Ostwald Ripening of Concentrated Alkane Emulsions: A preliminary report

Fiber optic dynamic light scattering (FODLS) was used to study the kinetics of aging processes in emulsions of n-alkanes stabilized by a surfactant. The method is particularly useful for this purpose because it permits measurements in concentrated emulsions. Complications that may occur in traditional DLS due to the extreme dilution, such as solubilization of the particles in the medium, can be easily avoided in this way. The experimental results show that the main aging process is Ostwald ripening. The results are in agreement with theoretical predictions based on the Lifshitz-Slyozov-Wagner (LSW) theory as far as it concerns the relation between the molecular solubility of the n-alkanes (in the aqueous phase) and the Ostwald ripening rate. This illustrates that the main rate-determining factor is the molecular diffusion of the alkane molecules through the continuous (aqueous) phase. The Ostwald ripening rate is affected by the concentration of surfactant but in all situations is higher than expected from LSW theory.     

The theory of Ostwald ripening

Developments in the theory of Ostwald ripening since the classic work of I. M. Lifshitz and V. V. Slyozov (LS) are reviewed and directions for future work are suggested. Recent theoretical work on the role of a finite volume fraction of coarsening phase on the ripening behavior of two-phase systems is reformulated in terms of a consistent set of notation through which each of the theories can be compared and contrasted. Although more theoretical work is necessary, these theories are in general agreement on the effects of a finite volume fraction of coarsening phase on the coarsening behavior of two-phase systems. New work on transient Ostwald ripening is presented which illustrates the broad range of behavior which is possible in this regime. The conditions responsible for the presence of the asymptotic state first discovered by LS, as well as the manner in which this state is approached, are also discussed. The role of elastic fields during Ostwald ripening in solid-solid mixtures is reviewed, and it is shown that these fields can play a dominant role in determining the coarsening behavior of a solid-solid system.     

Ostwald ripening, chiral crystallization, and the common-ancestor effect

We introduce an agent-based model for advection-mediated chiral autocatalysis in which we take into account dissolution-crystallization processes through Ostwald ripening. We demonstrate that the latter phenomenon is the key to explaining previously puzzling experimental results whereby complete chiral symmetry breaking is attained from an initially unbiased mixture of seed crystals. We show that this homochirality is achieved by what has been termed the common-ancestor effect: Ostwald ripening removes competing lineages, leaving only one common ancestor for the entire system.     

Ostwald ripening of beta-carotene nanoparticles

Ostwald ripening, the interfacial-energy-driven dissolution and reprecipitation of solutes, becomes an increasingly significant problem for nanoparticle formulations. We present the first quantitative study of Ostwald ripening for nanoparticle dispersions. The Lifshitz-Slyozov-Wagner (LSW) theory of particle growth driven by diffusion is applied to study beta-carotene nanoparticles with sizes of O(100 nm) formed by our block-copolymer protected Flash Nanoprecipitation process. A numerical implementation of the LSW theory that accounts for the original particle size distribution is presented. The predicted particle sizes from the numerical simulation are compared with the experimental results measured by dynamical light scattering. The results show quantitative agreement with no adjustable parameters. The addition of antisolvent results in the reduction of the ripening rate by dramatically decreasing bulk solubility.     

Mechanisms of heteroepitaxial growth of cadmium telluride thin films in a thermal field of a temperature gradient

The processes of forming cadmium telluride films upon vapor-phase deposition onto a substrate in a thermal field of the temperature gradient along the substrate plane are studied. The results of technological, geometric, electron diffraction, and electron microscopic investigations are reported. It is found that the thermal field of temperature gradient leads to a change in the duration of the Ostwald ripening stage and, under certain conditions, enhances the perfection of the formed structure. The mechanism of the influence of a thermal field on the Ostwald ripening is established. The results obtained are in agreement with the current theory of film formation.     

