On the Melting of Binary Organic Compounds - Crystal Growth

Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

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On the Melting of Binary Organic Compounds Simon N. Black,*,† Claire L. Woon,‡,# and Roger J. Davey‡ †

AstraZeneca, Chemical Development, Macclesfield SK10 2NA, U.K. University of Manchester, School of Chemical Engineering and Analytical Sciences, Manchester, M13 9PL, U.K.

‡

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S Supporting Information *

ABSTRACT: The melting behaviors of three binary organic compounds, a racemate, a cocrystal, and a salt, are compared with their individual components and with each other. The three compounds are the racemic compound of mandelic acid, the benzophenone−diphenylamine cocrystal, and ephedrine pimelate. Similarities and differences are accounted for by changes in entropy, hydrogen bonding, molecular conformation, and charged state on melting. An unusual combination of thermodynamic, structural, and spectroscopic data gives insight into the nature and extent of association in these melts. The three binary compounds show surprisingly similar melting thermodynamics. The main differences are in the salt system, driven by ionization and access to a 2:1 salt. The implications for melt and solution eutectics are discussed.

1. INTRODUCTION Ionic liquids, salts, cocrystals, and racemic compounds are examples of binary organic compounds of commercial interest, particularly as potential medicines. The ability to find, manufacture, and formulate such compounds is linked to their stability and solubility relative to their components. Melting-point phase diagrams are a useful way to explore the thermodynamic relationships in such systems. This approach is well-developed for racemic compounds.1 The use of “dry” methods for the synthesis of binary organic compounds has prompted similar investigations for cocrystals2,3 and salts.4 What happens when such binary organic compounds melt? The physical processes are related to nucleation from melts and solutions, solubility and dissolution. Walden5 derived a constant for the melting entropy of rigid nonassociating unary systems and then used the ratio of this constant to measure entropies to quantify association in the melt. For example, an association factor of 1.49 was deduced for acetic acid and attributed to partial association via hydrogen bonds in the melt. There are a few examples of this approach being extended to the melting of binary organic compounds.6,7 A separate refinement is to modify the predicted entropies to include the effects of flexibility in the molecule.8,9 Examination of crystal structures allows the easy identification of strong hydrogen bonds, for example, from −OH or −NH groups to carbonyl oxygen atoms. Calculated energies for these interactions are typically ∼27−36 kJ/mol.10 These energies are of a similar order to enthalpies of melting. The creation or destruction of intra- and intermolecular hydrogen bonds on melting may be reflected in the magnitude of melting enthalpies. The shape of the binary melting point phase diagram has been used to deduce information about deviations from © XXXX American Chemical Society

ideality and association in nonstoichiometric melts. A further refinement is to plot ln x against 1/T, where x denotes mole fraction and T denotes temperature in degrees K. The enthalpy of melting, ΔHm, can be calculated from the gradient and compared with ΔHm as measured directly by differential scanning calorimetry (DSC) for the pure binary compound.11 In ionic liquids, arbitrarily defined as solids having melting points lower than 100 °C, the extent of association is typically assessed using “Walden plots” relating conductivity to viscosity.12,13 In all of these studies, the emphasis has been on measured physical properties, with scant regard for either the molecular or the crystal structure. The aim of this study is to compare the melting behavior of three different types of binary organic compounds, focusing on change in hydrogen bonding, ionization state, and molecular flexibility. One system of each type (racemate, cocrystal, salt) was selected based on the availability of suitable data, as shown in Table 1. The six component molecules are all a similar size (11−14 non-hydrogen atoms), all contain oxygen and/or nitrogen atoms, and all (except pimelic acid) contain at least one phenyl ring. Table 1. Racemate, Cocrystal, and Salt Systems Selected compound

component A

component B

refs

racemate cocrystal salt

R-mandelic acid benzophenone (BZP) (1R,2S)-ephedrine

S-mandelic acid diphenylamine (DPA) pimelic acid

14 2, 3 4

Received: July 24, 2018 Revised: September 5, 2018

A

DOI: 10.1021/acs.cgd.8b01120 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Figure 1. A model binary melting point phase diagram. For further details see text and Table 2.

The options for intra- and intermolecular hydrogen bonds are enumerated for each molecule interacting with itself or with the other component. In the salt-forming system, the consequences of proton transfer are considered. The flexibility of each molecule is assessed by defining x as the number of freely rotatable bonds, and the entropy of melting (ΔSm) is estimated as 54 + 6x J/mol·K. In this formula, 54 J/mol·K is Walden’s constant for rigid molecules, as derived independently by Gavezzotti15 from 65 rigid mono- and disubstituted benzenes. The value of 6 J/mol·K for each rotatable bond is an approximation assuming two accessible and isoenergetic possibilities for each rotatable bond.9 This gives a quantitative estimate of the entropy of melting in the absence of association in the melt. In a simple extension of Walden’s approach, this is divided by the measured melting entropy of the compound to give an association factor, where a value of 1 indicates complete dissociation, and higher values indicate higher extents of association. Hydrogen bonds in the crystal structures were identified initially using default definitions in the Mercury software provided by the Cambridge Crystallographic Data Centre (CCDC); further details are given in the Supporting Information. Melting entropies per mole of binary compound were estimated by adding the measured molar melting entropies for the individual components. The association factor was then calculated by dividing this by the measured value, as above. Estimates of the molar melting enthalpies of the binary compounds were obtained by adding the melting enthalpies of the components. This is compared with the measured value, and the differences in hydrogen bonding in the crystal structures and potentially in the melts. Lattice energy calculations were not considered, as lattice energies are typically 5−10 times larger than melting enthalpies.16 Melting point diagrams were predicted from the melting temperatures and enthalpies of the solids. These predictions were compared with the measured diagrams, to estimate deviations from ideality at nonstoichiometric compositions.

