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Engineering tertiary chirality in helical biopolymers

Tertiary chirality describes the handedness of supramolecular assemblies and relies not only on the primary and secondary structures of the building blocks but also on topological driving forces that have been sparsely characterized. Helical biopolymers, especially DNA, have been extensively investigated as they possess intrinsic chirality that determines the optical, mechanical, and physical properties of the ensuing material. Here, we employ the DNA tensegrity triangle as a model system to locate the tipping points in chirality inversion at the tertiary level by X-ray diffraction. We engineer tensegrity triangle crystals with incremental rotational steps between immobile junctions from 3 to 28 base pairs (bp). We construct a mathematical model that accurately predicts and explains the molecular configurations in both this work and previous studies. Our design framework is extendable to other supramolecular assemblies of helical biopolymers and can be used in the design of chiral nanomaterials, optically active molecules, and mesoporous frameworks, all of which are of interest to physical, biological, and chemical nanoscience.

Science & Technology - Other Topics↗

The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nanotechnology for catalysis and solar energy conversion

This roadmap on Nanotechnology for Catalysis and Solar Energy Conversion focuses on the application of nanotechnology in addressing the current challenges of energy conversion: 'high efficiency, stability, safety, and the potential for low-cost/scalable manufacturing' to quote from the contributed article by Nathan Lewis. This roadmap focuses on solar-to-fuel conversion, solar water splitting, solar photovoltaics and bio-catalysis. It includes dye-sensitized solar cells (DSSCs), perovskite solar cells, and organic photovoltaics. Smart engineering of colloidal quantum materials and nanostructured electrodes will improve solar-to-fuel conversion efficiency, as described in the articles by Waiskopf and Banin and Meyer. Semiconductor nanoparticles will also improve solar energy conversion efficiency, as discussed by Boschloo et al in their article on DSSCs. Perovskite solar cells have advanced rapidly in recent years, including new ideas on 2D and 3D hybrid halide perovskites, as described by Spanopoulos et al 'Next generation' solar cells using multiple exciton generation (MEG) from hot carriers, described in the article by Nozik and Beard, could lead to remarkable improvement in photovoltaic efficiency by using quantization effects in semiconductor nanostructures (quantum dots, wires or wells). These challenges will not be met without simultaneous improvement in nanoscale characterization methods. Terahertz spectroscopy, discussed in the article by Milot et al is one example of a method that is overcoming the difficulties associated with nanoscale materials characterization by avoiding electrical contacts to nanoparticles, allowing characterization during device operation, and enabling characterization of a single nanoparticle. Besides experimental advances, computational science is also meeting the challenges of nanomaterials synthesis. The article by Kohlstedt and Schatz discusses the computational frameworks being used to predict structure–property relationships in materials and devices, including machine learning methods, with an emphasis on organic photovoltaics. The contribution by Megarity and Armstrong presents the 'electrochemical leaf' for improvements in electrochemistry and beyond. In addition, biohybrid approaches can take advantage of efficient and specific enzyme catalysts. These articles present the nanoscience and technology at the forefront of renewable energy development that will have significant benefits to society.

14 SOLAR ENERGY↗

Nanomechanical squeezing: Toward quantum imaging with atomic force microscopy

Leveraging quantum effects in mechanical oscillators promises major advancements in nanometrology, including sensing and imaging. Microscopic cantilevers serve as versatile force sensors with broad applications in nanoscience, nanotechnology, and, increasingly, quantum sensing. Here, we theoretically model and investigate the quantum mechanics of cantilever probes in atomic force microscopy under conditions of reduced thermal noise. Specifically, our model captures the cantilever interaction with a surface via long-range attractive van der Waals forces and short-range repulsive-adhesive interactions described by the Derjaguin-Muller-Toporov model. We find that when the probe resides within the attractive interaction regime, a coherent state emerges, whereas, in the repulsive regime, a squeezed state forms for the cantilever's deformation state. Our calculations explain the functional role of interaction potentials in the quantum dynamics of macroscopic mechanical systems, which are proving useful in quantum sensing and information processing. The presented calculations can be extended to investigate other interaction forces relevant to atomic force microscopy.

