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At least 451 records · Page 25

Anisotropic spall failure of additively manufactured 316L stainless steel

The dynamic high strain rate tensile (spall) failure of additively manufactured (AM) materials is an area of great interest but much less understood than material failure under other loading regimes. The research presented here examines the effects of microstructure anisotropy in 316L stainless steel fabricated by laser powder bed fusion (LPBF) on its spall failure and properties. In this work, plate-on-plate impact experiments were performed using an 80-mm gas gun to investigate the spall behavior of AM fabricated sample discs with impact along the perpendicular and parallel orientations relative to build directions. Experiments were also performed on wrought 316L stainless steel as baseline material with uniform equiaxed grain microstructure for comparison with the AM material of same composition. The spall experiments involved free-surface velocity profiles measured using Photon Doppler Velocimetry (PDV) to capture the spall pull-back signals, combined with post-mortem analysis of the microstructure of soft-recovered impacted samples. In the case of AM samples, spall failure initiated preferentially at melt pool boundaries in both impact directions. The spall plane location and spall strength, however, were both heavily influenced by the orientation of the impact direction relative to the build direction in the AM samples. The spall behavior is also observed to be more complex in the samples impacted perpendicular to the build (through-thickness) direction, due in large part to the orientation of the microstructural features such as melt pool boundaries, laser scan tracks, and general grain morphology.

36 MATERIALS SCIENCE↗

Tailoring material microstructure and property in wire-laser directed energy deposition through a wiggle deposition strategy

Developing effective strategies to directly control material microstructure, property, and anisotropy is an active research area in metal additive manufacturing. This work develops a wiggle deposition pattern for wire-laser directed energy deposition (DED) of 316L stainless steel (SS) to modify the solidification texture, particularly in the building direction, in as-deposited samples. Through multi-physics simulation, operando near-infrared imaging, and synchrotron x-ray characterization, it is found that the wiggle deposition strategy induces highly dynamic melt flow and oscillating thermal gradient in the melt pool, which is responsible for the variation of preferable grain growth direction and crystallographic texture in the sample. The specific texture reduces the anisotropy in the tensile strength of as-printed 316L SS samples cut along different directions. Also, it largely increases the ductility along the build direction. Crystal plasticity simulation is performed to correlate the sample texture with mechanical property. In conclusion, this work offers a unique approach for tailoring local properties through the control of melt pool instability by applying different tool paths.

36 MATERIALS SCIENCE↗

Dissolution zone model of the oxide structure in additively manufactured dispersion-strengthened alloys

The structural evolution of oxides in dispersion-strengthened superalloys during laser-powder bed fusion is considered in detail. Alloy chemistry and process parameter effects on oxide structure are assessed through a parameter study on the model alloy Ni-20Cr, doped with varying concentrations of Y 2 O 3 and Al. Small angle neutron scattering measurements of the dispersoid size distribution show the dispersoid size increases with higher laser power, slower scan speed, and increasing Y 2 O 3 and Al content. Complementary electron microscopy measurements reveal reactions between Y 2 O 3 and Al, even in nanoscale dispersoids, and the presence of micron-scale oxide slag inclusions in select specimens. A scaling analysis of mass and momentum transport within the melt pool, presented here, establishes that diffusional structural evolution mechanisms dominate for nanoscale dispersoids, while fluid forces and advection become significant for larger slag inclusions. These findings are developed into a theory of dispersoid structural evolution, integrating quantitative models of diffusional processes – dispersoid dissolution, nucleation, growth, coarsening – with a reduced order model of time-temperature trajectories of fluid parcels within the melt pool. Calculations of the dispersoid size in single-pass melting reveal a zone in the center of the melt track in which the oxide feedstock fully dissolves. Within this zone the final Y 2 O 3 size is independent of feedstock size and determined by nucleation and growth kinetics. If the dissolution zones of adjacent melt tracks overlap sufficiently with each other to dissolve large oxides, formed during printing or present in the powder feedstock, then the dispersoid structure throughout the build volume is homogeneous and matches that from a single pass within the dissolution zone. Gaps between adjacent dissolution zones result in oxide accumulation into larger slag inclusions. Predictions of final dispersoid size and slag formation using this dissolution zone model match the present experimental data and explain process-structure linkages speculated in the open literature.