Comparison between such different systems requires a systematic approach, focused on the links between thermodynamic and crystal structure data. Units and the treatment of experimental errors are standardized, and inconsistencies are identified and accounted for, as described in the Supporting Information. Only thermodynamically stable polymorphs were considered, although polymorphs are known for RS-mandelic acid, the BZP−DPA cocrystal, and pimelic acid. Crystal structures give precise data, whereas in melts the average state of each component is inferred from thermodynamic and spectroscopic data. The previously reported crystal structures and binary phase diagrams are examined as follows: (i) Options for conformers and hydrogen bonding are evaluated by inspection of the two-dimensional molecular structure. The melting entropy is estimated. (ii) The conformations and hydrogen bonding in the crystal structures are compared with each other and with expectations from the molecular structure. (iii) The measured melting entropies of the components are compared with the estimated entropies, and the melting entropies of the binary compounds. (iv) The enthalpies of melting of a binary compound are compared with the enthalpies of the components, and the estimated contribution from hydrogen bonding. (v) Melting point phase diagrams are predicted and compared with the experimental data. (vi) Where available, spectroscopic data for the melt are interpretedincluding new data for the (1R,2S)ephedrine/pimelic acid system. This allows a comprehensive comparison of the melting behaviors in the three systems of interest. The implications for melt eutectics, solution eutectics, and solubility are then discussed.

2. METHODOLOGY The methodology for each of the six steps listed above is described, with the aid of a model phase diagram. B



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For clarification, a model melting point phase diagram is presented in Figure 1. Melting point phase diagrams for binary compounds can be predicted from the thermodynamic data of the pure solid phases. The diagram, Figure 1, shows the variation of melting temperature with composition for four different cases in a model two-component system. The continuous lines show the melting behavior of two rigid molecules, denoted A and B respectively. The dashed and dotted lines show two different melting behaviors for the 1:1 compound of A and B, depending on whether the compound is fully dissociated (A + B, dashed line) or fully associated (AB, dotted line) in the melt. For A and B, the melting points were arbitrarily assigned as 100 °C. The melting entropies of both A and B were each set equal to Walden’s constant (54 J/mol·K), giving enthalpies of melting for both A and B of 20.2 kJ/mol. The variations of melting points with mole fraction were each plotted using the equation of Schröder-van Laar17 and are shown as continuous lines in Figure 1. This assumes ideal (adiabatic) mixing of A and B in all melt compositions. Further details are given in the Supporting Information. The compounds A−B and AB are both assigned the same melting temperature (100 °C) as their components. One mole of the binary compound is defined as containing one mole of each component, in contrast to some previous studies.1,11 The variations of melting points with mole fraction were plotted using the equation of Prigogine−Defay.18 Compound A−B (dashed line) dissociates completely, so that the enthalpy and entropy of melting are the sums of the values of the components A and B. In contrast, AB (dotted line) does not dissociate at all, so the entropy of melting is the same as for any rigid molecule, and the enthalpy of melting is also reduced. The figure demonstrates that lower melting enthalpies give steeper curves and lower eutectic melt temperatures.19 This effect can also arise from enthalpic changes in the melt as the composition changes. Any phase diagrams in which the two components have similar thermodynamics of melting will show continuous curves broadly similar to Figure 1. Where A and B are enantiomers, symmetry is inherent. The eutectic melting point for the two enantiomers, in the absence of any racemic compound, is much lower than that of either pure enantiomer. For molecules that follow Walden’s rule, the temperature of the enantiomer eutectic is given analytically by the expression T = Tm/1.11, where temperatures are in degrees Kelvin. Further details are given in the Supporting Information. For the model system in Table 2, the eutectic temperature is 36 °C below the melting point of the single enantiomers. For flexible molecules, with entropies >54 J/(mol K), this temperature difference will be less.

For the model system in Figure 1, the position of the eutectic between the compound AB and the component A (or B) is determined primarily by the melting points of the two materials. Where these melting points are the same and AB dissociates completely and ideally, the position of the eutectic is at x = 0.8 and T = Tm/(1.03); see the Supporting Information for further details. In the example given in Figure 1, the eutectic temperature is 13° lower than Tm. For other systems (cocrystals, salts), in which the individual components have similar properties, the phase diagrams may be expected to show similar, pseudosymmetrical features. This suggests ways to interpret thermal data from binary compounds. Comparison of the enthalpies and entropies of melting of a binary compound and its constituents gives an indication of the degree of association in the melt of the pure compound. The full experimental binary phase diagrams may also be compared with the ideal curves plotted using the known melting temperatures and enthalpies for single components and compounds. Where the predictions differ from the measurements, the curve can be fitted to the data by adjusting the enthalpy. This revised enthalpy gives insight into the changing interactions in the melt as stoichiometry varies. Finally, spectroscopic data can give information about the nature and extent of association in the melt. New data for melts of (1R,2S)-ephedrine and pimelic acid mixtures are reported here and analyzed for evidence of charged state and hydrogen bonding as a function of liquid compositions. The experimental details are provided with the results in section 5. In sections 3−5, these methodologies are applied to three different binary organic systemsa racemate, a cocrystal and a saltand their components.

3. RACEMATE: S- AND R-MANDELIC ACID The molecular structures of the two enantiomers are shown in Scheme 1. Scheme 1. S- and R-Enantiomers of Mandelic Acida

a

This molecule contains two rotatable bondsdesignated here as bond 1 from the phenyl ring to the chiral carbon, and bond 2 from the chiral carbon to the carboxylic acid. There is the potential for an intramolecular hydrogen bond between the carbonyl and the hydroxyl, giving a five-membered ring that prevents rotation about bond 2. Assuming that this bond exists in the melt gives predicted entropies of melting of 60 J/mol·K for the single enantiomer and 120 J/mol.K for the fully dissociating racemic compound. The crystal structures of the single enantiomer (CSD ref code FEGHAA) and the stable polymorph of the racemic compound (DLMAND03) show four different versions of this molecule. There are two conformers (Z′ = 2) in the Senantiomer structure, denoted here as “A” and “B”, The racemate contains both R and S configurations which in this case (as normally) are crystallographically related mirror images.

