Domain Growth Rate Research Articles

Segregation kinetics of miktoarm star polymers: A dissipative particle dynamics study.

We study the phase separation kinetics of miktoarm star polymer (MSP) melts/blends with diverse architectures using dissipative particle dynamics simulation. Our study focuses on symmetric and asymmetric miktoarm star polymer (SMSP/AMSP) mixtures based on arm composition and number. For a fixed MSP chain size, the characteristic microphase-separated domains initially show diffusive growth with a growth exponent ϕ∼1/3 for both melts that gradually crossover to saturation at late times. The simulation results demonstrate that the evolution morphology of SMSP melt exhibits perfect dynamic scaling with varying arm numbers; the timescale follows a power-law decay with an exponent θ≃1 as the number of arms increases. The structural constraints on AMSP melts cause the domain growth rate to decrease as the number of one type of arms increases while their length remains fixed. This increase in the number of arms for AMSP corresponds to increased off-criticality. The saturation length in AMSP follows a power-law increase with an exponent λ≃2/3 as off-criticality decreases. Additionally, macrophase separation kinetics in SMSP/AMSP blends show a transition from viscous (ϕ∼1) to inertial (ϕ∼2/3) hydrodynamic growth regimes at late times; this exhibits the same dynamical universality class as linear polymer blends, with slight deviations at early stages.

Ordered patterns in electroactive polymer ionic liquid blends: effect of long range interactions.

Designing multifunctional soft materials via pattern formation has been a major challenge for scientists and engineers. Soft materials based on polymers are the perfect candidates for designing such materials as they are not only easy to handle, but also offer diverse combinations of mechanical and chemical properties. Here, we present a polymer-based ternary system and reveal, using modelling and simulations, the mechanisms for creating patterned surfaces. Specifically, we consider polymer ionic liquid (PIL) blends and demonstrate that exposure to a uniform electric field results in the formation of ordered patterns through phase separation. Our approach is based on reaction-diffusion phenomena and utilizes Poisson-Boltzmann-Nernst-Planck equations to capture the long-range interactions of ionic liquids in both weak and strong segregation limits. Furthermore, we elucidate that the ordered patterns in our PIL blend can be tuned by changing the direction of the electric field. From the structural characterization point of view, we reveal that the presence of the electric field significantly enhances the domain growth rate and their respective ordering in a remarkable fashion. We believe this non-invasive technique is a significant step towards the development of ordered structures at microscopic length scales and can be utilized for micro-scale fabrication from soft materials.

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks.

The formed morphology during phase separation is crucial for determining the properties of the resulting product, e.g., a functional membrane. However, an accurate morphology prediction is challenging due to the inherent complexity of molecular interactions. In this study, the phase separation of a two-dimensional model polymer solution is investigated. The spinodal decomposition during the formation of polymer-rich domains is described by the Cahn-Hilliard equation incorporating the Flory-Huggins free energy description between the polymer and solvent. We circumvent the heavy burden of precise morphology prediction through two aspects. First, we systematically analyze the degree of impact of the parameters (initial polymer volume fraction, polymer mobility, degree of polymerization, surface tension parameter, and Flory-Huggins interaction parameter) in a phase-separating system on morphological evolution characterized by geometrical fingerprints to determine the most influential factor. The sensitivity analysis provides an estimate for the error tolerance of each parameter in determining the transition time, the spinodal decomposition length, and the domain growth rate. Secondly, we devise a set of physics-informed neural networks (PINN) comprising two coupled feedforward neural networks to represent the phase-field equations and inversely discover the value of the embedded parameter for a given morphological evolution. Among the five parameters considered, the polymer-solvent affinity is key in determining the phase transition time and the growth law of the polymer-rich domains. We demonstrate that the unknown parameter can be accurately determined by renormalizing the PINN-predicted parameter by the change of characteristic domain size in time. Our results suggest that certain degrees of error are tolerable and do not significantly affect the morphology properties during the domain growth. Moreover, reliable inverse prediction of the unknown parameter can be pursued by merely two separate snapshots during morphological evolution. The latter largely reduces the computational load in the standard data-driven predictive methods, and the approach may prove beneficial to the inverse design for specific needs.

