Search NASA⌕ Search

SEARCH · Search NASA

Results for “nanoscale optics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Selectively accessing the hotspots of optical nanoantennas by self-aligned dry laser ablation

Plasmonic nanostructures serve as optical antennas for concentrating the energy of incoming light in localized hotspots close to their surface. By positioning nanoemitters in the antenna hotspots, energy transfer is enabled, leading to novel hybrid antenna-emitter-systems, where the antenna can be used to manipulate the optical properties of the nano-objects. The challenge remains how to precisely position emitters within the hotspots. We report a self-aligned process based on dry laser ablation of a calixarene that enables the attachment of molecules within the electromagnetic hotspots at the tips of gold nanocones. Within the laser focus, the ablation threshold is exceeded in nanoscale volumes, leading to selective access of the hotspot areas. A first indication of the site-selective functionalization process is given by attaching fluorescently labelled proteins to the nanocones. In a second example, Raman-active molecules are selectively attached only to nanocones that were previously exposed in the laser focus, which is verified by surface enhanced Raman spectroscopy. Enabling selective functionalization is an important prerequisite e.g. for preparing single photon sources for quantum optical technologies, or multiplexed Raman sensing platforms.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Active Temporal Control of Radiative Heat Transfer with Graphene Nanodisks

The ability to dynamically control the radiative transfer of heat at the nanoscale holds the key to the development of a diverse number of technologies, ranging from nanoscale thermal-management systems to improved thermophotovoltaic devices. Recently, graphene has emerged as an ideal material to achieve this goal, since it can be electrically doped to support surface plasmons, collective oscillations of the conduction electrons. These resonances produce large and spectrally narrow optical cross sections, which dictate the emission and absorption properties of the graphene nanostructure and, thus, the heat that it radiatively exchanges with other objects and the environment. For attainable levels of doping, the plasmons supported by graphene nanostructures naturally lie in the midinfrared part of the spectrum, which is the most relevant wavelength range for radiative heat transfer under realistic temperatures. Furthermore, these resonances are actively tunable, thus providing full dynamic control over the heat transfer. Motivated by this great potential, we present a comprehensive analysis of the temporal evolution of the radiative heat transfer between arrangements of graphene nanodisks, showing that it is possible to exploit the tunability of these structures to obtain actively controlled heat transfer scenarios not possible with conventional passive nanostructures. We report the results of this work provide a framework for achieving fully dynamical control over nanoscale radiative heat transfer and thus provide fundamental insights into this process.

36 MATERIALS SCIENCE↗

Solution-Processable Polymer Donor-Small Molecule Acceptor Bulk Heterojunction Organocatalysts for Enhancing CO 2 -to-CO Photoconversion

Metal-free organic semiconductors have emerged as a kind of promising star material in photocatalysis. However, their photocatalytic efficacy is impeded by the great recombination rate of the photogenerated charge carriers. Herein, we demonstrate the devising of solution-processable organic semiconductor bulk heterojunction (BHJ) systems with varying ratios by using BP3DT and PC 61 BM as the donor (D) and acceptor (A) candidates, respectively, for enhanced selective CO production from CO 2 photoreduction. The prepared BP3DT/PC 61 BM BHJs are solution-processed on both glass substrates (GS) and molecular sieves (MS) via a drop-casting technique to form an active thin film and porous photocatalysts to catalyze CO production. All BP3DT/PC 61 BM BHJs efficiently produce CO as the primary product in the existence of trace-level TEA/H 2 O (0.5 mL). Our results show that the photocatalytic efficiency depended on the D/A w% ratios and its nanoscale phase separation morphology within the BHJ, contributing to the promotion of exciton dissociation. Additionally, the BHJ undergoes an ostensible morphological transition from large-scale phase-separation to a fine mixed homogeneous nanoscale by varying the BP3DT/PC 61 BM blend ratio from 30/70 w% to 70/30 w%, which increases the interfacial area and shortens the distance of the exciton to the D/A surface, and promotes charge carrier separation, corroborated by photo-optical and photoelectrochemical experimental results. Accordingly, the resulting BP3DT/PC 61 BM BHJ@MS with a D/A ratio of 70/30 w% achieves a CO yield of 819 μmol·g cat -1 h -1 , surpassing those of pure PC 61 BM (126 μmol·g cat -1 h -1 ) and BP3DT (72 μmol·g cat -1 h -1 ) by 6.5- to 11.3-fold and also exceeding that of metal-free linear conjugated polymer-based organocatalysts reported to date. Specifically, this is the first work to develop an organic-semiconductor-based BHJ photocatalyst, which may offer a nascent way to design more efficient organocatalysts for CO 2 reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient Nanoscopy of Exciton Dynamics in 2D Transition Metal Dichalcogenides

