Protocol for modeling and simulating lithiation-induced stress in largely deformed spherical nanoparticles using COMSOL.

Here, we present a finite element method-based scheme for solving coupled partial differential equations (PDEs) for the analysis of lithiation-induced stress in largely deformed spherical nanoparticles via the PDE module in COMSOL. We describe steps for software installation and setting PDEs, initial/boundary conditions, and mesh parameters. We then detail procedures for dividing the mesh and analyzing lithium trapping during electrochemical cycling. This protocol can also be extended to analyze a wide range of problems involving diffusion-induced stress. For complete details on the use and execution of this protocol, please refer to Li et al.1.

Green-route manufacturing towards future industrialization of metal halide perovskite nanocrystals.

Perovskite nanocrystals (PeNCs) with excellent optical properties have attracted tremendous research interests and have been considered as promising candidates for new-generation optoelectronic devices. Over the past few years, numerous efforts have been made to overcome the challenges in terms of sustainable manufacturing of PeNCs and related devices and systems, including the solvents used in precursor preparation, antisolvents and perovskite materials for the fabrication of devices and systems, and remarkable progress has been made. However, the usage of toxic, organic solvents in the synthesis of PeNCs poses a threat to the ecosystem and human health, which has hindered the progress in the commercialization and industrialization of PeNCs. This has promoted the development of green solvents for the sustainable manufacturing of PeNCs. In this Feature Article, a state-of-the-art green method for the synthesis of PeNCs is presented, in which the solvents of low toxicities are underlined in contrast to the reported Reviews which focus on toxic solvents for the preparation of precursor solutions. We then focus on green, aqueous methods for the preparation of PeNCs, including conventional perovskite and double PeNCs, by summarizing our previous research efforts and studies. In particular, pure water as the greenest solvent is introduced for the preparation of PeNCs, and the parameters affecting the size and optical characteristics of PeNCs, such as sonication time and ligands for post-treatment, are discussed. The strategies of using a passivation layer to improve the aqueous stability of PeNCs are reviewed, which are grouped into organic polymers and inorganic semiconductors. We highlight the challenges and possible solutions in the green manufacturing and applications of PeNCs. The green routes discussed in this article for the synthesis of PeNCs are expected to be a major step forward for the commercialization and industrialization of the fabrication of PeNCs. It is anticipated that green manufacturing will continue to be the mainstream in the synthesis and fabrication of PeNCs.

Diffusion of Solute Atoms in an Evaporated Liquid Droplet.

Controlling the evaporation of a solvent has made it possible to grow crystals, nanoparticles, and microparticles from liquid droplets. At the heart of this process is the evaporation-induced diffusion of solute atoms, causing the liquid solution of the solute atoms to be in a supersaturated state. In this work, we analyze the mass transport in a spherical liquid droplet, which experiences the loss or evaporation of the solvents across the droplet surface. Using a pseudo-steady-state method, two approximate solutions are derived for the moving boundary problem: one is a linear function of the square of radial variable with a constraint to the loss rate of the solvent, and the other is an exponential function of the square of radial variable without any constraint to the loss rate of the solvent. The numerical results obtained from both approximate solutions are in accord with the numerical results from the finite element method, validating the approximate solutions. The results reveal that a small evaporation/loss rate of the solvent is needed to maintain a relatively uniform distribution of solute atoms in a liquid droplet during the solvent evaporation/loss.

Microfluidics-enabled intelligent manufacturing of metal halide perovskite nanocrystals.

Large-scale and controllable fabrication is an indispensable step for the industrialization and commercialization of halide perovskite nanocrystals, which are new-generation semiconductor materials for optoelectronic applications. Microfluidics, which provides continuous and precise synthesis, has been considered as a promising technique to fulfill this aspect. The research studies over the past decades have witnessed the advancement of microfluidics as a powerful tool in the fabrication of halide perovskite nanocrystals. In this Perspective, the state-of-the-art research based on microfluidics is introduced initially, including the synthesis of functional structures and materials, devices, as well as the interdisciplinary interactions between microfluidics and artificial intelligence and machine learning, etc. We then detail the issues and challenges in hindering progress in the above areas. Finally, we provide future directions and trends for the technology to achieve its full potential. This Perspective is expected to benefit the collective efforts between the field of nanomaterials and microfluidics in advanced manufacturing.

Chemical stress in a largely deformed electrode: Effects of trapping lithium.

