Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture

Area of Science:

• Materials Science
• Civil Engineering
• Polymer Science

Background:

• Polyurethane (PU) mixtures offer novel pavement solutions with distinct dynamic properties compared to traditional hot-mixed asphalt (HMA).
• Understanding the viscoelastic behavior of PU mixtures is crucial for their effective application in pavement engineering.

Purpose of the Study:

• To investigate the applicability of the Kramers-Kronig (K-K) relation and thermorheologically simple properties for PU mixtures.
• To evaluate the time-temperature superposition principle (TTSP) and various models for constructing dynamic modulus master curves.
• To characterize the viscoelastic properties of PU mixtures using advanced analytical techniques.

Main Methods:

• Analysis of dynamic properties of PU mixtures under varying temperatures and loading frequencies.
• Application of the time-temperature superposition principle (TTSP) using Standard Logistic Sigmoidal (SLS), Generalized Logistic Sigmoidal (GLS), and Havriliak-Negami (HN) models.
• Utilizing Hilbert integral transformed models and Kramers-Kronig (K-K) relations for phase angle and modulus prediction.
• Construction and analysis of core-core and black space diagrams.

Main Results:

• The PU mixture demonstrated thermorheologically simple behavior under tested conditions.
• TTSP was successfully applied to develop dynamic modulus master curves using SLS, GLS, and HN models.
• Hilbert transformed SLS and GLS models accurately fitted and predicted phase angle data.
• K-K relations proved applicable for PU mixtures, enabling master curve modeling for phase angle, storage modulus, and loss modulus.

Conclusions:

• The PU mixture exhibits thermorheologically simple properties, validating the use of TTSP for master curve development.
• The Kramers-Kronig relation is a viable tool for characterizing the viscoelastic behavior of PU mixtures.
• While effective within a range, the K-K relation has limitations in predicting phase angles at extreme temperatures from dynamic modulus data.