Table 2. Melting Behavior of a Model Binary Compound AB and Its Constituents compound

line in Figure 1

A B A−B

green red dashed

AB

dotted

melting equilibrium A(s) = A(l) B(s) = B(l) A−B(s) = A(l) + B(l) AB(s) = AB(l)

Tm (°C)

ΔSm (J/mol K)

ΔHm (kJ/mol)

100 100 100

54 54 108

20.2 20.2 40.4

100

54

20.2

The two rotatable bonds in the S-enantiomer are numbered.

C



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Figure 2. Comparison of the three different conformations of S-mandelic acid in DLMANDL03 (center) and FEGHAA (“A” on the left, “B” on the right), viewed parallel to bond 1.

on melting are similarof the same order as the loss of one hydrogen bond. In Figure 3, the experimental melting point phase diagram is compared with that predicted from the data in Table 2. The diagram is broadly similar to Figure 2, but the melting point of the racemic compound is lower than that of the AB compound, with a corresponding shift in the eutectics to x = 0.31 and 0.69. The continuous curves were created using the Schröder−van Laar and Prigogine−Defay equations and thus represent ideal behavior in the melt. This prediction (mauve line in Figure 3) underestimates the reduction in melting point on either side of the racemic compound. The dotted line is a “best fit” obtained by decreasing the enthalpy of melting to 33 ± 3 kJ/mol. As discussed in Section 2, this is equivalent to deviations from ideality that give rise to preferential association between R and S (compared with R and R, or S and S) enantiomers in the melt. The reasons for the preference are not clear. In summary, the evidence suggests that when mandelic acid melts, it can rotate freely about bond 1 but not bond 2. The melting point data are consistent with a preference for heterochiral association in the molten state.

Figure 2 shows three different conformations, viewed along the direction of bond 1. The “B” FEGHAA conformation is similar to that in the racemate, as is also seen from the torsion angles in Table 3. The “A” conformation can be converted to Table 3. Torsions in Mandelic Acid structure

enantiomer/ conformer

torsion 1 (deg)

torsion 2 (deg)

O···O (Å)

FEGHAA FEGHAA DLMANDL03 DLMANDL03

S/“A” S/“B” R S

88.6 139.9 −130.8 130.8

−2.1 1.2 23.3 −23.3

2.650 2.666 2.726 2.726

the other two by a clockwise rotation of 50°. The conformations will have different energies, but their relative stability may depend on the environment. In all four conformations, the hydroxyl oxygen is close to the plane of the carboxyl group, in the correct orientation for an intramolecular hydrogen bond. However, in all three crystal structures, the hydroxyl hydrogens take part in intermolecular hydrogen bonds to a neighboring carbonyl and the acid hydrogens form intermolecular hydrogen bonds with hydroxyl oxygens. These bonds then link in different ways to form rings and chains.20 In the melt, if the hydroxyl group takes part in an intramolecular hydrogen bond, there is a net loss of one hydrogen bond per molecule on melting, for both racemate and enantiomer. Table 4 shows literature data for the melting of pure Smandelic acid and the stable polymorph of racemic R,S-

4. COCRYSTAL: BENZOPHENONE AND DIPHENYLAMINE Scheme 2 shows the molecular structures of benzophenone (BZP) and diphenylamine (DPA). These two molecules form a 1:1 cocrystal which has been studied extensively.2,3,17 The cocrystal is expected to contain a hydrogen bond from the amine to the carbonyl. If this is broken on melting, then the cocrystal is expected to have a correspondingly large enthalpy of melting compared to its components. Although carbonyl atoms can accept more than one hydrogen bond, in this case a 2:1 hydrogen bonded complex is unlikely because of steric hindrance. Examination of the molecular structures suggests that neither molecule can be planar, due to overlap of the ortho hydrogen atoms. Each molecule contains two rotatable bonds. Hence the predicted entropy of melting for both molecules is 66 J/mol·K. The relevant features of the crystal structures of the stable polymorphs are given in Table 5, and the conformations are shown in Figures 4 and 5. The two conformations of BZP in the cocrystal structure are mirror images of each other, consistent with the presence of a glide plane from the symmetry of space group. Only one of these conformations is present in each crystal of benzophenone, because Z′ = 1 and there are no mirror planes, glide planes, or inversion centers in the space group P212121. The torsion angles are as expected; the direction of the carbonyl bond bisects the angle of ∼60° between the two planes. A fully

Table 4. Melting Point Data for S-Mandelic Acid and (R,S)Mandelic Acid14 compound

MW

Tm (K)

ΔHm (kJ/mol)

ΔSm (J/mol·K)

S-mandelic acid R,S-mandelic acid

152.15 304.3

404 392

24.5 51.2

61 131

mandelic acid.14 As noted above, the enthalpy and entropy of melting for the racemic compound are quoted per mole of compound, for consistency with what follows. The measured entropy of melting for the single enantiomer agrees with the prediction based on the molecular structure, consistent with presence of an intramolecular hydrogen bond in the melt and an association factor of 1. The melting entropy of the racemate is 9% higher than that predicted for two moles of enantiomer. This is consistent with an increase in molecular flexibility due to less intramolecular hydrogen bonding in the molten racemate, but there is no obvious reason why this should only happen for the racemate. The reported enthalpy of melting of the racemate is close to twice that of the enantiomer, suggesting that the changes in hydrogen bonding D



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Figure 3. Predicted (this work, lines) and measured14 (points) melting point phase diagram for R,S-mandelic acid.

