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Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations † Gabriele C

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Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations † Gabriele C This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Review pubs.acs.org/CR Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations † Gabriele C. Sosso, Ji Chen, Stephen J. Cox, Martin Fitzner, Philipp Pedevilla, Andrea Zen, and Angelos Michaelides* Thomas Young Centre, London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, Gower Street WC1E 6BT London, U.K. ABSTRACT: The nucleation of crystals in liquids is one of nature’s most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments. CONTENTS 2.6.2. Homogeneous Nucleation 7101 2.6.3. Heterogeneous Nucleation 7103 1. Introduction 7078 3. Future Perspectives 7104 1.1. Theoretical Framework 7079 Author Information 7105 1.1.1. Classical Nucleation Theory 7079 Corresponding Author 7105 1.1.2. Two-Step Nucleation 7081 Present Address 7105 1.1.3. Heterogeneous Nucleation 7082 Notes 7105 1.1.4. Nucleation at Strong Supercooling 7082 Biographies 7105 1.2. Experimental Methods 7083 Acknowledgments 7106 1.3. Molecular Dynamics Simulations 7084 Abbreviations 7106 1.3.1. Brute-Force Simulations 7084 References 7106 1.3.2. Enhanced-Sampling Simulations 7085 2. Selected Systems 7086 2.1. Colloids 7086 2.2. Lennard-Jones Liquids 7088 1. INTRODUCTION 2.2.1. Nonspherical Nuclei 7088 Crystal nucleation in liquids has countless practical consequen- 2.2.2. Polymorphism 7088 ces in science and technology, and it also affects our everyday 2.2.3. Heterogeneous Nucleation 7089 experience. One obvious example is the formation of ice, which 2.2.4. Finite-Size Effects 7090 influences global phenomena such as climate change,1,2 as well as 2.3. Atomic Liquids 7090 processes happening at the nanoscale, such as intracellular 2.3.1. Phase-Change Materials 7091 freezing.3,4 On the other hand, controlling nucleation of 2.4. Water 7092 molecular crystals from solutions is of great importance to 2.4.1. Homogeneous Ice Nucleation 7092 pharmaceuticals, particularly in the context of drug design and 2.4.2. Heterogeneous Ice Nucleation 7095 production, as the early stages of crystallization impact the crystal 2.5. Nucleation from Solution 7098 polymorph obtained.5,6 Even the multibillion-dollar oil industry 2.5.1. Organic Crystals 7099 is affected by the nucleation of hydrocarbon clathrates, which can 2.5.2. Sodium Chloride 7100 2.6. Natural Gas Hydrates 7101 Received: December 18, 2015 2.6.1. Hydrate Structures 7101 Published: May 26, 2016 © 2016 American Chemical Society 7078 DOI: 10.1021/acs.chemrev.5b00744 Chem. Rev. 2016, 116, 7078−7116 Chemical Reviews Review ff * Figure 1. Sketch of the free energy di erence, ΔG5 , as a function of the crystalline nucleus size n. A free energy barrier for nucleation, ΔG5 , must be overcome to proceed from the (metastable) supercooled liquid state to the thermodynamically stable crystalline phase through homogeneous * nucleation (purple). Heterogeneous nucleation (green) can be characterized by a lower free energy barrier, ΔG5,het, and a smaller critical nucleus size, * nhet, whereas in the case of spinodal decomposition (orange), the supercooled liquid is unstable with respect to the crystalline phase, and the transformation to the crystal proceeds in a barrierless fashion. The three snapshots depict a crystalline cluster nucleating within the supercooled liquid phase (homogeneous nucleation) or as a result of the presence of a foreign impurity (heterogeneous nucleation), as well as the simultaneous occurrence of multiple crystalline clusters in the unstable liquid. This scenario is often labeled as spinodal decomposition, although the existence of a genuine spinodal decomposition from the supercooled liquid to the crystalline phase has been debated (see text). form inside pipelines, endangering extraction.7,8 Finally, crystal methods able to overcome this time-scale problem is now nucleation is involved in many processes spontaneously more competitive than ever, we are almost always forced to base occurring in living beings, from the growth of the beautiful our conclusions on the ancient grounds of classical nucleation Nautilus shells9 to the dreadful formation in our own brains of theory (CNT), a powerful theoretical tool that nonetheless dates amyloid fibrils, which are thought to be responsible for many back 90 years to Volmer and Weber.17 neurodegenerative disorders such as Alzheimer’s disease.10,11 In fact, these are exciting times for the crystal nucleation Each of the above scenarios starts from a liquid below its community, as demonstrated by the many reviews covering − melting temperature. This supercooled liquid12 is doomed, several aspects of this diverse field.18 24 This particular review is according to thermodynamics, to face a first-order phase focused almost exclusively on MD simulations of crystal transition, leading to a crystal.13,14 Before this can happen, nucleation of supercooled liquids and supersaturated solutions. however, a sufficiently large cluster of crystalline atoms (or We take into account several systems, from colloidal liquids to molecules or particles) must form within the liquid, such that the natural gas hydrates, highlighting long-standing issues as well as free energy cost of creating an interface between the liquid and recent advances. Although we review a substantial fraction of the the crystalline phase will be overcome by the free energy gain of theoretical efforts in the field, mainly from the past decade, our having a certain volume of crystal. This event stands at the heart goal is not to discuss in detail every contribution. Instead, we try of crystal nucleation, and how this process has been, is, and will to pinpoint the most pressing issues that still prevent us from be modeled by means of computer simulations is the subject of furthering our understanding of nucleation. this review. This article is structured in three parts. In the first part, we The past few decades have witnessed an impressive body of introduce the theoretical framework of CNT (section 1.1), the experimental work devoted to crystal nucleation. For instance, state-of-the-art experimental techniques (section 1.2), and the thanks to novel techniques such as transmission electron MD-based simulation methods (section 1.3) that in the past few microscopy at very low temperatures (cryo-TEM), we are now decades have provided insight into nucleation. In section 2,we 15 able to peek in real time into the early stages of crystallization. A put such computational approaches into context, describing both substantial effort has also been made to understand which achievements and open questions concerning the molecular materials, in the form of impurities within the liquid phase, can details of nucleation for different types of systems, namely, 16 either promote or inhibit nucleation events, a common colloids (section 2.1), Lennard-Jones (LJ) liquids (section 2.2), scenario known as heterogeneous nucleation. However, our atomic liquids (section 2.3), water (section 2.4), nucleation from understanding of crystal nucleation is far from being complete. solution (section 2.5), and natural gas hydrates (section 2.6). In This is because the molecular (or atomistic) details of the process the third and last part of the article (section 3), we highlight are largely unknown because of the very small length scale future perspectives and open challenges in the field. involved (nanometers), which is exceptionally challenging to 1.1. Theoretical Framework probe in real time even with state-of-the-art measurements. Hence, there is a need for computer simulations, and particularly 1.1.1. Classical Nucleation Theory. Almost every com- molecular dynamics (MD) simulations, where the temporal puter simulation of crystal nucleation in liquids invokes some evolution of the liquid into the crystal is more or less faithfully elements25 of classical nucleation theory (CNT). This theory has − reproduced. Unfortunately, crystal nucleation is a rare event that been discussed in great detail elsewhere,26 28 and we describe it can occur on time scales of seconds, far beyond the reach of any here for the sake of completeness
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