Exact sharp-fronted solutions for nonlinear diffusion on evolving domains

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either report numerical solutions or require an assumption of linear diffusion to determine exact solutions. Unfortunately, numerical solutions do not reveal the relationship between the model parameters and the solution features. Additionally, experimental observations typically report the presence of sharp fronts, which are not captured by linear diffusion. Here we address both limitations by presenting exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain. We obtain the solution by identifying a series of transformations that converts the model of a nonlinear diffusive process on an evolving domain to a nonlinear diffusion equation on a fixed domain, which admits known exact solutions for certain choices of diffusivity functions. We determine expressions for critical time scales and domain growth rates such that the diffusive population never reaches the domain boundaries and hence the solution remains valid.

The Diminishing Role of the Nucleation Rate as Crystallization Develops in Avrami-Type Models

By making use of an isothermal crystallization kinetics formulation in which growth and nucleation rates are functions of the degree of crystallization, we describe a process consisting of birth and growth of spherical crystalline domains. It is found that beyond the early stages of crystallization, the role played by the nucleation rate becomes quite insignificant as compared to the role of the crystalline domain growth rate. This is in contrast to what we would expect from the simplified Avrami exponential equation, where both rates play a symmetrical role. We argue that the asymmetric roles of the growth and nucleation rates greatly contribute to the wide applicability of Avrami-type expressions. A geometric explanation of the diminishing role of nucleation in the later stages of transformation is given. Future theoretical developments might benefit from the arguments and results presented.

Effect of obstructions on growing Turing patterns.

We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel-Epstein reaction-diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain, such as walls and slits, and local obstructions, such as small blocks. The pattern formation is significantly affected by the obstructions, leading to novel pattern morphologies. We show that obstructions can induce growth mode switching and disrupt local pattern formation and that these effects depend on the shape and placement of the objects as well as the domain growth rate. This work provides a customizable framework to perform numerical simulations on different types of obstructions and other heterogeneous domains, which may guide future numerical and experimental studies. These results may also provide new insights into biological pattern growth and formation, especially in non-idealized domains containing noise or discontinuities.

Effect of staged methane flow on morphology and growth rate of graphene monolayer domains by low-pressure chemical vapor deposition

Although many efforts have been spent on graphene growth, there is still a lack of comprehensive understanding about the growth mechanism and precise control for different morphologies of graphene domains synthesis though carbon precursor. In this work, controlled single-crystal graphene monolayer domains with different morphologies of four, six and multiple symmetry have been achieved just by staged modulation of methane flow through low-pressure chemical vapor deposition method on copper. The growth rate can also be regulated by the methane flow, and the highest growth rate can reach 25 μm/min corresponding to the multiple-dendritic shape. The schematic structure of the different shapes with active sites has been proposed to understand the formation mechanism of different graphene domains. Synthesis single crystal graphene with various morphologies will be of great promising potential applications in catalytic and many other fields.

Polarization switching behavior of (Pb,Nb)(Zr,Sn,Ti)O3 ferroelectric ceramics under high-power pulse condition in microsecond scale

In the present work, the polarization switching of polycrystalline (Pb,Nb)(Zr,Sn,Ti)O3 (PNZST) ferroelectric (FE) ceramics in microsecond scale was investigated by pulse switching experiment. Typical switching current similar to that of FE single crystal and thin films was observed in PNZST ceramics, directly proving the completion of the switching process in microsecond scale. The increase of switching current and decrease of switching time with increasing electric field and temperature were confirmed and explained by the acceleration of the nucleation and growth rate of domains. However, the distortion of the pulse voltage also results in difficulty to analyze the switching current via Merz’s equation, which was usually neglected in previous works. In addition, the pulse switching dynamic is also found to be a current-limiting process and strongly depends on the circuit parameters. By increasing the resistance of the in-series resistor, the switching process will be hindered, leading to the decrease of switching current and longer switching period. More importantly, the curve of polarization versus electric field (P–E) was obtained by the switching current and a distinct difference was observed compared with the 0.1 Hz P–E curve. The above results prove the possibility of using PNZST ceramics in high-power pulse technology and will give some important guidance for the designation of FE devices.

New Growth Frontier: Superclean Graphene.

The last 10 years have witnessed significant progress in chemical vapor deposition (CVD) growth of graphene films. However, major hurdles remain in achieving the excellent quality and scalability of CVD graphene needed for industrial production and applications. Early efforts were mainly focused on increasing the single-crystalline domain size, large-area uniformity, growth rate, and controllability of layer thickness and on decreasing the defect concentrations. An important recent advance was the discovery of the inevitable contamination phenomenon of CVD graphene film during high-temperature growth processes and the superclean growth technique, which is closely related to the surface defects and to the peeling-off and transfer quality. Superclean graphene represents a new frontier in CVD graphene research. In this Perspective, we aim to provide comprehensive understanding of the intrinsic growth contamination and the experimental solution of making superclean graphene and to provide an outlook for future commercial production of high-quality CVD graphene films.

