Polymorphism of Acylglycerols: A Stereochemical Perspective

Review pubs.acs.org/CR

Polymorphism of Acylglycerols: A Stereochemical Perspective R. John Craven and Robert W. Lencki* Department of Food Science, University of Guelph, Guelph, Ontario, Canada N1G 2W1 Biographies References

1. INTRODUCTION Molecular crystals of organic compounds are “... held together by a multitude of weak interactions, and a huge number of freeenergy minima (polymorphs) exist within a few kilojoules/mol of the global minimum.”1 As a result, many organic compounds are polymorphic (i.e., have more than one solid form) and this can have a significant impact on the physical properties of the materials produced, including the biological availability of some pharmaceutical products (e.g., acetaminophen, pentobarbital). The underlying causes for polymorphism are numerous and have not been completely elucidated.2 To date, the bestcharacterized polymorphic systems are probably those where chirality leads to more than one molecular arrangement.3 Racemic mixtures of mandelic acid and alanine are well-known examples of compounds that display polymorphism due to this phenomenon. The natural predominance of one enantiomer in biological molecules is known as homochirality: briefly, amino acids are predominantly L and not D , while carbohydrates are predominantly D and not L.4 If nature had not settled on one enantiomer, the thinking goes, life could not have developed. This is because the self-assembly processes critical to life (e.g., efficient function of natural enzymes, transfer and storage of genetic information in nucleic acids) rely on the production of predictable and reproducible molecular and supramolecular structures.5 This is no less true for the emerging field of nanotechnology, where molecular and supramolecular chirality is essential for predictable assembly of noncovalently bonded molecular assemblies. Many naturally occurring acylglycerols are chiral and some lipid classes are homochiral; phospholipids, for example. It is likely that this homochirality is essential to membrane integrity and biological function.6 Important aspects of lipid crystallization behavior remain uncharacterized due to the chemical complexity of lipids, the complex nature of the kinetics involved, and the scarcity of methods suitable for observing these systems. Lipids found in nature are, typically, complex heterogeneous mixtures; and they often form mixed crystals in one of at least two possible polymorphs.7 Triacylglycerols are the main component in most commercial fats and oils; consequently, their crystallization behavior has been the subject of most research to date.7,8 In biological systems, the polar lipids (monoacylglycerols, diacylglycerols, phospholipids, sphingolipids, glycolipids, etc.) are often components of biological membranes where they minimize or regulate interchange within and between cells and

CONTENTS 1. Introduction 2. Principles and Theory 2.1. Development of Principles and Theory 2.2. Current Approach to Acylglycerol Polymorphism 2.3. Crystallographic Space Groups 2.4. Binary Phase Behavior of Enantiomeric Mixtures (Crystalline Tendency) 2.5. Stereochemistry of Acylglycerols 2.5.1. Nomenclature 2.5.2. Optical Activity 3. Stereochemical Perspective on Polymorphism of Acylglycerols 3.1. Triacylglycerols 3.1.1. Triacylglycerol β′ Forms 3.1.2. Crystal Twinning in Triacylglycerol β′ Forms 3.1.3. Unusually Stable β′ Forms of β-Tending Triacylglycerol 3.1.4. Summary of Unit Cell Stereochemistry for Triacylglycerols 3.1.5. Stereoisomers of Triacylglycerol 3.1.6. Stereochemical Factors Leading to β′Form Stability in Triacylglycerols 3.1.7. Free-Energy Schematics 3.2. 1,2-Diacyglycerols 3.3. 1,3-Diacylglycerols 3.4. Monoacylglycerols 4. Crystallization Behavior of Other Glycerol-Derived Molecules 4.1. Aryl Derivatives of Glycerol 4.2. Self-Assembly of Chiral Membrane Lipids 5. Summary and Conclusions Author Information Corresponding Author Notes © XXXX American Chemical Society

R R

A B B C C D E E E E E F G H I I J J K K O O O P Q R R R

Received: January 8, 2013

A

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fragments, he noticed that not only were they identical in shape and size but also there was a relationship between the shape of the fragments and the external form of the crystal. Continued study led him to report (in 1801) that quartz crystals were hemihedral (nonsuperimposable mirror images).9 With the discovery of polarized light (Malus, 1809), Arago (1811) and later Biot (1812) were able to see that quartz plates rotated polarized light, Biot noting that there was a directionality to this rotation (some crystals rotated light one way and some the other).9 Biot (1815) later extended these observations to include some organic liquids (turpentine) and solids (sucrose, camphor, and tartaric acid). Crystals of sodium ammonium tartrate were studied by a number of innovators at this time including Berzelius, Mitscherlich, and Biot’s student Louis Pasteur. Pasteur sought and eventually found a molecular cause for the hemihedrism and the optical activity of tartrate crystals (1847).10 Using tweezers, he separated crystals of sodium ammonium tartrate on the basis of their hemihedrism, dissolved some of the crystals in water, and then demonstrated that the direction of optical rotation for the crystals and their solutions was the same. It was not until 1874 (van’t Hoff) or 1875 (leBel) however, that a structural basis for the observed rotation of polarized light based on the tetrahedral geometry of sp3 carbon was proposed.9 In the meantime, Mitscherlich had discovered that similar stoichiometries produce similar crystals (isomorphism) by comparing various arsenates and phosphates (1818).2 Mitscherlich is also credited with discovering polymorphism (1825), while his mentor, Berzelius, is credited with allotropism (polymorphism of elements) (1844).2 It should be noted that, prior to this, Klaproth (1798) determined that two different crystals, calcite and aragonite, had the same chemical structure and Davey (1798) had determined that diamond was another form of carbon.2 While these earlier workers were, in effect, studying polymorphism and allotropism, these concepts are, nevertheless, more commonly attributed to the work of Mitscherlich and Berzelius. The multiple-melting behavior of triacylglycerols was first noticed by Heintz (1849), who recorded two melting points for tristearin, and by Duffy (1853), who observed three melting points for the same compound.11 Later work has confirmed that tristearin, along with many common triacylglycerols, has three major melting points [Tm (tristearin) = 54, 64, and 73 °C for the α, β′, and β forms, respectively] (Figure 1).12 The discovery of X-rays (Roentgen, 1895) and later X-ray diffraction (Laue, 1912) led to new insights in crystal structure research.13 Thus, Malkin (1934−1936) was able to correlate X-ray diffraction and melting point data and declare that triacylglycerols had numerous melting points due to polymorphism.11 Further knowledge of polymorphism in acylglycerols was acquired in dilatometric studies because different polymorphs have different packing densities and thus different specific volumes.14 Regrettably, much of the scientific discussion from this time was marred by a very public debate between Lutton and Malkin regarding the interpretation of melting point and X-ray data and the assignment of polymorphs; in particular, Malkin’s insistence on the existence of a vitreous state. This led to some confusion of nomenclature because, all too often, both parties used the same labels (α, β′, and β) to identify different crystal forms. This issue was finally resolved by Chapman, who employed IR spectra to unequivocally categorize the various acylglycerol polymorphs. These developments were described by Chapman in his landmark article from 1962.11

cellular structures. Acylglycerols as a whole provide an interesting model for the study of polymorphism. Interactions between molecules range from hydrogen bonding between amphipathic molecules (polar lipids) to van der Waals interactions between lipophilic molecules. There are elements of hydrophilicity (e.g., phosphatidyl and hydroxyl groups) and lipophilicity (e.g., acyl chains) in corresponding molecules. Also, the chain length and degree of unsaturation (number of double bonds) of the acyl chains is variable and contributes to differences in crystal packing and melting temperature. Furthermore, because the glycerol backbone has a stereocenter, some classes of acylglycerol are chiral, some are achiral, and others contain both chiral and achiral compounds (depending on substituents). The physical properties of fat-containing materials are often related to the polymorph in which the crystalline fat resides. For instance, butter and margarine in the desirable β′ polymorph are typically smooth and creamy, whereas solids in the more thermodynamically stable β polymorph can have a grainy texture. Similarly, cocoa butter in form V produces chocolate that is glossy, snaps cleanly, and melts nicely, whereas the more thermodynamically stable form VI is associated with bloom, a dull white or gray film that does not melt as readily. In both cases, the production of crystals in a metastable (thermodynamically less favored) polymorph results in a desirable product, whereas the production of crystals in the most stable polymorph often results in an unacceptable product requiring further processing or disposal. As a result, research on the relationships between chemical structure and polymorphism has typically focused on obtaining or preserving the desired polymorph in commercially important applications. In fats and oils, the main research goal has been to find practical and inexpensive solutions for industry. Unfortunately, this goal has been pursued at the expense of developing a deeper understanding of the underlying mechanisms causing polymorphism in acylglycerols. Indeed, this stands in sharp contrast to the attention devoted to understanding polymorphism in the pharmaceutical industry, where this knowledge can be critical for patent protection and is, thus, pursued with vigor. As a result, while the interplay between chemical structure and polymorphism has been studied for numerous natural and model acylglycerol systems, the underlying phenomena have not been fully characterized, and the role of stereochemistry has been almost completely overlooked. The main objective of this review is to address this serious oversight.