Al-Sawai, Wael M. [Lamar Univ., Beaumont, TX (Unit↗

Interaction-expansion inchworm Monte Carlo solver for lattice and impurity models

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. We generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. So, the problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

36 MATERIALS SCIENCE↗

Reverse order-disorder transition of Janus particles confined in two dimensions

In this study Janus particles with different patch sizes, confined to two dimensions, generate a series of patterns of interest to the field of nanoscience. Here we observe reverse melting, where for some densities the system melts under cooling. For a broad range of hydrophobic patch sizes ( 60° < θ 0 < 90°), a reentrant transition from solid to liquid and then to an ordered phase emerges as temperature (T) decreases due to the formation of rhombus chains at low T. This reentrant phase has pseudo long-range orientational order but short-range translational order, similar to a hexatic phase. Our work provides guidelines to study the melting and assembly of Janus particles in two dimensions, as well as mechanisms to generate phases with specific symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Brief Survey of Data Streaming Technologies

Streaming data is data that is emitted at variable volumes in a continuous, incremental manner with the goal of low-latency processing often at a different physical location. Network infrastructure is used to facilitate the connection between data sources and sinks, and must be robust to handle the requirements of the workflow. The U.S. Department of Energy Office of Science (DOE SC) a federal agency supporting fundamental scientific research for energy and the Nation’s largest supporter of basic research in the physical sciences. DOE SC has the responsibility for operating $\mathbf{1 0}$ National Laboratories, and 28 scientific user facilities supporting advanced supercomputers, particle accelerators, large x-ray light sources, neutron scattering sources, and other specialized facilities for nanoscience and genomics. This paper investigates the state of streaming data workfows, and details some of the approaches to this challenging problem.

Kissel, Ezra↗

X-ray spectroscopic identification of strain and structure-based resonances in a series of saturated carbon-cage molecules: Adamantane, twistane, octahedrane, and cubane

Novel nanocarbons such as fullerenes, nanotubes, graphene, and nanodiamond reside at the cutting edge of nanoscience and technology. Along with chemical functionalization, geometric constraints (such as extreme curvature in nanotubes or defects within or at the surfaces of diamond nanoparticles) significantly alter the electronic states of the nanocarbon material. Understanding the effects of steric strain on the electronic structure is critical to developing nanoelectronic applications based on these materials. This paper presents a fundamental study of how strain affects the electronic structure in a benchmark series of some fundamental saturated carbon cage compounds. Adamantane, C10H16, the smallest diamondoid and arguably the smallest nanodiamond crystallite, has carbon atoms essentially commensurate with diamond lattice positions and possesses by far the least molecular strain of this series. Twistane also is a C10H16 isomer but the fixed cyclohexane twist conformation of the central ring introduces additional strain into the cage. Octahedrane [(CH)12] and cubane [(CH)8] are considerably more strained, culminating in cubane where carbon–carbon bonds lie either parallel or orthogonal to one another. Using gas-phase near-edge x-ray absorption fine structure spectroscopy to probe the unoccupied electronic states, we observe two major progressions across this series. First, a broad C–C σ* resonance in the absorption splits into two more narrow and intense resonances with increasing strain. Second, the first manifold of states previously associated with tertiary C–H σ* in the diamondoid series appears to broaden and shift to lower energy. This feature is more than twice as intense in cubane than in octahedrane, even though these two molecules have only tertiary carbons, with the chemical formula (CH)x. The spectral differences are entirely due to the shape of the molecules; in particular, in cubane, the features arise from a high degree of p-p interaction between parallel C–C bonds. In contrast to the conventional wisdom that near-edge x-ray absorption is primarily an atomically localized spectroscopy, molecular shape and associated strain lead to the dominant features in spectra acquired from this fundamental series of carbon cage structures.

36 MATERIALS SCIENCE↗

NANO.PTML model for read-across prediction of nanosystems in neurosciences. computational model and experimental case of study

Abstract Neurodegenerative diseases involve progressive neuronal death. Traditional treatments often struggle due to solubility, bioavailability, and crossing the Blood-Brain Barrier (BBB). Nanoparticles (NPs) in biomedical field are garnering growing attention as neurodegenerative disease drugs (NDDs) carrier to the central nervous system. Here, we introduced computational and experimental analysis. In the computational study, a specific IFPTML technique was used, which combined Information Fusion (IF) + Perturbation Theory (PT) + Machine Learning (ML) to select the most promising Nanoparticle Neuronal Disease Drug Delivery (N2D3) systems. For the application of IFPTML model in the nanoscience, NANO.PTML is used. IF-process was carried out between 4403 NDDs assays and 260 cytotoxicity NP assays conducting a dataset of 500,000 cases. The optimal IFPTML was the Decision Tree (DT) algorithm which shown satisfactory performance with specificity values of 96.4% and 96.2%, and sensitivity values of 79.3% and 75.7% in the training (375k/75%) and validation (125k/25%) set. Moreover, the DT model obtained Area Under Receiver Operating Characteristic (AUROC) scores of 0.97 and 0.96 in the training and validation series, highlighting its effectiveness in classification tasks. In the experimental part, two samples of NPs (Fe 3 O 4 _A and Fe 3 O 4 _B) were synthesized by thermal decomposition of an iron(III) oleate (FeOl) precursor and structurally characterized by different methods. Additionally, in order to make the as-synthesized hydrophobic NPs (Fe 3 O 4 _A and Fe 3 O 4 _B) soluble in water the amphiphilic CTAB (Cetyl Trimethyl Ammonium Bromide) molecule was employed. Therefore, to conduct a study with a wider range of NP system variants, an experimental illustrative simulation experiment was performed using the IFPTML-DT model. For this, a set of 500,000 prediction dataset was created. The outcome of this experiment highlighted certain NANO.PTML systems as promising candidates for further investigation. The NANO.PTML approach holds potential to accelerate experimental investigations and offer initial insights into various NP and NDDs compounds, serving as an efficient alternative to time-consuming trial-and-error procedures.

