Heterogeneous Nucleation Theory Research Articles

PHYSICAL AND CHEMICAL ANALYSIS OF PRACTICE MODIFYING ABILITY OF BARIUM-STRONTIUM CARBONATE BSK-2 IN CAST IRON MANUFACTURING

The absence of unambiguous interpretation of experimental data on the modifi cation of metals and alloys makes it relevant to search and prove hypotheses beyond the classical physical and chemical approach. The paper presents a quantum-mechanical theory of modifying infl uence of substances, in particular the oxides BaO, SrO, CaO in the composition of natural modifi er BSK-2 to metal properties, to complement the classical theory of heterogeneous nucleation of solids. The uniform nature of the modifying infl uence of substances, vibration and ultrasound on the molten metal is connected with the occurrence of the Friedel oscillations. The physics of the contact potential difference shows characteristics of the nucleation process in metal melts. The modifying ability of ultrafi ne inclusions is explained by the theory of free electrons.

Thermokinetics of heterogeneous droplet nucleation on conically textured substrates.

Within the framework of the classical theory of heterogeneous nucleation, a thermokinetic model is developed for line-tension-associated droplet nucleation on conical textures considering growth or shrinkage of the formed cluster due to both interfacial and peripheral monomer exchange and by considering different geometric configurations. Along with the principle of free energy extremization, Katz kinetic approach has been employed to study the effect of substrate conicity and wettability on the thermokinetics of heterogeneous water droplet nucleation. Not only the peripheral tension is found to have a considerable effect on the free energy barrier but also the substrate hydrophobicity and hydrophilicity are observed to switch over their roles between conical crest and trough for different growth rates of the droplet. Besides, the rate of nucleation increases and further promotes nucleation for negative peripheral tension as it diminishes the free energy barrier appreciably. Moreover, nucleation inhibition can be achievable for positive peripheral tension due to the enhancement of the free energy barrier. Analyzing all possible geometric configurations, the hydrophilic narrower conical cavity is found to be the most preferred nucleation site. These findings suggest a physical insight into the context of surface engineering for the promotion or the suppression of nucleation on real or engineered substrates.

Nucleation: The Birth of a New Protein Phase

Nucleation is a process that initiates phase transitions. Since the classical work of Gibbs on nucleation thermodynamics at the end of the nineteenth century, research into nucleation processes has been spread into a huge variety of scientific fields. To date, nucleation has been studied in disciplines ranging from biophysics to cosmology in systems spanning atomic to planetary scales and beyond (1). Proteins in solution are also known historically to form a variety of states and structures through nucleation (2,3).

Modifying effect of BSK-2 barium–strontium carbonate in cast-iron production

Failure to successfully interpret experimental data regarding the modification of metals and alloys suggests the need for nonclassical approaches. A quantum-mechanical theory of the influence of components in BSK-2 modifier (barium–strontium carbonate) on its metallic properties complements the classical theory of heterogeneous nucleation. The uniform influence of materials, vibration, and ultrasound on the metallic melt is associated with the appearance of Friedel oscillations. The nucleation process in the metallic melt is characterized on the basis of the physics of contact potential differences. The modifying effect of ultrasmall inclusions is explained on the basis of free-electron theory.

Orientation relationships and interfaces of the Fe–Zn intermetallic phases in galvannealed CMnSi-TRIP steels

Hot-dip galvannealed coatings of two Mn–Si TRIP steels have been characterized by transmission electron microscopy to study the crystallographic orientation relationships between the α-Fe and Γ1 phases, the Γ1 and Γ2 phases, as well as the Γ2 and δ phases. Both the α-Fe/Γ1 phases and the Γ1/Γ2 phases were found to exhibit a cube-on-cube orientation relationship. The orientation relationship at the Γ2/δ interface was identified to be 112¯0δ//[011]Γ2 and (0002) δ//111¯Γ2. The interfaces of Γ2/δ and Γ1/Γ2 are basically the close-packed plane of each phase. The nucleation of Γ2 phase between the δ and Γ1 phases was discussed by the heterogeneous nucleation theory based on the orientation relationships and the interfaces.

