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Official websites use. Share sensitive information only on official, secure websites. This is an open access article published under an ACS AuthorChoice License , which permits copying and redistribution of the article or any adaptations for non-commercial purposes. The present work focuses on the challenges that emerge in connection with the kinetics of mechanically activated transformations. This is an important topics to comprehend to enable the full exploitation of mechanical processing in a broad spectrum of areas related to chemistry and materials science and engineering. Emerging challenges involve a number of facets regarding materials and material properties, working principles of ball mills and milling conditions, and local changes occurring in series in processed materials. Within this context, it is highly desirable to relate the nature and rate of observed mechanochemical transformations to individual collisions and then to the processes induced by mechanical stresses on the molecular scale. Hence, it is necessary to characterize the milling regimes that can establish in ball mills regarding frequency and energy of collisions, map the relationship between milling dynamics and transformation kinetics, and obtain mechanistic information through proper time-resolved investigations in situ. A few specific hints are provided in this respect. The mechanical force of the ball milling BM technique is traditionally utilized in powder metallurgy and mineral processing to mix granular matter, reduce particle size, refine microstructure, and promote chemical reactivity. Processes on the mesoscopic and microscopic scales occur impulsively in the volumes of powder mixture, which are trapped either between the colliding balls or between a ball and the reactor wall. The resulting mechanical deformation of powder particles can give rise to cold-welding and fracturing as well as to physical and chemical transformations. The nature and extent of local processes activated by individual collisions strictly depend on the nature of the processed powder. For instance, the BM of individual metals promotes the formation of a fine microstructure comprising crystalline grains with characteristic lengths between 5 and 50 nm. In this respect, crystal engineering represents a good example. The increasing number of applications of mechanical activation to the synthesis of chemicals and the preparation of materials has recently driven a new, rapid surge of interest. As a consequence, the study of mechanically activated transformations is, presently, one of the most rapidly growing subjects in organic and materials chemistry. Yet, various menacing issues discourage attempts to transfer technology from the laboratory to industry. Milling dynamics has been characterized only in a few cases, and the kinetics and thermodynamics of mechanochemical transformations are still poorly understood. Within this context, in the present work we bring to the attention of researchers a few important facts: 1 Control of processing conditions is a necessary requisite to perform accurate kinetic studies. Ball mills involve simple working principles. The entire reactor, or part of it, undergoes periodic motion aimed at inducing collisions of the balls inside the reactor with each other and with the reactor walls. Non-hydrostatic mechanical stresses arise at every contact point between any pair of powder particles. Local collisional and frictional processes of variable intensity and duration take place at such locations. Working principles customarily allow ball mills to be divided into the two broad classes of mixers and attritors. In attritors, relatively low collision energy mostly results in frictional dynamics. However, it is worth noting that the modification of processing parameters makes it possible to move smoothly between the two milling regimes. Therefore, no rigid distinction between the two classes should be made. Numerous factors affect processing conditions. The effects of processing parameters on milling regimes have not yet systematically mapped. The reactor moves as schematically depicted in Figure 1 , undergoing angular harmonic displacement in the vertical plane simultaneously with rotation in the equatorial plane. It typically works at a frequency of The frequency range between A methodology combining experimental and modeling studies allow characterizing the milling dynamics. In the absence of powder, and with a reactor frequency of about As powder charge is increased, collisions move from perfectly elastic to perfectly inelastic regimes. Accordingly, the average collision frequency on the reactor bases drops from Two collisions per cycle take place, and the average collision velocity is equal to about 5. Collision velocity and milling frequency exhibit an approximately linear relationship. The methodology mentioned above displays its whole potential when the mechanical treatment is performed with a single milling ball. However, numerical integration methods can be used to gain insight into milling regimes establishing in the presence of two or more balls. Information on the milling dynamics, although fragmentary, has also been given for planetary