AMB and JKMS are grateful to the EPSRC for financial support. We thank C. A. Bland for the design and the mechanical setup and P. Donnelly for the software design of the automation of the grinders for repeat grinding. We thank Richard Nightingale, Ollie Norris and Simon Dowe from the mechanical workshop for the manufacture of the grinding jars, and the Solenoid holder for the &#34;Push a Button&#34; setup and Keith Parmenter from the glass workshop at the Department of Chemistry for the manufacture of the glass sample PXRD slides. We thank C. A. Bland for the maintenance and repair of the screw closure grinding jars. We thank Professor Bill Jones for the use of the PXRD equipment at the Department of Chemistry and Professor Chris Hunter for the use of his laboratory facilities. We thank the Department of Earth Sciences (GIL) for general support.

1. Validation of the precise dispensing of organic solvents
<ol>
	<li>Validation of precise pipetting of organic solvents in reverse pipette mode 
	NOTE: Air displacement pipettes in reverse pipetting mode were selected for a range of LAG solvents (acetone, acetonitrile (MeCN), tetrahydrofuran (THF), ethyl acetate (EtOAc), chloroform (CHCl3) and dimethylformamide (DMF)) because they soaked very efficiently into the powders of the starting materials (1-1 and 2-2<...

<ol>
	<li>James, S. L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanochemistry:+opportunities+for+new+and+cleaner+synthesis.">Mechanochemistry: opportunities for new and cleaner synthesis.</a> Chem Soc Rev. 41 (1), 413-447 (2012).</li><li>Braga, D., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Solvent+effect+in+a+"solvent+free"+reaction.">Solvent effect in a "solvent free" reaction.</a> CrystEngComm. 9 (10), 879-881 (2007).</li><li>Karki, S., Friscic, T., Jones, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Control+and+interconversion+of+cocrystal+stoichiometry+in+grinding:+stepwise+mechanism+for+the+formation+of+a+hydrogen-bonded+cocrystal.">Control and interconversion of cocrystal stoichiometry in grinding: stepwise mechanism for the formation of a hydrogen-bonded cocrystal.</a> CrystEngComm. 11 (3), 470-481 (2009).</li><li>Kaupp, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Solid-state+molecular+syntheses:+complete+reactions+without+auxiliaries+based+on+the+new+solid-state+mechanism.">Solid-state molecular syntheses: complete reactions without auxiliaries based on the new solid-state mechanism.</a> CrystEngComm. 5 (23), 117-133 (2003).</li><li>Biswal, B. 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Protocols. 8 (9), 1718-1729 (2013).</li><li>Ma, X., Yuan, W., Bell, S. E. J., James, S. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Better+understanding+of+mechanochemical+reactions:+Raman+monitoring+reveals+surprisingly+simple+'pseudo-fluid'+model+for+a+ball+milling+reaction.">Better understanding of mechanochemical reactions: Raman monitoring reveals surprisingly simple 'pseudo-fluid' model for a ball milling reaction.</a> Chem Commun. 50 (13), 1585-1587 (2014).</li><li>Tumanov, I. A., Michalchuk, A. A. L., Politov, A., Boldyreva, E., Boldyrev, V. 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E., Lou&#235;r, D., Scardi, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rietveld+refinement+guidelines.">Rietveld refinement guidelines.</a> J Appl Crystallogr. 32 (1), 36-50 (1999).</li><li>Allen, F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Cambridge+Structural+Database:+a+quarter+of+a+million+crystal+structures+and+rising.">The Cambridge Structural Database: a quarter of a million crystal structures and rising.</a> Acta Crystallogr Sect B. 58 (3 Part 1), 380-388 (2002).</li><li>Gra&#382;ulis, S., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Crystallography+Open+Database-an+open-access+collection+of+crystal+structures.">Crystallography Open Database-an open-access collection of crystal structures.</a> J Appl Crystallogr. 42 (4), 726-729 (2009).</li><li>Cheary, R. 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The authors have nothing to disclose

While most of the literature on mechanochemistry focuses either on pragmatic outcomes or on reaction mechanisms, this paper addresses the thermodynamic end point of ball mill grinding. From this perspective, kinetic studies are a necessary step to the definition of the final equilibrium plateaus. Through our kinetic and final equilibrium studies, we know that the ball mill grinding reactions here discussed are driven by thermodynamics, resulting in the most stable polymorph composition under the given milling conditions....