Orientation relationships of Au5Sn/Au interfaces and formation sequence of Au5Sn and AuSn at the Au/Sn interface

The orientation relationships and interfaces between ζ′-Au5Sn and Au have been studied by transmission electron microscopy. Epitaxial Au thin films were grown on the single-crystal NaCl surfaces and Sn was evaporated to form ζ′-Au5Sn. Results showed that on both the (1¯11)Au and (001)Au surfaces the (0001)ζ′ plane is the common interface surface with a common orientation relationship of (1¯100)ζ′//(110)Au, which has a small misfit of 1.9%. The Au atoms have good matches across both interfaces.That δ-AuSn forms before ζ′-Au5Sn in the solid-state Au/Sn interfacial reactions was discussed by heterogeneous nucleation theory. Both phases have good orientation relationships to Au and therefore low interfacial energies. Analysis of the interfaces indicated that the ζ′-Au5Sn/Au interfacial energies should be less than δ-AuSn/Au, which favors the nucleation of ζ′-Au5Sn. However, the energy of formation of δ-AuSn is much larger, about 2.3 times, than that of ζ′-Au5Sn by data from references. Therefore δ-AuSn forms before ζ′-Au5Sn.

Graphene-Induced Oriented Interfacial Microstructures in Single Fiber Polymer Composites.

Interfacial interactions between the polymer and graphene are pivotal in determining the reinforcement efficiency in the graphene-enhanced polymer nanocomposites. Here, we report on the dynamic process of graphene-induced oriented interfacial crystals of isotactic polypropylene (iPP) in the single fiber polymer composites by means of polarized optical microscopy (POM) and scanning electron microscopy (SEM). The graphene fibers are obtained by chemical reduction of graphene oxide fibers, and the latter is produced from the liquid crystalline dispersion of graphene oxide via a wet coagulation route. The lamellar crystals of iPP grow perpendicular to the fiber axis, forming an oriented transcrystalline (TC) interphase surrounding the graphene fiber. Various factors including the diameter of graphene fibers, crystallization temperature, and time are investigated. The dynamic process of polymer transcrystallization surrounding the graphene fiber is studied in the temperature range 124-132 °C. The Lauritzen-Hoffman theory of heterogeneous nucleation is applied to analyze the transcrystallization process, and the fold surface free energy is determined. Study into microstructures demonstrates a cross-hatched lamellar morphology of the TC interphase and the strong interfacial adhesion between the iPP and graphene. Under appropriate conditions, the β-form transcrystals occur whereas the α-form transcrystals are predominant surrounding the graphene fibers.

Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation.

The prevalence of heterogeneous nucleation in nature was explained qualitatively by the classical theory for heterogeneous nucleation established over more than 60 years ago, but the quantitative validity and the key conclusions of the theory have remained unconfirmed. Employing the forward flux sampling method and the coarse-grained water model (mW), we explicitly computed the heterogeneous ice nucleation rates in the supercooled water on a graphitic surface at various temperatures. The independently calculated ice nucleation rates were found to fit well according to the classical theory for heterogeneous nucleation. The fitting procedure further yields the estimate of the potency factor, which measures the ratio of the heterogeneous nucleation barrier to the homogeneous nucleation barrier. Remarkably, the estimated potency factor agrees quantitatively with the volumetric ratio of the critical nuclei between the heterogeneous and homogeneous nucleation. Our numerical study thus provides a strong support to the quantitative power of the theory and allows understanding ice nucleation behaviors under the most relevant freezing conditions.