(Invited) Wafer-Scale Epitaxy of Transition Metal Dichalcogenides By MOCVD

Monolayer semiconducting transition metal dichalcogenides (MX2, M=W, Mo and X=S, Se) exhibit novel electronic and optical properties. Availability of epitaxial single-crystal monolayers over a wafer scale is a major hurdle in integrating these materials with existing device fabrication processes. Our approach focusses on synthesis of these monolayers using gas source precursors, like those used in traditional III-V semiconductor industry. The precursors are kept in temperature and pressure-controlled bubblers outside the growth chamber and can be metered independently into the growth zone with precision. Uniform epitaxial binary TMD monolayers including MoS2, WS2, WSe2 and MoSe2 have been deposited on 2” sapphire wafers in a cold-wall CVD reactor using metal hexacarbonyl and hydride chalcogen precursors. A multi-step growth process comprising of precursor modulation was developed for WSe2 to independently control nucleation density and the lateral growth rate of monolayer domains on the sapphire substrate [1]. For the sulfides, additional temperature modulation was introduced to increase crystalline quality. Using this approach, uniform, coalesced monolayer and few-layer TMD films were obtained on 2” sapphire substrates. In-plane X-ray diffraction demonstrates that the films are epitaxially oriented with respect to sapphire with narrow X-ray full-width-at-half-maximum indicating minimal rotational misorientation of domains within the basal plane [2]. Deposition of these materials in the same reactor provides insight into the factors controlling their growth, which in essential for the growth of heterostructures and/or alloys. Transmission electron microscopy analysis of these materials revealed additional information about the coalesced film structure. For instance, ~95 % single oriented WS2 domains were observed when the film growth rate was modulated. For WS2, it was also confirmed that despite translational line defects present in the film, mirror boundaries were predominantly absent. WS2 also showed no defect related photoluminescence peak at 80 K, indicating its high quality.In this talk the factors affecting the growth of TMDs (MX2, M=W, Mo and X=S, Se) will be presented. The role of the substrate surface in the nucleation and growth of these TMDs will be discussed. In addition, the structural and optoelectronic characteristics for these films will also be presented.The authors acknowledge financial support of the U.S. National Science Foundation through the Penn State 2D Crystal Consortium – Materials Innovation Platform (2DCC-MIP) under NSF cooperative agreement DMR-1539916 and EFRI 2-DARE Grant EFRI-1433378.[1] Zhang X, Choudhury TH, Chubarov M et al., 2018. Nano Lett. 18(2):1049–56[2] Chubarov M, Choudhury TH, Zhang X et al., 2018. Nanotechnology. 29(5):55706

Unbiased on-lattice domain growth.

Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism.

Ultrafast Catalyst-Free Graphene Growth on Glass Assisted by Local Fluorine Supply.

High-quality graphene film grown on dielectric substrates by a direct chemical vapor deposition (CVD) method promotes the application of high-performance graphene-based devices in large scale. However, due to the noncatalytic feature of insulating substrates, the production of graphene film on them always has a low growth rate and is time-consuming (typically hours to days), which restricts real potential applications. Here, by employing a local-fluorine-supply method, we have pushed the massive fabrication of a graphene film on a wafer-scale insulating substrate to a short time of just 5 min without involving any metal catalyst. The highly enhanced domain growth rate (∼37 nm min-1) and the quick nucleation rate (∼1200 nuclei min-1 cm-2) both account for this high productivity of graphene film. Further first-principles calculation demonstrates that the released fluorine from the fluoride substrate at high temperature can rapidly react with CH4 to form a more active carbon feedstock, CH3F, and the presence of CH3F molecules in the gas phase much lowers the barrier of carbon attachment, providing sufficient carbon feedstock for graphene CVD growth. Our approach presents a potential route to accomplish exceptionally large-scale and high-quality graphene films on insulating substrates, i.e., SiO2, SiO2/Si, fiber, etc., at low cost for industry-level applications.

Standard and fractional Ornstein-Uhlenbeck process on a growing domain

We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive continuous-time random walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the aging of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing or contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

Multi-scale modeling of early-stage morphology in solution-processed polycrystalline thin films.