X-ray-assisted formation of gold nanoparticles in soda lime silicate glass: suppressed Ostwald ripening

The in situ formation of gold nanoparticles in soda lime silicate glass under constant x-ray irradiation is compared with the ex situ formation in preirradiated glasses. The ASAXS measurements confirm that pure Au particles are formed. The comparison shows that the number of particles nucleated under irradiation is about an order of magnitude higher than of those nucleated with preirradiation. The radius, R, remains slightly below 1 nm under in situ conditions and the Ostwald ripening stage is slowed down. Under ex situ conditions Ostwald ripening is clearly observed and R grows up to 3 nm.     

Coarsening of cracks in a uniaxially strained solid

We discuss the stress relaxation in a uniaxially strained solid due to the coarsening of a system of parallel cracks. We emphasize similarities and differences of this process to Ostwald ripening in a first order phase transition. A conventional mean-field approximation breaks down and several independent length scales have to be taken into account. Strong elastic interactions between the cracks determine the growth behavior. We derive scaling laws for the coarsening of the different length scales involved and the time evolution of stress relaxation, finally leading to the equilibrium state of a fractured body. The characteristic size of the cracks grows linearly in time which is much faster than in usual Ostwald ripening.     

Ostwald ripening in rarefied systems

Mass exchange between spherical molecular clusters is analyzed in the case when the mean free path of molecules in the intercluster space is much larger than the cluster sizes but much smaller than average intercluster separation. It is shown that there is a steady-state regime when big clusters grow at the expense of the smaller ones (Ostwald ripening), which is characterized by a one-parametric family of self-similar cluster size distribution functions and by an exponentially growing average cluster size. The obtained self-similar cluster size distributions are entirely different from those given by the classical theory of Ostwald ripening. Implications of the obtained results are discussed.     

Ostwald ripening of charged supported metal nanoparticles: Schottky model

Due to high surface area, supported metal nanoparticles are thermodynamically prone to sintering. The experimental studies of this process exhibit sometimes transient bimodal particle size distributions. Such observations may result from the support heterogeneity. Looking retrospectively, one can also find the prediction that in the case of Ostwald ripening this feature can be related to charge of metal nanoparticles. In real systems, this charge is often associated with the metal–support interaction and can be interpreted in the framework of the Schottky model. Using this model, the author shows that the charge redistribution cannot be behind bimodal particle size distributions. Moreover, the corresponding contribution to the driving force for Ostwald ripening is typically much smaller than the conventional one.     

Digestive Ripening,Nanophase Segregation and Superlattice Formation in Gold Nanocrystal Colloids

A novel digestive ripening process is shown to narrow the particle size distribution from a highly polydisperse dodecanethiol ligated gold colloid. Unlike the Ostwald ripening process, the digestion occurs through transferring materials from large particles to small particles. Temperature-induced size segregation can further select the particle sizes. By using these two methods, highly ordered superlattices using nanocrystals as building blocks can be synthesized directly from a polydisperse colloid.     

Kinetic frustration of Ostwald ripening in Ge/Si(100) hut ensembles

We show that low area density Ge/Si(100) island ensembles comprised solely of hut and pyramid clusters do not undergo Ostwald ripening during days-long growth temperature anneals. In contrast, a very low density of large, low chemical potential Ge islands reduce the supersaturation causing the huts and pyramids to ripen. By assuming that huts lengthen by adding single {105} planes that grow from apex-to-base, we use a mean-field facet nucleation model to interpret these experimental observations. We find that each newly completed plane replenishes the nucleation site at the hut apex and depletes the Ge supersaturation by a fixed amount. This provides a feedback mechanism that reduces the island growth rate. As long as the supersaturation remains high enough to support nucleation of additional planes on the narrowest hut cluster, Ostwald ripening is suppressed on an experimental time scale.     

Collapse of islands in freely suspended smectic nanofilms

A time-nonlinear stage of the collapse of islands in freely suspended smectic nanofilms is observed and investigated. Islands thicker than a nanofilm are prepared and studied, which are unstable inside the dislocation loops, since they increase the energy of the film. Such instability leads to the decrease in the size of islands and is terminated by their collapse. The time dependence of the size of islands is measured experimentally. It is shown that the found dependence is in agreement with the theory of the dynamics of dislocation loops in smectic films developed earlier with allowance for the dissipation of energy in the film and in the meniscus. A nontrivial dynamic coupling between islands in a film resembling Ostwald ripening is also found, though the nonequilibrium kinetics of unstable islands, at which the hydrodynamic flow through a film leads to the decrease in sizes of one island and the increase in those of the other, rather than of the growth of the nucleation centers in the thermodynamically stable phase from the metastable state of the system (described by the Lifshitz–Slezov theory in films), is studied in our experiments.     

