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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Groundwater and Surface Water Flow (GSFLOW) model files for the East River, Colorado

The data package contains model input files and executables for the East River, Colorado (750 km2) located in the headwaters of the Upper Colorado River Basin. The code applied is the U.S. Geological Survey (USGS) Groundwater and Surface Water Flow (GSFLOW) model. The model contains a 100-m grid resolution to represent topographic complexity and a daily timestep accounts for energy and water partitioning between the snowpack, vegetation, soil zone and bedrock. The land surface model is dynamically linked to a three-dimensional groundwater flow model that allows for streamflow gaining and losing conditions. The groundwater model accounts for nine stratigraphic units and extends 400 m below land surface. Using this modeling framework we explore historical water budgets (water year 1987-2022) and the influence of seasonal warming and associated mechanisms driving groundwater declines and streamflow loss. A Readme_062424.txt file provides instructions on how to download all files. Input and output files are provided for the historical simulation representative of water years 1987 to 2022 (i.e. baseline) and the all-year +4C warming scenario. Instructions are provided to run the seasonal warming scenarios with warming applied only to the autumn, winter, spring or summer months. Modeled output used in figures for Carroll et al., 2024 are also provided with metadata describing where these data were obtained. This dataset additionally includes a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.Updated on 06-24-2024: The dataset was updated to include model outputs (updated base.zip and 4C.zip files), figure source files (Figure_Source_Files.zip), an updated Readme file (Readme_062424.txt), climate input files (climate_input_files.zip), and the adoption of ESS-DIVE File Level Metadata and CSV reporting formats (inclusion of flmd.csv and dd.csv files).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1983

Automated control and data acquisition for a tunable diode laser heterodyne spectrometer

This paper describes the hardware and software design, development, and implementation of the control and data electronics of a laser heterodyne spectrometer instrument being built at NASA Langley Research Center for a technology demonstration. Functional partitioning, applied at all levels of hardware and software, has been found to provide expedient design, development, and testing of the instrument. The instrument is composed of distributed microprocessor-based units. A master/slave protocol is presented which can be simulated by a terminal for unit checkout. All but one of the units are implemented using a set of core boards, plus unique boards where necessary. This design has led to reduced hardware development, reduced parts inventory, and replication of software modules, while providing the flexibility needed for a development instrument. The development tools and documentation guidelines are discussed.

Shull, T. S.↗
NASA NTRS1997

Safety Standard for Hydrogen and Hydrogen Systems: Guidelines for Hydrogen System Design, Materials Selection, Operations, Storage and Transportation

The NASA Safety Standard, which establishes a uniform process for hydrogen system design, materials selection, operation, storage, and transportation, is presented. The guidelines include suggestions for safely storing, handling, and using hydrogen in gaseous (GH2), liquid (LH2), or slush (SLH2) form whether used as a propellant or non-propellant. The handbook contains 9 chapters detailing properties and hazards, facility design, design of components, materials compatibility, detection, and transportation. Chapter 10 serves as a reference and the appendices contained therein include: assessment examples; scaling laws, explosions, blast effects, and fragmentation; codes, standards, and NASA directives; and relief devices along with a list of tables and figures, abbreviations, a glossary and an index for ease of use. The intent of the handbook is to provide enough information that it can be used alone, but at the same time, reference data sources that can provide much more detail if required.

Source record↗
NASA NTRS2003

Acceptable Tolerances for Matching Icing Similarity Parameters in Scaling Applications

This paper reviews past work and presents new data to evaluate how changes in similarity parameters affect ice shapes and how closely scale values of the parameters should match reference values. Experimental ice shapes presented are from tests by various researchers in the NASA Glenn Icing Research Tunnel. The parameters reviewed are the modified inertia parameter (which determines the stagnation collection efficiency), accumulation parameter, freezing fraction, Reynolds number, and Weber number. It was demonstrated that a good match of scale and reference ice shapes could sometimes be achieved even when values of the modified inertia parameter did not match precisely. Consequently, there can be some flexibility in setting scale droplet size, which is the test condition determined from the modified inertia parameter. A recommended guideline is that the modified inertia parameter be chosen so that the scale stagnation collection efficiency is within 10 percent of the reference value. The scale accumulation parameter and freezing fraction should also be within 10 percent of their reference values. The Weber number based on droplet size and water properties appears to be a more important scaling parameter than one based on model size and air properties. Scale values of both the Reynolds and Weber numbers need to be in the range of 60 to 160 percent of the corresponding reference values. The effects of variations in other similarity parameters have yet to be established.