Supporting Information. Inspection of the torsion angles in QQQBVP02 shows that, although Z′ = 8 rather than 1, the eight conformations and their mirror images are all similar to those shown in Figure 5. There are no hydrogen bonds in the DPA structure. As expected, the amine donates a hydrogen bond to the carbonyl oxygen atom in the cocrystal. The O···N distance of 2.916 Å and the suboptimal linear CO···H arrangement suggest a hydrogen bond of intermediate strength. The melting point data for the cocrystal and its components are given in Table 6.2,3,17 The two components have similar melting properties. The melting entropies of the two components give values close to Walden’s rule. Indeed, both molecules were in the data set of 35 compounds from which the rule was devised.5 This is less than the expected value given that both structures contain two rotatable bonds. As discussed, rotations about these bonds are interdependent in both molecules, which may contribute to the lower observed value of melting entropies. The melting entropy of the cocrystal is 7% less than the sum of the entropies of the components, suggesting little association in the melt. The melting enthalpy of the cocrystal is 10% (3.4 kJ/mol) smaller than the sum of the melting enthalpies of its components. This seems surprising, given that the cocrystal contains a hydrogen bond that the components do not. However, it is consistent with the observation by Chadwick et al.3 that overall the spectral changes between the solid cocrystal and its pure solid components were small. Figure 6 shows the measured and predicted phase diagrams. Comparison with Figure 1 shows how the similarity in the physical properties of the two components produces a nearly

Scheme 2. Benzophenone (BZP, Left) and Diphenylamine (DPA, Right)

Table 5. Data from the Crystal Structures of the Cocrystal and Its Components compound

crystal structure

Z′

space group

BZP DPA cocrystal

BPHENO12 QQQBVP02 BZPPAM01

1 8 1

P212121 P1̅ P21/n

torsions (deg) +26.3, +26.8 5.5 to −5.5; 45.9 to −45.9 36.2, 21.4 (BZP) 5.8; 38.7 (DPA)

labeled version of the “Mogul” plot is provided in the Supporting Information. In the cocrystal, one of the two DPA torsions is close to zero, and the other lies in the range −45 to +45°. Interactions between the lone pair on the nitrogen and one of the phenyl rings favor torsions close to zero, but the second torsion must be larger to avoid a clash between the ortho hydrogen atoms. Figure 5 shows the two conformations in the cocrystal structure, viewed along the direction of the bond with the larger torsion angle. The two conformations are exact mirror images of each other and must be isoenergetic. The “Mogul” plot in Figure 5 suggests a slight energetic preference for the twisted torsion. A full version of the “Mogul” plot is in the

Figure 4. Two conformations of BZP in the cocrystal, and the “Mogul” analysis. E



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Figure 5. Conformations of DPA from the cocrystal structure, and “Mogul” geometry plots.

compound

MW

Tm (K)

ΔHm (kJ/mol)

ΔSm (J/mol·K)

5. SALT: EPHEDRINE AND PIMELIC ACID The molecular structures of ephedrine and pimelic acid are given in Scheme 3.

DPA BZP cocrystal

169.22 182.22 351.44

326 321 313

17.8 17.9 32.3

55 56 103

Scheme 3. Neutral Forms of (1R,2S)- Ephedrine (Left) and Pimelic Acid (Right)a

Table 6. Melting Point Data for DPA, BZP, and the Stable Cocrystal

symmetrical diagram, although (as in Figure 3) the melting point of the cocrystal is lower than those of both components. The eutectic compositions are predicted correctly (at 30% and 75% BZP), but the eutectic temperatures are not (37 and 34 °C compared with measured 34 and 32 °C). The dotted line is plotted to fit the experimental data using an enthalpy of melting of 26 kJ/mol, which is 6 kJ/mol lower than that measured for the 1:1 cocrystal. This may be accounted for by the persistence of some hydrogen bonding as the 1:1 cocrystal melts, and the disappearance of this interaction as the composition moves to pure single components. Chadwick et al.3 reported that Raman spectroscopy indicates the presence of weak hydrogen bonding in supersaturated melts of the cocrystal. It seems likely that this weak interaction persists in the saturated melts that are relevant for this phase diagram. In summary, the evidence in this system points to preferential pairing of the two components in the melt through hydrogen bonding, but the effect is weak.

a

The rotatable bonds in ephedrine are numbered 1−3.

Here the approach developed above for racemates and cocrystals is applied to a salt-forming binary system, combining literature data on thermodynamics and crystal structures4 with new spectroscopic data. This example thus introduces the additional complexity of charged states for both molecules. First, the molecular shapes and hydrogen bonding in ephedrine and pimelic acid are discussed. 5.1. Conformations and Hydrogen Bonding. The molecular structures are shown in Scheme 3. Pimelic acid contains six rotatable bonds, four hydrogen bond acceptors, and two, one, or zero hydrogen bond donors depending on the

Figure 6. Predicted (this work, lines) and measured2 (points) melting point data for the binary system DPA−BZP. F



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Table 7. Data from the Crystal Structures of the Salts and Their Components ephedrine in:

crystal structure

ephedrine 1:1 salt 2:1 salt 2:1 salt pimelic acid in:

EPHEDR01 INEDIP INEDOV INEDOV crystal structure

pimelic acid 1:1 salt 2:1 salt

PIMELA07 INEDIP INEDOV

space group P212121 P21 P21 P21 space group C2/c P21 P21

torsion 1 (deg)

torsion 2 (deg)

torsion 3 (deg)

N−H···O bond length

79.3 80.5 77.0 53.8 torsion 1 (deg)

167.4 167.9 166.4 172.3 torsion 2 (deg)

166.8 179.4 175.4 54.5 torsion 3 (deg)

2.517 2.462 2.519 2.706 torsion 4 (deg)

173.9 178.8 177.7

169.3 176.2 66.6

169.3a 175.2 172.4

173.9a 67.9 168.1

a

By symmetry.

