Heterogeneous dynamics, correlated time and length scales in ionic deep eutectics: Anion and temperature dependence

Breaking the Brownian barrier: models and manifestations of molecular diffusion in complex fluids

Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to molecular self-diffusion in fluids. The foundational principles of Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are insufficient for describing molecular diffusion, particularly in complex fluids characterized by intricate intermolecular interactions and hindered relaxation processes. This perspective delves into the nuanced behavior observed in diverse complex fluids, including molecular self-assembly systems, deep eutectic solvents, and ionic liquids, with a specific focus on modeling self-diffusion within these media. We explore the possibility of extending diffusion models to incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian model using non-local diffusion equations. Furthermore, we validate the applicability of these models by utilizing them to describe results from quasielastic neutron scattering and MD simulations.

Molecular dynamics insights into the dynamical behavior of structurally modified water in aqueous deep eutectic solvents (ADES)

Recent studies have demonstrated that the presence of water in deep eutectic solvents (DESs) significantly affects their dynamics, structure, and physical properties. Although the structural changes due to the addition of water are well understood, the microscopic dynamics of these changes have been rarely studied. Here, we performed molecular dynamics simulation of 30% (v/v) (∼0.57 molar fraction) water mixture of DES containing CH3CONH2 and NaSCN/KSCN at various salt fractions to understand the microscopic structure and dynamics of water. The simulated results reveal a heterogeneous environment for water molecules in aqueous DES (ADES), which is influenced by the nature of the cation. The diffusion coefficients of water in ADESs are significantly lower than that in neat water and concentrated aqueous NaSCN/KSCN solution. When Na+ ions are replaced by K+ ions in the ADES system, the diffusion coefficient increases, which is consistent with the measured nuclear magnetic resonance data. Self-dynamic structure factor for water and other simulated dynamic quantities, such as reorientation, hydrogen-bond, and residence time correlation functions, show markedly slower dynamics inside ADES than in the neat water and aqueous salt solution. Moreover, these dynamics become faster when Na+ ions in ADES are replaced by K+ ions. The results suggest that the structural environment of water in Na+-rich ADES is rigid due to the presence of cation-bound water and geometrically constrained water. The medium becomes less rigid as the KSCN fraction increases due to the relatively weaker interaction of K+ ions with water than Na+ ions, which accelerates the dynamical processes.

Unraveling relationship between complex lifetimes and microscopic diffusion in deep eutectic solvents

Aqueous mixtures of deep eutectic solvents (DESs) have emerged as a subject of interest in recent years for their tailored physicochemical properties. However, a comprehensive understanding of water's multifaceted influence on the microscopic dynamics, including its impact on improved transport properties of the DES, remains elusive. Additionally, the diffusion mechanisms within DESs manifest heterogeneous behavior, intricately tied to the formation and dissociation kinetics of complexes and hydrogen bonds. Therefore, it is imperative to explore the intricate interplay between bond kinetics, diffusion mechanism, and dynamical heterogeneity. This work employs water as an agent to explore their relationships by studying various relaxation phenomena in a DES based on acetamide and lithium perchlorate over a wide range of water concentrations. Notably, acetamide exhibits Fickian yet non-Gaussian diffusion across all water concentrations with Fickian (τf) and Gaussian (τg) timescales following a power-law relationship, τg∝τfγ, γ ∼ 1.4. The strength of coupling between bond kinetics and different diffusion timescales is estimated through various power-law relationships. Notably, acetamide-water hydrogen bond lifetime is linked to diffusive timescales through a single power-law over the entire water concentration studied. However, the relationship between diffusive timescales and the lifetime of acetamide-lithium complexes shows a sharp transition in behavior at 20 wt. % water, reflecting a change from vehicular diffusion below this concentration to structural diffusion above it. Our findings emphasize the critical importance of understanding bond dynamics within DESs, as they closely correlate with and regulate the molecular diffusion processes within these systems.

Nature of Subdiffusion Crossover in Molecular and Polymeric Glassformers

A crossover from a non-Gaussian to Gaussian subdiffusion has been observed ubiquitously in various polymeric and molecular glassformers. We have developed a framework that generalizes the fractional Brownian motion model to incorporate non-Gaussian features by introducing a jump kernel. We illustrate that the non-Gaussian fractional Brownian motion model accurately characterizes the subdiffusion crossover. From the solutions of the non-Gaussian fractional Brownian motion model, we gain insights into the nature of van Hove self-correlation in non-Gaussian subdiffusive regime, which is found to exhibit exponential tails, providing first such experimental evidence in molecular glassformers. The validity of the model is supported by comparison with incoherent quasielastic neutron scattering data obtained from several molecular and polymeric glassformers.

