{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T23:32:29Z","timestamp":1791415949704,"version":"4.3.3"},"reference-count":38,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T00:00:00Z","timestamp":1756857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University Research Scholarship Program of the Ministry for Culture and Innovation, via the National Research, Development, and Innovation Fund","award":["EK\u00d6P-24-3-I\/13"],"award-info":[{"award-number":["EK\u00d6P-24-3-I\/13"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>In the polyurethane industry, catalytically generated carbodiimides can modify the properties of isocyanate and, thus, the resulting foams. In this work, a kinetic reaction study was carried out to investigate the formation of a simple, bifunctional carbodiimide from a widely used polyurethane raw material: 4,4\u2032-methylenediphenyl diisocyanate (MDI). The experimental section outlines a catalytic process, using a 3-methyl-1-phenyl-2-phospholene-1-oxide (MPPO) catalyst in ortho-dichlorobenzene (ODCB) solvent, to model industrial circumstances. The reaction produces carbon dioxide, which was observed using gas volumetry at between 50 and 80 \u00b0C to obtain kinetic data. A detailed regression analysis with linear and novel nonlinear fits showed that the initial stage of the reaction is second-order, and the temperature dependence of the rate constant is k(T)=(3.4\u00b13.8)\u2027106\u22c5e\u22127192\u00b1389T. However, the other isocyanate group of MDI reacts with new isocyanate groups and the reaction deviates from the second-order due to oligomer (polycarbodiimide) formation and other side reactions. A linearized Arrhenius equation was used to determine the activation energy of the reaction, which was Ea = 60.4 \u00b1 3.0 kJ mol\u22121 at the applied temperature range, differing by only 4.6 kJ mol\u22121 from a monoisocyanate-based carbodiimide. In addition to experimental results, computationally derived thermochemical data (from simplified DFT and IRC calculations) were applied in transition state theory (TST) for a comprehensive prediction of rate constants and Arrhenius parameters. As a result, it was found that the activation energy of the carbodiimide bond formation reaction from theoretical and experimental results was independent of the number and position of isocyanate groups, which is consistent with the principle of equal reactivity of functional groups.<\/jats:p>","DOI":"10.3390\/ijms26178570","type":"journal-article","created":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T09:18:57Z","timestamp":1756977537000},"page":"8570","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Kinetic and Mechanistic Study of Polycarbodiimide Formation from 4,4\u2032-Methylenediphenyl Diisocyanate"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-8150-8650","authenticated-orcid":false,"given":"Marcell D.","family":"Cs\u00e9csi","sequence":"first","affiliation":[{"name":"Institute of Chemistry, University of Miskolc, Miskolc-Egyetemv\u00e1ros, H-3515 Miskolc, Hungary"},{"name":"Higher Education and Industrial Cooperation Centre, University of Miskolc, H-3515 Miskolc, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. Zsanett","family":"Boros","sequence":"additional","affiliation":[{"name":"BorsodChem Ltd., Bolyai t\u00e9r 1, H-3700 Kazincbarcika, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P\u00e9ter","family":"T\u00f3th","sequence":"additional","affiliation":[{"name":"BorsodChem Ltd., Bolyai t\u00e9r 1, H-3700 Kazincbarcika, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4328-486X","authenticated-orcid":false,"given":"L\u00e1szl\u00f3","family":"Farkas","sequence":"additional","affiliation":[{"name":"BorsodChem Ltd., Bolyai t\u00e9r 1, H-3700 Kazincbarcika, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0777-9569","authenticated-orcid":false,"given":"B\u00e9la","family":"Viskolcz","sequence":"additional","affiliation":[{"name":"Institute of Chemistry, University of Miskolc, Miskolc-Egyetemv\u00e1ros, H-3515 Miskolc, Hungary"},{"name":"Higher Education and Industrial Cooperation Centre, University of Miskolc, H-3515 Miskolc, Hungary"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ulrich, H. (2007). Chemistry and Technology of Carbodiimides, John Wiley and Sons.","DOI":"10.1002\/9780470516683"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1021\/ja01609a099","article-title":"A new method of forming peptide bonds","volume":"77","author":"Sheehan","year":"1955","journal-title":"J. Am. Chem. Soc."