[Paper Review] Modeling the nonlinear dielectric response of glass formers

U. Buchenau|arXiv (Cornell University)|Dec 1, 2015

Material Dynamics and Properties4 citations

TL;DR

This paper proposes a pragmatic model combining asymmetric double-well potentials with finite lifetime dynamics to describe the nonlinear dielectric response in glass-forming liquids. By distinguishing between cooperative, back-and-forth jumps (retardation) and irreversible viscous jumps (no-return), the model quantitatively explains nonlinear ω- and 3ω-data in glycerol and propylene carbonate, resolving inconsistencies in prior models and showing that the absence of the Onsager factor in 3ω signals arises from viscous effects rather than experimental artifacts.

ABSTRACT

The recently developed pragmatical model of asymmetric double-well potentials with a finite lifetime is applied to nonlinear dielectric data in polar undercooled liquids. The viscous effects from the finite lifetime provide a crossover from the cooperative jumps of many molecules at short times to the motion of statistically independent molecules at long times. The model allows to determine the size of cooperatively rearranging regions from nonlinear ω-data and throws a new light on a known inconsistency between nonlinear ω and 3ω-signals for glycerol and propylene carbonate.

Motivation & Objective

• To resolve the long-standing inconsistency between nonlinear ω and 3ω dielectric signals in glycerol and propylene carbonate, which previous models failed to explain quantitatively.
• To develop a unified theoretical framework that accounts for both cooperative rearrangements at short times and independent molecular motion at long times in undercooled liquids.
• To incorporate viscous effects via finite lifetime dynamics into the asymmetric double-well potential model, enabling a quantitative description of nonlinear dielectric spectra.
• To clarify why the Onsager factor is absent in 3ω responses of glycerol and propylene carbonate despite its presence in similar measurements on 1-propanol.
• To provide a physically consistent alternative to the 'box model' by linking energy storage to thermally activated jumps in asymmetric double wells with finite lifetimes.

Proposed method

• The model extends Diezemann’s equations for nonlinear response in asymmetric double-well potentials to include viscous effects through a finite lifetime of the potential wells.
• It distinguishes two components: a retardation component (cooperative, back-and-forth jumps) and a viscous component (irreversible, no-return jumps) that occur at the end of the retardation potential lifetime.
• The relaxation time of the viscous component is set to the terminal dielectric relaxation time, which is significantly longer in monoalcohols than in simple molecular glass formers.
• The average asymmetry of the double-well potential is adjusted to match the low-frequency limit of the dielectric response, ensuring consistency with the Onsager factor for single-molecule polarization.
• The model uses the Langevin function with an effective dipole moment and Onsager field correction to describe the low-frequency saturation behavior of the dielectric response.
• Nonlinear response is calculated for the ω and 3ω harmonics, with the viscous contribution dominating at low frequencies and the retardation contribution at high frequencies.

Experimental results

Research questions

• RQ1 Why do glycerol and propylene carbonate exhibit a strong 3ω signal without the expected Onsager factor, while 1-propanol shows the Onsager factor in its 3ω response?
• RQ2 How can the nonlinear dielectric response at ω and 3ω frequencies be consistently described within a single physical framework that accounts for both cooperative and independent molecular dynamics?
• RQ3 To what extent do viscous effects, modeled via finite lifetime of double-well potentials, explain the observed crossover from cooperative to independent molecular motion in dielectric relaxation?
• RQ4 Why does the 'box model' succeed qualitatively in predicting nonlinear ω-response but fail quantitatively in 3ω-response, and can this be explained by a more fundamental mechanism?
• RQ5 What is the role of the average asymmetry of double-well potentials in determining the nonlinear dielectric response, and how does it differ from a constant asymmetry distribution?

Key findings

• The model successfully describes the nonlinear ω-response in glycerol and propylene carbonate by combining retardation and viscous components, with the viscous contribution dominating at low frequencies.
• The absence of the Onsager factor in 3ω signals of glycerol and propylene carbonate is explained by the viscous component’s response, not by experimental error or missing physics.
• The average asymmetry of the double-well potential in the model is slightly larger than that for a constant distribution, indicating a non-uniform distribution of energy barriers.
• The model shows that the box model’s success in predicting ω-response is fortuitous, as it relies on a hidden proportionality between the jump angle and the number of cooperatively rearranging molecules.
• The 3ω response is qualitatively explained by the model, but quantitative agreement requires additional effects such as field-induced entropy reduction and saturation, which the box model alone cannot capture.
• The viscous component’s relaxation time is found to be about 100 times longer in monoalcohols like 2-ethyl-1-hexanol than in simple molecular glass formers, consistent with the observed transition from collective to single-molecule dynamics at low frequencies.