A Thermodynamic Resolution of Molecular Clustering: Eliminating Sticking Efficiency

A Thermodynamic Resolution of Molecular Clustering: Eliminating Sticking Efficiency | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Thermodynamic Resolution of Molecular Clustering: Eliminating Sticking Efficiency Nick Eaves This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6747999/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract In gas-phase chemistry, forward and reverse rates are governed by Gibbs free energy to ensure equilibrium. Yet in molecular clustering models, particularly for low or negative $\Delta G$ associations, reverse rates are often neglected and replaced with an empirical “sticking efficiency” $\eta$. This substitution violates thermodynamic consistency. We present a parameter-free framework in which equilibrium and dynamics emerge from microscopic reversibility and statistical mechanics. Applied to argon dimer formation—a chemically inert system with no free parameters, the model reproduces both transient and equilibrium behavior without approximation. Post hoc computation of $\eta$ reveals that it becomes negative and collapses to zero at equilibrium, exposing a structural failure in the parameter when reversibility is restored. This result is not merely theoretical. Climate models rely on molecular clustering to simulate black carbon and secondary organic aerosol formation, key drivers of radiative forcing. Models using $\eta$ inherit its inconsistencies. This framework offers a thermodynamically grounded and general replacement. Physical sciences/Chemistry/Physical chemistry/Thermodynamics Physical sciences/Chemistry/Theoretical chemistry/Statistical mechanics microscopic reversibility emergent kinetics sticking efficiency argon dimer molecular clustering statistical mechanics reversible dynamics Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6747999","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":463254809,"identity":"bb022aff-deec-41a1-8f03-2d465613c3fe","order_by":0,"name":"Nick Eaves","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABB0lEQVRIiWNgGAWjYDACZiBkKIBzbUAiDBKEtRjAuWlEaGFA1XIYTOLVYs7O/Njgg4GdPQN78zOJD3/OJ244znvw5o+Kewz87QewarFsZjNOnGGQnNjAc8xMcmbb7cQNh/mSrXnOFDNInEnAqsXgMA/zYR4D5gQGiQRjY96G24nbDvOYSTO2JQBdi1dLvT2D/PPPxn/+nANrkfwJ0sL/AKeWZB6Dw4wNEjyGjxnYDoC1SPCCtEjgsoXN2HCGwfHENp6cwoe9bcnG+w/zGAP9ksAjcQOHLecPP5b4UFFtz89+fMOBH3/sZGf2nzEEhliCHH8/dlvggA1dgAe/+lEwCkbBKBgF+AAAMD9WMce0GbgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-5165-1183","institution":"University of Windsor","correspondingAuthor":true,"prefix":"","firstName":"Nick","middleName":"","lastName":"Eaves","suffix":""}],"badges":[],"createdAt":"2025-05-26 07:15:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6747999/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6747999/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94986936,"identity":"37e18bd2-aec8-45d0-88d4-d8fc3010f194","added_by":"auto","created_at":"2025-11-03 07:00:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1549892,"visible":true,"origin":"","legend":"Article File","description":"","filename":"NatureStatMechClustering.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6747999/v1_covered_a91957df-b7e7-4787-931a-f9affbe5346d.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A Thermodynamic Resolution of Molecular Clustering: Eliminating Sticking Efficiency","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"microscopic reversibility, emergent kinetics, sticking efficiency, argon dimer, molecular clustering, statistical mechanics, reversible dynamics","lastPublishedDoi":"10.21203/rs.3.rs-6747999/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6747999/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In gas-phase chemistry, forward and reverse rates are governed by Gibbs free energy to ensure equilibrium. Yet in molecular clustering models, particularly for low or negative $\\Delta G$ associations, reverse rates are often neglected and replaced with an empirical “sticking efficiency” $\\eta$. This substitution violates thermodynamic consistency.\r\n\r\nWe present a parameter-free framework in which equilibrium and dynamics emerge from microscopic reversibility and statistical mechanics. Applied to argon dimer formation—a chemically inert system with no free parameters, the model reproduces both transient and equilibrium behavior without approximation. Post hoc computation of $\\eta$ reveals that it becomes negative and collapses to zero at equilibrium, exposing a structural failure in the parameter when reversibility is restored.\r\n\r\nThis result is not merely theoretical. Climate models rely on molecular clustering to simulate black carbon and secondary organic aerosol formation, key drivers of radiative forcing. Models using $\\eta$ inherit its inconsistencies. 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