Enthalpy vs. friction: heat flow modelling of unexpected temperature profiles in mechanochemistry of metal–organic frameworks

Numerical simulations for precise temperature profiles of milling reactions revealed dominant contribution of frictional heating, while reaction enthalpy remained negligible.


Introduction
Mechanochemical solid-state reactivity 1-3 offers advantages over traditional solvent-based chemistry reected in better yields and selectivity, 4,5 better energy-and atom-economy and reduced waste generation. 1 Despite the longstanding use, 6,7 range of applications, and industrial importance of mechanochemical reactions, an overarching mechanistic framework, which is a prerequisite for predictable and controllable mechanochemistry, has yet to be formulated. [8][9][10] Recent reports on the sensitivity of mechanochemical reactions to heating [11][12][13] as well as the observation of base-catalysis 14 suggest that it should be possible to formulate a mechanistic framework for mechanochemical milling reactions, similar to the one existing for solution reactions developed by methods of physical chemistry in the better part of the 20 th century. 15 Thus far, major theories of mechanochemical reactivity have focused on inorganic and metal systems and have ascribed mechanochemical reactivity to localised and sudden increases in temperature of the order of 10 3 K at the points of ball impacts. 16,17 However, there is growing evidence that these theories, which do not consider the temperature of the reaction mixture and the milling assembly, are not adequate 18 for describing milling reactions of soer organic or metal-organic materials, for which recent evidence shows that even a modest increase in bulk temperature (by ca. 25-50 K) may lead to signicantly faster reactions and changes to reaction mechanism. 18 Despite recent signicant advances in mechanistic understanding of mechanochemistry, the effect of temperature (one of the most basic factors for understanding kinetics and mechanisms in solution and gas chemistry) on mechanochemical milling reactions remains a challenge.
The study of kinetics and mechanochemical milling reaction mechanisms was virtually impossible until the recent development of techniques for in situ and direct monitoring of mechanochemical milling reactions through synchrotron powder Xray diffraction (PXRD) [19][20][21][22] or Raman spectroscopy. 23,24 It was revealed that mechanochemical reactions that can proceed through crystalline or amorphous intermediate phases are strongly dependent on different types of additives, and can provide access to short-lived metastable intermediate phases that are inaccessible by other synthetic methods. 25 Nevertheless, apart from temperature monitoring of highly-exothermic mechanochemical self-sustained reactions (MSR, exemplied by the "thermite" reaction), [26][27][28][29] the effect of temperature on the reactivity of soer materials (e.g. cocrystals, metal-organic frameworks, coordination polymers) is far less understood.
Measuring and monitoring the temperature of a reaction mixture within the milling vessel is challenging, as a temperature sensor is likely to be broken under ball impacts and mill vibrations. Thus far, it has mostly been attempted for milling in steel milling vessel planetary ball mills. 31,32 In MSR, the reaction-energy release is immense and sudden; consequently, temperature changes can be observed by attaching a sensor on the outside wall of the steel reaction vessel 27,33 or by employing an infrared thermometer along with a quartz reaction vessel. 34 More recently, an attempt has been made at monitoring the temperature by using infrared imaging. 35 This method is limited to the outside surface of the reaction vessel and consequently, does not directly convey the temperature of the milled sample.
Here, we demonstrate the rst methodology for the evaluation of temperature changes within an operating milling vessel. Using mechanochemical transformations of polymorphs of archetypal metal-organic frameworks (MOFs) such as the formation and mechanochemical transformations of ZIF-8 ( Fig. 1) or pillared MOFs as model systems, and by conducting thermal measurements simultaneously with in situ synchrotron X-ray powder diffraction, here we have reported the rst real-time temperature proles for a mechanochemical reaction and have shown how they can be correlated to structural transformations of milled materials. Numerical simulations revealed that the measured temperature proles are not signicantly inuenced by enthalpic changes of mechanochemical reactions, but are determined by changes in the frictional properties of materials in the reaction mixture. This provides a conceptually different way for thermal monitoring during the course of a mechanochemical reaction, which enables the detection of transformations even if the associated enthalpic change is small.

Results and discussion
To enable reaction mixture temperature measurements, we have developed a reaction vessel using thermally insulating polymethylmethacrylate (PMMA, thermal conductivity z 0.2 W m À1 K À1 ) (see ESI †) which contained a small aluminium plug (thermal conductivity z 200 W m À1 K À1 ) embedded in the vessel wall and was in direct contact with the inside of the vessel. A temperature sensor (Pt100 sensor) was in contact with the aluminium plug ensuring a good thermal contact between the temperature sensor and the reaction mixture (ESI Fig. 1 and 2 †). This setup avoided the low thermal conductivity of PMMA and achieved fast temperature readings with a precision within AE0.03 C (ESI Fig. 3 †).