Lithium trapping, which is associated with the immobilization of lithium and is one of key factors contributing to structural degradation of lithium-ion batteries during electrochemical cycling, can exacerbate mechanical stress and ultimately cause the capacity loss and battery failure. Currently, there are few studies focusing on how lithium trapping contributes to mechanical stress during electrochemical cycling. This study incorporates the contribution of lithium trapping in the analysis of mechanical stress and mass transport in the framework of finite deformation. Two de-lithiation scenarios are analyzed: one with a constant concentration of trapped lithium and the other with inhomogeneous distribution of trapped lithium. The results show that the constant concentration of trapped lithium increases chemical stress and the inhomogeneous distribution of trapped lithium causes the decrease of chemical stress. The findings can serve as a basis for developing effective strategies to mitigate the lithium trapping and improve the battery performance.

Flexible Piezoresistive Sensors from Polydimethylsiloxane Films with Ridge-like Surface Structures.

Developing flexible sensors and actuators is of paramount importance for wearable devices and systems. In this research, we developed a simple and facile technique to construct flexible piezoresistive sensors from polydimethylsiloxane films with ridge-like surface structures and laser-induced porous graphene. Using a replication strategy, we prepared the ridge-like surface structures from sandpapers. The piezoresistive sensors exhibit excellent sensitivity with a response time of less than 50 ms and long-term cyclic stability under mechanical loading. The smallest weight they can sense is ~96 mg. We demonstrated applications of the piezoresistive sensors in the sensing of bio-related activities, including muscle contraction, finger flexion, wrist flexion, elbow bending, knee bending, swallowing, respiration, sounds, and pulses.

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement.

Understanding mass transport in micro- and nanostructures is of paramount importance in improving the performance and reliability of the micro- and nanostructures. In this work, we solve the diffusion problem in a multilayer structure with periodic conditions under a constant heating rate via a Fourier series. Analytical relation is established between the coefficients of eigenfunctions and the intensity of X-ray or neutron Bragg peak. The logarithm of temporal variation of the intensity of X-ray or neutron Bragg peak is a linear function of the nominal diffusion time, with the nominal diffusion time being dependent on the heating rate. This linear relation is validated by experimental data. The Taylor series expansion of the linear relation to the first order of the diffusion time yields an approximately linear relation between the logarithm of temporal variation of the intensity of X-ray or neutron peak and the diffusion time for small diffusion times, which can be likely used to calculate the activation energy for the diffusion in a multilayer structure. The validation of such an approach is subjected to the fact that the characteristic time for heat conduction is much less than the characteristic time for the ramp heating as well as the characteristic time for diffusion.

Thermo-Mechanical and Creep Behaviour of Polylactic Acid/Thermoplastic Polyurethane Blends.

There is a great need to develop biodegradable thermoplastics for a variety of applications in a wide range of temperatures. In this work, we prepare polymer blends from polylactic acid (PLA) and thermoplastic polyurethane (TPU) via a melting blend method at 200 °C and study the creep deformation of the PLA/TPU blends in a temperature range of 10 to 40 °C with the focus on transient and steady-state creep. The stress exponent for the power law description of the steady state creep of PLA/TPU blends decreases linearly with the increase of the mass fraction of TPU from 1.73 for the PLA to 1.17 for the TPU. The activation energies of the rate processes for the steady-state creep and transient creep decrease linearly with the increase of the mass fraction of TPU from 97.7 ± 3.9 kJ/mol and 59.4 ± 2.9 kJ/mol for the PLA to 26.3 ± 1.3 kJ/mol and 25.4 ± 1.7 kJ/mol for the TPU, respectively. These linearly decreasing trends can be attributed to the weak interaction between the PLA and the TPU. The creep deformation of the PLA/TPU blends consists of the contributions of individual PLA and TPU.

Ultra-stable blue-emitting lead-free double perovskite Cs2SnCl6 nanocrystals enabled by an aqueous synthesis on a microfluidic platform.