Mechanochemistry using manual or ball mill grinding equipment has become increasingly popular in recent years as an attractive and sustainable alternative to traditional solution methods for the synthesis of materials.1 It is attractive because it allows for reaction between solids to be achieved effectively and quantitatively. It is a &#34;green&#34; sustainable technique, requiring little or no solvent. Milling or manual grinding can be performed neat, i.e. with no added solvent, or solvent assisted: in the latter, known as &#34;liquid assisted grinding&#34; (LAG),2,3,4 very small amounts of added liquid can accelerate or even enable otherwise inaccessible mechanochemical reactions between solids. Mechanochemical methods have been used for an ever-increasing number of different chemical reactions and syntheses of inorganic and organic compounds,5,6,7,8,9,11 as well as for the formation of supramolecular architectures such as molecular co-crystals,12,13,14 metalorganic frameworks,15,16,17 and even cages18 and rotaxanes19. It seems that many processes can proceed in the absence of solvent or with solvent present in minimal substoichiometric quantities.2,3,4 The mechanisms and the driving forces involved in the chemical syntheses and supramolecular reactions induced by mechanochemical conditions are subject of debate.1,13,20,21,22,23,24
Our research focuses on the final equilibrium outcomes of the ball mill grinding process and the role of solvent at equilibrium under ball mill LAG conditions. Indeed, after the ball mill grinding reaction reaches completion, thermodynamic equilibrium is achieved in the two systems we have investigated so far in our system, with a stable phase composition.25 The factors that can affect the final equilibrium are numerous and diverse: ball mill jar size and shape and material, ball bearing size and weight and material, milling frequency, temperature, and solvent nature and concentration. This is evidently the case when the thermodynamic outcome of the grinding reaction changes dramatically in response to a change in the solvent volume added, which can be sometime as low as 1&#181;L per 200 mg of total powder.25 Careful and strict experimental procedures have to be tested and followed in order to achieve reproducible precision and accuracy of the experimental results, from reactants and products storage, to pipetting and mixing pre-milling operations. It is difficult to control or even monitor parameters in a milling jar. Therefore, the use of a mechanical mixer mill (also called vibratory mill), which allows for reproducible and controlled milling frequencies and times, and sealed milling jars are essential. Ensuring that all ball mill grinding reactions reach equilibrium requires some preliminary kinetic investigation of the experimental conditions. The mechanical mixer used for the curves we present here was modified. In order to prevent the jars from warming up through the continuous flow of the exhausts of the motor in the sealed chamber over long periods of grinding, the safety cover sealing the front part of the grinder was removed, and an external safety screen was placed in its place.
The system that we used as a first example is the disulfide exchange reaction between bis-2-nitrophenyldisulfide (named 1-1) and bis-4-chlorophenyldisulfide (named 2-2) in the presence of a small amount of base catalyst 1,8-diazabicyclo[5.4.0]undec-7-ene (dbu) to produce upon ball mill neat grinding (NG) and LAG the compound 4-chlorophenyl-2-nitrophenyl-disulfide (named 1-2).26,27 The latter is formed by ball mill grinding as two different polymorphs, Form A and Form B. For many different LAG solvents, Form A is the thermodynamic product under ball mill NG conditions or when not enough solvent is used in the grinding reaction taken to equilibrium, while Form B is obtained as the thermodynamic product under ball mill LAG conditions at equilibrium when enough solvent is added to the milling jar.Indeed Form A can be obtained from Form B under ball mill NG, while Form B can be obtained from Form A under ball mill LAG. Such direct transformation in milling experiments has been reported before in other systems,28,29 and it has been reported that the nature and concentration of solvent determine the polymorph obtained under LAG conditions.30 Our published experimental results include the investigation of milling equilibrium curves for a range of organic solvents. Here the equilibrium phase composition ratio R = [Form B] / ([Form A] + [Form B]) is plotted against the volume of LAG solvent added for each experiment. The onset of the equilibrium curve and the sharpness of the curve were found to depend on the nature and molar amount of solvent added to the milling jar.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/56824/56824fig1.jpg" /> 
Figure 1: Reaction scheme of the ball mill grinding experiments and key concept of solvent equilibrium curves using the R value. 
