On the melting of binary organic compounds

*Simon N. Black$, Claire L. Woon+,# & Roger J. Davey+

$AstraZeneca, Chemical Development, Macclesfield SK10 2NA, UK.

+University of Manchester, School of Chemical Engineering and Analytical Sciences,

Manchester, M13 9PL, UK.

#Current address: AMICULUM, Clarence Mill, Bollington, SK10 5JZ, UK.

ABSTRACT: The melting behaviors of three binary organic compounds, a racemate, a co-crystal

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

1

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 cocrystals 2,3 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 non-associating unary systems, and then used the ratio of this

constant to measured 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 ideality and association in non-stoichiometric melts. A further refinement is to

2

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) as selected based on the

availability of suitable data, as shown in Table 1:

Table 1: Racemate, Cocrystal and Salt systems selected

Compound Component A Component B Refs.

Racemate R-mandelic acid S-mandelic acid 14Cocrystal benzophenone (BZP) diphenylamine (DPA) 2,3Salt (1R, 2S)– ephedrine pimelic acid 4

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.

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

3

errors are standardized, and inconsistencies identified and accounted for, as describe in the ESI.

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 2D

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 behaviours 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.

4

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 di-substituted benzenes. The value of 6

J/mol.K for each rotatable bond is an approximation assuming two accessible and iso-energetic

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 ESI.

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

5

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 non-stoichiometric compositions.

For clarification, a model melting point phase diagram is presented in Figure 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

A-BBAAB

Mole Fraction A

Tem

pera

ture

(°C)

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

6

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 2-component system. The continuous lines

show the melting behaviour of two rigid molecules, denoted A and B respectively. The dashed

and dotted lines show two different melting behaviours 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.

Table 2: Melting behavior of a model binary compound AB and its constituents

Compound Line Melting Tm ΔSm ΔHm

in Fig. 1, Equilibrium (˚C) (J/mol K) (kJ/mol)

A green A(s) = A(l) 100 54 20.2B red B(s) = B(l) 100 54 20.2A-B dashed A-B(s) = A(l) + B(l) 100 108 40.4AB dotted AB(s) = AB(l) 100 54 20.2

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 electronic supporting information (ESI).

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

7

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 ESI. 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 ESI for further details. In the example given in

Figure 1, the eutectic temperature is 13˚ lower than Tm. For other systems (cocrystals, salts), in

8

which the individual components have similar properties, the phase diagrams may be expected to

show similar, pseudo-symmetrical 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

analysed 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: R- and S-Mandelic Acid

The molecular structures of the two enantiomers are shown in Scheme 1

9

1

22

O

O HOH

OH

OO H

Scheme 1: S- and R-enantiomers of mandelic acid. The two rotatable bonds in the S-enantiomer are numbered.

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 H-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 S-enantiomer 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.

10

Table 3: Torsions in mandelic acid

Structure Enantiomer/Conformer Torsion 1 Torsion 2 O….O (Å)

FEGHAA S / ‘A’ 88.6 -2.1 2.650FEGHAA S / ‘B’ 139.9 1.2 2.666DLMANDL03 R -130.8 23.3 2.726DLMANDL03 S 130.8 -23.3 2.726

Figure 2: Comparison of the three different conformations of S-Mandelic acid in DLMANDL03 (centre) and FEGHAA (‘A’ on the left, ‘B’ on the right), viewed parallel to bond 1.

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 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 neighbouring 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

11

takes part in an intramolecular H-bond, there is a net loss of one hydrogen bond per molecule on

melting, for both racemate and enantiomer.

Table 4: Melting point data for S-mandelic acid and (R,S)-mandelic acid14

Compound MW Melting Point (K)

Melting Enthalpy (kJ/mol)

Melting Entropy (J/mol.K)

S-mandelic acid 152.15 404 24.5 61

R,S-mandelic acid 304.3 392 51.2 131

Table 4 shows literature data for the melting of pure S-mandelic acid and the stable polymorph

of racemic R,S-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 on

melting are similar - of the same order as the loss of one hydrogen bond.

12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1105

110

115

120

125

130

135enantiomer model racemate modelracemate data eutectic data

mole fraction R

Tem

pera

ture

(°C

)

Figure 3: Predicted (this work, lines) and measured 14 (points) melting point phase diagram for R,S-mandelic acid.

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.

13

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.

4. Cocrystal: benzophenone and diphenylamine

Scheme 2: benzophenone (BZP, left) and diphenylamine (DPA, right)

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

14

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.

Table 5: Data from the crystal structures of the cocrystal and its components

Compound Crystal Structure Z’ Space Group Torsions (°)

BZP BPHENO12 1 P212121 +26.3, +26.8DPA QQQBVP02 8 P-1 5.5 to 5.5; 45.9 to 45.9Cocrystal BZPPAM01 1 P21/n 36.2, 21.4 (BZP)

5.8; 38.7 (DPA)

Figure 4: The two conformations of BZP in the cocrystal, and the ‘Mogul’ analysis.

15

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 labelled version of the ‘Mogul’ plot is provided in the ESI

Figure 5: Conformations of DPA from the cocrystal structure, and ‘Mogul’ geometry plots.

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 favour

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 iso-energetic. 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 ESI.

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.

16

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 sub-

optimal 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.

Table 6: Melting point data for DPA, BZP and the stable cocrystal

Compound MW Melting Point Melting Enthalpy Melting Entropy(K) (kJ/mol) (J/mol.K)

DPA 169.22 326 17.8 55BZP 182.22 321 17.9 56Cocrystal 351.44 313 32.3 103

The melting entropies of the two components give values close to Walden’s rule. Indeed, both

molecules were in the dataset 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 only 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.