Abstract The electronic and optical properties of 2D transition metal dichalcogenides are dominated by strong excitonic resonances. Exciton dynamics plays a critical role in the functionality and performance of many miniaturized 2D optoelectronic devices; however, the measurement of nanoscale excitonic behaviors remains challenging. Here, a near‐field transient nanoscopy is reported to probe exciton dynamics beyond the diffraction limit. Exciton recombination and exciton–exciton annihilation processes in monolayer and bilayer MoS 2 are studied as the proof‐of‐concept demonstration. Moreover, with the capability to access local sites, intriguing exciton dynamics near the monolayer‐bilayer interface and at the MoS 2 nano‐wrinkles are resolved. Such nanoscale resolution highlights the potential of this transient nanoscopy for fundamental investigation of exciton physics and further optimization of functional devices.

2D materials↗

3ω techniques for measurement of volumetric heat capacity and anisotropic thermal conductivity of a solution processable, hybrid organic/inorganic film, Te-PEDOT:PSS

We report that measuring the thermal properties of anisotropic films of hybrid materials poses a challenge to existing metrology techniques. We have developed a new approach for measuring the volumetric heat capacity and anisotropic thermal conductivity of these systems using the 3ω method. While there exist many avenues for measuring the thermal properties of thin films, most carry with them difficult requirements such as smooth surfaces or advanced lithography. Here, we present measurements of a film's in-plane and cross-plane conductance and its volumetric heat capacity using relatively simple sample configurations, each requiring a single heater. For the measurement of volumetric heat capacity, we present a new model fitting method, relying on a standard film-on-substrate configuration. For the measurement of in-plane thermal conductance by 3ω, we have developed the use of an embedded micro-wire heater in suspended drop cast films, allowing for a 12 μm wide heater without the need for advanced lithography. We also expose the surprisingly significant effect of thermal radiation in the suspended film measurement and its associated error. Our measurements reveal a large anisotropy in the thermal conductivity of our test material, Te-PEDOT:PSS, of k in-plane / k cross-plane = 19, consistent with the nanoscale morphology of the material.

36 MATERIALS SCIENCE↗

Photocurrent Nanoscopy of Quantum Hall Bulk

Understanding nanoscale electronic and thermal transport of two-dimensional (2D) electron systems in the quantum Hall regime, particularly in the bulk insulating state, poses considerable challenges. One of the primary difficulties arises from the presence of chiral edge channels, whose transport behavior obscures the investigation of the insulating bulk. Using near-field optical and photocurrent nanoscopy, we probe real-space variations of the optical and thermal dynamics of graphene in the quantum Hall regime without relying on complex sample or electrode geometries. Near the charge-neutrality point, we detect strong optical and photothermal signals from resonant inter-Landau-level (LL) magnetoexciton excitations between the zeroth and ± 1 st LLs, which gradually weaken with increasing doping due to Pauli blocking. Interestingly, at higher doping levels and full-integer LL fillings, photothermal signals reappear across the entire sample over an approximately 10 − μ m scale, indicating unexpectedly long cooling lengths and nonlocal photothermal heating through the insulating bulk. This observation suggests that thermal conductivity persists for the localized states even as electronic transport is suppressed—a clear violation of the Wiedemann-Franz law. Our experiments provide novel insights into nanoscale thermal and electronic transport in incompressible 2D gases, highlighting the roles of magnetoexcitons and chiral edge states in the thermo-optoelectric dynamics of the Dirac quantum Hall state. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗

