1
|
Sanchez-Burgos I, Muniz MC, Espinosa JR, Panagiotopoulos AZ. A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water. J Chem Phys 2023; 158:2889532. [PMID: 37158636 DOI: 10.1063/5.0144500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 03/30/2023] [Indexed: 05/10/2023] Open
Abstract
Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.
Collapse
Affiliation(s)
- Ignacio Sanchez-Burgos
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue,Cambridge CB3 0HE, United Kingdom
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Maria Carolina Muniz
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue,Cambridge CB3 0HE, United Kingdom
- Departamento de Química Fisica, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | | |
Collapse
|
2
|
Gispen W, Coli GM, van Damme R, Royall CP, Dijkstra M. Crystal Polymorph Selection Mechanism of Hard Spheres Hidden in the Fluid. ACS NANO 2023; 17:8807-8814. [PMID: 37083204 PMCID: PMC10173683 DOI: 10.1021/acsnano.3c02182] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena, such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of the nucleation process, such as the polymorph selection mechanism in the early stages, are far from being understood. Here, we show that the hitherto unexplained excess of particles in a face-centered-cubic (fcc)-like environment, as compared to those in a hexagonal-close-packed (hcp)-like environment, in a crystal nucleus of hard spheres can be explained by the higher order structure in the fluid phase. We show using both simulations and experiments that in the metastable fluid phase, pentagonal bipyramids, clusters with fivefold symmetry known to be inhibitors of crystal nucleation, transform into a different cluster, Siamese dodecahedra. These clusters are closely similar to an fcc subunit, which explains the higher propensity to grow fcc than hcp in hard spheres. We show that our crystallization and polymorph selection mechanism is generic for crystal nucleation from a dense, strongly correlated fluid phase.
Collapse
Affiliation(s)
- Willem Gispen
- Soft Condensed Matter &and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - Gabriele M Coli
- Soft Condensed Matter &and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - Robin van Damme
- Soft Condensed Matter &and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - C Patrick Royall
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
| | - Marjolein Dijkstra
- Soft Condensed Matter &and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| |
Collapse
|
3
|
Montero de Hijes P, Vega C. On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system. J Chem Phys 2022; 156:014505. [PMID: 34998350 DOI: 10.1063/5.0072175] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.
Collapse
Affiliation(s)
- P Montero de Hijes
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - C Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| |
Collapse
|
4
|
Sanchez-Burgos I, Sanz E, Vega C, Espinosa JR. Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate. Phys Chem Chem Phys 2021; 23:19611-19626. [PMID: 34524277 DOI: 10.1039/d1cp01784e] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Hard-sphere crystallization has been widely investigated over the last six decades by means of colloidal suspensions and numerical methods. However, some aspects of its nucleation behaviour are still under debate. Here, we provide a detailed computational characterisation of the polymorphic nucleation competition between the face-centered cubic (fcc) and the hexagonal-close packed (hcp) hard-sphere crystal phases. By means of several state-of-the-art simulation techniques, we evaluate the melting pressure, chemical potential difference, interfacial free energy and nucleation rate of these two polymorphs, as well as of a random stacking mixture of both crystals. Our results highlight that, despite the fact that both polymorphs have very similar stability, the interfacial free energy of the hcp phase could be marginally higher than that of the fcc solid, which in consequence, mildly decreases its propensity to nucleate from the liquid compared to the fcc phase. Moreover, we analyse the abundance of each polymorph in grown crystals from different types of inserted nuclei: fcc, hcp and stacking disordered fcc/hcp seeds, as well as from those spontaneously emerged from brute force simulations. We find that post-critical crystals fundamentally grow maintaining the polymorphic structure of the critical nucleus, at least until moderately large sizes, since the only crystallographic orientation that allows stacking close-packed disorder is the fcc (111) plane, or equivalently the hcp (0001) one. Taken together, our results contribute with one more piece to the intricate puzzle of colloidal hard-sphere crystallization.
Collapse
Affiliation(s)
- Ignacio Sanchez-Burgos
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK.
| | - Eduardo Sanz
- Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Carlos Vega
- Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK.
| |
Collapse
|
5
|
Charbonneau P, Gish CM, Hoy RS, Morse PK. Thermodynamic stability of hard sphere crystals in dimensions 3 through 10. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:101. [PMID: 34370117 DOI: 10.1140/epje/s10189-021-00104-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.
