Challenges of Mechanochemistry: Is In Situ Real‐Time Quantitative Phase Analysis Always Reliable? A Case Study of Organic Salt Formation

Mechanochemical methods offer unprecedented academic and industrial opportunities for solvent‐free synthesis of novel materials. The need to study mechanochemical mechanisms is growing, and has led to the development of real‐time in situ X‐ray powder diffraction techniques (RI‐XRPD). However, despite the power of RI‐XRPD methods, there remain immense challenges. In the present contribution, many of these challenges are highlighted, and their effect on the interpretation of RI‐XRPD data considered. A novel data processing technique is introduced for RI‐XRPD, through which the solvent‐free mechanochemical synthesis of an organic salt is followed as a case study. These are compared to ex situ studies, where notable differences are observed. The process is monitored over a range of milling frequencies, and a nonlinear correlation between milling parameters and reaction rate is observed. Kinetic analysis of RI‐XRPD allows, for the first time, observation of a mechanistic shift over the course of mechanical treatment, resulting from time evolving conditions within the mechanoreactor.

S1.4 Data Processing: S1. 4.1 Hybrid-Methodology: To ensure sufficient sampling across the time domain, 20 integrated powder diffraction patterns were Rietveld refined using GSAS, 4,5 Figure S1.4.1.1, and quantitative phase information extracted, Figure S1.4.1.2. Patterns were selected so as to capture key phase evolutions throughout the process. We note that the refined quantities of G2O are within the error limits of the Rietveld refinement (< 3 weight%), and its resulting dynamics profile therefore an upper estimate of its phase composition throughout the process. Integrated data were subsequently background corrected using the Sonneveld-Visser algorithm 6 in Powder3D. 7 All patterns were numerically normalisation to unity, in order to account for stochastic fluctuations in the quantity of diffracting sample, and the major peak of each phase integrated; both procedures performed using a custom-designed programme. Integration was performed using a trapezoidal algorithm on an evenly spaced grid. Integration is thus defined by the precision of experimental data points, collected here in steps of 0.00762 2θ. The refined compositions and integrated intensities were subsequently used to create calibration curves, Figure S1.4.1. 3. We note that due to limitations in Rietveld refinement, a calibration curve for G2O was not possible. Instead, the raw dynamics profile was scaled to match the maximum Rietveld refined composition. This introduces an error to phase composition of no more than 3%. However, it is again worth noting a benefit over pure ARR techniques: processing data in this way continues to offer at least an approximate dynamics curve of the correct shape for low intensity phases. ARR, instead, produces only noise. For general use of this methodology, note: we expect for more complex systems, in which multiple product phases appear in large quantities, that a cross-correlation (e.g. a ratio between integrated phase peaks) term will be required in creating the calibration curves, or indeed in normalisation. That is, to account for possible non-linear scattering strengths between multiple products. In the current example, only one product is observed to any notable extent, and errors associated with neglecting this cross-correlation term are expected to be less than inherent experimental error.    (ARR). Integrated data were used without background correction. ARR was performed in TOPAS 8 . All lattice parameters were left to refine for Gly, OAD and GO. However, due to abnormal peak shapes and background, profile parameters were fixed to manually refined values. We note that phase composition of G2O is within the error limits of ARR.

S1.4.3 General Notes on Data Processing for in Situ Diffraction.
In view of studying mechanochemical mechanisms, it is of interest to highlight the normalization stage of Section 1.4.1. It is often assumed that the quantity of powder being treated throughout a milling process remains constant; that is that the ball:powder ratio remains constant. Changes to the quantity of powder present, or similarly the packing of powder, 9 drastically change the nature of mechanical treatment. Comparing the non-normalized to normalized dynamics profiles for the two reactant species, Gly and OAD, two considerably different profiles are seen, Figure  S1.4.3.1. In the first, reactant is consumed exponentially, while in the latter, this becomes linear. This exponential loss observed in the non-normalized patterns does not reflect physical conversion of the material, but instead loss of free-flowing powder. Thus any sampling through in situ real time XRPD samples an exponentially smaller portion of the powder mixture, and may therefore give erroneous insight into the true nature of the mechanochemical conversion. 9 Of further importance are the implications to mechanical treatment itself. First, compaction leads to changes in the ball:powder ratio at impact zones and second, a compact powder is subject to considerably higher forces on impact, where powder compression is no longer an alternative energy dissipation channel. Powder compaction is a highly ubiquitous, seldom reported and often unavoidable occurrence in organic mechanochemistry, where liquids (atmospheric, crystalline or added) play a central role. Such considerations are therefore critical when investigating mechanochemical mechanisms by ball milling.