36 MATERIALS SCIENCE↗

Formation mechanisms of Sn-rich δ phase and its role in strengthening Cu-10Sn manufactured by laser powder bed fusion

Cu-Sn alloys produced via laser powder bed fusion (L-PBF) additive manufacturing (AM) have gained significant attention because they combine the advantages of AM relevant to intricate component design with outstanding combinations of strength, ductility, and resistance to wear and corrosion. However, a detailed understanding of the microstructure that contributes to the enhancement of the mechanical properties of L-PBF Cu-10Sn alloys remains unclear. In particular, there is a lack of understanding of the formation mechanisms of the Sn-rich δ phase commonly observed in Cu-10Sn. This study reveals two distinct variants of the δ phase possessing unique morphological characteristics. These characteristics are attributed to the local solidification conditions inherent to the melt pool boundaries versus those at the interiors of melt pools. A phase transformation pathway that elucidates the origin of the morphological variants of the δ phase from the Sn-rich metastable phases during the cyclic heating of the AM process is proposed. We report superior mechanical properties in L-PBF Cu-10Sn compared to those of conventionally manufactured counterparts due to the synergistic contributions from grain boundaries, dislocations, and the δ phase. Notably, the δ phase alone contributes approximately 22 % to the overall strength observed in the L-PBF Cu-10Sn alloy. The discovery of two types of distinct Sn-rich δ phase offers key insights into precise microstructural control in AM Cu-Sn alloys to enhance mechanical properties, providing practical strategies for improving material performance for diverse applications in automotive, aerospace, and machinery industries.

36 MATERIALS SCIENCE↗

Harnessing on-machine metrology data for prints with a surrogate model for laser powder directed energy deposition

In this study, we leverage the massive amount of multi-modal on-machine metrology data generated from Laser Powder Directed Energy Deposition (LP-DED) to construct a comprehensive surrogate model of the 3D printing process. By employing Dynamic Mode Decomposition with Control (DMDc), a data-driven technique, we capture the complex physics inherent in this extensive dataset. This physics-based surrogate model emphasizes thermodynamically significant quantities, enabling us to accurately predict key process outcomes. The model ingests 21 process parameters, including laser power, scan rate, and position, while providing outputs such as melt pool temperature, melt pool size, and other essential observables. Furthermore, it incorporates uncertainty quantification to provide bounds on these predictions, enhancing reliability and confidence in the results. We then deploy the surrogate model on a new, unseen part and monitor the printing process as validation of the method. Our experimental results demonstrate that the predictions align with actual measurements with high accuracy, confirming the effectiveness of our approach. Furthermore, this methodology not only facilitates real-time predictions but also operates at process-relevant speeds, establishing a basis for implementing feedback control in LP-DED.

Digital twins↗

Real-time tracking and analysis of gas bubble dynamics in laser powder bed fusion using in-situ X-ray characterization and machine learning

Porosity defects remain a significant challenge in the laser powder bed fusion (LPBF) process, adversely affecting the mechanical properties and reliability of additively manufactured components. Here, this study investigates the real-time formation and trajectory of gas bubbles during LPBF of Al6061 alloy using advanced in-situ X-ray characterization and machine learning. The unsupervised Gaussian mixture model and particle tracking algorithm developed are able to precisely track and quantify the properties of gas bubbles and keyhole pores. Our analysis identified five distinct types of gas bubble formation and movement patterns, emphasizing the diverse origins and behaviors of these defects. It enables precise quantification of trajectories, velocities, and morphological changes of gas bubbles, offering a granular view of the subsurface dynamics within the melt pool. Additionally, we explored keyhole-induced pore dynamics, revealing the critical role of keyhole oscillation and collapse for the formation of both large and small gas pores. It defines four different regions of gas bubble movement within the melt pool, providing a clearer understanding of how local fluid dynamics affect pore behavior. The results underscore the importance of integrating in-situ experimental observation and automated machine learning to develop a more robust predictive model for defect formation in LPBF.

