Non-exponential relaxation without dynamic heterogeneity in van der Waals liquids above the melting point

Technical Summary: Non-exponential Relaxation without Dynamic Heterogeneity in van der Waals Liquids above the Melting Point

Problem Statement
The prevailing view of rotational dynamics in molecular glass formers suggests a transition from homogeneous dynamics at high temperatures to increasingly heterogeneous dynamics as the liquid cools toward the glass transition temperature ($T_g$). This growing dynamic heterogeneity is widely believed to manifest as the stretching of orientational correlation functions, quantified by the stretching parameter $\beta$ (where $\beta < 1$ indicates non-exponential decay). While compelling evidence supports the purely heterogeneous scenario near $T_g$, experimental results above the melting point ($T_m$) present a contradiction: many liquids exhibit pronounced, temperature-independent non-exponential relaxation ($\beta_{hi} < 1$) well above $T_m$, yet do not show the expected crossover to simple exponential dynamics. The central question addressed is whether this non-exponential relaxation in the liquid regime is inherent to the local molecular properties or if it arises from a form of dynamic heterogeneity that persists at high temperatures.

Methodology
The authors employed depolarized dynamic light scattering (DDLS) to investigate the spectral shape of structural relaxation in van der Waals liquids above their melting points. The study utilized a multipass tandem Fabry-Perot interferometer and a double monochromator to cover frequencies from ~200 MHz to 5 THz.

The experimental design focused on comparing the relaxation behavior of optically anisotropic probe molecules in two states:

1. Bulk: Pure liquids of the probe molecules.
2. Dilution: The probe molecules diluted in an optically isotropic solvent, carbon tetrachloride ($CCl_4$).

Three specific scenarios were tested to probe the origin of relaxation stretching:

• Single-component liquids: Diethyl phthalate (DEP), tributyl phosphate (TBP), and n-tridecane (C13). These were chosen because they exhibit distinct, temperature-independent non-exponential relaxation shapes in bulk but lack internal degrees of freedom or size distributions that would inherently cause heterogeneity.
• Probe molecules with internal degrees of freedom: 1-phenyltridecane (P13), which exhibits bimodal relaxation due to internal ring rotation, serving as a system with explicit intramolecular dynamic heterogeneity.
• Probe molecules with size distributions: Binary and tertiary mixtures of n-tetradecane (C14) and n-heptane (C7), creating a system with explicit intermolecular dynamic heterogeneity due to varying molecular weights and mobilities.

Measurements were conducted at 300 K, a temperature moderately above the melting points of the selected liquids, to ensure reproducible conditions without the need for cryostats.

Key Results

1. Single-Component Liquids (DEP, TBP, C13):

   • Upon dilution with $CCl_4$ (up to molar fractions of 0.99), the spectral shape of the relaxation peak for these probe molecules remained indistinguishable from their pure bulk forms.
   • While the amplitude of the relaxation peak decreased relative to the vibrational background, the width parameter ($\beta_{CD}$) and the overall asymmetric broadening were preserved.
   • Subtraction of the $CCl_4$ contribution confirmed that the relaxation shape of the probe molecules was invariant to the change in local environment.

2. Systems with Explicit Heterogeneity (P13 and Alkane Mixtures):

   • P13 (Intramolecular): Dilution significantly altered the relaxation shape. The separation between the fast (ring rotation) and slow (whole molecule) contributions decreased, indicating that the relaxation shape is sensitive to the solvent concentration when internal dynamic heterogeneity is present.
   • Alkane Mixtures (Intermolecular): In mixtures of C14 and C7, the relaxation peak was already broader than in pure C14 due to the distribution of molecular sizes. Upon further dilution with $CCl_4$, the relaxation peak broadened even more, and the width parameter $\beta_{CD}$ decreased significantly (from 0.85 for pure C14 to 0.52 for the highly diluted mixture). This demonstrates that when a distribution of relaxation times exists, dilution sensitively affects the spectral shape.

Key Contributions and Claims
The paper provides experimental evidence that challenges the assumption that non-exponential relaxation above the melting point is solely a symptom of dynamic heterogeneity.

• Negligible Influence of Dynamic Heterogeneity: The authors conclude that for single-component van der Waals liquids above $T_m$, dynamic heterogeneity has a negligible influence on rotational dynamics. The fact that dilution does not alter the relaxation shape implies that the observed stretching is not caused by a distribution of relaxation times arising from spatial heterogeneity in the solvent environment.
• Intrinsic Origin of Stretching: The results suggest that the non-exponential character ($\beta < 1$) in these liquids reflects intrinsic properties of the individual molecules, such as molecular shape and internal flexibility, rather than collective heterogeneous dynamics.
• Mechanism Change between $T_g$ and $T_m$: The findings imply a drastic change in the relaxation mechanism between the deeply supercooled regime and the liquid regime. While the heterogeneous scenario (distinct sub-ensembles with mono-exponential decay) likely holds near $T_g$, the liquid regime above $T_m$ appears to be effectively homogeneous, with the stretching being an inherent property of the correlation decay itself.
• Orientational Cross-Correlations: The independence of the relaxation shape from solvent concentration also suggests that orientational cross-correlations (dipole-dipole interactions) have a negligible influence on the DDLS spectra of these specific liquids above $T_m$, as such correlations would be expected to be suppressed by dilution.

Significance
The paper argues that the asymmetrically broadened relaxation peaks observed above the melting point are not necessarily indicators of dynamic heterogeneity that vanishes at high temperatures. Instead, they may purely reflect specific molecular properties. This distinction is crucial for understanding the transition from liquid to glassy dynamics, suggesting that the "simple liquid" limit (mono-exponential decay) may not be reached simply by increasing temperature, but rather that the nature of the relaxation mechanism itself changes between $T_g$ and $T_m$. The authors propose that the transition from heterogeneous dynamics near $T_g$ to homogeneous dynamics with inherent stretching at high temperatures is a fundamental feature of molecular glass formers.