Small temperature changes of the reaction mixture could be detected with a minimal time delay. However, we noted that due to localised ball impacts and having the sample in the form of a loose powder, the temperature of the sample might possibly be not uniform and variations in the sample temperature at different parts of the reaction vessel would not be revealed from this setup. Nevertheless, as far as we are aware, this represents the most precise and immediate temperature monitoring of mechanochemical reactions performed thus far.
As milling is initiated, temperature of the reaction mixture rises due to dissipation of the kinetic energy of the milling assembly into its internal energy. This process includes inelastic collisions between the milling media and the vessel walls, as well as the friction between the moving balls, the vessel, and the milled material. From now on, we shall refer to this overall process as friction. 36 In parallel with energy input via friction, the reaction vessel constantly transfers energy to the cooler surroundings, which was air-conditioned at 20.5 C. As the temperature of the milling assembly rises aer initiation of milling, so does the rate of heat transfer to the surroundings. Eventually, when the rate of such heat transfer to the surroundings becomes equal to the energy dissipated by friction during milling, the system reaches a steady state in which the temperature does not change in time.
The rst target in our study was the recently reported mechanochemical crystallization-amorphization-recrystallization of the zeolitic imidazolate framework zinc 2-methylimidazolate (Zn(MeIm) 2 ), also known as ZIF-8, by liquid-assisted grinding (LAG) with dilute aqueous acetic acid as the liquid additive ( Fig. 1). 25 The ZIF-8 framework is one of the few commercially relevant MOFs, and has received attention for its chemical and thermal stability, as well as for its applications in gas storage and catalysis. [37][38][39][40][41][42][43][44] Also, it was oen used as a model system in mechanochemical MOF amorphisation, 45 MOF alloying, 46 and shock dissipation. 47 As previously reported, 25 milling of ZnO with 2methylimidazole (HMeIm) leads to rapid formation of ZIF-8, which gradually becomes amorphous upon milling. Herein measured in situ X-ray diffraction data show that upon extended milling, the amorphous matrix (am-ZIF-8) recrystallizes into one of two Zn(MeIm) 2 polymorphs. That is, recrystallization can yield either a metastable phase with katsenite (kat) topology, 25 which upon further milling transforms into the thermodynamically stable, non-porous diamondoid (dia) topology polymorph 48 (Fig. 2a, bottom). Alternatively, the dia-framework can also be formed directly 25 from the amorphous matrix, circumventing the intermediate formation of the kat-phase (Fig. 2b, bottom).
The observed structural transformations of Zn(MeIm) 2 frameworks could also be detected through temperature measurements. Formation of ZIF-8 from ZnO and 2-methylimidazole was very fast, and was accompanied by a steep increase in temperature during the rst two minutes of milling. The formation of ZIF-8 was rapidly followed by its amorphisation, and at the same time the heating curve reached a steadystate temperature just below 33 C, as the amorphisation process was complete. Recrystallisation of amorphous ZIF-8 manifested itself with the emergence of new Bragg reections, and the temperature of the reaction mixture simultaneously dropped by ca. 2.5 C over a period of ca. 15 minutes, aer which it reached a new steady-state temperature just below 31 C (Fig. 2a, top). In another experiment, the amorphous phase recrystallised directly to the dia ZIF phase, resulting in a ca. 2 C temperature drop of the reaction mixture (Fig. 2b, top). Importantly, in both experiments, the temperature drop was directly correlated with the recrystallization of the amorphous Zn(MeIm) 2 .
The observed drops in temperature are surprising, since the observed polymorphic transformations should be exothermic. According to the recent calorimetric and theoretical studies, the close-packed dia polymorph is the most stable among the three polymorphs. 30 The enthalpies of formation of the ZIF-8 and kat polymorph are 10.6 kJ mol À1 and 2.3 kJ mol À1 , respectively, which are smaller than that of the dia polymorph. In accordance with the Ostwald's rule of stages, am-ZIF-8 has the energy of formation between that of ZIF-8 and the kat polymorph. Also, measured enthalpy of formation of ZIF-8 (ref. 30) corresponded to the empty-pore ZIF-8 while here, its pores were lled by the liquid additive leading to stabilisation of ZIF-8.