Liquid–Liquid Phase Separation in Supermicrometer and Submicrometer Aerosol Particles

The interactions of aerosol particles with light and clouds are among the most uncertain aspects of anthropogenic climate forcings. The effects of aerosol particles on climate depend on their optical properties, heterogeneous chemistry, water uptake behavior, and ice nucleation activity. These properties in turn depend on aerosol physics and chemistry including composition, size, shape, internal structure (morphology), and phase state. The greatest numbers of particles are found at small, submicrometer sizes, and the properties of aerosol particles can differ on the nanoscale compared with measurements of bulk materials. As a result, our focus has been on characterizing the phase transitions of aerosol particles in both supermicrometer and submicrometer particles. The phase transition of particular interest for us has been liquid–liquid phase separation (LLPS), which occurs when components of a solution phase separate due to a difference in solubilities. For example, organic compounds can have limited solubility in salt solutions especially as the water content decreases, increasing the concentration of the salt solution, and causing phase separation between organic-rich and inorganic-rich phases. To characterize the systems of interest, we primarily use optical microscopy for supermicrometer particles and cryogenic-transmission microscopy for submicrometer particles. This Account details our main results to date for the phase transitions of supermicrometer particles and the morphology of submicrometer aerosol. Herein, we have found that the relative humidity (RH) at which LLPS occurs (separation RH; SRH) is highly sensitive to the composition of the particles. For supermicrometer particles, SRH decreases as the pH is lowered to atmospherically relevant values. SRH also decreases when non-phase-separating organic compounds are added to the particles. For submicrometer particles, a size dependence of morphology is observed in systems that undergo LLPS in supermicrometer particles. In the limit of slow drying rates, particles <30 nm are homogeneous and larger particles are phase-separated. This size dependence of aerosol morphology arises because small particles cannot overcome the activation barrier needed to form a new phase when phase separation occurs by a nucleation and growth mechanism. Additionally, the inhibition of LLPS in small particles is observed for mixtures of ammonium sulfate with single organic compounds as well as complex organics like α-pinene secondary organic matter. The morphology of particles affects activation diameters for the formation of cloud condensation nuclei. These results more generally have implications for aerosol properties that affect the climate system. In addition, LLPS is also widely studied in materials and biological chemistry, and our results could potentially translate to implications for these fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-temperature nanoscale heat transport in a gadolinium iron garnet heterostructure probed by ultrafast x-ray diffraction

Time-resolved x-ray diffraction has been used to measure the low-temperature thermal transport properties of a Pt/Gd3Fe5O12//Gd3Ga5O12 metal/oxide heterostructure relevant to applications in spin caloritronics. A pulsed femtosecond optical signal produces a rapid temperature rise in the Pt layer, followed by heat transport into the Gd3Fe5O12 (GdIG) thin film and the Gd3Ga5O12 (GGG) substrate. The time dependence of x-ray diffraction from the GdIG layer was tracked using an accelerator-based femtosecond x-ray source. The ultrafast diffraction measurements probed the intensity of the GdIG (1 −1 2) x-ray reflection in a grazing-incidence x-ray diffraction geometry. The comparison of the variation of the diffracted x-ray intensity with a model including heat transport and the temperature dependence of the GdIG lattice parameter allows the thermal conductance of the Pt/GdIG and GdIG//GGG interfaces to be determined. Complementary synchrotron x-ray diffraction studies of the low-temperature thermal expansion properties of the GdIG layer provide a precise calibration of the temperature dependence of the GdIG lattice parameter. The interfacial thermal conductance of the Pt/GdIG and GdIG//GGG interfaces determined from the time-resolved diffraction study is of the same order of magnitude as previous reports for metal/oxide and epitaxial dielectric interfaces. The thermal parameters of the Pt/GdIG//GGG heterostructure will aid in the design and implementation of thermal transport devices and nanostructures.

