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Cite This: J. Am. Chem. Soc. 2018, 140, 17051−17059
Understanding the Influence of Surface Solvation and Structure on Polymorph Stability: A Combined Mechanochemical and Theoretical Approach Ana M. Belenguer,*,† Giulio I. Lampronti,*,†,‡ Nicola De Mitri,*,† Mark Driver,† Christopher A. Hunter,† and Jeremy K. M. Sanders*,† †
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
‡
J. Am. Chem. Soc. 2018.140:17051-17059. Downloaded from pubs.acs.org by IOWA STATE UNIV on 01/14/19. For personal use only.
S Supporting Information *
ABSTRACT: We explore the effect of solvent concentration on the thermodynamic stability of two polymorphs of a 1:1 cocrystal of theophylline and benzamide subjected to ball-mill liquid assisted grinding (LAG) and we investigate how this can be related to surface solvent solvation phenomena. In this system, most stable bulk polymorph form II converts to metastable bulk polymorph form I upon neat grinding (NG), while form I can fully or partially transform into form II under LAG conditions, depending on the amount of solvent used. Careful and strict experimental procedures were designed to achieve polymorph equilibrium under ball-mill LAG conditions for 16 different solvents. This allowed us to determine 16 equilibrium polymorph concentration curves as a function of solvent concentration. Ex-situ powder X-ray diffraction (PXRD) was used to monitor the polymorph concentration and crystallite size. The surface site interactions point (SSIP) description of noncovalent interactions was used in conjunction with the SSIMPLE method for calculating solvation energies to determine which functional groups are more or less exposed on the polymorph crystal surfaces. Our results demonstrate that (i) ball-mill LAG equilibrium curves can be successfully achieved experimentally for a cocrystal system; (ii) the equilibrium curves vary from solvent to solvent in onset values and slopes, thus confirming the generality of the interconversion phenomenon that we interpret here in terms of cooperativity; (iii) the concentration required for a switch in polymorphic outcome is dependent on the nature of the solvent; (iv) the SSIP results indicate that the theophylline π-system face is more exposed on the surface of form I while the theophylline N-methyl groups are more exposed in form II; and (v) for some solvents, form II has a significantly smaller crystal size at equilibrium than form I in the investigated solvent concentration range. Therefore, the free energy of the 1:1 cocrystal of theophylline and benzamide polymorphs studied here must be affected by surface solvation under ball-mill LAG conditions.
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ology.8,9 Even without knowing which crystal faces exactly define the morphology of these nanocrystals, we have been able to tentatively identify which functional groups become buried or more exposed in the polymorphic transition. Although our experimental focus has been an exploration of ball-mill grinding, we believe the principles emerging from this work will have general applicability to nanocrystalline materials however they have been generated. Equilibria in Mechanochemistry. Mechanochemistry using manual or ball-mill grinding equipment is becoming a routine solid-state synthesis tool.10 It is “greener” and generally less expensive than traditional solution methods because it requires little or no solvent.11 It is also effective because it often gives quantitative yields.12−14 Manual or mechanical grinding can be performed in the absence of solvent or in the
INTRODUCTION It is becoming clear that surface structures and energies play major roles in determining the relative stabilities of different polymorphs when the crystal size is sufficiently small. Experimental evidence in support of this view has emerged from studies of inorganic nanocrystals,1,2 from crystallization studies in nanopores3,4 and nanodroplets,5 and from our own studies using ball-mill grinding.6,7 We have previously shown in two different systems that in liquid-assisted grinding (LAG) the position of equilibrium between two polymorphs depends on the nature and concentration of the added solvent, but the relationship between the solvent properties and the position of equilibrium has been unclear.6 We now report a detailed set of studies exploring the effect of solvent concentration on the thermodynamic stability of polymorph forms I and II of a 1:1 theophylline/benzamide cocrystal subjected to ball-mill liquidassisted grinding (LAG) and a complementary theoretical study using the surface site interaction point (SSIP) method© 2018 American Chemical Society
Received: August 9, 2018 Published: October 15, 2018 17051
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
Article
Journal of the American Chemical Society
