Open questions in organic crystal polymorphism

Polymorphs, crystals with different structure and properties but the same molecular composition, arise from the subtle interplay between thermodynamics and kinetics during crystallisation. In this opinion piece, the authors review the latest developments in the field of polymorphism and discuss standing open questions.

Molecular basis of polymorphism Q1 Why are some compounds polymorphic and others not?. This is perhaps the first fundamental question which remains open. In some cases, compounds having very similar chemical structure behave in a completely different manner when it comes to polymorphism. To our knowledge, 9,10-anthraquinone crystallises in one unique crystal form, phenazine crystallises in two polymorphs, anthracene in three polymorphs, whilst acridine has been reported to have at least nine polymorphs (Fig. 2) 4 . We know from various databases that between 37-66% of compounds exhibit polymorphism 3 . The vast majority of polymorphic compounds are reported to only have a pair of polymorphs (89%), 9% three polymorphs and only 2% four polymorphs or more 2 . Yet, it remains impossible to know, based on molecular structure alone, whether a compound will be polymorphic or indeed how to decide if all possible polymorphs have been found in experimentation.
Q2 Are polymorphs predictable from molecular structure?. In the last 20 years or so, there has been enormous progress in the field of crystal structure prediction (CSP) 5 . CSP is a computational technique allowing for the generation of all possible crystal packings of a given compound. A polymorphic landscape is produced whereby hundreds of crystal structures are generated computationally, and their lattice energies calculated. These landscapes are sometimes successful at predicting the most stable low temperature crystal structure, if extremely accurate energy models are used 6 . Predicting which polymorphs might appear experimentally, however, still remains a major challenge. The fact that a crystal structure is generated computationally does not mean it can be obtained experimentally 7 and indeed making the link between prediction and practical realisation remains an unsolved, yet vital goal simply because while thermodynamic stability can be computed from structural information, rate constants for nucleation and growth cannot yet. However, some progress is being made here. Increasing evidence is appearing for the direct link between nucleation and growth rates with fast growers also being fast nucleators 8 . In this sense the problem may reduce to the computation of growth rates for which the literature is replete with methodologies. Here we mention the simple attachment energy methodology, the mechanistic models of Snyder and Doherty 9 and most recent work in which surface rugosity is used as a comparative measure of growth rates 10 .
Experimental preparation of polymorphs Q3 Why are some polymorphs so difficult to crystallise?. Nucleation, the origin of a crystal, is perhaps the least well understood step in the area of polymorphism. Kinetics and thermodynamics play a fine game in nucleation and crystal growth of various polymorphs. For example, theophylline form IV, despite being the most thermodynamically stable polymorph, is extremely difficult to crystallise because it is hard to nucleate and grows much slower than the common form II 11 . Ostwald's rule of stages, with its central tenet that metastable forms will always appear first, has provided a useful experimental guide to the kinetics of solution crystallisation processes 12 . However, recently the rule has been shown to be only a special case of a much bigger experimental landscape, the details of which are currently beyond computation. Gaining a better understanding of the kinetics of crystal nucleation and growth for a wide range of polymorphic systems 13 is thus a must if we are able to establish better links between crystal forms and the conditions that afford them. Beyond detailed kinetic studies, the community would benefit from abundant and accurate reports of exact crystallisation conditions that lead to new polymorphs. The problem here, however, lies in the fact that often the presence of small amounts of impurities may play an important role. As a consequence, reports of irreproducibility of polymorphic observations or of disappearing polymorphs abound not only across labs but also within one's own 14 . Another aspect to consider in the crystallisation of polymorphs is the conformational problem whereby polymorphs with high energy conformers have been found to be very difficult to produce 2 . Other polymorphs cannot be nucleated directly from solution but have to be produced via desolvation of intermediate solvates 15 or through mechanochemistry 16 .