In-situ X-ray imaging↗

Selection-enriched genomic loci (SEGL) reveals genetic loci for environmental adaptation and photosynthetic productivity in Chlamydomonas reinhardtii

This work demonstrates an approach to produce and select hybrid algal strains exhibiting increased photosynthetic productivity under multiple environmental conditions. This simultaneously addresses two major impediments to improving algal bioenergy production: 1) generating new genetic variants with improved performance; and 2) disentangling complex interactions between genetic and physiological factors contributing to these improvements. We pooled progeny generated from mating two environmental isolates of the green alga Chlamydomonas reinhardtii and cultured the pools under multiple environmental conditions. Strains from the outcompeting populations showed substantial (in some cases over 3 fold) increases in productivity over the parental lines under certain environments related to biomass production, including laboratory conditions as well as hyperoxia, fluctuating light, high salinity and high temperature. The results indicate that C. reinhardtii has remarkable, untapped, directed evolution capacity that may be harnessed using breeding and competition approaches. The populations were deep sequenced at multiple time points to identify “Selection-Enriched Genomic Loci” (SEGL) that accumulated in the populations, and thus likely confer increased fitness under the respective environmental conditions. With improved resolution, SEGL mapping can identify allelic combinations used for targeted breeding approaches, generating elite algal lines with multiple desirable traits, as well as to further understand the genetic and mechanistic bases of photosynthetic productivity. Increasing the photosynthetic efficiency of algae during biomass production is perhaps the most critical hurdle for economically sustainable algal based biofuels. This presents unique challenges because modifications designed to increase photosynthesis often result in decreased fitness, due to production of toxic reactive oxygen species when photosynthesis is not adequately regulated. These problems are exacerbated under natural and outdoor production environments because of the complex nature of photosynthesis and the multifaceted interactions between genetic, environmental and physiological factors. Here, we demonstrate a high throughput biotechnological screening approach that simultaneously produces algal strains with highly increased autotrophic productivity and identifies genomic loci contributing to these improvements. Our results demonstrate that Chlamydomonas reinhardtii exhibits high directed evolutionary capacity readily accessed through breeding and selection.

59 BASIC BIOLOGICAL SCIENCES↗

Spectroscopic insight into carbon speciation and removal on a Cu/BEA catalyst during renewable high-octane hydrocarbon synthesis

Conversion of methanol and dimethyl ether (DME) to high-octane gasoline catalyzed by beta zeolite (BEA) provides an opportunity for the production of high-quality fuels from renewable carbon sources (e.g., gasified biomass). Recent research demonstrated that a Cu-modified BEA zeolite catalyst (Cu/BEA) offered advantages over the unmodified BEA catalyst due to multifunctional Cu species that enabled incorporation of co-fed H2, reactivation of light alkanes, and reduction of products from the aromatic hydrocarbon pool. The shift in hydrocarbon pool chemistry has the potential to influence the identity and relative composition of surface carbon species that are often linked to deactivation. A detailed understanding of these carbon species is important to develop an effective and efficient regeneration procedure that can enable the transition from fundamental catalyst development to commercial application. Here, we applied complementary ex situ and in situ characterization techniques to compare the structures of surface carbon species on post-reaction Cu/BEA and unmodified BEA catalysts. Both catalysts contained acyclic and aromatic hydrocarbons along with graphitic carbon species. However, the post-reaction Cu/BEA catalyst had a lower polycyclic aromatic content, and further, the graphitic species were more hydrogenated and defective. It was also found that the presence of Cu promoted carbon removal at lower temperatures than for unmodified BEA through activation of O2 by Cu oxide during thermal oxidation. The fundamental insight into the composition of surface carbon species enabled the design of an effective and efficient regeneration strategy for the DME homologation reaction over Cu/BEA, resulting in full recovery of the catalyst activity.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Underground hydrogen storage resource assessment for the Cook Inlet, Alaska

Underground hydrogen storage will be essential to a hydrogen economy. This work focuses on the challenge of identifying and screening candidate storage systems, given the unique behavior of hydrogen in the subsurface. Here, we describe a resource assessment methodology and apply it to Alaska’s Cook Inlet region. Alaska provides an interesting case study because of its abundant renewable energy resources, relatively low energy demand, and isolated electrical grid. The assessment framework considers each site’s ability to (1) store a specific volume, (2) physically-contain the stored gas, and (3) limit biogeochemical activity. We estimate that reservoirs in the Cook Inlet area could theoretically store a total of 286 TWh (or 8.6 million tonnes [Mt]) in hydrogen working gas in 92 pools. This is likely sufficient to meet both local hydrogen demand and support an array of exportable products. We further identify seven pools that may be especially well-suited for hydrogen storage. Broadly, this work demonstrates a framework for regional resource assessments. On a finer scale, this work supports an early demonstration of porous–media hydrogen storage in the United States.

