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Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.

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Title: Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.
Authors: Itriago, J.1,2 (AUTHOR), Pradille, C.3 (AUTHOR), Laure, P.1,4 (AUTHOR), Peuvrel‐Disdier, E.1 (AUTHOR) edith.peuvrel‐disdier@minesparis.psl.eu, Fabre, V.2 (AUTHOR), Bujeau, B.2 (AUTHOR)
Source: Polymer Engineering & Science. Jun2026, Vol. 66 Issue 6, p3961-3973. 13p.
Subjects: Vulcanization, Chemical kinetics, Porosity, Finite element method, Crosslinking (Polymerization), Foamed materials, Gases, Blowing agents
Abstract: A key issue in the modeling of the chemical foaming of rubbers is the description of the foam density evolution. This modeling must combine both a comprehensive physical description of the process and sufficient robustness and simplicity to be used in finite element computation software dedicated to reactive fluid injection. With this in mind, a simple model based on the kinetics of vulcanization and decomposition of the blowing agent was developed to simulate the chemical foaming process in rubbers. The kinetic parameters were identified by fitting the experimental data obtained using standard techniques (RPA, DSC) to autocatalytic models. In this model, the total foam volume is assumed to be the sum of the contributions from the rubber matrix and the gas bubbles it contains. The gas content of the system mainly depends on the extent to which the blowing agent decomposes. Free‐foaming dilatometry experiments under controlled non‐isothermal conditions were used to identify and validate the model. Agreement between the experimental data and the model predictions can be achieved by adjusting two parameters difficult to measure experimentally: Henry's constant, which represents the amount of dissolved gas in the rubber; and the gel point, which defines an upper limit for bubble growth. Highlights: Kinetic‐based model developed to predict the chemical foaming of rubbers.Foaming heat rate dependence explained by curing & gas generation balance.Gel point defined as an upper limit for bubble growth.Design of original free‐foaming experiments to validate the model.Additional source of gases (volatiles) in free‐foaming conditions.Experiment‐prediction agreement after adjusting gas solubility and gel point. [ABSTRACT FROM AUTHOR]
Copyright of Polymer Engineering & Science is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.
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  Data: <searchLink fieldCode="AR" term="%22Itriago%2C+J%2E%22">Itriago, J.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Pradille%2C+C%2E%22">Pradille, C.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Laure%2C+P%2E%22">Laure, P.</searchLink><relatesTo>1,4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Peuvrel‐Disdier%2C+E%2E%22">Peuvrel‐Disdier, E.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> edith.peuvrel‐disdier@minesparis.psl.eu</i><br /><searchLink fieldCode="AR" term="%22Fabre%2C+V%2E%22">Fabre, V.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Bujeau%2C+B%2E%22">Bujeau, B.</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Polymer+Engineering+%26+Science%22">Polymer Engineering & Science</searchLink>. Jun2026, Vol. 66 Issue 6, p3961-3973. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Vulcanization%22">Vulcanization</searchLink><br /><searchLink fieldCode="DE" term="%22Chemical+kinetics%22">Chemical kinetics</searchLink><br /><searchLink fieldCode="DE" term="%22Porosity%22">Porosity</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Crosslinking+%28Polymerization%29%22">Crosslinking (Polymerization)</searchLink><br /><searchLink fieldCode="DE" term="%22Foamed+materials%22">Foamed materials</searchLink><br /><searchLink fieldCode="DE" term="%22Gases%22">Gases</searchLink><br /><searchLink fieldCode="DE" term="%22Blowing+agents%22">Blowing agents</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: A key issue in the modeling of the chemical foaming of rubbers is the description of the foam density evolution. This modeling must combine both a comprehensive physical description of the process and sufficient robustness and simplicity to be used in finite element computation software dedicated to reactive fluid injection. With this in mind, a simple model based on the kinetics of vulcanization and decomposition of the blowing agent was developed to simulate the chemical foaming process in rubbers. The kinetic parameters were identified by fitting the experimental data obtained using standard techniques (RPA, DSC) to autocatalytic models. In this model, the total foam volume is assumed to be the sum of the contributions from the rubber matrix and the gas bubbles it contains. The gas content of the system mainly depends on the extent to which the blowing agent decomposes. Free‐foaming dilatometry experiments under controlled non‐isothermal conditions were used to identify and validate the model. Agreement between the experimental data and the model predictions can be achieved by adjusting two parameters difficult to measure experimentally: Henry's constant, which represents the amount of dissolved gas in the rubber; and the gel point, which defines an upper limit for bubble growth. Highlights: Kinetic‐based model developed to predict the chemical foaming of rubbers.Foaming heat rate dependence explained by curing & gas generation balance.Gel point defined as an upper limit for bubble growth.Design of original free‐foaming experiments to validate the model.Additional source of gases (volatiles) in free‐foaming conditions.Experiment‐prediction agreement after adjusting gas solubility and gel point. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Polymer Engineering & Science is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1002/pen.70455
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 13
        StartPage: 3961
    Subjects:
      – SubjectFull: Vulcanization
        Type: general
      – SubjectFull: Chemical kinetics
        Type: general
      – SubjectFull: Porosity
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Crosslinking (Polymerization)
        Type: general
      – SubjectFull: Foamed materials
        Type: general
      – SubjectFull: Gases
        Type: general
      – SubjectFull: Blowing agents
        Type: general
    Titles:
      – TitleFull: Development and Validation of a Simple Kinetic‐Based Model to Simulate the Chemical Foaming Process During Rubber Vulcanization.
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            NameFull: Itriago, J.
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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