Anderson, David N.↗
DOE OSTI2024

Avoiding pitfalls in molecular simulation of vapor sorption: Example of propane and isobutane in metal–organic frameworks for adsorption cooling applications

This study introduces recommendations for conducting molecular simulations of vapor adsorption, with an emphasis on enhancing the accuracy, reproducibility, and comparability of results. The first aspect we address is consistency in the implementation of some details of typical molecular models, including tail corrections and cutoff distances, due to their significant influence on generated data. We highlight the importance of explicitly calculating the saturation pressures at relevant temperatures using methods such as Gibbs ensemble Monte Carlo simulations and illustrate some pitfalls in extrapolating saturation pressures using this method. For grand canonical Monte Carlo (GCMC) simulations, the input fugacity is usually calculated using an equation of state, which often requires the critical parameters of the fluid. We show the importance of using critical parameters derived from the simulation with the same model to ensure internal consistency between the simulated explicit adsorbate phase and the implicit bulk phase in GCMC. We show the advantages of presenting isotherms on a relative pressure scale to facilitate easier comparison among models and with experiment. Extending these guidelines to a practical case study, we evaluate the performance of various isoreticular metal–organic frameworks (MOFs) in adsorption cooling applications. This includes examining the advantages of using propane and isobutane as working fluids and identifying MOFs with a superior performance.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Stream discharge and temperature data collected within the East and Taylor Watershed, Colorado for the Lawrence Berkeley National Laboratory Watershed Function Science Focus Area (water years 2019 to 2025)

This dataset contains stream discharge and temperature data for water years 2019 to 2025 from the East and Taylor Watersheds in Colorado, United States. This data was collected to understand hydrological processes occurring in the East River and Taylor River Watersheds, Colorado, which is part of the Lawrence Berkeley National Laboratory Watershed Function Scientific Focus Area. Data includes instantaneous observed discharge using salt dilution and acoustic doppler velocimeter techniques, raw pressure transducer downloaded data, sub-hourly temperature as well as corrected water level and associated stream discharge and mean daily values. Notes on water level corrections, rating curve development and metadata provided. A rating curve is the translation of depth to streamflow. The rating curve can be used as a quantitative measure of the “quality of the data.” Data within this dataset is formatted using ESS-DIVE’s Hydrological Monitoring Reporting Format. This data package contains (1) a zip file (Stream_Discharge_Data_WY19-WY25.zip) containing stream discharge and temperature data organized by location; (2) an InstallationMethods file (InstallationMethods.csv) describing metadata about the installation; (3) a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; (4) a data dictionary (dd.csv) file that contains terms/column_headers used throughout the files along with a definition, units, and data type; (5) a locations metadata file (locations.csv); (6) and a sensor metadata file (sensors.csv). All data files are in non-proprietary formats (csv, png, or pdf formats). Please contact Rosemary Carroll, Curtis Beutler, or Austin Shirley for any support in accessing the files. Update on 2023-05-12: Additional data from WYs 2021 and 2022 were added. Additionally, the dataset was converted using ESS-DIVE’s Hydrological Monitoring Reporting Format. Data files were reformatted to match reporting format guidance, new metadata files were added, and files were converted from excel to CSV. Update on 2025-05-16: Additional data from WYs 2022 (for locations not previously included), 2023, and 2024 were added. An additional descriptive PDF (WFSFA_Streamflow_Hydrograph_Disclaimer.pdf) was added. Metadata files were updated to reflect the addition of new data and locations. Update on 2026-05-18: Additional data from WY 2025 were added, including a new location Upper Trail Creek (TR-TCG2). Metadata files were updated to reflect the addition of new data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Evaluation of Multi-cell Failure Propagation