These equilibrium curves shows graphically the effect of the addition of a few drops of solvent (x axis) on the phase composition of the product (y axis) when ball mill grinding for long enough to achieve equilibrium conditions. The bottom part of the graph accounts for Form A being quantitatively formed, the top part of the graph for Form B being quantitatively formed while a mixture of Form A and Form B is formed for the volume range of the solvent accounting for the sigmoidal part of the graph. This figure has been reprinted with minor changes from the Supplementary information in Chem. Sci., 2016, 7, 6617 (Ref. 25). <a href="//cloudflare.jove.com/files/ftp_upload/56824/56824fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Thermodynamic aspects are general and must apply to any given milling system. As a further example to show the generality of our observations, an analogous equilibrium curve was also produced for a second system: the two polymorphs of 1:1 co-crystal of theophylline (tp) with benzamide (bzm), form I and form II, where the outcome depends on the volume of water in the grinding mixture.25 These phase composition versus solvent concentration equilibrium curves are essential for investigating the interaction between the nanocrystal surfaces and the solvent molecules at equilibrium on ball mill grinding reactions. Our results demonstrate that some equilibrium curves are very sharp, showing an &#34;all-or-nothing&#34; behaviour, which is characteristic of particles with a large number of adsorption sites and positive cooperativity of the binding process.31 Shallower equilibrium curves indicate a lower level of cooperativity and suggest the presence of a third phase at equilibrium, possibly an amorphous phase involving the solvent itself. Such milling equilibrium curves have been produced for no other system to our knowledge. We believe this to be partly due to the inherent sensitivity of the solid state system to even very small environmental changes under ball mill LAG conditions.
Preparation of good and reliable solvent concentration curves can only be achieved if the experimentalists carefully validate their pipetting skills with training sets and if they fully understand (i) how pipettes and syringes work and (ii) if the equipment they have selected for delivering accurate and precise volume of a solvent is suitable to perform the intended job. The delivery of an exact volume of solvent can be accomplished with a variety of equipment, this being pipettes or syringes and their choice can depend on availability, user preference and skills, vapor pressure of the solvent used and intended application for the ball mill grinding experiments.
Pipettes are commercially available as air displacement or positive displacement covering many solvent ranges. Both types of pipettes are commercially available as manually operated or electronically automated. Automatic pipettes are generally preferred as they are less dependent on the experimentalist skills to be able to aspirate or dispense a solvent evenly at a given speed. The experimentalist must rely on the capability of the pipettes to deliver the exact volume of solvent. This can only happen if the pipettes are accurate to start with, well maintained, serviced and periodically calibrated. Typically, external pipette calibration services will calibrate pipettes to the ISO 8655 standard using water as the solvent. Therefore, for each organic solvent the experimentalist should validate their accuracy and precision of pipetting through accurate weighing experiments over the intended volume range to be dispensed.
The most commonly used solvent delivery equipment is the air displacement pipettes to which a tip needs to be fitted to the syringe barrel. They work on an air-cushion principle; upward movement of the piston produces a partial vacuum in the tip, causing the liquid to be drawn into the tip which is separated from the end of the piston by the air cushion. The vapor phase of the pipetted solvent will start to equilibrate within the air cushion, the extent of evaporation will depend on its vapor pressure. Pre-wetting is crucial when using variable-volume pipettes set at their lowest volume range, since the ratio of airspace to liquid and the potential for evaporation increases dramatically as compared to when the pipette is set at the top of its volume range. The experimentalist will know when this equilibrium is achieved, as the solvent aliquot will be hanging but separated from the end of the piston as from a spring, the solvent at the end of the tip staying firm when the pipette is held in vertical position over a few seconds: the solvent inside the tip should not sag or drip. Air displacement pipettes can be used in two modes; the most generally used is the forward pipetting mode where all the aspirated solvent is quantitatively dispensed by one full movement of the piston. The other mode is the reverse pipetting mode; in this mode a calculated excess of solvent is aspirated by the pipette, and therefore after quantitative dispensing, a residual volume of solvent remain in the pipette tip which needs to be disposed to waste. Reverse pipetting mode can be more suitable for viscous and dispensing very small volume of solvents. However, for high vapor pressure solvents like dichloromethane (DCM) or diethyl ether, equilibration in the air displacement pipette cannot be easily achieved. Positive displacement pipettes or syringes are more suitable in this case.