mills, which exhibit mechanical action and working conditions quite different from those arising in a shaker mill. These milling devices consist of one or more reactors lying in an eccentric position on a support disk. The disk and reactor rotate around their own axes in opposite directions, as shown in Figure 2. The two centrifugal forces generated by the synchronous rotations give rise to a net force that undergoes a periodic variation during the mill working cycle. Within a wide interval of rotation speeds, such force first makes the ball roll on the reactor wall, then pushes it across the reactor chamber, and finally determines its collision with the reactor wall. Figure 2 also shows the typical ball trajectory inside the moving reactor. Schematic description of a planetary mill. The typical trajectory of a ball inside the reactor is shown in the vertical projection in the top right position. The Fritsch Pulverisette P5 and P6 models are equipped with vials and balls made of different materials and cover capacities between 12 and mL. However, no attempt has been made in such direction to date. Thus, most available information comes from numerical simulations and strictly phenomenological empirical evidence. Numerical simulations suggest that the amount of mechanical energy that can be transferred to the powder during a collision depends on the velocity of the ball and on the angle of contact between the colliding milling media. Correspondingly, the specific power dissipated during collisions can span the interval from approximately 2. The Uni-Ball Mill, which mainly finds application in the preparation of nanostructured materials and alloys, also deserves mention. This setup allows the coexistence of shearing and impact operation modes. The impact velocity can reach to 1. Collision frequency in the impact mode ranges from 1 to 2 Hz. Calculations based on Hertz impact theory suggest maximum impact stress of 37 kbar. For other ball mills, essentially no information is available. Therefore, it would be highly desirable to deepen the insight into their milling dynamics in the light of the usefulness of such devices for preparing chemicals and materials as well as for monitoring mechanically activated transformations. This is the case, for instance, of the recently developed planetary milling system shown in Figure 3 , which has been developed by Automaxion SARL. It uses adapters to hold multiple vials instead of normal jars, thus allowing the simultaneous processing of various samples. It has also been used to reduce the particle size of diverse materials down to 0. A A multisample planetary mill. C An 8-position jar hosting 20 mL glass vials. E Variation of force intensity depending on the vial position. Panels C—E reproduced with permission from ref Copyright The Royal Society of Chemistry. The eccentric position of vials and the combined rotation of jar and support disk, evident from Figure 3 D, impart the milling ball a net force different from the one typically experienced by balls in a conventional planetary mill, depicted in Figure 3 E. Therefore, characterizing the milling dynamics is of primary importance for the suitable control of experimental conditions. Analogous considerations hold for the Retsch MM and MM Mixer Mills, which can work with 2—50 mL samples at frequencies between 3 and 30 Hz, and the compact benchtop mill FTS released by FormTechSci, with a comparable range of grinding frequency and a mechanical action described in Figure 4 a. Such operational features allow, depending on the powder charge, a variation of the impact velocity of milling balls against the reactor walls approximately between 0. Similarly, characterization of milling dynamics is highly desirable for the Fritsch Mini-Mill Pulverisette 23 shown in Figure 4 b, which imparts a spherical grinding bowl containing 0. The need of a complete characterization of milling conditions appears even more urgent in the case of the milling equipment dedicated to the in situ monitoring of mechanically activated transformations Figure 5 using synchrotron X-ray diffraction 52 and time-resolved Raman spectroscopy, 53 also in tandem. Experimental setup for collecting data in situ during mechanical processing through a synchrotron X-ray diffraction, b Raman spectroscopy, and c Raman spectroscopy and X-ray diffraction in tandem. Panel a is reproduced with permission from J. Copyright American Chemical Society. Panels b—d are reproduced by kind permission from In Solido Technologies, Croatia. A modified Retsch Mixer mill MM, shown in Figure 5 a, was used for the quantitative in situ powder X-ray diffraction analysis of a mechanochemical process. It is equipped with a plug-and-play in situ monitoring system, evident from Figure 5 c, enabling synchrotron X-ray diffraction and Raman spectroscopy. Allocating up to four jars with a volume between 1 and mL, the mill works at frequencies ranging between 3 and 33 Hz. When equipped with a ThermoJar system, the in situ measurement of local temperatures under milling conditions is also possible. Very recently, a new experimental setup for the study of milling reactions in real-time was released. It consists of an in situ triple coupling associating the simultaneous recording of X-ray