Rheologica Acta

, Volume 57, Issue 1, pp 57–70 | Cite as

An empirical constitutive model for complex glass-forming liquids using bitumen as a model material

  • Olli-Ville Laukkanen
  • H. Henning Winter
  • Hilde Soenen
  • Jukka Seppälä
Original Contribution


While extensive research efforts have been devoted to understand the dynamics of chemically and structurally simple glass-forming liquids (SGFLs), the viscoelasticity of chemically and structurally complex glass-forming liquids (CGFLs) has received only little attention. This study explores the rheological properties of CGFLs in the vicinity of the glass transition. Bitumen is selected as the model material for CGFLs due to its extremely complex chemical composition and microstructure, fast physical aging and thermorheological simplicity, and abundant availability. A comprehensive rheological analysis reveals a significant broadening of the glass transition dynamics in bitumen as compared to SGFLs. In particular, the relaxation time spectrum of bitumen is characterized by a broad distribution of long relaxation modes. This observation leads to the development of a new constitutive equation, named the broadened power-law spectrum model. In this model, the wide distribution of long relaxation times is described by a power-law with positive exponent and a stretched exponential cut-off, with parameter β serving as a measure of the broadness of the distribution. This characteristic shape of the bitumen spectrum is attributed to the heterogeneous freezing of different molecular components of bitumen, i.e., to the coexistence of liquid and glassy micro-phases. Furthermore, as this type of heterogeneous glass transition behavior can be considered as a general feature of complex glass-forming systems, the broadened power-law spectrum model is expected to be valid for all types of CGFLs. Examples of the applicability of this model in various complex glass-forming systems are given.


Glass transition Glass-forming liquids Linear viscoelasticity Relaxation time spectrum Bitumen 



O.V.L. thanks the Vilho, Yrjö, and Kalle Väisälä Foundation and Nynas AB for financial support. The authors also gratefully acknowledge technical support from Malvern Instruments Ltd. The rheological data of sucrose benzoate, m-toluidine, and glycerol were kindly provided by Prof. Gregory McKenna (Texas Tech), and the rheological data of tetraphenyl-tetramethyl-trisiloxane (DC704), 1,2-propanediol and pentaphenyl-trimethyl-trisiloxane (DC705) were retrieved from the data repository of the Glass and Time group at Roskilde University (

Supplementary material

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ESM 1 (PDF 738 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017
corrected publication January/2018

Authors and Affiliations

  • Olli-Ville Laukkanen
    • 1
    • 2
  • H. Henning Winter
    • 1
  • Hilde Soenen
    • 3
  • Jukka Seppälä
    • 2
  1. 1.Department of Polymer Science and Engineering and Department of Chemical EngineeringUniversity of MassachusettsAmherstUSA
  2. 2.Department of Chemical and Metallurgical Engineering, School of Chemical EngineeringAalto UniversityAaltoFinland
  3. 3.Nynas NVAntwerpBelgium

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