A phenomenological kinetic equation for mechanochemical reactions involving highly deformable molecular solids

Mechanochemical comparison of ball milling processes for levofloxacin amorphous polymeric systems

This study aimed to investigate the amorphization capabilities of levofloxacin hemihydrate (LVXh), a fluoroquinolone drug, using a polymer excipient, Eudragit® L100 (EL100). Ball milling (BMing) was chosen as the manufacturing process and multiple mill types were utilized for comparison purposes. The product outcomes of each mill were analyzed in detail. The solid-state of the samples produced was comprehensively characterized by Powder X-ray Diffraction (PXRD), In-situ PXRD, Differential Scanning Calorimetry (DSC), Solid-State Fourier Transform Infrared Spectroscopy (FT-IR), and Dynamic Vapor Sorption (DVS). The crystallographic planes of LVXh were investigated by in-situ PXRD to disclose the presence or absence of weak crystallographic plane(s). The mechanism of LVXh:EL100 system formation was discovered as a two-step process, first involving amorphization of LVXh followed by an interaction with EL100, rather than as an instantaneous process. DVS studies of LVXh:EL100 samples showed different stability properties depending on the mill used and % LVXh present. Overall, a more sustainable approach for achieving full amorphization of the fluoroquinolone drug, LVXh, was accomplished, and advancements to the fast-growing world of pharmaceutical mechano- and tribo-chemistry were made.

Modeling Mechanochemical Depolymerization of PET in Ball-Mill Reactors Using DEM Simulations

Developing efficient and sustainable chemical recycling pathways for consumer plastics is critical for mitigating the negative environmental implications associated with their end-of-life management. Mechanochemical depolymerization reactions have recently garnered great attention, as they are recognized as a promising solution for solvent-free transformation of polymers to monomers in the solid state. To this end, physics-based models that accurately describe the phenomena within ball mills are necessary to facilitate the exploration of operating conditions that would lead to optimal performance. Motivated by this, in this paper we develop a mathematical model that couples results from discrete element method (DEM) simulations and experiments to study mechanically-induced depolymerization. The DEM model was calibrated and validated via video experimental data and computer vision algorithms. A systematic study on the influence of the ball-mill operating parameters revealed a direct relationship between the operating conditions of the vibrating milling vessel and the total energy supplied to the system. Moreover, we propose a linear correlation between the high-fidelity DEM simulation results and experimental monomer yield data for poly(ethylene terephthalate) depolymerization, linking mechanical and energetic variables. Finally, we train a reduced-order model to address the high computational cost associated with DEM simulations. The predicted working variables are used as inputs to the proposed mathematical expression which allows for the fast estimation of monomer yields.

A kinetic study of mechanically activated atom exchange: the effect of milling frequency and ball mass

This study investigates the mechanochemical reaction of hydrogen isotope exchange between solid benzoic acid and liquid heavy water. The systematic change of milling conditions revealed that the reaction rate scales with the milling frequency and the mass of the milling balls. The ball size being always the same, faster reactions stem from the use of higher milling frequencies and heavier balls. The kinetic curves are described by a kinetic model that accounts for the statistical, deformational and chemical factors involved in mechanochemical transformations. The results indicate that the reaction is driven by the generation of a new interface area caused by the deformation of the solid reactants.

Mechanochemical ignition of self-propagating reactions in equimolar Al-Ni powder mixtures and multilayers

This work addresses a long standing question in the field of mechanochemistry, namely the role of mesostructure in the initiation of self-propagating high-temperature reactions in exothermic chemical systems, commonly referred to as ignition. In an attempt to find robust evidence in this regard, we compare the ignition behaviour of equimolar Al-Ni powder mixtures and equimolar Al-Ni multilayers. To achieve the best possible control of experimental conditions and allowing high reproducibility, we used elemental powders sieved in the range between 20 μm and 44 μm, and multilayers with bi-layer thickness between 10 nm and 800 nm. We carried out systematic ball milling experiments involving pristine powder mixtures and multilayers as well as a mix of pristine material and material prone to ignition suitably prepared. Experimental findings suggest that pristine powder mixtures and multilayers with bi-layer thickness of 240 nm have analogous ignition behaviour. Along the same lines, data suggest that pristine powder mixtures undergo ignition when they attain a mesostructure similar to that of multilayers with bi-layer thickness of 10 nm.