Blue emitting Sn-based lead-free halide perovskite nanocrystals (NCs) are considered to be a promising material in lighting and displays. However, industrialised fabrication of blue-emitting NCs still remains a significant challenge due to the use of toxic solvents and optical instability, not mentioning in large-scale synthesis. In this work, a green-route synthesis of blue-emitting lead-free halide perovskite Cs2SnCl6 powders is developed, in which deionized water with a small amount of inorganic acid is used as the solvent and the synthesis of the Cs2SnCl6 powders is achieved on a microfluidic platform. Using the Cs2SnCl6 powders, we prepare Cs2SnCl6 NCs via an ultrasonication process. Changing the volume ratio of the ligands (oleic acid to oleylamine) can alter the photoluminescence (PL) characteristics of the prepared NCs, including the PL-peak wavelength, PL-peak intensity and quantum yield. The highest photoluminescence quantum yield (PLQY) of 13.4% is achieved by the Cs2SnCl6 NCs prepared with the volume ratio of oleic acid to oleylamine of 40 µL to 10 µL. A long-term PL stability test demonstrates that the as-synthesized Cs2SnCl6 NCs can retain a stable PLQY over a period of 60 days. This work opens up a new path for a large-scale green-route synthesis of blue-emitting Sn-based lead-free NCs, such as Cs2SnX6 (Cl, Br and I), towards their applications in optoelectronics.

Kinetic analysis of the growth behavior of perovskite CsPbBr3 nanocrystals in a microfluidic system.

Understanding the growth behavior of nanoparticles and semiconductor nanocrystals under dynamic environments is of profound importance in controlling the sizes and uniformity of the prepared nanoparticles and semiconductor nanocrystals. In this work, we develop a relation between the bandgap (the photoluminescence peak wavelength) of semiconductor nanocrystals and the total flow rate for the synthesis of semiconductor nanocrystals in microfluidic systems under the framework of the quantum confinement effect without the contribution of Coulomb interaction. Using this relation, we analyze the growth behavior of CsPbBr3 nanocrystals synthesized in a microfluidic system by an antisolvent method in the temperature range of 303 to 363 K. The results demonstrate that the square of the average size of the CsPbBr3 nanocrystals is inversely proportional to the total flow rate and support the developed relation. The activation energy for the rate process controlling the growth of the CsPbBr3 nanocrystals in the microfluidic system is 2.05 kJ mol-1. Increasing the synthesis temperature widens the size distribution of the CsPbBr3 NCs prepared in the microfluidic system. The method developed in this work provides a simple approach to use photoluminescent characteristics to in situ monitor and analyze the growth of semiconductor nanocrystals under dynamic environments.

Heterogeneous Nucleation of an Embryo in the Shape of Square Prism: Effect of Surface Roughness.

The solution-based synthesis in a confined space between two parallel plates has been demonstrated to be a potential approach to grow single-crystal perovskite films of large sizes, such as CH3NH3PbX3 (X = Br and I) single-crystal films. In this work, we study the effects of surface roughness on the separation between two parallel, rough plates, and heterogeneous nucleation of an embryo in the shape of square prism for the Wenzel contact between the embryo and the rough surface. Analytical relations are derived for the separation of two parallel, rough plates under mechanical loading and the critical dimensions of a square embryo on a rough surface. The analytical relation reveals that one can control the thickness of perovskite films grown between two parallel plates by changing the surface tension of the precursor solution and mechanical loading. The critical dimensions of a square embryo and the corresponding formation energy are dependent on interface energies and the root mean square of surface roughness. There exists a critical root mean square of surface roughness, above which it is very difficult to form an embryo in the shape of square prism. The results illustrate the important roles of the interface energies and surface roughness of substrates in the growth of single-crystal films, including perovskites and ionic crystals, and the need to include the anisotropic characteristics of surface/interface energies in the nucleation analysis of crystalline materials.

Modeling analysis of the growth of a cubic crystal in a finite space.

The applications of semiconductor nanocrystals in optoelectronics are based on the unique characteristic of quantum confinement. There is great interest to tailor the performance of optoelectronic nanodevices and systems through the control of the sizes of nanocrystals. In this work, we develop a general mathematical formulation for the growth of a crystal/particle in a liquid solution, which takes account of the combinational effect of diffusion-limited growth and reaction-limited growth, and formulate the growth equations for the size of a cubic crystal grown under three different scenarios - isothermal and isochoric conditions, isothermal growth with the evaporation and/or extraction of the solvent and isochoric growth with continuous change in temperature. For the growth of a cubic crystal under isothermal and isochoric conditions, there are three growth stages - linear growth, nonlinear growth and plateau, and the growth rate in the stage of linear growth and the final size of the cubic crystal are dependent on the degree of supersaturation. For the growth of multi-crystals with a Gaussian distribution of crystal sizes, the change of the monomer concentration in a liquid solution is dependent on the change rates of average size and the standard deviation of the crystal sizes.

In Situ Growth Mechanism for High-Quality Hybrid Perovskite Single-Crystal Thin Films with High Area to Thickness Ratio: Looking for the Sweet Spot.

