Understanding the Influence of Surface Solvation and Structure on

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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 J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b08549 • Publication Date (Web): 15 Oct 2018 Downloaded from http://pubs.acs.org on October 19, 2018

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Journal of the American Chemical Society

Scheme 1: Polymorphic interconversion in the theophylline-benzamide co-crystal system. 53x15mm (300 x 300 DPI)

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Figure 1: Schematic representation of a cocrystal polymorph interconversion equilibrium curve under ball mill LAG conditions as a function of solvent concentration. 84x48mm (300 x 300 DPI)


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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 sixteen solvents tested. The estimated standard deviations of the polymorph concentrations as obtained from the Rietveld refinements are smaller than the symbols. 177x85mm (300 x 300 DPI)



Figure 3: Computational modelling 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 (2013). 8 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 parametrise a SSIP-swapping model (see text) to obtain the relative amount of each SSIP class exposed on the crystal surface of the two polymorphs. 177x82mm (300 x 300 DPI)


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Figure 4: Comparison of the value of the polymorph interconversion transition points (T S ) calculated with the SSIPswapping model (see text) with the corresponding experimental values. 84x73mm (300 x 300 DPI)



Figure 5: Scherrer crystal size as calculated from the Rietveld refinements for the most abundant cocrystal polymorph for the ball mill LAG equilibrium experiments with EtOH. The estimated standard deviations as calculated from the refinements are smaller than the symbols. 84x48mm (300 x 300 DPI)


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ToC 84x48mm (300 x 300 DPI)



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Understanding the influence of surface solvation and structure on polymorph stability: a combined mechanochemical and theoretical approach. Ana M. Belenguer,*1 Giulio I. Lampronti,*1,2 Nicola De Mitri,* 1 Mark Driver,1 Christopher A. Hunter1 and Jeremy K. M. Sanders*1 1

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK

2

Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK

KEYWORDS: mechanochemistry; milling; nanocrystals; surface site interaction point (SSIP); polymorphs. ABSTRACT: We explore solvent concentrations under ball-mill liquid assisted grinding (LAG) to investigate the surface solvent solvation effects on the thermodynamic stability of two polymorphs of a 1:1 theophylline : benzamide cocrystal. In this system, the most stable-bulk polymorph form II converts to the 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 polymorph concentration and crystallite size. The surface site interactions point (SSIP) description of non-covalent interactions was used in conjunction with the SSIMPLE method for calculating solvation energies to infer 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 co-crystal 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 solvent nature; (iv) the SSIP results indicate 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; (iv) 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 theophyllinebenzamide cocrystal polymorphs here studied must be affected by surface solvation under ball mill LAG conditions.

Introduction It is becoming clear that surface structures and energies play a major role in determining the relative stabilities of different polymorphs when 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 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 polymorphs form I and form II of a 1:1 theophylline : benzamide cocrystal subjected to ballmill liquid assisted grinding (LAG), and a complementary theoretical study using the surface site interaction point (SSIP) methodology.8-9 Even without knowing which crys-

tal 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 presence of very small quantities of added solvent that can accelerate or even enable specific reactions between solids.15-17 We


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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 inorganic,19-20 and organic21-22 compounds, including the formation of supramolecular architectures such as co-crystals and metalorganic frameworks,12, 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 subject 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 glass transition 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 glass transition 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, 3943 Many authors comment that powders subjected to ball mill grinding become nanocrystalline35-38, 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) and 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 and 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 "stable-bulk" polymorph the most stable polymorph under a given set of temperature and pressure and micrometer or above crystal size. 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, moisture acting as added water.45 For a few systems it has been observed that while the poly-

morph 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 turnover polymorph transformation; polymorph transformation from stable-bulk to metastable-bulk polymorph by neat grinding and from 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 an equilibrium is reached with a phase composition that does not change as long as the milling conditions are maintained.67, 10, 46-47 This thermodynamic equilibrium depends on numerous factors: ball mill jar size and shape and material as well as 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 1µL per 200 mg of total powder.6 The idea that the free energy can be affected by such 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 stable-bulk polymorph is formed when a large volume of solvent is added. However, both Neat and LAG polymorph can be found to coexist when an intermediate volume of solvent is added.54 55 Despite the common perception that ball mill grinding results in poorly reproducible data, we have previously demonstrated that LAG experiments can be very reproducibly performed6-7.To achieve this level of accuracy and reproducibility the experiments must be performed with grinding jars and ball bearings manufactured to the same specification. A mechanical grinding device must be used to have 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 here studied are given in this manuscript and its relative supplementary information (see Section 5 in 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 depend on the crystal size because of the effect of surface energies.1-2 However these effects only becomes significant 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 self-evident 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 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 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 forms free energy.

