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© 2008 Springer.

CRYSTAL POLYMORPHISM

JOEL BERNSTEIN Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, Israel 84105

Abstract. The importance of understanding and considering the role of the existence of different crystal forms in the design and preparation of new materials is discussed.

Keywords: polymorphism; solvates; hydrates; concomitant polymorphism; confor-mational polymorphism; disappearing polymorphs; thermodynamic form; kinetic form; stability; growth conditions; structure-property relationships

1. Introduction

The concept of engineering implies that a considerable measure of control has been achieved and maintained over some process or procedure. When that process is the engineering of crystalline materials properties, as in the title of this School, then the implication is that specific desired properties can be designed and built into materials, just as specific properties can be designed and built into a bridge or an electronic circuit. In the end, of course, the properties of the two latter examples depend intimately on the structure of the materials. Variations in structure can and do lead to varia-tion in properties. Therefore, in the engineering of crystalline materials the desired properties must be designed into the material and in order to achieve those design goals control must be obtained over the structure.

The existence of different crystal forms (polymorphs and solvates) of the same molecule or of aggregates of the same molecule with other mole-cules (co-crystals) can be an anathema to this engineering effort. Changes in structure are likely to be accompanied by undersigned and undesired chan-ges in properties. On the other hand, changes in structure can also lead to improved properties, so that the search for, and preparation of a variety of crystal forms can be a crucial aspect of the whole engineering process. In

J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 87–109.

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fact the search for and characterization of crystal forms is one of the most active and challenging research areas of modern solid state chemistry. The effort is by no means theoretical or academic. In the pharmaceutical field, the existence of multiple crystal forms is relevant for the choice of the solid dosage form of an active pharmaceutical ingredient (API) most suitable for drug development and marketing and has important implications both in terms of the drug’s ultimate efficacy and in terms of the protection of the intellectual property rights associated with the pharmaceutical product. Similarly, the properties of pigments, explosives, electrically conducting organic materials, organic magnetic materials, etc. are all intimately related to their solid state structure, so that the understanding and control over that structure is one of the key aspects of engineering those materials for their desired properties.

This chapter deals with some of the fundamental aspects of the varia-tion of structure and properties of various crystal forms. Strictly speaking, the term “polymorphism” refers to but one aspect of this variation, but in the lingua franca among practitioners the term “polymorphism” is often used and meant to include all crystal forms of a material [e.g. Ref. 1].

2. What is Polymorphism and the Multiplicity of Crystal Forms?

Materials are traditionally classified in three states of matter: gases, liquids and solids and distinguished by their properties. In addition to different crystal structures, called polymorphs, which are characterized by long range order, a material may appear as an amorphous solid, characterized by the lack of long range order. The polymorphism of calcium carbonate (calcite, vaterite and aragonite) was identified more than 200 years ago by Klaproth in 1788,2 but formal recognition of the phenomenon is generally credited to Mitscherlich.3 Diamond, graphite, fullerenes and nanotubes are polymor-phic forms (denoted as allotropes for elements) of carbon all exhibiting very different properties. Cocoa butter can crystallize in at least five different ways, the various crystal structures affecting the perception of the epicurean quality of the prepared chocolate, although all forms are chemically identical.4

In this chapter we discuss the different crystal forms of molecular crys-tals, in which a particular molecule crystallizes in different ways (polymor-phs) and/or with a solvent molecules (solvates). When the solvent is water then they are referred to as hydrates. As we will attempt to show, although the subject has been widely investigated, mainly in the field of solid state organic chemistry, the polymorphism of molecular crystals is still a fasci-nating phenomenon, and it still represents a substantial scientific challenge to the very idea of rational design and construction of crystalline solids with

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predefined architectures and physical properties starting from the choice of the molecular components, which is the paradigm of molecular crystal engineering.5

Although some classic works still provide an excellent entry to the fundamental aspects of crystal forms,6–8 the last dozen years have witnessed an almost exponential increase in the interest in crystal forms and the number of publications and conferences devoted to the subject.1,5,9–16

Figure 1. Schematic representation of the structural relationship between “true” polymorphs, solvates, polymorphs of solvates and the amorphous phase.

