Kinetics Of Domain Growth Research Articles

Domain growth kinetics in active binary mixtures.

We study motility-induced phase separation in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ρi(r⃗,t). Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function C(r, t) and the structure factor S(k, t), both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, Δ. For k → ∞, S(k, t) follows Porod's law: S(k, t) ∼ k-(d+1) and the average domain size L(t) shows a diffusive growth as L(t) ∼ t1/3 for all mixtures.

Kinetics of phase separation and aging dynamics of segregating fluid mixtures in the presence of quenched disorder.

Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in an Ising model with quenched disorder. But there is a paucity of research on the phase-separation kinetics in fluids with quenched disorder. In this paper, we present results from a detailed molecular dynamics simulation, showing the effects of randomly placed localized impurities on the phase separation kinetics of binary fluid mixtures. Two different models are offered for representing the impurities. We observe a dramatic slowing down in the pattern formation with increasing impurity concentration. This sluggish domain growth kinetics follows a power-law with a disorder-dependent exponent. The correlation function and structure factor show a non-Porod behavior, indicating the roughening of the domain interfaces. We have also studied the effect of quenched disorder on the aging dynamics by calculating the two-time order parameter auto correlation function and find that the Fisher and Huse scaling law holds good in the presence of quenched disorder.

Domain engineering in ferromagnetic morphotropic phase boundary with enhanced and non-hysteretic magnetostriction: A phase-field simulation

Giant and non-hysteretic magnetostriction is critical for magneto-mechanical applications, such as transducers, sensors, and actuators. In this work, the introduction of domain engineering into the single crystals near the ferromagnetic morphotropic phase boundary (MPB) is achieved through phase-field simulation, with the aim of exerting control over domain configuration and magnetostriction. It is found that intermediate external magnetic fields applied along non-easy magnetic axes during the nucleation stage can significantly affect the subsequent domain growth and evolution kinetics. The simulations reveal a domain wall broadening mechanism to explain the significantly improved non-hysteretic magnetoelastic responses observed in engineered tetragonal crystals. Our simulation results additionally demonstrate a discernible correlation between the domain wall densities and external fields in the engineered tetragonal domain. This research provides a potential pathway for the advancement of giant and non-hysteretic magnetostrictive material designs.

Disentangling growth and decay of domains during phase ordering.

Using Monte Carlo simulations we study phase-ordering dynamics of a multispecies system modeled via the prototype q-state Potts model. In such a multispecies system, we identify a spin state or species as the winner if it has survived as the majority in the final state, otherwise, we mark them as loser. We disentangle the time (t) dependence of the domain length of the winner from losers, rather than monitoring the average domain length obtained by treating all spin states or species alike. The kinetics of domain growth of the winner at a finite temperature in space dimension d=2 reveal that the expected Lifshitz-Cahn-Allen scaling law ∼t^{1/2} can be realized with no early-time corrections, even for system sizes much smaller than what is traditionally used. Up to a certain period, all others species, i.e., the losers, also show a growth that, however, is dependent on the total number of species, and slower than the expected ∼t^{1/2} growth. Afterwards, the domains of the losers start decaying with time, for which our numerical data appear to be consistent with a ∼t^{-2} behavior. We also demonstrate that this approach of looking into the kinetics even provides new insights for the special case of phase ordering at zero temperature, both in d=2 and d=3.

Domain Size Regulation in Phospholipid Model Membranes Using Oil Molecules and Hybrid Lipids.

