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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Porous Sb with three-dimensional Sb nanodendrites as electrode material for high-performance Li/Na-ion batteries.

The increasing demand in energy consumption and the use of clean energy from sustainable energy sources have driven the research in the development of advanced materials for Li-ion and Na-ion batteries. In this work, we have developed a simple technique to synthesize a porous Sb structure through a galvanic replacement reaction between Sb3+ and Zn particles. The porous Sb structure consists of a three-dimensional-hierarchical structure with tree-like nanoscale Sb dendrites. The Sb in the nanodendrites is crystal of a rhombohedral structure. We construct Li-/Na-ion half cells and Li-/Na-ion full cells with the Sb nanodendrites as the active material in the working electrode and anode, respectively, and introduce an additive of vinylene carbonate for the Li-ion half/full cells and an additive of fluoroethylene carbonate for the Na-ion half/full cells. All the Li-/Na-ion half cells and Li-/Na-ion full cells exhibit excellent electrochemical performance and cycling stability. Such excellent performance can be attributed to the synergistic interaction between the three-dimensional-dendritic structure and electrolyte, which likely ensures fast transport of ions and electrons and the formation of a stable solid-state interphase.

Sb nanocrystal-anchored hollow carbon microspheres for high-capacity and high-cycling performance lithium-ion batteries.

There is a great need to develop sustainable and clean energy storage devices and systems of high-energy and high-capacity densities. In this work, we synthesize antimony (Sb) nanocrystal-anchored hollow carbon microspheres (Sb@HCMs) via the calcination of cultivated yeast cells and the reduction of SbCl3 in an ethylene glycol solution on the surface of hollow carbon microspheres. The Sb@HCMs possess hollow and porous structure, and the Sb is present in the form of nanocrystals. Using the Sb@HCMs as the active-electrode material, we assemble lithium (Li)-ion half cells and full cells and investigate their electrochemical performance. The Li-ion half cells possess a charge capacity of 605 mA h g-1 after 100 cycles at a current density of 100 mA g-1 and a charge capacity of 469.9 mA h g-1 at a current density up to 1600 mA g-1, which is much higher than the theoretical capacity of 372 mA h g-1 for commercial graphite electrode. The Li-ion full cells with Sb@HCMs//LiCoO2 deliver a charge capacity of 300 mA h g-1 at a current density of 0.2 A g-1 after 50 cycles, and have potential in applications of energy storage.

Solvent-induced deflection of polydimethylsiloxane plates: Effects of dimensions and solvent volume.

The development of flexible electronics and robots has stimulated interest in the deformation behavior of polymers under liquid environments. In this work, we introduce a "local" method to study the toluene-induced deflection of polydimethylsiloxane (PDMS) plates. Placing a graphite rod on the surface of a PDMS plate, we are able to confine the spreading and evaporation of toluene and the uptake of toluene by the PDMS plate. The local uptake of toluene by a PDMS plate causes the deflection of the PDMS plate, which is dependent on the geometric dimensions of the plate and the toluene volume. An empirical relationship is proposed to correlate the largest deflection of a PDMS plate induced by local uptake of toluene to geometric dimensions of the plate and toluene volume. The approach used in this work provides a simple approach to study the kinetics of the solvent-induced deformation of a polymer, which can contribute to the design and applications of a stimuli-sensitive self-shaping polymer.

Nucleation in a liquid droplet.

The droplet-based microreactors in microfluidic systems have been used to synthesize nanocrystals of a variety of metals and semiconductors, which involves the nucleation and growth processes. Considering the limited numbers of solvent atoms and solute atoms/particles in a stationary droplet, we derive analytical expressions of the changes of the Gibbs free energy and the Helmholtz free energy for the concurrent formation of multiple microclusters of the same size in the liquid droplet. Both the changes of the Gibbs free energy and the Helmholtz free energy are dependent on the ratio of the number of microclusters to the solvent atoms and the interface energy between the solution and the microclusters. Using the change of the free energy, which is an approximation of the Gibbs free energy and the Helmholtz free energy, we obtain the critical nucleation number of the solute atoms/particles in the microclusters for the concurrent nucleation of multiple nuclei of the same size. The critical nucleation number of the solute atoms/particles is dependent on the ratio of the number of nuclei in the droplet to the solvent atoms, and the maximum change of the free energy for the concurrent nucleation of multiple nuclei of the same size increases with the increase of the ratio of the number of the nuclei in the droplet to the number of the solvent atoms.