diffraction patterns, Raman spectra, and thermograms to correlate structural evolution with temperature information during milling. The availability of detailed information on the relationship between milling dynamics and the nature and rate of physical and chemical transformations, and the real-time in situ measurement of physical properties, show the promise of leading mechanochemistry to a crucial turning point. In fact, it can give considerable help in the development of kinetic models aimed at linking empirical observation to local microscopic processes taking place during individual collisions. In this respect, a relatively simple, phenomenological modeling approach can be derived starting from the fundamental features of the mechanical processing by BM. This latter is characterized by the continual stirring of the powder charge, which then keeps a high degree of chemical uniformity during the entire mechanical processing. Equations 1 and 2 can be used to describe the kinetics of mechanically induced transformations. For instance, the mass fraction of material transformed can be expressed as. Along the same line, if the material transforms only after two CLCs, the mass fraction of material transformed can be expressed as. The model is quite versatile and allows the definition of a set of equations able, in principle, to best fit experimental kinetic curves. Similarly, eqs 1 and 2 can also be used to describe the microstructural evolution of a given phase. For instance, it can be assumed that the powder fraction subjected to i CLCs has average crystallite size L i. Therefore, the average crystallite size L that can be obtained by averaging over the total powder charge is equal to. L i are the average crystallite sizes of the powder fractions that have undergone CLCs 0, 1, 2, Quite often, experimental evidence indicates that the crystallite size of any given fraction of powder submitted to CLCs drops from the initial L 0 value to the final L f one after a single CLC event. Similar expressions can be written starting from eq 5 and specializing L i values. According to eqs 1 — 6 , the rate of a mechanically activated transformation depends on the quantity k. The larger its value, the faster the transformation is. Therefore, k can be regarded as the apparent rate constant of the transformation. Since mechanically activated transformations do not necessarily involve chemical reaction, k does not necessarily correspond to rate constants typically defined in chemical kinetics. Nevertheless, it can be considered a chemical rate constant whenever the mechanically activated transformation involves a chemical reaction. Instead, it is the sum of smaller volumes that can be thought to be irregularly distributed within the volume of powder subjected to mechanical loading during individual collisions. In turn, such smaller volumes can be regarded as the volumes within which the local mechanical stresses generated during the collision induce the transformation. Therefore, k represents merely an estimate of the amount of pristine material involved in the mechanically activated transformation. Since no information is available on the mechanism governing the transformation, and no assumption is made in such regard, it cannot be excluded that the overall rate of transformation depends on two or more stages. Therefore, following in this classical chemical kinetics, it is more appropriate to look at k as an apparent rate constant. Although the model is phenomenological, and therefore k is a phenomenological constant, a better understanding of its physical meaning is strictly necessary to foster further progress in the modeling description of the transformation kinetics. In this respect, existing literature focusing on the development of a kinetic approach for mechanochemical transformations based on non-equilibrium thermodynamics can be quite useful. Hopefully, this specific subject will become an active and popular area of research. All the model equations developed heretofore hold validity if expressed as a function of time, t. K expresses merely the volume of powder subjected to CLCs per unit time. In the following, a few specific examples will be discussed to show the capability of the model for interpolating experimental points. Literature is relatively lacking in reports including experimental curves describing transformation kinetics quantitatively. Despite the considerable attention devoted in the past to mechanical activation, only in a few cases have the formation of inorganic phases from a set of reactants, the phase transition from one polymorph to the other, and the reaction between two or more chemicals been satisfactorily investigated in this respect. In most cases, only qualitative and indirect kinetic and mechanistic inferences have been gathered starting from empirical observation. The kinetic analysis of refined experimental data sets, even with a simple kinetic model such as the one described above, can provide interesting information on the way mechanical activation by BM works. A few case studies, spanning from individual metals to mixtures of organic compounds, are discussed. Mechanical activation has been extensively used to induce the reduction of grain size, L , in pristine