The formation of domains in multicomponent lipid mixtures has been suggested to play a role in moderating signal transduction in cells. Understanding how domain size may be regulated by both hybrid lipid molecules and impurities is important for understanding real biological processes; at the same time, developing model systems where domain size can be regulated is crucial to enable systematic studies of domain formation kinetics and thermodynamics. Here, we perform a model study of the effects of oil molecules, which swell the bilayer, and line-active hybrid phospholipids using a thermally induced liquid-solid phase separation in planar, free-standing lipid bilayers consisting of DOPC and DPPC (1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine, respectively). The experiments show that the kinetics of domain growth are significantly affected by the type and molecular structure of the oil (squalene, hexadecane, or decane), with the main contributing factors being the degree of swelling of the bilayer and the changes in line tension induced by the different oils, with smaller domains resulting from systems with smaller values of the line tension. POPC (1-palmitoyl-sn-2-oleoyl-glycero-3-phosphocholine), on the other hand, acts as a line-active hybrid lipid, reducing the domain size when added in small amounts and slowing down domain coarsening. Finally, we show that despite the regulation of domain size by both methods, the phase transition temperature is influenced by the presence of oil molecules but not significantly by the presence of hybrid lipids. Overall, our results show how to regulate domain size in binary membrane model systems, over a wide range of length scales, by incorporating oil molecules and hybrid lipids.

Discrete switching in the ion sliced lithium niobate thin films with thick dielectric layer

Domain growth and shape evolution during local switching under the action of biased conductive tip of scanning probe microscope were studied in Z + cut lithium niobate on insulator (LNOI) with 1 µm-thick SiO2 layer between LN film and grounded electrode. Piezoresponse force microscopy and confocal Raman microscopy were used for domain imaging. The domain shape evolution during switching was qualitatively reconstructed. The crucial role of discrete switching on the kinetics of domain growth was revealed. The stability of the switched domains was confirmed. The obtained knowledge will be used for creation of the periodical domain structures by local switching.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals.

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

Domain Growth in the Active Model B: Critical and Off-critical Composition

ABSTRACT We study the ordering kinetics of an assembly of active Brownian particles (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter ,where and denote space and time, respectively. The model is similar to the Cahn-Hilliard equation orModel B (MB) for a conserved order parameter with an additional activity term of strength . This model has been introduced by Wittkowski et al., Nature Comm. 5, 4351 (2014), and is termed Active Model B (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity governs the asymptotic growth kinetics for the off-critical AMB, where denotes the average order parameter. For negative ,the domain growth law is the usual Lifshitz-Slyozov growth law with . For positive ,the growth law shows a crossover to a novel growth law . Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on and . We also study the effects of both additive and multiplicative noise on the AMB.

Kinetics of the two-dimensional long-range Ising model at low temperatures.

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling J(r)∼r^{-(d+σ)}, where d=2 is the dimensionality. According to the Bray-Rutenberg predictions, the exponent σ controls the algebraic growth in time of the characteristic domain size L(t),L(t)∼t^{1/z}, with growth exponent z=1+σ for σ<1 and z=2 for σ>1. These results hold for quenches to a nonzero temperature T>0 below the critical temperature T_{c}. We show that, in the case of quenches to T=0, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely, we find that in this case the growth exponent takes the value z=4/3, independently of σ, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for single domains.

Kinetics of domain growth and aging in a two-dimensional off-lattice system.

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w},ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Influence of growth kinetics on graphene domains shape under atmospheric pressure chemical vapor deposition

In this work, the role of gas kinetics in the growth of lobed graphene domains by atmospheric pressure chemical vapor deposition (AP-CVD) is elucidated by sandwiching Cu foil between Si/SiO2 wafers. Two different growths were carried out: (1) A Cu foil was placed at the center of a quartz tube in AP-CVD for graphene growth and (2) another Cu foil was sandwiched between Si/SiO2 wafers to alter the nucleation growth kinetics of graphene domains to mimic those in low-pressure chemical vapor deposition (LP-CVD). From the scanning electron microscopy (SEM) images, the graphene domains of the sandwiched Cu foil displayed mostly four-lobed, parallel-sided domains which are usually obtained under LP-CVD as compared to Cu foil without sandwiching which showed typical hexagonal graphene domains of AP-CVD. The Raman spectroscopy confirmed that the domains are single-layer graphene. An electron backscatter diffraction (EBSD) showed that the Cu foil is predominantly (001). The results of this study agree with the theoretical predictions of growth kinetics in graphene synthesis by CVD and showed that it is possible to obtain single-layer graphene domains which are usually obtained under LP-CVD by restricting the gas flux through the boundary layer.Graphic abstract