2. PRINCIPLES AND THEORY 2.1. Development of Principles and Theory

Though they are often viewed as separate and independent areas of study, crystal structure, polymorphism, and chirality all share a common historic origin. From a historical perspective, crystallography can be viewed as the increasing appreciation of the contribution made by ever-smaller units of crystalline solids, accompanied by development of the technologies that make these observations possible. As one would expect, this began with the examination of large mineral samples with the naked eye under natural light and proceeded through microscopy and the discovery of polarized light to the development of modern X-ray techniques that can determine the relative positions of constituent atoms. It all began with an accident, in 1781, when René Just Haüy mishandled and dropped a large piece of Icelandic spar (calcite).1 Upon examining the resulting B

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polymethylene chain) and those of the unit cell (i.e., the whole molecule) for waxes and paraffins, a distinction that is virtually absent from the literature on fats and oils.19 This is relevant because, while waxes are chemically similar to acylglycerols, they lack the stereochemical contributions of the glycerol backbone. This review represents a significant departure from previous attempts to understand the polymorphism of acylglycerols because it focuses on the crystallographic space group and the stereochemistry of the unit cell instead of the more commonly discussed subcell. It therefore takes into account the relative arrangement of whole molecules instead of the distance between methylene units, as is done in other works in the field. The distances between methylene units in adjacent polymethylene chains, measured by X-ray diffraction, correlate well with polymorphic form and are, thus, useful for identifying acylglycerol polymorphs (Table 1). Nonetheless, they are not necessarily the ultimate cause of the observed polymorphism. Indeed, the relative arrangement of other components of the molecule (e.g., glycerol backbone) may facilitate or limit the level of interaction and thus the distance between methylene units of adjacent acyl chains. The evidence presented in this review suggests that this is indeed the case: that the stereochemistry of acylglycerol molecules, based around the sn-2 position of the glycerol moiety, establishes the range of possible molecular conformations and interactions. Energy contributions from hydrogen bonding and van der Waals interactions determine the relative favorability of any specific molecular conformations within the resulting crystalline environment, and the relative spatial arrangement of molecules in the crystal lattice determines the polymorph. One of the challenges for a work like this is to correctly identify general and exceptional cases. To date, the majority of studies have examined the crystallization and polymorphic behavior of simple triacylglycerols (TAG; see section 2.5.1 for nomenclature) and consequently their behavior is considered to be the general case.7 For instance, a typical melting curve for tripalmitin (a simple TAG) is seen in Figure 1 with corresponding melting curves for α, β′ and β polymorphs. In nature and industry, however, mixed TAG (with two or three different acyl groups) are common and simple TAG are rarely encountered.7 For the purpose of this review, any acylglycerol having polymorphic behavior similar to that of a simple acylglycerol will be considered as following the general case. For example, a TAG with melting points β > β′ > α (like tripalmitin) will be considered to follow the general case, and a TAG with melting points β′ > β > α (like CnCn+2Cn, discussed in sections 3.1.2−3.1.4) will be considered an exceptional case.

Figure 1. Typical differential scanning calorimetry melting curve for a simple triacylglycerol (tripalmitin in this case) showing a sequence of polymorphs with increasing thermodynamic stability: α melt (Tp ≈ 44 °C), β′ crystallization (Tp ≈ 47 °C), β′ melt (Tp ≈ 55 °C), β crystallization (Tp ≈ 60 °C), and β melt (Tp ≈ 68 °C).

2.2. Current Approach to Acylglycerol Polymorphism

A great deal of data has been accrued since Chapman’s review article was published, and collected results have been discussed in a number of review articles and textbooks.7,8,15−17 In the published literature on acylglycerol polymorphism, the distance between methylene units (short spacings) in adjacent acyl chains has been a major focus. Short spacings, measured by Xray powder diffraction, have been associated with different polymethylene chain packings, and these have in turn been attributed to the different acylglycerol polymorphs (Table 1).18 Table 1. Short Spacing Data for Acylglycerols polymorph α β′ β α β′ β α β′ β β

short spacings (Å) Triacylglycerols 4.2 4.2 and 3.8 4.6 and 3.7, 3.8, or 3.9 1,2(2,3)-Diacylglycerols 4.1 4.3 m, 4.0 vs, 3.8 s 1,3-Diacylglycerols 4.6 and 3.7, 3.8, or 3.9 1(3)-Monoacylglycerols 4.68 w, 4.18 vs, 3.99 vw, 3.81 w 4.15 vs, 3.87 vw, 3.65 w, 3.30 w 4.55 s, 4,37 s, 3.86 s, 3.74 w 2-Monoacylglycerols 4.65 s, 4.4 vs, 3.9 vs

ref 20 21 21 20 20 22 12 12 12

2.3. Crystallographic Space Groups

12

The unit cell is a description of the smallest three-dimensional shape that can contain all the components necessary to reproduce the crystal lattice. As a result, a sample taken from anywhere within the crystal will contain all the elements required to reproduce the crystal lattice if it is of unit-cell dimension (lengths and angles) and the axes are properly aligned. It is not necessary, but when possible, a unit cell that contains whole molecules is chosen for illustration because it is simpler to describe. To construct the crystal lattice, unit cells (with their contents) are stacked and placed end-to-end with no rotation taking place (i.e., translation only). The collection of symmetry operations required to produce the unit cell is known as the space group. Among the many references that

In addition to short spacings, X-ray powder diffraction also provides the distance between methyl-end planes of the lamella (often referred to as the long spacing). This measurement, combined with knowledge of the typical acyl-chain length, has been used to determine the number of acyl chains stacked in each lamella (e.g., 2L, 3L; generally referred to as polytypism), whether a chair or asymmetric tuning fork configuration (ATF) is adopted (see section 3.1.5), and the chain-to-basal plane angle (β > β′ > α). This approach is identical to the one traditionally used to understand polymorphism in waxes and paraffins.18 Recently, however, researchers have made a clear distinction between properties of the subcell (i.e., the C

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explain crystal structure and space groups, Crystals and Crystal Structures23 is probably one of the most accessible and is recommended for those who are unfamiliar with these concepts. Space groups are a three-dimensional concept and thus are difficult to depict on plane paper. Nevertheless, the two-dimensional depictions available from the Web site A Hypertext Book of Crystallographic Space Group Diagrams and Tables24 are very helpful for visualizing the concepts presented in this review. While the crystallographic space group provides a host of information, this review will focus on the stereochemical information it provides. Of the 230 possible space groups, 65 are chiral and do not contain any reflective symmetry operations, indicating the unit cell is of uniform composition (containing pure enantiomer or stereoisomer) (Figure 2a). The

stereoisomers) (Figure 2c). Crystal structures of pure enantiomers can, in principle, be described only by one of the 65 chiral space groups. On the other hand, the 165 achiral space groups may be used to describe crystal structures of achiral molecules or racemic mixtures of molecules.26 Crystal structures are determined by either single-crystal X-ray (SCXR) or, more recently, high-resolution powder diffraction (XRPD) methods. Single-crystal X-ray is a more rigorous technique, whereas an existing model (usually derived from single-crystal X-ray) is required to determine crystal structure on the basis of powder diffraction data. 2.4. Binary Phase Behavior of Enantiomeric Mixtures (Crystalline Tendency)

To derive a typical phase diagram, both compounds are prepared separately, mixtures are made, and then the melting behavior of the pure compounds and their mixtures is plotted and evaluated. Phase diagrams for mixtures of enantiomers can be derived in a simpler fashion by preparing one pure enantiomer, the racemic mixture, and blends of the two. In this way, half of the phase diagram is derived with the understanding that the other half is its mirror image, and the need to synthesize and purify two enantiomers is avoided. The phase behavior of enantiomeric mixtures was first characterized by Roozeboom (1899) on the basis of his investigations of the phase rule (Gibbs, 1870s).3 He found that enantiomeric phase behavior can be categorized into three basic crystalline tendencies for subject enantiomers: eutectic behavior between enantiomers indicates formation of a mechanical mixture (conglomerate); molecular compound formation between enantiomers in a 1:1 ratio indicates formation of a racemic compound; and solid solution behavior between enantiomers is known as a pseudoracemate (Figure 2). For chiral molecules, crystal structures with chiral space groups are associated with conglomerate formation, whereas achiral space groups are associated with racemic compound formation. Pasteur (1847) was the first to report conglomerate formation and the resultant resolution of enantiomers into separate crystals when he physically separated crystals of sodium ammonium tartrate.9 In many of these chiral systems, polymorphism occurs because the racemic mixture has more than one crystalline tendency, each with its own chemical potential. This phenomenon is described more thoroughly in chapter 2.5, Polymorphism in Binary Systems, in the text Enantiomers, Racemates, and Resolutions,3 and the mechanism (in terms of free energy) is described below in section 3.1.7.

Figure 2. Summary of (top row) unit cell stereochemistry and (bottom row) characteristic liquidus lines for phase diagrams of enantiomeric mixtures for (a, b) conglomerate (eutectic), (c, d) racemic compound, and (e, f) pseudoracemate (solid solution). For schematics in the top row, unit cells are represented by the small squares, one stereoisomer is represented by an open circle and the opposite stereoisomer by a circle containing a comma, and molecules with undefined stereochemistry are represented by shaded circles. The relative proportion (and not the total number) of molecules is indicated by this scheme. Panels represent (a) chiral and (c) achiral space groups. Typically, only half of each phase diagram (bottom row) is derived by use of binary mixtures of pure enantiomer (E) and racemic mixture (R). Data can be extrapolated to include the opposite enantiomer (E′) if desired. Reprinted with permission from reference 25. Copyright 2012 Wiley−VCH Verlag GmbH & Co. KGaA, Weinheim, Germany.

remaining 165 space groups (achiral space groups) contain reflective symmetry operations; this means the unit cell is of mixed composition (containing both enantiomers or both

Figure 3. General structures for (a) 1,2-isopropylidene-sn-glycerol, (b) 1-monoacyl-sn-glycerol, (c) 1,2-diacyl-sn-glycerol, and (d) triacylglycerol. D

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Table 2. Melting Points32 and Polymorphism of Enantiopure and Racemic Triacylglycerols enantiomer

a

racemic mixture

positional isomer

Tm (°C)

polymorph

Tm (°C)

polymorph

12:0−16:0−16:0 16:0−18:1−18:0 18:0−16:0−16:0 18:0−16:0−16:0 12:0−12:0−18:0 12:0−12:0−14:0 16:0−16:0−14:0 10:0−10:0−16:0

53.6−53.9 33.9−34.5 63.2−64.0 60 45 43 54.8 32.90

β′ β′ β′ β′ β′ β′ β′ β′

55.0−55.8 37.5−38 62.0−62.9 61 45 42

β β β β β β β β

β racemic compound.

b

33.38

crystalline tendency a a

a, b

ref 27 27 27 33 33 33 34 21

β′ conglomerate.

2.5. Stereochemistry of Acylglycerols

demonstrated by measuring the rotation of polarized light. In addition, the optical rotation of mono- and diacylglycerols is usually negligible or nonexistent, and there are few existing literature values available for comparison. Consequently, measurements of optical rotations, even when they do occur, are often of little use in determining the enantiomeric purity (or excess) of partial acylglycerols. On the other hand, the optical rotation for enantiopure isopropylideneglycerol is large (>14° neat at 20 °C) and well-known (Figure 3a). Consequently, the best confirmation that prepared compounds are indeed pure enantiomers is measurement of the appropriate (significant and well-documented) optical rotation for the starting material (e.g., isopropylideneglycerol). Without this key parameter, the enantiomeric purity of any resulting products cannot be assured.