the stable bulk to metastable bulk polymorph by neat grinding and from the metastable bulk to stable bulk polymorph by LAG grinding.6,31,39,41,42 It is generally accepted that after the milling reaction reaches completion in a sealed system, equilibrium is reached with a phase composition that does not change as long as the milling conditions are maintained.6,7,10,46,47 This thermodynamic equilibrium depends on numerous factors: the ball-mill jar size and shape and material as well as the ball bearing size and weight and material,34,48,49 milling frequency,50 temperature,33 and solvent nature and concentration.51−53 Experimental evidence shows that this latter parameter is remarkably important: the thermodynamic outcome of the grinding reaction changes dramatically in response to a small change in the solvent volume added, sometime as little as 1 μL per 200 mg of total powder.6 The idea that the free energy can be affected by such a small amount of solvent has been considered by other authors.54 It has been observed that when a very small volume of solvent is added to the grinding experiment the metastable bulk polymorph is obtained, while the stable bulk polymorph is formed when a large volume of solvent is added. However, both polymorphs can be found to coexist when an intermediate volume of solvent is added.5455 Despite the common perception that ball-mill grinding results in poorly reproducible data, we have previously demonstrated that LAG experiments can be very reproducibly performed.6,7To achieve this level of accuracy and reproducibility, the experiments must be performed with grinding jars and ball bearings manufactured to the same specifications. A mechanical grinding device must be used to have a reproducible frequency. Furthermore, any experimental detail, however trivial, has to be considered. Very careful, strict, and validated experimental procedures have to be tested and followed in order to investigate how the milling equilibrium changes as a function of solvent concentration. While experimental procedures for the system studied here are given in this manuscript and its relative Supporting Information (Section 5 in the SI), we refer to our methodology paper for further and more general details and considerations.51 Other systematic studies of ball-mill LAG grinding of cocrystals have clarified the role of the solvent and how a range of metastable cocrytals can be formed during the grinding experiment.56,57 The thermodynamics of polymorphs depends on the crystal size because of the effect of surface energies.1,2 However, these effects become significant only for nanosized crystals,58 which is why they become visible after mechanochemical processing.6 We previously demonstrated that polymorph relative stabilities can change depending on the presence, nature, and concentration of solvent under milling conditions: the selfevident conclusion is that crystal surface energies must be affected by the nature and concentration of the solvent.6 There are many ways in which this can be achieved. Crystal surface solvation phenomena, i.e., the absorption of solvent on the crystal surface, can change the surface free energy itself. Indeed we believe that the cooperativity of solvent binding at the surfaces is the only way to interpret the shape of polymorph concentration equilibrium curves as a function of solvent concentration. The solvent can affect the crystal growth rate by facilitating the transport of molecules within the milling mash: this affects the final crystal equilibrium size, thus changing the surface to volume (S/V) ratio and the total polymorph free energy. Solvents (as well as other additives)59 can also inhibit
presence of very small quantities of added solvent that can accelerate or even enable specific reactions between solids.15−17 We refer to the latter case as “kneading” or liquid-assisted grinding (LAG),18 while we talk of neat grinding (NG) where no solvent is added. Mechanochemical methods have been used for an ever-growing number of different syntheses and chemical reactions of inorganic19,20 and organic21,22 compounds, including the formation of supramolecular architectures such as cocrystals and metal−organic frameworks12,23−25 and even cages26 and rotaxanes.27 Most of these studies are purely empirical, lacking the sound theoretical framework that is required for the systematic application of these methods: the mechanisms and the driving forces involved in mechanochemical synthesis and supramolecular reactions are poorly understood and yet subjects of scientific debate.6,7,12,14,16,19,25,28−34 The evolution of nanocrystallite size in polymorphic systems during the milling process and its relationship to the glasstransition temperature has been studied by differential scanning calorimetry.35,36 The results suggest that a complex process takes place which may or may not involve an amorphous intermediate phase depending on the glasstransition temperature. The observation that a metastable polymorph could be obtained by NG from the thermodynamically bulk stable polymorph has been reported initially for alloys37 and pure metals38 and later for organic compounds.6,7,15,35,36,39−43 Many authors comment that powders subjected to ball-mill grinding become nanocrystalline,35−38,44 and some believe that the extra stability in the nanocrystals is due to the high density of structure defects.37,38,43 Other authors report the product of grinding reaching a stable phase composition which they designate as “steady state”, “dynamical steady state,”39,43,44 or “far from equilibrium”.37 These terminologies have been adopted to avoid a conflict with the accepted Ostwald rule. Under this rule, only one thermodynamic form can exist under a given pressure (p) and temperature (T); the other polymorphic forms are metastable. Linot et al. propose that the stability inversion observed must depend on the intensity of grinding (I); therefore, the stabilization of such metastable polymorphs must be explained by its dependence on p, T, and I.39 However, these authors do not study the particle size reduction.39 When the crystallite size reduction makes the interfacial Gibbs enthalpy non-negligible, a stability inversion is expected below a critical crystallite diameter.36 Our experimental evidence shows that nanocrystalline