Modeling analysis for the growth of a Li sphere and Li whisker in a solid-state lithium metal battery.

One of the challenges when using lithium metal as the anode in rechargeable lithium batteries is the formation and growth of lithium dendrites. The recent observation by He et al. (Nat. Nanotechnol., 2019, 14, 1042-1047) and Zhang et al. (Nat. Nanotechnol., 2020, 15, 94-98) confirm the presence of the root-growth mode for the growth of lithium dendrites (whiskers, spheres and hillocks). In this work, we introduced a non-Newtonian flow model to describe the flow of lithium in lithium metal and incorporate the contributions of viscous dissipation, surface energy, kinetic energy and strain energy in the analysis of the stress relaxation and the growth of a Li-sphere and a Li-whisker. Nonlinear second-order differential equations are derived for the growth of the Li-sphere and the Li-whisker. Closed-form solutions for the temporal evolution of the Li-sphere and the Li-whisker are obtained under the conditions such that the contributions of the surface energy, kinetic energy and strain energy stored in the cantilever beam to the stress relaxation in the lithium metal are negligible. Using the Lippmann relation in specific surface energy, we demonstrated that increasing the electric potential reduces the resistance to the flow of lithium into the Li-sphere and the Li-whisker. The results reveal the need to suppress the cycling-induced strain energy (misfit strain and biaxial modulus) in order to mitigate the growth of Li dendrites (whiskers, spheres and hillocks).

Growth of Polystyrene Pillars in Electric Field.

Surface patterning on polymer films, which is a self-assembly process under the action of external and/or internal impetus, has a variety of applications, including drug delivery and flexible electronics. In this work, we study the growth of polystyrene pillars in the electric field for different combinations of annealing temperature, film thickness, and electrode separation (electric field intensity). There are five stages for the growth of the polystyrene pillars for all the configurations used in this work, including a nucleation stage, a linear growth stage, an acceleration stage in the pillar length prior to the contact between the top surface of a pillar and the upper electrode, a radial growth stage after the contact, and a stationary stage without further growth of the pillar. In the linear growth stage, there exist linear relationships between the pillar length and the annealing time and between the square of the pillar diameter and the annealing time. The activation energies for the rate processes controlling the radial growth and the length growth in the linear growth stage are 30.2 and 25.3 kJ/mol, respectively. There are two rate processes controlling the radial growth of the pillars: one is the field-induced flow of polymer through the polymer film to the roots of pillars and the other is the coalescence of pillars. The activation energy for the coalescence is 16.5 kJ/mol. The results obtained in this work offer a practical route to control the geometrical dimensions of polymer pillars through the processing parameters.

Coexistence and Sudden Entrapment between Two Dissimilar, Miscible Oil Lenses.

The property of substrates is one of the important factors determining the interaction between two lenses (droplets). There likely exist different interactions between two dissimilar oil lenses (droplets) floating on the surface of a liquid phase from the interaction between two dissimilar oil droplets on a rigid substrate, for example, coalescence or coexistence. The interaction between two dissimilar oil lenses (droplets) is dependent on the intrinsic properties of both oil lenses (droplets) and external environmental factors. In this work, we investigate the contact interaction between two dissimilar, miscible oil lenses (toluene and silicone oil) on the surface of deionized water (DI water). The morphological evolution of two dissimilar, miscible oil lenses during the interaction under different experimental conditions is recorded and analyzed. The effects of the volume ratio of two dissimilar, miscible oil lenses, temperature of DI water, and viscosity of silicone oil on characteristic parameters are systematically studied. A sudden "entrapment" of a toluene lens into a silicone oil lens occurs after a period of the "mass exchange" (coexistence) between these two oil lenses. Several characteristic parameters, including the duration of the "mass exchange" and critical sizes of the toluene lens at the onset of the entrapment and after the entrapment, are found to be dependent on experimental conditions.