3. Importance of Polymorphism – Concomitant and Disappearing

Chemists who encounter polymorphism for the first time are often unaware of its existence and baffled by its manifestations. Experimental problems might include, for example, variable or diffuse melting point, crystal batc-hes with inconsistent physical properties (electrical or thermal conductivity, filtering, drying, flow, tabletting, dissolution), two (or more) different colo-red or different shaped crystals in the same batch of (chemically) “pure” material, etc. (for example, see Brittain11). These problems result because the conditions of that particular crystallization have led to the production of a number of polymorphs, which are present in the crystallizing medium or vessel at the time of harvesting or collection of the crystals. The fact that polymorphs of a substance can appear concomitantly (accompanying each other or happening together) has long been recognized but has only recently been reviewed.17

Is the phenomenon of concomitant polymorphs a curse or a blessing? Both. It is a curse for the chemist seeking a pure substance and a robust procedure to repeatedly and consistently produce that pure material, and the

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existence of concomitant polymorphs corrupts that procedure. It is a bless-ing, however, because (the recognition of) the existence of polymorphs in general, and concomitant polymorphs in particular can provide the informa-tion and the opportunity to gain control over the crystallization process, and to achieve the desired specificity and robustness.

On the other end of the spectrum of crystallization phenomena of poly-morphs is that of disappearing polymorphs.18 There are many documented tales of difficulties in obtaining crystals of a particular known form or in reproducing results from another laboratory, or even ones own. There are cases where it was difficult to obtain a given polymorphic form even though this had previously been obtained routinely over long time periods. This phenomenon also suggests a loss of control over the crystallization process, so widely used by chemists for the purification of materials. The reasons for the sudden appearance of a new crystal modification are not always clear, even after the fact, but its presence may make the production of the previ-ously obtained form particularly difficult, or apparently impossible. How-ever, once a particular polymorph has been obtained it should always be possible to obtain it again; it is only a matter of finding the right experi-mental conditions.

Both concomitant and disappearing polymorphs depend on the experi-mental conditions governing the crystallization process. Two of the funda-mental ones (but certainly not the only ones) are the thermodynamics and kinetics of crystallization. An understanding of the competing thermodyna-mic and kinetic factors governing the crystallization of polymorphs in gene-ral, or of a particular substance in particular helps to facilitate the control over the production of the desired polymorph, at the exclusion of undesired ones. Such control has important implications in a variety of industrial applications, of which pharmaceutical production and formulation is but one important example. This next section deals with the essentials of the ther-modynamics involved; more detailed accounts may be found elsewhere. 19–24 The following section deals with kinetic factors.

4.

Thermodynamics tells us that crystallization must result in an overall decrease in the free energy of the system. This means that in general the crystal structures that appear will be those having the greater (negative) lattice (free) energies. In polymorphic systems there are evidently a number of possible structures that have similar lattice energies.

This drive towards free energy minimization will be balanced, as in all chemical changes, by the kinetic tendency of the system to crystallize as quickly as possible so as to relieve the imposed supersaturation. From the

Thermodynamic and Kinetic Stability Amongst Polymorphs

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molecular point of view the process of crystallization is one of a supramole-cular assembly in which the building blocks of the crystal assemble through the utilization of molecular recognition forces involving an array of intermolecular interactions as well as stereochemical packing constraints. If some structures are able to form more quickly than others then the system may in the short term settle for less than the maximum energy decrease, providing such a situation can be achieved at speed. A secondary transfor-mation to a lower energy state can subsequently take place.

The distinction between thermodynamic and kinetic influences is often demonstrated using the example of the graphite and diamond forms of carbon. The former is the thermodynamically preferred crystalline form, but kinetic factors (in particular, a high activation barrier) make the rate of transformation from diamond to graphite infinitely slow.25

4.1. ENERGY VERSUS TEMPERATURE DIAGRAM

The energy versus temperature diagram was introduced into crystallography by Buerger26 without application to any specific example. The theoretical derivation and practical application of this diagram have been described and discussed by Burger and Ramberger22,23 and by Grunenberg et al.24 For simplicity we will limit the discussion to two polymorphic solids, although the extension to a larger number is based on the same principles.