For the employed scale of the reaction (196 mg of the reaction mixture or 0.80 mmol of ZnO and 1.6 mmol of HMeIm), these energy differences should produce a net energy release on the order of 10 J. Over a period of ca. 30 minutes, which is the duration of amorphization and recrystallization to the kat polymorph and the nal dia-phase formation, this amount of energy would generate a heat ow of around 3-6 mW. Polymorphic transformations in this system were expected to lead to a temperature increase, rather than the experimentally observed temperature drop. Moreover, if the temperature drop was related to some endothermic process, the constant input of energy by milling should have resulted in the return of the temperature to the previous steady-state aer the endothermic process has ended, as was generally observed for MSR reactions. 27 Clearly, both the conversion of mechanical energy of the vibrating milling assembly into its internal energy, and the reaction enthalpy can cause a temperature change in the vessel. The main difference is that milling produces a continuous heat ow via friction during the entire milling process, while the reaction energy release/absorption is limited and occurs only over a relatively short period of time. To understand the observed temperature proles and heat ow during mechanochemical processing, we applied the First law of thermodynamics: where Q friction corresponds to heat input via conversion of mechanical energy, Q reaction is heat input from the reaction enthalpy, and Q out is heat output to the environment. The difference between heat input and output results in the change of the internal energy of the milling assembly in time: The above equation is valid for any period of time. Since the friction heat is of rapid stochastic nature (a large number of isolated impacts in time), if we use its mean value over a reasonably short time interval and consider it as a continuous variable, we can write the equation for the innitesimally short period of time: Integration over the entire duration of the reaction reveals that the second term on the le is constant, as it occurs over a limited period of time and therefore becomes increasingly negligible compared to the other two constantly increasing terms as the integration time becomes longer and the heat exchange approaches its steady state: ð t t¼0 F friction dt |fflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflffl ffl} Heat ow generated by friction, F friction , is temperature-and time-independent if the milling parameters including the milled material remain unchanged, while heat transfer to the environment, F out depends on the temperature difference between the outer surface and the ambient environment, and increases as the whole milling assembly warms up. A more elaborate analysis of energy conversion and heat transfer during milling is given in the Experimental section.
If milling proceeds with no chemical reaction or polymorphic transformation, temperature prole should exhibit monotonous heating until a steady state is reached. Indeed, this is observed in the temperature prole of an empty vessel (containing milling balls but without any material) and in the temperature prole of milling of pure ZnO, which was one of the reactants in the studied ZIF transformations (ESI Fig. 4 and 5 †). An empty vessel heats up slower than a vessel containing ZnO, which is explained by the better absorption of kinetic energy of the milling balls upon collisions when some material is present in the reaction vessel. Difference in energy absorption was veried by a bouncing test where a steel ball was dropped onto a PMMA plate and the height of its bounce was measured. It was revealed that balls bounce from the PMMA plate with 0.86 coefficient of restitution (the ratio of the bounced height and the initial height from which the ball was dropped). On the other hand, a ball bounced on the same PMMA surface but now lined with a 1 mm thick layer of ZnO powder resulted in a less elastic collision (0.3 coefficient of restitution), indicating a more efficient conversion of the kinetic energy of the ball into the internal energy of the system. In support of such interpretation, signicant heating of the mixture was observed when so milling balls were used instead of hard ones. So milling balls were able to deform and thus efficiently dissipated their kinetic energy resulting in a temperature rise of over 100 C. 49 Characteristics of collisions between milling balls and the vessel walls thus determine the amount of the dissipated energy by friction during ball milling, which causes an increase in temperature of the milling assembly. To gain a quantitative insight into temperature proles and heat exchange, we have performed numerical simulations of heat transfer between the milling assembly and the environment during milling. Energy dissipation from milling ball impacts was described as a heat source on the whole inside surface of the milling vessel, in accordance with the assumed random motion of milling balls.
At the start of the simulation, the heat ow immediately increased the temperature of the inside vessel surface. The heat was then conducted through vessel walls towards the environment. While energy dissipation remained constant throughout milling, heat ow to the environment increased with the increase in temperature of the whole milling assembly, nally reaching a steady state when the heat loss equalled the input energy dissipation. In our simulations, we have modied energy dissipation for each experiment in order to reproduce the observed temperature proles. This has enabled us to estimate the energy dissipation for an empty vessel to be 272 mW while it was estimated to be 496 mW for the vessel containing ZnO.