powders from ball-mill grinding have very large surface to volume ratios; therefore, the free energy of the surface structures must play a significant role in the relative stabilities of polymorphs under ball-mill grinding conditions.6 We call the “stable bulk” polymorph the most stable polymorph under a given set of temperature, pressure, and above a certain crystal size generally larger than one micrometer. We have been investigating the outcomes of the ball-mill grinding process with a focus on the role of solvent in the final equilibrium under ball-mill LAG conditions.6 Environmental moisture has been investigated with hydroscopic samples, with moisture acting as added water.45 For a few systems, it has been observed that while the polymorph stable under room conditions is obtained under ball-mill LAG conditions, neat grinding yields a polymorph that is metastable under room conditions.31,39,41 Various authors have reported a turnover polymorph transformation: polymorph transformation from 17052
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
Article
Journal of the American Chemical Society the growth rate of specific crystal faces due to preferential absorption phenomena: this alters the final crystal equilibrium morphology and the surface free energy because for a given crystal form different crystal faces have different free energies. These hypotheses do not contradict each other, and further evidence is needed to understand how the solvent affects the relative crystal form free energy. Theophylline/Benzamide Cocrystal System. The system here studied is the 1:1 cocrystal of theophylline and benzamide (tp/ba), which presents two different polymorphs, forms I and II,42,60 with the latter shown to be the thermodynamically stable bulk polymorph under ambient conditions by slurry experiments (Section 3.2 in the SI). Form I is quantitatively transformed to form II under LAG conditions with 250 μL of water per 1 g of powder, while form II is quantitatively transformed to form I under NG conditions (Scheme 1).6
Figure 1. Schematic representation of a cocrystal polymorph interconversion equilibrium curve under ball-mill LAG conditions as a function of solvent concentration.
concentration range (Section 5 in the SI). This is a further indication that the crystal surface−solvent interaction plays a crucial role in the relative polymorph stabilities.
Scheme 1. Polymorphic Interconversion in the Theophylline−Benzamide Cocrystal Systema
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EXPERIMENTAL METHODS
The procedure described by Fischer et al.42 was used to prepare a 1:1 tp/ba cocrystal in forms I and II on a 7g scale (Section 4 in the SI). Slurry experiments were performed to confirm which is the most stable polymorph under ambient conditions. Supersaturated solvent suspensions of 1:1 mixtures of forms I and II were stirred until the metastable polymorph had fully converted to the stable form. These slurry experiments were performed in benzene, diethyl ether, hexane, and cyclohexane (Section 3.2 in the SI). Equilibrium was reached within a week. Form I/II equilibrium experiments as a function of the solvent concentration were performed starting from 1 g of form I added to a 14.5 mL stainless steel screw-closure milling jar together with two 10mm-diameter stainless steel ball bearings. The solvent was added in a known quantity ranging from 5 to 250 μL as measured by direct pipetting. (Sections 2.2.1 to 2.2.5 in the SI for details.) Different experimental precautions have to be taken for different solvents (Section 2.2.1 in the SI). This also depends on the properties of the solid.51 The experimental procedure used ensured that all of the solvent was in close contact with the powder, and grinding ensured that the solvent was distributed evenly throughout the powder (using presoaking if necessary) before grinding was started. The jars were closed and sealed with Teflon washer covers, and milling was performed at 30 Hz on a MM400 Retsch automated grinder until equilibrium was achieved. The sealing avoids the evaporation of the grinding solvent and was found to be essential for the accurate reproducibility of the results. The ball-mill grinder was programmed to achieve the total grinding times in consecutive 10−15 min runs separated by 5 min intervals to avoid heating the powder when using such large, heavy balls. The grinder shielding was removed and replaced with an external safety shield in order to prevent the ventilation system of the motor from heating the milling jar over prolonged milling times. For each solvent, different milling times were tested in the concentration range where both polymorphs coexist to prove the thermodynamic equilibrium nature of the phase concentrations (Section 2.2.1 in the SI). This is an essential step in the design of milling equilibrium experiments.51 Depending on the width of such a concentration range, the kinetic study can give more or less reproducible results. However, if the range is narrow, then the estimate of its width will have a smaller absolute error. We are currently looking for ways to improve the solvent concentration resolution. Scaling up is one possible strategy. In the experiments we present here we have worked with a total powder content of 1 g rather than the 200 mg we have used in previous experimental settings:6,7,51 this improved the resulting solvent concentration resolution. Immediately after the completion of grinding, jars were opened and
a
Form I (metastable bulk): CSD refcode RABXIE02. Form II (stable bulk): CSD refcode RABXIE01.