The relative stability of two polymorphs depends on their free energies, the more stable one having a lower free energy. The Gibbs free energy of a substance is expressed as G = H – TS (1) G and H are clearly functions of temperature and this variation may be plotted for one possible relationship between the two polymorphs and the melt (liquid) in Figure 2. Such diagrams contain a great deal of information in a compact form, and provide a visual and readily interpretable summary of the often complex relationships among polymorphs.

At absolute zero TS vanishes so that the enthalpy is equal to the Gibbs free energy. As a consequence, at absolute zero the most stable polymorphic modification should have the lowest Gibbs free energy. Above absolute zero the entropy term will play a role which may differ for the two poly-morphs so that the free energy as a function of the temperature follows a different trajectory for the two polymorphs, as represented by the GI and GII curves in Figure 2. The two G curves cross at the thermodynamic transition point Tp,I/II, but since the enthalpy of I is lower than that of II a quantity of

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energy ΔHt,I/II is required to be input for the phase transition.. The endo-thermic solid to liquid transitions at the melting points may be understood in the same way, with ΔHf,I and ΔHf,II denoting the respective enthalpies of fusion. Figure 2 represents an enantiotropic situation, since Tp,I/II lies at a temperature below the melting points for the two polymorphs.

The monotropic situation is represented in Figure 3. In this case, there is no transition point below the melting points of the two polymorphs. The

Figure 2. Energy versus temperature (E/T) diagram of a dimorphic system. G is the Gibbs free energy and H is the enthalpy. This diagram represents the situation for an enantiotropic system, in which form I is the stable form below the transition point, and presumably at room temperature.

Figure 3. Energy versus temperature (E/T) diagram for a monotropic dimorphic system. The symbols have the same meaning as in Figure 1. Form I is more stable at all temperatures.

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phenomenological manifestation of enantiotropism is that there can be a reversible transition from one phase to another without going through the gas or liquid phase. If the thermodynamic relationship is one of monotro-pism the two modifications are not interconvertible. In the context of simultaneously crystallizing polymorphs the thermodynamics is clear. First, only at thermodynamic transition points can two forms have the same stability and hence coexist as mixtures at equilibrium. At any other tempe-rature there will be a thermodynamic tendency to transform to the more stable structure. This implies that except at the thermodynamic transition point mixtures of polymorphs will have limited lifetimes, with transfor-mation kinetics playing a role in those lifetimes.

4.2. VAPOR PRESSURE VERSUS TEMPERATURE DIAGRAM

Another common representation of phase relationships is the pressure versus temperature diagram. Figure 4 shows the prototypical plots of pressure versus temperature for the enantiotropic and monotropic cases. These are best understood by traversing along various curves, which represent equilibrium situations between two phases. The l./v. line in the high temperature region of Figure 4a is the boiling point curve for the (common) melt of the two polymorphs. Moving to lower temperatures along that line one encounters the II/v. line, which is the sublimation curve for form II. The intersection is the melting point for form II. Under

Figure 4. Pressure versus temperature (P/T) plots. I/v. and II/v. represent sublimation curves; l./v. is the boiling point curve. Broken lines represent regions which are thermodynamically unstable or inaccessible. (a) Enantiotropic system; (b) monotropic system. The labeling corresponds to Figures 1 and 2 to indicate that form I is stable at room temperature, which is below the transition point in the enantiotropic case.

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thermodynamic conditions form II would crystallize out at this point and the solid part of the II/v. line would govern the behavior. However, if kinetic conditions prevail (for example, if the temperature is lowered rapidly) the system may proceed along the broken l./v. line to the intersection with the I/v. line, at which point form I would crystallize. Continuing downward along the solid part of the II/v. curve, the crossing point with the I/v. sublimation curve is the transition point between the two polymorphic phases. Once again, if thermodynamic conditions prevail form II will be transformed to form I. Under kinetic conditions form II may continue to exist (even indefinitely in some cases) along the II/v. sublimation curve. Figure 4a represents the enantiotropic case because the transition point between the two phases is found at a temperature below the melting point of form II, while Figure 4b represents the monotropic situation, in which the transition point is above the melting points of both forms.