Collapse
Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, NC, 27708, USA
- Department of Physics, Duke University, Durham, NC, 27708, USA
| | - Caitlin M Gish
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA
| | - Peter K Morse
- Department of Chemistry, Duke University, Durham, NC, 27708, USA.
| |
Collapse
|
6
|
Wood JA, Liu Y, Widmer-Cooper A. Crystal nucleation in colloidal rod suspensions: The effect of depletant size. J Chem Phys 2021; 154:244505. [PMID: 34241344 DOI: 10.1063/5.0052623] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In order to better control the assembly of nanorods, knowledge of the pathways by which they form ordered structures is desirable. In this paper, we characterize crystal nucleation in suspensions of spherocylindrical rods with aspect ratio L/D = 2.3 in the presence of both small and large polymer depletants. Using a combination of Langevin dynamics and Monte Carlo simulations, together with biased sampling techniques, we show that the preferred pathway always involves the formation of monolayer assemblies irrespective of the volume fraction of the initial isotropic phase and the diameter of the depletants. This includes the previously neglected case of nucleation from the colloidal liquid phase and shows that the presence of depletion attraction can alter nucleation pathways even when the initial phase is dense.
Collapse
Affiliation(s)
- Jared A Wood
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Yawei Liu
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Asaph Widmer-Cooper
- ARC Centre of Excellence in Exciton Science, School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
| |
Collapse
|
7
|
Eaton D, Saika-Voivod I, Bowles RK, Poole PH. Free energy surface of two-step nucleation. J Chem Phys 2021; 154:234507. [PMID: 34241260 DOI: 10.1063/5.0055877] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Dean Eaton
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| | - Ivan Saika-Voivod
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland A1B 3X7, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan 57N 5C9, Canada
| | - Peter H Poole
- Department of Physics, St. Francis Xavier University, Antigonish, Nova Scotia B2G 2W5, Canada
| |
Collapse
|
8
|
Omar AK, Klymko K, GrandPre T, Geissler PL. Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation. PHYSICAL REVIEW LETTERS 2021; 126:188002. [PMID: 34018789 DOI: 10.1103/physrevlett.126.188002] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Revised: 03/06/2021] [Accepted: 04/05/2021] [Indexed: 06/12/2023]
Abstract
Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.
Collapse
Affiliation(s)
- Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- NERSC, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| |
Collapse
|
9
|
Coli GM, Dijkstra M. An Artificial Neural Network Reveals the Nucleation Mechanism of a Binary Colloidal AB 13 Crystal. ACS NANO 2021; 15:4335-4346. [PMID: 33619953 PMCID: PMC7992132 DOI: 10.1021/acsnano.0c07541] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 02/18/2021] [Indexed: 06/12/2023]
Abstract
Colloidal suspensions of two species have the ability to form binary crystals under certain conditions. The hunt for these functional materials and the countless investigations on their formation process are justified by the plethora of synergetic and collective properties these binary superlattices show. Among the many crystal structures observed over the past decades, the highly exotic colloidal icosahedral AB13 crystal was predicted to be stable in binary hard-sphere mixtures nearly 30 years ago, yet the kinetic pathway of how homogeneous nucleation occurs in this system is still unknown. Here we investigate binary nucleation of the AB13 crystal from a binary fluid phase of nearly hard spheres. We calculate the nucleation barrier and nucleation rate as a function of supersaturation and draw a comparison with nucleation of single-component and other binary crystals. To follow the nucleation process, we employ a neural network to identify the AB13 phase from the binary fluid phase and the competing fcc crystal with single-particle resolution and significant accuracy in the case of bulk phases. We show that AB13 crystal nucleation proceeds via a coassembly process where large spheres and icosahedral small-sphere clusters simultaneously attach to the nucleus. Our results lend strong support for a classical pathway that is well-described by classical nucleation theory, even though the binary fluid phase is highly structured and exhibits local regions of high bond orientational order.
