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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Unprecedented Multifunctionality in 1D Nb 1- x Ta x S 3 Transition Metal Trichalcogenide Alloy

One-dimensional (1D) van der Waals materials, such as nanofibers or nanoribbons are considered as the future ultimate limit of downscaling for modern electrical and electrochemical devices. Here, for the first time, we successfully synthesize nanofibers of a solid solution transition metal trichalcogenide (TMTC), Nb 1-x Ta x S 3 , with outstanding electrical, thermal, and electrochemical characteristics rivaling the performance of the-state-of-the art materials for each application. This material shows nearly unchanged sheet resistance (≈740 Ω/sq -1 ) versus bending cycles tested up to 90 cycles, stable sheet resistance in ambient conditions tested up to 60 days, remarkably high electrical breakdown current density of ≈ 30 MA cm -2 , strong evidence of successive charge density wave (CDW) transitions, and outstanding thermal stability up to ≈900 K. Additionally, this material demonstrates excellent activity and selectivity for CO2 conversion to CO reaching ≈ 350 mA cm -2 at – 0.8 V vs RHE with an outstanding turnover frequency number of 25 for CO formation. It also exhibits an excellent performance in a high-rate Li-air battery with the specific capacity of 3000 mAhg -1 at a high current density of 0.3 mAcm -2 . This study uncovers the multifunctionality in 1D TMTC alloys for a wide range of high-impact applications and opens a new direction for the design of the next generation of low-dimensional materials with high performance.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Fast Photoactuation Driven by Supramolecular Polymers Integrated into Covalent Networks

Abstract The design of robotic soft matter capable of emulating the complex movements of living organisms such as mechanical actuation, shape transformation, and autonomous translation remains a grand challenge in soft materials science. Functionalized hydrogels are excellent candidates for such materials since they can operate in water and are highly responsive to their environment, but their response times can be slow. This work investigates fast photoactuation of hybrid bonding hydrogels composed of peptide amphiphile (PA) supramolecular nanofibers bonded covalently to merocyanine‐based (MCH + ) photoresponsive networks. By incorporating ionizable acrylic acid (AA) co‐monomers in these networks, photoactuation at nearly neutral pH is observed, which in turn enables a new mechanism to accelerate the response by triggering the bundling of supramolecular nanofibers by rapid proton exchange reactions. Furthermore, this rapid response and its consequent large shape transformations lead to hydrogels capable of spontaneously tracking external light sources inspired by pedicellariae, defensive organs present in echinoderms like the starfish and the sea urchin. This work suggests that hybrid bonding polymers (HBPs), which leverage the interplay between supramolecular assemblies and covalent networks, offer novel strategies to design rapidly actuating soft robotic materials.

Cezan, S. Doruk↗
DOE OSTI2022

Role of nanocellulose in tailoring electroanalytical performance of hybrid nanocellulose/multiwalled carbon nanotube electrodes

Abstract Nanocellulose has emerged as a promising green dispersant for carbon nanotubes (CNTs), and there is an increasing trend in developing nanocellulose/CNT hybrid materials for electrochemical detection of various small molecules. However, there have been very few comprehensive studies investigating the role of nanocellulosic material properties upon the electroanalytical performance of the resultant hybrid electrodes. In this work, we demonstrate the influence of both nanocellulose functionalization and geometry, utilizing sulfated cellulose nanocrystals, sulfated cellulose nanofibers, and TEMPO-oxidized cellulose nanofibers. Transmission electron microscopy tomography enables direct visualization of the effect of nanocellulosic materials on the hybrid architectures. High resolution X-ray absorption spectroscopy verifies that the chemical nature of CNTs in the different hybrids is unmodified. Electroanalytical performances of the different nanocellulose/CNT hybrid electrodes are critically evaluated using physiologically relevant biomolecules with different charge such as, dopamine (cationic), paracetamol (neutral), and uric acid (anionic). The hybrid electrode containing fibrillar nanocellulose geometry with a high degree of sulfate group functionalization provides the highest electroanalytical sensitivity and strongest enrichment towards all studied analytes. These results clearly demonstrate for the first time, the extent of tailorability upon the electroanalytical response of nanocellulose/CNT hybrid electrodes towards different biomolecules, offered simply by the choice of nanocellulosic materials.