2.5.1. Nomenclature. Acylglycerols are fatty acid esters of glycerol that have one, two, or three fatty acid substituents forming mono-, di-, or triacylglycerols, respectively (Figure 3). Each acyl group (fatty acid residue) is covalently bonded to the glycerol backbone at one of three stereospecifically unique locations: sn-1, sn-2, or sn-3. Enantiopure acylglycerols are identified with the appropriate stereospecific number and snshort forms (e.g., 1,2-bisdecanoyl-3-palmitoyl-sn-glycerol or sn10:0−10:0−16:0, where m = o = 9, q = 15, n = p = 19, and r = 31 in Figure 3). Racemic mixtures are identified with a more general name and the rac- short forms [e.g., bisdecanoyl-1(3)palmitoyl-rac-glycerol or rac-10:0−10:0−16:0]. Most scientific studies have focused on “simple” acylglycerols with identical fatty acid residues (m = o = q and n = p = r in Figure 3), whereas most naturally occurring diacylglycerols (DAG) and TAG are “mixed”, having two or three different acyl groups. Acylglycerol molecules are achiral if the acyl groups in the αpositions are the same (i.e., m = q and n = r) and chiral if they are different (i.e., m ≠ q or n ≠ r). For every chiral acylglycerol, two enantiomers are possible (e.g., sn-10:0−10:0−16:0 and sn16:0−10:0−10:0), and depending on the source or means of preparation, compositions can range from pure enantiomer to racemic mixture. Enantiomers are stereoisomers that are nonsuperimposable mirror images of each other (like hands), and a racemic mixture is a 1:1 mixture of the two enantiomers (e.g., rac-10:0−10:0−16:0 is 50% sn-10:0−10:0−16:0 and 50% sn-16:0−10:0−10:0). In the literature, achiral and chiral acylglycerols are usually described by the terms symmetric and asymmetric. These terms are misleading because all acylglycerols are rotationally dissymmetric and adopt reflectively dissymmetric configurations in the higher-melting forms (except 2-monoacylglycerols). Accordingly, the more rigorous terms achiral and chiral are used throughout this review. 2.5.2. Optical Activity. Optical rotation is an important property of many chiral molecules. This property has contributed greatly to the development of understanding regarding chemical structure (section 2.1). Optical rotation is routinely used to confirm the enantiomeric purity (or excess) of chiral compounds. It is, unfortunately, of limited value in acylglycerol chemistry because, in general, triacylglycerols are not optically active. In fact, prior to the introduction of lessambiguous terminology, Wilhelm Schlenk Jr.27 described triacylglycerols as “crypto-optically active” because the term “chiral”, coined by Lord Kelvin (1873), had yet to be reintroduced to describe the stereochemical properties of molecules regardless of their effect on polarized light.9 So, chirality or enantiomeric excess of triacylglycerols cannot be

3. STEREOCHEMICAL PERSPECTIVE ON POLYMORPHISM OF ACYLGLYCEROLS 3.1. Triacylglycerols

Triacylglycerols are the most abundant of the commercially available acylglycerols. Historically, TAG products have been divided, somewhat arbitrarily, into fats, which are solid at room temperature, and oils, which are liquid at room temperature. The bulk of existing crystallization studies have focused on optimizing the properties of fats by obtaining or stabilizing the solid fraction in the desired polymorph, or in oils by crystallizing out any solids likely to form during refrigeration so that oils will remain solid-free during typical usage. Consequently, most of the data and the current theoretical approach to polymorphism in acylglycerols are focused almost exclusively on the crystallization behavior of TAG.7,8,15−17 The current approach to understanding polymorphism in TAG has recently been summarized by Larsson et al.:8 “... the following three major molecular interactions... are most influential in stabilizing the polymorphic structures of TAG crystals... 1) Aliphatic chain packing results from the molecular interactions between saturated and unsaturated fatty acid chains. It determines the subcell structures, olefinic conformation, and chain-length structure. 2) Glycerol conformation among the glycerol groups determines the total configuration (straight or bent) of the TAG molecule. ... 3) Methyl-end stacking may play important roles in organizing the chain inclination and chain-length structures. ... These three factors interrelate in a complicated manner.” The discussion of glycerol conformation referred to in point 2 (above), while detailed, does not consider the stereochemistry of the glycerol backbone. Instead, the configuration of glycerol is argued on the basis of the interaction of p-orbitals and rotation of the E

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glycerol moiety to minimize eclipsing of hydrogen atoms.28−30 Apart from this, there is little to distinguish the current consensus approach (as outlined above) from the approach previously suggested by Chapman8 or from the approach taken to understanding polymorphism in waxes (see section 2.2).31 One of the main shortcomings of the current approach to understanding polymorphism in acylglycerols is that it does not explain why, for many TAG, the pure enantiomer is β′-tending (i.e., β′ is the most thermodynamically stable polymorph) while the racemic mixture is β-tending (i.e., β is the most thermodynamically stable polymorph) (Table 2). For these systems, pure enantiomers and corresponding racemic mixtures have similar melting points but different polymorphic tendencies. Clearly, a plausible explanation for this observation must consider the stereochemistry of the constituent molecules. This is best explored by deriving a phase diagram for mixtures of enantiomers. To date, enantiomeric phase behavior (crystalline tendency) has been examined for three of the chiral TAG systems listed in Table 2: 12:0−16:0−16:0, 18:0− 16:0−16:0, and 10:0−10:0−16:0 (Figures 4 and 5). Both

Figure 5. Liquidus data for enantiomeric mixtures of 10:0−10:0−16:0, reported as mole fraction of racemic mixture (XR). Triangles are for data collected at 2 °C/min; diamonds, at 5 °C/min; and squares, at 10 °C/min, by differential scanning calorimetry. Solid symbols represent melting data for tempered samples, and open symbols represent data obtained from cooling/heating cycles on melted samples. Solid line was derived by linear regression; dashed line is the suggested highmelting liquidus. Reprinted with permission from reference 21. Copyright 2011 American Chemical Society.

TAG (P1̅ for the most part) indicate that the unit cell (with one exception) contains both stereoisomers (Table 3). It is wellknown that acetoyl acylglycerols adopt atypical configurations and exhibit unusual polymorphic behavior.52 Thus, it is not surprising that 1,2-dipalmitoyl-3-acetoyl-sn-glycerol (sn-16:0− 16:0−2:0) is an exception (P21 space group) with characteristics more akin to dimyristoyl-sn-glycero-3-phosphocholine than to TAG in general.41 The remaining 33 results in Table 3 confirm the previously discussed crystalline tendency results that showed β-form TAG is a racemic compound and therefore both stereoisomers are present in the unit cell (Figure 2c,d). 3.1.1. Triacylglycerol β′ Forms. Stable crystals of achiral or chiral-racemic TAG in the β′ form are uncommon since TAG are, in general, β-tending. The β′-form TAG listed in Table 4 for which crystal structures have been determined can be divided into five separate categories: (1) TAG with oddnumbered acyl chains,53 (2) CnCn+2Cn series TAG,54−57 (3) a chiral-enantiopure TAG,34 (4) chiral-racemic TAG,57 and (5) a TAG with exceptional polymorphic behavior.50 The chiralenantiopure TAG (3) and the CnCn+2Cn series TAG (2) are not atypical since these molecules appear to be β′-tending in all cases. The remaining TAG (1, 4, and 5) are considered βtending but have β′ forms that are sufficiently stable to be studied by X-ray diffraction. Single-crystal X-ray results for a pure enantiomer of TAG (sn-16:0−16:0−14:0) led to a chiral space group (C2) being assigned.34 This agrees with the results from Table 2 and with the enantiomeric phase diagrams (Figure 5) indicating the β′ unit cell contains pure enantiomer. Similarly, Birker et al.54 conducted a thorough investigation of CnCn+2Cn-type TAG that included single-crystal X-ray results for 12:0−14:0−12:0 along with light micrographs and scanning electron micrographs of twinned β′ TAG crystals. When the role and effect of crystal twinning were completely accounted for, the C2 space group

Figure 4. Liquidus data for enantiomeric mixtures of (●) 18:0−16:0− 16:0 and (■) 12:0−16:0−16:0, reported as mole fraction of racemic mixture (XR). Melting points for mixtures were determined by capillary melting point apparatus as described in the reference. Data replotted with permission from reference 27. Copyright 1965 American Oil Chemists’ Society.

studies found that chiral-racemic TAG form a stable racemic compound (β polymorph). In the most recent study it was also determined that the metastable β′ form was associated with eutectic behavior between the two enantiomers (conglomerate) (Figure 5). As mentioned previously, the relative stereochemistry of molecules within the unit cell can also be determined by X-ray diffraction (single-crystal and powder diffraction). This information is expressed by the crystallographic space group determined for the crystal structure. Crystallographic space groups have been assigned for many β- and β′-form TAG, and as a result the relative stereochemistry of their unit cells can be determined from the absence or presence of reflective symmetry operations. Space group assignments for β-form F

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Table 3. Space Group Assignments for β-Form Triacylglycerols S# d

compda

SCXR/XRPDb

chair/ATFc

2L/3L

10:0−10:0−10:0 12:0−12:0−12:0 18:0−18:0−18:0 10:0−C11Br:0−10:0 various SSS sn-16:0−16:0−2:0f 16:0−16:0−16:0f 18:1t−18:1t−18:1tf