Metastable precipitation kinetics in NaCl:Pb2+ crystals at room temperature

The RT precipitation kinetics have been studied for the metastable phase in NaCl:Pb²⁺ crystals by precise density measurements. The results obtained seem to be unaccountable in terms of the diffusion-controlled growth of constant or increasing number of particles. The observed process is concluded to be a coalescence (Ostwald ripening). At the late stage the experimental data fit the $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ law for solute depletion predicted by the asymptotic coalescence theory of Lifshitz and Slezov. A diffusion coefficient of Pb²⁺ in the NaCl lattice and the particle size have been estimated by using the theory.     

偏晶合金液-液相分离的格子玻尔兹曼方法模拟

本文建立了一个模拟在弥散相液滴的扩散长大、碰撞凝并和Ostwald熟化等因素的作用下偏晶合金液-液相分离过程的二维格子玻尔兹曼方法 (lattice Boltzmann method, LBM) 模型.该模型结合了Shan-Chen的两相流模型和Qin的介观粒子相互作用势模型的优点,并在LB演化方程中引入了反映相变的源项.应用该模型模拟研究了偏晶合金液-液相分离过程中单液滴的生长、两液滴的合并和多液滴的生长规律.结果表明在两液相区中第二相单个液滴的生长是一个通过扩散从非平衡态到平衡态过渡的过程.两液滴合并 关键词： 偏晶合金 液-液相分离 格子玻尔兹曼方法     

Evolution of the heterogeneous structure of model sodium silicate glasses during binodal decomposition: X-ray small-angle scattering investigation

The kinetics of binodal decomposition in model glasses of the Na₂O-SiO₂ system from the initial stage to the stage of the Ostwald ripening inclusive has been investigated in situ. It has been found that the spatial-temporal evolution of the heterogeneous structure during binodal decomposition has a multistage character. The characteristic size of the phase regions at each stage of the binodal decomposition varies with time according to the power law L ～ t ^β. The values of exponents β for different stages of the binodal decomposition are as follows: 1/20 (fluctuation stage), 1/2 (growth stage), 0 (transient stage), and 1/3 (Ostwald ripening stage). The particle size distributions for all stages of the binodal decomposition have been presented.     

Coarsening and self-organization in dilute diblock copolymer melts and mixtures

This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns.We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.     

Novel SiGe island coarsening kinetics: ostwald ripening and elastic interactions

Real-time light scattering measurements of coherent island coarsening during SiGe/Si heteroepitaxy reveal unusual kinetics. In particular, the mean island volume increases superlinearly with time, while the areal density of islands decreases at a faster-than-linear rate. Neither observation is consistent with standard considerations of Ostwald ripening. Modification of the standard theory to incorporate the effect of elastic interactions in the growing island array reproduces the observed behavior.     

Surface Modification of Silver Iodide Films by Electron Irradiation

It has been found experimentally that electron irradiation of polycrystalline AgI films leads to the formation of a nanocrystalline silver particle monolayer. With an increase in the irradiation time, the nanoparticle size grows but the concentration of the particles first increases and then drops. Formation mechanisms of the nanoparticles and the dynamics of their growth have been considered. Ostwald’s ripening, fieldinduced migration, and nanoparticle charge variation during irradiation by low-energy electrons have been shown to be the main processes responsible for the above effects.     

1D Cahn-Hilliard dynamics: Ostwald ripening and application to modulated phase systems

We use a family of stationary solution of the Cahn-Hilliard dynamics in order to describe the coalescence during a first order phase transition. With this analytical ansatz, we compute the characteristic time for one step of period doubling in Langer's self similar scenario for Ostwald ripening. As an application, the same ansatz is also used to compute the thermodynamically stable period of a 1D modulated phase pattern, described by a Cahn-Hilliard dynamics with long range interaction terms.