A two-parameter extension of classical nucleation theory

Lutsko, James F.; Durán-Olivencia, Miguel A.

doi:10.1088/0953-8984/27/23/235101

Cited by 33 publications

(60 citation statements)

References 51 publications

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“…, the saddle point of the energy barrier), perturbing slightly along the unstable direction and integrating the deterministic parts of the governing equations for R and ρ 0 (see figure A1). This yields the curve Γ, red solid line in figure 2 [47]. As can be observed, the MLP does not follow the Cartesian gradient of the free-energy, i.e.…”

Section: Resultsmentioning

confidence: 79%

“…The nucleation rate is commonly characterized by the MFPT, the inverse of which is assumed proportional to the nucleation rate. However, in general, there is no exact expression for the MFPT for more than one-parameter, but an approximation only valid in the WNL [47,[54][55][56]. The main advantage of the most-likely approach adopted here is that the nucleation process is entirely described in terms of only one-parameter, the arc-length.…”

Section: Nucleation Rate and Timementioning

confidence: 99%

“…Therefore, describing the evolution of a single density fluctuation using FH would provide an alternative theory of nucleation. A decisive first step in this direction was the recent mesoscopic nucleation theory (MeNT) put forward in [45][46][47][48]. In MeNT the number of parameters (so-called order parameters) we may choose to effectively describe a nucleation cluster is free.…”

Section: Introductionmentioning

confidence: 99%

“…However, the rising complexity of such multi-parameter models means that exact expressions for observables, such as nucleation rate and cluster distribution, do not necessarily exist, even for the vanilla two-parameter model accounting for changes in the size and inner density of the cluster (the first necessary step towards a nonCNT). Under the MeNT picture, such observable quantities are approximated by utilizing the concepts of mean first-passage time (MFPT) and the equilibrium distribution derived from the corresponding Fokker-Planck equation, respectively [45][46][47][48]. Nevertheless, beyond the simplest one-parameter model, these approximations also rise in complexity, which might be an important factor that has hindered the applicability of MeNT so far.…”

Section: Introductionmentioning

confidence: 99%

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General framework for nonclassical nucleation

et al. 2018

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A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new theoretical tools to explain the occurrence and nature of these ubiquitous intermediate phases. Here we outline a unified and self-consistent theoretical framework to describe both classical and nonclassical nucleation. Our framework provides a detailed explanation of the whole multistage nucleation pathway showing in particular that the pathway involves a single energy barrier and it passes through a dense phase, starting from a lowdensity initial phase, before reaching the final stable state. Moreover, we demonstrate that the kinetics of matter inside subcritical clusters favors the formation of nucleation clusters with an intermediate density, i.e. nucleation precursors. Remarkably, these nucleation precursors are not associated with a local minimum of the thermodynamic potential, as commonly assumed in previous phenomenological approaches. On the contrary, we find that they emerge due to the competition between thermodynamics and kinetics of cluster formation. Thus, the mechanism uncovered for the formation of intermediate phases can be used to explain recently reported experimental findings in crystallization: up to now such phases were assumed a consequence of some complex energy landscape with multiple energy minima. Using fundamental concepts from kinetics and thermodynamics, we provide a satisfactory explanation for the so-called nonclassical nucleation pathways observed in experiments.

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Section: Resultsmentioning

confidence: 79%

Section: Nucleation Rate and Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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General framework for nonclassical nucleation

et al. 2018

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“…Also this assumption has been shown to fail to capture the dynamics of the transition, especially in simulation works where different reaction coordinates can be followed during nucleation [26][27][28][29][30][31]. Also recent theoretical investigations are focusing on the extension of classical nucleation theory to more than one dimension [32,33].…”

Section: Beyond Cntmentioning

confidence: 99%

Nonclassical pathways of crystallization in colloidal systems

Russo

Tanaka

2016

MRS Bull.

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Colloidal systems offer the ideal conditions to study the nucleation process, both from an experimental viewpoint, due to their relative large size and long time-scales, and from a modeling point of view, due to the tunability of their interactions. Here we review some recent works that study the process of colloidal crystallization from a microscopic perspective. We focus in particular on non-classical pathways to nucleation where the appearance of the solid crystals involves fluctuations of two (or more) order parameters. We interpret the non-classical behavior as a decoupling of positional and orientational symmetry breaking. We then consider how the nucleation pathway determines which polymorph is selected upon nucleation from the melt. Moreover we show how the study of nucleation pathways not only sheds new light on the microscopic mechanism of nucleation, but also provides important information regarding its avoidance, thus suggesting a deep link between crystallization and vitrification.

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Molecular simulation approaches to study crystal nucleation from solutions: Theoretical considerations and computational challenges

Finney,

Salvalaglio

2023

WIREs Comput Mol Sci

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Nucleation is the initial step in the formation of crystalline materials from solutions. Various factors, such as environmental conditions, composition, and external fields, can influence its outcomes and rates. Indeed, controlling this rate‐determining step toward phase separation is critical, as it can significantly impact the resulting material's structure and properties. Atomistic simulations can be exploited to gain insight into nucleation mechanisms—an aspect difficult to ascertain in experiments—and estimate nucleation rates. However, the microscopic nature of simulations can influence the phase behavior of nucleating solutions when compared to macroscale counterparts. An additional challenge arises from the inadequate timescales accessible to standard molecular simulations to simulate nucleation directly; this is due to the inherent rareness of nucleation events, which may be apparent in silico at even high supersaturations. In recent decades, molecular simulation methods have emerged to circumvent length‐ and timescale limitations. However, it is not always clear which simulation method is most suitable to study crystal nucleation from solution. This review surveys recent advances in this field, shedding light on typical nucleation mechanisms and the appropriateness of various simulation techniques for their study. Our goal is to provide a deeper understanding of the complexities associated with modeling crystal nucleation from solution and identify areas for further research. This review targets researchers across various scientific domains, including materials science, chemistry, physics and engineering, and aims to foster collaborative efforts to develop new strategies to understand and control nucleation.This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Molecular and Statistical Mechanics > Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics

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A two-parameter extension of classical nucleation theory

Cited by 33 publications

References 51 publications

General framework for nonclassical nucleation

General framework for nonclassical nucleation

Nonclassical pathways of crystallization in colloidal systems

Molecular simulation approaches to study crystal nucleation from solutions: Theoretical considerations and computational challenges

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