SCXR SCXR SCXR SCXR XRPD SCXR SCXR SCXR

ATF ATF ATF ATF ATF chair ATF ATF

2L 2L 2L 2L 3L 2L 2L 2L

P1̅ P1̅

both both

P1̅ P1̅ P21 P1̅ P1̅

14:0−14:0−14:0f 18:0−18:0−18:0f

XRPD

ATF

2L

13:0−13:0−13:0f 15:0−15:0−15:0f 17:0−17:0−17:0f 19:0−19:0−19:0f

XRPD

ATF

18:0−18:1−18:0

XRPD

14:0−18:1−14:0f 16:0−18:1−16:0f 18:0−18:1−18:0f 16:0−18:1−18:0f 18:0−18:1−20:0f

notes

ref

both both one both both

T∥ subcell T∥ subcell T unit cell T∥ subcelle g T unit cellh T unit celli

36 37 38 39 40 41 42 43

P1̅

both

T unit cell

44

2L

P1̅

both

T unit cell

45

ATF

3L

P1̅

both

T∥ subcellj

46

XRPD

ATF

3L

P21/n

both

M∥ subcellk

47

16:0−18:1−16:0f 18:0−18:1−18:0f 16:0−18:1−18:0f 18:0−18:1−20:0f

XRPD

ATF

3L

Cc

both

M∥ subcelll

48

18:0−18:0−18:1tf 16:0−18:0−18:0f 16:0−16:0−18:0f 16:0−16:0−18:1tf 14:0−14:0−16:0f 12:0−14:0−14:0f 12:0−12:0−14:0f 18:0−18:1t−18:0f 16:0−18:1t−16:0f 16:0−18:0−16:0f,m

XRPD

ATF chair chair chair chair chair chair ATF ATF ATF

2L

P1̅

both

T unit cell

49

12:0−18:1−12:0f

XRPD

ATF

3L

Cc

both

M unit celln

50

a

space group

b

S = saturated fatty acid; U = monounsaturated fatty acid; t = trans. SCXR = single-crystal X-ray; XRPD = X-ray powder diffraction. cATF = asymmetric tuning fork. dOne or both stereoisomers present in the unit cell. eCalculations for a series. fListed in the Cambridge Structural Database 2012.51 gExceptional polymorphic behavior common for acetoyl acylglycerols. hReview of literature for SSS. iError; refer to ATF as chair. jAlso cocoa butter. kCocoa butter TAG in β1 form. lCocoa butter TAG in β2 form. mTm (16:0−18:0−16:0): β form (66.35 °C) < β′ form (69.85 °C). nChair for metastable β′ form (see Table 4), ATF for stable β form.

was assigned to molecules in this series. Once again, unit cells of the β′-stable TAG contained pure stereoisomer (Figure 2a,b). This supports crystalline tendency results previously discussed, indicating that β′-form TAG is a conglomerate and that enantiopure TAG are β′-tending (Figure 5 and Table 2). 3.1.2. Crystal Twinning in Triacylglycerol β′ Forms. Other results for chiral-racemic β′-form TAG (16:0−16:0− 18:1t, 16:0−16:0−18:0, and 16:0−18:0−18:0) and CnCn+2Cntype TAG are less consistent than those already discussed. Sometimes chiral and other times achiral space groups have been assigned to compounds within the same series. However, evidence suggests these discrepancies exist because the role and

effect of crystal twinning were not taken into account (cf. Table 4, footnote d). The formation of crystal twins and their effect on crystal structure determinations for β′ forms of TAG is welldocumented.17,54 According to Larsson,17 “The structure of the β′ form has not been determined completely. It forms thin needles with a remarkable tendency for twin growth, making the determination of single-crystal structure complicated.” Crystal twinning is “the growth of two or more differently oriented domains of a single structure into a twinned crystal... twinning can be described in terms of a symmetry element, the twin-element, which, unlike normal symmetry elements, does G

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Table 4. Space Group Assignments for β′-Form Triacylglycerols SCXR/XRPDa

compd 11:0−11:0−11:0

d

chair/ATFb

2L/3L

SCXR

space group

S# c

notes

ref

P21/c

both

e

53

12:0−14:0−12:0

SCXR

chair

2L

C2

one

f,g

54

10:0−12:0−10:0d 12:0−14:0−12:0d 14:0−16:0−14:0d 16:0−18:0−16:0d

XRPD

ATF

2L

Ic2a

both

f,h

55

10:0−12:0−10:0d,i 12:0−14:0−12:0 14:0−16:0−14:0d,i.k 16:0−18:0−16:0d

SCXR XRPD XRPD XRPD

chair

2L

Iba2 I2 I2/Iba2 Iba2

both one one/both both

f,j

56

sn-16:0−16:0−14:0i

SCXR

chair

2L

C2

one

l

34

16:0−18:1t−16:0i 16:0−18:0−16:0i,f,n 16:0−16:0−18:1ti 16:0−16:0−18:0i 16:0−18:0−18:0d,i

XRPD

chair

2L

I2 I2 I2 I2 C2/c

one one one one both

m

57

12:0−18:1−12:0i,o

XRPD

chair

2L, 3L

P1̅

both

p

50

a

Single-crystal X-ray or X-ray powder diffraction. bAsymmetric tuning fork. cOne or both stereoisomers present in the unit cell. dInconsistencies may be attributed to crystal twinning. eTwinning observed but not taken into account. fCnCn+2Cn series. gM; twinning characterized. hPseudo-O; did not consider twinning; later corrected ATF to chair and revised space group assignment.56 iListed in the Cambridge Structural Database 2012.51 j Pseudo-O or M; did not consider twinning, . kI2 at 250 K, Iba2 at 298 K.56 lM; β′-tending enantiomer and β-tending racemic mixture. mM. nTm (16:0−18:0−16:0): β form (66.35 °C) < β′ form (69.85 °C). oUnusual molecular configuration. pT; chair for metastable β′ form, ATF for stable β form (see Table 3), t = trans.

not occur in every unit cell but relatively few times  or even only once  on a macroscopic scale.”58 Unfortunately, several X-ray studies on β′-form TAG did not take the role and effect of crystal twinning into consideration.53,55−57 As a result, compounds within the same series were assigned different space groups (cf. Table 4, footnote d). For example, the C2/c space group was assigned to 16:0− 18:0−18:0, thereby contradicting the assignment of the I2 space group to 16:0−16:0−18:0 and 16:0−16:0−18:1t. These compounds are chiral-racemic TAG crystallized in the chair configuration and it is likely they would all have the same space group. Another example of different space groups being assigned to molecules in the same series is Iba2 (achiral space group) for 10:0−12:0−10:0, 16:0−18:0−16:0, and 14:0− 16:0−14:0 at 295 K and I2 (chiral space group) for 12:0− 14:0−12:0 and 14:0−16:0−14:0 at 250 K.56 In addition, while the space group Iba2 was assigned to 16:0−18:0−16:0 in the aforementioned study, the space group I2 was later assigned to this compound by the same research group.57 As the authors freely admit, “Birker et al also reported cell parameters of β′LML comparable to the parameters as determined in this study. They also observed Ic2a pseudosymmetry but concluded finally that the space group was C2.”55,56 It seems Birker et al.54 assigned C2 to 12:0−14:0−12:0 because they were aware of the role played by crystal twinning, whereas van Langevelde et al.55,56 assigned I2 and Iba2 to compounds within the same series, in spite of the apparent contradiction. Furthermore, in the study of CnCn+2Cn-type β′-tending TAG, the authors reported difficulties in crystal structure determination due to peak broadening and splitting as well as higher-than-normal

residuals (R-values) resulting from the comparison of observed and calculated structure factors.55,56 All told, this suggests more satisfactory results would have been attained in these studies if the prevalence and effects of crystal twinning had been duly considered. This would have led to chiral space groups (C2 or I2) being assigned to all β′-form CnCn+2Cn TAG. It should be noted that, for the most part, these inconsistent results originate from crystal structure determinations based on powder diffraction and not single-crystal analyses. While single crystals can be prescreened for the existence of crystal twins and other defects, such procedures are, for obvious reasons, not employed in powder diffraction experiments. In addition, interpretation of powder diffraction data relies on the availability of a suitable model, usually derived from singlecrystal experiments. 3.1.3. Unusually Stable β′ Forms of β-Tending Triacylglycerol. In addition to the incongruities introduced by crystal twinning (section 3.1.2), the space group assignments for the β′ forms of 12:0−18:1−12:0 also require further explanation (cf. Table 4 footnote o).50 Molecules in the β′ form of this compound adopt the chair configuration (section 3.1.5) with methylene units of the oleic acid chain lying parallel to methylene units of the lauric acid chain up to the kink produced by the cis double bond. The tail end of the oleic acid chain extends beyond the methyl-end plane formed by the lauric acid terminal methyl groups and is interdigitated with the tail end of oleic acid chains from molecules in the adjacent leaflet. This unusual molecular configuration is stabilized by van der Waals interactions between the methylene groups of the interdigitated oleic acid tails. This exceptional case is far H

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Figure 6. Possible stereoisomers for (a) crystallographic symbol, (b) chair, and (c) asymmetric tuning fork configurations. Stereoisomers are achiral conformers or chiral enantiomers of triacylglycerol. Numbers in circles represent stereospecific numbering for acyl chains (sn-1, -2, and -3). Reprinted with permission from reference 25. Copyright 2012 Wiley−VCH Verlag GmbH & Co. KGaA, Weinheim.