Growth of perovskite nanocrystals in poly-tetra fluoroethylene based microsystem: on-line and off-line measurements.

Cesium lead halide perovskite nanocrystals are photoelectric nanomaterials that have potential applications in a variety of areas due to their excellent photoelectric and tunable photo luminescent properties. In this work, we investigate the synergetic effects of reaction temperature, reaction-capillary length and flow rate on the growth kinetics of perovskite nanocrystals in a PTFE-based microsystem and the photoluminescence characteristics of the perovskite nanocrystals both on-line and off-line. The on-line measurement finds that increasing the reaction temperature leads to the increase of the wavelength of the PL emission peak of the synthesized nanocrystals and reduces the average size of the perovskite nanocrystals synthesized in long reaction-capillaries. The intensity of the PL emission peak of the nanocrystals synthesized at different reaction temperatures decreases with the increase of the flow rate. The off-line measurement reveals that increasing the flow rate generally leads to the blueshift of the PL emission peaks and the decrease of the average size of the perovskite nanocrystals synthesized at the reaction temperature of 160 °C in the capillary length of 60 cm. Increasing temperature leads to the increase of the emission wavelength of the perovskite nanocrystals from 560 to 608 nm. The temperature dependence of the average size of the synthesized nanocrystals with the same synthesis conditions at different temperatures can be described by the Arrhenius relationship with an activation energy of 8.54 kJ mol-1. Five different cross-sections of the synthesized perovskite nanocrystals are observed, including rhombus, hexagon, rectangle, square and quadrangle with three of them being observed for the first time.

Brownian motion and Einstein relation for migration of coffee particles in coffee suspensions.

BACKGROUND: The migration of particles in a liquid plays an important role in determining the stability of the corresponding suspension. The preparation of a cup of coffee involves the migration/dispersion of coffee particles in aqueous solutions. We investigate the Brownian motion of coffee particles in coffee suspensions at different temperatures for three different coffee beans via the migration of the coffee particles of the coffee suspensions in water. RESULTS: The activation energies for the Brownian motion of the coffee particles are in the range 23.5-32.0 kJ mol-1 , relatively independent of the size of the coffee particles used in the present study. The viscosities of the coffee suspensions are measured as a function of temperature and then used to correlate with the gradient-diffusion coefficient for the Brownian motion of the coffee particles. The activation energies of the rate process controlling the viscous flow of the coffee suspensions are in the range 12.7-14.1 kJ mol-1 . CONCLUSION: The correlation between the viscosity and gradient-diffusion coefficient of the coffee suspensions generally follows the Einstein relation. A temperature dependence exists for the viscosity and gradient-diffusion coefficient of the coffee suspensions, which can be used to understand the brewing of coffee at high temperatures with respect to product refinement. © 2019 Society of Chemical Industry.

Contact Interaction of Two Oil Lenses Floating on Surface of Deionized Water.

Droplets on the surface of liquid play an important role in a variety of areas, including the petroleum industry, pollution control, and environmental processes. In this work, we study the contact interaction between two floating oil lenses on the surface of immiscible water. The contact interaction between the two floating oil lenses can be divided into three different regimes: (a) the collision involving deformation for low-viscous oils, (b) the direct coalescence for high-viscous oils, and (c) the coexistence (noncoalescence) of oil lenses at relatively high temperatures. The temperature dependence of the coalescence time for the coalescence of two silicone-oil lenses of large viscosities follows the Arrhenius equation.