Constant energy dissipation leads to a monotonous temperature increase and a steady state temperature. However, more complicated temperature proles which involve chemical changes, required modelling of heat ow in each stage of the reaction. During ZIF-8 formation and amorphization (Fig. 3), the heat ow upon 33 minutes of milling amounted to ca. 540 mW. A short period followed when the heat ow was reduced to ca. 500 mW and the nal period aer recrystallisation to the katphase, when the heat-ow rate was further reduced to ca. 410 mW.
The milling reaction was thus separated into three periods that have different friction properties generating different heat ows and consequently, leading to different steady-state temperatures. To illustrate that the steady-state temperature under the same ambient conditions is determined only by frictional properties of the material in the vessel and the associated rate of heat ow, this three-stage simulation was compared to a simulation of a putative milling process in which the frictional properties were immediately set to be identical to those of the third stage of the reaction, with the corresponding heat ow rate of 410 mW. This simulation resulted in a signicantly lower temperature prole but reached the same steadystate temperature, conrming that the steady-state temperature under unchanged ambient conditions is determined by a permanent heat source inside the vessel.
The steady-state temperature depends on the rate of heat ow generated by the milling process and according to the Newton's law of cooling on ambient conditions. At the same time, the effect of any short-term heating events e.g. reactionrelated release or absorption of energy, is expected to diminish over time. Thus, contrary to recent suggestions 35,52 it is not possible to directly compare the temperature prole for milling of one inert material, to the prole of milling another reactive material, as these are characterized by very different frictional properties. Consequently, it is also not possible to interpret any differences between such temperature proles in terms of reaction enthalpies. A more detailed account of heat exchange of the milling process is given in the ESI. † Fig. 3 Numerical modelling of temperature profiles. Three-stages of the reaction: formation of ZIF-8, its amorphisation and finally, recrystallisation of the amorphous matrix into the kat phase are depicted with red, blue and purple curves, respectively (from Fig. 2a). The heat flow rate (in milliwatts) is divided into sections where each section corresponds to a specific reaction mixture composition. After recrystallisation to the kat phase, the heat flow rate dropped from 500 mW to 410 mW. In a hypothetical milling experiment using identical ambient conditions, the same steady-state temperature was reached by using heat flow rate of 410 mW from the beginning (green curve). Fig. 4 Amorphisation of ZIF-8 without recrystallization. Milling was started but had to be interrupted to restart diffraction data collection. The temperature profile first shows heating, followed by a cooling step before another onset of heating after milling was restarted. ZIF-8 is already present and the mixture seems homogenous at the beginning of PXRD monitoring because of the first interrupted milling period. After milling was stopped, the reaction vessel spontaneously cooled as per Newton's law of cooling. Homogeneity and uniformity of the reaction mixture is evident from the uniformity of the diffraction signal from crystalline silicon (at 2.6 in 2theta) which was used as an internal scattering standard. 22 Our interpretation of the cause of temperature drops upon recrystallisation of the amorphous ZIF-8, is supported by an experiment in which no recrystallization took place and consequently, a temperature drop was not observed aer the steady-state temperature was reached (Fig. 4).
The ZIF-8 / kat / dia polymorphic transformations was suitable to study reaction temperature proles since the reaction mixture is always in the form of a free-owing powder which ensures a reasonably uniform distribution of the reaction mixture inside the reaction vessel and a good thermal contact between it and the temperature sensor. However, we have also monitored the formation of other MOF materials. Mechanochemical formation of a pillared MOF 50,51 exhibited pronounced jumps in the temperature prole (Fig. 5). Aer milling commenced, the temperature of the reaction mixture rose by almost 3 C in only two minutes, followed by a short interruption in steady heating simultaneously with the formation of an intermediate phase that lived for one and a half minutes. The temperature stabilized at 29.8 C aer 30 minutes of milling, when the mechanochemical formation of pillared MOF was nished. This steady state, with minor deviations (AE0.2 C), remained during the next 30 minutes, until milling stopped and the milling assembly began to cool. We also noted that in some cases of sticky reaction mixtures, the temperature proles may exhibit features that poorly correlate with composition changes but rather to the variations in a non-uniform distribution of the material inside the vessel (ESI Fig. 6 †).