The development of in situ growth methods for the fabrication of high-quality perovskite single-crystal thin films (SCTFs) directly on hole-transport layers (HTLs) to boost the performance of optoelectronic devices is critically important. However, the fabrication of large-area high-quality SCTFs with thin thickness still remains a significant challenge due to the elusive growth mechanism of this process. In this work, the influence of three key factors on in situ growth of high-quality large-size MAPbBr3 SCTFs on HTLs is investigated. An optimal "sweet spot" is determined: low interface energy between the precursor solution and substrate, a slow heating rate, and a moderate precursor solution concentration. As a result, the as-obtained perovskite SCTFs with a thickness of 540 nm achieve a record area to thickness ratio of 1.94 × 104  mm, a record X-ray diffraction peak full width at half maximum of 0.017°, and an ultralong carrier lifetime of 1552 ns. These characteristics enable the as-obtained perovskite SCTFs to exhibit a record carrier mobility of 141 cm2 V-1 s-1 and good long-term structural stability over 360 days.

MAPbBr3nanocrystals from aqueous solution for poly(methyl methacrylate)-MAPbBr3nanocrystal films with compression-resistant photoluminescence.

In this work, we develop an environmental-friendly approach to produce organic-inorganic hybrid MAPbBr3(MA = CH3NH3) perovskite nanocrystals (PeNCs) and PMMA-MAPbBr3NC films with excellent compression-resistant PL characteristics. Deionized water is used as the solvent to synthesize MAPbBr3powder instead of conventionally-used hazardous organic solvents. The MAPbBr3PeNCs derived from the MAPbBr3powder exhibit a high photoluminescence quantum yield (PLQY) of 93.86%. Poly(methyl methacrylate) (PMMA)-MAPbBr3NC films made from the MAPbBr3PeNCs retain ∼97% and ∼91% of initial PL intensity after 720 h aging in ambient environment at 50 °C and 70 °C, respectively. The PMMA-MAPbBr3NC films also exhibit compression-resistant photoluminescent characteristics in contrast to the PMMA-CsPbBr3NC films under a compressive stress of 1.6 MPa. The PMMA-MAPbBr3NC film integrated with a red emissive film and a blue light emitting source achieves an LCD backlight of ∼114% color gamut of National Television System Committee (NTSC) 1953 standard.

A physics-inspired neural network to solve partial differential equations - application in diffusion-induced stress.

Analyzing and predicting diffusion-induced stress are of paramount importance in understanding the structural durability of lithium- and sodium-ion batteries, which generally require solving initial-boundary value problems, involving partial differential equations (PDEs) for mechanical equilibrium and mass transport. Due to the complexity and nonlinear characteristics of the initial-boundary value problems, numerical methods, such as finite difference, finite element, spectral analysis, and so forth, have been used. In this work, we propose two whole loss functions as the sum of the residuals of the PDEs, initial conditions and boundary conditions for the problems with decoupling and coupling between diffusion and stress, respectively, and apply a physics-inspired neural network under the framework of DeepXDE to solve diffusion-induced stress in an elastic sphere in contrast to traditional numerical methods. Using time-space coordinates as inputs and displacement and the solute concentration as outputs of artificial neural networks, we solve the spatiotemporal evolution of the displacement and the solute concentration in the elastic sphere for both the decoupling and coupling problems. The numerical results from the physics-inspired neural network are validated by analytical solutions and a finite element simulation using the COMSOL package. The method developed in this work opens an approach to analyze the stress evolution in electrodes due to electrochemical cycling.

Cycling-induced structural damage/degradation of electrode materials-microscopic viewpoint.

Most analyses of the mechanical deformation of electrode materials of lithium-ion battery in the framework of continuum mechanics suggest the occurring of structural damage/degradation during the de-lithiation phase and cannot explain the lithiation-induced damage/degradation in electrode materials, as observed experimentally. In this work, we present first-principle analysis of the interaction between two adjacent silicon atoms from the Stillinger-Weber two-body potential and obtain the critical separation between the two silicon atoms for the rupture of Si-Si bonds. Simple calculation of the engineering-tensile strain for the formation of Li-Si intermetallic compounds from the lithiation of silicon reveals that cracking and cavitation in lithiated silicon can occur due to the formation of Li-Si intermetallic compounds. Assuming the proportionality between the net mass flux across the tip surface of a slit crack and the migration rate of the crack tip, we develop analytical formulas for the growth and healing of the slit crack controlled by lithiation and de-lithiation, respectively. It is the combinational effects of the state of charge, the radius of curvature of the crack tip and local electromotive force that determine the cycling-induced growth and healing of surface cracks in lithiated silicon.