Figure 7. “Mogul” Geometry check for torsions in the pimelic acid backbone.

cations and a mixture of hydrogen pimelate acid anions and neutral species. Ion pairs may form and be reinforced by hydrogen bonding. At the 1:1 stoichiometry ion pairs may predominate, leaving an equal number of protonated carboxylic acid groups free to interact with each other. As more (1R,2S)-ephedrine is added, dianions of pimelic acid may predominate, which may form hydrogen-bond reinforced ion triplets with one ephedrine cation at each end. When (1R,2S)ephedrine is present at stoichiometries greater than 2:1, there will be some uncharged (1R,2S)-ephedrine species that can form hydrogen bonds with each other, as in pure (1R,2S)ephedrine melts. Similar reasoning applies to the options for hydrogen bond formation in stoichiometric 1:1 and 2:1 salts. The molecular conformations in the four relevant crystal structures are summarized in Table 7. Previous discussions of these structures4,16,22,23 are summarized and extended here, with a focus on relevant molecular conformations and hydrogen bonding. This includes the two (1R,2S)-ephedrine conformations in the 2:1 salt, which were not discussed previously.4 In pimelic acid, the central carbon atom lies on a 2-fold axis. As noted previously,4 the carbon backbone is extended, and

extent of dissociation of the acid groups. Preferred conformations of this molecule have an extended backbone and may be symmetric (2-fold axis and/or mirror plane). The predicted entropy of melting if not associated is 54 + (6 × 6) = 90 J/mol·K. Neutral (1R,2S)-ephedrine contains three rotatable bonds, two hydrogen bond acceptors, and two hydrogen bond donors. There are two mutually exclusive options for a five-membered intramolecular hydrogen bond. The hydrogen bond from the hydroxyl hydrogen to the amine nitrogen is expected to be stronger than the hydrogen bond from the amine hydrogen to the hydroxyl oxygen.21 In the protonated state, the amine has two bond donors, but is no longer an acceptor. This leaves only the weaker amine to hydroxyl option for an intramolecular hydrogen bond. If the intramolecular hydrogen bond is present in the melt, then rotatable bonds 2 and 3 are locked, and the predicted enthalpy of melting is 60 J/mol·K. In the melt, the options for hydrogen bonding will vary with stoichiometry. Pure pimelic acid, uncharged and fully protonated, can form hydrogen bonds with itself to give dimers and chains. As (1R,2S)-ephedrine is added, if proton exchange occurs, then the melt will be dominated by ephedrine G



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contains charged species and the individual components do not. This apparent conundrum is resolved if the species retain their charges in the melt, and the charge separation is similar to that in the solid. The entropy of melting is 11% higher than the sum of the components. This corresponds to an associated ion pair with nine rotatable bonds that are “free”. This is consistent with six rotatable bonds in the hydrogen pimelate anion and three in the charged ephedrine cation, which as discussed above is less likely to form an intramolecular hydrogen bond. It seems extraordinary that the molar thermodynamic data for the 2:1 salt are so similar to those for the 1:1 salt, given that this “mole” contains an additional molecule of ephedrine. The simplest explanation is that the second ephedrine molecule is attached as a rigid body to the 1:1 ion pair, but it is not clear why the two ephedrine molecules should behave differently on melting. 5.3. Binary Phase Diagram. Figure 8 shows the binary phase diagram for the system ephedrine−pimelic acid. The data are taken from Cooke et al.4 As was stated in that paper, the phase diagram was prepared by heating physical mixtures of the solid phases, and incomplete mixing is probably responsible for some of the scatter in these data. Nevertheless, the results do permit a semiquantitative interpretation, as for the cocrystal and racemate. The three solidus temperatures were obtained by averaging the relevant data (diamonds). The vertical lines indicate the composition of the 1:1 salt (at x = 0.5) and the 2:1 salt (at x = 0.33). The continuous curves are best fits using the equations of Schröder−van Laar1 and Prigogine−Defay18 and allowing the enthalpy of melting to vary. This is to accommodate the influence of proton exchange, as discussed in more detail below. Starting at the right-hand side of the diagram (1 > x > 0.9), the decrease in melting point as ephedrine is added to pimelic acid is far greater than would be predicted from the enthalpy of melting of pimelic acid. The line was plotted using an enthalpy of 3 kJ/mola difference of ∼28 kJ/mol, not unreasonable for proton exchange between ephedrine and pimelic acid in the melt (compare the measured value of ∼30 kJ/mol for ephedrine/mandelic acid in solution26). For consistency, a similar reduction should be required to fit the curve for 0.9 > x > 0.5. The dashed line (“1:1 salt (A)”) corresponds to an enthalpy of melting of 26 kJ/mol, compared with 44.7 kJ/mol for the pure salt. This smaller difference may be due to the disruption of carboxylic acid to carboxylic acid interactions in the melt at lower pimelic acid concentrations. For 0.5 > x > 0.23, the best fit to the data (dotted line, “1:1 salt (B)”) is with an even smaller enthalpy of melting of 18 kJ/molthe difference from the “ideal” value is largely due to the second ionization of pimelic acid. The existence of a eutectic between the 2:1 and the 1:1 salt seems improbable, and was not proposed previously.4 The alternative suggested here is that the 2:1 salt melts incongruently at 105 °C, but a pure sample can exist as a metastable solid up to a melting point of 120 °C.26 At x ≈ 0.23−0.20, the liquidus appears to be almost vertical, implying a melting enthalpy close to zero. For 0.23 > x > 0.0, the apparently almost horizontal liquidus is probably due to unmixed regions of ephedrine in the sample. For consistency with the other data, the true liquidus must be close to the line plotted using a value of 24 kJ/mol, twice the melting enthalpy for ephedrinethe difference is probably due to ionization.