We propose that equilibrium phase composition versus solvent concentration curves could be obtained for any system under sufficiently well-designed, performed and controlled ball mill LAG conditions.

<table>
	<tbody>
		<tr>
			<td>Bis(2-nitrophenyl) disulfide named 1-1</td>
			<td>Aldrich</td>
			<td>215228-25G</td>
			<td>[1155-00-6] 
			(98%)</td>
		</tr>
		<tr>
			<td>Bis(4-chlorophenyl) disulfide named 2-2</td>
			<td>TCI</td>
			<td>D0360</td>
			<td>[1142-19-4] 
			(98+%)</td>
		</tr>
		<tr>
			<td>1,8-Diazabicyclo [5.4.0]undec-7-ene (dbu)</td>
			<td>Acros Organics</td>
			<td>160610250</td>
			<td>[6674-22-2] 
			(&#62;97.5 % by GC)</td>
		</tr>
		<tr>
			<td>2-nitrophenyl-4-chlorophenyl-disulfide named 1-2</td>
			<td>in house synthesis</td>
			<td></td>
			<td>Synthesised by ball mill grinding: 1:1 of 1-1 + 2-2 + 2%M dbu</td>
		</tr>
		<tr>
			<td>Form A</td>
			<td>in house synthesis</td>
			<td></td>
			<td>Polymorph of 1-2 prepared by ball mill neat grinding</td>
		</tr>
		<tr>
			<td>Form B</td>
			<td>in house synthesis</td>
			<td></td>
			<td>Polymorph of 1-2 prepared by ball mill liquid assisted grinding</td>
		</tr>
		<tr>
			<td>Formic Acid</td>
			<td>Scientific Laboratory Supplies</td>
			<td>56302-50ML</td>
			<td>[64-18-6] 
			Mass spectrometry grade</td>
		</tr>
		<tr>
			<td>Trifluoroacetic acid (TFA)</td>
			<td>ThermoFisher</td>
			<td>85183</td>
			<td>[76-05-1] 
			Reagent-Plus 99%</td>
		</tr>
		<tr>
			<td>Water (H2O)</td>
			<td>Rathburn</td>
			<td>W/0106/PB17</td>
			<td>[7732-18-5] 
			HPLC gradient analysis grade used also for HPLC analysis</td>
		</tr>
		<tr>
			<td>Acetonitrile (MeCN),</td>
			<td>Merck</td>
			<td>160610250</td>
			<td>[75-05-8] 
			Hypergrade for LCMS grade LiChrosolv used also for HPLC analysis</td>
		</tr>
		<tr>
			<td>Acetone</td>
			<td>Fisher Scientific</td>
			<td>A/0606/17</td>
			<td>[67-64-1] 
			HPLC grade</td>
		</tr>
		<tr>
			<td>Methanol (MeOH)</td>
			<td>Fisher Scientific</td>
			<td>M/4062/17</td>
			<td>[67-56-1] 
			LCMS grade</td>
		</tr>
		<tr>
			<td>Ethanol (EtOH)</td>
			<td>Sigma Aldrich</td>
			<td>15727-5L</td>
			<td>[64-17-5] 
			laboratory reagent, absolute,</td>
		</tr>
		<tr>
			<td>isopropanol (IPA)</td>
			<td>Fisher Scientific</td>
			<td>P/7508/17</td>
			<td>[67-63-0] 
			HPLC grade</td>
		</tr>
		<tr>
			<td>Tetrahydrofurane (THF)</td>
			<td>Acros Organics</td>
			<td>268290010</td>
			<td>[109-99-9] 
			For HPLC; 99%8, unstabilised</td>
		</tr>
		<tr>
			<td>Ethyl acetate (EtOAc)</td>
			<td>Fisher Scientific</td>
			<td>E/0906/15</td>
			<td>[141-78-6]</td>
		</tr>
		<tr>
			<td>Chloroform (CHCl3,)</td>
			<td>Fisher Scientific</td>
			<td>C/4966/17</td>
			<td>[67-66-3] 
			HPLC grade, stabilised with amylene</td>
		</tr>
		<tr>
			<td>Dichloromethane (DCM)</td>
			<td>Fisher Scientific</td>
			<td>D/1857/17</td>
			<td>[75-09-2] 
			HPLC grade, unstabilised</td>
		</tr>
		<tr>
			<td>Dimethylformamide (DMF)</td>
			<td>Alfa Aesar</td>
			<td>22915</td>
			<td>[68-12-2] very toxic 
			HPLC grade 99+% pure</td>
		</tr>
		<tr>
			<td>Dimethylsulfoxide (DMSO)</td>
			<td>Alfa Aesar</td>
			<td>36480</td>
			<td>[67-68-5] very toxic 
			ACS, 99.9% min</td>
		</tr>
		<tr>
			<td>Cyclohexane</td>
			<td>Fisher Scientific</td>