Figure 7. Schematic depicting polymorphic transition mechanics for (a) achiral and (b) chiral triacylglycerols (TAG). A change in conformation of constituent molecules results in a polymorphic transition for achiral TAG, whereas physical transport of at least one enantiomer is required for the β′ to β transition in chiral TAG.

chair configuration, an acyl chain in the α-position (sn-1 or sn3) extends in the direction opposite to the other two acyl chains. In the ATF configuration, the β-position (sn-2) acyl chain extends away from the α-position acyl chains and the sn-1 or -3 position acyl chain is aligned with the chain in the sn-2 position (Figure 6). Typically, chiral TAG adopt the chair configuration while achiral TAG adopt the ATF, but occasionally achiral TAG adopt the chair configuration; for example, CnCn+2Cn series TAG in the β′ form (section 3.1.1). For each configuration (chair or ATF), two conformations are possible; these are the stereoisomers discussed previously, which are related by a reflective symmetry operation (Figure 6). For achiral TAG, there is no energy difference between molecules in either conformation and thus no preferred conformation. For chiral TAG, however, each enantiomer has a preferred conformation: the conformation with the lowest energy. This difference has a profound effect on the crystal growth and polymorphism of TAG positional isomers. Achiral TAG will adapt to the requirements of the crystal lattice, adopting the conformation most appropriate for the growing crystal surface. On the other hand, chiral TAG enantiomers will be added to the growing crystal surface only when their preferred conformation is required. So, for a racemic mixture, a growing β′-form crystal composed of one enantiomer (E) will be surrounded by a liquid phase diminished in that enantiomer (E) and enriched in the opposite enantiomer (E′). There will also be large differences between achiral and chiral TAG as they undergo polymorphic transitions. For achiral TAG in the ATF configuration, transition from β′ to β may simply require that

removed from the general case or other special cases already discussed, so it does not warrant further discussion, apart from mentioning that it provides an interesting example of a relatively stable TAG crystal form with incomplete chain-end matching. The more stable β form, on the other hand, adopts the asymmetric tuning fork (ATF) configuration with complete chain-end matching (Table 3).50 3.1.4. Summary of Unit Cell Stereochemistry for Triacylglycerols. To summarize, the unit cell of β-form TAG contains both stereoisomers, the exceptional polymorphism of acetoyl acylglycerols notwithstanding (viz. sn16:0−16:0−2:0). In contrast, the unit cell of β′-form TAG is uniform and contains pure stereoisomer once the effects of twinning and other exceptional behaviors are taken into account. Pure enantiomers must, therefore, be β′-tending; this explains the results presented in Table 2. Thus far in this review, the stereochemistry of the α form, the least thermodynamically stable polymorph, has not been discussed. However, since two of three possible behaviors have already been identified (i.e., β′ = conglomerate, β = racemic compound), the α form must be, by default, a pseudoracemate with solid solution behavior between opposite enantiomers and stereochemistry being of little to no consequence for this polymorph. At present, there are insufficient data to confirm this suggestion for TAG, although it does appear to be the case for 1,2-DAG (section 3.2). 3.1.5. Stereoisomers of Triacylglycerol. In the highermelting polymorphs (β′ and β) TAG adopt one of two possible configurations: chair or asymmetric tuning fork (ATF). In the I

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Figure 8. Free-energy versus temperature schematics for (a) enantiotropic and (b) monotropic systems. Dashed line indicates liquid, solid lines indicate possible polymorphs (I and II), and gray line indicates path.

3.1.7. Free-Energy Schematics. Free-energy versus temperature schematics are perhaps the simplest way to illustrate the relative thermodynamic stability of polymorphic forms and to understand resultant melting behavior.61 Freeenergy schematics are frequently used to define enantiotropic and monotropic systems where the polymorphic transition occurs either below or above the melting point (Figure 8). As they undergo thermal treatment (at constant pressure), systems will follow a path (along the curves) that provides the lowest possible free energy and highest melting point allowed for that temperature and sample history. The polymorphic transition for enantiotropic systems is reversible, while the polymorphic transition for a monotropic system is irreversible. For chiral molecules, liquid lines corresponding to the pure enantiomer and the racemic mixture can be plotted separately (Figure 9).62

sections of the molecule rearrange to adopt the opposite conformation (stereoisomer) (Figure 7a). In principle, this could occur in the solid state but would proceed faster in the melt. For chiral-racemic TAG, however, the same transition from β′ to β will, in most cases, require that molecules physically relocate from one unit cell (of pure enantiomer) to a new unit cell (containing both enantiomers) (Figure 7b). A transition like this will not occur in the solid state, and if it occurs in the melt, will be very slow. Consequently, β-form crystals of chiral-racemic TAG are most easily prepared by crystallizing from solvent.11 3.1.6. Stereochemical Factors Leading to β′-Form Stability in Triacylglycerols. In the past, β′-stability has been attributed to molecular characteristics such as (1) fatty acid chain length and diversity, (2) TAG carbon number and diversity, (3) TAG structure, (4) concentration of liquid fraction, and (5) fluctuations in temperature.8,59 These observations are consistent with the perspective laid out above in describing the reticence of chiral-racemic TAG to undergo polymorphic transitions from β′ to β. The existence of β′-tending achiral or racemic systems is, however, an entirely different matter. For example, molecules in the saturated CnCn+2Cn series are β′-tending and adopt a chair configuration, instead of the usual ATF configuration more commonly associated with achiral TAG. In addition, the metastable β forms of CnCn+2Cn series TAG are unusual because they have lower melting points than the stable β′ forms (e.g., for 16:0− 18:0−16:0, Tm for β = 66.35 °C and for β′ = 69.85 °C) (Tables 349 and 457). These systems are the achiral counterpart of a chiral monotropic system with a metastable racemic compound (cf. Figure 4e in ref 3, p 135). As a result, their exceptional behavior is difficult to explain without considering stereochemistry. By use of the concepts developed so far, however, these systems can be described in simple terms as a system having both stereoisomers in the unit cell of the metastable form (β) and pure stereoisomer (i.e., resolution of conformers) in the unit cell of the stable form (β′). Positional isomers of chiral-racemic TAG that have oleic acid in one of the α-positions (sn-1 or sn-3) and palmitic or stearic acid in the other two positions (i.e., rac-18:1−16:0−16:0, rac18:1−18:0−18:0, rac-18:1−18:0−16:0, and rac-18:1−16:0− 18:0) are also β′-tending.60 These molecules adopt a 3L chair configuration with the oleoyl chains lying side-by-side sandwiched between two leaflets containing the saturated acyl chains. These molecules have no detectable β form. The favorability of the β′ form must be due to the combined effects of molecular configuration and uniformity of conformation in the separate enantiomeric domains.

Figure 9. Free-energy versus temperature schematic for a system with conglomerate formation (eutectic behavior between enantiomers). Free-energy difference between liquid lines is due to the entropy of mixing term (indicated by arrow).62 Black lines indicate racemic mixture (R) and gray lines indicate pure or resolved enantiomers (E). All other features are defined in Figure 8.

The free-energy difference between the two liquid curves is, in theory, equal to the entropy of mixing (or unmixing) term (i.e., TΔS). In addition, a solid line corresponding to the resolved enantiomers (or the pure enantiomer) can also be added to the schematic. Chiral TAG can crystallize at three of the line intersects: two β′ forms (β′E = pure enantiomer and β′R = racemic conglomerate) and one β form (racemic compound) (Figure 10a). There is no β form for the pure enantiomer because this form requires both enantiomers. For achiral TAG, a pure liquid stereoisomer does not exist. Consequently, there is only one liquid curve (corresponding to the racemic mixture liquid) and two line intersects denoting crystallization for achiral TAG: one β′ form (corresponding to β′R in Figure 10a) and one β form. The free-energy difference between β′ and β forms for achiral TAG is caused, in part, by segregation of the J

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Figure 10. Free-energy versus temperature schematics for (a) general case and (b) special case (CnCn+2Cn-type) for triacylglycerols (TAG). In chiral TAG, eutectic behavior leads to a metastable conglomerate β′ form for the racemic mixture (β′R), and the highest-melting form for pure enantiomer is β′ (β′E). In general, the most stable polymorph for the racemic mixture is a racemic compound (β); however, in some special cases, CnCn+2Cn-type TAG for example, the β′ form has greater stability due to additional considerations. Features are defined in Figure 9.

commercial interest than TAG, partial acylglycerols are also harder to study since they are less stable due to acyl migration. This is an intramolecular reaction whereby fatty acids on the glycerol backbone transition from one hydroxyl to another via de- and re-esterification.64 At equilibrium, 1,3-DAG are favored over 1,2-DAG by approximately 3:2 (relative concentration) due to differences in the nucleophilic character of primary and secondary hydroxyls. Crystalline samples of monoacylglycerols (MAG) and DAG for X-ray or thermal analysis must therefore be prepared with care and analyzed immediately. X-ray data for enantiopure (α and β′ forms) and racemic (α form) 1,2-DAG are consistent with findings from the binary phase diagram (Table 5). Unfortunately, there are as yet no crystal structure determinations for β′-form racemic mixtures of 1,2-DAG; α to β′ transitions are slow (see below) and acyl migration probably occurs concurrently. Evidently, the unit cell of the β′ form contains pure enantiomer, whereas the unit cell stereochemistry has little or no consequence for the α form. While α to β′ transitions proceed smoothly for pure enantiomers (1,2- or 2,3-DAG), it is difficult to induce direct α to β′ transitions for racemic mixtures during DSC experiments, regardless of heating rate. Transition from α to β′ can eventually be induced by holding solids in the α form slightly above the α melting temperature for 7 h.70 The relationship between possible crystal forms for 1,2-DAG can be illustrated by a free-energy versus temperature schematic in Figure 13. The transition from α to β′ is impeded for the racemic mixture because spontaneous resolution into enantiomeric domains is required (β′R in Figure 13). The pure enantiomer, on the other hand, requires no further resolution and has a higher melting point than β′R (β′E in Figure 13). In addition, the concentration of each enantiomer in the racemic mixture (1,2- and 2,3-DAG) is half the concentration for the enantiomer in the enantiopure system. As a result, the degree of supersaturation and consequently the driving force for the transition is far greater for β′E than for β′R.

two stereoisomers into separate domains (analogous to the resolution of enantiomers for chiral TAG). In addition to the resolution of stereoisomers, however, other factors (e.g., changes to methylene packing, changes to basal plane angle, crystal twinning) may also contribute to differences in free energy between β′ and β forms. These additional factors can have a huge influence on polymorphic behavior for a given compound. For example, the exceptional CnCn+2Cn-type TAG, discussed above, are β′-tending and have a metastable β form (Figure 10b). 3.2. 1,2-Diacyglycerols

The positional isomers 1,2- and 2,3-diacylglycerol are commonly referred to collectively as 1,2-DAG. Along with 1(3)-monoacylglycerol and the membrane lipids (e.g., phospholipid, glycolipid), they are the only completely chiral acylglycerol compound classes; there are no achiral counterparts. Enantiomers of 1,2-DAG adopt conformations similar to the chair forms for TAG (Figure 11). These molecules

Figure 11. Enantiomers 1,2- and 2,3-diacylglycerol. Features are defined in Figure 6.

crystallize in polymorphs designated α and β′ on the basis of their short spacings, which are similar to those for the corresponding TAG forms (Table 1). In order to assess crystalline tendency, Iwahashi et al.63 investigated the phase behavior of binary mixtures of enantiopure and racemic 1,2DAG of palmitic and stearic acid (Figure 12). In both cases, racemic mixtures of 1,2(2,3)-DAG formed a eutectic (conglomerate) in the highest-melting form (β′) and a solid solution (pseudoracemate) in the metastable (α) form. Far fewer crystal structure data have been collected for the partial acylglycerols than for TAG. In addition to being of less