crystalline materials. For some metals, minerals, and ceramics processed individually and in the mixture, L varies with the number of collisions, n , as can be seen in Figure 6. It undergoes a smooth monotonic decrease from an initial value, L 0 , to a final asymptotic one, L f. L 0 is not a meaningful quantity, being mostly determined by the process employed to produce the commercial powders. Conversely, L f depends on both material properties and processing conditions. Average crystallite size L of Cu as a function of the number of collisions, n. The best-fitted curve is also shown. As evident from Figure 6 , eq 6 satisfactorily reproduces the experimental behavior. This suggests that the assumptions underlying the mathematical expression, namely the fact that the grain size in a volume subjected to CLCs once changes discontinuously from the initial value, L 0 , to the final one, L f , can represent a physical situation. According to the best fitting, the apparent rate constant, k , is approximately equal to 3. Since the data shown in Figure 6 were obtained from experiments using a total mass of Cu of 8 g, the amount of powder effectively processed during any individual collision, i. Previous work has shown that BM induces the formation of radical species at the surface of quartz powder subjected to BM. The reaction scheme can be summarized as indicated below: N DPPH decreases smoothly at a rate that becomes increasingly lower as n increases. Best-fitted curves are also shown. The surface area S shown in Figure 7 b can be satisfactorily described by the mathematical expression. Such expression is similar to eq 5 and suggests that S can be regarded as the weighted average of the surface areas S in and S fin exhibited by the fractions of quartz powders e —kn and 1 — e —kn. Thus, e —kn measures the fraction of quartz powders that retains the initial specific surface area S in , whereas 1 — e —kn is the fraction that has reached the final specific surface area S fin. Accordingly, any given collision makes a certain amount of quartz powders change abruptly its average specific surface area from S in to S fin. The rate constant k is approximately equal to 1. The total mass of powder subjected to processing being equal to 2 g, the mass of quartz powders effectively involved in collisions corresponds to about 2. Two different kinds of active sites can be thought to coexist at the surface, namely those generated by fracture of quartz particles involved in a collision, which increases the specific surface area S , and those generated by attrition between quartz particles, which does not lead to a change of S. The active sites formed by fracture or by attrition can have different chemical activities. If N f and N a are the numbers of active sites formed, respectively, by fracture and attrition, the DPPH consumption can be described by the expression. N f and N a are proportional, respectively, to the surface area generated by fracture at individual collisions and to the total surface area of powder particles involved in individual collisions. The increase of specific surface area as a function of the number of collisions can be obtained by differentiating eq 7 , whereas the surface area generated by fracture can be obtained by multiplying the specific surface area increase by the mass m p of powder charge. Therefore, N f and N a can be expressed as. Based on eqs 9 and 10 , the solution of eq 8 is. These numbers provide a quantitative estimate of the surface density of active sites generated by fracture or attrition, respectively. A comparison with the maximum possible number of dangling bonds that can be formed at the surface, equal to about 2. The mutual dissolution of Ag and Cu represents a typical example of mechanical alloying. The formation of the solid solution follows relatively complex kinetics. The dissolution of Ag atoms into the Cu matrix forms a Cu-rich solid solution, hereafter indicated as Cu Ag. At the same time, the dissolution of Cu atoms into the Ag matrix forms an Ag-rich solid solution, hereafter indicated as Ag Cu. A third solid solution, hereafter indicated as AgCu , forms as a result of the combination of the two Ag Cu and Cu Ag solid solutions, which can be then regarded as intermediates. Starting from eqs 1 and 2 , the kinetic model provides suitable expressions for describing the kinetic evolution of Cu in reactants, intermediates, and products. The kinetics of Cu in intermediates is described by. It follows that Cu becomes involved in the formation of the intermediate Ag Cu and Cu Ag solid solutions already after the first collisions, and that the intermediates transform into the final AgCu solid solution after the third collision. It appears that the whole sequence of transformations can be described satisfactorily using a single rate constant, k. Best fitting suggests a k value of about 2. The mechanical processing of Ni 40 Ti 60 powder mixtures by BM induces the formation of an amorphous phase. With the sigmoidal conversion to the amorphous phase obtained for collision energy of about 0. According to the assumptions employed to develop the kinetic model, the results mentioned above indicate that amorphization takes place in fractions of Ni 40 Ti 60 powders that have