Q4 Do polymorphs change stability under different conditions?. Most CSP landscapes only illustrate the system state at one unique set of conditions, usually 0 K and no external pressure. Polymorphs, however, are known to change in stability with conditions such as temperature, pressure and even particle size 17 . Therefore, the generation, understanding and prediction of phase diagrams under a number of conditions is an area that deserves careful further consideration within the context of polymorphism. In recent years, a number of approaches have been developed for the computation of crystal free energies 18 (beyond lattice energies) but these remain computationally expensive. Similarly, exploring polymorph stabilities experimentally with pressure may lead to stability changes between forms and the realisation of new polymorphs 19 . Finally, polymorph stability changes as a function of crystal size have rarely been studied although this has been shown to be important in the context of mechanochemistry 17 and crystallisation in nanoconfinement 20 .
Q5 Can the crystallisation of polymorphs be directed by templating?. Many polymorphs can only be obtained by crystallisations in the presence of other compounds either in solution, with solid polymers 21 or crystallisation within gels 22 . Growing compounds onto isostructural (or mixed) seeds of related analogues has been proven as a way to produce some predicted forms but only in a handful of examples including form V carbamazepine 23 and ROY 24 . When such templating strategies are possible and how to achieve them remain open questions.
Characterisation of polymorphs Q6 Are we able to detect and determine all polymorphs?. Despite advances in instrumentation over the last 50 years often compounds, especially large flexible pharmaceuticals, are difficult to crystallise as single crystals amenable to X-ray diffraction. In those cases, structure solution from powders or from a combination of methods may be the only possibility. In recent years, there has been some development in electron diffraction techniques which are able to solve complex structures, and even determine absolute configurations, from crystals of just a few hundreds of nm in size 25 . These techniques are still in need of further development so that they may be used more routinely in solid-state labs around the world. Related to this, tiny amounts of other polymorphs may be present in final products but are not detectable with current analytical techniques 26 . Increased sensitivity of analytical methods at the lab scale is therefore required, though this remains an issue of characterisation of materials in general. Finally, it is possible for true polymorphs to have very similar structures to the extent that that they may be overlooked experimentally, having only subtle differences in the X-ray diffraction patterns. Hence expert use of a combination of structural analysis techniques will be important in the future to uncover the true extent of polymorphism 27 .
Structural basis for physical properties of polymorphs Q7 Do crystal dynamics, defects and disorder effect polymorph properties?. The notion of an idealised perfect crystal is only true in theory. Real crystals are full of defects and many also have structural disorder. Beyond our average static view of crystals (averaged positions determined by XRD often at low temperatures), molecules are able to vibrate, librate and in some cases some of their groups are able to rotate (i.e. methyl group rotations or pedal motions). Our view of crystals and polymorphs is too static and to be able to better understand and model disorder or entropic contributions to free energies, we need to move towards a better understanding of crystal dynamics. This may require of further experimental data on high temperature structures and their dynamics as well as dynamic simulations of crystals. Disorder can manifest in many ways. It can be static or dynamic positional disorder of parts of the molecule within the unit cell, as well as more macroscopic phenomena such as mosaicity, twinning or stacking faults possibly also with loss of order at the crystal surfaces 28,29 . Each of these will have a precise effect on the physical properties of 'real' crystalline materials yet they remain difficult to characterise experimentally and model computationally even by expert practitioners.
Q8 Can we predict structure-property relationships?. We need to start establishing links between structure and properties in polymorphs so that we can enable computational prediction 30 . For this, first, properties of polymorphs need to be accurately measured, reported and reviewed. For example, Pudippeddi and Serajuddin compiled the solubility differences of a large set of polymorphs revealing solubility ratios between polymorphs is usually less than 2 31 . In recent years, with the development of nanoindentation there has been some novel work in trying to link crystal structure to mechanical properties of crystals 32 . More such studies would benefit the field tremendously since ultimately, the exploitation of polymorphs will be determined by their physical properties.

Outlook
In theory, one would want to generate the polymorphic landscape of a compound computationally, link it to crystal properties, retrieve the crystallisation conditions of the desired form and crystallise it. In practice, computationally generated polymorphic landscapes are challenging, structure-property relationships are not yet accurately predictable, we can rarely design crystallisation conditions for the discovery of specific polymorphic forms and crystallisation process design remains a challenging engineering exercise. Whilst we have learnt so much in the last fifty years or so, many fundamental questions remain open for us to solve in the coming decades.