Failure propagation testing is of increasing interest to the designers and end users of battery systems. One of the chief difficulties, however, is choosing an appropriate initiation method to perform the test. Single cell abuse testing is typically used to initiate thermal runaway but this can involve a large amount of additional energy injected into the system. It is assumed that this will have some impact on the behavior of a propagating thermal runaway event, but there is little data available as to how significant this would be. Further, it is ultimately difficult to develop viable propagation tests for compliance and public safety activities without better knowledge of how test methods will impact the results. This work looks at propagating battery failure with a variety of chemistries, formats, configurations and initiation methods to determine the level of significance of the chosen initiation method on the test results. We have ultimately found while there is some impact on the detailed results of propagation testing, in most cases other factors, particularly the energy density of the system play a much greater role in the likelihood of a propagation event consuming an entire battery. We have also provided some guidelines for test design to support best practices in testing.

25 ENERGY STORAGE↗
DOE OSTI2024

Responses of Drying-rewetting (Transient Soil Moisture) and Steady State Soil Moisture Incubation on Soil Organic Carbon Dynamics in Three US Soils, 2017

This data set contains measurements of soil characteristics (aggregate size distribution and mean size, total aggregate associated carbon, extractable organic C, and microbial biomass C), microbial respiration, and soil metabolite concentrations from a transient and steady soil moisture incubation experiment using soils of different textures (sandy, loamy, and clayey). The study investigated mechanisms driving the Birch effect (increased carbon mineralization pulses with wetting following a drying period) in differing soil textures. Three different soils of distinctly different textures were collected from 0-15cm depth in Georgia (sandy, 2017-05-01), Missouri (loamy, 2017-06-14), and Texas (clayey, December 2017). Soils were incubated for 140 days with destructive harvests done on days 1, 29, 33, 56, 112, 116, and 140 in transient soil moisture incubation and on days 1, 33, 116, and 140 in steady state soil moisture incubation. This dataset contains six data files in comma separate (.csv) format. Additional metadata are provided: six data dictionaries and a file-level metadata file in comma separate (*.csv) format and a user guide in PDF (*.pdf) format.

1-Methyladenosine concentration↗
NASA NTRS1994

(abstract) A Low-Cost Mission to 2060 Chiron Based on the Pluto Fast Flyby

The Pluto Fast Flyby-based mission to Chiron described in this paper is a low cost, scientifically rewarding, focused mission in the outer solar system. The proposed mission will make a flyby of 2060 Chiron, an active 'comet' with over 10(sup 4) times the mass of Halley, and an eccentric, Saturn-crossing orbit which ranges from 8.5 to 19 AU. This mission concept achieves the flyby 4.2 years after launch on a direct trajectory from Earth, is independent of Jupiter launch windows, and fits within Discovery cost guidelines. This mission offers the scientific opportunity to examine a class of object left unsampled by the trail-blazing Mariners, Pioneers, Voyagers, and missions to Halley. Spacecraft reconnaissance of Chiron addresses unique objectives relating to cometary science, other small bodies, the structure of quasi-bound atmospheres on modest-sized bodies, and the origin of primitive bodies and the giant planets. Owing to Chiron's large size (180<D<370 km), unique nature, and unusual orbit, this mission is likely to draw significant public interest. As described by COMPLEX, the SSEC, and later the SSES, flybys are the appropriate scale missions for initial reconnaissance missions. Carrying three sophisticated instruments, the proposed flyby will return critical data about Chiron's size, shape, polar obliquity, atmosphere, surface morphology, surface composition, internal structure, surface activity (including the nature of Chiron's outbursts), and origin. Engineering analysis indicates that the spacecraft is capable of navigating to and encountering Chiron at close approach distances of less than 5 000 km, well inside the 50 000 to 150 000 km coma, and perhaps within the collisional chemistry zone of the coma. The low cost of the proposed Chiron mission is based on the opportunity to use the planned Pluto Flyby spare spacecraft and a Proton Expendable Launch Vehicle (ELV) (the pluto spacecraft is being designed to be compatible with a Proton launch). Backup launch opportunities on Delta II and Atlas ELVs are available. The Pluto Fast Flyby mission plans to develop a low cost ($150M), lightweight (<150 kg) outer planet spacecraft which is well suited to flyby reconnaissance in the outer solar system. This Chiron flyby mission is designed to leverage SSED's Pluto spacecraft investment into a scientifically valuable successor mission within the Discovery cost cap. Taking advantage of the spare spacecraft, we estimate the Discovery Chiron intercept mission can be launched for less than $100 M. We believe this makes a highly attractive proposal, which maintains US presence and leadership in the study of the outer solar system, and enables the first-time exploration of a wholly new class of planetary target, an outer solar system planetesimal.