The equilibrium polymorph concentration curve (i.e., the experimental polymorph concentration at equilibrium as a function of solvent concentration) shows this transition point (i.e., the solvent concentration for which [form II]/[form I] = 1 in such curve) at a water concentration of 0.2 mol·mol−1 corresponding to 10 μL·g−1.6 The solvent concentration transition zone where both polymorphs are present at equilibrium was found to be very narrow (2 μL between 10 and 12 μL·g−1). Here, we extend the work to 16 different solvents, namely, acetonitrile (MeCN), acetone, N,N-dimethylformamide (DMF), nitromethane (MeNO2), tetrahydrofuran (THF), ethyl acetate (EtOAc), chloroform (CHCl3), methanol (MeOH), ethanol (EtOH), isopropanol (IPA), dichloromethane (DCM), benzene, toluene, cyclohexane, F18-decalin, and water. This work is further proof that ballmill LAG equilibrium curves (Figure 1) can be successfully achieved experimentally for a cocrystal system, confirming that these solvent−crystal surface interaction phenomena are general. In order to try to understand the underlying causes for these polymorphic transitions, we explore here a computational approach to inferring which functional groups are relatively more or less exposed in the crystal surfaces of the two polymorphs. This method is based on the SSIMPLE method for calculating the solvation energies of surface site interaction points (SSIP) for each functional group that can be exposed on the crystal surface.8,9 The results suggest that the theophylline π-system face is more exposed in the surface of form I while the theophylline N-methyl groups are more exposed in form II. Finally, according to our Rietveld microtextural analysis of the PXRD data, for some solvents the stable bulk polymorph has a significantly smaller crystal size at equilibrium than the metastable bulk polymorph in the investigated solvent 17053
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
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Figure 2. tp/ba cocrystal polymorph interconversion equilibrium curve under ball-mill LAG conditions as a function of solvent concentration for the 16 solvents tested. The estimated standard deviations of the polymorph concentrations as obtained from the Rietveld refinements are smaller than the symbols. samples were analyzed using PXRD. The solid-state composition of the samples was determined by quantitative Rietveld refinements from powder XRD data (details in Sections 2.3.2 and 5 in the SI). The results are presented as equilibrium curves in which %form II is plotted versus solvent concentration (in millimoles of solvent per mole of cocrystal). Each equilibrium curve required tens of individual grinding experiments at varying solvent concentration. The exact number of independent milling experiments required for the definition of the curves for each solvent was determined by the form I to II transition profile.