A model is introduced for treating early-stage nucleation, growth kinetics, and mesoscale domain structure in submonolayer polycrystalline films prepared by solution-phase processing methods such as spin casting, dip coating, liquid-based printing, and related techniques. The model combines a stochastic treatment of nucleation derived from classical nucleation theory with deterministic computation of the spatiotemporal dynamics of the monomer concentration landscape by numerical solution of the two-dimensional diffusion equation, treating nuclei as monomer sinks. Results are compared to experimental measurements of solution-processed submonolayer tetracene films prepared using a vapor-liquid-solid deposition technique. Excellent agreement is observed with most major kinetic and structural film characteristics, including the existence of distinct induction, nucleation, and growth regimes, the onset time for nucleation, the number of domains formed per unit area, and the micron- to millimeter-scale spacing statistics of those domains. The model also provides a detailed description the dynamically-evolving monomer concentration landscape during film formation as well as quantities derived from it, such as time- and position-dependent domain nucleation and growth rates.

Bridging the Gap between Reality and Ideal in Chemical Vapor Deposition Growth of Graphene.

Graphene, in its ideal form, is a two-dimensional (2D) material consisting of a single layer of carbon atoms arranged in a hexagonal lattice. The richness in morphological, physical, mechanical, and optical properties of ideal graphene has stimulated enormous scientific and industrial interest, since its first exfoliation in 2004. In turn, the production of graphene in a reliable, controllable, and scalable manner has become significantly important to bring us closer to practical applications of graphene. To this end, chemical vapor deposition (CVD) offers tantalizing opportunities for the synthesis of large-area, uniform, and high-quality graphene films. However, quite different from the ideal 2D structure of graphene, in reality, the currently available CVD-grown graphene films are still suffering from intrinsic defective grain boundaries, surface contaminations, and wrinkles, together with low growth rate and the requirement of inevitable transfer. Clearly, a gap still exits between the reality of CVD-derived graphene, especially in industrial production, and ideal graphene with outstanding properties. This Review will emphasize the recent advances and strategies in CVD production of graphene for settling these issues to bridge the giant gap. We begin with brief background information about the synthesis of nanoscale carbon allotropes, followed by the discussion of fundamental growth mechanism and kinetics of CVD growth of graphene. We then discuss the strategies for perfecting the quality of CVD-derived graphene with regard to domain size, cleanness, flatness, growth rate, scalability, and direct growth of graphene on functional substrate. Finally, a perspective on future development in the research relevant to scalable growth of high-quality graphene is presented.

Phase separation dynamics in binary systems containing mobile particles with variable Brownian motion

This study investigates the spinodal decomposition dynamics in binary mixtures containing mobile particles by combining the Cahn–Hilliard equation with Langevin dynamics for particles with Brownian motion changes proportional to their mobility. We solve the Cahn–Hilliard equation numerically using a semi-implicit Fourier spectral method, and show that the domain growth rate first increases with the increase in particle mobility, and then decreases. The effect of filler particle concentration on the domain growth depends on its mobility: when the particle mobility is low, the domain growth rate decreases with the increase in particle concentration; whereas when the particle mobility is high, the domain growth rate decreases and then increases and finally decreases again with the increase in particle concentration. The proposed model suggests the possibility of controlling macroscopic behaviour of binary alloys by altering filler particle properties.

Computational Understanding of the Growth of 2D Materials

AbstractOver the last two decades, remarkable progress has been made in use of computational methods for understanding 2D materials growth. The aim of this Review is to provide an overview of several state‐of‐the‐art computational methods for the modelling and simulation of 2D materials growth. First, the current status of 2D materials, and their major growth methods are addressed. Next, the applications of the ab initio method in 2D materials growth is discussed, focusing on reaction of precursors, diffusion of adatoms, energetics and kinetics of growth fronts, and effects of substrates. Then, the applications of the molecular dynamics approach in 2D materials growth is discussed, with emphasis on the growth of graphene on various substrates and the growth of boron nitride and silicene. Furthermore, the applications of the kinetic Monte Carlo method in 2D materials growth are discussed. The parametrization of the method and its application in dimer distribution, and nonlinear edge growth of graphene are discussed. Subsequently, the applications of the phase‐field method in 2D materials growth are discussed, focusing on the growth rate and morphological evolution of 2D domains. Finally, perspectives and conclusions are presented.