3.3. 1,3-Diacylglycerols

Similar to TAG, 1,3-diacylglycerols can be either chiral (diacid) or achiral (monoacid). Two polymorphic forms are associated with 1,3-DAG, a high-melting β1 form and a low-melting β2 form; the only discernible difference between the two is a small difference in melting point (i.e., same IR, X-ray, etc.).70 Crystalline tendency has been assessed by investigating the phase behavior for mixtures of enantiopure and racemic 10:0− OH−16:0.22 These mixtures demonstrated eutectic behavior, indicating the formation of a conglomerate with separate K

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Figure 12. Phase diagram data for enantiomeric mixtures of enantiopure and racemic (R) (a) 16:0−16:0−OH and (b) 18:0−18:0−OH. (●) Liquidus data for β′ form; (■) solidus data for β′ form; (○) α-form melting points. Data replotted with permission from reference 63. Copyright 1984 The Chemical Society of Japan.

propane-1,2-diol (cf. Figure 4 in ref 71). The data suggest that, in addition to the phase behavior of stable forms already discussed, a solid solution of enantiomers, in a 3:1 ratio, forms an unstable solid solution with its less-prevalent enantiomer at low concentrations (cf. dashed gray line in Figure 15). Additionally, there also appears to be a metastable eutectic between the solid solution of enantiomers (3:1) and its lessprevalent enantiomer (cf. black line in Figure 15). It seems reasonable to suggest that the metastable eutectic between the solid solution (3:1) and the pure enantiomer is responsible for producing the metastable forms (β2) and that the eutectic between the two pure enantiomers produces the stable form (β1) in chiral-racemic 1,3-DAG. Three single-crystal X-ray studies have been conducted for 1,3-DAG (Table 6). In all three cases, the researchers’ original intent was to investigate other compounds and single crystals of 1,3-DAG were obtained by accident. Larsson72 was trying to produce TAG of 3-thiadodecanoic acid and instead produced the achiral 1,3-bis(3-thiadodecanoyl)glycerol (C11S:0−OH− C11S:0). An achiral space group (Pca21) was assigned, indicating that both stereoisomers are present in the unit cell. The configuration suggested for the solid 1,3-DAG was the unusual herringbone structure (Figure 16) with hydrogen bonding between the hydroxyl group in the sn-2 position and a carbonyl oxygen in either the sn-1 or sn-3 position of an adjacent molecule. In this case, molecules were thought to be stacked as in Figure 16, with alternating conformations as illustrated in Figure 17 (acac... or bdbd...). This asymmetric conformation was used to explain the occurrence of two peaks in the carbonyl stretch region of the IR spectrum (1710 and 1750 cm−1), which indicates that hydrogen-bonding environments of the two carbonyl oxygens are not equivalent.72 Craven and Lencki22 found that unit cell lengths for enantiopure and racemic 10:0−OH−16:0 were the same (39.75 Å). This indicates that, in both cases, acyl chains are segregated on the basis of chain length; that is, decanoyl with decanoyl and

Table 5. Space Group Assignments for 1,2-Diacylglycerols compd sn-HO−12:0−12:0 sn-16:0−16:0−OH rac-16:0−16:0−OH

form

space group

Enantiomers P21 P21 Racemic Mixture α subcell plane group: p6m β′ β′

#a

Z

E

2 2

one one

ref 28 65−68 69b

a

Unit cell is populated by one or both enantiomers as determined by the absence or presence of a reflective symmetry operation for the designated space group. bBy electron diffraction.

Figure 13. Free-energy versus temperature schematic for 1,2diacylglycerols. Features are defined in Figure 9.

crystalline domains for each enantiomer (Figure 14). In addition, there is evidence of solid solution behavior (at concentrations of xR < 0.5) between pure enantiomer (E) and a crystal form accommodating that same enantiomer and racemic mixture (E:R of 1:1 or E:E′ of 3:1). The phase behavior of metastable forms appears to be considerably more complex than that of the stable forms when additional data points are included (Figure 15). The result is a phase diagram similar to those reported for some anomalous racemic forms (cf. ref 3, p 147) and the glycerol derivative 3-(2-tert-butylphenoxy)L

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Figure 14. Phase diagrams for enantiomeric mixtures of 10:0−OH−16:0: (a) liquidus data for tempered samples and (b) phase diagram for untempered samples. Line in panel a was derived by linear regression on data for untempered samples (panel b). Samples were melted at 2 °C/min (triangles), 5 °C/min (diamonds), or 10 °C/min (squares). Solid symbols indicate Tp (peak melting temperature) and open symbols represent Te (extrapolated onset of melting). Reproduced with permission from reference 22. Copyright 2011 American Chemical Society.

Figure 15. Phase diagram data for enantiomeric mixtures of 10:0−OH−16:0, including melting of metastable forms. Dashed vertical lines mark solid compositions of E:E′ 3:1 and 1:3. Solid gray liquidus line delineates solid solution behavior between E:E′ 3:1 and E and between E:E′ 1:3 and E′. Dashed gray liquidus line suggests an unstable solid solution for E:E′ 3:1 and E′ and for E:E′ 1:3 and E. Solid black liquidus traces a possible eutectic for E:E′ 3:1 and E′ and for E:E′ 1:3 and E. Other features are defined in Figure 14.

possible for the enantiopure molecule. It should be noted that, like C11S:0−OH−C11S:0, both enantiopure and racemic 10:0− OH−16:0 had two peaks in the carbonyl stretch region of the IR spectrum (E, 1707 and 1730 cm−1; R, 1712 and 1730 cm−1).22 When all these factors are taken into account, it is likely that the finer details of the proposed crystal structure are somewhat different from those suggested by Larsson.72 In another study, Hybl and Dorset73 produced the achiral 1,3-bis(11-bromoundecanoyl)-glycerol (C 11 Br:0−OH− C11Br:0) while attempting to prepare the sn-1,2-DAG of 11bromoundecanoic acid. The formation of solid 1,3-DAG was attributed to acyl migration and the space group assigned is achiral (C2/c), indicating both stereoisomers are present in the unit cell. Like Larsson,72 they observed two asymmetric

Table 6. Space Group Assignments for 1,3-Diacylglycerols compd

form

space group

Z

C11S:0−OH−C11S:0 C11Br:0−OH−C11Br:0 sn-18:0−OH−18:1

β β β

Pca21 C2/c Cc

4 4 4

S

#a

see text see text see text

ref 72 73 74

a

Unit cell is populated by one or both stereoisomers as determined by the lack or presence of a reflective symmetry operation for the designated space group.

palmitoyl with palmitoyl. For an enantiopure 1,3-DAG in a chain-matched herringbone lamella, two conformations are possible: a and b in Figures 17 and 18. The conformation suggested by Larsson72 (acac... and bdbd...) is, therefore, not M

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Figure 16. Configuration along b-axis of 1,3-dilaurin. Dashed line indicates hydrogen bonding between molecules in adjacent layers. Axes in the plane of the page are, horizontal c-axis and vertical a-axis. Figure redrawn with permission from ref 72. Copyright 1963 International Union of Crystallography.

Figure 17. Conformations for, and relative positions of, glycerol region based on the crystal structure proposed for achiral 1,3-DAG (C11S:0− OH−C11S:0).72 Dashed lines indicate hydrogen bonding, and sn-3 carbon is labeled. Hydroxyl group in sn-2 position points into, or out of, the plane of the page. A chain-matched leaflet of chiral-enantiopure 1,3-DAG (e.g., sn-10:0−OH−16:0 or sn-16:0−OH−10:0) can only adopt two conformations: a and b or c and d. As a result, enantiopure 1,3-DAG cannot adopt the proposed structure. These conformations are depicted as Fischer projections in Figure 18.

Figure 18. Conformations for glycerol region of solid chiral 1,3diacylglycerol with dashed lines to indicate direction of hydrogen bonding. Conformations are related by reflective symmetry; the horizontal and vertical lines are mirror planes parallel to the b- and caxes, respectively. Stereospecific numbering (sn-1 and sn-3 in large white circles signifying oxygen atoms) is applied on the basis of relative stereochemistry after the reflection. Acyl chains for corresponding conformations are fixed in position because, in the solid, molecules assemble with chains of equal length collected together. Possible conformations for chiral-enantiopure 1,3-DAG (sn-10:0−OH−16:0) are a and b; the opposite enantiomer adopts conformations c and d. Letters assigned in this figure correspond to conformations depicted in Figure 17.

conformations for the molecule in the solid. They also observed, but were unable to explain, what they refer to as “disorder” in the hydrogen-bonding direction for molecules in the lattice. Crystal twinning was raised as a possible cause; however, Larsson72 reported that “neither cleavage nor twin formation have been observed” in crystalline 1,3-DAG. The occurrence of these “disordered” regions of hydrogen bonding may be attributable to the occurrence of metastable crystal forms (Figure 15). Goto et al.74 intended to prepare large crystals of 1-stearoyl2-oleoyl-sn-glycerol but instead produced 1-stearoyl-3-oleoylglycerol (18:0−OH−18:1). In all likelihood, solid 1,3-DAG was obtained due to acyl migration. An achiral space group (Cc) was assigned to this solid, indicating both stereoisomers are present in the unit cell. They also suggested that rac-1,3-DAG was produced from pure sn-1,2-DAG by acyl migration. However, since the crystallization was conducted under conditions employed to encourage the growth of large single crystals (4 °C in ethyl acetate), this explanation seems unlikely. Of course, it is possible that the starting material was, in fact, racemic and, thus, rac-1,3-DAG was produced. Another

possibility is that enantiopure sn-18:0−OH−18:1 was, indeed, prepared and some other factor led to the measurement of reflective symmetry. As Larsson72 has suggested, on the basis of two peaks in the carbonyl region of the IR spectrum, there are two possible hydrogen bonding directions for the sn-2 position hydroxyl group (toward sn-1 or sn-3). As a consequence, two asymmetric conformations are possible for chiral-enantiopure 1,3-DAG (Figures 17 and 18, a and b). As illustrated, the glycerol region of these two asymmetric conformations is related by reflective symmetry (Figure 18). Thus, the possibility that reflective symmetry in this crystal structure determination arises due to the asymmetric conformations of the glycerol region for a chiral-enantiopure 1,3-DAG, and not due to N

