Stability of nanoparticles in solution: A statistical description of crystallization as a finite particle size effect in a lattice-gas model

Schmid, R.; Nielaba, Peter

doi:10.1063/1.5063665

Cited by 10 publications

(9 citation statements)

References 37 publications

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“…14 for the FES for TSN in a form that can be directly compared with simulation results for the FES obtained in terms of n and x. These order parameters have been chosen in previous studies of the FES for TSN 29,37 including Ref. 36.…”

Section: Theory For the Free Energy Surfacementioning

confidence: 99%

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Free energy surface of two-step nucleation

Eaton,

Saika-Voivod,

Bowles

et al. 2021

Preprint

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We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] by comparing the predictions of the theory to numerical results for the FES recently reported from Monte Carlo simulations of TSN in a simple lattice system [James, et al., J. Chem. Phys. 150, 074501 (2019)]. No adjustable parameters are used to make this comparison. That is, all the parameters of the theory are evaluated directly for the model system, yielding a predicted FES which we then compare to the FES obtained from simulations. We find that the theoretical FES successfully predicts the numerically-evaluated FES over a range of thermodynamic conditions that spans distinct regimes of behavior associated with TSN. All the qualitative features of the FES are captured by the theory and the quantitative comparison is also very good. Our results demonstrate that Iwamatsu's extension of classical nucleation theory provides an excellent framework for understanding the thermodynamics of TSN.

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Section: Theory For the Free Energy Surfacementioning

confidence: 99%

“…In the second step, the stable phase appears and grows from within the finite cluster of the intermediate phase. TSN has been identified and studied in a growing range of systems, both in experiments 11,13,16,[21][22][23][24][25][26][27][28] and simulations 16,[29][30][31][32][33][34][35][36][37][38][39][40][41] .…”

Section: Introductionmentioning

confidence: 99%

Free energy surface of two-step nucleation

Eaton,

Saika-Voivod,

Bowles

et al. 2021

Preprint

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“…This problem was addressed to some extent by selectively grouping CVs 51 . The method has been applied to a wide spectrum of complex chemical and biological problems; See references 52–60; see also references 39, 61. Several other attempts to improve the sampling using a MTD‐like bias have also been proposed lately 25,49,62–64 …”

Section: Introductionmentioning

confidence: 99%

Exploration of high dimensional free energy landscapes by a combination of temperature‐accelerated sliced sampling and parallel biasing

et al. 2022

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Temperature‐accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high‐dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide‐and‐conquer strategy for computing high‐dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated‐temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low‐dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high‐dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four‐dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight‐dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four‐dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β‐lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high‐dimensional free energy landscapes.

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“…We base this work on a past study 14 of the free energy of crystallization. With a lattice gas, we calculate a phase diagram of two-step nucleation of a confined system.…”

Section: Introductionmentioning

confidence: 99%

Two-step nucleation in confined geometry: Phase diagram of finite particles on a lattice gas model

Holder

Schmid

Nielaba

2022

The Journal of Chemical Physics

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We use a degenerated Ising model to describe nucleation and crystallization from solution in a confined two-component system. The free energy is calculated using metadynamics simulation with coordination numbers as the reaction coordinates. We deploy nudged elastic band simulation to determine the minimum energy path and give properties of the crystallization path. In this confined system, depletion effects, which could also be caused by slow material transport in the solution, prevent the post-critical cluster from further growth, and the crystalline state would only be stable at larger cluster sizes. Fluctuation of the higher coupling strength of the crystalline state enables further growth until the crystalline cluster is in equilibrium with the solvent, and this way, a second barrier is crossed. From the parameters and setup, we find necessary conditions for the occurrence of two-step nucleation in our system. These findings can be adapted to real systems as biomineralization, colloidal crystallization, and the solidification of metals.

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Stability of nanoparticles in solution: A statistical description of crystallization as a finite particle size effect in a lattice-gas model

Cited by 10 publications

References 37 publications

Free energy surface of two-step nucleation

Free energy surface of two-step nucleation

Exploration of high dimensional free energy landscapes by a combination of temperature‐accelerated sliced sampling and parallel biasing

Two-step nucleation in confined geometry: Phase diagram of finite particles on a lattice gas model

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