The orientation relationships and interfaces of Ag3Sn and Ag4Sn on Ag and a discussion of their formation sequence

The orientation relationships and interfacial planes of the ε-Ag3Sn/Ag and ζ-Ag4Sn/Ag interfaces have been studied by transmission electron microscopy. Epitaxial Ag thin films were grown on the NaCl (001) and (111) surfaces and Sn was evaporated at various temperatures or by further annealing to form ε-Ag3Sn and ζ-Ag4Sn. Results showed that both phases have good orientation relationships with Ag on the (111)Ag surface but none on the (001)Ag surface.The energy of formation of ε-Ag3Sn is 1.62 times that of ζ-Ag4Sn. According to the heterogeneous nucleation theory, the critical nucleus size can be significantly reduced by coherent interfaces. The above interfaces results indicate that the interfacial energies of the ζ-Ag4Sn/Ag and ε-Ag3Sn/Ag interfaces are similar. Therefore ε-Ag3Sn should have a smaller critical nucleus size. Consequently ε-Ag3Sn nucleates first and forms before ζ-Ag4Sn in the Ag/Sn interfacial reaction.

Bidirectional impact of undercooling on eutectic structural formation of hypoeutectic grey iron and its physical connotation

Bidirectional impact of the undercooling during eutectic solidification of hypoeutectic grey iron on the number of eutectic cells under different cooling rates and nucleation conditions was studied. The causes of this experimental phenomenon were explained by melt heterogeneous nucleation theory combined with the features of actual measured cooling curves. By deeply revealing the physical connotation of solidification undercooling, the undercooling nature and its impact on the solidification parameters were discussed with a wider view of phase transformation driving force and resistance. This discussion not only gives a reasonable explanation to the specific experimental phenomena in more depth, but also applies to a wide range of analysis.

A unifying model for adsorption and nucleation of vapors on solid surfaces.

Vapor interaction with solid surfaces is traditionally described with adsorption isotherms in the undersaturated regime and with heterogeneous nucleation theory in the supersaturated regime. A class of adsorption isotherms is based on the idea of vapor molecule clustering around so-called active sites. However, as the isotherms do not account for the surface curvature effects of the clusters, they predict an infinitely thick adsorption layer at saturation and do not recognize the existence of the supersaturated regime. The classical heterogeneous nucleation theory also builds on the idea of cluster formation, but describes the interactions between the surface and the cluster with a single parameter, the contact angle, which provides limited information compared with adsorption isotherms. Here, a new model of vapor adsorption on nonporous solid surfaces is derived. The basic assumption is that adsorption proceeds via formation of molecular clusters, modeled as liquid caps. The equilibrium of the individual clusters with the vapor phase is described with the Frenkel-Halsey-Hill (FHH) adsorption theory modified with the Kelvin equation that corrects for the curvature effect on vapor pressure. The new model extends the FHH adsorption isotherm to be applicable both at submonolayer surface coverages and at supersaturated conditions. It shows good agreement with experimental adsorption data from 12 different adsorbent-adsorbate systems. The model predictions are also compared against heterogeneous nucleation data, and they show much better agreement than predictions of the classical heterogeneous nucleation theory.

Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions.

A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θc), obtained from the generalized Young's equation and the stability analysis, is θ∞ < θc < θ' for positive line tension and is θM < θc < θ∞ for negative line tension. θ∞ is the macroscopic contact angle, θ' is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θM is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ∞ and higher values of θc for positive line tension. The combined effect due to the presence of the triple line and the interfacial areas (f(L) + f(S)) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θc(0 < θc < θ∞) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.

ISING MODEL SIMULATIONS AS A TESTBED OF NUCLEATION THEORY

In this short review article we discuss the use of Ising lattice model as a testbed for improvement of theory of both homogeneous and heterogeneous nucleation theory. First we briefly overview the classical nucleation theory (CNT), and two typical simple systems on which simulations are performed - hard spheres, and Ising lattice model. Than we overview some results obtained by this approach and point to possible new directions of research and improvement.

Controlled Deposition of Tin Oxide and Silver Nanoparticles Using Microcontact Printing

This report describes extensive studies of deposition processes involving tin oxide (SnOx) nanoparticles on smooth glass surfaces. We demonstrate the use of smooth films of these nanoparticles as a platform for spatially-selective electroless deposition of silver by soft lithographic stamping. The edge and height roughness of the depositing metallic films are 100 nm and 20 nm, respectively, controlled by the intrinsic size of the nanoparticles. Mixtures of alcohols as capping agents provide further control over the size and shape of nanoparticles clusters. The distribution of cluster heights obtained by atomic force microscopy (AFM) is modeled through a modified heterogeneous nucleation theory as well as Oswald ripening. The thermodynamic modeling of the wetting properties of nanoparticles aggregates provides insight into their mechanism of formation and how their properties might be further exploited in wide-ranging applications.