Conclusions
We have presented here the rst method for precise temperature monitoring of the sample during a mechanochemical reaction, and coupled it in tandem with in situ synchrotron powder X-ray diffraction, to reveal unexpected temperature proles which correlate with changes in the reaction mixture. These unexpected temperature proles in which the reaction mixture cools during slightly exothermic transformations, were explained by numerical simulations of heat ow during milling, which revealed the dominant inuence of frictional heating to the observed temperature proles, with the contributions of reaction enthalpies being signicantly smaller and even negligible. Specically, we showed by experiments and modelling that changes in reaction mixture composition due to the formation of new materials are found to result in changes to frictional properties of the milled mixture, which permit the thermal detection of transformations with even very small reaction enthalpies. The results presented here offer a new perspective to understand the development of thermal effects during milling and also provide a novel method to use temperature in monitoring mechanochemical reactions, even when enthalpy contribution may be too small to be of signicance.

Experimental
Tandem in situ temperature and X-ray diffraction reaction monitoring Milling experiments were performed using a modied Retsch MM301 ball mill operating at 30 Hz. The modication to the mill allowed for the X-ray beam (300 mm in diameter) to pass through the mill and through the bottom of the inside reaction vessel. A special reaction vessel was manufactured which had an embedded resistance temperature sensor (RTD) Pt-100 that was placed in thermal contact with a small piece of aluminum (aluminium plug) which was in direct contact with the reaction mixture (ESI Fig. 1 and 2 †). In this manner, we have avoided collisions of the milling balls with the temperature sensor while still having a good thermal contact between the sensor and the reaction mixture. The reaction vessel was equipped with electronics which transformed the RTD readings into a digital signal which was sent to a computer for logging via an infrared transmitter. Electronics were powered by a set of batteries and was autonomous. Temperature readings were typically collected once every second. To ensure reproducibility and transferability of previous in situ monitoring experiments, the reaction vessel was manufactured to have the same internal volume of 14 mL and two stainless steel balls of 7 mm in diameter (mass of 1.4 g) were used as milling media. 25 Tandem in situ experiments were performed at the old ID15B beamline of the European Synchrotron Radiation Facility (ESRF) in Grenoble, using high-energy monochromatic radiation (E ¼ 88.0 keV, l ¼ 0.141Å). Simultaneously with temperature monitoring, the course of studied reactions was monitored using X-ray diffraction of high-energy synchrotron radiation as described previously. 20 The X-ray beam was passed through the lower part of the reaction vessel and the diffraction data were collected typically every 6 seconds on a at-panel twodimensional X-ray detector from Perkin-Elmer. The X-rays were selected using a bent double silicon monochromator. The X-ray wavelength and detector distance were calibrated using the NIST CeO 2 standard sample which was packed in a capillary and was positioned at the bottom inside of the reaction vessel. Calibration and radial integration of raw diffraction images was performed using the program Fit2D (ESRF Internal Report, ESRF98HA01T, FIT2D V9.129 Reference Manual V3.1, 1998). Time-resolved diffractograms were plotted using the program Mathematica, using diffraction patterns with the background removed using the Sonneveld-Visser algorithm. 53 Simulations of temperature proles A 3D model of the vessel was made in the soware package SolidWorks and simulations of temperature proles were performed in SolidWorks Simulation module. Geometry of the model corresponded to the actual reaction vessel and is shown in ESI Fig. 7. † Materials used in simulation were PMMA for the reaction vessel and aluminium for the plug which is in contact with the temperature sensor. Since the plug was embedded in the vessel, the contact between these two components was set to bonded.
Two boundary conditions were dened for the inner surfaces of the vessel; zero heat ux density along the two planes of symmetry and the given amount of total heat ux on the surface that is in contact with the milling balls and the reaction mixture. Boundary conditions on vessel outer surfaces were set according to Newton's law of cooling with a heat transfer coef-cient of 15.5 W m À2 K À1 and the bulk temperature equal to the simulation initial temperature.
Since the materials of the aluminium plug and the vessel differ, the density of the mesh was increased in the contact zone. The mesh (ESI Fig. 7 †) was created in high quality (element size is 0.5 mm) with standard Voronoi-Delaunay meshing scheme and it consists of total 440 003 parabolic tetrahedral solid elements. The transient iterative solver was used with 10 s time step.
Since the temperature variations on the plug surface inside the vessel were within 2 mK, resulting output was an average temperature on the aluminium plug surface for every time step.

Author contributions
Project was conceived by KU and supervised by KU, IH and TF. Temperature-measuring device was built by TM. Experiments were performed by KU, TM, IH, PAJ and TF. Heat ow was analysed by NF and BH. Numerical simulations were performed by NF. Figures were prepared by IH and NF. IH wrote the initial dra of the manuscript. All authors discussed the results and contributed to the nal preparation of the manuscript.

Conflicts of interest
There are no conicts to declare.