Molecular-level understanding of nucleation
CECAM-HQ-EPFL, Lausanne, Switzerland
Crystallisation is an extremely important problem in the food, pharmaceutical, construction, and chemical industries, among others. Particularly, in the pharmaceutical industry, crystallisation is the most important unit operation, since about 90% of pharmaceutical products contain one or more crystalline materials . Despite its importance, however, designing and controlling crystallisation processes remains a very challenging task. Many molecules can crystallise into different polymorphs depending on the precipitation conditions (e.g. solvent, co- solvents, degree of supersaturation). These polymorphs frequently exhibit different physical properties, which affects their suitability for various applications. In drugs, for example, different polymorphs may dissolve at different rates and hence be absorbed differently in the digestive tract, which means that controlling the crystalline form of a drug is crucial for its effectiveness. This can be challenging, and failure can be disastrous, as evidenced by examples such as the drugs Ritonavir  and Rotigotine  – both drugs had to be recalled after production had started due to the sudden appearance of a new crystalline form in the formulated product. Such recalls can cost hundreds of millions of dollars, and deprive patients of necessary treatment. In part for these reasons, regulatory agencies require that the crystallisation process is well understood and the crystalline form of the drug produced is characterised before granting approval to a new drug. However, no currently available theoretical or experimental protocol can guarantee that everything is known about the crystallisation of a new material.
Besides pharmaceuticals, crystallisation is relevant to other industrial applications: many food products contain crystalline materials . High explosives used in military and construction applications are also polymorphic, and different crystalline forms have varying degrees of stability . Controlling the polymorphic outcome of crystallisation processes is also important in the production of dyes and pigments , construction materials , and nonlinear optical materials for integrated photonics . All these applications would benefit from a clear understanding of the processes leading to the formation of a particular crystalline form.
The polymorphic outcome of a crystallisation process depends, to a large extent, on the initial stages of formation of a small crystalline nucleus in the liquid, which typically involves only a few molecules or ions, a process that is quite challenging to study. In a real system, it is impossible to predict in advance where or when this nucleus will form, which makes experimental studies of nucleation extremely difficult. Additionally, the presence of very small impurities or the surface of acontainer can dramatically affect the nucleation process. On the other hand, theoretical and simulation studies are also difficult because of the complexity of the problem: the typical time scales involved in nucleation are many orders of magnitude larger than those accessible to traditional molecular simulation methods, and because of the diffusive nature of the process, reactive flux methods [9, 10] or path sampling methods  are not always effective to model it. Additionally, transport limitations can have a large impact on the nucleation process , further complicating a full theoretical description of the process.
In this workshop, we intend to bring together scientists studying different aspects of crystal nucleation, both experimentally and through molecular theory and simulation. We consider five particular key aspects of the problem: (1) The theoretical description of nucleation dynamics, (2) The impact of nucleation on the polymorph selection, (3) Understanding nucleation on surfaces and confined systems, (4) The effect of transport limitations on nucleation, and (5) How best to design joint theoretical/simulation/experimental projects.
There are different research groups over the world working on different aspects of nucleation, using a wide variety of experimental and theoretical approaches. We believe that bringing them together to discuss their findings and learn from each other will lead to major advances in the study of this difficult problem.
Nucleation and polymorph selection are very active areas of current research: according to the Web of Knowledge database, over 30% of all papers ever written on crystal nucleation were published in the last 4 years . This reflects both the importance and the difficulty of the problem. We will consider in turn the state of the art in the different aspects mentioned in the introduction.