4.3. SOME PRACTICAL ASPECTS OF RELATIVE STABILITIES OF POLYMORPHS

A knowledge of the enantiotropic or monotropic nature of the relationship between polymorphs can be used to steer crystallization processes to obtain a desired polymorph at the exclusion of an undesired one. For a dimorphic system there are four possibilities:

1. the thermodynamically stable form in a monotropic system: no transformation can take place to another form, and no precautions need be taken to preserve that form or to prevent a transformation.

2. the thermodynamically stable form in an enantiotropic system: precautions must be taken to maintain the thermodynamic conditions (temperature, pressure, relative humidity, etc.) at which the G curve for the desired polymorph is below that for the undesired one.

3. the thermodynamically metastable form in a monotropic system: a kinetically controlled transformation may take place to the undesired thermodynamically stable form. To prevent such a transformation it may be necessary to employ drastic conditions to reduce kinetic effects (e.g. very low temperatures, very dry conditions, storage in the dark, etc.).

4. the thermodynamically metastable form in an enantiotropic system: the information for obtaining and maintaining this form is essentially found in the energy-temperature diagram.

Therefore, it is of practical importance (e.g. preformulation studies of a drug substance24,25) to determine whether a system of polymorphs is mono-tropic or enantiotropic to enable the choice of and control over the desired polymorphic form. The combination of experience with polymorphic systems

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and the accumulation of sufficient thermodynamic and structural data have permitted the development of some useful “rules” for determining the relative positions of the G and H isobars, as well as the enantiotropic or monotropic nature of the relationship between polymorphs.22–24

4.4. KINETIC CONSIDERATIONS

4.4.1. Solubility and Dissolution Rates

In addition to differences in melting points, heats of fusion, entropies of fusion, densities, heat capacities and virtually every chemical and physical property, different modifications can also exhibit different solubilities and dissolution rates. Since the solubility is directly proportional to the free energy of a modification, determination of solubility curves is the most reliable method of assessing the relative free energies of polymorphs. The differ-ence in solubility of two polymorphs is a direct measure of the ΔG between them. It is important to note that although the absolute solubility (and hence the dissolution rate) of a polymorph will be solvent dependent, the relative solubility of different forms will not depend on the solvent used.27

The situations in which polymorphs concomitantly crystallize are deter-mined by the experimental conditions in relation to both the free energy – temperature relationships and the relative kinetic factors. These situations may arise either because specific thermodynamic conditions prevail or because the kinetic processes have equivalent rates. In thermodynamic terms we have seen that polymorphs can only exist in true equilibrium at the thermodynamic transition temperature (where the G curves cross). The chance of carrying out a crystallization precisely at such a temperature must be small, with the inevitable conclusion that kinetics play at least some role in the overall process. The final consequence of this of course is that a system of concomitantly crystallizing polymorphs will be subject to change in the direction favoring the formation of the most stable structure. If the crystals have grown from and remain in contact with solution then the most likely route for this transformation is via solution by dissolution and recry-stallization.21,28 If the crystals have formed from the melt or vapor phase or have been isolated from their mother phase, the solid state transformation is possible.29

4.4.2. Kinetic Factors

The starting point for a discussion of the kinetic factors is the traditional energy – reaction coordinate diagram, Figure 5. This shows G0, the free energy per mole of a solute in a supersaturated fluid which transforms by crystallization into one of two crystalline products, I or II, in which I is the

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more stable (GII > GI). Associated with each reaction pathway is a transition state and an activation free energy which is implicated in the relative rates of formation of the two structures. Unlike a chemical reaction, crystalli-zation is complicated by the nature of the activated state since it is not a simple bi- or trimolecular complex as would be expected for a process in which a covalent bond is formed; rather it relates to a collection of self assembled molecules having not only a precise packing arrangement but also existing as a new separate solid phase.