Exploring mechanochemistry of pharmaceutical cocrystals: effect of incident angle on molecular mixing during simulated indentations of two organic solids

The solid-state reaction of the active pharmaceutical ingredient theophylline with citric acid is a well-established example of a mechanochemical reaction, leading to a model pharmaceutical cocrystal. Here, classical force field molecular dynamics was employed to investigate the molecular mixing and structural distortion that take place on the mechanically driven indentation of a citric acid nanoparticle on a slab of crystalline theophylline. Through non-equilibrium molecular dynamics simulations, a 6 nm diameter nanoparticle of citric acid was introduced onto an open (001) surface of a theophylline crystal, varying both the angle of incidence of the nanoparticle between 15° and 90° and the indentation speed between 1 m s-1 and 16 m s-1. This theoretical study enabled the evaluation of how these two parameters promote molecular mixing and overall structural deformation upon the mechanical contraction of theophylline and citric acid, both of which are important parameters underlying mechanochemical cocrystallisation. The results show that the angle of incidence plays a key role in the molecular transfer ability between the two species and in the structural disruption of the initially spherical nanoparticles. Changing the indentation speed, however, did not lead to a discernible trend in molecular mixing, highlighting the importance of the incident angle in mechanochemical events in the context of supramolecular chemistry, such as the disruption of the crystal structure and molecular transfer between molecular crystals.

Kinetic Phenomena in Mechanochemical Depolymerization of Poly(styrene)

Synthetic polyolefinic plastics comprise one of the largest shares of global plastic waste, which is being targeted for chemical recycling by depolymerization to monomers and small molecules. One promising method of chemical recycling is solid-state depolymerization under ambient conditions in a ball-mill reactor. In this paper, we elucidate kinetic phenomena in the mechanochemical depolymerization of poly(styrene). Styrene is produced in this process at a constant rate and selectivity alongside minor products, including oxygenates like benzaldehyde, via mechanisms analogous to those involved in thermal and oxidative pyrolysis. Continuous monomer removal during reactor operation is critical for avoiding repolymerization, and promoting effects are exhibited by iron surfaces and molecular oxygen. Kinetic independence between depolymerization and molecular weight reduction was observed, despite both processes originating from the same driving force of mechanochemical collisions. Phenomena across multiple length scales are shown to be responsible for differences in reactivity due to differences in grinding parameters and reactant composition.

Mechanistic model for quantifying the effect of impact force on mechanochemical reactivity

Conventional mechanochemical synthetic tools, such as ball mills, offer no methodology to quantitatively link macroscale reaction parameters, such as shaking frequency or milling ball radius, to fundamental drivers of reactivity, namely the force vectors applied to the reactive molecules. As a result, although mechanochemistry has proven to be a valuable method to make a wide variety of products, the results are seldom reproduceable between reactors, difficult to rationally optimize, and hard to ascribe to a specific reaction pathway. Here we have developed a controlled force reactor, which is a mechanochemical ball mill reactor with integrated force measurement and control during each impact. We relate two macroscale reactor parameters-impact force and impact time-to thermodynamic and kinetic transition state theories of mechanochemistry utilizing continuum contact mechanics principles. We demonstrate force controlled particle fracture of NaCl to characterize particle size evolution during reactions, and force controlled reaction between anhydrous copper(II) chloride and (1, 10) phenanthroline. During the fracture of NaCl, we monitor the evolution of particle size as a function of impact force and find that particles quickly reach a particle size of ∼100 μm largely independent of impact force, and reach steady state 10-100× faster than reaction kinetics of typical mechanochemical reactions. We monitor the copper(II) chloride reactivity by measuring color change during reaction. Applying our transition state theory developed here to the reaction curves of copper(II) chloride and (1, 10) phenanthroline at multiple impact forces results in an activation energy barrier of 0.61 ± 0.07 eV, distinctly higher than barriers for hydrated metal salts and organic ligands and distinctly lower than the direct cleavage of the CuCl bond, indicating that the reaction may be mediated by the higher affinity of Fe in the stainless steel vessel to Cl. We further show that the results in the controlled force reactor match rudimentary estimations of impact force within a commercial ball mill reactor Retsch MM400. These results demonstrate the ability to quantitatively link macroscale reactor parameters to reaction properties, motivating further work to make mechanochemical synthesis quantitative, predictable, and fundamentally insightful.

Extending the Hammett correlation to mechanochemical reactions

Using Raman in situ monitoring and mechanochemistry-specific kinetic analysis, we find a correlation between the reaction probability and the Hammett constants in a model mechanochemical reaction of imine formation, indicating that the body of knowledge developed in physical-organic chemistry could be transferable to ball milling reactions in the solid state.

Spiers Memorial Lecture: Mechanochemistry, tribochemistry, mechanical alloying - retrospect, achievements and challenges

The paper presents a view on the achievements, challenges and prospects of mechanochemistry. The extensive reference list can serve as a good entry point to a plethora of mechanochemical literature.

