Reaching One Single and Stable Critical Cluster through Finite-Sized Systems

Grossier, Romain; Veesler, Stéphane

doi:10.1021/cg801165b

Cited by 66 publications

(84 citation statements)

References 30 publications

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“…26. Our final expression is in agreement with those derived by Veesler and coworker (27) for the nucleation of proteins in a droplet as well as with other theoretical results obtained for the description of first-order phase transitions in confined volumes (28)(29)(30). Consider the free energy of a system composed of N c solute molecules in the crystal state, N ℓ solute molecules in solution, and N s solvent molecules.…”

Section: Significancesupporting

confidence: 88%

Molecular-dynamics simulations of urea nucleation from aqueous solution

Salvalaglio

Perego

Giberti

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

161

231

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Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the freeenergy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.T he nucleation of crystals from solution plays an important role in a variety of chemical and engineering processes. However, the very small scale that characterizes the early stages of nucleation makes its experimental study rather challenging. In this regard, molecular simulations play an important role and much work has been devoted to the study of homogeneous nucleation in simple model systems like Lennard-Jones particles or hard spheres (1-3). More recently, growing attention has been paid to the computer simulation of nucleation from solution of organic and inorganic materials (4-11).However, these simulations have to face an important challenge. Nucleation is a typical example of a rare event occurring on a timescale that is much longer than what atomistic simulations can typically afford. The problem is most easily understood if we focus on molecular dynamics (MD), which is the sampling method used here but it plagues other methods as well. In MD, the shortest timescale to be used for a correct integration of the equation of motion is dictated by the fastest atomic motions such as vibrations or rotations. Due to this constraint in the integration step, present MD simulations can reach timescales up to microseconds unless specific hardware, accessible only to few, is used. Even in this case the scale of the accessible times can be stretched only to the milliseconds range, a far cry from the much longer scale of nucleation phenomena.These timescale limitations affect molecular simulations in several other research fields, such as ligand protein binding, protein folding, or slow chemical reactions, to name just a few. To overcome this limit, many enhanced sampling methods have been proposed (12-21). Several of them are based on the application of a suitable external bias potential (12-14) that speeds up configurational sampling and permits free energies to be evaluated and transition rates to be computed (22)(23)(24). Here, we shall use well-tempered (WT) metadynamics to enhance the nucleation...

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Section: Significancesupporting

confidence: 88%

Molecular-dynamics simulations of urea nucleation from aqueous solution

Salvalaglio

Perego

Giberti

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

161

231

View full text Add to dashboard Cite

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“…In contrast, if the system is too small, the maximal cluster size is less than the critical radius and no transition takes place. This indeed agrees with the supersaturation threshold found in previous works devoted to study nucleation at fixed volumes [40][41][42][43][44][45]. Such a system-size-dependent threshold has to be overcome so that the phase transition can take place.…”

Section: Introductionsupporting

confidence: 89%

Mesoscopic nucleation theory for confined systems: A one-parameter model

Durán-Olivencia

Lutsko

2015

Phys. Rev. E

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Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J. F. Lutsko and M. A. Durán-Olivencia, Classical nucleation theory from a dynamical approach to nucleation, J. Chem. Phys. 138, 244908 (2013).]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nucleation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.

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“…-A thermodynamic limitation appears because the critical size and energy barrier required for nucleation increase when the crystallization volume decreases [56]. When the volume decreases, the concentration in solution can no longer be considered constant during the nucleation process but is decreasing.…”

Section: Influence Of Volume On Nucleationmentioning

confidence: 99%

“…Hence the critical supersaturation, where no nucleation can occur, increases with confinement (Fig. 11), widening the metastable zone [13,56]. Thus "scale-down" requires creation of sufficient supersaturation within each droplet to ensure nucleation, with a risk of unwanted nucleation before droplet formation.…”

Section: Influence Of Volume On Nucleationmentioning

confidence: 99%

“…11 Critical supersaturation (below which no nucleation can occur) vs droplet size, the red curve for a single nucleation event and the blue curve for a second event: (a) for lysozyme in NaCl solution [56]; (b) for NaCl [13]. To summarize, two effects occur depending on droplet volume: 1) for nL range droplets, a kinetic effect increases the induction time; 2) for pL-fL range droplets, the same kinetic effect is accompanied by a thermodynamic effect.…”

Section: Influence Of Volume On Nucleationmentioning

confidence: 99%

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