It is the existence of the phase boundary that complicates matters since this is associated with an increase in free energy of the system that must be offset by the overall loss of free energy. For this reason the magnitudes of the activation barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best guide today.30

Figure 5. Schematic diagram of the reaction coordinate for crystallization in a dimorphic system, showing the activation barriers for the formation of polymorphs I and II.

One of the key outcomes of this theory is the concept of critical size that

an assembly of molecules must have in order to be stabilized by further growth. The higher the operating level of supersaturation the smaller this size is (typically a few tens of molecules). In Figure 5 the supersaturation with respect to I is simply G0-GI and is higher than G0-GII for structure II. However it can now be seen that if for a particular solution composition the critical size is lower for II than for I then the activation free energy for

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nucleation is lower and kinetics will favor form II. Ultimately form II will have to transform to form I, a process that we discuss later. Overall we can say that the probability that a particular form I will appear is given by

P(i) = f(ΔG, R) (2)

in which ΔG is the free energy for forming the n-th polymorph and R is the rate of some kinetic process associated with the formation of a crystal by molecular aggregation. Thus, for example, if we follow the above reasoning we could equate the rate process with J, the rate of nucleation of the form. If all polymorphs had the same rates of nucleation then their appearance probability would be dominated by the relative free energies of the possible crystal structures.

The rates of nucleation as expressed by the classical expression of Volmer are related to various thermodynamic and physical properties of the system such as bulk and surface free energy (γ), temperature (T), degree of supersaturation (σ), solubility (hidden in the pre-exponential factor An) which will not be the same for each structure but will correctly reflect the balance between changes in bulk and surface free energies during nucleation. This is seen in equation 3 which relates the rate of nucleation to the above parameters (ν is the molecular volume):

J = Anexp(–16πγ3ν2/3κ3T3σ2) (3) From this analysis it is clear that the tradeoff between kinetics and

thermodynamics is not at all obvious. Consider a monotropic, dimorphic system (for simplicity) whose solubility diagram is shown schematically in Figure 5. It is quite clear that for the occurrence given by solution compo-sitions and temperatures that lie between the form I and II solubility curves only polymorph II can crystallize. However, the outcome of an isothermal

Figure 6. chematic solubility diagram for a dimorphic system (polymorphs I and II) showing a hypothetical crystallization pathway (vertical arrow) at constant temperature.

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crystallization that follows the crystallization pathway indicated by the vector in Figure 6 s not so obvious since the initial solution is now super-saturated with respect to both polymorphic structures, with thermodynamics favoring form II and kinetics favoring form I.

Experimentally, the reality of this overall scenario of kinetic versus ther-modynamic control was known long before the development of nucleation theory and is encompassed by Ostwald in his Rule of Stages of 1897.31–33 The German scientific literature between 1870 and 1914 contains many organic and inorganic examples in which crystallization from melts and solutions yields an initial metastable form which is ultimately replaced by a stable structure and Ostwald was led to conclude that ‘when leaving a metastable state, a given chemical system does not seek out the most stable state, rather the nearest metastable one that can be reached without loss of free energy’.

Of course this conclusion is significantly flawed: when a crystallization experiment yields only a single form there is no way of knowing whether it contradicts the rule or whether the material is simply not polymorphic. There is no way of answering this question. However, a sufficient number of cases of successively crystallizing polymorphic forms have been observed (see for instance Ciechanowicz et al.34) to warrant considering the principles behind Ostwald’s Rule as guidelines for understanding the phenomenon.

By making use of Volmer’s equations some attempts have been made by Becker and Doering,35 Stranski and Totomanov,36 and Davey32 to explain the rule in kinetic terms. In it becomes apparent that the situation is by no means as clear cut as might be inferred from Ostwald’s Rule. Figure 7 shows the three possible simultaneous solutions of the nucleation equations that indicate that by careful control of the occurrence domain there may be conditions in which the nucleation rates of the two forms are equal and hence their appearance probabilities are nearly equal. Under such conditions we might expect the polymorphs to crystallize concomitantly.

