{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T14:45:33Z","timestamp":1774881933834,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T00:00:00Z","timestamp":1774828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>The Johnson\u2013Mehl\u2013Avrami\u2013Kolmogorov (JMAK) formalism provides a classical framework for describing polymer crystallization kinetics; its applicability under finite-domain confinement requires quantitative assessment. In this work, the influence of one-dimensional geometric restriction on cylindrical growth in polymer thin films is investigated using a stochastic Monte Carlo approach. The model considers site-saturated nucleation on randomly distributed cylindrical nanofibers with constant radial growth velocity under hard-wall boundary conditions. Crystallization kinetics were evaluated through automated segmented regression of the double-logarithmic JMAK representation. Under confinement, the Avrami plot departs from single-slope linearity and exhibits two successive quasi-linear regimes characterized by effective parameter pairs n1,lnk1 and n2,lnk2. The primary exponent n1 remains thickness-independent, consistent with early-stage radial expansion prior to boundary interaction. The secondary exponent n2 displays a non-monotonic dependence on reduced film thickness, reflecting the competing influence of wall-induced truncation and inter-domain impingement on late-stage transformation. These results support a geometric interpretation in which finite-domain constraints modify the apparent Avrami response through the competing effects of wall-induced truncation and inter-domain impingement and provide a reproducible framework for analyzing dual-regime Avrami behavior in confined crystallization systems.<\/jats:p>","DOI":"10.3390\/polym18070840","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:41:53Z","timestamp":1774878113000},"page":"840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Avrami Kinetics of Cylindrical Growth Under Hard-Wall Confinement: A Monte Carlo Study of Thin-Film Crystallization"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5569-6338","authenticated-orcid":false,"given":"Catalin","family":"Berlic","sequence":"first","affiliation":[{"name":"Faculty of Physics, University of Bucharest, 405 Atomistilor Street, 077125 Magurele, Romania; <email>cataliniulian.berlic@g.unibuc.ro<\/email>"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gedde, U.W., and Hedenqvist, M.S. (2019). Fundamental Polymer Science, Springer.","DOI":"10.1007\/978-3-030-29794-7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.progpolymsci.2006.05.001","article-title":"Critical Assessment of Overall Crystallization Kinetics Theories and Predictions","volume":"31","author":"Piorkowska","year":"2006","journal-title":"Prog. Polym. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhang, M.C., Guo, B.H., and Xu, J. (2017). A Review on Polymer Crystallization Theories. Crystals, 7.","DOI":"10.3390\/cryst7010004"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"128522","DOI":"10.1016\/j.polymer.2025.128522","article-title":"Crystallization Kinetics, Avrami Analysis, and Fast-Scanning DSC of Polymers","volume":"332","author":"Toda","year":"2025","journal-title":"Polymer"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Christian, J.W. (2002). The Theory of Transformations in Metals and Alloys, Pergamon.","DOI":"10.1016\/B978-008044019-4\/50022-2"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1063\/1.1750380","article-title":"Kinetics of Phase Change. I General Theory","volume":"7","author":"Avrami","year":"1939","journal-title":"J. Chem. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1063\/1.1750631","article-title":"Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei","volume":"8","author":"Avrami","year":"1940","journal-title":"J. Chem. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1063\/1.1750872","article-title":"Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III","volume":"9","author":"Avrami","year":"1941","journal-title":"J. Chem. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1007\/BF03185527","article-title":"The Johnson-Mehl-Avrami-Kolmogorov Model: A Brief Review","volume":"20","author":"Fanfoni","year":"1998","journal-title":"Il Nuovo C."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/0001-6160(56)90041-4","article-title":"The Kinetics of Grain Boundary Nucleated Reactions","volume":"4","author":"Cahn","year":"1956","journal-title":"Acta Metall."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Piorkowska, E., and Rutledge, G.C. (2013). Handbook of Polymer Crystallization, Wiley.","DOI":"10.1002\/9781118541838"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"20230242","DOI":"10.1098\/rsif.2023.0242","article-title":"A Critical Review on Applications of the Avrami Equation beyond Materials Science","volume":"20","author":"Shirzad","year":"2023","journal-title":"J. R. Soc. Interface"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bin, Y., and Wang, H. (2018). Transcrystallization in Polymer Composites and Nanocomposites. Crystallization in Multiphase Polymer Systems, Elsevier Inc.","DOI":"10.1016\/B978-0-12-809453-2.00012-8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1016\/j.compscitech.2004.11.015","article-title":"On Transcrystallinity in Semi-Crystalline Polymer Composites","volume":"65","author":"Quan","year":"2005","journal-title":"Compos. Sci. Technol."