Durairaj, Vasuki↗
DOE OSTI2023

Superhydrophobic composite asymmetric electrospun membrane for sustainable vacuum assisted air gap membrane distillation

Membrane distillation (MD) relies on superhydrophobic membranes that must achieve the competing goals of high liquid entry pressure (LEP) and high permeability. Here, in this study, we developed the first superhydrophobic composite electrospun asymmetric membrane using fluorinated graphite (FG). We also provided among the first comparisons of the relative benefits of membrane asymmetry and composite coatings via 3D electrospinning and spraying. FG particles increased the roughness and reduced the zeta potential of the membranes. Superhydrophobic composite membranes had a contact angle of 157° (sliding angle of 7°) and an LEP of 327 kPa. Long-term MD testing revealed that FG particles could increase MD's sustainability while decreasing membrane wetting. Vacuum-assisted air gap membrane distillation (V-AGMD) showed that the composite asymmetric membrane outperformed the non-asymmetric version (composite nanofiber) membrane by 21 % in average water flux and 25 % in average thermal efficiency because of the asymmetric structure of the membrane. The numerical model developed for the V-AGMD system also successfully predicted the water flux generated experimentally from the composite nanofiber and composite asymmetric membranes. Our results confirmed that electrospun asymmetric FG membranes with high contact angle, low sliding angle, high permeability, and high gained output ratio (GOR) would be promising candidates for sustainable MD.

36 MATERIALS SCIENCE↗
DOE OSTI2022

U(VI) binding onto electrospun polymers functionalized with phosphonate surfactants

We previously observed that phosphonate functionalized electrospun nanofibers can uptake U(VI), making them promising materials for sensing and water treatment applications. Here, we investigate the optimal fabrication of these materials and their mechanism of U(VI) binding under the influence of environmentally relevant ions (e.g., Ca 2+ and CO 3 2- ). We found that U(VI) uptake was greatest on polyacrylonitrile (PAN) functionalized with longer-chain phosphonate surfactants (e.g., hexa- and octadecyl phosphonate; HDPA and ODPA, respectively), which were better retained in the nanofiber after surface segregation. Subsequent uptake experiments to better understand specific solid-liquid interfacial interactions were carried out using 5 mg of HDPA-functionalized PAN mats with 10 μM U at pH 6.8 in four systems with different combinations of solutions containing 5 mM calcium (Ca 2+ ) and 5 mM bicarbonate (HCO 3 -). U uptake was similar in control solutions containing no Ca 2+ and HCO 3 - (resulting in 19 ± 3% U uptake), and in those containing only 5 mM Ca2+ (resulting in 20 ± 3% U uptake). A decrease in U uptake (10 ± 4% U uptake) was observed in experiments with HCO 3 -, indicating that UO 2 -CO 3 complexes may increase uranium solubility. Results from shell-by-shell EXAFS fitting, aqueous extractions, and surface-enhanced Raman scattering (SERS) indicate that U is bound to phosphonate as a monodentate inner sphere surface complex to one of the hydroxyls in the phosphonate functional groups. New knowledge derived from this study on material fabrication and solid-liquid interfacial interactions will help to advance technologies for use in the in-situ detection and treatment of U in water.

42 ENGINEERING↗
DOE OSTI2024

Underlying mechanism of structural transformation between GaSb and GaAs response to intense electronic excitation