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(DCM), benzene, toluene, cyclohexane, F18-decalin, plus water. This work is further proof that ball-mill LAG equilibrium curves (Figure 1) can be successfully achieved experimentally for a cocrystal system, confirming that these solvent - crystal surfaces interaction phenomena are general. In order to try to understand the underlying causes for these polymorphic transitions we explore here a computational approach to infer 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 to calculate 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 tp π-system face is more exposed in the surface of form I while the tp N-methyl groups are more exposed in form II.

The theophylline-benzamide co-crystal system The system here studied is the 1:1 co-crystal of theophylline (tp) and benzamide (ba), which presents two different polymorphs, form I and form II,42, 60 the latter shown to be the thermodynamically stable-bulk polymorph in ambient conditions by slurry experiments (see Section 3.2 in ESI). Form I is quantitatively transformed into form II under LAG conditions with 250 µL of water per 1 g of powder, while form II is quantitatively transformed into form I under NG conditions (Scheme 1).6 Scheme 1: Polymorphic interconversion in the theophylline-benzamide co-crystal system.

Figure 1: Schematic representation of a cocrystal polymorph interconversion equilibrium curve under ball mill LAG conditions as a function of solvent concentration.

Form I (metastable bulk): CSD refcode RABXIE02. Form II (stable bulk): CSD refcode RABXIE01.

Finally, according to our Rietveld microtextural analysis on the PXRD data, for some solvents the stable-bulk polymorph has a significantly smaller crystal size at equilibrium than the metastable-bulk in the investigated solvent concentration range (see Section 5 in ESI). This is further indication that the crystal surface - solvent interaction plays a crucial role in the relative polymorph stabilities.

The equilibrium polymorph concentration curve (i.e. the experimental polymorph concentration at equilibrium as a function of solvent concentration) shows that 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 (2µL between 10 and 12 µL·g-1). In here we extend the work to sixteen 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

Experimental Methods The procedure described by Fischer et al. (2016)42 was used to prepare 1 : 1 tp : ba co-crystal in forms I and II at a 7g scale (see Section 4 in ESI). Slurry experiments were performed to confirm which is the most stable polymorph under ambient conditions. Supersaturated solvent suspensions of 1 : 1 mixtures of form I and form II were stirred until the kinetic polymorph had fully converted to the stable form. These slurry experiments were performed in benzene, diethylether, hexane and cyclohexane (see Section 3.2 in ESI). Equilibrium was reached within a week.


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Form I/II equilibrium experiments as a function of the solvent concentration were performed starting from 1g of form I added to a 14.5 mL stainless steel screw-closure milling jar together with two 10 mm diameter stainless steel ball bearings. The solvent was added in a known quantity ranging between 5 and 250 μL measured by direct pipetting (see Section 2.2.1 to 2.2.5 in ESI for details). Different experimental precautions have to be taken for different solvents (see Section 2.2.1 in ESI). This depends also on the properties of the solid.51 The experimental procedure used ensured that all the solvent is in close contact with the powder and that grinding ensures that the solvent is distributed evenly throughout the powder (using pre-soaking if necessary) before grinding is 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 evaporation of the grinding solvent and was found to be essential for accurate reproducibility of results. The ball mill grinder was programmed to achieve the total grinding times in consecutive 10-15 minute runs separated by 5 minute 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 co-exist to prove the thermodynamic equilibrium nature of the phase concentrations (see Section 2.2.1 in ESI). This is an essential step for the design of milling equilibrium experiments.51 Depending on the width of such concentration range the kinetic study can give more or less reproducible results. However if the range is narrow 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 for experiment rather than the 200 mg we have used in previous experimental settings:6-7, 51 this improved the resulting solvent concentration resolution. Immediately after completion of grinding, jars were opened and samples were analyzed using PXRD. The solid-state composition of the samples was determined by quantitative Rietveld refinements from powder XRD data (see Section 2.3.2 and Section 5 in ESI for details). The results are presented as equilibrium curves in which the % 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.

Computational methods For the computational modelling of cocrystal solvation, the geometry of each of the components and the solvents was optimised 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 = 0.002 a0-3. All the DFT calculations were carried out with NWChem.62 For each molecule the molecular electrostatic potential surface (MEPS) was converted into a set of surface site interaction points (SSIP) by means of the footprinting algorithm described in by Calero et al. (2013).8 Lastly, the solvation energy of each SSIP in each solvent was computed.9



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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 sixteen solvents tested. The estimated standard deviations of the polymorph concentrations as obtained from the Rietveld refinements are smaller than the symbols.