			<td>C/8936/15</td>
			<td>[110-82-7] 
			HPLC grade, 99.8+%</td>
		</tr>
		<tr>
			<td>Toluene</td>
			<td>Fisher Scientific Ltd</td>
			<td>T/2306/15</td>
			<td>[108-88-3] 
			HPLC grade</td>
		</tr>
		<tr>
			<td>Benzene</td>
			<td>Sigma Aldrich</td>
			<td>401765</td>
			<td>[71-43-2] 
			puriss pa reagent</td>
		</tr>
		<tr>
			<td>5 -120 mL automatic pipette</td>
			<td>Sartorius</td>
			<td>Picus eLine</td>
			<td>systematic error in specification: 
			for 120mL is &#177;0.48 mL, 
			for 60 mL is &#177;0.36 mL, 
			for 12 mL is &#177;0.24 mL</td>
		</tr>
		<tr>
			<td>VIAL screw clear 1.5ml + CAP bakelite solid screw PTFE lined for 10mm vial</td>
			<td>Jaytee Biosciences</td>
			<td>JW41110 + 
			JW43927</td>
			<td>Capped vial used for validating accuracy and precision of dispensed solvent</td>
		</tr>
		<tr>
			<td>Crystal Structural Database</td>
			<td>The Cambridge Crystallogra-phic Data Centre (CCDC)</td>
			<td>Cambridge Structural Database (CSD)</td>
			<td>Containing over 900,000 entries from x-ray and neutron diffraction analyses</td>
		</tr>
		<tr>
			<td>powder X-ray diffractometer</td>
			<td>Panalytical</td>
			<td>X-Pert PRO MPD</td>
			<td>Equipped with an X&#8217;Celerator detector with Cu K&#945; radiation</td>
		</tr>
		<tr>
			<td>powder X-ray diffractometer data Collector software</td>
			<td>Panalytical</td>
			<td>X&#8217;Pert HighScore Plus v3.0</td>
			<td>solftware package used to adquire the PXRD data</td>
		</tr>
		<tr>
			<td>Rietveld refinement software including Scherrer equation</td>
			<td>BRUKER</td>
			<td>Version 6 of TOPAS-Academic</td>
			<td>To prepare phase composition and crystal size from PXRD scans</td>
		</tr>
		<tr>
			<td>HPLC equipment</td>
			<td>Agilent</td>
			<td>HP1200 Series modular HPLC system</td>
			<td>HPLC high pressure binary pump, autosampler, Peltier type column oven with 6 &#181;L heat exchanger and Diode Array Detector with a semi-micro flow cell (1.6uL, 6mm pathlength).</td>
		</tr>
		<tr>
			<td>HPLC column</td>
			<td>Agilent</td>
			<td>1.8mm Zorbax XDB C18,</td>
			<td>(4.6mm ID &#215; 50 mm length)</td>
		</tr>
		<tr>
			<td>Ball mill grinder</td>
			<td>Retsch</td>
			<td>MM400</td>
			<td>modified: replaced safety cover for external safety screen</td>
		</tr>
		<tr>
			<td>14 mL snap closure stainless steel jars</td>
			<td>In house</td>
			<td></td>
			<td>manuctured from 316 stainless steel</td>
		</tr>
		<tr>
			<td>14 mL screw closure stainless steel jars</td>
			<td>In house</td>
			<td></td>
			<td>manuctured from 316 stainless steel - 
			contains a PTFE washer</td>
		</tr>
		<tr>
			<td>Stainless steel ball bearings:</td>
			<td>Dejay Distribution Ltd</td>
			<td>7.0 mm (1.37g)</td>
			<td>Stainless Steel Balls A.I.S.I. 420 Carbon (0.25/0.35%) &#38; Chromium (12/14%)</td>
		</tr>
		<tr>
			<td>&#34;Push a Button&#34; software</td>
			<td>Developed at Department of Chemistry</td>
			<td></td>
			<td>Written in Visual Basic. It activates an electronically controlled switch (relay).</td>
		</tr>
		<tr>
			<td>&#34;Push a Button&#34; Solenoid</td>
			<td>Magnet Schultz</td>
			<td>Type 609RP 
			12 Volt DC</td>
			<td>609RP (RP stands for) 
			R - for spring-return 
			P - for push-rod</td>
		</tr>
		<tr>
			<td>&#34;Push a Button&#34; 
			Solenoid holder</td>