undergone at least two CLCs. The apparent rate constant, k , for the amorphization process is approximately equal to 1. The experiments were performed with a total mass of powder of 8 g. The mechanical processing by BM allows mixing two or more chemicals on the molecular scale, resulting in the formation of co-crystals. Mechanical processing in the presence of methanol leads to the formation of polymorph II co-crystal, the process being complete within approximately 6 min. Further mechanical treatment up to 3 h does not induce modifications. Under the assumption that a linear relationship between the number of collisions, n , and the time, t , exists, the model equation. It is able to best fit satisfactorily the experimental points, suggesting for the apparent rate constant K value of about 0. As shown in Figure 11 , the strongest reflection for ZIF-8 varies according to a sigmoidal trend. Panels b and c are adapted from ref 52 with permission from Springer. An expression similar to eq 15 can be written to interpolate the experimental points as a function of time, t. Specifically, the variation of the relative intensity of the reflection belonging to the X-ray diffraction pattern of the ZIF-8 final product can be described using the expression. The above equation can interpolate satisfactorily the experimental data set with an apparent rate constant K of about 0. Mechanical activation by BM has also been successfully used to the preparation of organic compounds. In situ Raman analyses have been performed to monitor the mechanochemical condensation between benzyl and o -phenylenediamine described in Scheme 1. Such dependence has been tentatively explained invoking different mechanical activation regimes at low and high milling frequencies, essentially due to the differences in the mechanical energy transferred to powders when frictional or impulsive processes prevail. Effects of milling frequency on the kinetic behavior of a condensation reaction. Reproduced with permission from ref Copyright Julien et al. Concerning the mechanochemical organic synthesis, it is worth noting that not all of the data available can be subjected to satisfactory interpolation by the model equations. For instance, this is the case of the Knoevenagel condensation reaction between vanillin and barbituric acid, described in Scheme 2 , and with data summarized in Figure Kinetic profiles for the Knoevenagel condensation reaction in solution or under mechanical processing conditions. The reaction kinetics was independent of both the amount of water inside the jar and the particle size of reactants. Nonetheless, the reaction rate increased changing the milling frequency from 15 to 30 Hz and decreased when the reaction scale passed from 0. Interestingly, milling induces the transformation of the initial granular body into a sticky material that adheres to the ball almost uniformly, giving rise to a homogeneous coating. Sigmoidal kinetic profiles, obtained by ex situ analyses, were observed during the formation of 1- 4-chlorophenyl 2-nitrophenyl disulfane heterodimer. Depending on the experimental milling conditions, achieved neat or adding acetonitrile, different polymorphs were formed as indicated in Scheme 3. The in situ investigation of kinetic behavior allows attaining unprecedented detail on the transformation path, unveiling short-lived intermediates and disclosing minute aspects of experimental evidence. All of that bears the great promise of deeply impacting the field, catalyzing progress in the definition of kinetic schemes and the description of macroscopic differential and integral kinetic laws involved in mechanically induced processes. Coupled with the time-resolved investigation, in situ observation can be also exploited to gain information on mechanistic issues. In particular, examining the response of the material to impulsive loading can allow obtaining mechanistic evidence on the effects of mechanical stresses on the molecular level. Toward this aim, ball drop experiments offer an interesting opportunity. Indeed, it is relatively easy to combine them with experimental methods enabling the exploration of the time and length scales of local processes activated by individual collisions. The preliminary data on mechanistic inferences have been obtained by performing luminescence measurements. The experiments were performed on thin layers of coumarin 1 powder deposited on a transparent alumina window. Coumarin 1 has a characteristic broad emission around the wavelength of nm, with an excitation band in the near UV region. Coumarin 1 powder was continuously excited with a focalized laser beam and its luminescence was analyzed with an intensified CCD camera equipped with a Peltier thermoelectric cooling. Spectrally resolved luminescence before, during and after collisions was monitored using a temporal gate below 10 ms. A picture of the zone affected by the ball drop, obtained using an optical microscope, is shown in Figure 14 a. Relative luminesce recorded after the collision in steady time PL condition is shown in Figure 14 b together with the emission of the pristine coumarin 1 for comparison. Luminescence measurements show that the coumarin 1 located in the region affected by ball drop exhibits a blue