Results and discussion The sixteen 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) (see Section 5 in ESI for individual solvent plots). No fitting was performed and the curves 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, partly 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 are coexisting. Only two very apolar solvents, cyclohexane and F18decalin, do not yield form II in the concentration ranges that that we studied, although it is 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 cooperativity of solvent binding at the crystal surface. With a crystal size of tens of nm there must be thousands of adsorption sites per crystallite. If the adsorption reactions have strong positive cooperativity 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 twostate "all occupied" or "all free" system. This is the case for acetone, MeCN and THF.

As we previously reported for the 4-chlorophenyl-2nitrophenyl-disulfide (compound 1-2) case,6 some of these curves have a shallower slope (notably IPA, water and CHCl3), with both form I and form II present over a range of solvent concentrations. We further noticed a correlation between the width of solvent concentration transition zone where both polymorphs coexist at equilibrium and the solvent size and polarity of the solvents (see Figure S53 and Figure S54 in ESI). We believe 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 form II or 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 conversion. We have reported analogous observations and conclusions for polymorphs form A and form 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, dermined as the midpoint of the transition zone,


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must be related to the solvent properties. In the ESI Section 6.1 we show how the solvents can be grouped on the basis of their α (the Taft scale of solvent hydrogen-bonddonor acidities) and β (the Taft scale of solvent hydrogenbond-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 (see Figure S40 in ESI). More crucially, we suggest that such transitions can be rationalised 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 crystal. Figure 3 is a flow chart of the computational approach applied here. It also shows the SSIPs used to describe the molecular surfaces of tp, ba and the solvents. The free energy of solvation of the surface of the cocrystal in solvent S is given in Eq. 1 ୗୗ୍୔ୱ

ΔGୗ = ෍ χ୧ ΔG୧ ୗ ୧

(1)

Where ΔG ୧ ୗ is the solvation energy of SSIP i in solvent S, and χ୧ is the number of SSIP of type i that are exposed on the crystal surface in a given form. The difference in crystal surface solvation energy between two polymorphs in solvent S is therefore given by Eq. 2. ୗୗ୍୔ୱ

ΔΔGୗ = ෍ Δχ୧ ΔG୧ ୗ ୧

(2)

Where Δχ୧ represents the change in the number of SSIPs of type i that are exposed on the crystal surface in the two polymorphs. The polymorph interconversion transition point Tୗ is the quantity of solvent needed to cover enough of the crystal surface in order to make the difference in crystal solvation energy big enough to invert the stability of the two polymorphs. In other words, Tୗ multiplied by ΔΔGୗ should be related to the energy difference between the two polymorphs in the absence of

solvent, which is a constant. Thus Tୗ can be related to the solvation energies of the individual SSIPs in the two molecules of the cocrystal by Eq. 3. ୗୗ୍୔ୱ

1 − ∝ ෍ Δχ୧ ΔG୧ ୗ Tୗ ୧

(3)

The values of ΔG୧ ୗ can be directly calculated according to Hunter (2013)9 (see Table S40 in ESI), so the parameters Δχ୧ , 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 Tୗ . There are 27 SSIPs in total, but the number of variables Δχ୧ can be reduced to 10 by grouping together SSIPs that correspond either to similar functional groups (e.g. the two tp 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 Tୗ is excellent (r2 = 0.904) and the resulting Δχ୧ coefficients are shown in Table 1. The results suggest that the main difference between the surfaces of the crystals of the two polymorphs is due to a change in the orientation of tp, 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 (see Figure S49 and Figure S50 ESI). In addition to the phase quantification the Rietveld refinements yield an estimate of the crystal size for both polymorphs (see Section 2.3.3 and Section 5 in ESI for details). 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 form II, depending on the solvent concentration) for all the PXRD scans: the stable-bulk form II has a significantly smaller crystal size at equilibrium than the 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 (see summary figure S38 in the ESI). The equilibrium crystal size must be determined by the ratio between crystal breaking rate and crystal growth rate under the given ball mill 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.



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Figure 3: Computational modelling 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 (2013).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 parametrise a SSIP-swapping model (see text) to obtain the relative amount of each SSIP class exposed on the crystal surface of the two polymorphs.

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 polymorph relative stabilities 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 becomes 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.