Ion irradiation of semiconductors has emerged as a promising approach for fabricating self-organized nanosystems with high atomic precision, despite often being accompanied by undesirable phenomena. Exploring the mechanisms underlying structural transformations is crucial for assessing nanostructure array types under complex irradiation environments. By quantitatively calculating the thermodynamically driven processes and analyzing the impact of intrinsic structural parameters, distinct structural transformations in response to intense electronic excitation are systematically investigated in gallium antimonide (GaSb) and gallium arsenide (GaAs) systems. In high-energy regimes, the nanofibers layer of GaSb exhibits intriguing structural discrepancy, characterized by partial nanofibers with coherent boundaries, interspersed nanopores accompanied by antisite defects and Ga precipitates, distinguishing to a series of discontinuous latent tracks that emerged within cylindrical trajectories in GaAs. Furthermore, significant diffusion behaviors of the nanohillocks are discovered in GaAs, with higher average roughness than GaSb, driven by the gradient stress distribution influenced by the free-surface effects. The deposition energy for melting phase formation, Gibbs free energy, and Ga diffusion coefficients contribute to the distinctive structural features, evidencing relatively stable morphological configurations and higher irradiation resistance in GaAs. Consequently, special optoelectronic properties associated with structural discrepancies facilitate the design and optimization of material functionalities by irradiation technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Ultrafine Interwoven Dendritic Cu 2 Se/CuFeSe 2 Composites with Enhanced Thermoelectric Performance

As an effort to develop high-performance and stable copper chalcogenide thermoelectrics, several (1-x)Cu 2 Se/(x)CuFeSe 2 composites were successfully synthesized via a one-step solid-state transformation of CuSe 2 template. Uniform ultrafine dendritic structures consisting of interweaving Cu 2 Se and CuFeSe 2 nanofibers were observed in samples with low Fe content (0.05 ≤ x ≤ 0.1). Increasing the Fe content to x = 0.5 led to phase segregation into Cu 2 Se-rich region with embedded CuFeSe 2 fine structures interwoven with CuFeSe 2 -rich region containing Cu 2 Se nanofibers. The formation of such an entwined dendritic structure is believed to arise from the temperature-dependent solubility of CuFeSe 2 in the Cu 2 Se matrix. The dynamic dissolution of CuFeSe 2 into the Cu 2 Se at high temperatures leads to temperature-dependent doping of the Cu 2 Se matrix, enabling drastic enhancements of thermoelectric power factor at high temperatures. As a result, such a strategy is expected to be a powerful tool for properties modulation in thermoelectric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Copper–Carbon Nanotube Composites Enabled by Electrospinning for Advanced Conductors

The power losses associated with the electrical resistance of copper (Cu) have generated considerable interest in the development of advanced conductors that incorporate carbon nanotubes (CNTs) into the Cu matrix—ultraconductive Cu (UCC) composites—to increase energy efficiency in various industrial and residential applications, ranging from electric power transmission and rotating machinery to electronic devices. To meet this demand, we describe an electrospinning-based polymer nanofiber templating strategy for the fabrication of UCC composites with electrical and mechanical performance exceeding that of Cu. Our approach involves electrospinning of polyvinylpyrrolidone (PVP)-based solutions containing CNTs into aligned PVP/CNT nanofibers onto Cu foil substrates, followed by vacuum-assisted thermal removal of organic solvent/polymer from the CNT matrix to achieve a uniformly distributed CNT layer on the Cu surface. Following additional Cu deposition, the Cu–CNT–Cu composites demonstrated similar electrical conductivity, higher current carrying capacity, and improved mechanical properties compared with those obtained from reference Cu. Importantly, after the heat treatment, Raman analysis of the CNT network displayed an increased metallic character that supports the enhanced electrical properties of the UCC composites. Thus, we believe that these performance characteristics together with the commercial viability of the present approach could open new possibilities in designing advanced conductors for a broad range of electrical systems and industrial applications.

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

High-performance piezoelectric composites via β phase programming

Polymer-ceramic piezoelectric composites, combining high piezoelectricity and mechanical flexibility, have attracted increasing interest in both academia and industry. However, their piezoelectric activity is largely limited by intrinsically low crystallinity and weak spontaneous polarization. Here, we propose a Ti 3 C 2 T x MXene anchoring method to manipulate the intermolecular interactions within the all-trans conformation of a polymer matrix. Employing phase-field simulation and molecular dynamics calculations, we show that OH surface terminations on the Ti 3 C 2 T x nanosheets offer hydrogen bonding with the fluoropolymer matrix, leading to dipole alignment and enhanced net spontaneous polarization of the polymer-ceramic composites. We then translated this interfacial bonding strategy into electrospinning to boost the piezoelectric response of samarium doped Pb (Mg1/3Nb 2/3 )O 3 -PbTiO 3 /polyvinylidene fluoride composite nanofibers by 160% via Ti 3 C 2 T x nanosheets inclusion. With excellent piezoelectric and mechanical attributes, the as-electrospun piezoelectric nanofibers can be easily integrated into the conventional shoe insoles to form a foot sensor network for all-around gait patterns monitoring, walking habits identification and Metatarsalgi prognosis. This work utilizes the interfacial coupling mechanism of intermolecular anchoring as a strategy to develop high-performance piezoelectric composites for wearable electronics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Hybrid gels via bulk interfacial complexation of supramolecular polymers and polyelectrolytes

