A two-parameter extension of classical nucleation theory

Sulfate mineral scaling: From fundamental mechanisms to control strategies

Sulfate scaling, as insoluble inorganic sulfate deposits, can cause serious operational problems in various industries, such as blockage of membrane pores and subsurface media and impairment of equipment functionality. There is limited article to bridge sulfate formation mechanisms with field scaling control practice. This article reviews the molecular-level interfacial reactions and thermodynamic basis controlling homogeneous and heterogeneous sulfate mineral nucleation and growth through classical and non-classical pathways. Common sulfate scaling control strategies were also reviewed, including pretreatment, chemical inhibition and surface modification. Furthermore, efforts were made to link the fundamental theories with industrial scale control practices. Effects of common inhibitors on different steps of sulfate formation pathways (i.e., ion pair and cluster formation, nucleation, and growth) were thoroughly discussed. Surface modifications to industrial facilities and membrane units were clarified as controlling either the deposition of homogeneous precipitates or the heterogeneous nucleation. Future research directions in terms of optimizing sulfate chemical inhibitor design and improving surface modifications are also discussed. This article aims to keep the readers abreast of the latest development in mechanistic understanding and control strategies of sulfate scale formation and to bridge knowledge developed in interfacial chemistry with engineering practice.

Semiflexible oligomers crystallize via a cooperative phase transition

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Long-wavelength density fluctuations as nucleation precursors

Recent theories of nucleation that go beyond classical nucleation theory predict that diffusion-limited nucleation of both liquid droplets and of crystals from a low-density vapor (or weak solution) begins with long-wavelength density fluctuations. This means that in the early stages of nucleation, "clusters" can have low density but large spatial extent, which is at odds with the classical picture of arbitrarily small clusters of the condensed phase. We present the results of kinetic Monte Carlo simulations using forward flux sampling to show that these predictions are confirmed, namely, that on average, nucleation begins in the presence of low-amplitude, but spatially extended density fluctuations thus confirming a significant prediction of the nonclassical theory.

Microcanonical Nucleation Theory for Anisotropic Materials Validated on Alumina Clusters

Nucleation kinetics in gas phase remains an open issue with no general model. The derivation of the reaction constants assuming a canonical ensemble fails to describe anisotropic materials such as oxides. We have developed a general and versatile model using activated complex kinetics with a microcanonical approach. This approach handles the kinetics issue in cluster growth when the transient nature of the processes hinders the use of the canonical ensemble. The model efficiently reproduces experimental size distributions of alumina clusters formed by laser ablation with different buffer gas densities, including magic numbers. We show that the thermodynamic equilibrium is not reached during the growth. The bounding energy measured is 10 times lower than the one deduced from DFT calculation, but also the one expected from the bulk cohesive energy.

Diamond growth from organic compounds in hydrous fluids deep within the Earth

At subduction zones, most diamonds form by carbon saturation in hydrous fluids released from lithospheric plates on equilibration with mantle rocks. Although organic molecules are predicted among dissolved species which are the source for carbon in diamonds, their occurrence is not demonstrated in nature, and the physical model for crustal diamond formation is debated. Here, using Raman microspectroscopy, I determine the structure of carbon-based phases inside fluid inclusions in diamond-bearing rocks from the Alps. The results provide direct evidence that diamond surfaces are coated by sp²-, and sp³-bonded amorphous carbon and functional groups of carboxylic acids (e.g., carboxyl, carboxylate, methyl, and methylene), indicating the geosynthesis of organic compounds in deep hydrous fluids. Moreover, this study suggests diamond nucleation via metastable molecular precursors. As a possible scenario, with carbon saturation by reduction of carboxylate groups, I consider tetrahedral H-terminated C groups as templates for the growth of sp³-structured carbon.

Diamonds can give us clues to the processes regulating deep carbon transport within the Earth. Here, the author discovers evidence from diamond coatings that organic compounds exist at great depth in Earth’s interior, and furthermore, that organic molecules may provide scaffolds for diamond nucleation and growth.