Conclusions Ball mill grinding processes often lead to nanocrystalline powder material. At the nanosize, surface effects become visible, and can affect the stability of crystal forms. Thermodynamics of polymorphs depend 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 con-

centration of 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 polymorphs form A and form B of compound 1-2 under LAG conditions for a range of solvents and solvent concentrations.6 We here extended our investigation on the role of solvent at equilibrium in polymorphic systems by producing equilibrium polymorph concentration curves with sixteen different solvents as a function of solvent concentration for the 1:1 tp : ba cocrystal. We experimentally showed that the metastable-bulk polymorph form I fully or partially transforms into the 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 slopes indicating that reaction cooperativity of solvent binding to the crystal surfaces depends on the solvent nature. We conclude that the milling equilibrium in the solvent concentration ranges where both form I and form II co-exist involves a third phase. We suggest that this third phase represents an intermediate state with partially occupied adsorption sites of the continuous conversion of form I and form II into each other. Since we observed analogous phenomena for polymorphs form A and form B of compound 1-2,6 our


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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.

Figure 5: Scherrer crystal size as calculated from the Rietveld refinements for the most abundant cocrystal polymorph for the ball mill LAG equilibrium experiments with EtOH. The estimated standard deviations as calculated from the refinements are smaller than the symbols.

Figure 4: Comparison of the value of the polymorph interconversion transition points (ࢀࡿ ) calculated with the SSIPswapping model (see text) with the corresponding experimental values.

Table 1: Optimised ࢤ࣑࢏ parameters from the SSIPswapping model.

Finally, for some solvents - IPA, EtOAc, MeNO2, MeOH, THF, EtOH, and CHCl3 - the stable-bulk polymorph form II has a significantly smaller crystal size at equilibrium than the 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 form I and form II and/or affecting significantly the crystal morphology via preferential solvation of specific crystallographic faces.

Benzamide

߂߯௜

Theophylline

߂߯௜

ASSOCIATED CONTENT

Amide nitrogen face

+ 3.2

π-face

- 10.9

Supporting Information

π-face

- 1.8

N-methyl

+ 4.8

π-edge

+ 1.5

Nitrogen acceptor

- 2.8

Carbonyl acceptors

- 0.3

Carbonyl acceptors

+ 1.2

Amide donors

- 0.1

Ring NH/CH donors

+ 0.0

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 tp, 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.

The Electronic Supporting Information is available free of charge on the ACS Publications website. The ESI PDF file contains: general experimental details; discussion on 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; polymorph crystal structures plots.

AUTHOR INFORMATION Corresponding Author * [email protected]; [email protected]; [email protected]; [email protected].

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

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding Sources We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) grant code EP/K025627/2 for Nicola De Mitri and a EPSRC doctoral training studentship (grant code EP/M506485/1) for Mark Driver.

ACKNOWLEDGMENT We thank: C. A. Bland for the mechanical 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; S. A. T. Redfern and the Department of Earth Sciences (University of Cambridge) for general support.

ABBREVIATIONS ESI, electronic supporting information; LAG, liquid assisted grinding; NG, neat grinding; tp, Theophylline anhydrous; ba, Benzamide; Form I, polymorph of 1:1 tp:ba obtained typically from ball mill NG (CSD refcode RABXIE02); Form II, polymorph of 1:1 tp:ba obtained typically from ball mill LAG (CSD refcode RABXIE01); MeCN, acetonitrile; THF, tetrahydrofuran; EtOAc, ethyl acetate; CHCl3, chloroform; DCM, dichloromethane; DMF, dimethylformamide; NO2Me, nitromethane; MeOH, methanol; EtOH, ethanol; IPA, isopropanol or 2-propanol; H2O, water; cHexane, cyclohexane; F18-decalin, octadecafluorodecahydro-naphthalene; MM400, Retsch automated grinder model used; S/V, surface to volume; CSD, Cambridge structural database; PXRD, powder X-ray diffractometry; ID, internal diameter; ss, stainless steel; Hz; Hertz;12 compound, 4-chlorophenyl-2-nitrophenyl-disulfide; form A, polymorph of 1-2 obtained typically from ball mill NG; form B, polymorph of 1-2 obtained typically from ball mill LAG; SSIP, surface site interactions point; experimental; Calc., calculated; α Taft scale of solvent hydrogen-bonddonor acidities; β Taft scale of solvent hydrogen-bondacceptor basicities; MEPS, molecular electrostatic potential i surface; ∆G s, solvation energy of SSIP i in solvent S; ∆χi , number of SSIP of type i that are exposed on the crystal surface.

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