Hierarchical self-assembly leading to organized supramolecular structures across multiple length scales has been of great recent interest. Earlier work from our laboratory reported the complexation of peptide amphiphile (PA) supramolecular polymers with oppositely charged polyelectrolytes into a single solid membrane at a macroscopic interface. We report here the formation of bulk gels with many internal interfaces between the covalent and supramolecular polymer components formed by the rapid chaotic mixing of solutions, one containing negatively charged PA nanofibers and the other the positively charged biopolymer chitosan. We found that formation of a contact layer at the interface of the solutions locks the formation of hydrogels with lamellar microstructure. The nanofiber morphology of the supramolecular polymer is essential to this process since gels do not form when solutions of supramolecular assemblies form spherical micelles. Here, we found that rheological properties of the gels can be tuned by changing the relative amounts of each component. Furthermore, both positively and negatively charged proteins are easily encapsulated within the contact layer of the gel, which provides an interesting biomedical function for these systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Resource Recovery and Environmental Protection in Wyoming’s Greater Green River Basin Using Selective Nanostructured Membranes (Final Report)

Produced water (PW) represents a sizable waste stream that is co-generated with oil and natural gas production. In 2021 Wyoming ranked 8th and 9th, respectively in domestic oil and natural gas production. In 2017 Wyoming ranked as the 4th highest generator of PW in the U.S, accounting for 7% of the total volume generated. In the context of being the 3rd most arid state in the U.S., the value of water reuse becomes obvious. PW reuse, and resource recovery, in any form requires some level of treatment to remove particulates, residual (free, dispersed) hydrocarbons, organics, and salts. The level of treatment depends on the requirements of the reuse, or resource recovery, application. PW management systems in Wyoming employ in order of volume of PW managed the following management strategies: reinjection for enhanced oil recovery, surface discharge, deep well injection, evaporation ponds (impoundments), and commercial management/treatment. Complicating treatment efforts are the relatively high concentrations of organics (natural and synthetic), dispersed/free hydrocarbons, benzene-toluene-ethylbenzene, and xylenes (BTEX) compounds, biologicals, salts, and minerals. Hydrocarbons (dispersed/dissolved crude oils) and BTEX compounds, as well as synthetic organics, present economic and environmental concerns. The former represents lost revenue, while the latter results in negative environmental impacts like emissions from surface impoundments. The overall objective of this proposal was to synthesize superhydrophilic/oleophobic and superhydrophobic/oleophilic membranes for selectively concentrating and then separating BTEX compounds and oil and grease (O&G) from PW originating from the Greater Green River Basin (GGRB) in Wyoming. Three specific research aims were pursued to accomplish this overall objective. This final report details the development of the superhydrophobic and superhydrophilic membranes, as well as the design of the membrane module prototypes specifically. The technoeconomic assessment is separately reported in another document. 1. Aim #1 – Material optimization and performance evaluation of superhydrophilic/oleophobic and superhydrophobic/oleophilic membranes made by electrospinning/spraying. 2. Aim #2 – Design and construction of cross-flow membrane modules for selectively concentrating and then separating BTEX/oil from GGRB produced water. 3. Aim #3 – Techno-economic assessment of BTEX/oil recovery, and clean water production, using superhydrophilic/oleophobic and superhydrophobic/oleophilic membrane separation for GGRB PW. Superhydrophobic membranes were synthesized by electrospinning poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) nanofibers onto polyester (PET) substrates and electrospraying nano-carbon black/PVDF-HFP onto the nanofibrous layer. These membranes were characterized by high (>8000 liters per square meter per hour per bar (LMH/bar)) permeance values for pure hydrocarbon phases and a high hydrocarbon selectivity (>96%) when treating GGRB PW. All results were obtained when operating the membrane in a crossflow configuration representative of actual field operating conditions. Solvent/oil properties, specifically viscosity and total surface energy/tension, affected permeance across the membrane, which resulted in light mineral oil (394 LMH/bar) and o-xylene (1834 LMH/bar) being characterized by lower permeance values in the pure phase tests. Mixed phase fluxes between 40 to 80 LMH were obtained for the PW when operating the membrane at a feed pressure of 0.3 bar. Flux decreased as the mixed phase concentration in the feed decreased pointing to the importance of maximizing the collision efficiency between the emulsion and the membrane surface and maximizing the emulsion concentration in the feed and the turbulence within the feed channel. These tests demonstrated that the superhydrophobic membranes developed here are a viable hydrocarbon recovery method for GGRB PWs and should be pursued for testing in pilot-scale trials. Superhydrophilic membranes were successfully synthesized via electrospinning/spraying using polyacrylonitrile (PAN) nanofibers as a base nanofibrous matrix. Integration of polyaniline (PANI) into the nanofibrous matrix produced a superior membrane, for water filtration applications, relative to PAN alone and reduced graphene oxide (RGO) when integrated into the nanofibrous matrix. This conclusion was based on the PANI-PAN resistance to flux loss (fouling) when treating model solvent/oil solutions representative of GGRB PWs and field collected PW from the GGRB. The synthesized PAN membranes outperformed a commercially available PAN membrane designed for oil/water separation. This finding indicates that the surface chemical and physical characteristics of the electrospun membranes presents improved properties for filtration of challenging waters like GGRB PWs. The electrospun membranes therefore show promise overall as a substitute for conventionally polymerized membranes in PW treatment applications. The PANI-PAN membrane specifically presents superior performance characteristics for concentration O&G prior to treatment by the hydrocarbon recovery membrane and producing high-quality filtrate for reuse and/or additional treatment (desalination).