(Invited) Epitaxial Growth of 2D Transition Metal Dichalcogenide Monolayers, Alloys and Heterostructures

Two-dimensional (2D) transition metal dichalcogenides (TMDs) comprise a compelling class of new materials with intriguing properties that arise from their ultra-thin form, thickness-dependent bandstructure, large exciton binding energies and unusual spin and valley polarization physics. The majority of the research that has been carried out thus far employs ultra-thin TMD flakes exfoliated from bulk crystals but future device development requires the ability to synthesize large area single crystal films and heterostructures. Our research is aimed at the development of an epitaxial growth technology for TMDs and related layered chalcogenides based on gas source/metalorganic chemical vapor deposition (CVD/MOCVD) to enable monolayer growth over large substrate areas and layer-by-layer growth of heterostructures. Our recent studies have focused on the epitaxial growth of WSe2 and (Mo,W)S2 monolayer films, alloys and heterostructures using metal hexacarbonyl and hydride chalcogen precursors on substrates including sapphire and hexagonal boron nitride (hBN). A multi-step precursor modulation growth method was developed to independently control nucleation density and the lateral growth rate of TMD domains on the substrate. This approach also enables an estimation of metal-species surface diffusivity and domain growth rate as a function of growth conditions providing insight into the fundamental mechanisms of monolayer growth. Using the multi-step growth process, coalesced monolayer and few-layer TMD films were obtained on sapphire substrates up to 2” in diameter at growth rates on the order of ~ 1 monolayer/hour. In-plane X-ray diffraction demonstrates that the films are epitaxially oriented with respect to the sapphire resulting from a merging of 0o and 60o oriented domains. Room temperature photoluminescence (PL) measurements demonstrate strong emission peaks in the range of ~1.6 eV for WSe2 and ~2.0 eV for WS2 monolayers with lateral variations that may arise from residual strain in the films. (Mo,W)S2 alloy growth using simultaneous flows of Mo and W hexacarbonyl precursors reveals evidence of atomic scale ordering of Mo and W atoms within the monolayer. Growth and characterization of MoS2/WS2 and WSe2/WS2 vertical heterostructures will also be discussed.

(Invited) Epitaxy of 2D Transition Metal Dichalcogenide Monolayers and Heterostructures

There is growing interest in monolayer transition metal dichalcogenides (TMDs) such as MoS2 and WSe2 and related 2D heterostructures due to their compelling electronic and photonic properties. The majority of this work has been carried out using ultra-thin flakes exfoliated from bulk chalcogenide crystals but future device development requires the ability to synthesize large area single crystal films and heterostructures. Our research is aimed at the development of an epitaxial growth technology for layered dichalcogenides, similar to that which exists for III-V and other compound semiconductors, based on gas source chemical vapor deposition (CVD). This approach provides a high overpressure of chalcogen species needed to maintain stable growth at elevated temperature and excellent control of the precursor partial pressures to achieve layer-by-layer and heterostructure growth. Our recent studies have focused on the epitaxial growth of WSe2 and WS2 monolayer films and heterostructures using metal hexacarbonyl and hydride chalcogen precursors on substrates including sapphire and hexagonal boron nitride (hBN). A multi-step precursor modulation growth method was developed to independently control nucleation density and the lateral growth rate of WSe2 and WS2 monolayer domains on the substrate. This approach also enables measurement of W-species surface diffusivity and domain growth rate as a function of growth conditions providing insight into the fundamental mechanisms of monolayer growth. Using this approach, coalesced monolayer and few-layer TMD films were obtained on sapphire substrates up to 2” in diameter at growth rates on the order of ~ 1 monolayer/hour. In-plane X-ray diffraction demonstrates that the films are epitaxially oriented with respect to the sapphire resulting from a merging of an equal mixture of 0o and 60o oriented domains. WSe2 also grows epitaxially on hBN single crystal flakes but in this case the domains exhibit a predominant direction resulting in a reduced density of anti-phase boundaries. Applications and challenges of this approach in the growth of 2D heterostructures will also be discussed.

Phase segregation of metastable quenched liquid mixtures and the effect of the quenching rate

ABSTRACTThe effect of the quenching rate on the phase separation of partially miscible liquid mixtures is studied, showing that it may influence the growth rate of single-phase domains. In particular, the phase separation of metastable binary mixtures in the presence of strong emulsifiers appears to be heavily retarded. These effects constitute an important limitation to the phase transition extraction process introduced by the authors in previous works, which is based on the fact that phase separation of unstable mixtures is rapid, even in the presence of surface active compounds.