Noncanonical Relationship between Heterogeneity and the Stokes-Einstein Breakdown in Deep Eutectic Solvents

The relationship between Stokes-Einstein breakdown (SEB) and dynamical heterogeneity (DH) is of paramount importance in the physical chemistry of complex fluids. In this work, we employ neutron scattering to probe the DH and SEB in a series of deep eutectic solvents (DESs) composed of acetamide and lithium salts. Quasielastic neutron scattering experiments reveal SEB in the jump diffusion of acetamide, represented by a fractional Stokes-Einstein relationship. Among these DESs, lithium perchlorate exhibits the most pronounced SEB while lithium bromide displays the weakest. Concurrently, elastic incoherent neutron scans identify that bromide DES is the most heterogeneous and perchlorate is the least. For the first time, our study unveils a counterintuitive incommensurate relationship between DH and SEB. Further, it reveals the intricate contrasting nature of the SEB-DH relationship when investigated in proximity to the glass-transition temperature and further away from it.

Dielectric relaxation and dielectric decrement in ionic acetamide deep eutectic solvents: Spectral decomposition and comparison with experiments

Frequency-dependent dielectric relaxation in three deep eutectic solvents (DESs), (acetamide+LiClO4/NO3/Br), was investigated in the temperature range, 329 ≤ T/K ≤ 358, via molecular dynamics simulations. Subsequently, decomposition of the real and the imaginary components of the simulated dielectric spectra was carried out to separate the rotational (dipole-dipole), translational (ion-ion), and ro-translational (dipole-ion) contributions. The dipolar contribution, as expected, was found to dominate all the frequency-dependent dielectric spectra over the entire frequency regime, while the other two components together made tiny contributions only. The translational (ion-ion) and the cross ro-translational contributions appeared in the THz regime in contrast to the viscosity-dependent dipolar relaxations that dominated the MHz-GHz frequency window. Our simulations predicted, in agreement with experiments, anion-dependent decrement of the static dielectric constant (ɛs ∼ 20 to 30) for acetamide (ɛs ∼ 66) in these ionic DESs. Simulated dipole-correlations (Kirkwood g factor) indicated significant orientational frustrations. The frustrated orientational structure was found to be associated with the anion-dependent damage of the acetamide H-bond network. Single dipole reorientation time distributions suggested slowed down acetamide rotations but did not indicate presence of any "rotationally frozen" molecule. The dielectric decrement is, therefore, largely static in origin. This provides a new insight into the ion dependence of the dielectric behavior of these ionic DESs. A good agreement between the simulated and the experimental timescales was also noticed.

Difference in "Supercooling" Affinity between (Acetamide + Na/KSCN) Deep Eutectics: Reflections in the Simulated Anomalous Motions of the Constituents and Solution Microheterogeneity Features

Deep depression of freezing points of ionic amide deep eutectic solvents (DESs) is known to exhibit a significant dependence on the identity of ions present in those systems and the nature of the functional group attached to the host amide. This deep depression of the freezing point is sometimes termed as "supercooling". For (acetamide + electrolyte) DESs, experiments have revealed signatures of ion-dependent spatiotemporal heterogeneity features. The focus of this work is to provide microscopic explanations of these experimentally observed macroscopic system properties in terms of particle jumps and insights about the origin of the cation dependence. For this purpose, extensive molecular dynamics simulations have been performed employing (acetamide + Na/KSCN) deep eutectics as representative ionic systems at 303, 318, 333, and 348 K. The individual translational motions of acetamide and the ions are followed, and their connections to solution heterogeneity are explored. The center-of-mass motion for Na⁺ has been found to be more anomalous than that for K⁺. This difference corroborates well with experimental reports on heterogeneous relaxations in these systems. Simulated viscosity coefficients and dynamic heterogeneity features also reflect this difference. Moreover, simulated reorientational relaxations of acetamide molecules in these ionic DESs suggest that a Na⁺-containing DES is more heterogeneous than the corresponding K⁺-containing system. Estimated void and neck distributions for acetamide molecules differ as the alkali metal ions differ. In brief, this study provides a detailed microscopic view of the cation dependence of the microheterogeneous relaxation dynamics of these DESs reported repeatedly by different experiments.