Molecular dynamics simulation on the wetting characteristic of micro-droplet on surfaces with different free energies

The wetting characteristic of micro-droplets on surfaces with different free energies is crucial to heterogeneous nucleation theory and the growth mechanism of micro-droplets during vapor condensation. In this paper, the spreading processes and wetting characteristics of nanoscale water droplets on various surfaces are explored by molecular dynamics simulation method. The surfaces are constructed from face centered cubic copper-like atoms with different Lennard-Jones potential parameters. The Lennard-Jones interaction energy well-depth of the surface atoms is adjusted to acquire different surface free energies, and the ratio of surface-water interaction energy well-depth to the water-water interaction energy well-depth is defined as the interaction intensity. In the present study, the relationship between interfacial free energies and solid-liquid interaction intensities is evaluated using molecular dynamics simulations. The wetting characteristics of TIP4P/2005 water droplets on surfaces with various free energies are simulated and analyzed as well, using molecular dynamics simulations under an NVT ensemble. Results indicate that the solid-liquid interfacial free energy increases as the solid-liquid interaction intensity increases, with different spreading processes and wetting characteristics achieved for the water droplets on these surfaces. For the surfaces with lower interaction intensities, water cannot spread on the solid surfaces and hydrophobic surfaces are obtained when the interaction intensity ratio between surface atoms and water molecules is lower than 1.6. As the interaction intensity increases, the surface translates from hydrophobic into hydrophilic, and finally into a complete wetting state as the interaction intensity reaches up to 3.5. Due to the limitation of nanoscale dimensions, the forces that exert on droplet surface are non-continuous and asymmetric. As a result, significant fluctuations of liquid-vapor interface and local solid-liquid contact line can be observed for the droplet in nanoscale. The transient contact angle of nano-droplets is also fluctuating within a certain range, which is different from that observed for macro-droplets. From the viewpoint of statistics, an apparent contact angle can be obtained for the droplet on each surface. The contact angle decreases with solid-liquid interaction intensities linearly, which is in accordance with the calculated results of classic Young's theory using the interfacial free energies obtained from molecular dynamics simulations. The fact that an apparent contact angle is already established for a droplet in nanoscale, supporting the capillary assumption that is widely adopted in classic nucleation theory. The fluctuation of liquid-vapor interface and contact angle also provides a qualitative explanation for the discrepancy between experimental nucleation rates and predictions in classic nucleation theory.

Amorphous calcium phosphate phase-mediated crystal nucleation kinetics and pathway.

Generally, a solution nucleation model is used to study biomineralization kinetics. However, we found that the amorphous calcium phosphate (ACP)-mediated hydroxyapatite (HAP) nucleation in simulated body fluids (SBF) had a different profile from the linear relationship between ln J and ln(-2) S (J, nucleation rate; S, supersaturation). This behaviour was alternatively explained by a developed heterogeneous nucleation theory, which indicated that HAP was nucleated at the ACP-solution interface via a polymorph transformation. Based upon this new model, we demonstrated experimentally that the embedded polymer molecules inside ACP were inert on HAP nucleation kinetics; rather, the polymers adsorbed on ACP surface could inhibit HAP nucleation from ACP. It further confirmed the heterogeneous nucleation pathway of HAP on the precursor phase. The present study provides an in-depth understanding of HAP formation for ACP-mediated crystallization.

