Linear-limit aging times of three monoalcohols

TL;DR

The study addresses whether physical aging in monoalcohols occurs on the timescale of the dielectric $\alpha$ relaxation or the Debye process. By applying single-parameter-aging (SPA), the authors extract the linear-limit aging function $R_{\rm lin}(t)$ from nonlinear temperature-jump data and determine the linear aging time $\tau_R$ via the Laplace transform. For two alcohols with well-separated Debye and $\alpha$ processes (2E1B and 5M2H), $\tau_R$ tracks the temperature dependence of the $\alpha$ relaxation rather than the Debye process; for 1P1P the Debye and $\alpha$ times are too close to allow a firm conclusion. The results suggest distinct origins for Debye cross-correlations in different systems and demonstrate that aging in these hydrogen-bonded liquids is often governed by the $\alpha$ process, with SPA providing a robust bridge from nonlinear aging data to linear-age dynamics.

Abstract

This paper presents data for the physical aging of the three monoalcohols 2-ethyl-1-butanol, 5-methyl-2-hexanol, and 1-phenyl-1-propanol. Aging is studied by monitoring the dielectric loss at a fixed frequency in the kHz range following temperature jumps of a few Kelvin's magnitude, starting from states of equilibrium. The three alcohols differ in the Debye relaxation strength and how much the Debye process is separated from the $α$ process. We first demonstrate that single-parameter aging describes all data well and proceed to utilize this fact to identify the linear-limit normalized aging relaxation functions. From the Laplace transform of these functions, the linear-limit aging loss-peak angular frequency defines the inverse of the linear aging relaxation time. This allows for a comparison to the temperature dependence of the Debye and $α$ dielectric relaxation times of the three monoalcohols. We conclude that the aging response for 5-methyl-2-hexanol and 2-ethyl-1-butanol follows the $α$ relaxation, not the Debye process, while no firm conclusion can be reached for 1-phenyl-1-propanol because its Debye and $α$ processes are too close to be reliably distinguished.

Figures (4)

• Figure 1: Equilibrium dielectric spectra at different temperatures of 2E1B, 5M2H, and 1P1P. The figure shows log-log plots of the imaginary part of the frequency-dependent dielectric constant, $\varepsilon"$, as a function of the frequency $\nu$. The insets show the molecular structures of each monoalcohol.
• Figure 2: Examples of dielectric loss peaks of 2E1B (green), 5M2H (orange), and 1P1P (blue). The Debye peak is marked by the letter D and the $\alpha$ peak by an $\alpha$. For 2E1B the latter is clearly visible, while it for 5M2H is manifested as a change of slope. In contrast, the 1P1P loss peak is asymmetric and looks much like those of typical non-monoalcohol organic glass formers nie09pab21. For 1P1P supplementary dynamic light scattering measurements have revealed the existence of separate Debye and $\alpha$ peaks, albeit close to each other boh14ahansen1997dynamics.
• Figure 3: Aging data and SPA analysis. The left panels show data for 2E1B, the middle panels for 5M2H, the right panels for 1P1P. (a)-(c) show data for the imaginary part of the dielectric susceptibility measured at the indicated frequency after a temperature jump at $t=0$. (d)-(f) show the normalized relaxation functions corresponding to the data of (a)-(c) defined by Eq. (\ref{['R_def']}). (g)-(i) show for each final temperature collapse of the different jump data when these are transformed into a linear aging relaxation function by means of Eq. (\ref{['recipe']}). This transformation involves the material-specific parameter, $c$, which for each liquid is determined to optimize the data collapse for jumps to the same temperature. (j)-(l) collapse the linear aging relaxation function for different target temperatures onto a single one by empirically rescaling the time axis. The data collapse seen here confirms time-temperature superposition, a prerequisite of the TN formalism and therefore also for SPA.
• Figure 4: Characteristic times $\tau$ plotted as functions of temperature for the three monoalcohols, including here also light-scattering data. The full symbols are defined as follows (compare the lower left corners): $\tau_R$ is the linear-limit aging time calculated as one over the loss-peak angular frequency of the Laplace transform of $R_{\rm lin}(t)$ determined from the nonlinear aging data by SPA via Eq. (\ref{['SPA']}) (though only visible upon magnification, the figure reports one point for each temperature jump); $\tau^{max}_\varepsilon$ is the inverse dielectric loss-peak angular frequency; $\tau^{\alpha}_\varepsilon$ is the dielectric $\alpha$ relaxation time estimated as the inverse dielectric loss-peak angular frequency (identified by visual inspection); the open symbols are data from the literature bauer2013debyeGabriel:2018aGabriel:2018Gabriel:2018cGabriel:2018a. For 2E1B and 5M2H the linear aging times follow the $\alpha$ times, not the Debye times, in their values and temperature dependencies. For 1P1P, which is characterized by an almost complete merging of the dielectric Debye and $\alpha$ processes (Fig. \ref{['fig1']}), it would be premature to conclude anything about the temperature dependence. We note, however, that the linear-limit aging times are closer to the Debye times than to the $\alpha$ times.