02 PETROLEUM↗
DOE OSTI2022

Carbon Electrodes from Powder River Basin Coal Development of Competitive Supercapacitor Electrodes of Diverse Compositions from Coal Extract

Recent demand for coal as a thermal energy source has decreased significantly and will likely continue to decrease as renewable sources of energy become more available and environmental concern and cost from burning coal makes it more costly than renewables. Given that Powder River Basin (PRB) coal in Wyoming has relatively low thermal energy, it is critical for Wyoming to employ coal in other capacities at the current energy transition period in history. Among many potential non-thermal applications, PRB coal can be utilized for membrane and electrode applications through the formation of carbon fibers. Coal-derived membranes can become low-cost, conductive membranes for use in electrodialysis separation processes. Carbon fiber derived electrodes have been shown be a cost-effective alternative to typical electrode materials that can meet or exceed the performance of current carbon electrode materials. In this talk, we demonstrate the manufacture of supercapacitor electrodes from Powder River Basin (PRB) coal-derived precursors. Specifically, PRB coal was treated in cheap solvents, partitioned into liquid extract and solid residue. An electropinning process has been developed that can convert either the liquid extract or the solid residue into carbon fiber mats. The electrospinning process is versatile with many tunable process parameters to achieve desirable physiochemical properties. For example, the coal residue can be manipulated by additional heat treatment, or by adding binders, salts, or surfactants to create a solution that can be electrospun into advanced carbon electrodes with desirable structural and surface properties. Similarly, some of the liquid extract (tar fraction) can be subsequently reacted with toluene diisocyanate to create resinous coal-derived polyurethane (PUs) as a spinnable ink. Carbon nanofiber mats made from our proprietary electrospinning process were further carbonized at temperature ranging from 700°C to 900°C before they are used as electrodes in supercapacitors. Galvanostatic charge-discharge (GCD) results show that the best performing PU fiber mats can deliver a specific capacitance of 604 F g -1 at the current density of 1 A g -1 . A carbon fiber mat from a different solvent extraction residue also delivered the specific capacitance of 508 F g -1 . These specific capacitance values are comparable to or better than commercial activated carbons, demonstrating the viability of manufacturing carbon nanofiber electrodes from coal without the use of a commercial polymer as binder in the spinning ink.