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possible that these solvents could yield form II at higher concentration. We have previously proposed that the shape of solvent equilibrium curves can be interpreted in terms of the cooperativity of solvent binding at the crystal surface. With a crystal size of tens of nanometers, there must be thousands of adsorption sites per crystallite. If the adsorption reactions have strong positive cooperativity, then the many potential states in which the n adsorption sites are only partially occupied are never populated. This leads to an almost vertical equilibrium curve slope corresponding to a two-state “all occupied” or “all free” system. This is the case for acetone, MeCN, and THF. As we previously reported for the 4-chlorophenyl-2-nitrophenyl-disulfide (compound 1−2) case,6 some of these curves have a shallower slope (notably IPA, water, and CHCl3), with both forms I and II present over a range of solvent concentrations. We further noticed a correlation between the width of the solvent concentration transition zone where both polymorphs coexist at equilibrium and the solvent size and polarity of the solvents (Figures S53 and S54 in the SI). We believe that this may indicate energetically disfavored intermolecular interactions between the adsorbed solvent molecules and a consequent drop in cooperativity over a certain ratio of full to empty adsorption sites: the smaller and more polar the solvent molecule, the more energetically significant the interactions between adjacent adsorbed solvent molecules. According to the theory of cooperativity,63 the presence of a third phase at equilibrium in that specific solvent concentration range is necessary to justify such a slope. This third phase or state could be a crystalline form I or II or an amorphous one in which the surface adsorption sites are only partially occupied. A liquid phase seems unlikely considering the amount of solvent used in the LAG experiments and the high melting points of the components. This equilibrium would be a dynamic one where polymorphs continuously transform into each other while the partially occupied adsorption site phase is the intermediate state of such a conversion. We have reported analogous observations and conclusions for polymorphic forms A and B of compound 1− 2.6 Therefore, we suggest that the presence of a third state in polymorphic equilibria is a general phenomenon. The solvent-dependent values of the experimental polymorph interconversion concentration transition points, deter-
COMPUTATIONAL METHODS
For the computational modeling of cocrystal solvation, the geometry of each of the components and the solvents was optimized in the gas phase using density functional theory, employing the B3LYP exchange-correlation functional61 and the 6-31G* set of atomic functions. The molecular electrostatic potential surface was computed for each molecule at the isosurface defined by ρ = 0.002a0−3. All of the DFT calculations were carried out with NWChem.62 For each molecule, the molecular electrostatic potential surface (MEPS) was converted to a set of surface site interaction points (SSIP) by means of the footprinting algorithm described by Calero et al.8 Finally, the solvation energy of each SSIP in each solvent was computed.9
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RESULTS AND DISCUSSION The 16 milling equilibrium experimental curves as a function of solvent concentration are shown in Figure 2. The experimental data are shown as %form II as obtained from the Rietveld quantitative analyses versus solvent molar concentration (mmol of solvent/mol of solid, Section 5 in the SI for individual solvent plots). No fitting was performed, and the curves that are drawn are only a guide to the eye. While the curves vary in onset values and slopes, 14 solvents give form II at equilibrium above a certain solvent concentration. This demonstrate that form II can be stable under ball-mill LAG conditions using appropriate amounts of polar and apolar solvents, partially challenging a previous report for this polymorphic system.42 This could be categorically established only after focused milling kinetic studies, i.e., testing different milling times in the concentration range where both polymorphs coexist. Only two very apolar solvents, cyclohexane and F18-decalin, do not yield form II in the concentration ranges that we studied, although it is 17054
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
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Figure 3. Computational modeling of the polymorph crystal faces. The crystal and solvent molecules were described by means of surface site interaction points (SSIPs), displayed in the blue boxes. The solvation energy was calculated for each SSIP in each solvent from Hunter.9 The SSIPs were grouped into classes with similar solvation energies, and the solvation energies were used in combination with the experimental polymorph interconversion transition points to parametrize an SSIP-swapping model (see the text) to obtain the relative amount of each SSIP class exposed on the crystal surface of the two polymorphs.
energy between two polymorphs in solvent S is therefore given by eq 2