4.5. EXAMPLES OF CONCOMITANT AND DISAPPEARING POLYMORPHS

Many additional aspects and examples of concomitant polymorphs have been reviewed.17 Those for disappearing polymorphs appeared in a slightly older review.18 As noted above, one of the challenges of disappearing polymorphs is to be able to prepare modifications that apparently vanished with the appearance of new forms. Some successful attempts have been surveyed37 and a detailed study has been reported.38

One recent example of a disappearing polymorph that had particularly important consequences in the pharmaceutical industry was that of ritonavir, a component of cocktail administered for treatment of AIDS.39

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Figure 7. The rates of nucleation as functions of supersaturation for the dimorphic system defined in Figure 6. The three diagrams a, b and c represent the three possible solutions for the simultaneous nucleation of two polymorphs each of which follows a rate equation of the form of equation 3. Note that solutions a and c both allow for simultaneous nucleation of the forms at supersaturations corresponding to the crossover of the curves.

5. Conformational Polymorphism

The differences in energy between polymorphs (1–2 kcal/mol) are generally of the same order of magnitude as the energetics of rotations about single bonds. This similarity in energy allows for conformationally flexible mole-cules to adopt different conformations in different polymorphs, a pheno-menon known as conformational polymorphism.40,41

For cases of conformational polymorphism one can ask the following questions:

1. What are the structural differences among the polymorphs? 2. What are the differences in energy, if any, in the molecular conforma-

tions observed in the various crystal forms? 3. How does the energetic environment of the molecule vary from one crystal

form to another?

To answer these questions, a typical study might proceed according to the following scenario:

Determination of the existence of polymorphism in the system under study. Determination of the existence of conformational polymorphism by the

appropriate physical measurements. Determination of the crystal structures to obtain the geometrical information

– molecular geometries and packing motif – of the various polymorphs. Determination of the differences in molecular energetics, by appropriate

computational techniques. Determinaton of differences in lattice energy and the energetic environment

of the molecule by appropriate computational methods.

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Examples of conformational polymorphism, along with the application of this strategy have been given.40 The computational aspects of such inves-tigations combine both molecular energetics and lattice energetics within rather limited energy ranges, and therefore provide quite demanding bench-marks for both the algorithms and the force fields used in such calculations. A minimum requirement would be the correct ordering of the relative stabi-lity of the polymorphs, without any regard for the differences in energy or the absolute value of the lattice energies (compared, say, to the sublimation energy). Increasingly stricter demands would require the differences in computed lattice energies to match those measured by thermal (e.g. differ-ential scanning calorimetry) methods or for the absolute energies to match experimentally determined sublimation energies.

6. Phase Transformations and Conversions

From thermodynamic principles, under specified conditions only one poly-morph is the stable form (except at a transition point).42 In practice, however, due to kinetic considerations, metastable forms can exist or coexist in the presence of more stable forms. Such is the case for diamond, which is meta-stable with regard to graphite, the thermodynamically stable form of carbon under ambient conditions. In practice, the relative stability of the various crystal forms and the possibility of interconversion between crystal forms, between crystals with different degree of solvation and between an amor-phous phase and a crystalline phase, can have very serious consequences on the life and effectiveness of a polymorphic product and the persistence over time of the desired properties (therapeutic effectiveness in the case of a drug, chromatic properties in the case of pigment, etc).

Conversions between different crystal forms are possible and often take place. Among the many possibilities for conversion, depending on variables such as temperature, pressure, relative humidity, etc. specific examples are:

a metastable form can convert to a thermodynamically more stable crystal form with very slow kinetics;

an unsolvated crystal form can form solvates and co-crystals with other “innocent” molecules which will nonetheless alter significantly the physical properties with respect to the “homomolecular” crystals;

an anhydrous crystalline form can be transformed into a crystal hydrate via vapor uptake from the atmosphere;

a solvate can, in turn, be transformed into another crystal form with a different degree of solvation up to the anhydrous crystal via stepwise solvent/water loss;

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a (metastable) amorphous phase may transform into a stable crystalline phase over time.

The variety of phenomena related to polymorphism (hydration, solvation,

amorphicity and interconversions) demonstrates the importance of acquiring a thorough mapping of the “crystal space” of a substance that is ultimately intended for some specific application.