Collapse
|
10
|
Sanchez-Burgos I, Garaizar A, Vega C, Sanz E, Espinosa JR. Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase. SOFT MATTER 2021; 17:489-505. [PMID: 33346291 DOI: 10.1039/d0sm01680b] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Colloidal particles have been extensively used to comprehend the main principles governing liquid-crystal nucleation. Multiple mechanisms and frameworks have been proposed, through either experiments or computational approaches, to rationalise the ubiquitous formation of colloidal crystals. In this work, we elucidate the nucleation scenario behind the crystallization of oppositely charged colloids. By performing molecular dynamics simulations of colloidal electrolytes in combination with the Seeding technique, we evaluate the fundamental factors, such as the nucleation rate, free energy barrier, surface tension and kinetic pre-factor, that determine the liquid-to-solid transition of several crystalline polymorphs. Our results show that at a high packing fraction, there is a cross-over between the nucleation of the CsCl structure and that of a substitutionally disordered fcc phase, despite the CuAu crystal being the most stable phase. We demonstrate that the crucial factor in determining which phase nucleates the fastest is the free energy cost of the cluster formation rather than their kinetic ability to grow from the liquid. While at a low packing fraction, the stable phase, CsCl, is the one that nucleates and subsequently grows, we show how at moderate and high packing fractions, a disordered fcc phase subsequently grows regardless of the nature of the nucleating phase, termed parasitic crystallization. Taken together, our results provide a panoramic perspective of the complex nucleation scenario of oppositely charged colloids at moderate temperature and rationalise the different thermodynamic and kinetic aspects behind it.
Collapse
Affiliation(s)
- Ignacio Sanchez-Burgos
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK.
| | - Adiran Garaizar
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK.
| | - Carlos Vega
- Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Eduardo Sanz
- Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK.
| |
Collapse
|
11
|
Goswami A, Singh JK. Homogeneous nucleation of sheared liquids: advances and insights from simulations and theory. Phys Chem Chem Phys 2021; 23:15402-15419. [PMID: 34279013 DOI: 10.1039/d1cp02617h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
One of the most ubiquitous and technologically important phenomena in nature is the nucleation of homogeneous flowing systems. The microscopic effects of shear on a nucleating system are still imperfectly understood, although in recent years a consistent picture has emerged. The opposing effects of shear can be split into two major contributions for simple atomic and molecular liquids: increase of the energetic cost of nucleation, and enhancement of the kinetics. In this perspective, we describe the latest computational and theoretical techniques which have been developed over the past two decades. We collate and unify the overarching influences of shear, temperature, and supersaturation on the process of homogeneous nucleation. Experimental techniques and capabilities are discussed, against the backdrop of results from simulations and theory. Although we primarily focus on simple systems, we also touch upon the sheared nucleation of more complex systems, including glasses and polymer melts. We speculate on the promising directions and possible advances that could come to fruition in the future.
Collapse
Affiliation(s)
- Amrita Goswami
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India.
| | - Jayant K Singh
- Department of Chemical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India.
| |
Collapse
|
12
|
Sanchez-Burgos I, de Hijes PM, Rosales-Pelaez P, Vega C, Sanz E. Equivalence between condensation and boiling in a Lennard-Jones fluid. Phys Rev E 2020; 102:062609. [PMID: 33466022 DOI: 10.1103/physreve.102.062609] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Accepted: 11/30/2020] [Indexed: 06/12/2023]
Abstract
Condensation and boiling are phase transitions highly relevant to industry, geology, and atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid, respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard-Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.