mined as the midpoint of the transition zone, must be related to the solvent properties. In SI Section 6.1, we show how the solvents can be grouped on the basis of their α (the Taft scale of solvent hydrogen-bond-donor acidities) and β (the Taft scale of solvent hydrogen-bond-acceptor basicities) parameters in order to investigate such correlations. Intriguingly, there is also a correlation for apolar solvents between the transition point and the solvent boiling point (Figure S40 in the SI). More crucially, we suggest that such transitions can be rationalized in terms of the differences in solvation energy of the crystal faces of the two polymorphs. The chemical functionality exposed to the solvent is different for the two different polymorphs. The experiments suggest that form II has a smaller (i.e., more favorable) solvation energy than form I: in other words, form II is relatively stabilized by the presence of solvent. We propose that fewer solvent molecules would be required for the polymorph switch if solvation energies of the crystal surfaces differed more from one polymorph to the other. Indeed, it is possible to describe the solvation energy of a molecule as the sum of the solvent interactions with discrete sites on the van der Waals surface (surface site interaction points, or SSIP).8 Thus, it is possible to relate the difference in the solvation energies of the two polymorphs to changes in the SSIP distribution on the surfaces of the two types of crystals. Figure 3 is a flowchart of the computational approach applied here. It also shows the SSIPs used to describe the molecular surfaces of theophylline, benzamide, and the solvents. The free energy of solvation of the surface of the cocrystal in solvent S is given in eq 1
SSIPs
ΔΔGS =
∑ i
χi ΔGi S
Δχi ΔGi S
i
(2)
where Δχi represents the change in the number of SSIPs of type i exposed on the crystal surface in the two polymorphs. The polymorph interconversion transition point TS is the quantity of solvent needed to cover enough of the crystal surface in order to make the difference in crystal solvation energy large enough to invert the stability of the two polymorphs. In other words, TS multiplied by ΔΔGS should be related to the energy difference between the two polymorphs in the absence of solvent, which is a constant. Thus, TS can be related to the solvation energies of the individual SSIPs in the two molecules of the cocrystal by eq 3. −
1 ∝ TS
SSIPs
∑
Δχi ΔGi S
i
(3)
The values of ΔG S can be directly calculated according to Hunter9 (Table S40 in the SI), so parameter Δχi, describing the differences in the functional group distribution of the surface of the crystals of the two polymorphs, can be determined by a linear fit of eq 3 to the experimental values of TS. There are 27 SSIPs in total, but the number of variables Δχi can be reduced to 10 by grouping together SSIPs that correspond either to similar functional groups (e.g., the two theophylline carbonyl groups) or to one part of the molecule (e.g., all of the CH groups on the edge of the benzamide aromatic ring). The result of the fit is shown in Figure 4. The Pearson correlation coefficient between the experimental and calculated TS is excellent (r2 = 0.904), and the resulting Δχi coefficients are shown in Table 1. The results suggest that the main i
SSIPs
ΔGS =
∑
(1)
where ΔGiS is the solvation energy of SSIP i in solvent S and χi is the number of SSIPs of type i exposed on the crystal surface in a given form. The difference in crystal surface solvation 17055
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
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Journal of the American Chemical Society
Figure 5. Scherrer crystal size as calculated from the Rietveld refinements for the most abundant cocrystal polymorph for the ballmill LAG equilibrium experiments with EtOH. The estimated standard deviations as calculated from the refinements are smaller than the symbols.
polymorph relative stability switch cannot be explained by a mere change in the S/V ratio, and surface solvation phenomena have to be invoked. One possible explanation is that the crystal surfaces of form II become relatively more stable than the crystal surfaces of form I by increasing the amount of solvent absorbed: in other words, the unsolvated surfaces of form I are more stable than the unsolvated surfaces of form II, while the opposite is true when the crystal surfaces are solvated. Alternatively, the solvent is selectively absorbed on specific crystallographic faces of form I and/or form II nanocrystals, altering the crystal morphology and thus the total crystal surface free energy. These two interpretations are not contradictory, and both phenomena might occur simultaneously.
Figure 4. Comparison of the value of the polymorph interconversion transition points (TS) calculated with the SSIP-swapping model (see the text) with the corresponding experimental values.
Table 1. Optimized Δχi parameters from the SSIP-Swapping Model benzamide
Δχi
theophylline
Δχi
amide nitrogen face π-face π-edge carbonyl acceptors amide donors
+3.2 −1.8 +1.5 −0.3 −0.1
π-face N-methyl nitrogen acceptor carbonyl acceptors ring NH/CH donors
−10.9 +4.8 −2.8 +1.2 +0.0
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difference between the surfaces of the crystals of the two polymorphs is due to a change in the orientation of theophylline, which exposes more of the face of the π-system in form I and more of the N-methyl groups in form II. This is consistent with faces parallel to c* being relatively more extended in the crystal morphology of form I as well as in the crystal morphology of form II (Figures S49 and S50 in the SI). In addition to the phase quantification the Rietveld refinements yield an estimate of the crystal size for both polymorphs (details in Sections 2.3.3 and Section 5 in the SI). As an example, the plot in Figure 5 shows the milling equilibrium curve for EtOH together with the Scherrer crystal size as calculated from the Rietveld refinements for the most abundant cocrystal polymorph (form I or II, depending on the solvent concentration) for all of the PXRD scans: stable bulk form II has a significantly smaller crystal size at equilibrium than metastable bulk form I in the investigated EtOH concentration range. Analogous results can be observed for EtOAc, MeNO2, MeOH, THF, and CHCl3, DMF, water, and IPA (summary Figure S38 in the SI). The equilibrium crystal size must be determined by the ratio between the crystal breaking rate and the crystal growth rate under the given ballmill grinding conditions. Such rates must depend on the crystal form as well as on the solvent nature and concentration, hence the different equilibrium sizes for different experiments. This is the opposite to what we observed for the polymorphic system of compound 1−2, where the stable bulk polymorph tends to be consistently larger than the metastable bulk polymorph for the solvents used in the investigated concentration ranges.6 In the cocrystal case, the