Modulation of Diffusion Mechanism and Its Correlation with Complexation in Aqueous Deep Eutectic Solvents

Aqueous mixtures of deep eutectic solvents (DESs) have gained traction recently as an effective template to tailor their physicochemical properties. But detailed microscopic insights into the effects of water on the molecular relaxation phenomenon in DESs are not entirely understood. DESs are strong network-forming liquids due to the extensive hydrogen bonding and complex formation between their species, and therefore, water can behave as a controlled disruptor altering the microscopic structure and dynamics in DESs. In this study, the role of water in the diffusion mechanism of acetamide in the aqueous mixtures of DESs synthesized using acetamide and lithium perchlorate is investigated using molecular dynamics (MD) simulation and quasielastic neutron scattering (QENS). The acetamide dynamics comprises localized diffusion within transient cages and a jump diffusion process across cages. The jump diffusion process is observed to be strongly enhanced by about a factor of 10 as the water content in the system is increased. Meanwhile, the geometry of the localized dynamics is unaltered by addition of water, but the localized diffusion becomes significantly faster and more heterogeneous with increasing water concentration. The accelerating effects of water on localized diffusion are also substantiated by QENS experiments. The water concentration in the DES is observed to control the solvation structure of lithium ions, with the ions becoming significantly hydrated at 20 wt % water. The formation of interwater and water-acetamide hydrogen bonds is observed. The increase in water concentration is found to increase the number of H-bonds; however, their lifetimes are found to decrease substantially. Similarly, the lifetimes of acetamide-lithium complexes are also found to be diminished by increasing water concentration. A power-law scaling relationship between lifetimes and diffusion constants is established, elucidating the extent of coupling between diffusive processes and hydrogen bonding and microscopic complexation. This study demonstrates the ability to use water as an agent to probe the role of structural relaxation and complex lifetimes of diffusive processes at different time and length scales.

Dynamic Heterogeneity at the Interface of an Intrinsically Disordered Peptide

It is believed that water around an intrinsically disordered protein or peptide (IDP) in an aqueous environment plays an important role in guiding its conformational properties and aggregation behavior. However, despite its importance, only a handful of studies exploring the correlation between the conformational motions of an IDP and the microscopic properties of water at its surface are reported. Attempts have been made in this work to study the dynamic properties of water present in the vicinity of α-synuclein, an IDP associated with Parkinson's disease (PD). Room temperature molecular dynamics (MD) simulations of eight α-synuclein_1-95 peptides with a wide range of initial conformations have been carried out in aqueous media. The calculations revealed that due to solid-like caging motions, the translational and rotational mobility of water molecules near the surfaces of the peptide repeat unit segments R1 to R7 are significantly restricted. A small degree of dynamic heterogeneity in the hydration environment around the repeat units has been observed with water near the hydrophobic R6 unit exhibiting relatively more restricted diffusivity. The time scales involving the overall structural relaxations of peptide-water and water-water hydrogen bonds near the peptide have been found to be correlated with the time scale of diffusion of the interfacial water molecules. We believe that the relatively more hindered dynamic environment near R6 can help create water-mediated contacts centered around R6 between peptide monomers at a higher concentration, thereby enhancing the early stages of peptide aggregation.

Computer Simulations of Deep Eutectic Solvents: Challenges, Solutions, and Perspectives

Deep eutectic solvents (DESs) are one of the most rapidly evolving types of solvents, appearing in a broad range of applications, such as nanotechnology, electrochemistry, biomass transformation, pharmaceuticals, membrane technology, biocomposite development, modern 3D-printing, and many others. The range of their applicability continues to expand, which demands the development of new DESs with improved properties. To do so requires an understanding of the fundamental relationship between the structure and properties of DESs. Computer simulation and machine learning techniques provide a fruitful approach as they can predict and reveal physical mechanisms and readily be linked to experiments. This review is devoted to the computational research of DESs and describes technical features of DES simulations and the corresponding perspectives on various DES applications. The aim is to demonstrate the current frontiers of computational research of DESs and discuss future perspectives.

