On the Role of Internal Degrees of Freedom in Structural Relaxation of Ring-Tail Structured Liquids Across Temperature Regimes

TL;DR

The paper investigates how anisotropic rotation and internal molecular flexibility shape structural relaxation in simple ring-tail liquids, using a triad of DDLS, $^2$H NMR, and MD simulations on $1$-phenylalkanes with varying chain lengths. It identifies a robust, moiety-specific origin of bimodal DDLS relaxation: fast phenyl-ring rotation and slow end-to-end reorientation, aligned with NMR timescales and corroborated by MD-derived susceptibilities. As the temperature decreases into the supercooled regime, these moieties exhibit increasing cooperativity, causing the two relaxation processes to converge and the spectrum to resemble the generic shape observed near the glass transition. The results provide a mechanistic link between molecular-level motions and macroscopic relaxation spectra, with implications for understanding spectral shapes in other molecular liquids with comparable complexity.

Abstract

We investigate how anisotropic molecular rotation and internal molecular flexibility influence liquid dynamics in 1-phenylalkanes. To this end, we combine depolarized dynamic light scattering, nuclear magnetic resonance spectroscopy and molecular dynamics simulations. Our results show that anisotropic rotations and internal molecular flexibility substantially contribute to structural relaxation in the liquid state. However, their influence diminishes on entering the supercooled-liquid regime, where the relaxation behavior develops towards the previously identified generic relaxation shape, likely due to the increasing cooperativity of rotational dynamics. Because 1-phenylalkanes are simple model systems with similarities to many other molecular liquids, this study suggests that effects of anisotropic rotation and internal flexibility are relevant in various liquids with similar molecular complexity, and provides a proof of concept for how these effects can be identified.

Figures (7)

• Figure 1: Structural formula of 1-phenyloctane ($n=8$). In the present MD simulations, we calculate rotational correlation functions for the end-to-end vector (blue), the C--H bond vectors of the alkyl chain (CH-chain, pink), and the C--H bond vectors of the phenyl ring (CH-ring, green).
• Figure 2: DDLS spectra of 1-phenylalkanes of varying length of the alkyl chain $n$ normalized to their maximum amplitude and mildly shifted in frequency for a detailed comparison of the peak shape. The temperatures of the measurements were chosen such that the peak frequencies amounted to $\sim$1.5 GHz for all studied samples (see text for details).
• Figure 3: a) DDLS spectrum of 1-phenyloctane ($n=8$) at 300 K. The solid orange curve is the total fit function developed in a previous workzeissler2023influence and described in the text, while the solid blue and green curves are the two involved contributions. The vertical dashed line marks the frequency corresponding to the $^2$H NMR timescale. Moreover, dynamical susceptibilities, which were obtained from Fourier-Laplace transformation of second rank orientational correlation functions from MD simulations and shifted along the frequency axis as described in the text, are included. The results for the end-to-end vector (MD end-to-end) and the C--H bonds of the phenyl ring (MD CH-ring) are shown as black dashed and dashed-dotted lines, respectively. The dotted curve represents the superposition of the scaled MD susceptibilities (see text). b) Mean relaxation times of the slow (solid blue dots) and the fast (solid green triangles) contribution to the DDLS relaxation peak together with mean rotational correlation times from $^{2}$H NMR (solid red squares) and MD simulations (open symbols).
• Figure 4: a) Second rank orientational correlation functions of different intramolecular vectors for $n=8$ at 300$\,$K from MD simulations. The data are shown on a reduced time scale $t/\tau_\text{e}$, where $\tau_\text{e}$ is the rotational correlation time of the end-to-end vector. The considered vectors are visualized in Fig. \ref{['fig:figure1']}. While the data for the phenyl ring (CH-ring) represents the average over all C--H bond vectors in this molecular moiety, we discriminate between C--H bond vectors at various positions along the alkyl tail. Specifically, we show results for bonds in the first (CH-chain-1) and the seventh (CH-chain-7) CH$_2$ unit of the tail, counting from the phenyl ring. b) The same second rank orientational correlation functions of the artificially stiffened molecule for $n=8$ at 300 K.
• Figure 5: DDLS spectra for $n=4$ (a) and $n=6$ (b) from temperatures close to the glass transition up to temperatures far above the melting point (see text). Dashed curves represent fits to the peak regions by the Cole-Davidson model.