CONCLUSIONS Ball mill grinding processes often lead to nanocrystalline powder material. At the nanoscale, surface effects become visible and can affect the stability of crystal forms. The thermodynamics of polymorphs depends on the crystal size because of the effect of the surface energies. Because surface energy is affected by the nature and concentration of the solvent, polymorph relative stabilities can change depending on the presence (or absence), nature, and concentration of a solvent under milling conditions. These thermodynamic aspects are general and must apply to any milling system, independent of the nature of the chemical or supramolecular bonds involved in the transformation studied. These effects must be even more significant in small-molecule polymorphs, which generally differ in lattice energy by less than 4 kJ mol−1.64,65 We previously studied the relative stabilities of polymorph forms A and form B of compound 1−2 under LAG conditions for a range of solvents and solvent concentrations.6 Here we extended our investigation into the role of solvent at equilibrium in polymorphic systems by producing equilibrium polymorph concentration curves with 16 different solvents as a function of solvent concentration for the 1:1 tp/ba cocrystal. We experimentally showed that metastable bulk polymorph form I fully or partially transforms to stable bulk polymorph form II under LAG conditions depending on the amount of solvent, further confirming the generality of the phenomenon. The curves vary in slope, indicating that the reaction cooperativity of solvent binding to the crystal surfaces depends 17056
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K025627/2) for N.D.M. and an EPSRC doctoral training studentship (grant code EP/M506485/1) for M.D.
on the solvent nature. We conclude that the milling equilibrium in the solvent concentration ranges where both forms I and II coexist involves a third phase. We suggest that this third phase represents an intermediate state with partially occupied adsorption sites of the continuous conversion of forms I and II into each other. Since we observed analogous phenomena for polymorph forms A and B of compound 1−2,6 our impression is that such third phase at equilibrium under LAG conditions could exist in any polymorphic system where the relative polymorph stabilities switch over a certain solvent concentration under milling conditions. SSIP solvation energies were used to relate the difference in the total solvation energies of the two polymorphs to changes in the SSIP distribution on the crystal surfaces. The results suggest that the main difference lies in the orientation of theophylline, which exposes more of the face of the π-system in form I and more of the N-methyl groups in form II. This would indicate that in both polymorphs the crystals are relatively more elongated along the c*-axis direction under milling conditions. Finally, for some solvents such as IPA, EtOAc, MeNO2, MeOH, THF, EtOH, and CHCl3, stable bulk polymorph form II has a significantly smaller crystal size at equilibrium than metastable bulk polymorph form I in the investigated solvent concentration range. This cannot be explained by a mere change in the S/V ratio, and surface solvation phenomena must play a major role either by significantly changing the surface free energy difference between forms I and II and/or significantly affecting the crystal morphology via the preferential solvation of specific crystallographic faces.
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Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank C. A. Bland for the mechanical design and P. Donnelly for the software design of the automation of the grinders for repeat grinding; Richard Nightingale and his team from the mechanical workshop at the Department of Chemistry, University of Cambridge, for the manufacture of the jars; M. J. Williamson for his contributions to the SSIP code; and S. A. T. Redfern and the Department of Earth Sciences (University of Cambridge) for general support.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b08549. General experimental details; discussion of the Rietvelt refinement quantification and Scherrer size determination from PXRD data; tabulation and plots of solvent equilibrium curves for 16 solvents; results from the Rietveld refinements including goodness of fit indices; correlation between experimental data with published physicochemical parameters of solvents; correlation between experimental and computational data; and polymorph crystal structures plots (PDF)
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AUTHOR INFORMATION
Corresponding Authors
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REFERENCES
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ORCID
Ana M. Belenguer: 0000-0002-0443-4856 Giulio I. Lampronti: 0000-0002-1430-3446 Nicola De Mitri: 0000-0002-7127-9585 Mark Driver: 0000-0002-8329-888X Christopher A. Hunter: 0000-0002-5182-1859 Jeremy K. M. Sanders: 0000-0002-5143-5210 Funding
We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) (grant code EP/ 17057
DOI: 10.1021/jacs.8b08549 J. Am. Chem. Soc. 2018, 140, 17051−17059
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