			<td>Department of Chemistry</td>
			<td></td>
			<td>To hold solenoid over START button on the MM400</td>
		</tr>
		<tr>
			<td>&#34;Push a Button&#34; Relay</td>
			<td>KM Tronic</td>
			<td>USB one relay</td>
			<td>USB Relay Controller - One Channel - HyperTerminal ASCII commands. Connection to a PC&#39;s USB port using VCP (Virtual COM port).</td>
		</tr>
		<tr>
			<td>re-usable adhesive putty</td>
			<td>Bostik</td>
			<td>Blu-Tack</td>
			<td>Used to hold the jar fixed on the bench.</td>
		</tr>
	</tbody>
</table>

reliable mechanochemistry: protocols for reproducible outcomes of neat and liquid assisted ball-mill grinding experiments

The equilibrium outcomes of ball mill grinding can dramatically change as a function of even tiny variations in the experimental conditions such as the presence of very small amounts of added solvent. To reproducibly and accurately capture this sensitivity, the experimentalist needs to carefully consider every single factor that can affect the ball mill grinding reaction under investigation, from ensuring the grinding jars are clean and dry before use, to accurately adding the stoichiometry of the starting materials, to validating that the delivery of solvent volume is accurate, to ensuring that the interaction between the solvent and the powder is well understood and, if necessary, a specific soaking time is added to the procedure. Preliminary kinetic studies are essential to determine the necessary milling time to achieve equilibrium. Only then can exquisite phase composition curves be obtained as a function of the solvent concentration under ball mill liquid assisted grinding (LAG). By using strict and careful procedures analogous to the ones here presented, such milling equilibrium curves can be obtained for virtually all milling systems. The system we use to demonstrate these procedures is a disulfide exchange reaction starting from the equimolar mixture of two homodimers to obtain at equilibrium quantitative heterodimer. The latter is formed by ball mill grinding as two different polymorphs, Form A and Form B. The ratio R = [Form B] / ([Form A] + [Form B]) at milling equilibrium depends on the nature and concentration of the solvent in the milling jar.

This protocol is always started by the experimentalist validating his or her pipetting skills and inspecting the quality and performance of the pipettes or syringes used. This is best done by performing training sets on pipetting accurate volumes of the specific solvent intended to be used for the ball mill grinding experiments. The accuracy of the dispensed volumes is validated by weighing checks and this validation is repeated until the desired accuracy and precision is achieved. This v...

Watch this Scientific Journal Video about Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments at JoVE.com

Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-mill Grinding Experiments

We present detailed procedures to produce experimental equilibrium curves of the phase composition as a function of solvent concentration in a solid state system under milling conditions.

The equilibrium outcomes of ball mill grinding can dramatically change as a function of even tiny variations in the experimental conditions such as the ...