2060 Chiron planetesimal flyby Pluto Fast Flyby sp↗
NASA NTRS1996

Bubble and Slug Flow at Microgravity Conditions: State of Knowledge and Open Questions

Based on the experiments carried out over the past decade at microgravity conditions, an overview of our current knowledge of bubbly and slug flows is presented. The transition from bubble to slug flow, the void fraction and the pressure drop are discussed from the data collected in the literature. The transition from bubble to slug flow may be predicted by introducing a critical void fraction that depends on the fluid properties and the pipe diameter; however, the role of coalescence which controls this transition is not clearly understood. The void fraction may be accurately calculated using a drift-flux model. It is shown from local measurements that the drift of the gas with respect to the mixture is due to non-uniform radial distribution of void fraction. The pressure drop happens to be controlled by the liquid flow for bubbly flow whereas for slug flow the experimental results show that pressure drops is larger than expected. From this study, the guidelines for future research in microgravity are given.

Colin, C.↗
DOE OSTI2024

Development of a Practical Secondary Control for Hardware Microgrids

Practical, vendor-agnostic interoperability guidelines for the secondary control architecture of microgrids (MGs) with multiple grid-forming (GFM) inverter-based resources (IBRs) have not yet been developed. Therefore, this paper proposes a generic and vendor-agnostic secondary control architecture that operates with all GFM IBRs and synchronous generators. This secondary control does not require the use of additional measurement devices in the MG and utilizes the inherent communication systems of the GFM units, such as Modbus TCP/IP. The practical challenges of Modbus registers, such as packet loss and quantization error, and their detrimental impacts on secondary control actions are investigated. The proposed three-stage modification for any secondary control architecture to mitigate these impacts includes: 1) averaging the data read, 2) situational event-triggering of the controller, and 3) finite iteration of the controlling action. The proposed method is validated using a three-phase electric power, 480 V, 60 Hz, 500 kVA laboratory hardware microgrid with commercial two GFM IBRs and one diesel generator. The experimental results corroborates the fact the proposed modification in the secondary control architecture is advantageous for practical usage under erroneous measurements.

grid-forming inverter↗
DOE OSTI2025

Hourly gap-filled meteorological data from PIE LTER measurements (2004-2023) used as drivers to run ELM PFLOTRAN simulations

This dataset contains continuous gap-filled precipitation, solar radiation, photosynthetically active radiation (PAR), air temperature, relative humidity, wind speed, and barometric pressure data recorded primarily at the Marshview Farm weather station within the Plum Island Long Term Ecosystems Research (PIE LTER) in Newbury Massachusetts (MA) from 2004 to 2023. We compiled the data set from published annual data packages in 15min resolution available on DataOne. Gaps were filled using different statistical techniques or available observations from the vicinity, e.g. the US-PLo and the US-PHM Ameriflux sites, also located within the PIE LTER. Flags are included in this dataset to indicate the origin of each data point. Metadata files ELMPFLOTRAN_met_dd.csv and ELMPFLOTRAN_met_flmd.csv contain more information on site locations, gap filling protocols, data variables, flags, and QA/QC methods. The data set was used in the spin up and simulations of a land surface model coupled to a biogeochemical reaction network (ELM PFLOTRAN) assessing impacts of hydrology and salinity input on methane fluxes in 2022 and 2023 (Sulman et al., 2024).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

SPRUCE Aboveground Vegetation Coverage in Root Ingrowth Core Plots, Marcell Experimental Forest, Minnesota, August 2022