(1) Theoretical description of nucleation dynamics: For decades, the ruling theory in describing nucleation was classical nucleation theory (CNT), which describes the nucleation as the result of a competition between two effects: the free energy gain from forming the stable phase, and the free energy penalty to create an interface between the child and mother phases. The shortcomings of CNT to describe nucleation have been amply described in the literature [5,14-19], and competing descriptions, such as the two-step nucleation theory, have been proposed [14,15,20-22]. However, a detailed, molecular-level description of crystal nucleation remains elusive: recent molecular simulation studies using modern techniques to identify important coordinates suggest that, for simple fluids of spherical molecules, a weighted size metric is enough to characterize the nucleation process . For more complex molecular fluids, nucleus size is not enough to fully describe nucleation , and more complex collective variables are needed [25,26], but there is currently no consensus on what constitutes a good molecular-level descriptor for nucleation, or even what would be a good way to obtain one. Ideally, one would use the committor probability  as a reaction coordinate, but the slow dynamics and complex free energy landscape in the “critical nucleus” ensemble make it extremely difficult to estimate this quantity. Other approaches [28-30] have been used to construct good numerical approximations, but these, though mathematically correct, may not yield much physical insight on the process. The definition of good coordinates to characterize nucleation remains an important challenge to overcome in describing the problem, and is an area of much current research.
(2) Impact of nucleation on polymorph selection: Molecular modelling and experiments have been used toward understanding the role of nucleation and growth on polymorph selection . However, even fluids of spherical molecules can exhibit complex behaviour in this respect [32-34]. Empirical rules such as the Ostwald rule of stages , or the link hypothesis , are not generally valid. Given the importance of polymorph selection in practical applications, there are many research groups currently researching this problem, both via experimental and simulation approaches .
(3) Understanding nucleation on surfaces and in confined systems: Most nucleation processes that happen in practice are, in fact, heterogeneous, as it is quite difficult to prepare a system that does not contain any impurities or surfaces that can affect the process. However, this process is even harder to study theoretically, not only because of the additional complication of describing the surface and the surface-solute interactions, but also because the surface energy heterogeneity is usually very important. Some recent studies have used molecular simulation to explain the trends seen in heterogeneous nucleation experiments on complex surfaces [38, 39], but these have assumed that the adsorption free energies correlate with the nucleation kinetics, which is not necessarily true. Both physical and chemical interactions with a surface [40, 41], as well as confinement, can affect not only nucleation [42-45], but also the possible final crystal forms [46-51], in a complex manner. A molecular-level understanding of these phenomena could be used, for example, to design surfaces or materials to template the formation of specific polymorphs, which would be extremely useful in practice.
(4) Mass transfer effects in nucleation: Understanding solute precipitate nucleation poses even more challenges than nucleation from the melt. There are additional solute-solvent interactions, but also the transfer of solute molecules between solution and the nucleus poses serious difficulty. Simulations are most conveniently performed with a constant number of solutes and solvents, but in a closed system transfer of solutes from solution to the nucleus depletes the supersaturation driving force. Nucleation rates depend strongly on supersaturation, so there is a need for grand or semi-grand ensemble simulation
methods [52, 53] or for theories of nucleation in extremely small systems [54, 55]. Additionally, slow diffusion can affect the nucleation prefactor  and even the nucleation pathway . Molecular simulation methods to account for these effects might improve quantitative predictions of nucleation kinetics.
(5) How best to design joint theoretical/simulation/experimental approaches to understand nucleation: Although some studies [32, 38, 39, 44, 45, 47, 50, 51] have combined molecular simulation and experiments results, usually the simulations are done afterwards in order to interpret experimental findings. It is rare for a combined simulation/experimental project to integrate both elements since the beginning. Given the complementary nature of these approaches, this could lead to valuable insight into the molecular-level details of nucleation. This is an aspect of the problem that would greatly benefit from a dialogue between experts in theory, simulations and experiments, as proposed for this workshop.
We expect that, in the near future, there will be major advances in understanding the issues described above, via a combination of theoretical, simulation, and experimental approaches. Collaboration between scientists using these different techniques will play a crucial role in resolving the current major challenges to a molecular-level understanding of crystal nucleation.
Giovanni Ciccotti (University "La Sapienza") - Organiser
Keith Gubbins (North Carolina State University) - Organiser
Baron Peters (University of California, Santa Barbara) - Organiser
Erik Santiso (North Carolina State University) - Organiser