},{"key":"ref_3","unstructured":"Hermanson, G.T. (2013). Bioconjugate Techniques, Elsevier. [3rd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4288","DOI":"10.1021\/ja00881a019","article-title":"Carbodiimides. II. Mechanism of the Catalytic Formation from Isocyanates","volume":"84","author":"Monagle","year":"1962","journal-title":"J. Am. Chem. Soc."},{"key":"ref_5","unstructured":"(2025, February 04). Polyurethane Market Size, Share, Growth Report|Trends [2032]. Available online: https:\/\/www.fortunebusinessinsights.com\/industry-reports\/polyurethane-pu-market-101801."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1002\/anie.196206211","article-title":"The Preparation of Carbodiimides from Isocyanates","volume":"1","author":"Neumann","year":"1962","journal-title":"Angew. Chemie Int. Ed. English"},{"key":"ref_7","unstructured":"Holtschmidt, H., Loew, G., Nischk, G., and Moosm\u00fcller, F. (1957). Stabilisierendes Mittel Gegenueber den Einfluessen von Waerme und Feuchtigkeit in Durch Polysocyanate Modifizierten Polyestermassen. (DE1005726B), German Patent."},{"key":"ref_8","unstructured":"(2025, February 04). ONGRONAT\u00ae 3000 Technical Data Sheet. Available online: https:\/\/borsodchem.com\/uploads\/product_documents\/technical-data-sheet-ongronat-3000-07-en-07082019-1618222238.pdf."},{"key":"ref_9","unstructured":"Haynes, W.M. (2017). Physical Constants of Organic Compounds. CRC Handbook of Chemistry and Physics, CRC Press Inc.. [97th ed.]."},{"key":"ref_10","unstructured":"Savino, T., and Bananto, S. (2010). Uretonimine-Modified Isocyanate Composition and Method of Forming the Same. (7,777,054), U.S. Patent."},{"key":"ref_11","unstructured":"Savino, T., and Lebedinski, N. (2010). Method of Producing a Uretonimine-Modified Isocyanate Composition. (7,790,907 B2), U.S. Patent."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"43737","DOI":"10.1002\/app.43737","article-title":"Characteristics of polyurethane adhesives with various uretonimine contents in isocyanate and average alcohol functionalities","volume":"133","author":"Sung","year":"2016","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1913","DOI":"10.1021\/jo01269a044","article-title":"Reactions of 1,3-Diphenyl-4-(Phenylimino)-2-uretidinone","volume":"33","author":"Farrissey","year":"1968","journal-title":"J. Org. Chem."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1177\/0021955X8502100509","article-title":"Chemistry and properties of low density poly(carbodiimide) foams","volume":"21","author":"Ulrich","year":"1985","journal-title":"J. Cell. Plast."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1021\/jo01043a029","article-title":"Carbodiimides. IV. High Polymers Containing the Carbodiimide Repeat Unit","volume":"28","author":"Campbell","year":"1963","journal-title":"J. Org. Chem."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1070\/RC1993v062n12ABEH000068","article-title":"Polycarbodiimides","volume":"62","author":"Pankratov","year":"1993","journal-title":"Russ. Chem. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hiemenz, P.C., and Lodge, T.P. (2007). Polymer Chemistry, CRC Press LLC. [2nd ed.].","DOI":"10.1201\/9781420018271"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, M., June, S.M., Long, T.E., and Kong, J. (2016). Principles of Step-Growth Polymerization (Polycondensation and Polyaddition). Ref. Modul. Mater. Sci. Mater. Eng., 1\u201351.","DOI":"10.1016\/B978-0-12-803581-8.01410-7"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3673","DOI":"10.1021\/ja00878a015","article-title":"Carbodiimides. I. Conversion of Isocyanates to Carbodiimides with Phospholine Oxide Catalyst","volume":"84","author":"Campbell","year":"1962","journal-title":"J. Am. Chem. Soc."