated. The metal most commonly used for this experiment is soft copper. Its material properties are well known and soft copper is also easy to shape with precision machining. During the cylinder test the radial expansion of the cylinder is measured over time and this data is used to determine the amount of work applied to the cylinder wall by the product gas as a function of time. Since volume increases in this problem, the time dependence can be seen as a volume dependence. The volume dependent work yields a path in thermodynamic space. The cylinder test experiment can be modeled using simulation. The simulation gives you the answer, but it cannot tell you why. The goal of the proposed work is to use analytic analysis methods to give insight into the simulation solution.

36 MATERIALS SCIENCE↗

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid’s centerline, creating a variety of rotational and translational dynamics dependent upon the particle’s aspect ratio, κ, and the component of the stratification unit vector in the gravity direction, d g . Spheroids with 0.55 ⪅ κ ⪅ 2.0 exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on κ and d g , but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

Geophysical and Geological Flows: Stratified flows↗

tinyIFD: A High-Throughput Binding Pose Refinement Workflow Through Induced-Fit Ligand Docking

A critical step in structure-based drug discovery is predicting whether and how a candidate molecule binds to a model of a therapeutic target. However, substantial protein side chain movements prevent current screening methods, such as docking, from accurately predicting the ligand conformations and require expensive refinements to produce viable candidates. Here, we present the development of a high-throughput and flexible ligand pose refinement workflow, called “tinyIFD”. The main features of the workflow include the use of specialized high-throughput, small-system MD simulation code mdgx.cuda and an actively learning model zoo approach. We show the application of this workflow on a large test set of diverse protein targets, achieving 66% and 76% success rates for finding a crystal-like pose within the top-2 and top-5 poses, respectively. We also applied this workflow to the SARS-CoV-2 main protease (M pro ) inhibitors, where we demonstrate the benefit of the active learning aspect in this workflow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-performance multiblock PEMs containing a highly acidic fluorinated-hydrophilic domain for water electrolysis

The present paper describes the design and evaluation of novel hydrophilic–hydrophobic poly(arylene ether sulfone) (PAES) multiblock copolymers for their synergistic effects upon transport properties and their potential use in proton exchange membrane water electrolysis. The multiblock copolymers are prepared via a coupling reaction between (i) a hydrophilic segment consisting of a disulfonated quinone fluorinated biphenyl group that contains fluorine moieties next to the sulfonated groups to increase the acidity, and (ii) hydrophobic segments composed of non-sulfonated biphenyl sulfone to provide dimensional stability. Two different lengths (molecular weights; 5k and 10k, where k represents 10 3 g mol -1 ) of hydrophobic segments are used to investigate the effects of the membrane properties compared with those of Nafion® and PAES random copolymer (i.e., BPSH40). Atomic force microscopy images of the BPSH40 and multiblock membranes are shown to agree closely with a mesoscale simulation, thus confirming the importance of the morphological effect upon the transport properties. Furthermore, the multiblock copolymer with a higher proportion of hydrophilic segments (10 k–5k) was shown to provide enhanced performance (3.41 A cm -2 at 1.9 V) compared to the multiblock copolymer with equal proportions of hydrophilic and hydrophobic segments (10 k–10 k) due to the greater continuity of nano-sized ionic channels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiscale water drop contact angles at selected silica surfaces

In this paper, multiscale advancing contact angles for glycerol/water drops at silica surfaces are reported for millidrops, submicron-drops, and nanodrops. Selected silica surfaces were muscovite, silicon, and talc. The contact angles for millidrops (1–2 mm) were determined by the traditional sessile drop technique. For submicron-drops (0.1–1.0 μm), a hollow tip Atomic Force Microscope (AFM) procedure was used. The contact angles for nanodrops (~7 nm) were examined from Molecular Dynamics (MD) simulation. The results were compared to evaluate the effect of drop size on the contact angle. In the case of the hydrophobic talc surface, the 75° advancing contact angle did not vary significantly with drop size. For the hydrophilic muscovite surface, the water drop wet the surface and an advancing contact angle of about 10° was found for the millidrops and submicron-drops. However, for the MD simulated nanodrops, attachment and spreading of the ~7 nm drop created a 2D film of molecular dimensions, the contact angle of which was difficult to define and varied from 0° to 17°. Perhaps of equal interest from the MD simulation results was that the spreading of the glycerol/water nanodrop at the muscovite surface resulted in crystallographic directional transport of water molecules to the extremities of the 2D film. Such separation and segregation left the center of the film with an increased concentration of glycerol. Based on these results, the line tension, which has been found in other investigations to account for contact angle decrease with a decrease in drop size, does not seem to be a significant factor in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations

There is considerable interest in the application of quantum information science to advance computations in plasma physics. A particular point of curiosity is whether it is possible to take advantage of quantum computers to speed up numerical simulations relative to conventional computers. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments to heat a plasma or to generate currents in the plasma. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers electromagnetic wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. Following an analytical formulation for the scattering of a Gaussian pulse, it is deduced that the maximum transmission coefficient for a pulse is $\sqrt{n_2/n_1}$ times that for a plane wave; the incident and transmitted pulses propagating in dielectric media with refractive indices $n_1$ and $n_2$, respectively. The analytical theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber representation of the electromagnetic fields and expressed in term of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses. Apart from their time-asymptotic forms, the simulations display an interplay between the incident, reflected, and transmitted pulses in the vicinity of the transition region between two dielectric media.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Predicting chemical reaction equilibria in molten carbonate fuel cells via molecular simulations

It has been recently suggested that hydroxide ions can be formed in the electrolyte of molten carbonate fuel cells when water vapor is present. The hydroxide can replace carbonate in transporting electrons across the electrolyte, thereby reducing the CO 2 separation efficiency of the fuel cell although still producing electricity. In this work, we obtain the equilibrium concentration of hydroxide in five molten alkali carbonate salts from molecular simulations. The results reveal that there can be a substantial amount of hydroxide in the electrolyte at low partial pressures of CO 2 . In addition, we find that the equilibrium concentration of molecular water dissolved in the electrolyte is over two orders of magnitude higher than that of CO 2 . Increasing the size and polarizability (or in other words reducing the “hardness”) of the cations present in the electrolyte can reduce the hydroxide fraction, but at the cost of lowering ionic conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MARTINI-Compatible Coarse-Grained Model for the Mesoscale Simulation of Peptoids

Peptoids (poly-N-substituted glycines) are a class of synthetic polymers that are regioisomers of peptides (poly-C-substituted glycines), in which the point of side-chain connectivity is shifted from the backbone C to the N atom. Peptoids have found diverse applications as peptidomimetic drugs, protein mimetic polymers, surfactants, and catalysts. Computational modeling is valuable in the understanding and design of peptoid-based nanomaterials. In this work, we report the bottom-up parameterization of coarse-grained peptoid force fields based on the MARTINI peptide force field against all-atom peptoid simulation data. Our parameterization pipeline iteratively refits coarse-grained bonded interactions using iterative Boltzmann inversion and nonbonded interactions by matching the potential of mean force for chain extension. We assure good sampling of the amide bond cis/trans isomerizations in the all-atom simulation data using parallel bias metadynamics. We develop coarse-grained models for two representative peptoids—polysarcosine (poly(N-methyl glycine)) and poly(N-((4-bromophenyl)ethyl)glycine)—and show their structural and thermodynamic properties to be in excellent accord with all-atom calculations but up to 25-fold more efficient and compatible with MARTINI force fields. Here, this work establishes a new rigorously parameterized coarse-grained peptoid force field for the understanding and design of peptoid nanomaterials at length and time scales inaccessible to all-atom calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Locating fast-varying line disturbances with the frequency mismatch

In an attempt to provide an efficient method for line disturbance identification in complex networks of diffusively coupled agents, we recently proposed to leverage the frequency mismatch. The frequency mismatch filters out the intricate combination of interactions induced by the network structure and quantifies to what extent the trajectory of each agent is affected by the disturbance. In this previous work, we provided some analytical evidence of its efficiency when the perturbation is assumed to be slow. Here we claim that the frequency mismatch performs actually well for most disturbance regimes. This is shown through a series of simulations and is backed up by an analytical argument. Therefore, we argue that the frequency mismatch is an efficient and elegant tool for line disturbance location in complex networks of diffusively coupled agents.

97 MATHEMATICS AND COMPUTING↗

Shock state distributions in porous tantalum and characterization with multipoint velocimetry

Heterogenous materials under shock compression can be expected to reach different shock states throughout the material according to local differences in microstructure and the history of wave propagation. Here, in this work, a compact, multiple-beam focusing optic assembly is used with high-speed velocimetry to interrogate the shock response of porous tantalum films prepared through thermal-spray deposition. The distribution of particle velocities across a shocked interface is compared to results obtained using a set of defocused interferometric beams that sampled the shock response over larger areas. The two methods produced velocity distributions along the shock plateau with the same mean, while a larger variance was measured with narrower beams. The finding was replicated using three-dimensional, mesoscopically resolved hydrodynamics simulations of solid tantalum with a pore structure mimicking statistical attributes of the material and accounting for radial divergence of the beams, with agreement across several impact velocities. Accounting for pore morphology in the simulations was found to be necessary for replicating the rise time of the shock plateau. The validated simulations were then used to show that while the average velocity along the shock plateau could be determined accurately with only a few interferometric beams, accurately determining the width of the velocity distribution, which here was approximately Gaussian, required a beam dimension much smaller than the spatial correlation lengthscale of the velocity field, here by a factor of ∼30×, with implications for the study of other porous materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Zeolite-templated carbons as effective sorbents to remove methylsiloxanes and derivatives: A computational screening