Cincotta, Robert↗
DOE OSTI2024

Multiphysics Simulations of Thermal Shock Testing of Nanofibrous High Power Targets

Increase of primary beam power for neutrino beam-lines leads to a reduced lifespan for production targets. The field of High Power Targetry (HPT) is generating new concepts to meet the need for robust targets. One idea being investigated by the HPT Research and Development Group at Fermilab is an electrospun nanofiber target. As part of their evaluation, samples with different densities were sent to the HiRadMat facility at CERN for thermal shock tests. The samples with the higher density, irradiated under a high intensity beam pulse, exhibit major damages at the impact site whereas those with the lower density show no apparent damages. The exact cause of this failure was unclear at the time. In this paper, we present the results of multiphysics simulations of the thermal shock experienced by the nanofiber targets that suggest the failure originates from the reduced permeability of the high density sample to airflow. The air present in the porous target expands due to heating from the beam, but is unable to flow freely in the high density sample, resulting in a larger back pressure that blows apart the mat. We close with a discussion on how to further validate this hypothesis.

43 PARTICLE ACCELERATORS↗
NASA NTRS2001

Carbon Nanotube Anodes Being Evaluated for Lithium Ion Batteries

The NASA Glenn Research Center is evaluating the use of carbon nanotubes as anode materials for thin-film lithium-ion (Li) batteries. The motivation for this work lies in the fact that, in contrast to carbon black, directed structured nanotubes and nanofibers offer a superior intercalation media for Li-ion batteries. Carbon lamellas in carbon blacks are circumferentially oriented and block much of the particle interior, rendering much of the matrix useless as intercalation material. Nanofibers, on the other hand, can be grown so as to provide 100-percent accessibility of the entire carbon structure to intercalation. These tubes can be visualized as "rolled-up" sheets of carbon hexagons (see the following figure). One tube is approximately 1/10,000th the diameter of a human hair. In addition, the high accessibility of the structure confers a high mobility to ion-exchange processes, a fundamental for the batteries to respond dynamically because of intercalation.

Raffaelle, Ryne P.↗
NASA NTRS2007

Multifunctional Composites for Improved Polyimide Thermal Stability

The layered morphology of silicate clay provides an effective barrier to oxidative degradation of the matrix resin. However, as resin thermal stability continues to reach higher limits, development of an organic modification with comparable temperature capabilities becomes a challenge. Typically, phyllosilicates used in polymer nanocomposites are modified with an alkyl ammonium ion. Such organic modifiers are not suited for incorporation into high temperature polymers as they commonly degrade below 200oC. Therefore, the development of nanoparticle specifically suited for high temperature applications is necessary. Several nanoparticles were investigated in this study, including pre-exfoliated synthetic clay, an organically modified clay, and carbon nanofiber. Dispersion of the layered silicate increases the onset temperature of matrix degradation as well as slows oxidative degradation. The thermally stable carbon nanofibers are also observed to significantly increase the resin thermal stability.

Miller, Sandi G.↗
NASA NTRS2007

Nanowicks

Nanowicks are dense mats of nanoscale fibers that are expected to enable the development of a variety of novel capillary pumps, filters, and fluidic control devices. Nanowicks make it possible obtain a variety of novel effects, including capillary pressures orders of magnitude greater than those afforded by microscale and conventional macroscale wicks. While wicking serves the key purpose of transporting fluid, the nanofiber geometry of a nanowick makes it possible to exploit additional effects -- most notably, efficient nanoscale mixing, fluidic effects for logic or control, and ultrafiltration (in which mats of nanofibers act as biomolecular sieves).

Noca, Flavio↗
NASA NTRS2010

Probabilistic Simulation for Nanocomposite Fracture

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions from low probability to high.

Chamis, Christos C.↗