Collapse
Affiliation(s)
- I Sanchez-Burgos
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - P Montero de Hijes
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - P Rosales-Pelaez
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - C Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - E Sanz
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| |
Collapse
|
13
|
Montero de Hijes P, Shi K, Noya EG, Santiso EE, Gubbins KE, Sanz E, Vega C. The Young–Laplace equation for a solid–liquid interface. J Chem Phys 2020; 153:191102. [DOI: 10.1063/5.0032602] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- P. Montero de Hijes
- Faculty of Chemistry, Chemical Physics Department, Universidad Complutense de Madrid, Plaza de las Ciencias, Ciudad Universitaria, Madrid 28040, Spain
| | - K. Shi
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27606, USA
| | - E. G. Noya
- Instituto de Química Física Rocasolano, Consejo Superior de Investigaciones Científicas, CSIC, Calle Serrano 119, 28006 Madrid, Spain
| | - E. E. Santiso
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27606, USA
| | - K. E. Gubbins
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27606, USA
| | - E. Sanz
- Faculty of Chemistry, Chemical Physics Department, Universidad Complutense de Madrid, Plaza de las Ciencias, Ciudad Universitaria, Madrid 28040, Spain
| | - C. Vega
- Faculty of Chemistry, Chemical Physics Department, Universidad Complutense de Madrid, Plaza de las Ciencias, Ciudad Universitaria, Madrid 28040, Spain
| |
Collapse
|
14
|
Kashchiev D. Nucleation work, surface tension, and Gibbs-Tolman length for nucleus of any size. J Chem Phys 2020; 153:124509. [PMID: 33003745 DOI: 10.1063/5.0021337] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
In the framework of the Gibbs approach to nucleation thermodynamics, expressions are derived for the nucleation work, nucleus size, surface tension, and Gibbs-Tolman length in homogeneous single-component nucleation at a fixed temperature. These expressions are in terms of the experimentally controlled overpressure of the nucleating phase and are valid for the entire overpressure range, i.e., for nucleus of any size. Analysis of available data for bubble and droplet nucleation in Lennard-Jones fluid shows that the theory describes well the data by means of a single free parameter, the Gibbs-Tolman length of the planar liquid/vapor interface. It is found that this length is about one-tenth of the Lennard-Jones molecular-diameter parameter and that it is positive for the bubble nucleus and negative for the droplet nucleus. In a sufficiently narrow temperature range, the nucleation work, nucleus radius, scaled surface tension, and Gibbs-Tolman length are apparently universal functions of scaled overpressure.
Collapse
Affiliation(s)
- Dimo Kashchiev
- Institute of Physical Chemistry, Bulgarian Academy of Sciences, ul. Acad. G. Bonchev 11, Sofia 1113, Bulgaria
| |
Collapse
|
15
|
Dasgupta T, Coli GM, Dijkstra M. Tuning the Glass Transition: Enhanced Crystallization of the Laves Phases in Nearly Hard Spheres. ACS NANO 2020; 14:3957-3968. [PMID: 32250589 PMCID: PMC7199208 DOI: 10.1021/acsnano.9b07090] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Colloidal crystals with a diamond and pyrochlore structure display wide photonic band gaps at low refractive index contrasts. However, these low-coordinated and open structures are notoriously difficult to self-assemble from colloids interacting with simple pair interactions. To circumvent these problems, one can self-assemble both structures in a closely packed MgCu2 Laves phase from a binary mixture of colloidal spheres and then selectively remove one of the sublattices. Although Laves phases have been proven to be stable in a binary hard-sphere system, they have never been observed to spontaneously crystallize in such a fluid mixture in simulations nor in experiments of micron-sized hard spheres due to slow dynamics. Here we demonstrate, using computer simulations, that softness in the interparticle potential suppresses the degree of 5-fold symmetry in the binary fluid phase and enhances crystallization of Laves phases in nearly hard spheres.