08 HYDROGEN↗

The rhizosphere and cropping system, but not arbuscular mycorrhizae, affect ammonia oxidizing archaea and bacteria abundances in two agricultural soils

Arbuscular mycorrhizal fungi (AMF) form symbioses with roots that can enhance plant nutrition. While AMF have been shown to have a role in soil nitrogen (N) cycling, it is unclear whether AMF affect N cycling microbes such as ammonia-oxidizing bacteria (AOB) and archaea (AOA), which convert ammonium into nitrite in the first step of nitrification. In this study, we examined the effects of AMF on AOA and AOB abundances within the corn rhizosphere and bulk soil of conventional (corn-soybean rotation with inorganic fertilizer) and diversified (cornsoybean- oats/alfalfa-oats rotation with composted manure) systems. We hypothesized that AMF would decrease AOA and AOB abundances in a cropping-system dependent manner, possibly due to competition for ammonium. We grew corn deficient or proficient in AMF symbiosis in microcosms for 10 weeks. At the end of the experiment, both soils planted with the AMF-proficient corn genotype had higher ammonium and lower nitrate pool sizes compared to the same soils planted with the AMF-deficient corn genotype. Likewise, total plant N was higher in the AMF-proficient genotype compared to the AMF-deficient genotype. Despite changes in soil inorganic N pool sizes, AOA and AOB abundances were unaffected by plant AMF-proficiency. Instead, AOA abundance was greater in the rhizosphere than in the bulk soil regardless of cropping system, and AOB abundance was greater in the conventional than the diversified cropping system soil regardless of proximity to the root. These data indicate that 1) AMF did not affect AOA or AOB abundance in these N-rich soils but other factors such as root proximity and inorganic fertilization did and 2) AOA and AOB have differing ecological niches within rhizosphere and bulk soil that should be considered when managing for nitrogen losses.

Wattenburger, Cassandra↗

Through a glass darkly: In-situ x-ray computed tomography imaging of feed melting in continuously fed laboratory-scale glass melter

his study describes the first direct in-situ 3-D observation of a steady-state melting process by imaging a laboratory-scale slurry-fed glass melter in operation by x-ray computed tomography. Features of the reacting glass-feed, the foam layer underneath, and cavities in the glass melt pool are reconstructed in three-dimensional images. A slurry pool formed in a deep central caldera of dense dried feed, which penetrated into the glass melt. Slurry overflow from the caldera led to fast-dried and highly porous feed structure. A thin layer of foam separated the caldera from the melt. Bubbles ?5-15 mm in diameter were seen to grow beneath the reacting feed and move through the melt to escape at the edge. Pore morphology is benchmarked against computed tomography scans of a pellet of reacting simulated waste glass feed, and evolved gas analysis describes the gases generated as a function of temperature. Cooling artifacts are imaged and compared to previous studies of quenched cold caps. Detailed understanding of processes occurring during the conversion process in and below the reacting feed layer is necessary for the development of representative models of the melting process.

36 MATERIALS SCIENCE↗

High-speed X-ray study of process dynamics caused by surface features during continuous-wave laser polishing

During high-speed X-ray imaging of laser surface polishing experiments of specimens of 316L stainless steel at Argonne National Lab's Advanced Photon Source, it was discovered that the induced keyhole changes shape and dimensions while crossing an engineered surface feature without altering process parameters. It was observed that the post-surface feature keyhole was deeper than that of the pre surface feature keyhole. Here, this work reports on the first in-situ observation of the effect of localized surface geometry on underlying melt pool behavior. This has implications for defect formation mechanisms during laser melting processes that rely on melt pool geometry.