},{"key":"ref_15","first-page":"167","article-title":"Study of Non-Isothermal Crystallization Kinetics of Single-Walled Carbon Nanotubes Filled Polypropylene Using Avrami and Mo Models","volume":"18","year":"2009","journal-title":"Iran. Polym. J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8852","DOI":"10.1007\/s10853-024-09683-5","article-title":"Heterogeneous Nucleation of Polyethylene Crystals on Binary Hexagonal Nanoplatelets","volume":"59","author":"Volchko","year":"2024","journal-title":"J. Mater. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1002\/app.11469","article-title":"Effects of Single-Walled Carbon Nanotubes on the Crystallization Behavior of Polypropylene","volume":"87","author":"Valentini","year":"2003","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_18","unstructured":"Kelton, K.F., and Greer, A.L. (2010). Nucleation in Condensed Matter: Applications in Materials and Biology, Pergamon."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2246","DOI":"10.1021\/acs.macromol.3c02632","article-title":"Fiber-Induced Crystallization in Elongational Flows","volume":"57","author":"Looijmans","year":"2024","journal-title":"Macromolecules"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"123134","DOI":"10.1016\/j.molliq.2023.123134","article-title":"Monte Carlo Simulation of the Crystallization of Polyethylene Nanocomposites with Different Shape Nanofillers","volume":"390","author":"Rueangsri","year":"2023","journal-title":"J. Mol. Liq."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Samanta, P., Liu, C.L., Nandan, B., and Chen, H.L. (2018). Crystallization of Polymers in Confined Space. Crystallization in Multiphase Polymer Systems, Elsevier Inc.","DOI":"10.1016\/B978-0-12-809453-2.00013-X"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1016\/j.ccr.2010.02.017","article-title":"Polymer Crystallization of Ultrathin Films on Solid Substrates","volume":"254","author":"Liu","year":"2010","journal-title":"Coord. Chem. Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"102","DOI":"10.4028\/www.scientific.net\/AMR.466-467.102","article-title":"Study on the Crystallization Kinetics of Polymer Thin Films","volume":"466\u2013467","author":"Ren","year":"2012","journal-title":"Adv. Mater. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ezquerra, T.A., and Nogales, A. (2020). Crystallization of Polymers Under 1D Confinement. Crystallization as Studied by Broadband Dielectric Spectroscopy, Springer.","DOI":"10.1007\/978-3-030-56186-4"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Rahman, M.U., Xi, Y., Li, H., Chen, F., Liu, D., and Wei, J. (2021). Dynamics and Structure Formation of Confined Polymer Thin Films Supported on Solid Substrates. Polymers, 13.","DOI":"10.3390\/polym13101621"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yang, J., Chen, Y., Yang, Z., Dai, L., Choi, H., and Meng, Z. (2024). Unveiling the Nanoconfinement Effect on Crystallization of Semicrystalline Polymers Using Coarse-Grained Molecular Dynamics Simulations. Polymers, 16.","DOI":"10.3390\/polym16081155"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1021\/mz300641x","article-title":"Crystallization of Thin Polymer Layers Confined between Two Adsorbing Walls","volume":"2","author":"Vanroy","year":"2013","journal-title":"ACS Macro Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4059","DOI":"10.1016\/j.polymer.2013.05.029","article-title":"Confinement Effects on Polymer Crystallization: From Droplets to Alumina Nanopores","volume":"54","author":"Michell","year":"2013","journal-title":"Polymer"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF00657416","article-title":"Determination of Nucleation Rate in Polymers Using Isothermal Crystallization Experiments and Computer Simulation","volume":"271","author":"Billon","year":"1993","journal-title":"Colloid. Polym. Sci"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1007\/BF00659278","article-title":"Transcrystallinity Effects in Thin Polymer Films. Experimental and Theoretical Approach","volume":"272","author":"Billon","year":"1994","journal-title":"Colloid. Polym. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"126748","DOI":"10.1016\/j.physa.2021.126748","article-title":"Connection between Phantom and Spatial Correlation in the Kolmogorov\u2013Johnson\u2013Mehl\u2013Avrami-Model: A Brief Review","volume":"590","author":"Tomellini","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.eurpolymj.2015.10.001","article-title":"Simulating Polymer Crystallization in Thin Films: Numerical and Analytical Methods","volume":"73","author":"Durin","year":"2015","journal-title":"Eur. Polym. J."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Stauffer, D., and Aharony, A. (2003). Introduction to Percolation Theory, Taylor & Francis. [2nd ed.].","DOI":"10.1016\/B0-12-227410-5\/00550-0"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1007\/BF01496926","article-title":"Overall Crystallization Kinetics of Thin Polymer Films. General Theoretical Approach. I. Volume Nucleation","volume":"267","author":"Billon","year":"1989","journal-title":"Colloid. Polym. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1007\/BF01524369","article-title":"Isothermal Crystallization Kinetics in a Limited Volume. A Geometrical Approach Based on Evans\u2019 Theory","volume":"267","author":"Billon","year":"1989","journal-title":"Colloid. Polym. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1021\/acsmacrolett.3c00146","article-title":"Molecular Simulations of Controlled Polymer Crystallization in Polyethylene","volume":"12","author":"Fall","year":"2023","journal-title":"ACS Macro Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"908","DOI":"10.59277\/RomRepPhys.2025.77.908","article-title":"Exploring Polymer Crystallization Through Monte Carlo Simulations: An Educational Perspective","volume":"77","author":"Berlic","year":"2025","journal-title":"Rom. Rep. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4657","DOI":"10.1016\/S0032-3861(02)00316-6","article-title":"Structure of Polymers in the Vicinity of Convex Impenetrable Surfaces: The Athermal Case","volume":"43","author":"Ozmusul","year":"2002","journal-title":"Polymer"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21014\/acta_imeko.v11i2.1206","article-title":"Monte Carlo-Based 3D Surface Point Cloud Volume Estimation by Exploding Local Cubes Faces","volume":"11","author":"Covre","year":"2022","journal-title":"Acta IMEKO"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1002\/app.21802","article-title":"Spherulitic Structure Development during Crystallization in Confined Space II. Effect of Spherulite Nucleation at Borders","volume":"97","author":"Piorkowska","year":"2005","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_41","first-page":"20","article-title":"Segmented: An R Package to Fit Regression Models with Broken-Line Relationships","volume":"8","author":"Muggeo","year":"2008","journal-title":"R News"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"107299","DOI":"10.1016\/j.sigpro.2019.107299","article-title":"Selective Review of Offline Change Point Detection Methods","volume":"167","author":"Truong","year":"2020","journal-title":"Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.progpolymsci.2015.10.007","article-title":"Confined Crystallization of Polymeric Materials","volume":"54\u201355","author":"Michell","year":"2016","journal-title":"Prog. Polym. Sci."},{"key":"ref_44","unstructured":"Lin, G. (2005). Volume Computation Using a Direct Monte Carlo Method. Proceedings of the Computing and Combinatorics, Springer."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Allen, M.P., and Tildesley, D.J. (2017). Computer Simulation of Liquids, Oxford University Press.","DOI":"10.1093\/oso\/9780198803195.001.0001"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Frenkel, D., and Smit, B. (2002). Understanding Molecular Simulation: From Algorithms to Applications, Academic Press.","DOI":"10.1016\/B978-012267351-1\/50005-5"},{"key":"ref_47","unstructured":"Bevington, P.R., and Robinson, D.K. (2003). Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill."},{"key":"ref_48","first-page":"355","article-title":"On the Statistical Theory of Crystallization of Metals","volume":"1","author":"Kolmogorov","year":"1937","journal-title":"Bull. Acad. Sci. USSR Math. Ser."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"014206","DOI":"10.1103\/PhysRevB.78.014206","article-title":"Impingement Factor in the Case of Phase Transformations Governed by Spatially Correlated Nucleation","volume":"78","author":"Tomellini","year":"2008","journal-title":"Phys. Rev. B Condens. Matter Mater. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1412","DOI":"10.1002\/polb.23577","article-title":"Crystallization and Orientation of Isotactic Poly(Propylene) in Cylindrical Nanopores","volume":"52","author":"Reid","year":"2014","journal-title":"J. Polym. Sci. B Polym. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"247802","DOI":"10.1103\/PhysRevLett.97.247802","article-title":"Confinement Effects in Polymer Crystal Nucleation from the Bulk to Few-Chain Systems","volume":"97","author":"Massa","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Yu, C., Xie, Q., Bao, Y., Shan, G., and Pan, P. (2017). Crystalline and Spherulitic Morphology of Polymers Crystallized in Confined Systems. Crystals, 7.","DOI":"10.3390\/cryst7050147"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"101725","DOI":"10.1016\/j.progpolymsci.2023.101725","article-title":"Crystallization in Thin Films of Polymer Glasses: The Role of Free Surfaces, Solid Interfaces and Their Competition","volume":"144","author":"Yang","year":"2023","journal-title":"Prog. Polym. Sci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"175304","DOI":"10.1063\/1.4919725","article-title":"Modeling Interface-Controlled Phase Transformation Kinetics in Thin Films","volume":"117","author":"Pang","year":"2015","journal-title":"J. Appl. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"122734","DOI":"10.1016\/j.polymer.2020.122734","article-title":"Competition between Nucleation and Confinement in the Crystallization of Poly(Ethylene Glycol)\/Large Aspect Ratio Hectorite Nanocomposites","volume":"202","author":"Habel","year":"2020","journal-title":"Polymer"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1021\/acs.macromol.0c02585","article-title":"Crystallization of Poly(Methyl Methacrylate) Stereocomplexes under Cylindrical Nanoconfinement","volume":"54","author":"Lin","year":"2021","journal-title":"Macromolecules"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"9953","DOI":"10.1021\/acsami.9b21391","article-title":"Impact of Nanoconfinement on Polylactide Crystallization and Gas Barrier Properties","volume":"12","author":"Delpouve","year":"2020","journal-title":"ACS Appl. Mater. Interfaces"}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/7\/840\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:46:41Z","timestamp":1774878401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/7\/840"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,30]]},"references-count":57,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["polym18070840"],"URL":"https:\/\/doi.org\/10.3390\/polym18070840","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,30]]}}}