The overall goal of this procedure is to obtain reliable results from ball-mill liquid-assisted grinding, or LAG, experiments as illustrated by equilibrium crystal phase composition curves obtained using various solvent conditions. This method can help answer key questions about the final equilibrium outcomes of the ball mill grinding process and the role of solvent at equilibrium under LAG conditions. The main advantage of this technique is that the rigorous approach to experimental design allows exploration of the key factors controlling the polymorphism of very small crystals.Our findings suggest that surface effects are significant in polymorphism at the nanoscale and that the outcomes of equilibrium milling experiments are generally controlled by thermodynamics. To begin calibration, set an air-displacement pipette to reverse pipetting mode, which aspirates an excess of solvent. Set the aspiration and dispensing speeds to the lowest values and the volume to 10.0 microliters.Tare a capped, two-milliliter glass vial on a five-figure analytical balance. Then, fit a pipette tip to the pipette nozzle with a single, firm, vertical motion, being careful not to twist or bend the pipette tip on the pipette nozzle. Aspirate and dispense 10 microliters of the selected solvent five times in a continuous sequence to prime the pipette tip.Then, immediately aspirate 10 microliters of the solvent with the pipette held vertically and the tip two to three milliliters below the surface of the liquid. Place the end of the pipette tip against the inner wall of the tared, two-milliliter glass vial, holding the pipette at a 30 to 45 degree angle to the vial wall. Dispense the solvent, and gently tap the tip against the vial wall to recover any exposed droplets on the tip.Immediately cap and weigh the vial. Record the weight. Dispose of the pipette tip and any excess solvent contained therein.Repeat the process at least three more times at this volume, using a new pipette tip each time. Calculate the average weight for that volume. Determine the actual dispensed volumes by weight in the same way at 10-microliter intervals up to 100 microliters.Then, determine the actual dispensed volumes at one-microliter intervals over a narrower range around the target volume for the experiment. For each volume range, plot the dispensed volumes on the x-axis in the actual dispensed volumes calculated from the average weights and the solvent density on the y-axis. Apply a linear fit, and verify that the correlation coefficient is above 0.99.To begin the procedure, sonicate 14-milliliter, screw-closure, stainless steel grinding jars with PTFE washers in acetone. Then, wash the jars with laboratory detergent, and rinse the jars with deionized water and acetone in sequence. Dry the jars in a drying cabinet at 70 degrees Celsius for at least 30 minutes.Allow the jars to cool to room temperature before use. Next, shape greaseproof weighing paper into a U-shaped weighing boat small enough to fit into the aperture of the male half of a grinding jar. Tare the weigh boat, and then weigh 104.82 milligrams of one-one crystals in the weighing boat.Transfer the one-one crystals quantitatively to the male half of a clean grinding jar. Weigh 97.66 milligrams of two-two, and quantitatively transfer the crystals to the same grinding jar. Thoroughly mix the reagents with a micro-spatula.Then, carefully fix the male half of the jar to the workbench with reusable adhesive putty. Ensure that the jar is immobilized so that the ball bearings will not roll on the powder when added. Gently rest two 7.0-millimeter diameter, hardened stainless steel ball bearings on the powdered reagents.Pipette two microliters of dbu on top of one of the ball bearings, being careful not to allow that ball bearing to roll. Set a calibrated electronic air-displacement pipette in reverse pipetting mode to 17.0 microliters with the slowest aspiration and dispensing speeds. Equip the pipette with a tip, and aspirate the acetone by the same methods used in the calibration.Homogeneously drip the acetone on the exposed powder, being careful not to allow the pipette tip to contact the powder. Promptly but carefully screw the female half of the grinding jar onto the male half. Wrap the joint with insulating tape to seal the jar.Install the sealed grinding jar in one arm of a ball mill grinder. Tighten the safety clamp screw until the jar is immobilized. Turn the self-locking clamping device to the lock position.Set the grinder frequency to 30 hertz and the timer to 45 minutes, determined from preliminary kinetic studies. Start the grinder, and install an external safety screen in front of the grinder. Preliminary kinetic studies are critical to establish for how long the ball mill grinding experiments must run to reach equilibrium.Over-grinding unnecessarily must be avoided, as decomposition can occur. Upon completion, promptly remove the insulating tape and open the jar. Take a sample of powder, and determine the chemical composition by HPLC.Smooth another powder sample with an agate mortar and pestle, prepare a powder X-ray diffraction slide, and determine the phase composition with PXRD. Calculate percent R to determine the ratio of thermodynamic polymorph under equilibrium at LAG conditions, called Form B, to the total amount of heterodimer one-two synthesized. Grind the same amounts of one-one and two-two to equilibrium using other volumes of acetone, and calculate the percent R values.Plot the percent R values versus the volumes of acetone used in the LAG experiments to generate a solvent milling equilibrium curve for acetone. First, clean 