42 ENGINEERING↗

Solid-state transformations during laser directed energy deposition of Ti-6Al-4V powder hydride-dehydrided from scrap metals

During laser directed energy deposition (DED-LB), thermal cycling and powder chemical composition produce distinct thermal histories, which vary mechanical properties. Using real-time X-ray diffraction, this study investigates solid-state transformations during DED-LB to understand process-structure-property relationships for angular Ti-6Al-4V powder hydride–dehydrided from scrap metals. Results showed that regions near the molten pool experienced high cooling rates, leading to martensitic transformation from the β phase and increased hardness. Regions farther from the molten pool underwent tempering without solid-state transformation and decreased hardness. These findings support alternative feedstocks for metal additive manufacturing for a circular economy and resilient supply chains.

Additive manufacturing (AM)↗

New insights into fuel blending effects: Intermolecular chemical kinetic interactions affecting autoignition times and intermediate-temperature heat release

Fuel blending effects on chemically-dominated fuel properties, such as gasoline anti-knock quality, are influenced by fundamental chemical kinetic interactions between the blending agent and the base fuel. Historically, quantification of such interactions has focused on changes to the radical pool, including $\dot{O}$H and HO 2 , while intermolecular interactions pertaining to carbonated, non-fuel-specific intermediates are typically overlooked. In this regard, this work aims to derive new insight into intermolecular chemical kinetic interactions that are intrinsic to fuel blending effects via a case study on blends of 0–30% ethanol (by volume) into FGF-LLNL (a multi-component gasoline surrogate for FACE-F research gasoline) using a rapid compression machine at a diluted/stoichiometric fuel loading, compressed pressure of 40 bar and low- to intermediate-temperature regimes that are representative of boosted SI engine operation. Ethanol blending effects on the intermediate temperature heat release (ITHR) of FGF-LLNL are characterized using experimental measurements, where ethanol is found to promote the extent of ITHR and suppress the transition from ITHR to main ignition. Chemical kinetic modeling is undertaken using a recently updated gasoline surrogate model. Sensitivity analyses on ITHR characteristics further corroborate the ethanol blending effects, and highlight the significant dependence of ITHR on both fuel-specific and non-fuel-specific reactions. An approach allowing comprehensive characterization of the complex intermolecular chemical kinetic interactions between constitutes in a fuel blend is then proposed. Application of the approach to FGF-LLNL/E0–E30 reveals that ethanol perturbs the heat release and autoignition characteristics of FGF-LLNL not only by directly changing the $\dot{O}$H and HO 2 radical pools via fuel-specific reactions, but also through intermolecular interactions where participating intermediates can be produced and consumed by various sub-chemistries. Disabling the intermolecular interactions in carbonated species between ethanol and FGF-LLNL sub-chemistries leads to somewhat slower ITHR evolution and lower ignition reactivity. The role of the individual intermolecular interaction is also characterized using the proposed approach. Lastly, implications of intermolecular interactions for future studies that aim to improve model performance are highlighted, where it is found that further investigations on the core C0-C4 chemistry are needed for developing highly accurate chemistry models for complex fuel blends.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Gaussian Process-Based extended Goldak heat source model for finite element simulation of laser powder bed fusion additive manufacturing process

In this study, laser powder bed fusion (L-PBF) additive manufacturing (AM) is a key enabling technology to manufacture highly complex and integrated metallic structures. In L-PBF AM process, the melting of the metal powders and the layers underneath can be governed by either “conduction mode” or “keyhole mode”, with the keyhole mode reportedly leading to porosity and decreased strength and ductility by many studies. In part scale simulations, finite element (FE) model is often used to study the temperature distribution during printing and to predict the residual stress, where a volumetric heat flux with a Gaussian or a double ellipsoidal (Goldak) distribution is often applied as the laser heat source. However, the above heat source models can only capture the melt pool shape in the conduction mode, and fail to capture the transition to keyhole melting mode when the process parameters change. To overcome this inaccuracy, an extended Goldak heat source model is proposed by introducing a laser penetration term as a function of laser parameters obtained from a Gaussian-Process (GP) model. The model is validated by “2D pad” AlSi10Mg L-PBF experiments under a wide range of laser power, scan speed, and laser focus offset, and the results show the model successfully captures the measured melt pool shape in all conditions.