7. Why are Polymorphism and Multiple Crystal Forms Important?

The example of the polymorphs (allotropes) of carbon point on the key messages of this chapter: different crystal forms of a substance can possess very different properties and behave as different materials. This concept has important implications in all fields of chemistry associated with the produc-tion and commercialization of molecules in the form of crystalline materials (drugs, pigments, agrochemicals and food additives, explosives, etc). The producer, in fact, needs to know not only the exact nature of the material in the production and marketing process, but also its stability with time, the variability of its chemical and physical properties as a function of the crystal form, etc. In some areas, e.g. the pharmaceutical industry, the search for and characterization of crystal forms of the API has become a crucial step for the choice of the best form for formulation, production, stability and for intellectual property protection.

Table 1 summarizes some major possible differences in chemical and physical properties between crystal forms and solvates of the same substance. Different crystal forms are often recognized by differences in the color and TABLE 1. Examples of chemical and physical properties that can differ among crystal forms and solvates of the same substance

PHYSICAL AND THERMODYNAMIC PROPERTIES

density and refractive index, thermal and electrical conductivity, hygroscopicity, melting points, free energy and chemical potential, heat capacity, vapor pressure, solubility, thermal stability

SPECTROSCOPIC PROPERTIES electronic, vibrational and rotational properties, nuclear magnetic resonance spectral features

KINETIC PROPERTIES rate of dissolution, kinetics of solid state reactions, stability

SURFACE PROPERTIES surface free energy, crystal habit, surface area, particle size distribution

MECHANICAL PROPERTIES hardness, compression, thermal expansion CHEMICAL PROPERTIES chemical and photochemical reactivity

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shape of crystals. A striking example of these two properties is provided by the differences in color and form of the crystal forms of ROY (ROY = red, orange, yellow polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophene carbonitrile)43 (color figure in original reference).

8. How do we Detect and Characterize Multiple Crystal Forms?

In spite of the efforts of a great number of research groups worldwide, and of a familiarity with the experimental factors that can lead to multiple crystal forms, our ability to predict or control the occurrence of polymor-phism is still embryonic. In many cases the crystallization of a new crystal form or of an amorphous phase of a given substance turns out to be the result of serendipity44 rather than a process under complete human control.

The exploration of the “crystal form space” (polymorph screening) of a substance is the search of the polymorphs and solvates with a twofold purpose: 1) identification of the relative thermodynamic stability of the various forms including the existence of enantiotropic crystalline forms (that interconvert as a function of the temperature) or of monotropic forms (that do not interconvert) and of amorphous and solvate forms and 2) physical characterization of the crystal forms with as many analytical tech-niques as possible. The relationships between the various phases and com-monly used industrial and research laboratory processes are schematically illustrated in Figure 8.

Figure 8. Some general relationships between polymorphs, solvates and amorphous phases and the type of research lab or industrial or process for preparation and interconversion. 1, Crystallization; 2, Desolvation; 3, Exposure to solvent/vapor uptake; 4, Freeze drying; 5, Heating; 6, Melting; 7, Precipitation; 8, Quench cooling; 9, Milling; 10, Spray drying; 11, Kneading; 12, Wet granulation. Analogous relationships apply to polymorphic modifications of solvate forms. Note that the figure represents general trends rather than every possible transformation; the presence or absence of an arrow or number does not represent the exclusive existence or absence of a transformation.

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Polymorph assessment, on the other hand, is part of the system of quality control. It is necessary to make sure that the scale-up from laboratory preparation to industrial production does not introduce variations in crystal form. Polymorph assessment also guarantees that the product conforms to the guidelines of the appropriate regulatory agencies and does not infringe the intellectual property protection that may cover other crystal forms.