14-milliliter, stainless steel, screw-top grinding jars, and load reagents one-one and two-two into a clean jar as previously described. Mix the reagents well with a micro-spatula.Then, transfer about 60 milligrams of the reagent mixture to a weighing boat for later use. Obtain an electronic air-displacement pipette, and set it to normal pipetting mode, which dispenses all aspirated solvent. Set the aspirating and dispensing speeds to the lowest values.Set the volume to 65.0 microliters. Prime the calibrated pipette, and aspirate 65 microliters of methanol. Understanding if the adsorption of the solvent into the reagent powder is fast, as with acetonitrile, or very slow, as with methanol, is critical for developing a procedure that incorporates the entire solvent volume into the powder during ball mill grinding.Homogeneously apply the methanol to the powder, being careful not to allow methanol to contact the inner wall of the jar. Gently touch the wet pipette tip to the powder surface to quantitatively transfer the solvent residue. Pour the remaining 60 milligrams of the reagent mixture over the wetted patches of powder in the grinding jar to trap the solvent in the powder.Gently tap the jar to compact the wetted powder, taking care to avoid evaporation. Fix the bottom of the male half of the grinding jar to the bench with adhesive putty to ensure that the ball bearings will not roll on the powder when added. Then, place two 7.0-millimeter diameter, hardened stainless steel ball bearings on the reagent mixture.Apply two microliters of dbu to one of the ball bearings. Ensure that the ball bearing with dbu does not roll on the powder. Promptly but carefully screw the female half of the grinding jar onto the male half.Let the grinding jar stand undisturbed for 20 minutes to allow the solvent to soak into the powder. Then, tighten the joint of the jar, and secure it with insulating tape. Secure the jar in a ball mill grinder equipped with the solenoid positioned over the start button.Set the grinder frequency to 30 hertz and the timer to 60 minutes. Install a counterweight and safety screen as previously described. Configure the solenoid to automatically start the grinder four times at 65-minute intervals.Run the solenoid process. Analyze the heterodimer product as previously described. Repeat with other volumes of methanol to generate the equilibrium curve.To ensure that good solvent milling equilibrium curves were obtained, pipetting accuracy was validated with weighing checks for each solvent. Correlation coefficients above 0.99 indicated acceptable pipetting technique and pipette performance. Preliminary kinetic studies of the ball mill LAG reaction of one-one and two-two using dbu were performed for each solvent to determine the grinding times required to reach milling equilibrium.A method was developed for solvents with high affinity for the reagent mixture, such as dimethylformamide. The DMF solvent milling equilibrium curve was accurately defined with 17 ball mill LAG experiments forming one-two as Form A and Form B.13 and 30 microliters of DMF yielded Form A and Form B, respectively, in quantitative yield. 19 microliters of DMF yielded a mixture of Form A and Form B.A modified method was required to obtain good equilibrium curves for solvents with low reagent mixture affinities, such as methanol, as the previous method gave poor correlation curves.Using an adjusted method, an accurate solvent milling equilibrium curve was defined for methanol with 17 ball mill LAG experiments. By selecting the correct method and precisely measuring reagents, good solvent milling equilibrium curves were prepared for 12 typical organic solvents. Some solvents gave Form B with a few microliters, while others required more.Once mastered, a grinding jar containing the powder mixture, dbu, and the precise volume of solvent can be prepared in 15 minutes. Some laboratory chemicals and solvents used in this process are hazardous to health. Always wear a lab coat, safety glasses, and gloves to minimize exposure.You can now demonstrate that the concentration of Form B at equilibrium increases sigmoidally with solvent concentration. For some solvents, such as acetonitrile and acetone, a one-microliter difference suffices to switch quantitatively from Form A to Form B.While attempting this procedure, make sure that the chosen pipetting mode is suitable for the specific solvent used. Ensure that you have developed the skills to pipette the solvents accurately and reproducibly.We believe that such milling equilibrium curves can be obtained for any system under sufficiently well-designed, performed, and controlled ball mill LAG conditions. After watching this video, you should have a good understanding of how to carry out accurate and reliable ball mill LAG experiments. There is the potential to discover new polymorphs by varying the added solvent.This applies to most organic and inorganic reactions, as well as to supramolecular systems, and may have practical implications in industrial settings.

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10.3K visualizações.  University of Cambridge. The overall goal of this procedure is to obtain reliable results from ball-mill liquid-assisted grinding, or LAG, experiments as illustrated by equilibrium crystal phase composition curves obtained using various solvent conditions. This method can help answer key questions about the final equilibrium outcomes of the ball mill grinding process and the role of solvent at equilibrium under LAG conditions. The main advantage of this technique is that the rigorous approach to experimental design a...