This dataset contains vegetation survey measurements from root ingrowth core plots (Määttä et al. 2025) inside SPRUCE Experiment plots at the Marcell Experimental Forest in northern Minnesota. Vegetation surveys were conducted in 0.25 meter2 plots containing root ingrowth cores on August 8th and 9th, 2022 (2022-08-08 to 2022-08-09). The warming and elevated carbon dioxide (CO2) treatments in the dataset include the full treatment gradient: +0 degrees Celsius (C) (+0 and +500 parts per million (ppm) elevated CO2), +2.25 degrees C (+0 and +500 ppm), +4.5 degrees C (+0 and +500 ppm elevated CO2), +6.75 degrees C (+0 and +500 ppm) and +9 degrees C (+0 and +500 ppm elevated CO2) for both hummocks and hollows. This dataset includes measurements of the height and absolute coverage (%) for each vascular plant and moss species, as well as organic litter and dead overstory vascular plants, and the distance from the grid center to the nearest tree and the species of the nearest tree. These data were used as species-specific aboveground plant metadata for assessing the warming and elevated CO2 response of fine roots across different peatland microtopographical features (hummocks and hollows) and plant functional types (shrub, spruce and larch). This dataset contains one data file in comma separate (.csv) format. Additional metadata are provided: one data dictionary and a file-level metadata file in comma separate (.csv) format and a user guide in PDF (*.pdf) format.

ESS-DIVE CSV File Formatting Guidelines Reporting ↗
NASA NTRS2013

Longitudinally Jointed Edge-Wise Compression HoneyComb Composite Sandwich Coupon Testing And Fe Analysis: Three Methods of Strain Measurement, And Comparison

Three distinct strain measurement methods (i.e., foil resistance strain gages, fiber optic strain sensors, and a three-dimensional digital image photogrammetry that gives full field strain and displacement measurements) were implemented to measure strains on the back and front surfaces of a longitudinally jointed curved test article subjected to edge-wise compression testing, at NASA Goddard Space Flight Center, according to ASTM C364. The pre-test finite element analysis (FEA) was conducted to assess ultimate failure load and predict strain distribution pattern throughout the test coupon. The predicted strain pattern contours were then utilized as guidelines for installing the strain measurement instrumentations. The foil resistance strain gages and fiber optic strain sensors were bonded on the specimen at locations with nearly the same analytically predicted strain values, and as close as possible to each other, so that, comparisons between the measured strains by strain gages and fiber optic sensors, as well as the three-dimensional digital image photogrammetric system are relevant. The test article was loaded to failure (at ~167 kN), at the compressive strain value of ~10,000 micro epsilon. As a part of this study, the validity of the measured strains by fiber optic sensors is examined against the foil resistance strain gages and the three-dimensional digital image photogrammetric data, and comprehensive comparisons are made with FEA predictions.

Farrokh, Babak↗
DOE OSTI2024

Leaf phenology data at The Morton Arboretum Forestry Plots 2019-2023

We are collecting long-term leaf phenology data at The Morton Arboretum to determine seasonal patterns of leaf production in trees. This data on leaf phenology will be integrated with other ongoing data streams to create a connection between above- and below-ground tree processes. This data package contains raw and smooth outputs from phenology data, as well as extracted phenophase dates (i.e., start, peak, and end of season): the raw and smooth outputs from the PhenoCam GUI can be found in the "leafRaw.csv" and "leafSmooth.csv" files, respectively, and the extracted phenophase dates can be found in the "leafPhenophaseDates2019-2023.csv" file. Extracted phenophase dates for evergreen species in 2023 are currently unavailable, and the files will be updated once they are extracted. Additional information on units and other file-level metadata can be found within each data file's respective data dictionary, and metadata for each of the 23 surveyed plots can be found within the "Location_metadata.csv" file. While the "leafRaw.csv" and the "leafSmooth.csv" files contain all data for all species, the "leafPhenophaseDates2019-2023.csv" file currently excludes the dates for evergreen species in 2023. Another version of the file will be added as those dates are extracted.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2004