Mechanochemistry: New Tools to Navigate the Uncharted Territory of "Impossible" Reactions

Mechanochemical transformations have made chemists enter unknown territories, forcing a different chemistry perspective. While questioning or revisiting familiar concepts belonging to solution chemistry, mechanochemistry has broken new ground, especially in the panorama of organic synthesis. Not only does it foster new "thinking outside the box", but it also has opened new reaction paths, allowing to overcome the weaknesses of traditional chemistry exactly where the use of well-established solution-based methodologies rules out progress. In this Review, the reader is introduced to an intriguing research subject not yet fully explored and waiting for improved understanding. Indeed, the study is mainly focused on organic transformations that, although impossible in solution, become possible under mechanochemical processing conditions, simultaneously entailing innovation and expanding the chemical space.

N-Formylsaccharin: A Sweet(able) Formylating Agent in Mechanochemistry

The acylation of amines has always attracted a deep interest as a synthetic route due to its high versatility in organic chemistry and biochemical processes. The purpose of this article is to present a mechanochemical acylation procedure based on the use of acyl-saccharin derivatives, namely N-formylsaccharin, N-acetylsaccharin, and N-propionylsaccharin. This protocol furnishes a valuable solvent-free alternative to the existing processes and aims to be highly beneficial in multi-step procedures due to its rapid and user-friendly workup.

Controlling Nonlinear Dynamics of Milling Bodies in Mechanochemical Devices Driven by Pendular Forcing

Understanding the dynamics of milling bodies is key to optimize the mixing and the transfer of mechanical energy in mechanochemical processing. In this work, we present a comparative study of mechanochemical reactors driven by harmonic pendular forcing and characterized by different geometries of the lateral borders. We show that the shape of the reactor bases, either flat or curved, along with the size of the milling body and the elasticity of the collisions, represents relevant parameters that govern the dynamical regimes within the system and can control the transition from periodic to chaotic behaviors. We single out possible criteria to preserve target dynamical scenarios when the size of the milling body is changed, by adapting the relative extent of the spatial domain. This allows us to modulate the average energy of the collisions while maintaining the same dynamics and paves the way for a unifying framework to control the dynamical response in different experimental conditions. We finally explore the dynamical and energetic impact of an increasingly asymmetric mechanical force.

Toward Mechanistic Understanding of Mechanochemical Reactions Using Real-Time In Situ Monitoring

The past two decades have witnessed a rapid emergence of interest in mechanochemistry-chemical and materials reactivity achieved or sustained by the action of mechanical force-which has led to application of mechanochemistry to almost all areas of modern chemical and materials synthesis: from organic, inorganic, and organometallic chemistry to enzymatic reactions, formation of metal-organic frameworks, hybrid perovskites, and nanoparticle-based materials. The recent success of mechanochemistry by ball milling has also raised questions about the underlying mechanisms and has led to the realization that the rational development and effective harnessing of mechanochemical reactivity for cleaner and more efficient chemical manufacturing will critically depend on establishing a mechanistic understanding of these reactions. Despite their long history, the development of such a knowledge framework for mechanochemical reactions is still incomplete. This is in part due to the, until recently, unsurmountable challenge of directly observing transformations taking place in a rapidly oscillating or rotating milling vessel, with the sample being under the continuous impact of milling media. A transformative change in mechanistic studies of milling reactions was recently introduced through the first two methodologies for real-time in situ monitoring based on synchrotron powder X-ray diffraction and Raman spectroscopy. Introduced in 2013 and 2014, the two new techniques have inspired a period of tremendous method development, resulting also in new techniques for mechanistic mechanochemical studies that are based on temperature and/or pressure monitoring, extended X-ray fine structure (EXAFS), and, latest, nuclear magnetic resonance (NMR) spectroscopy. The new technologies available for real-time monitoring have now inspired the development of experimental strategies and advanced data analysis approaches for the identification and quantification of short-lived reaction intermediates, the development of new mechanistic models, as well as the emergence of more complex monitoring methodologies based on two or three simultaneous monitoring approaches. The use of these new opportunities has, in less than a decade, enabled the first real-time observations of mechanochemical reaction kinetics and the first studies of how the presence of additives, or other means of modifying the mechanochemical reaction, influence reaction rates and pathways. These studies have revealed multistep reaction mechanisms, enabled the identification of autocatalysis, as well as identified molecules and materials that have previously not been known or have even been considered not possible to synthesize through conventional approaches. Mechanistic studies through in situ powder X-ray diffraction (PXRD) and Raman spectroscopy have highlighted the formation of supramolecular complexes (for example, cocrystals) as critical intermediates in organic and metal-organic synthesis and have also been combined with isotope labeling strategies to provide a deeper insight into mechanochemical reaction mechanisms and atomic and molecular dynamics under milling conditions. This Account provides an overview of this exciting, rapidly evolving field by presenting the development and concepts behind the new methodologies for real-time in situ monitoring of mechanochemical reactions, outlining key advances in mechanistic understanding of mechanochemistry, and presenting selected studies important for pushing forward the boundaries of measurement techniques, data analysis, and mapping of reaction mechanisms.