# Model for the alpha and beta shear-mechanical properties of supercooled liquids and its comparison to squalane data

## TL;DR

This paper introduces a model for the shear response of supercooled liquids, specifically squalane, incorporating alpha and beta processes, and compares the model's predictions with experimental data across a wide frequency and temperature range.

## Contribution

The paper proposes a novel electrical equivalent-circuit model for supercooled liquids' shear response, including alpha and beta processes with Cole-Cole elements, and validates it against experimental data for squalane.

## Key findings

- Alpha relaxation time follows the shoving model.
- Beta relaxation peak frequency is nearly temperature independent.
- Beta compliance magnitude decreases significantly with cooling.

## Abstract

This paper presents data for supercooled squalane's frequency-dependent shear modulus covering frequencies from 10 mHz to 30 kHz and temperatures from 168 K to 190 K; measurements are also reported for the glass phase down to 146 K. The data reveal a strong mechanical beta process. A model is proposed for the shear response of supercooled liquids. The model is an electrical equivalent-circuit characterized by additivity of the dynamic shear compliances of the alpha and beta processes. The nontrivial parts of the alpha and beta processes are represented by a "Cole-Cole retardation element", resulting in the Cole-Cole compliance function well-known from dielectrics. The model, which assumes that the high-frequency decay of the alpha shear compliance loss varies with angular frequency as $\omega^{-1/2}$, has seven parameters. Assuming time-temperature superposition for the alpha and the beta processes separately, the number of parameters varying with temperature is reduced to four. From the temperature dependence of the best-fit model parameters the following conclusions are drawn: 1) the alpha relaxation time conforms to the shoving model; 2) the beta relaxation loss-peak frequency is almost temperature independent; 3) the alpha compliance magnitude, which in the model equals the inverse of the instantaneous shear modulus, is only weakly temperature dependent; 4) the beta compliance magnitude decreases by a factor of three upon cooling in the temperature range studied. The final part of the paper briefly presents measurements of the dynamic adiabatic bulk modulus covering frequencies from 10 mHz to 10 kHz in the temperature range 172 K to 200 K. The data are qualitatively similar to the shear data by having a significant beta process. A single-order-parameter framework is suggested to rationalize these similarities.