Collapse
Affiliation(s)
- Tonnishtha Dasgupta
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Department
of Physics, Utrecht University, Princetonplein 1, Utrecht 3584 CC, The Netherlands
| | - Gabriele M. Coli
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Department
of Physics, Utrecht University, Princetonplein 1, Utrecht 3584 CC, The Netherlands
- E-mail:
| | - Marjolein Dijkstra
- Soft
Condensed Matter, Debye Institute for Nanomaterials Science, Department
of Physics, Utrecht University, Princetonplein 1, Utrecht 3584 CC, The Netherlands
| |
Collapse
|
16
|
Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
17
|
Fiorucci G, Coli GM, Padding JT, Dijkstra M. The effect of hydrodynamics on the crystal nucleation of nearly hard spheres. J Chem Phys 2020; 152:064903. [DOI: 10.1063/1.5137815] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Giulia Fiorucci
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Gabriele M. Coli
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Johan T. Padding
- Process and Energy Department, TU Delft, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Department of Physics, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| |
Collapse
|
18
|
Espinosa JR, Vega C, Valeriani C, Frenkel D, Sanz E. Heterogeneous versus homogeneous crystal nucleation of hard spheres. SOFT MATTER 2019; 15:9625-9631. [PMID: 31613303 DOI: 10.1039/c9sm01142k] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Hard-sphere model systems are well-suited in both experiment and simulations to investigate fundamental aspects of the crystallization of fluids. In experiments on colloidal models of hard-sphere fluids, the fluid is unavoidably in contact with the walls of the sample cell, where heterogeneous crystallization may take place. In this work we use simulations to investigate the competition between homogeneous and heterogeneous crystallization. We report simulations of wall-induced nucleation for different confining walls. Combining the results of these simulations with earlier studies of homogeneous crystallization allows us to assess the competition between homogeneous and heterogeneous nucleation as a function of the wall type, fluid density and the system size. On flat walls, heterogeneous nucleation will typically overwhelm homogeneous nucleation. Even for surfaces randomly coated with spheres with a diameter that was some three times larger than that of the fluid spheres - as has been used in some experiments - heterogeneous nucleation is likely to be dominant for volume fractions smaller than ∼0.535. Only for a disordered coating that has the same structure as the liquid did we find that nucleation was likely to occur in the bulk. Hence, such coatings might be used to suppress heterogeneous nucleation in experiments. Finally, we report the apparent homogeneous nucleation rate taking into account the formation of crystallites both in the bulk and at the walls. We find that the apparent overall nucleation rates coincide with those reported in "homogeneous nucleation" experiments. This suggests that heterogeneous nucleation at the walls could partly explain the large discrepancies found between experimental measurements and simulation estimates of the homogeneous nucleation rate.
Collapse
Affiliation(s)
- Jorge R Espinosa
- Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
| | | | | | | | | |
Collapse
|
19
|
Montero de Hijes P, Espinosa JR, Sanz E, Vega C. Interfacial free energy of a liquid-solid interface: Its change with curvature. J Chem Phys 2019; 151:144501. [PMID: 31615240 DOI: 10.1063/1.5121026] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
We analyze the changes in the interfacial free energy between a spherical solid cluster and a fluid due to the change of the radius of the solid. Interfacial free energies from nucleation studies using the seeding technique for four different systems, being hard spheres, Lennard-Jones, and two models of water (mW and TIP4P/ICE), were plotted as a function of the inverse of the radius of the solid cluster. In all cases, the interfacial free energy was a linear function of the inverse of the radius of the solid cluster and this is consistent with Tolman's equation. This linear behavior is shown not only in isotherms but also along isobars. The effect of curvature on the interfacial free energy is more pronounced in water, followed by hard spheres, and smaller for Lennard-Jones particles. We show that it is possible to estimate nucleation rates of Lennard-Jones particles at different pressures by using information from simple NpT simulations and taking into account the variation of the interfacial free energy with the radius of the solid cluster. Neglecting the effects of the radius on the interfacial free energy (capillarity approximation) leads to incorrect values of the nucleation rate. For the Lennard-Jones system, the homogeneous nucleation curve is not parallel to the melting curve as was found for water in previous work. This is due to the increase in the interfacial free energy along the coexistence curve as the pressure increases. This work presents a simple and relatively straightforward way to approximately estimate nucleation rates.
Collapse
Affiliation(s)
- P Montero de Hijes
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Jorge R Espinosa
- Maxwell Centre, Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0H3, United Kingdom
| | - Eduardo Sanz
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | - Carlos Vega
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| |
Collapse
|
20
|
Richard D, Speck T. Classical nucleation theory for the crystallization kinetics in sheared liquids. Phys Rev E 2019; 99:062801. [PMID: 31330660 DOI: 10.1103/physreve.99.062801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Indexed: 06/10/2023]
Abstract
While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds of particles.
Collapse
Affiliation(s)
- David Richard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| |
Collapse
|
21
|
Ren S, Sun Y, Zhang F, Travesset A, Wang CZ, Ho KM. Calculation of critical nucleation rates by the persistent embryo method: application to quasi hard sphere models. SOFT MATTER 2018; 14:9185-9193. [PMID: 30398506 DOI: 10.1039/c8sm01415a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced persistent embryo method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing comparison with other existing predictions. Implications for experiments are also discussed.
Collapse
Affiliation(s)
- Shang Ren
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
| | | | | | | | | | | |
Collapse
|