Mathematical modelling and thermodynamic parameters of total polyphenol extraction using ultrasound in Ilex guayusa Loes

Mathematical modelling and thermodynamic parameters of total polyphenol extraction using ultrasound in Ilex guayusa Loes | 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 Research Article Mathematical modelling and thermodynamic parameters of total polyphenol extraction using ultrasound in Ilex guayusa Loes Sting Brayan Luna-Fox, Elder Javier Calle-Cunyarache, Matteo Radice, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9457648/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigated the applicability of mathematical models to describe ultrasound-assisted extraction of total phenolic compounds (TPC) from Ilex guayusa leaves and determined thermodynamic parameters associated with the extraction process. The effect of temperature (40 to 80°C) and extraction time (5 to 60 min) on TPC yield was studied. Five non-linear models, including Peleg, Power law, Weibull parabolic diffusion, and Elovich models, were evaluated to determine their accuracy in the extraction process. The results indicated that the highest TPC concentration of 3.88 ± 0.44 g gallic acid equivalent/100 g dry weight was found at 60 min and 80°C. The Power law model presented the best fit with R 2 , adjusted R 2 , and predicted R 2 values greater than 0.98, describing a temperature-sensitive nonlinear diffusion kinetics (n ≈ 0.24–0.28) temperature sensitive. In addition, the mean square deviation, normalised mean square deviation and chi-square statistic values were less than 0.072, 2.126% and 0.209%, respectively. The thermodynamic parameters showed that the TPC extraction process was endothermic, spontaneous and controlled by diffusion with activation energy, enthalpy, entropy and Gibbs free energy values of 8.79 kJ/mol, 3.925 kJ/mol, 145.03 J/molK and − 47.271 kJ/mol, respectively. The findings provide key information for the design of efficient TPC extraction processes in I. guayusa , supporting its industrial application as a sustainable raw material. Extraction kinetics activation energy non-linear models power law Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted 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. 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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-9457648","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628916966,"identity":"b546f0f9-4961-4380-9c94-0a92a272947c","order_by":0,"name":"Sting Brayan Luna-Fox","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYFACxgYGhgo5HiDLAIiZidDBBtJyxpgkLSCL2owZiNciP7+57eHXeQYyDGKHtz1gqLBObGA/+wCvFoNjjO3GstsMeBik08oNGM6kJzbwpBvg18LG2CYtue0PUEuOmQRj2+HEBoY0Ag5rA2mZYwDV8g+ohf8ZAc8cY2yT/NgA09IA1CJBwBaDY4lt0gzHDHjYQH5JOJZu3CZBwBb55uPPJH/UGNjzSydve/Chxlq2n5+ALSDADIpHNhBKgDAIA8YfEJooxaNgFIyCUTACAQByXjpTn/U3CwAAAABJRU5ErkJggg==","orcid":"","institution":"Institute for Research in Materials Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Sting","middleName":"Brayan","lastName":"Luna-Fox","suffix":""},{"id":628916967,"identity":"9afbaed0-54ce-4af2-a36b-170e9123171d","order_by":1,"name":"Elder Javier Calle-Cunyarache","email":"","orcid":"","institution":"Dirección Regional Agraria de Cajamarca","correspondingAuthor":false,"prefix":"","firstName":"Elder","middleName":"Javier","lastName":"Calle-Cunyarache","suffix":""},{"id":628916968,"identity":"f8a25cb8-3cdb-4f6f-9a24-f842b55a4bf7","order_by":2,"name":"Matteo Radice","email":"","orcid":"","institution":"Universidad Estatal Amazónica","correspondingAuthor":false,"prefix":"","firstName":"Matteo","middleName":"","lastName":"Radice","suffix":""},{"id":628916969,"identity":"cbd31804-c758-4058-93ca-b83379b2f649","order_by":3,"name":"Yudel García-Quintana","email":"","orcid":"","institution":"Universidad Estatal Amazónica","correspondingAuthor":false,"prefix":"","firstName":"Yudel","middleName":"","lastName":"García-Quintana","suffix":""},{"id":628916970,"identity":"cce9e921-289a-43ce-84af-3281576f1b8d","order_by":4,"name":"Yasiel Arteaga-Crespo","email":"","orcid":"","institution":"Universidad Estatal Amazónica","correspondingAuthor":false,"prefix":"","firstName":"Yasiel","middleName":"","lastName":"Arteaga-Crespo","suffix":""}],"badges":[],"createdAt":"2026-04-18 19:08:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9457648/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9457648/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108181796,"identity":"b8c00814-993b-48d0-aeb8-47be8610230d","added_by":"auto","created_at":"2026-04-30 08:58:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":609252,"visible":true,"origin":"","legend":"","description":"","filename":"Text..pdf","url":"https://assets-eu.researchsquare.com/files/rs-9457648/v1_covered_82bc1943-6cd4-432c-a7b4-a6221c3ac596.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eMathematical modelling and thermodynamic parameters of total polyphenol extraction using ultrasound in \u003cem\u003eIlex guayusa\u003c/em\u003e Loes\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Extraction kinetics, activation energy, non-linear models, power law","lastPublishedDoi":"10.21203/rs.3.rs-9457648/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9457648/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigated the applicability of mathematical models to describe ultrasound-assisted extraction of total phenolic compounds (TPC) from \u003cem\u003eIlex guayusa\u003c/em\u003e leaves and determined thermodynamic parameters associated with the extraction process. The effect of temperature (40 to 80\u0026deg;C) and extraction time (5 to 60 min) on TPC yield was studied. Five non-linear models, including Peleg, Power law, Weibull parabolic diffusion, and Elovich models, were evaluated to determine their accuracy in the extraction process. The results indicated that the highest TPC concentration of 3.88\u0026thinsp;\u0026plusmn;\u0026thinsp;0.44 g gallic acid equivalent/100 g dry weight was found at 60 min and 80\u0026deg;C. The Power law model presented the best fit with R\u003csup\u003e2\u003c/sup\u003e, adjusted R\u003csup\u003e2\u003c/sup\u003e, and predicted R\u003csup\u003e2\u003c/sup\u003e values greater than 0.98, describing a temperature-sensitive nonlinear diffusion kinetics (n\u0026thinsp;\u0026asymp;\u0026thinsp;0.24\u0026ndash;0.28) temperature sensitive. In addition, the mean square deviation, normalised mean square deviation and chi-square statistic values were less than 0.072, 2.126% and 0.209%, respectively. The thermodynamic parameters showed that the TPC extraction process was endothermic, spontaneous and controlled by diffusion with activation energy, enthalpy, entropy and Gibbs free energy values of 8.79 kJ/mol, 3.925 kJ/mol, 145.03 J/molK and \u0026minus;\u0026thinsp;47.271 kJ/mol, respectively. The findings provide key information for the design of efficient TPC extraction processes in \u003cem\u003eI. guayusa\u003c/em\u003e, supporting its industrial application as a sustainable raw material.\u003c/p\u003e","manuscriptTitle":"Mathematical modelling and thermodynamic parameters of total polyphenol extraction using ultrasound in Ilex guayusa Loes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-28 13:57:07","doi":"10.21203/rs.3.rs-9457648/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"03c652bd-90a3-43b9-9528-94ca4954b3c4","owner":[],"postedDate":"April 28th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-28T13:57:07+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-28 13:57:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9457648","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9457648","identity":"rs-9457648","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}