36 MATERIALS SCIENCE↗

Myna: Connecting powder bed fusion build data to simulation tools for digital twin applications

Additive manufacturing (AM), as a digital process, can generate a detailed digital thread linking a part’s design and manufacturing to its operational performance. As AM systems advance, an increasing amount of process data is stored in manufacturing databases. In principle, this data can be utilized by simulation-based digital twin approaches, such as real-time process control and asynchronous post-processing guidance. However, few tools currently exist for systematically integrating digital thread data with computational tools. Here, in this study, we propose a software package, called Myna, for connecting data from powder bed fusion processes to simulation tools. The utility of such a platform is demonstrated using build data from the Oak Ridge National Laboratory Manufacturing Demonstration Facility “Peregrine v2023-10” public dataset to automatically configure and run 54 semi-analytical 3DThesis melt pool simulations, 78 numerical Additive FOAM melt pool simulations, and 3 ExaCA microstructure simulations. The simulated, spatially registered microstructures are then compared directly with electron backscatter diffraction characterization of the corresponding as-built part locations. The resulting simulated microstructure showed variation as a function of process parameters, particularly stripe width; however, the experimental data had little variation between the microstructure texture and grain size resulting from different processing conditions. Analysis of the discrepancies suggest that it is possible a two-phase ferritic-austenitic solidification model is needed to accurately predict grain size and texture for certain stainless steel 316L feedstock compositions under powder bed fusion conditions, providing direction for future research. As illustrated here, due to the number and complexity of the simulations involved in AM process-structure–property predictions, automated methods to connect process data and simulations will remain necessary tools for testing hypotheses and implementing digital twin applications.

Knapp, Gerald L. [Oak Ridge National Laboratory (O↗

Using taxa-based approaches to delineate stream macroinvertebrate assemblage responses to stressor gradients in modified alluvial agroecosystems

Alluvial plain landscapes are some of the most agriculturally productive lands in the world but often have modified stream ecosystems due to cultivation history. This context requires consideration when establishing water quality management goals. We analyzed state water quality databases to demonstrate that Mississippi Alluvial Plain (MAP) ecoregion streams have elevated specific conductivity (SC) and nutrients and lower macroinvertebrate local and regional taxa pools compared to streams in other ecoregions, potentially reducing the efficacy of traditional biomonitoring approaches within the region. To overcome these challenges, we used threshold indicator taxa analysis (TITAN) to compare macroinvertebrate assemblage responses to water quality gradients among ecoregions in Mississippi. We identified individual taxa and assemblage-level responses to increasing water quality degradation in MAP streams. Observed responses occurred at higher concentrations for SC, total organic carbon (TOC) and total phosphorus (TP), but not total nitrogen (TN) relative to other ecoregions. These responses appeared to be driven by a large proportion of indicator taxa considered tolerant or unresponsive in other ecoregions, responding negatively to increasing water quality stressors in MAP streams. Our observed assemblage-level stressor responses to WQ gradients in MAP streams demonstrate shifting tolerance in highly altered ecosystems may require adjustments to recovery expectations but also provide useful measures for monitoring improvements in regional water quality. For example, our observed macroinvertebrate assemblage response to increasing TP identified a management goal similar to guidance based on distributional analysis of water quality data within the MAP ecoregion (0.11 vs 0.128 mg L –1 ) and thus provide some biological basis for previously identified nutrient goals for the region. Our approach can guide and monitor success of nutrient reduction efforts in MAP watersheds and other alluvial plain agroecosystems where reference conditions do not exist, and local and regional taxa pools are less diverse and may not support full recovery of ecological assemblages. While our results are promising, they should also be compared with more sensitive and less habitat-limited biological assemblages (e.g., algae or bacteria) to better understand complex ecological responses to best management practices designed to increase sustainability of high production agricultural regions.

59 BASIC BIOLOGICAL SCIENCES↗

A step-wise ion hydration model of aqueous electrolyte solution: The 2:2, 2:1 and 1:2 punches

In prior work we showed that the current step-wise hydration framework shows promise for modeling the concentration-activity relationship in aqueous solutions of ions representing 1:1 electrolytes, alcohols, and sugars, and accurately predicting the partitioning of the water between the bound (hydrated) pool and an unbound (free) pool. Here, in the current work, we continue developing this framework by applying it to ions representing 2:2, 2:1 and 1:2 electrolyte in aqueous solutions. Properly treating ion hydration as an ideal solution along with employing mean spherical approximation of the long-range electrostatic interactions yields an accurate model for most electrolytes considered. This simple model of aqueous solutions is robust for electrolytes and organic solutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