the carboxyl groups are twisted out of the plane of the carbon backbone.22 This facilitates chains in which molecules are linked by centrosymmetric carboxylic acid dimers, as is usual for straight-chain dicarbxoylic acids. In the two salts, the pimelate and hydrogen pimelate anions have one twist each in the carbon backbone. The “Mogul” plot in Figure 7 shows that planar conformations are by far the most common, but “staggered” conformations with torsions ∼60 °C occur in ∼10% of cases. Hence the enthalpic penalties associated with conformational changes as these salts melt are small. Ephedrine can adopt either an “extended” or a “folded” conformation, as discussed previously.14,24 One of the two ephedrine conformations in the 2:1 salt is “folded”, whereas all the others are extended. The previous assertion25 that only the “folded” conformation possesses an intramolecular hydrogen bond is not supported by the N−H···O bond lengths. In EPHEDR01 the amine hydrogen does not take part in any intermolecular hydrogen bonds, whereas both amine hydrogen atoms in the salt structures are hydrogen bonded to pimelate oxygen atoms. A recent study of gas phase conformations of ephedrine using molecular beam Fourier transform microwave spectroscopy confirmed that the preferred conformations of ephedrine in the gaseous state favor the formation of an intramolecular hydrogen bond and assume that this is from the hydrogen atom of the hydroxyl group to the lone pair in the nitrogen.24 This preferred conformation is also described as “extended” due to the orientation of the methyl groups. In summary, although ephedrine adopts conformations that favor intramolecular hydrogen bonds, none exist in available crystal structures. Similar behavior was noted above for mandelic acid. 5.2. Melting Point Data. Table 8 shows the melting point data for the compounds in this system,4 with the added Table 8. Melting Point Data for Ephedrine, Pimelic Acid, and Their Two Salts compound

MW

Tm (K)

ΔHm (kJ/mol)

ΔSm (J/mol·K)

(1R,2S)-ephedrine pimelic acid 1:1 salt 2:1 salt

165.2 160.2 325.4 490.6

310 378 403 393

12.0 31.8 44.7 45.5

39 84 111 116

calculated entropies of melting. In contrast to the previous two systems, the two components have very different properties, as is often the case for organic salts, giving a very asymmetrical binary phase diagram. The enthalpy and entropy of melting for (1R,2S)-ephedrine are much lower than that for any of the other molecules in this study, and the entropy of melting is considerably lower than “Walden’s constant” for a rigid molecule, giving an association factor of 1.54. This suggests considerable self-association of (1R,2S)-ephedrine in the melt, probably via hydrogen bonding. The enthalpy and entropy of melting of pimelic acid are higher than for the other four unary solids in this study. The association factor is 1.07, suggesting much weaker association in the melt than in the case of acetic acid. The enthalpy of melting is higher than for mandelic acid, which may be related to the inability of pimelic acid to form intramolecular hydrogen bonds. The enthalpy of melting of the 1:1 salt is insignificantly different from the sum of the melting enthalpies of the components. This may appear surprising, given that the 1:1 salt H



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Figure 8. An interpretation of the melting-point phase diagram for the system ephedrine−pimelic acid.4 Vertical solid lines denote the 1:1 (right) and 2:1 (left) salt compositions. Horizontal solid lines denote best fits for the liquidus. For further explanation, see text.

Figure 9. FTIR spectra for liquid melts of ephedrine/pimelic acid mixtures with ephedrine mole fractions of 0.3 (top left), 0.39 (top right), 0.54 (bottom left) and 0.65 (bottom right).

The key difference between this diagram and those above for the cocrystal and racemates is the much larger deviations from ideality, both positive and negative, which arise from ionization or its reverse during melting of nonstoichiometric mixtures. The asymmetry in the diagram has three causes: the large difference in the melting points of the two components, the ability of only one of the components (pimelic acid) to be doubly charged, and the existence of the 2:1 salt.

The ternary phase diagram for water, ephedrine, and pimelic acid was also determined in the previous study of this system.4 Ephedrine and pimelic acid have similar solubilities, although their melting points are very different. This has been accounted for by the unfavorable interactions between ephedrine and water, which counteract the lower melting point.17 The solubility of the 1:1 salt is considerably higher, as expected due to ionization. In the melt, the eutectic between ephedrine and the 1:1 salt occurs at x ≈ 0.2, which is similar to the I



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Table 9. Spectroscopic Data for the Carbonyl Peaks in Ephedrine/Pimelic Acid Meltsa peak intensities sample

mole fraction of pimelic acid

pimelic acid 1:1 salt 2:1 salt 2:1 salt + ephedrine

1.0 0.5 0.33 0.1−0.3

1694 cm−1

1681 cm−1

1624 cm−1

1559 cm−1

m sh sh

s s

1548 cm−1

s m

m

a

s = strong, m = medium, sh = shoulder.