S2 ARR vs Hybrid Technique:
S.2.1: OAD dynamics. While qualitatively the ARR and hybrid techniques produce the same profiles, see Fig 2 (in text), a comparison of the OAD dynamics profile for the two techniques is surprising. While the hybrid technique reveals an obvious transition in the OAD dynamics profile, it is considerably subtler in the ARR-deduced curve, most clearly seen for milling at 30 Hz, Figure S2.1.1. It is believed to be the result of restrictions imposed on the ARR, such as restricted profile parameters, which were required to ensure successful ARR.
To ensure this was not an artefact of the data-processing methodology, a number of possibilities can be considered. First is the data integration stage, where one might expect that the sudden introduction of a new phase may skew the normalized intensities. However, it is clear that, in all cases, the point at which the OAD mechanistic transition is observed does not correspond to the introduction of any new phase, Figure S1 An alternative explanation may rest in the migration of the integrated peak, outwith the integration zone. As is clear from Figure S.2.2.2, however, this is not the case. Integrated peak remains within the integration zone at all times, and no other peaks are seen to encroach.

S3. Ex Situ Mechanochemistry
To mimic the effects observed in tableted powder found at the ends of a milling jar, powder samples were treated in a drop-hammer device. This mimics the lack of mixing experienced by strongly tableted powders in mechanochemistry. The general progression of the reaction is the same as observed in situ in the ball mill: reactant species decrease with time, and the product phases increase, Figure S3.1. In contrast, however, the quantity of G2O is substantially higher than the ca. 3 mol% observed with in situ sampling of the ''free'' powder. The discontinuous evolution of each phase is due to the creation of new samples for each experiment. Thus, mixing will differ slightly between samples. The overall trend, however, is significant and demonstrates the very different evolution of the powder in a tableted sample.
Ex situ sampling of a ball milling reaction reveals much the same trend: that, if the tableted powder is sampled, the G2O quantity extends well above the 3 mol% observed by in situ monitoring, Figure S3

S4. Solid State Dynamic Profiles
We first note that with current limitations of real time in situ XRPD technologies, one cannot justify use of the word kinetics in its traditional sense. That is to say that kinetics has traditionally been used to describe fundamental, elementary processes on the atomic/molecular scale. While the mathematical formalisms derived for these fundamental kinetic processes are universal, their interpretation must be re-considered in light of limitations in resolution. In that regard, it is more appropriate to discuss mechanochemical dynamics, where interpretation of formal equations reflects the macroscopic mechanisms associated with particle-particle interactions. The same must be said for the application of traditional solid-state kinetics models, such as the Avrami-Erofeyev equations, and related diffusion-based models. While the mathematical formalisms of these models can be used universally, where they accurately reflect the shape of the time-evolving data, interpretation of their derived constants in light of the original atomistic models would be erroneous. Many introductory texts are available on solid state kinetics, including Refs.10 and 11.
In order that bulky organic molecules are able to interact beyond the 1:1 interaction at particle surfaces (which is required to reach a critical nucleus size), the mobility of these materials must be greatly enhances. This ( ) This linearization is general, and its use not reliant on any specific kinetic model. In the present case, where macroscopic dynamics of mechanochemistry are concerned, it is most logical to interpret k as a critical mixing constant, which describes the time required for sufficient contacts to be formed in order to observe product formation (note that this constant will be resolution dependent, and is thus only meaningful when comparing identical experimental set-ups). Constant k is therefore indicative of mixing rate, and can be used to compare mixing parameters, including the effects of pre-mixing. The formal constant, n, is then indicative of the rate of product growth at contacts. Fits of the GO dynamics curve, Figure S4.1, yield values for k and n that correlate well to those reported in the main text, derived from Sharp-Hancock plots. We note that critical time where ⁄ is a characteristic point, where the rate of product formation becomes greater than the formation of new contacts, and the deceleration regime begins, Figure S4.2. This offers an intriguing method to analyse mechanochemical dynamics, where the inflexion point may offer a means to study mixing rates and particle size effects, where more contacts become available more quickly. Here, this inflexion point is seen much more COMMUNICATION rapidly for 30 Hz than 27.5 Hz. It is further worth noting that the second feature observed in Figure S4.2 directly correlates to the time at which the mechanistic shift is seen in the dynamics profiles. Additional features require future investigation.  The mechanistic shift observed in the zeroth order OAD profile is also observed in the 1 st order Gly profile (ln(Gly)), Figure S4. 3. This suggests that any consequence of this transition plays an indirect role on consumption of Gly. The observed transition at approximately 100 s in Gly is consistent with that observed in OAD.