shift with respect to the pristine powder. The shift observed was up to 20 nm in the inner zone of the region and progressively decreased with the distance from the center. The Raman spectra collected from the pristine sample and the coumarin 1 region affected by ball drop are shown in Figure They reveal that the irreversible changes in luminescence spectra induced by collisions cannot be ascribed to a variation of molecular structure, which remains unaffected. Raman spectra collected from black curve pristine coumarin 1 and from samples subjected to blue curve ball drop and red curve BM. Kinetics of luminescence during collisions was reconstructed collecting emitted radiation from the inner zone of the region affected by ball drop using temporal windows of 10 ms. The obtained spectra are shown in Figure The spectroscopic evidence points out that the blue shift takes place irreversibly on a time scale of about 30 ms. Photoluminescence sampled from the inner zone of the region affected by ball drop. Curves refer to coumarin 1 at the beginning of the ball collision black curve and after 10 green curve , 20 red curve , and 30 blue curve ms. The obtained experimental findings can be connected with the fact that fluorescence in coumarin 1 is mainly due to its monomeric form. In particular, decay kinetics is related to the conversion of fluorescent intramolecular charge transfer ICT states to non-fluorescent twisted intramolecular charge transfer TICT related phenomena. Therefore, the observed blue-shift in the luminescence spectra can be reasonably ascribed to the emission from H-type aggregates. According to previous works, 76 , 77 in coumarin 1 the emission related to the formation of H-type aggregates is mainly due to higher excitonic states, and, hence, generating a blue shift of the overall emission. It follows that the measured luminescence spectra indicate a local rearrangement of coumarin 1 molecules in the region of the powder layer affected by ball drop, due to the formation of highly interacting aggregates due to the collision. The measurement of time-resolved luminescence spectra provides a direct tool to follow in situ the effects of mechanical stresses generated in the powder layer during ball collisions. Deeper insight into the local processes governing the rearrangement of coumarin 1 molecules can be gained by decreasing area and time scale of investigation. This can be expected to give access to information regarding the way the collision generates mechanical stresses within the granular body. In principle, this offers the unique opportunity of relating the phenomenological interpretation of transformation kinetics to refined mechanistic evidence, enabling the explanation of kinetic data on a fundamental basis. The kinetics of mechanically activated transformations is a critical issue along the road to the fundamental understanding of mechanochemical processes and the rational design of effective mechanical processing methods and tools. The general strategy for taking on the kinetic challenge is relatively clear. It involves the development of methods for characterizing and controlling the milling dynamics, the collection of refined experimental data and their interpretation with the help of specific kinetic models, and the study of microscopic processes activated by individual collisions. In this respect, the present state of the art appears quite fragmentary and contradictory. The kinetic evidence is still scarce and barely connected with milling dynamics. The use of in situ investigations and the availability of new processing tools show promise to promote progress in the field. The interpretation of refined kinetic data with a simple, phenomenological model provides valuable information on the amount of powder susceptible to effective processing during individual collisions. In turn, this provides a first link to the local processes activated by the mechanical stresses generated at the point of collision. Combining time-resolved studies with in situ investigation allows the direct measurement of the effects of mechanical stresses on individual molecules. Thus, it can help to enlighten researchers on the way mechanical loads act at the molecular level. The correct interpretation of experimental findings in the light of milling dynamics and the mechanistic study of mechanochemical transformations represent crucial objectives to achieve. We hope that the present work will stimulate progress in the field. This work has been supported by the University of Cagliari Italy. The authors are grateful to Dr. The authors are grateful to M. Walter Oliveira Fritsch Gmbh, Germany; www. Authors are grateful to Dr. Amit Kumar for the final reading and editing of the manuscript in the light of his full professional proficiency in English, which greatly helped in improving its readability. As a library, NLM provides access to scientific literature. ACS Omega. Find articles by Evelina Colacino. Find articles by Maria Carta. Find articles by Giorgio Pia. Find articles by Andrea Porcheddu. Find articles by Pier Carlo Ricci. Find articles by Francesco Delogu. Open in a new tab. Similar articles. Add to Collections. Create a new collection. 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