corresponding position for the solution eutectic.4 This may be coincidence, arising from similar deviations from ideality for the ephedrine cation and the pimelate dianion. The melt eutectic between pimelic acid and the 1:1 salt occurs at x ≈ 0.9, far from the corresponding solution eutectic (x = 0.6),4 possibly due to the (relatively) more ideal behavior of the hydrogen pimelate anion. 5.4. Spectroscopy. The IR spectra of solid pimelic acid and the two salts4 show clear differentiation in the carbonyl region between 1730 and 1500 cm−1. This was exploited by examining molten mixtures of ephedrine and pimelic acid at various compositions using a Thermo Continuum FTIR microscope linked to a Thermo Nexus FTIR spectrometer. The spectra were analyzed using Nicolet’s OMNIC software. The microscope was used in reflectance mode and only provided spectra if the samples were very thin or molten. Samples were prepared by grinding predetermined ratios of ephedrine, pimelic acid, and the 1:1 salt in a pestle and mortar, and melting on a microscope slide using a sealed hot plate. The molten samples were then placed under the microscope and imaged, and spots for analysis were selected. Samples were analyzed between 4000 and 600 cm−1. The results are summarized in Table 9. Figure 9 shows data from 1900 to 1300 cm−1 for four compositions, showing the shift in the carbonyl peaks. At each composition, four patterns were recorded from different locations in the samples. The variation in the patterns at x = 0.30 and 0.39 was not seen at other compositions and may be due to inadequate mixing of the sample before or during melting. The patterns for x = 0.1 and 0.2 (not shown) are broadly similar to those for x = 0.3, although the shoulder at ∼1625 cm−1 is more pronounced. The patterns for x = 0.7, 0.8, and 0.9 (not shown) are broadly similar to those for x = 0.65, with the peak at 1540 cm−1 decreasing steadily as x increases. The carbonyl peaks shift from typical values for double ionization at low values of x to typical values for uncharged, fully protonated carboxylic acid at high values of x. This confirms that the molten species retain the charges that they possess in the crystalline state. The singly charged anion, characterized by peaks at 1625 and 1540 cm−1, seems to be present at all concentrations, albeit at varying concentrations. The spectra do not allow any conclusions about the extent of hydrogen bonding in the melts.

the 1:1 salt is better explained by association in the melt. The additivity of the enthalpies may be understood in terms of preservation of hydrogen-bonded ion pairs in the melt. The melting point phase diagrams help to clarify why these binary compounds form at all, and the reasoning is the same for racemates, salts, and cocrystals. In the absence of the binary compound, the melting points of the equimolar mixtures are much lower than the individual components. For uncharged systems, this difference is quite predictable and is about 35 °C for the two uncharged systems here. For the salt-forming system in Figure 7, the differences are larger. As this behavior is driven by proton transfer, and does not require the existence of the salt, it is general. It follows that the enthalpic interactions in binary compounds do not need to be stronger than those in its solid components. This has implications for supramolecular synthonic engineering, and particularly for the search for energetically favorable supramolecuar synthons.10 As Ricci points out,27 structural explanations are required for the formation of solids with fixed stoichiometries rather than solid solutions. This is what supramolecular synthons and ionic interactions provide in the examples studied here. The ephedrine pimelate system is the only one of the three that can form specific 2:1 interactions in the melt and the solid. Calculating entropies of melting is easy, yet interpreting them is unfashionable. The general observation8,9 that more flexible molecules have higher melting entropies is borne out in this study. In the examples studied here, crystal structures help to interpret measured entropies of melting. The approximation of 6 J/mol·K for each flexible bond seemed reasonable for pimelic acid but was too crude for the other four unary solids. Further investigation of the interplay between entropies of melting and interdependency of rotations (as in BZP, DPA) and intramolecular hydrogen bonding (as in ephedrine and mandelic acid) is merited. Many of these considerations are also relevant for solubility. Specifically, the melting point phase diagrams provide a useful starting point for the ternary diagrams with solvents in both R/ S-mandelic acid14 and BZP/DPA3 systems. The eutectic positions are similar in both melts and liquids. Deviations from ideality are most pronounced for the single componentsin water at low temperatures for mandelic acid, and in methanol for DPA and BZP. A similar study of a cocrystal system containing two different cocrystal stoichiometries would be a good test of the methodology developed here. In the salt forming systems, the deviations from ideality in the melting-point phase diagram are much larger. They are larger still in the presence of the dianion. This is also seen in the ternary diagram in water, where the acid/base ratios of the eutectics are also shifted, presumably due to preferential hydration of some species.4 A relevant parameter may be the dielectric constant of the melt. Typical values for ionic liquids are in the range 9−15,28 suggesting that similar ion paring may

6. CONCLUSION An unexpected but striking feature of all three systems studied here is that the entropies and enthalpies of melting of the 1:1 compounds (racemate, cocrystal, and salt) were all similar to the sums of corresponding data for the component pairs. For the racemate and the cocrystal, this may be explained by nearcomplete dissociation in the melt. The entropy of melting of J