Controlled calcite nucleation on polarized calcite single crystal substrates in the presence of polyacrylic acid

We studied theoretically and experimentally the effects of the surface electric field generated by polarization and polyacrylic acid (PAA) additives on the heterogeneous nucleation of calcite on the calcite single crystal substrates with (10.4), (10.0) and (00.1) orientations. A set of “in-situ” experiments with optical microscopy was performed to determine the waiting time of CaCO3 nucleation, defined as the time interval between the onset of the diffusion of CO2 and the appearance of the first visible precipitation. Calcite was nucleated on the oriented calcite substrates through diffusion of NH3 and CO2 gas from a solid ammonium carbonate into calcium chloride solutions. A theoretical analysis showed that the surface electric field of the polarized calcite substrate decrease the activation energy for nucleation and consequently promotes nucleation. Experimentally, the surface electric field and PAA addition were found to decrease both contact angles and waiting times, and as a result, promote the heterogeneous nucleation. Combined effect of PAA and surface electric field further reduced contact angles and waiting times regardless of orientation differences of the calcite substrates. The cooperation acts remarkably on N-surface of the respective calcite substrates. The results were explained by the Cassie׳s equation, a classical heterogeneous nucleation theory under a surface electric field, and matching of the charged sites on the PAA chain with the ion arrangement on the calcite substrate.

Nanocalorimetric Characterization of the Heterogeneous Nucleation of Rapidly Solidified Bismuth Droplets Embedded in a Zinc Matrix

In this paper, Zn-10Bi (wt.%) alloy with Bi droplets in size from micro- to nanometers embedded in the Zn matrix was prepared. Nanocalorimetry was used to investigate the melting and solidification behavior of the embedded Bi droplets. In the heating process, two endothermic peaks were observed attributing to the high sensitivity of the nanocalorimeter. One is close to the eutectic temperature of Zn-Bi alloy (527 K), while the other is close to the melting point of bulk Bi (544 K). In the cooling process, the Bi droplets solidify in a wide temperature range. The results demonstrate that the Bi droplets melt at the higher temperature but their solidification demand a larger undercooling. In addition, the nucleation kinetics of rapidly solidified nano-sized Bi droplets was studied based on the hemispherical cap model of heterogeneous nucleation, and the calculated results reveal the validity of classical heterogeneous nucleation theory in nano-scale at relative high cooling rates. In a word, due to the high sensitivity and large controllable cooling rate, nanocalorimetry will be a promising technique to investigate the rapid solidification behavior of embedded nano-sized droplets.

Droplet nucleation on a well-defined hydrophilic-hydrophobic surface of 10 nm order resolution.

Water condensation on a hybrid hydrophilic-hydrophobic surface was investigated to reveal nucleation mechanisms at the microscale. Focused ion beam (FIB) irradiation was used to change the wettability of the hydrophobic surface with 10 nm order spatial resolution. Condensation experiments were conducted using environmental scanning electron microscopy; droplets, with a minimum diameter of 800 nm, lined up on the FIB-irradiated hydrophilic lines. The heterogeneous nucleation theory was extended to consider the water molecules attracted to the hydrophilic area, thereby enabling explanation of the nucleation mechanism under unsaturated conditions. Our results showed that the effective surface coverage of the water molecules on the hydrophilic region was 0.1-1.1 at 0.0 °C and 560 Pa and was dependent on the width of the FIB-irradiated hydrophilic lines and hydrophobic area. The droplet nucleation mechanism unveiled in this work would enable the design of new surfaces with enhanced dropwise condensation heat transfer.

Study on the supercooling degree and nucleation behavior of water-based graphene oxide nanofluids PCM

This article aimed to study the supercooling degree and nucleation behavior of nanofluids phase change material. The nanofluids were prepared by adding small fraction of graphene oxide nanosheets in deionized water without any dispersants. The supercooling degree of nanofluids with different concentrations was tested experimentally. The results show that the supercooling degree can be reduced by 69.1%, and the nucleation was started in advance, shorting the time by 90.7%. Theoretical analysis based on the heterogeneous nucleation theory indicates that ice crystal nucleus cannot grow on the thickness surface of the graphene oxide nanosheet, while it can grow on the top or bottom surface of the nanosheet only when the supercooling degree ΔT and the nanosheets size D meet the formulaD⋅ΔT≥4.2×10−8. Our study implies that graphene oxide nanofluids have the potential to be used as PCMs in cold storage applications because of their low supercooling degree and rapid nucleation behavior.