60 APPLIED LIFE SCIENCES↗

Benchmark problems for the Me soscale M ultiphysics Ph ase F i eld S imulator (MEMPHIS)

This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Me soscale M ultiphysics Ph ase F i eld S imulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported 'classical' phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hydration Mechanisms in Nanoparticle Interaction and Surface Energetics

Work on the project advanced molecular level understanding, prediction and control of nanoscale hydration in salt solutions under electric stimuli or ionic patterning. Permeation of nanoporous electrodes at preset voltage underlies the function of ultracapacitors. Transitory regulation of wetting in nanoporous media by electric field spans an array of applications in materials, energy storage, and separation sciences. The physically related modulation of nanoparticle solubility by surface charges can significantly extend the range of the nanomaterial applications, improve processing techniques, and potentially alleviate environmental concerns. Pore/solution equilibria, and activated kinetics of liquid gating by nanoconfined electrolytes are challenging problems at the forefront of experimental and theoretical research. Addressing these problems from a molecular perspective required the development of state-of-the-art simulation algorithms in statistical mechanics to capture complex processes in open systems under electric control. Parallel studies of wetting and dispersibility of polar and ionizing particles aim to uncover predictive relations between electrowetting, chemical functionalization, and geometry of nanomaterial particles. By nonequilibrium dynamic modeling, we elucidated electrolyte flow in nanochanels and associated electrokinetic energy conversion. Research on the program provided training opportunities for the next generation of scientists in computational chemistry. Insights, and methods from the project implicate broad segment of researchers in energy and nanosciences, materials and surface chemistry.

74 ATOMIC AND MOLECULAR PHYSICS↗

Benchmark problems for the Mesoscale Multiphysics Phase Field Simulator (MEMPHIS)

This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported classical phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.

74 ATOMIC AND MOLECULAR PHYSICS↗

Mechanical Behavior of Hybrids with Hyper-Connected Molecular Networks

Our research is focused on fundamental studies related to the molecular design, synthesis, characterization and modeling of molecular-reinforced hybrid glass films for superior mechanical and fracture properties. Molecular-reinforced hybrid glass films exhibit unique electro-optical properties while maintaining excellent thermal stability. They have important technological application for emerging nanoscience and energy technologies including anti-reflective and ultra-barrier layers in photovoltaics, display technologies, as well as quantum technologies. However, they are often inherently brittle in nature, do not adhere well to adjacent substrates, and exhibit poor mechanical properties. Furthermore, a robust understanding of the underlying mechanisms of deformation, fracture and fatigue has been lacking particularly given their mechanically fragile nature. The related lack of structure-property relationships between molecular structure, mechanical properties and processing represents a fundamental challenge to their integration into device technologies, compromises their thermomechanical reliability and has thwarted efforts to improve mechanical and, particularly, fracture properties.

36 MATERIALS SCIENCE↗

Center for Gas Separations (CGS)