S5. Non-Linearity in Mechanochemistry
Increasing the frequency from 25 Hz to 27.5 Hz and further to 30 Hz is met with a non-linear shift in the rate of the milling reaction. For example, the approximate time at which the accumulation of GO plateaus (Acc-Plat Transition), increases roughly 25% from 25 Hz to 27.5 Hz, yet by nearly 65% on increasing from 25 Hz to 30 Hz, Table T5.1. It is not obvious why such non-linearity exists, but is likely due to heating, particle size effects or the accumulation of mechanical energy.

S6. Practicalities of Mechanochemical Experiments
Very many parameters can affect the result of a mechanochemical process, including moisture, temperature, milling ball size, particle size and shape, powder mixing, and many others. In many cases, such factors are very difficult, or impossible, to control, particularly when concerning particle characteristics, which change with time on milling. While it is of the utmost importance to understand how each of these parameters in turn affects a mechanochemical process, much remains to be understood about the mechanochemical process itself, under apparently constant conditions. The present work has highlighted how even under consistent controllable conditions, a mechanochemical process may not proceed as straightforwardly as believed. To highlight the immense additional complexity of planning mechanochemical procedures, we conducted the reaction under various milling frequencies, as highlighted in the preceding sections.

S6.1 Practical Limitations on Milling Frequencies
Typically, laboratory-scale ball mills are limited to a maximum frequency of 25-30 Hz, as is the case with the MM400 Retsch ball mill. Thus, no milling could be performed above 30 Hz in the present work. It is very easy to reduce milling frequency, as is reportedly done. Less often, however, is one able to visually observe the state of the powder mixture under various milling conditions. Below ca 25 Hz, it was found that the milling body is no longer propelled through the milling vessel, but instead remains within the central shaft of the milling vessel, ''rolling'' back and forth as the vessel moves around it. This results in a ''snow balling'' effect, Figure S6.1. In such cases, the reaction cannot be expected to proceed in a typical mechanochemical fashion, if at all, and thus milling frequencies below 25 Hz could not be reliably tested. While within this work the milling frequency is varied by only 5 Hz, this amounts to an extra 300 impacts per minute, or an extra 300 possible reaction events every minute. It is therefore not surprising to find that such small adjustments to milling frequency yield different reaction rates. This is analogous to increasing the temperature of a gas or solution phase reaction, where reaction rate , that is, the collision frequency.

S6.2 Modifying Initial Particle Size
Particle size is often ignored as a control parameter, as the milling process is believed to immediately micronize the initial sample. In the main body of the present study, as with most reported mechanochemical investigations, particle size was taken as available from the supplier, aiming to highlight complexities with current methods of conducting mechanochemical experiments.
In related work, we performed initial assessment of particle size effects on milling processes. Here, micronized glycine was mixed with OAD and milled at 25 Hz. The resulting product profiles demonstrate considerably different compositions, Figure S6.2a. Where micronized glycine is used as initial reagent, considerably higher quantities of the 2:1 G2O product are observed. We therefore propose that a mechanochemical process is not driven by the overall composition of the mixture, as is the case with solution phase processes, but is instead determined by the local reaction composition at the impact zone, Figure S6.2b. Further investigation into controlling reactions through particle size is therefore of great importance to the continued development of mechanochemistry.