The Multistage Compressor Facility

Research and developments of new aerospace technologies is one of Glenn Research Center's specialties. One facility that deals with the research of aerospace technologies is the High-speed Multistage Compressor Facility. This facility will be testing the performance and efficiency of an Ultra Efficient Engine Technology (UEET) two-stage compressor. There is a lot of preparation involved with testing something of this caliber. Before the test article can be installed into the test rig, the facility must be fully operational and ready to run. Meaning all the necessary instrumentation must be calibrated and installed in the facility. The test rig should also be in safe operating condition, and the proper safety permits obtained. In preparation for the test, the Multistage Compressor Facility went through a few changes. For instance the facility will now be utilizing slip rings, the gearbox went through some maintenance, new lubrications systems replaced the old ones, and special instrumentation needs to be fine tuned to achieve the maximum amount of accurate data. Slips rings help gather information off of a rotating device - in this case from a shaft - onto stationary contacts. The contacts (or brushes) need to be cooled to reduce the amount of frictional heat produced between the slip ring and brushes. The coolant being run through the slip ring is AK-225, a material hazardous to the ozone. To abide by the safety regulations the coolant must be run through a closed chiller system. A new chiller system was purchased but the reservoir that holds the coolant was ventilated which doesn t make the system truly closed and sealed. My task was to design and have a new reservoir built for the chiller system that complies with the safety guidelines. The gearbox had some safety issues also. Located in the back of the gearbox an inching drive was set up. When the inching drive is in use the gears and chain are bare and someone can easily get caught up in it. So to prevent anyone from getting hurt in the gears I designed a chain guard. Additional information is included in the original extended abstract.

Flegel, Ashlie↗
DOE OSTI2024

Development of a Practical Secondary Control for Hardware Microgrids: Preprint

Practical vendor-agnostic interoperability guidelines for the secondary control architecture of microgrids (MGs) with multiple grid-forming (GFM) inverter-based resources (IBRs) have not yet been developed. Therefore, this paper proposes a generic and vendor-agnostic secondary control architecture that works with all GFM IBRs and synchronous generators. This secondary control does not need to employ any additional measurement devices in the MG and uses the inherent communication systems of the GFM units, such as Modbus TCP/IP. The practical challenges of Modbus holding registers such as packet loss, quantization error, etc. and their deteriorating impacts on the secondary control action are investigated. The proposed three-stage modification of any secondary control architecture to eliminate these impacts includes 1) averaging the data read, 2) situational event-triggering of the controller, and 3) the finite iteration of the controlling action. The proposed method is validated using a laboratory hardware MG with commercial GFM units.

inverter based resources↗
DOE OSTI2022

Medium controlled aggregative growth as a key step in mesoporous silica nanoparticle formation

Near monodisperse mesoporous silica nanoparticles (MSN) represent a promising and rapidly developing type of mesoporous silica materials; however, the vast data on their synthesis remains unorganized and ill-understood. We systematically studied the formation of MSN under basic and neutral conditions using various temperatures, CTAB concentrations, hydrolyzing agents (triethanolamine, ammonia, phosphate buffers), and media with different colloidal stabilization properties (with ethanol as a cosolvent and monovalent salts). In the typical conditions for the preparation of stable MSN colloids, the particle size was controlled by colloidal stabilization by the medium (solvent type, ionic strength, and surfactant concentration) in agreement with the “aggregative growth” mechanism, rather than by solely the hydrolysis and condensation rates conventionally used for data interpretation in the classical nucleation theory. Medium properties (pH, ion types and concentration, polarity) also defined the efficiency of silica-surfactant cooperative self-assembly, which directly affected the porosity, mesopore size and pore wall thickness. Interestingly, this traditional silica-surfactant route showed a limited effect on the particle size, emphasizing the dominating role of colloidal stabilization in the studied reaction conditions. In situ pH measurements showed that every reaction medium has unique pH evolution profiles depending on the buffer capacity, hydrolysis and condensation rates. Reaction systems that fail to maintain the working pH can lead to non-porous products or undesired particle morphology and size distribution. The established particle formation mechanism allowed us to formulate comprehensive guidelines for preparing relatively concentrated colloids of near monodisperse (PDI 5–15%) mesoporous 30–700 nm silica spheres with variable porosity and mesopore size. Here, these findings will be particularly useful in designing new mesoporous silica-containing materials for biomedical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