36 MATERIALS SCIENCE↗

Ultrafast valley polarization of graphene nanorings

Here, we study theoretically electron dynamics of a graphene nanoring placed in the field of an ultrashort optical pulse. We describe the graphene nanoring within an effective model with infinite mass boundary conditions. For an optical pulse with a duration of just a few femtoseconds, the electron dynamics is coherent and is described by a time-dependent Schrödinger equation. If the optical pulse is circularly polarized, then two valleys of graphene are populated differently, resulting in a finite valley polarization of the system after the pulse. Such a valley polarization is a unique property of graphene nanoscale systems, while for a graphene monolayer, a circularly polarized pulse does not produce any valley polarization. The valley polarization of the graphene nanoring depends on parameters of the system, such as inner and outer radii. With the system's size increasing, the valley polarization monotonically decreases, converging to its zero value for the infinite graphene monolayer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Ultrafast snapshots of terahertz electric potentials across ring-shaped quantum barriers

Probing the time evolution of the terahertz electric field within subwavelength dimensions plays a crucial role in observing the nanoscale lightwave interactions with fundamental excitations in condensed-matter systems and in artificial structures, such as metamaterials. Here, we propose a novel probing method for measuring terahertz electric potentials across nanogaps using a combination of optical and terahertz pulse excitations. To achieve this, we employ ring-shaped nanogaps that enclose a metallic island, allowing us to capture tunneling charges when subjected to terahertz electromagnetic pulse illumination. By controlling and manipulating the terahertz tunneling charges through a focused optical gate pulse, we can obtain the terahertz potential strength as a function of spatial coordinates and time delays between pulses. To accurately quantify the time evolution of terahertz electric potential across quantum barriers, we carefully calibrate the recorded nonlinear tunneling current. Its on-resonance and off-resonance behaviors are also discussed, providing valuable insights into the antenna’s characteristics and performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of Thermal Oxidation on the Structure, Surface Texturing, and Microstructure Evolution in Nanocrystalline Ga-O-N Films

An extensive examination of the nanoscale, crystallographic growth dynamics of the system, which is impacted by the thermal energy given to the GaN, is carried out to derive a deeper understanding of the growth kinetics, morphology and microstructure evolution, chemical bonding, and optical properties of Ga-O-N films. Thermal annealing of GaN films is performed in the temperature range of 900–1200 °C. Crystal structure, phase formation, chemical composition, surface morphology, and microstructure evolution of Ga-O-N films are investigated as a function of temperature. Increasing temperature induces surface oxidation, which results in the formation of stable β-Ga2O3 phase in the GaN matrix, where the overall film composition evolves from nitride (GaN) to oxynitride (Ga-O-N). While GaN surfaces are smooth, planar, and featureless, oxidation induced granular-to-rod shaped morphology evolution is seen with increasing temperature to 1200 °C. The considerable texturing and stability of the nanocrystalline Ga-O-N on Si substrates can be attributed to the surface and interface driven modification because of thermal treatment. Corroborating with structure and chemical changes, Raman spectroscopic analyses also indicate that the chemical bonding evolution progresses from fully Ga-N bonds to Ga-O-N. While the GaN oxidation process starts with the formation of β-Ga 2 O 3 at an annealing temperature of 1000 °C, higher annealing temperatures induce structural distortion with the potential formation of Ga-O-N bonds. The structure-phase-chemical composition correlation, which will be useful for nanocrystalline materials for selective optoelectronic applications, is established in Ga-O-N films made by thermal treatment of GaN.

