{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T20:00:31Z","timestamp":1792267231015,"version":"4.4.0"},"reference-count":21,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T00:00:00Z","timestamp":1570406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>We focus on understanding the kinetics of a mechanically activated Knoevenagel condensation conducted in a ball mill, that is characterized by sigmoidal kinetics and the formation of a rubber-like cohesive intermediate state coating the milling ball. The previously described experimental findings are explained using a phenomenological kinetic model. It is assumed that reactants transform into products already at the very first collision of the ball with the wall of the jar. The portion of reactants that are transformed into products during each oscillation is taken to be a fraction of the amount of material that is trapped between the ball and the wall of the jar. This quantity is greater when the reaction mixture transforms from its initial powder form to the rubber-like cohesive coating on the ball. Further, the amount of reactants processed in each collision varies proportionally with the total area of the layer coating the ball. The total area of this coating layer is predicted to vary with the third power of time, thus accounting for the observed dramatic increase of the reaction rate. Supporting experiments, performed using a polyvinyl acetate adhesive as a nonreactive but cohesive material, confirm that the coating around the ball grows with the third power of time.<\/jats:p>","DOI":"10.3390\/molecules24193600","type":"journal-article","created":{"date-parts":[[2019,10,7]],"date-time":"2019-10-07T03:34:01Z","timestamp":1570419241000},"page":"3600","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Phenomenological Inferences on the Kinetics of a Mechanically Activated Knoevenagel Condensation: Understanding the \u201cSnowball\u201d Kinetic Effect in Ball Milling"],"prefix":"10.3390","volume":"24","author":[{"given":"Maria","family":"Carta","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universit\u00e0 degli Studi di Cagliari, via Marengo 2, 09123 Cagliari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stuart L.","family":"James","sequence":"additional","affiliation":[{"name":"School of Chemistry and Chemical Engineering, Queen\u2019s University Belfast, David Keir Building, Stranmillis Road, Belfast BT9 5AG, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Delogu","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Universit\u00e0 degli Studi di Cagliari, via Marengo 2, 09123 Cagliari, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7571","DOI":"10.1039\/c3cs35468g","article-title":"Hallmarks of mechanochemistry: From nanoparticles to technology","volume":"42","author":"Billik","year":"2013","journal-title":"Chem. Soc. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11851","DOI":"10.1007\/s10853-017-1174-7","article-title":"Chalcogenide mechanochemistry in materials science: Insight into synthesis and applications (a review)","volume":"52","year":"2017","journal-title":"J. Mater. Sci."},{"key":"ref_3","unstructured":"Margetic, D., and \u0160trukil, V. (2016). Mechanochemical Organic Synthesis, Elsevier."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.3762\/bjoc.13.186","article-title":"Mechanochemical synthesis of small organic molecules","volume":"13","author":"Bose","year":"2017","journal-title":"Beilstein J. Org. Chem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1039\/C7GC03797J","article-title":"Mechanochemistry and organic synthesis: From mystical to practical","volume":"20","author":"Andersen","year":"2018","journal-title":"Green Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.1039\/C7SC05370C","article-title":"Multicomponent mechanochemical synthesis","volume":"9","author":"Leonardi","year":"2018","journal-title":"Chem. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"El-Sayed, T.H., Aboelnaga, A., El-Atawy, M.A., and Hagar, M. (2018). Ball milling promoted N-heterocycles synthesis. Molecules, 23.","DOI":"10.3390\/molecules23061348"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"15252","DOI":"10.1002\/anie.201706723","article-title":"Feedback kinetics in mechanochemistry: The importance of cohesive states","volume":"56","author":"Hutchings","year":"2017","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3753","DOI":"10.1016\/S0040-4020(03)00554-4","article-title":"Solvent-free Knoevenagel condensations and michael additions in the solid state and in the melt with quantitative yield","volume":"59","author":"Kaupp","year":"2003","journal-title":"Tetrahedron"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1039\/C3FD00144J","article-title":"Scale-up of organic reactions in ball mills: Process intensification with regard to energy efficiency and economy of scale","volume":"170","author":"Stolle","year":"2014","journal-title":"Faraday Discuss."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1002\/ceat.201300738","article-title":"Experimental and computational investigation of Knoevenagel condensation in planetary ball mill","volume":"37","author":"Burmeister","year":"2014","journal-title":"Chem. Eng. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1021\/op5003787","article-title":"Effect of reaction parameters on the synthesis of 5-arylidene barbituric acid derivatives in ball mills","volume":"19","author":"Schmidt","year":"2015","journal-title":"Org. Process Res. Dev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4981","DOI":"10.2174\/1381612822666160804093120","article-title":"Non-ambient conditions in the investigation and manufacturing of drug forms","volume":"22","author":"Boldyreva","year":"2016","journal-title":"Curr. Pharm. Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7572","DOI":"10.1039\/c0cc02635b","article-title":"Direct structure elucidation by powder X-ray diffraction of a metal\u2013organic framework material prepared by solvent-free grinding","volume":"46","author":"Fujii","year":"2010","journal-title":"Chem. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7719","DOI":"10.1039\/c3cs60052a","article-title":"Mechanochemistry of inorganic and organic systems: What is similar, what is different?","volume":"42","author":"Boldyreva","year":"2013","journal-title":"Chem. Soc. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1011382008963","article-title":"Relating single-impact events to macrokinetic features in mechanical alloying processes","volume":"8","author":"Delogu","year":"2000","journal-title":"J. Mater. Synth. Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.actamat.2014.08.036","article-title":"Mechanochemistry of Ti-C powder mixtures","volume":"80","author":"Delogu","year":"2014","journal-title":"Acta Mater."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"13331","DOI":"10.1007\/s10853-018-2090-1","article-title":"Information on the mechanism of mechanochemical reaction from detailed studies of the reaction kinetics","volume":"53","author":"Delogu","year":"2018","journal-title":"J. Mater. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1023\/A:1011308025376","article-title":"Toward a quantitative understanding of the mechanical alloying process","volume":"8","author":"Cocco","year":"2000","journal-title":"J. Mater. Synth. Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1063\/1.166393","article-title":"Hyperchaotic qualities of the ball motion in a ball milling device","volume":"9","author":"Caravati","year":"1999","journal-title":"Chaos"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1063\/1.1484016","article-title":"Onset of chaotic dynamics in a ball mill: Attractors merging and crisis induced intermittency","volume":"12","author":"Manai","year":"2002","journal-title":"Chaos"}],"container-title":["Molecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1420-3049\/24\/19\/3600\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:27:59Z","timestamp":1760189279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1420-3049\/24\/19\/3600"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,7]]},"references-count":21,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["molecules24193600"],"URL":"https:\/\/doi.org\/10.3390\/molecules24193600","relation":{},"ISSN":["1420-3049"],"issn-type":[{"value":"1420-3049","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,7]]}}}