Kinetics of domain growth in Ising systems with bond disorder at regularly selected sites

We study the structure, phase behaviour and growth laws in Ising ferromagnets and binary mixtures with bond disorder introduced at regularly selected sites for a critical quench. The results presented here are from extensive Monte Carlo simulations on two-dimensional Ising systems. Domain growth in a ferromagnet is modelled by using nonconserved spin-flip (Glauber) kinetics, and phase separation in a binary (AB) mixture is modelled by conserved spin-exchange (Kawasaki) kinetics. In both cases, we observed that the domain growth law is consistent with the respective power-law growth with the variable growth exponent that depends on the number of disordered sites. The nonconserved Ising system follows dynamical scaling for all the number of disordered sites studied here; however, a small deviation is noticed for $$r\rightarrow 0$$ at a large number of disordered sites. Whereas, for the conserved case, dynamical scaling deviates from the master curve after a reasonable number of disordered lattice sites; we notice the formation of lamellar evolution morphology at a higher number of disordered sites at later times.

Effect of hydrogen concentration on CVD synthesis of graphene

The paper is devoted to the study of AP-CVD synthesis of graphene on a copper substrate. In this work, the effect of hydrogen concentration in the synthesis gas mixture on the growth of a graphene coating is studied experimentally. Two series of experiments with methane concentrations of 0.02% and 0.05% are presented. It is shown that a change in concentration of hydrogen has a nonmonotonic effect on the degree of substrate covering with graphene. This indicates that hydrogen is involved in several competing processes. One of these processes is stabilization of the edges of growing graphene domains. Another is etching of the forming graphene structures and reduction of hydrocarbon radicals on the copper substrate surface and in the bulk. It is shown that an increase in methane concentration leads to an increase in the rate of graphene crystal growth. To preserve the kinetics of graphene domain growth, it is necessary to reduce the H2/CH4 coefficient in the working mixture.

Effect of surface nature of carbonaceous nanosized fillers on properties of polyurethane based nanocomposites

Polyurethane (PU) composites containing uniformly dispersed nanosized and macrosized carbonaceous fillers (fullerene C60, fullerene soot, detonation nanodiamonds, and nanodiamonds soot) with loadings varying from 0.1 to 0.5 wt.% were prepared by in situ polymerization. The kinetics of PU synthesis catalyzed by dibutyltin dilaurate was studied as a function of amount of nanosized filler. It was found that the reaction is zero-order. The kinetics of the hard domain growth of the PU matrix was studied and described successfully using the two-parameter Avrami model for isothermal crystallization. It was found that the growth of polymers induces athermal primary nucleation for hard domain growth, and that nanosized fillers do not change the nucleation mechanism. Our results show that the mechanical strength of PU composites increases in the presence of all types of nanoparticles under study. This can be related to the antiplasticization effect of the nanoparticles on the polymer matrix. The dielectric spectroscopy demonstrated that Tg values of the composites increase in comparison with neat PU. However, the effects of hydrophilic/hydrophobic properties of nanoparticles on the secondary relaxations are not obvious Microphase separation in these nanocomposites was studied using FTIR spectroscopy, but no effect of surface properties of the nanoadditives on this phenomenon has been observed.

Disordered dipolar solids: Anisotropic growth laws and their slowing-down

We use Monte Carlo simulations to study the kinetics of domain growth in the d = 3 random-field Ising model with dipolar interactions (RFIM+DI). This system models a large class of magnetic and dielectric solids. Our main results are as follows: i) The domains are anisotropic and elongated along the Ising (z) axis. The system exhibits generalized dynamical scaling with two distinct length scales and , where . However, the scaling function is not robust with respect to the disorder Δ. ii) For a fixed value of Δ, the interfaces are fractal with distinct fractal dimensions in the xy-plane and the z-direction. iii) The domain growth laws are also anisotropic, and exhibit distinct power laws on the time-scales of our simulations: and . iv) The exponents and have a simple dependence on Δ. Our results are novel and provide a fresh outlook to interpret experiments in disordered dipolar solids.

Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method.

This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.

Columnar domains and anisotropic growth laws in dipolar systems.

Magnetic and dielectric solids are well-represented by the Ising model with dipolar interactions (IM+DI). The latter are long-ranged, fluctuating in sign, and anisotropic. Equilibrium studies have revealed novel consequences of these complicated interactions, but their effect on nonequilibrium behavior is not explored. We perform a deep temperature quench to study the kinetics of domain growth in the d=3 IM+DI. Our main observations are (i) the emergence of columnar domains along the z axis (Ising axis) with a transient periodicity in the xy plane; (ii) anisotropic growth laws: ℓ_{ρ}(t)∼t^{ϕ}; ℓ_{z}(t)∼t^{ψ}, where ρ[over ⃗]=(x,y) and ℓ is the characteristic length scale; (iii) generalized dynamical scaling for the correlation function: C(ρ,z;t)=g(ρ/ℓ_{ρ},z/ℓ_{z}); and (iv) an asymptotic Porod tail in the corresponding structure factor: S(k_{ρ},0;t)∼k_{ρ}^{-3}; S(0,k_{z};t)∼k_{z}^{-2}. Our results explain the experimentally observed columnar morphologies in a wide range of dipolar systems, and they have important technological implications.

Kinetics formation of nanostructure of polyurethanes in the presence of graphene

ABSTRACTThe kinetics of catalyzed by dibutyltin dilaurate reaction of polyurethane (PU) synthesis was studied in dependence of amount of aromatic amine (cuamine A) chain extender and amount of nanosized filler (graphene). It was found that the reaction is zero order. The addition of graphene in the reaction system did not change this kinetics. Our data show that the reaction rate decreases with increasing amount of chain extender and graphene. The mechanical performance of PU increases with the increase of hard segment contains and values of the degree of the phase separation. The value of the degree of the phase separation is dominated factor influenced on mechanical properties. The introduction of graphene blocks the PU phase separation and, therefore, leads to fall in mechanical properties. The kinetics of the hard domain growth of the PU matrix was studied and successfully described using the two-parameter Avrami model for isothermal crystallization. The growth of polymers induces a thermal primary nucleation for hard domain growth. It is shown that nanosized graphene does not change the nucleation mechanism.

Growth kinetics of induced domains in Ba0.8Sr0.2TiO3 ferroelectric thin films

The possibility of the formation of stable domain states in Ba0.8Sr0.2TiO3 films on the initial surface and in a preliminarily polarized region of the film has been demonstrated using piezoresponse force microscopy. The velocity of lateral motion of a domain wall, coercive field, minimal domain size, and recording time for the domain formation under the applied voltage have been calculated.

Blockage of domain growth by nanoscale heterogeneities in a relaxor ferroelectric Sr0.61Ba0.39Nb2O6

The growth of localized subsurface domains in a relaxor ferroelectric Sr0.61Ba0.39Nb2O6 is studied using the technique of piezoresponse force microscopy (PFM). Ferroelectric domains are created by applying moderate voltages of 10–50 V to the conductive tip of a scanning force microscope brought into contact with a nonpolar face of a Sr0.61Ba0.39Nb2O6 crystal. PFM images of written domains are acquired and analyzed quantitatively to determine the domain length along the polar axis and its width in the transverse direction. The dependences of domain sizes on the applied voltage, pulse duration, and the time passed after completion of the voltage pulse are reported and analyzed theoretically. It is shown that the observed kinetics of domain growth can be explained by the creep of domain boundaries occurring in the presence of random electric fields inherent in Sr0.61Ba0.39Nb2O6. The comparison of measured domain sizes with their equilibrium values calculated with the aid of the thermodynamic theory demonstrates that the growth of subsurface domains in Sr0.61Ba0.39Nb2O6 is blocked by nanoscale heterogeneities characteristic of this relaxor ferroelectric. These results may have important implications for the development of nonlinear optical devices based on nanoheterogeneous ferroelectrics.