36 MATERIALS SCIENCE↗

Task Sharing of Proton Incorporation in Vertically Aligned Nanocomposite Triple Conductors: Growth, Structure, and Surface Exchange Kinetics

As protonic ceramic electrolysis cells emerge for efficient H 2 production, there is a need to develop air electrode materials enabling fast, durable steam splitting and proton incorporation. Single-phase triple conductors may fail to satisfy the myriad performance/stability requirements, and their critical charge-carriers (holes, oxygen vacancies, and protons) are in competition, limiting their concentrations. Instead, we propose task-sharing, vertically aligned nanocomposites (VANs), comprising a proton conductor (BaZr 0.9 Y 0.1 O 3-δ ) and a redox-active mixed ionic electronic conductor (Ce 0.9 Pr 0.1 O 2-δ ), that may enable rapid proton surface exchange at the solid–gas interface and transport along the solid–solid heterointerfaces. We grew VANs by pulsed laser deposition and investigated the interplay between their processing conditions, structure, and proton and oxygen surface exchange kinetics. We varied the substrate temperature, laser repetition rate, laser fluence, and processing oxygen pressure. The crystallinity and phases were characterized by grazing-incidence X-ray diffraction, and the strain and structural order as a function of depth were evaluated by angle-dependent synchrotron X-ray pair distribution function analysis. To evaluate the potential for interdiffusion, the formation energies of substitutional defects were simulated with density functional theory. Corresponding structural analysis and elemental mapping were performed by scanning/transmission electron microscopy, energy-dispersive X-ray spectroscopy, and electron energy-loss spectroscopy, indicating distinct nanoscale compositional regions with a hierarchical structure embedded in individual VANs columns and minimal interdiffusion across a bilayer film. Proton and oxygen surface exchange coefficients (k H , k O ) and polarization resistances were evaluated by electrical and optical relaxations and impedance spectroscopy of VAN-incorporated protonic ceramic electrochemical cells, respectively, at 400–500 °C, demonstrating values comparable to some of the best-known triple and mixed conductors.

36 MATERIALS SCIENCE↗

Infrared Signatures for Phase Identification in Hafnium Oxide Thin Films

Phase identification in HfO 2 -based thin films is a prerequisite to understanding the mechanisms stabilizing the ferroelectric phase in these materials, which hold great promise in next-generation non-volatile memory and computing technology. While grazing-incidence X-ray diffraction is commonly employed for this purpose, it has difficulty unambiguously differentiating between the ferroelectric phase and other metastable phases that may exist due to similarities in the d-spacings, their low intensities, and the overlapping of reflections. Infrared signatures provide an alternative route. However, their use in phase identification remains limited because phase control has overwhelmingly been accomplished via substituents, thereby convoluting infrared signatures between the substituent and the phase changes they induce. Herein, we report the infrared optical responses of three undoped hafnium oxide films where annealing conditions have been used to create films consisting primarily of the ferroelectric polar orthorhombic Pca2 1 , antipolar orthorhombic Pbca, and monoclinic P2 1 /c phases, as was confirmed via transmission electron microscopy (TEM), UVvisible optical properties, and electrical property measurements. Vibrational signatures acquired from synchrotron nano-Fourier transform infrared spectroscopy (nano-FTIR) are shown to be capable of differentiating between the phases in a non-destructive, rapid, and nanoscale manner. The utility of nano-FTIR is illustrated for a film exhibiting an antiferroelectric polarization response. In this sample, it is proven that this behavior results from the Pbca phase rather than the often-cited tetragonal phase. Here, by demonstrating that IRspectroscopy can unambiguously distinguish phases in this material, this work establishes a tool needed to isolate the factors dictating ferroelectric phase stability in HfO 2 -based materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observation of the modification of quantum statistics of plasmonic systems

Abstract For almost two decades, researchers have observed the preservation of the quantum statistical properties of bosons in a large variety of plasmonic systems. In addition, the possibility of preserving nonclassical correlations in light-matter interactions mediated by scattering among photons and plasmons stimulated the idea of the conservation of quantum statistics in plasmonic systems. It has also been assumed that similar dynamics underlie the conservation of the quantum fluctuations that define the nature of light sources. So far, plasmonic experiments have been performed in nanoscale systems in which complex multiparticle interactions are restrained. Here, we demonstrate that the quantum statistics of multiparticle systems are not always preserved in plasmonic platforms and report the observation of their modification. Moreover, we show that optical near fields provide additional scattering paths that can induce complex multiparticle interactions. Remarkably, the resulting multiparticle dynamics can, in turn, lead to the modification of the excitation mode of plasmonic systems. These observations are validated through the quantum theory of optical coherence for single- and multi-mode plasmonic systems. Our findings unveil the possibility of using multiparticle scattering to perform exquisite control of quantum plasmonic systems.