},{"key":"ref_20","unstructured":"Vilaboy, J.T., Diczh\u00e1zi, S.S., Koz\u00e1r, Z., R\u00e9ti, J., Klement, T., and Purzsa, T. (2009). Process for the Preparation of Polyisocyanates of the Diphenylmethane Series. (WO 2009\/077795 A1), Worldwide Patent."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cs\u00e9csi, M.D., Kondor, V., Reizer, E., Boros, R.Z., T\u00f3th, P., Farkas, L., Fiser, B., Mucsi, Z., Nagy, M., and Viskolcz, B. (2024). Theoretical and Experimental Study on Carbodiimide Formation. Int. J. Mol. Sci., 25.","DOI":"10.3390\/ijms25147991"},{"key":"ref_22","unstructured":"Li, W., Vilaboy, J.T., and Fekete, L. (2016). Process for the Preparation of Light Coloured, Stable to Storage Uretonimine-Modified Polyisocyanate. (EP2990429A1), European Patent."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1007\/s10973-018-7211-1","article-title":"New thermal study of polymerization and degradation kinetics of methylene diphenyl diisocyanate","volume":"133","author":"Alarcon","year":"2018","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_24","unstructured":"Bevington, P.R., and Robinson, D.K. (2003). Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill. [3rd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1021\/acs.jchemed.6b00629","article-title":"Linear or Nonlinear Least-Squares Analysis of Kinetic Data?","volume":"94","author":"Perrin","year":"2017","journal-title":"J. Chem. Educ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1039\/D3RE00684K","article-title":"A machine learning based approach to reaction rate estimation","volume":"9","author":"Johnson","year":"2024","journal-title":"React. Chem. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"12940","DOI":"10.1021\/acs.iecr.7b00593","article-title":"Kinetics of Performic Acid Synthesis and Decomposition","volume":"56","author":"Santacesaria","year":"2017","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Upadhyay, S.K. (2006). 1.11 Determination of Order of Reaction. Chemical Kinetics and Molecular Dynamics, Anamaya Publishers.","DOI":"10.1007\/978-1-4020-4547-9"},{"key":"ref_29","unstructured":"Laidler, K.J. (1987). Chemical Kinetics, Harper & Row. [3rd ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1063\/1.1744539","article-title":"Additivity Rules for the Estimation of Molecular Properties. Thermodynamic Properties","volume":"29","author":"Benson","year":"1958","journal-title":"J. Chem. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4497","DOI":"10.1021\/jp992355e","article-title":"Application of the Group Additivity Method to Alkyl Radicals: An ab Initio Study","volume":"104","author":"Marsi","year":"2000","journal-title":"J. Phys. Chem. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1002\/macp.1983.021840111","article-title":"On the principle of equal reactivity in solution polycondensation","volume":"184","author":"Kuchanov","year":"1983","journal-title":"Die Makromol. Chem."},{"key":"ref_33","unstructured":"Flory, P.J. (1953). Principles of Polymer Chemistry, Cornell University Press."},{"key":"ref_34","unstructured":"(OriginPro, 2018). OriginPro, Version 2018."},{"key":"ref_35","unstructured":"Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Petersson, G.A., and Nakatsuji, H. (2016). Gaussian 16, Revision C.01, Gaussian Inc."},{"key":"ref_36","unstructured":"Dennington, R., Keith, T.A., and Millam, J.M. (GaussView, 2016). GaussView, Version 6.0."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5648","DOI":"10.1063\/1.464913","article-title":"Density-functional thermochemistry. III. The role of exact exchange","volume":"98","author":"Becke","year":"1993","journal-title":"J. Chem. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"6378","DOI":"10.1021\/jp810292n","article-title":"Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions","volume":"113","author":"Marenich","year":"2009","journal-title":"J. Phys. Chem. 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