17

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 125

30

35

40

45

50

55

co-crystal fitbzp databzp fitdpa data

Mole Fraction BZP

Tem

pera

ture

(°C)

Figure 6: Predicted (this work, lines) and measured 2(points) melting point data for the binary system DPA-BZP.

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

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°C and 34°C compared with measured 34°C 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.

18

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.

5. Salt: ephedrine and pimelic acid

The molecular structures of ephedrine and pimelic acid are given in Scheme 3

Scheme 3: Neutral forms of (1R, 2S)- ephedrine (left) and pimelic acid (right). 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 structures 4 with new

spectroscopic data. This example thus introduces the additional complexity of charged states for

both molecules. Firstly, the molecular shapes and H-bonding in ephedrine and pimelic acid are

discussed

5.1. Conformations and H-bonding

19

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 extent of

dissociation of the acid groups. Preferred conformations of this molecule have an extended

backbone, and may be symmetric (two-fold axis and/or mirror plane). The predicted entropy of

melting if not associated is 54 + (6 x 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 5-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 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

20

(1R, 2S)-ephedrine melts. Similar reasoning applies to the options for hydrogen bond formation

in stoichiometric 1:1 and 2:1 salts.

The four relevant crystal structures are summarized in Table 7. Previous discussions of these

structures4,16,22 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

Table 7: Data from the crystal structures of the salts and their components

Ephedrine Compound

Crystal Structure

Space Group

Torsion 1 Torsion 2 Torsion 3 N-H…O bond length

Ephedrine EPHEDR01 P212121 79.3 167.4 166.8 2.5171:1 salt INEDIP P21 80.5 167.9 179.4 2.4622:1 salt INEDOV P21 77.0 166.4 175.4 2.5192:1 salt INEDOV P21 53.8 172.3 54.5 2.706Pimelic Acid Compound

Crystal Structure

Space Group

Torsion 1 Torsion 2 Torsion 3 Torsion 4

Pimelic Acid PIMELA07 C2/c 173.9 169.3 169.3a 173.9a

1:1 salt INEDIP P21 178.8 176.2 175.2 67.92:1 salt INEDOV P21 177.7 66.6 172.4, 168.1 aby symmetry

In pimelic acid the central carbon atom lies on a two-fold axis. As noted previously4, the carbon

backbone is extended, and 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.

21

Figure 7: ‘Mogul’ Geometry check for torsions in the pimelic acid backbone.

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

22

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 favour 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 favour 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

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.

…………………………………………………………………………………………………

Table 8: Melting point data for ephedrine, pimelic acid, and their two salts

Compound MW Melting Point (K)

Melting Enthalpy (kJ/mol)

Melting Entropy (J/mol.K)

(1R, 2S)- Ephedrine 165.2 310 12.0 39Pimelic Acid 160.2 378 31.8 841:1 salt 325.4 403 44.7 1112:1 salt 490.6 393 45.5 116

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

23

‘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 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

24

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 semi-quantitative interpretation, as

for the cocrystal and racemate.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

140

solidusliquiduspimelic acid1:1 salt (A)ephedrine

mole fraction pimelic acid

mel

ting

poin

t (°C

)

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.

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-

25

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 solution 26). 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 ionisation 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 meta-stable 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 ionisation.

26

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 ionisation or

its reverse during melting of non-stoichiometric 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

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 analysed using

Nicolet’s OMNIC software. The microscope was used in reflectance mode and only provided

27

spectra if the samples were very thin or molten. Samples were prepared by grinding pre-

determined ratios of ephedrine, pimelic acid and the 1: 1 salt in a pestle and mortar, and melting

on a microscope slide using a sealed hotplate. The molten samples were then placed under the

microscope, imaged and spots for analysis were selected. Samples were analysed between 4000

cm-1 and 600 cm-1. The results are summarised in Table 9. Figure 9 shows data from 1900 cm-1 to

1300 cm-1 for four compositions, showing the shift in the carbonyl peaks.

Table 9: Spectroscopic data for the carbonyl peaks in ephedrine/pimelic acid melts

Sample Mole fraction of pimelic acid

Peak intensities

1694 cm-1 1681 cm-1 1624 cm-1 1559 cm-1 1548 cm-1

Pimelic Acid 1.0 - s - - -1:1 salt 0.5 m - m - m2:1 salt 0.33 - - sh s -2:1 salt + ephedrine

0.1-0.3 - - sh s -

(s= strong, m = medium, sh = shoulder)

28

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).

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.

29

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, characterised by peaks at 1625 cm-1 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.

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 near-complete dissociation in the melt. The entropy of melting of 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.

30

This has implications for supramolecular synthonic engineering, and particularly for the search

for energetically favourable 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 from specific

2:1 interactions in the melt and the solid.

Calculating entropies of fusion 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

31

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 9-1528, suggesting that similar ion-

paring may be common in solvent systems containing little or no water. This suggests that

ternary phase diagrams in non-aqueous solvents may more closely resemble those of cocrystals.

This would be simpler to test in systems which do not form di-anions.

Corresponding Author

*simon.black@astrazeneca.com

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval

to the final version of the manuscript.

Electronic Supporting Information (ESI)

A separate word file contains further details of

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.

32

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For Table of Contents Use Only

On the melting of binary organic compounds

Simon N. Black, Claire L. Woon & Roger J. Davey

Synopsis

The fates of a racemate (mandelic acid), a cocrystal (benzophenone-diphenylamine) and a salt

(ephedrine pimelate) on melting are compared. Phase diagrams, crystal structures and

spectroscopy suggest similar melting thermodynamics - but different extents of association.

Xm

Ym

[XY]m

Y-m

[X+Y-]m

X+mXYs

35