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production of chiral-racemic 1,3-DAG from chiral-enantiopure 1,2-DAG, should also be considered. To summarize, investigation of the phase behavior for mixtures of enantiomers indicates that the polymorphism of 1,3-DAG is due to two different eutectics: one between domains of pure stereoisomer (resulting in stable β1) and one between domains of pure enantiomer and domains with stereoisomers in 3:1 or 1:3 ratios (resulting in metastable β2). In addition, pure enantiomers of 1,3-DAG adopt asymmetric conformations that do not lead to the currently proposed crystal structure, whereas chiral-racemic 1,3-DAG would have to adopt four separate asymmetric conformations to yield a structural fit. Inevitably, future crystal structure determinations will have to take the full range of possible conformations and phase behavior data into account. Then, perhaps, a more complete picture of the crystal structures for, and the role of stereochemistry in, the polymorphism of these acylglycerols will emerge. 3.4. Monoacylglycerols

Two separate compound classes exist for monoacylglycerols (MAG): the chiral 1- and 3-monoacylglycerols, and the achiral 2-monoacylglycerols. The positional isomers, 1- and 3-MAG, are commonly referred to collectively as 1-MAG. Enantiomers of 1-MAG adopt conformations similar to the chair forms for TAG (Figure 19). Interestingly, 2-MAG have only one crystal

Figure 20. Phase diagram data for enantiomeric mixtures of enantiopure and racemic (R) 18:0−OH−OH. (●) Liquidus; (■) solidus. Data replotted with permission from reference 75. Copyright 1984 The Chemical Society of Japan.

with chiral TAG systems, the unit cell of the 1-MAG β′ form contains pure or resolved enantiomers while the β form contains both enantiomers. Crystal structure investigations have shown that pure enantiomers (1- or 3-MAG) are β′-tending while their racemic mixtures are β-tending and that their crystal structures have the appropriate space groups (Table 7). In addition, the spontaneous resolution of 1- and 3-MAG from a racemic mixture to produce the β′-form conglomerate has also been reported.78 Table 7. Space Group Assignments for 1(3)Monoacylglycerols Figure 19. Enantiomers 1- and 3-monoacylglycerol. Features are defined in Figure 6.

compd

form and thus display less polymorphism than their component fatty acids (i.e., free fatty acids).16 Presumably, this is due to the dominance of hydrogen bonding and the absence of appreciable strength differences between the hydrogen bonds of the primary hydroxyl groups (i.e., sn-1 and sn-3 hydroxyls). Short-spacing values for the acyl chains of 2-MAG are similar to those for other β-form acylglycerols, indicating polymethylene chains within the crystal structure are optimally arranged when these hydrogen-bond requirements are met (Table 1). As seen for the majority of TAG, 1(3)-MAG may crystallize in α, β′, and β forms. Interestingly, one additional subform is associated with each major polymorph; listed in order of increasing melting point, the polymorphs and subforms for 1MAG are sub-α, α, β′2, β′1, β2, and β1.16 In a study of the melting behavior of enantiomeric mixtures of 1- and 3-MAG, Iwahashi et al.75 found phase behavior similar to that of chiral TAG (Figure 20). The β form was associated with formation of a racemic compound, the highest-melting form for the pure enantiomer was β′, and for the racemic mixture the metastable β′ form was associated with a eutectic (conglomerate). Thus, as

sn-C11Br:0−OH−OH sn-HO−HO−18:0 rac-18:0−OH−OH rac-16:0−OH−OH

form

space group

Enantiomer β′ P21 β′ P212121 Racemic Mixture β1 P21/m β2 Am

Z

Z′

E# a

ref

4 8

2 2

one one

76 77

both both

78 78

8 8

a

Unit cell is populated by one or both enantiomers as determined by the lack or presence of a reflective symmetry operation for the designated space group.

4. CRYSTALLIZATION BEHAVIOR OF OTHER GLYCEROL-DERIVED MOLECULES 4.1. Aryl Derivatives of Glycerol

Bredikhin et al.71 chose to study the crystallization behavior of enantiomeric mixtures of terminal aromatic glycerol ethers (TAGE) because the crystallization behavior of these compounds is invariably influenced by their stereochemistry. In their words, “... the secondary hydroxyl... directly bonded to the chiral centre ensures the sensitivity of the crystal packing to O

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chirality effects.” (see Figure 21). In addition, the position and nature of functional groups on the phenyl ring also influences

Figure 22. General structure for (a) phospholipids and (b) sphingosine. Examples of R groups for common phospholipids are phosphatidylcholine (lecithin), R = choline, and phosphatidylethanolamine (cephalin), R = ethanolamine.

Figure 21. General structure for (a) terminal aromatic glycerol ethers (TAGE) and (b) phthalate ester of isopropylideneglycerol with phenylethylamine.

biological membranes will also often include some MAG and DAG. One common property of phospholipids and other membrane lipids is self-assembly.82 The lipid bilayers that result have hydrophilic head groups at the surface and acyl chains directed inward, with the structure being stabilized by van der Waals interactions between the acyl chains.81 These amphipathic lipids form flat, convex, or concave surfaces, depending on their shape (cylinder, cone, or inverted cone), which is determined by the relative size of a cross-sectional diameter of the headgroup compared to the acyl chain portion of the molecule. Pascher et al.81 have cataloged the crystal structures and related parameters (including space group) for >35 membrane lipids, analogues, and associated molecules. Crystallographic space groups for the naturally occurring enantiopure membrane lipids are typically P21, while racemic mixtures (which must be at least 50% synthetic) are typically P1̅ or P21/a.83 From this evidence alone, it appears that racemic mixtures of phospholipid generally form racemic compounds. Data on polymorphism in phospholipids seem to confirm this, but results are difficult to compare because experiments are typically multivariate. Their capacity for polymorphism in various biological, experimental, or food systems appears to be complex and is well beyond the scope of this particular review. For further reading, Stewart and Arnett’s6 review of the importance of stereochemistry in the biological and physical chemistry of membrane lipids is an excellent resource. Depending on conditions, chiral membrane lipids, which are typically associated with bilayer and liposome formation, will produce swirls, helices, and tubules whose direction of rotation (handedness) often correlates with the stereochemistry of the constituent molecules.82 In one graphic example, Weiss and McConnell84 produced impressive spirals in scalemic mixtures of 1,2-dipalmitoyl-3-phosphorylcholine-sn-glycerol and its enantiomeric opposite. Spector et al.82 have reviewed the selfassembly of helices and tubules formed by chiral amphipathic lipids. The many examples of phospholipids, glycolipids, and cerebrosides (saccharide-derived sphingolipids) they discuss are driven to aggregate primarily by hydrophobic interactions in polar solvents, with additional interactions due to hydrogenbonding or steric effects also playing an important role. The regular symmetry of the crystal forms produced relies on the chirality of the molecular components. These examples further illustrate the role of the stereocenter and of chirality in the crystallization behavior of glycerol-derived (and sphingosinederived) molecules.

the crystal form obtained (e.g., pseudoracemate, conglomerate, racemic compound). In this review we have made a similar case for acylglycerols; that is, glycerol stereochemistry, hydrogen bonding, positional isomerism, and acyl chain compatibility combine to determine crystal polymorph. TAGE are also of interest because many of these compounds are precursors for enantiopure pharmaceuticals (e.g., mephenoxalone, methocarbamol). If the pure enantiomer can be resolved from a racemic mixture by crystallization, this often represents a more costeffective means for producing the target compound than stereospecific synthesis.71 Compounds in the series of TAGE examined produced stable conglomerates, racemic compounds, and solid solutions, as well as an unusual scalemic conglomerate (E:E′ 3:1 and E:E′ 1:3) for 3-(2-tert-butylphenoxy)propane1,2-diol (cf. Figure 4 in ref 71). Phthalic acid esters of enantiopure isopropylideneglycerol (and some naphthoate analogues) have been used as resolving agents for chiral amines such as phenylethylamine (Figure 21).79 This procedure attempts to resolve enantiomerically enriched crystals of the target base (or acid) from organic salts of chiral acid−base pairs. In their experiments, Pallavicini et al.79 were able to recover enantiomeric acid or base from a racemic mixture, at >98% enantiomeric excess in several cases, by choosing appropriate acid−base pairs. This is one further example of how the stereochemical character of the glycerol moiety has been employed to practical advantage. 4.2. Self-Assembly of Chiral Membrane Lipids

Membranes are ubiquitous in biological systems: they contain and control the flow of material into and out of cells and organelles, as well as participating in and providing substrates for important metabolic processes.80 Biological membranes are composed of protein and lipid, with the lipids generally belonging to one of three categories: glycerolipids, sphingolipids, and steroids. Glycerolipids can, in turn, be divided further into phosphorus-containing phosphoglycerols, which predominate in higher animals, and saccharide-containing glycosylglycerols, which are important in plants. The phospholipid sphingomyelin, on the other hand, is derived from the longchain base sphingosine, rather than glycerol (Figure 22). In sphingolipids, the amine or amide group is in a position analogous to the sn-2 position of glycerol and there is a second chiral center at secondary hydroxyl in the position analogous to sn-1. The phosphate group is bonded to the terminal hydroxyl, which is analogous to the sn-3 position of glycerol. Diacylglycerophospholipids, having two acyl chains, are the most common phospholipids, while monoacylglycerophospholipids, with one acyl chain (usually in the sn-2 position) are commonly referred to as lysophospholipids.81 Lipids in P