Temperature-Dependent Dielectric Relaxation in Ionic Acetamide Deep Eutectics: Partial Viscosity Decoupling and Explanations from the Simulated Single-Particle Reorientation Dynamics and Hydrogen-Bond Fluctuations

We report here temperature-dependent (293 ≤ T (K) ≤ 336) dielectric relaxation (DR) measurements of (acetamide + LiBr/NO₃^-/ClO₄^-) deep eutectic solvents (DESs) in the frequency window of 0.2 ≤ ν (GHz) ≤ 50 and explore, via molecular dynamics simulations, the relative roles for the collective single-particle reorientational relaxations and the H-bond dynamics of acetamide in the measured DR response. In addition, DR measurements of neat molten acetamide were performed. Recorded DR spectra of these DESs require multi-Debye fits and produce well-separated DR time scales that are spread over several picoseconds to ∼1 ns. Simulations suggest DR time scales derive contributions from both the collective reorientational (Cl(t)) relaxation and structural H-bond (C_HB(t)) dynamics of acetamide. A good correlation between the measured and simulated activation energies further reveals a strong connection between the measured DR and the simulated Cl(t) and C_HB(t). Average DR times exhibit a strong fractional viscosity dependence, suggesting substantial microheterogeneity in these media. Simulations of Cl(t) and C_HB(t) reveal strong stretched exponential relaxations with a stretching exponent, 0.4 ≤ β ≤ 0.7. The ratio between the average reorientational correlation times of first and second ranks, ⟨τ⟩l=1/⟨τ⟩l=2, deviates appreciably from Debye's l(l+1) law for homogeneous media. Importantly, a pronounced translation-rotation decoupling between the simulated reorientation and center-of-mass diffusion times was observed.

Can the microscopic and macroscopic transport phenomena in deep eutectic solvents be reconciled?

Deep eutectic solvents (DESs) have become ubiquitous in a variety of industrial and pharmaceutical applications since their discovery. However, the fundamental understanding of their physicochemical properties and their emergence from the microscopic features is still being explored fervently. Particularly, the knowledge of transport mechanisms in DESs is essential to tune their properties, which shall aid in expanding the territory of their applications. This perspective presents the current state of understanding of the bulk/macroscopic transport properties and microscopic relaxation processes in DESs. The dependence of these properties on the components and composition of the DES is explored, highlighting the role of hydrogen bonding (H-bonding) interactions. Modulation of these interactions by water and other additives, and their subsequent effect on the transport mechanisms, is also discussed. Various models (e.g. hole theory, free volume theory, etc.) have been proposed to explain the macroscopic transport phenomena from a microscopic origin. But the formation of H-bond networks and clusters in the DES reveals the insufficiency of these models, and establishes an antecedent for dynamic heterogeneity. Even significantly above the glass transition, the microscopic relaxation processes in DESs are rife with temporal and spatial heterogeneity, which causes a substantial decoupling between the viscosity and microscopic diffusion processes. However, we propose that a thorough understanding of the structural relaxation associated to the H-bond dynamics in DESs will provide the necessary framework to interpret the emergence of bulk transport properties from their microscopic counterparts.

Water accelerates the hydrogen-bond dynamics and abates heterogeneity in deep eutectic solvent based on acetamide and lithium perchlorate

Deep eutectic solvents (DESs) have become a prevalent and promising medium in various industrial applications. The addition of water to DESs has attracted a lot of attention as a scheme to modulate their functionalities and improve their physicochemical properties. In this work, we study the effects of water on an acetamide based DES by probing its microscopic structure and dynamics using classical molecular dynamics simulation. It is observed that, at low water content, acetamide still remains the dominant solvate in the first solvation shell of lithium ions, however, beyond 10 wt. %, it is replaced by water. The increase in the water content in the solvent accelerates the H-bond dynamics by drastically decreasing the lifetimes of acetamide-lithium H-bond complexes. Additionally, water-lithium H-bond complexes are also found to form, with systematically longer lifetimes in comparison to acetamide-lithium complexes. Consequently, the diffusivity and ionic conductivity of all the species in the DES are found to increase substantially. Non-Gaussianity parameters for translational motions of acetamide and water in the DES show a conspicuous decrease with addition of water in the system. The signature of jump-like reorientation of acetamide is observed in the DES by quantifying the deviation from rotational Brownian motion. However, a notable decrease in the deviation is observed with an increase in the water content in the DES. This study demonstrates the intricate connection between H-bond dynamics and various microscopic dynamical parameters in the DES, by investigating the modulation of the former with addition of water.