Though widely used in our daily lives, volatile methylsiloxanes and derivatives are emerging contaminants and becoming a high-priority environment and public health concern. Developing effective sorbent materials can remove siloxanes in a cost-effective manner. Herein, by means of Grand Canonical Monte Carlo (GCMC) simulations, we evaluated the potentials of the recently proposed 68 stable zeolite-templated carbons (ZTCs) for the removal of four linear methylsiloxanes and derivatives as well as two cyclic methylsiloxanes by the calculated average loading and average adsorption energy values. Four ZTCs, namely ISV, FAU1, FAU3, and H8326836, were identified with the top 50% adsorption performance toward all the six targeted contaminants, which outperform activated carbons. Further first principles computations revealed that steric hindrance, electrostatic interactions (further enhanced by charge transfer), and CH-π interactions account for the outstanding adsorption performance of these ZTCs. This work provides a quick procedure to computationally screen promising ZTCs for siloxane removal, and help guide future experimental and theoretical investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular-based analysis of nanoparticle solvation: Classical density functional approach

Proper statistical mechanics understanding of nanoparticle solvation processes requires an accurate description of the molecular structure of the solvent. Achieving this goal with standard molecular dynamics (MD) simulation methods is challenging due to large length scales. An alternative approach to this problem can be formulated using classical density functional theory (cDFT), where a full configurational description of the positions of all the atoms is replaced by collective atomic site densities in the molecule. Using an example of the negatively charged silica-like system in an aqueous polar environment represented by a two-site water model, we demonstrate here that cDFT can reproduce MD data at a fraction of the computational cost. An important implication of this result is the ability to understand how the solvent molecular features may affect the system’s properties at the macroscopic scale. A concrete example highlighted in this work is the analysis of nanoparticle interactions with sizes of up to 100 nm in diameter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrolytically Assisted Surface Decontamination (EASD{sup TM}) for POCO Operations - 20282

NNL in collaboration with C-Tech Innovation Ltd and Sellafield Ltd has been exploring innovative technologies to enable a significant reduction of radiological hazards within facilities during the Post Operational Clean Out (POCO) phase of a nuclear plant's life cycle. Reducing the hazard by effectively decontaminating plants in-situ during POCO delivers huge cost reductions for future decommissioning operations. These cost reduction benefits are realized by reducing the number and complexity of remote operations as well as lowering the long-term waste disposal costs. Whilst chemical decontamination can achieve the desired level of decontamination, applying aggressive chemical reagents is hazardous, potentially difficult to control and requires there to be complimentary effluent treatment and waste routes. This work has aimed to develop flexible and controllable decontamination processes which could be operated without the additional complexity and issues associated with chemical decontamination. The processes needed to be relatively fast and effective to minimize the time operators would spend in an active area. In addition, there was a driver to produce decontamination methodologies which generated a secondary waste compatible with current routes and which takes advantage of current waste capacity. The strategy therefore was to come up with a solution that works with, rather than against, the science and engineering behind process plants at Sellafield. Electrolytically Assisted Surface Decontamination (EASD{sup TM}) is an innovative electrochemical decontamination process (developed by NNL and C-Tech Innovation Ltd) that can remove activity from contaminated metal in very short time periods. Application of the patented electric waveform to the surface when treating contaminated metal with nitric acid has been shown to significantly enhance the decontamination performance. When compared to proposed baseline washout procedures at Sellafield, the only change to the process is the applied electrical waveform which is temporary and controllable. The current causes dissolution of the metal surface being decontaminated which leads to activity transferring from the plant item into the nitric acid effluent stream. This innovation has the potential to transform the POCO process and allow a nitric acid based washout approach to deliver POCO quickly and cost effectively within the existing infrastructure. Several devices have now been designed that incorporate this EASD{sup TM} technology and enable the decontamination process to be applied to a range items commonly identified as being contaminated during nuclear decommissioning programmes such as pipework, tanks and hotspots of walls/floors. Inactive and active laboratory-scale testing has been completed using both simulated and 'real-life' contaminated (low level waste) metallic items retrieved from different nuclear sites. Active trials demonstrated that contaminated items could be treated to free release levels within minutes. Engineering scale tests are currently being performed, with guidance from Sellafield's system engineers and plant managers, to provide the necessary re-assurance the designed devices could be successfully deployed in an on-plant scenario. The final stage of this development work is to carry out an active demonstration of the decontamination technology on Thorp at Sellafield. This paper aims to highlight progress made to date with the EASD{sup TM} technology and, more specifically, the development of an in-situ decontamination device for deployment within radioactive pipework. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Furthermore, our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