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(13) Stoimenovski, J.; MacFarlane, D. R.; Bica, K.; Rogers, R. D. Crystalline vs. Ionic Liquid Salt Forms of Active Pharmaceutical Ingredients: A Position Paper. Pharm. Res. 2010, 27 (4), 521−526. (14) Lorenz, H.; Sapoundjiev, D.; Seidel-Morgenstern, A. Enantiomeric Mandelic Acid System − Melting Point Phase Diagram and Solubility in Water. J. Chem. Eng. Data 2002, 47, 1280−1284. (15) Gavezzotti, A. Molecular symmetry, melting temperature and melting enthalpies of substituted benzenes and naphthalenes. J. Chem. Soc., Perkin Trans. 2 1995, 2, 1399−1404. (16) Black, S. N.; Collier, E. A.; Davey, R. J.; Roberts, R. J. Structure, solubility, screening and synthesis of molecular salts. J. Pharm. Sci. 2007, 96 (5), 1053−1068. (17) Rastogi, R. P.; Nigam, R. K.; Sharma, R. N.; Girdhar, H. L. Entropy of Fusion of Molecular Complexes. J. Chem. Phys. 1963, 39 (11), 3042−3044. (18) Prigogine, I.; Defay, R. Chemical Thermodynamics; translated by Everett, D. H.; Longmans Green & Co.: London, 1954. (19) Rastogi, R. P. Thermodynamics of Phase Equilibria and Phase Diagrams. J. Chem. Educ. 1964, 41, 443−448. (20) Profir, V. M.; Rasmuson, A. C. Influence of Solvent and Operating Conditions on the Crystallisation of Racemic Mandelic Acid. Cryst. Growth Des. 2004, 4 (2), 315−323. (21) Hunter, C. A. Quantifying Intermolecular Interactions; Guidelines for the Molecular Recognition Toolbox. Angew. Chem., Int. Ed. 2004, 43, 5310−5324. (22) Thalladi, V. R.; Nüsse, M.; Boese, R. The Melting Point Alternation in α,ω-Alkanedicarboxylic Acids. J. Am. Chem. Soc. 2000, 122 (38), 9227−9236. (23) Mitchell, C. A.; Yu, L.; Ward, M. D. Selective Nucleation and Discovery of Organic Polymorphs through Epitaxy with Single Crystal Substrates. J. Am. Chem. Soc. 2001, 123 (44), 10830−10839. (24) Collier, E. A.; Davey, R. J.; Black, S. N.; Roberts, R. J. 17 Salts of ephedrine; crystal structures and packing analysis. Acta Crystallogr., Sect. B: Struct. Sci. 2006, 62, 498−505. (25) Alonso, J. L.; Sanz, M. E.; Lopez, J. C.; Cortijo, V. Conformational Behaviour of Norephedrine, Ephedrine and Pseudoephedrine. J. Am. Chem. Soc. 2009, 131, 4320−4326. (26) Zingg, S. P.; Arnett, E. M.; McPhail, A. T.; Bothner-By, A. A.; Gilkerson, W. R. Chiral Discrimination in the Structures and Energetics of Association of Stereoisomeric Salts of Mandelic Acid with α-Phenethylamine, Ephedrine and Pseudoephedrine. J. Am. Chem. Soc. 1988, 110, 1565−1580. (27) Ricci, J. E. The Phase Rule and Heterogeneous Equilibrium; Dover Publications Inc.: New York, 1966; p 128. (28) Wakai, C.; Oleinikova, A.; Ott, M.; Weingartner, H. How polar are ionic liquids? Determination of the static dielectric constant of an imidazolium-based ionic liquid by microwave dielectric spectroscopy. J. Phys. Chem. B 2005, 109 (36), 17028−17030.

be common in solvent systems containing little or no water. This suggests that ternary phase diagrams in nonaqueous solvents may more closely resemble those of cocrystals. This would be simpler to test in systems that do not form dianions.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.8b01120..

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Data handling and consistency; crystal structure interpretation; eutectics temperature for two equivalent components; eutectic temperatures and mole fractions for a fully dissociating binary compound and its components (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Simon N. Black: 0000-0003-3147-376X Roger J. Davey: 0000-0002-4690-1774 Present Address #

(C.L.W.) AMICULUM, Clarence Mill, Bollington, SK10 5JZ, UK. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Jacques, J.; Collet, A.; Wilen, S. H. Enantiomers, Racemates, and Resolutions, reissue; Krieger Publishing Co.: FL, 1994. (2) Lee, H. H.; Warner, J. C. The Systems (I) DiphenylDiphenylamine, (II) Diphenyl-Benzophenone, (III) Benzophenone − Diphenylamine. J. Am. Chem. Soc. 1933, 55, 209−214. (3) Chadwick, K.; Davey, R. J.; Dent, G.; Pritchard, R. G.; Hunter, C. A.; Musumeci, D. Cocrystallization: A Solution Chemistry Perspective and the Case of Benzophenone and Diphenylamine. Cryst. Growth Des. 2009, 9 (4), 1990−1999. (4) Cooke, C. L.; Davey, R. J.; Black, S. N.; Muryn, C.; Pritchard, R. G. Binary and Ternary Phase Diagrams as Routes to Salt Discovery: Ephedrine and Pimelic Acid. Cryst. Growth Des. 2010, 10, 5270− 5278. (5) Walden, P. Ü ber die Schmelzwärme, spezifische kohäsion und molekulargrösse bei der Schemlztemparatur. Z. Elektrochem. Angew. Phys. Chem. 1908, 14, 713−724. (6) Rastogi, R. P.; Nigam, R. K. Thermodynamic Properties of Associated Mixtures. J. Phys. Chem. 1960, 64, 722−726. (7) Bondi, A. A correlation between the entropy of fusion of molecular crystals and molecular structure. Chem. Rev. 1967, 67 (5), 565−580. (8) Yalkowsky, S. H. ‘Estimation of Entropies of Fusion of Organic Compounds’. Ind. Eng. Chem. Fundam. 1979, 18 (2), 108−111. (9) Gilbert, A. S. Entropy-enthalpy compensation in the fusion of organic molecules: implications for Walden’s rule and molecular freedom in the liquid state. Thermochim. Acta 1999, 339, 131−142. (10) Dunitz, J. D.; Gavezzotti, A. Supramolecular Synthons: Validation and Ranking of Intermolecular Interaction Energies. Cryst. Growth Des. 2012, 12, 5873−5877. (11) Duddu, S. P.; Grant, D. J. W. Formation of the Racemic Compound of Ephedrine Base from a Physical Mixture of Its Enantiomers in the Solid, Liquid, Solution or Vapor State. Pharm. Res. 1992, 9, 1083−1091. (12) Fraser, K. J.; Izgorodina, E. I.; Scott, J. L.; MacFarlane, D. R.; Forsyth, M. Liquids intermediate between “molecular” and “ionic” liquids: Liquid Ion Pairs? Chem. Commun. 2007, 3817−3819. K


On the Melting of Binary Organic Compounds - Crystal Growth

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