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many of these discrepancies have arisen because the majority of crystal structure studies were conducted with little appreciation for the role played by the glycerol stereocenter. Data presented in this review demonstrate that acylglycerol polymorphs can be delineated by their unit cell stereochemistry. The relative thermodynamic stability of resultant crystal forms are, in addition, determined by hydrogen bonding and acyl chain compatibility. Thus, unit cell stereochemistry for common acylglycerols can, in general, be summarized as in Table 8. There is almost universal correspondence, for the acylglycerols listed, between polymorph (assigned on the basis of short spacing data) and stereochemistry of the unit cell. The main exception is the β form of 1,3-DAG, which is associated with a unit cell containing pure or resolved stereoisomer (based on the enantiomeric phase diagram). This is probably due to the unusual herringbone configuration that 1,3-DAG adopts in the solid phase. Presumably, the polymethylene chains are able to pack in the triclinic parallel subcell characteristic of β forms in this configuration, whereas for other acyglycerols, both stereoisomers must be present in the unit cell to achieve the same subcell packing. The relative thermodynamic stability for acylglycerol polymorphs in general is depicted by a free-energy versus temperature schematic in Figure 23. All four possible forms, labeled in the schematic, have been reported for TAG and 1MAG (A, B, C, and D); three have been reported for 1,2-DAG (A, B, and C); and two for 1,3-DAG (B and C). Thus, all acylglycerols adopt at least one polymorph where stereoisomers resolve into separate crystalline domains (B), and for pure enantiomers (C) this is always the most thermodynamically stable polymorph obtained. Moreover, pure enantiomers cannot adopt the form labeled D because it requires both stereoisomers (enantiomers) to complete the unit cell. On the basis of material presented here, it is clear that polymorphism in acylglycerols is essentially a stereochemical phenomenon. Consequently, crystallization behavior and polymorphism of acylglycerols is similar to, and can be treated in the same manner as, other molecules having a stereocenter.3,71 In addition, the crystallization behavior and relative stability of solid acylglycerols is strongly influenced by interactions between adjacent acyl chains (van der Waals, methyl-end match etc.) and hydrogen bonding (to varying degrees). When it occurs, exceptional crystallization behavior can usually be attributed to the accommodation of acyl chains

Table 8. Summary of Unit Cell Stereochemistry for Acylglycerol Polymorphs S# a

TAG

1,2-DAG

1,3-DAG

1-MAG

one both

α β′ β

α β′

β

α β′ β

a

Unit cell is populated by one or both stereoisomers as determined by the lack or presence of a reflective symmetry operation for the designated space group and by analysis of the enantiomeric phase diagram.

5. SUMMARY AND CONCLUSIONS It is evident that glycerol stereochemistry is critically important in the crystallization behavior of glycerol-derived molecules. This phenomenon is clearly demonstrated by the self-assembly of noncovalently bonded lipid molecules into swirls, tubules, and helices with consistent and predictable handedness. It is also evident from an examination of the phase behavior for enantiomeric mixtures of acylglycerols and TAGE. Among acylglycerols, 1-MAG and 1,2-DAG provide the clearest examples for the role stereochemistry plays in polymorphism since there is complete agreement between phase diagram and X-ray diffraction results. This may be attributed to greater awareness of the stereochemical aspects of crystallization behavior because compounds in these series are always chiral. Results for 1,3-DAG and β′-form TAG, on the other hand, required more discussion and a greater degree of interpretation due to some inconsistencies between results. Depending on their positional isomerism, these molecules can be either chiral or achiral. Thus, researchers were probably less aware of the role stereochemistry might play in these systems. The crystal structure data for 1,3-DAG suggests that discrepancies between X-ray and phase diagram results are due to molecules adopting an asymmetric configuration. Further interpretation of existing crystal structure data and any future experimental data should take this and the enantiomeric phase behavior (determined by phase diagram) into account. For TAG, X-ray and phase diagram data for βform TAG were in complete agreement, whereas data for TAG with stable β′ forms were less consistent. These discrepancies are likely due to the exceptional properties required to produce long-lived β′ forms in TAG and because researchers did not take crystal twinning into consideration. From our perspective,

Figure 23. Free-energy versus temperature schematic for (a) acylglycerols in general. Unit-cell stereochemistry of polymorphs listed from highest to lowest free energy is (A) undefined (α form); (B) resolved stereoisomers (β′ form and 1,3-DAG β form); (C) pure enantiomer (β′ form and 1,3DAG β form); and (D) both stereoisomers (β form). (b) In some cases, unit cells containing resolved stereoisomer (B) may offer higher thermodynamic stability than has been indicated here for the general case. In addition, there are special cases (e.g., CnCn+2Cn-type TAG) where a unit cell containing two stereoisomers has a higher free energy and lower melting point than a unit cell containing resolved stereoisomers (cf. Figure 10b). Features are defined in Figure 9. Q

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(2) Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: Oxford, U.K., 2002. (3) Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates and Resolutions; John Wiley and Sons: New York, 1981. (4) Wagniere, G. H. On Chirality and the Universal Asymmetry; Wiley−VCH: New York, 2007. (5) Mateos-Timoneda, M. A.; Crego-Calama, M.; Reinhoudt, D. N. Chem. Soc. Rev. 2004, 33, 363. (6) Stewart, M. V.; Arnett, E. M. In Topics in Stereochemistry; Allinger, N. L., Eliel, E. L., Wilen, S. H., Eds.; John Wiley & Sons: New York, 1982; Vol. 13. (7) Timms, R. E. Prog. Lipid Res. 1984, 23, 1. (8) Larsson, K.; Quinn, P.; Sato, K.; Tiberg, F. Lipids: Structure, Physical Properties and Functionality; PJ Barnes & Associates: Bridgwater, U.K., 2006. (9) Eliel, E. L.; Wilen, S. H.; Doyle, M. P. Basic Organic Stereochemistry; Wiley−Interscience: New York, 2001. (10) Kostyanovsky, R. G. Mendeleev Commun. 2003, 3, 1. (11) Chapman, D. Chem. Rev. 1962, 62, 433. (12) Lutton, E. S. J. Am. Oil Chem. Soc. 1950, No. July, 276. (13) Cullity, B. D. Elements of X-Ray Diffraction, 2nd ed.; AddisonWesley: Reading, MA, 1978. (14) Coffey, C. A.; Spannuth, H. T. Oil Soap 1940, 17, 41. (15) Small, D. M. The Physical Chemistry of Lipids: From Alkanes to Phospholipids; Plenum Press: New York, 1986. (16) Hagemann, J. W. In Crystallization and Polymorphism of Fats and Fatty Acids; Garti, N., Sato, K., Eds.; Marcel Dekker, Inc.: New York, 1988. (17) Larsson, K. Lipids: Molecular Organization, Physical Functions and Technical Applications; The Oily Press: Dundee, Scotland, 1994. (18) Dorset, D. L. Crystallography of the Polymethylene Chain: An Inquiry into the Structure of Waxes; Oxford University Press: Oxford, U.K., 2005. (19) “In the crystalline state, there is often a well-defined methylene subcell for the close packing of these chains within a symmetry group that may be quite different from that of the entire molecular packing in the crystal of the unit cell.” Reference 18, p 1. (20) Chapman, D. The Structure of Lipids by Spectroscopic and X-ray Techniques: with a chapter on separation techniques including thin layer and gas liquid chromatography; Methuen and Co Ltd: London, 1965. (21) Craven, R. J.; Lencki, R. W. Cryst. Growth Des. 2011, 11, 1723. (22) Craven, R. J.; Lencki, R. W. Cryst. Growth Des. 2011, 11, 1566. (23) Tilley, R. J. D. Crystals and Crystal Structures; John Wiley & Sons Ltd: Chichester, U.K., 2006. (24) Cockcroft, J. K. A Hypertext Book of Crystallographic Space Group Diagrams and Tables; http://img.chem.ucl.ac.uk/sgp/ mainmenu.htm, accessed July 25, 2011. (25) Craven, R. J.; Lencki, R. W. Lipid Technology 2012, 24, 204. (26) The terms chiral and achiral commonly refer to molecules, but, they can also be applied to objects (e.g., building blocks, structures) and crystallographic space groups. In principle, a pure enantiomer will not produce an achiral space group whereas a racemic compound or an achiral molecule can. The occurrence of a chiral space group for a racemic mixture indicates enantiomeric resolution (conglomerate formation). Occurrence of a chiral space group for an achiral molecule often indicates resolution of stereoisomers into separate domains; this can happen if the achiral molecules produce chiral building blocks (section 3.1.5). However, it may also mean that the molecules lack a stereocenter or that they crystallize in a symmetric conformation. (27) Schlenk, W., Jr. J. Am. Oil Chem. Soc. 1965, 42, 945. (28) Pascher, I.; Sundell, S.; Hauser, H. J. Mol. Biol. 1981, 153, 791. (29) Hauser, H.; Pascher, I.; Sundell, S. Biochemistry 1988, 27, 9166. (30) Pascher, I. Curr. Opin. Struct. Biol. 1996, 6, 439. (31) The following description of polymorphism in waxes is identical to most current descriptions of polymorphism in TAG: “Polymorphism includes the differences of methylene chain packing as well as the layer tilt, while polytypism considers only different possible stacking sequences of chain layers.” Reference 18, p 32.

and the resultant adoption of atypical conformations (e.g., CnCn+2Cn-type TAG, sn-16:0−16:0−2:0).

AUTHOR INFORMATION Corresponding Author

*Telephone 519-824-4120, ext 54327; e-mail rlencki@ uoguelph.ca. Notes

The authors declare no competing financial interest. Biographies

John Craven obtained Ph.D. and M.Sc. degrees in Food Science from the University of Guelph and a B.Sc. in Chemistry from the University of Waterloo. He has held research and production roles in industry, including work in organic synthesis for Uniroyal Chemical Co. At present, he is a research associate in the laboratory of Professor Robert Lencki. His current research interests include lipid chemistry, crystallization and polymorphism, and the role of stereochemistry in self-assembly processes.

After obtaining his B.A.Sc. in Chemical Engineering at the University of Toronto, Robert W. Lencki worked for 2 years in the Foods Division of Proctor and Gamble, developing new fats and oils processes. He then returned to academia to do an M.Sc. at the University of Waterloo followed by a Ph.D. at McGill University. After 2 years as a professor in the Chemical Engineering Department at Université Laval, he came to the Department of Food Science at the University of Guelph, where he is now an Associate Professor. Current research interests involve understanding biomolecular self-assembly, specifically lipid crystallization and casein micelle structure formation.

REFERENCES (1) Hollingsworth, M. D. Science 2002, 295, 2410. R

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