The total energy consumption in the U.S. has been rising steadily for decades, and it currently amounts to ~98,000 TBtu/yr, with approximately 30% of this total attributable to the industrial sector. Reasonable estimates indicate that 45–55% of total industry energy consumption derives from chemical separations, and for example, over 120 TBtu/yr alone is used in carrying out olefin/paraffin separations via energy-intensive cryogenic distillation. Therefore, the pursuit of new, even radically different approaches to some of the most energy-intensive industrial separations processes is an imperative scientific pursuit for reducing energy consumption toward a more sustainable future. Adsorbent and membrane-based separations can require a fraction of the energy needed for distillation methods, and as such are considered promising solutions for balancing increasing energy demand in the U.S. with the need for a massive reduction in energy consumption. Although considerable research effort has been devoted to the design of materials capable of carrying out various gas separations, usually operating through size-selective, chemisorptive, or physisorptive mechanisms, it remains a great challenge to design materials that function adequately for real-world applications. Indeed, the chemical and physical differences between molecules in gas mixtures of interest are often small, and therefore it is necessary, through the use of nanoscience and synthetic chemistry, to engineer unprecedented molecular-level control in adsorbate–adsorbent interactions. The overarching mission of the Center for Gas Separations (CGS) was to discover fundamental innovations that have the potential to dramatically reduce the energy associated with critical gas separations. In particular, the CGS developed novel synthetic routes, guided by molecular chemistry principles, as well as advanced characterization and computational methods, that have enabled the discovery of new materials and membranes tailor-made to exhibit exceptional performance for a range of gas separations processes, as required in the clean use of fossil fuels and in reducing CO 2 emissions from industry. A challenge of this magnitude required the collaboration and synergy of a large team of researchers with expertise in materials synthesis, characterization, and computations. During the 11-year project period, the CGS created a range of new materials within the family of highly-tunable, porous solids known as metal–organic frameworks (MOFs). These new frameworks demonstrate novel mechanisms for key industrial gas separations, including revolutionary new cooperative adsorption processes that enable low-energy CO 2 and CO capture, and are capable of efficiently separating olefins from paraffins, O 2 from air, and the shape-selective separation of alkane isomers. In addition, the CGS developed new strategies for incorporating these materials into composite membranes toward highly efficient and selective membrane-based separations. As a testament to the success of the CGS, two start-up companies, Mosaic Materials,4 Inc. and Flux Technology, Inc., grew out of these research efforts, and these companies are seeking to commercialize MOF and composite membranes materials for key separations in industry, including large-scale CO 2 capture and hydrocarbon separations, respectively. Another company, framergy, Inc., licensed IP resulting from CGS research toward the commercialization of adsorbents for various energy-relevant applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

EFRC-MUSE: Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials

Phase interactions and fluid properties in geological and other environments are critical in applications ranging from hydrogen production and geologic storage and recovery, carbon dioxide storage and sequestration, and the sustainable use of water resources. The four goals of EFRC-MUSE: Multi-Scale Fluid-Solid Interactions in Architected and Natural Materials were based on the priority directions articulated in the Basic Research Needs documents, and the scientific needs in nanoscience. 1. Develop a fundamental understanding of confinement and surface interactions in mesoscale media with nanometer-sized pores on the phase behavior, thermodynamic and multiphase flow properties of multicomponent fluid mixtures. 2. Examine the impact of mineralogy and material heterogeneity on mechanical properties to better understand chemo-mechanical interactions in material failure. 3. Determine in-operando cross-scale structural and nanostructural material properties with fluids in confinement and flow under realistic condi

58 GEOSCIENCES↗

Recyclable Graphene Sheets as a Growth Template for Crystalline ZnO Nanowires

Recent advances in nanoscience have opened ways of recycling substrates for nanomaterial growth. Novel materials, such as atomically thin materials, are highly desirable for the recycling substrates. In this work, we report recycling of monolayer graphene as a growth template for synthesis of single crystalline ZnO nanowires. Selective nucleation of ZnO nanowires on graphene was elucidated by scanning electron microscopy and density functional theory calculation. Growth and subsequent separation of ZnO nanowires was repeated up to seven times on the same monolayer graphene film. Raman analyses were also performed to investigate the quality of graphene structure along the recycling processes. The chemical robustness of graphene enables the repetitive ZnO nanowire growth without noticeable degradation of the graphene quality. This work presents a route for graphene as a multifunctional growth template for diverse nanomaterials such as nanocrystals, aligned nanowires, other two-dimensional materials, and semiconductor thin films.

36 MATERIALS SCIENCE↗

Interference Control of Fano Resonances and Dynamical Imaging of an Electron Wave Packet

The Fano line shape, arising from the interference of pathways for the excitation of discrete and continuum states, plays a fundamental role in many branches of physics, chemistry, and materials science. Exciting the resonance with a high harmonic provides naturally a phase delay between the pathways leading to a complex asymmetry parameter. We demonstrate that its amplitude and phase can be controlled on the femtosecond and attosecond time scales, respectively. With our high-energy-resolution (10-meV) experiment, we dynamically image a resonance-enhanced electron wave packet during its temporal evolution, extracting both the amplitude and the phase. Calculations reproduce our experimental results. Our approach constitutes a method for measuring the photoionization delays of a resonance and enables the reconstruction of the electron wave packet in the time domain. This concept of an interference-controlled Fano line shape is a step toward attosecond quantum optics with potential ramifications into nanoscience and next-generation optical materials.

Han, Meng [ETH Zürich (Switzerland); Kansas State ↗

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