How crystals form: A theory of nucleation pathways

Recent advances in classical density functional theory are combined with stochastic process theory and rare event techniques to formulate a theoretical description of nucleation, including crystallization, that can predict nonclassical nucleation pathways based on no input other than the interaction potential of the particles making up the system. The theory is formulated directly in terms of the density field, thus forgoing the need to define collective variables. It is illustrated by application to diffusion-limited nucleation of macromolecules in solution for both liquid-liquid separation and crystallization. Both involve nonclassical pathways with crystallization, in particular, proceeding by a two-step mechanism consisting of the formation of a dense-solution droplet followed by ordering originating at the core of the droplet. Furthermore, during the ordering, the free-energy surface shows shallow minima associated with the freezing of liquid into solid shells, which may shed light on the widely observed metastability of nanoscale clusters.

Experimental measurement of the diamond nucleation landscape reveals classical and nonclassical features

Nucleation is a core scientific concept that describes the formation of new phases and materials. While classical nucleation theory is applied across wide-ranging fields, nucleation energy landscapes have never been directly measured at the atomic level, and experiments suggest that nucleation rates often greatly exceed the predictions of classical nucleation theory. Multistep nucleation via metastable states could explain unexpectedly rapid nucleation in many contexts, yet experimental energy landscapes supporting such mechanisms are scarce, particularly at nanoscale dimensions. In this work, we measured the nucleation energy landscape of diamond during chemical vapor deposition, using a series of diamondoid molecules as atomically defined protonuclei. We find that 26-carbon atom clusters, which do not contain a single bulk atom, are postcritical nuclei and measure the nucleation barrier to be more than four orders of magnitude smaller than prior bulk estimations. These data support both classical and nonclassical concepts for multistep nucleation and growth during the gas-phase synthesis of diamond and other semiconductors. More broadly, these measurements provide experimental evidence that agrees with recent conceptual proposals of multistep nucleation pathways with metastable molecular precursors in diverse processes, ranging from cloud formation to protein crystallization, and nanoparticle synthesis.

Microscopic aspects of wetting using classical density functional theory

Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions brings about an entire 'zoo' of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid-gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid-gas interface is already highly complex and non-trivial.

Classical density functional theory, unconstrained crystallization, and polymorphic behavior

While in principle, classical density functional theory (cDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have plagued the study of the crystalline systems using the most sophisticated fundamental measure theory models. In this paper, the reasons for the difficulties are examined and it is proposed that the tensor functionals currently favored are in fact numerically unstable. By reverting to an older, more heuristic model it is shown that all of the technical difficulties are eliminated. Application to a Lennard-Jones fluid results in a demonstration of power of cDFT to describe crystallization in a highly inhomogeneous system. First, we show that droplets attached to a slightly hydrophobic wall crystallize spontaneously upon being quenched. The resulting crystallites are clearly faceted structures and are predominantly HCP structures. In contrast, droplets in a fully periodic calculational cell remain stable to lower temperatures and eventually show the same spontaneous localization of the density into "atoms" but in an amorphous structure having many of the structural characteristics of a glass. A small change of the protocol leads, at the same temperature, to the formation of crystals, this time with the fcc structure typical of bulk Lennard-Jones solids. The fcc crystals have lower free energy than the amorphous structures which in turn are more stable than the liquid droplets. It is demonstrated that as the temperature is raised, the free energy differences between the structures decrease until the solid clusters become less stable than the liquid droplets and spontaneously melt. The presence of energy barriers separating the various structures is therefore clearly demonstrated.

Classical nucleation theory in the phase-field crystal model

A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

Classical density functional study of wetting transitions on nanopatterned surfaces

Even simple fluids on simple substrates can exhibit very rich surface phase behaviour. To illustrate this, we consider fluid adsorption on a planar wall chemically patterned with a deep stripe of a different material. In this system, two phase transitions compete: unbending and pre-wetting. Using microscopic density-functional theory, we show that, for thin stripes, the lines of these two phase transitions may merge, leading to a new two-dimensional-like wetting transition occurring along the walls. The influence of intermolecular forces and interfacial fluctuations on this phase transition and at complete pre-wetting are considered in detail.