The polymorph pre-screening, screening and assessment are best achieved by the combined use of several solid-state techniques, among them (not exclusively or in any preferential order): microscopy and hot stage microscopy (HSM), differential scanning calorimetry (DSC), thermogravi-metric analysis (TGA), infrared and Raman spectroscopy (IR and Raman), single crystal/powder X-ray diffraction (SCXD, PXD), solid state nuclear magnetic resonance spectroscopy (SSNMR).45

It is also important to mention in the context of this discussion the advantages offered by the possibility of determining the molecular and crystal structure of a crystal form by means of single crystal X-ray diffrac-tion. This technique, although generally much more demanding than powder diffraction in terms of experiment duration and data processing, has the great advantage of providing detailed structural information on the molecular geometry, but more important for this discussion, it provides information on the packing of the molecules in the crystal and the nature and structural role of solvent molecules. Moreover, the knowledge of the single-crystal struc-ture allows calculating the X-ray powder diffraction pattern that can be compared with the one measured on the polycrystalline sample as demon-strated in Figure 9. Importantly, the calculated diffraction pattern is not affected by the typical sources of errors or the experimental powder diffrac-tion (preferential orientation, mixtures, presence of amorphous) that often complicate or render uncertain the interpretation of the measured powder diffractograms; hence the calculated powder pattern is often referred to as the “gold standard” pattern for a crystal form.

Figure 9. Comparison between measured and calculated X-ray diffraction patterns for form II of gabapentine (single crystal data from reference 46).

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The search for various crystal forms requires that the behavior of a solid phase is investigated as a function of the variables that can influence or determine the outcome of the crystallization process, e.g. temperature, choice of solvents, crystallization conditions, rate of precipitation, interconversion between solid forms (from solvate to un-solvate and vice versa), pressure and mechanical treatment, absorption and release of vapor, etc. The most effective way to search for crystal forms is to evaluate the effect of the changes of one variable at a time. There has been a recent burst of activity in developing crystallization techniques and variables for obtaining new crystal forms,47 some of which are described in the next section.

The efficiency of screening protocols, whether high throughput automa-tic methods or manual procedures, can be considerably increased by carrying out preliminary HSM, DSC and variable temperature XPD investigations for initial detection of multiple phases and the temperature ranges of their existence, as well as transformations among them. These observations can then be summarized with a semiempirical energy-temperature diagram24,48 that can be helpful in designing protocols for screening for crystal forms. In particular, it is possible to determine if various phases are related enantio-tropically (reversibly) or monotropically (non-reversibly). Once the thermo-dynamic screening of the crystalline product has been completed, the quest for new forms can extend to the investigation of the effect of changing the solvent or the mixture of solvents and/or to the temperature gradient, the pre-sence of templates or seeds. Examples of the utilization of variable tempera-ture diffraction methods (VTXPD) to investigate phase transitions between

Figure 10. VTXPD measurements applied to the investigation of phase transitions between Form I and Form II of anthranilic acid.49

CRYSTAL POLYMORPHISM 105

Figure 11. VTXPD measurements applied to the investigation of the de-hydration of barbituric acid dihydrate with formation of Form I of barbituric acid.50

9. New Developments in Detecting and Characterizing Multiple Crystal Forms

The last decade has witnessed many developments in the generation and detection of new crystal forms. These have resulted from the increased awareness of the possibility of multiple crystal forms of a substance, the utility that may derived by preparing a crystal form with enhanced proper-ties and the potential intellectual property implications of new crystal forms. These factors, combined with the development of new technology,51 the attempts to design and control crystal structure,52 combined with some spec-tacular encounters with new (and undesired) crystal forms53 and some high profile pharmaceutical patent litigations,9 have led to many new techniques for exploring the crystal form space of any particular substance. Some of these depend simply on an awareness of the older literature,54 the applica-tion of crystal engineering principles, based on hydrogen-bonding patterns, to the preparation of new multicomponent solids,55 the induction of crystal forms by incorporating a variety of functional groups onto a polymer back-bone,56 the development of high throughput crystallization technology,57 the utilization of solid-solid and solid-gas reactions,58 solvent-free synthesis,59 the desolvation of solvated crystals60 and crystallization from a supercritical solvent.61

enantiotropic systems (in the case of anthranilic acid49) and desolvation processes (water removal from barbituric acid dihydrate50) are shown in Figures 10 and 11, respectively.

J. BERNSTEIN 106

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