Kinetics for the Slip Motion of Ripple Dislocations on Gold-Coated Poly(dimethylsiloxane).

Understanding the evolution of the defects in surface patterns is of practical importance to improve the performance and structural durability of the pattern-based micro- and nanodevices. In this work, we investigate the effects of temperature, compressive strain, and relative direction of the compression to the prestretch on the slip motion of ripple dislocations formed on the surface of gold-coated poly(dimethylsiloxane) films. Applying compression in the direction parallel to the direction of prestretch cannot cause the slip motion of the ripple dislocations. The initial velocity of the slip motion of the ripple dislocations increases with the increases in temperature and compressive strain. The temperature dependence of the ratios of the configuration force to the viscous coefficient and the viscous coefficient to the effective mass of the ripple dislocations follows the Arrhenius equation.

Diffusion-Limited Growth of a Spherical Nanocrystal in a Finite Space.

Reason for the work: The potential applications of nanoscale materials in nanophotonics, nanoelectronics, bioimaging, and biosensing have stimulated the research in the synthesis of nanocrystals, nanowires, and so forth. There is a great need to understand the spatiotemporal evolution of nanocrystals in the solution-route synthesis in order to better design advanced synthesis techniques for the manufacturing of monodisperse nanocrystals of high quality. Most significant results: We analyze the size effect on the diffusion-limited growth of a spherical nanoparticle in a finite space (spherical cavity) on the basis of the Gibbs-Thomson relation and obtain an analytical formulation of the monomer concentration in the finite space in an implicit form and an integro-differential equation for the growth rate of the spherical nanoparticle. The monomer concentration in the finite space decreases slower than that with a stationary nanoparticle. The growth of the spherical nanoparticle consists of two stages-an initially linear growth stage and a later power-law stage. The result from the infinite space with a stationary nanoparticle is inapplicable to the analysis of the growth of spherical nanoparticles in a finite space. Conclusions: There exists a size effect on the growth of nanocrystals in a finite space. The dependence of the growth behavior of nanocrystals on the growth time and temperature needs to be investigated in order to experimentally determine the fundamental mechanisms controlling the growth of nanocrystals in the solution-route synthesis.

Homogeneous nucleation in a Poiseuille flow.

Nucleation in a dynamical environment plays an important role in the synthesis and manufacturing of quantum dots and nanocrystals. In this work, we investigate the effects of fluid flow (low Reynolds number flow) on the homogeneous nucleation in a circular microchannel in the framework of the classical nucleation theory. The contributions of the configuration entropy from the momentum-phase space and the kinetic energy and strain energy of a microcluster are incorporated in the calculation of the change of the Gibbs free energy from a flow state without a microcluster to a flow state with a microcluster. An analytical equation is derived for the determination of the critical nucleus size. Using this analytical equation, an analytical solution of the critical nucleus size for the formation of a critical liquid nucleus is found. For the formation of a critical solid nucleus, the contributions from both the kinetic energy and the strain energy are generally negligible. We perform numerical analysis of the homogeneous nucleation of a sucrose microcluster in a representative volume element of an aqueous solution, which flows through a circular microchannel. The numerical results reveal the decrease of the critical nucleus size and the corresponding work of formation of a critical nucleus with the increase of the distance to axisymmetric axis for the same numbers of solvent atoms and solute atoms/particles.

Spreading of Water Droplets on Cellulose-Based Papers: the Effect of Back-Surface Coating.

Regulation of wetting and spreading of liquid on porous material plays an important role in a variety of applications, such as waterproofing, anti-icing, antioxidation, self-cleaning, etc. In this work, we reveal the role of back-surface coating with superhydrophobic nanoparticles in controlling the spreading of water droplets on cellulose-based papers. A layer of superhydrophobic polydivinylbenzene (PDVB) nanoparticles is spin-coated on the back surface of different types of papers. The spreading of a water droplet on the top, uncoated surface is dependent on the size of the PDVB nanoparticles in the coating. Using a relationship derived from Darcy's law, we observe that the energy barrier for the spreading of water droplets on three types of papers (heavy-weight, light-weight, and slight-weight papers) decreases with the decrease of the nanoparticle size in the back-surface coating. The spreading of the water droplet is dependent on the porous structure, permeability, and compressibility of the papers. The method presented in this work provides a feasible approach to use the back-surface coating to control the wettability of papers.