36 MATERIALS SCIENCE↗

Laser particles with omnidirectional emission for cell tracking

The ability to track individual cells in space over time is crucial to analyzing heterogeneous cell populations. Recently, microlaser particles have emerged as unique optical probes for massively multiplexed single-cell tagging. However, the microlaser far-field emission is inherently direction-dependent, which causes strong intensity fluctuations when the orientation of the particle varies randomly inside cells. Here, we demonstrate a general solution based on the incorporation of nanoscale light scatterers into microlasers. Two schemes are developed by introducing either boundary defects or a scattering layer into microdisk lasers. The resulting laser output is omnidirectional, with the minimum-to-maximum ratio of the angle-dependent intensity improving from 0.007 (-24 dB) to > 0.23 (-6 dB). After transfer into live cells in vitro, the omnidirectional laser particles within moving cells could be tracked continuously with high signal-to-noise ratios for 2 h, while conventional microlasers exhibited frequent signal loss causing tracking failure.

59 BASIC BIOLOGICAL SCIENCES↗

On-Chip Single-Layer Integration of Diamond Spins with Microwave and Plasmonic Channels

On-chip scalable integration represents a major challenge for practical quantum devices. One particular challenge is to implement on-chip optical readout of spins in diamond. This readout requires simultaneous application of optical and microwave fields along with the efficient collection of fluorescence. These requirements are typically met using bulk optical components and dedicated microwave lines. Here, we experimentally demonstrate an on-chip integrated interface for diamond nitrogen vacancy (NV) spin-state preparation and readout, implemented in a planar single layer with only one patterning step. A nanodiamond with NV centers is positioned inside a v-groove waveguide milled in a thick gold film. The gold film carries the microwave control signal, while the v-groove acts as a fluorescence collector and, potentially, as an integrated pump filter. Hence, the device dimensions and fabrication complexity are substantially reduced. Our approach fosters further development of ultracompact nanoscale quantum sensors and quantum information processing devices on a monolithic platform.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-qubit nanoscale sensing with entanglement as a resource

Nitrogen vacancy (NV) centres in diamond are widely deployed as local magnetic sensors, using single-qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators or using entangled states to enhance measurement sensitivity. Here, in this work, we describe protocols for using optically unresolved NV centre pairs and nuclear spins as multi-qubit sensors for measuring correlated noise at nanometre length scales. For noninteracting NV centres, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations, leveraging the presence of a third qubit, a 13 C nucleus, to effect coherent single-NV spin flips and enable phase cycling even for co-aligned NV centres that are spectrally unresolved. For length scales around 10 nm, we create maximally entangled Bell states through dipole–dipole coupling between two NV centres and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centres. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV centre spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in more than an order of magnitude improvement in sensitivity. Finally, we demonstrate methods for detecting high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centres.

condensed-matter physics↗

Developments in SRW Code and Sirepo Framework Supporting Simulation of Time-Dependent Coherent X-ray Scattering Experiments

Physical optics simulations for beamlines and experiments are essential for the effective use of synchrotron light source facilities such as NSLS-II at BNL. The SRW software package supports such source-to-detector simulations for coherent X-ray scattering and imaging experiments through its Python interface and Sirepo browser-based graphical user interface. This allows one to define custom sample models, assess the feasibility of an experiment, and estimate most appropriate beamline settings before using valuable beamtime. We discuss the recent use of general-purpose GPU resources and coherent mode decomposition algorithms in SRW to accelerate physical optics simulations with partially coherent X-rays. To illustrate these new capabilities, we describe simulations of typical time series of partially coherent scattering images used in X-ray Photon Correlation Spectroscopy (XPCS) experiments; aiming to characterize the nanoscale dynamics of a disordered sample, representing a solution of nanoparticles undergoing Brownian diffusion.

36 MATERIALS SCIENCE↗