Spatially resolved dielectric constant of confined water and its connection to the non-local nature of bulk water

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Dielectric Constant of Aqueous Solutions of Proteins and Organic Polymers from Molecular Dynamics Simulations

The dielectric constant of water/oligomer mixtures, spanning the range from pure water to pure oligomeric melts, is investigated using molecular dynamics (MD) simulations. As prototypical water-soluble organic substances we consider neutral poly-glycine, poly-ethylene glycol and charged monomeric propanic acid. As the water content is reduced, the dielectric constant decreases but does not follow an ideal mixing behavior. The deviations from ideal mixing originate primarily in the non-linear relation between the oligomer mass fraction and collective polarization effects. We find that the dielectric constant is dominated by water polarization, even if the oligomer mass fraction exceeds 50%. By a double extrapolation of the MD simulation results to the limit of vanishing water fraction and to the limit of infinite oligomeric chain length, we estimate the orientational contribution to the dielectric constant of the pure polymeric melts. By this procedure, we obtain ε = 17 {plus minus} 2 for polyglycine and ε = 1 {plus minus} 0.3 for polyethylene glycol. The large difference is rationalized by polarization correlations of glycine units. Interestingly, we find constant temperature simulations to outperform replica exchange simulations in terms of equilibration speed.

Tuning the Dielectric Response of Water in Nanoconfinement through Surface Wettability

The tunable polarity of water can be exploited in emerging technologies including catalysis, gas storage, and green chemistry. Recent experimental and theoretical studies have shown that water can be rendered into an effectively apolar solvent under nanoconfinement. We furthermore demonstrate, through molecular simulations, that the static dielectric constant of water can be modified by changing the wettability of the confining material. We find the out-of-plane dielectric response to be highly sensitive to the level of confinement and can be reduced up to 40× , in accordance with experimental data. By altering the surface wettability from superhydrophilic to superhydrophobic, we observe a 36% increase for the out-of-plane and a 31% decrease for the in-plane dielectric constants. Our findings demonstrate the feasibility of tunable water polarity, a phenomenon with great potential for scientific and technological impact.

Abnormal Properties of Low-Dimensional Confined Water

Water molecules confined to low-dimensional spaces exhibit unusual properties compared to bulk water. For example, the alternating hydrophilic and hydrophobic nanodomains on flat silicon wafer can induce the abnormal spreading of water (contact angles near 0°) which is caused by the 2D capillary effect. Hence, exploring the physicochemical properties of confined water from the nanoscale is of great value for understanding the challenges in material science and promoting the applications of nanomaterials in the fields of mass transport, nanofluidic designing, and fuel cell. The knowledge framework of confined water can also help to better understand the complex functions of the hydration layer of biomolecules, and even trace the origin of life. In this review, the physical properties, abnormal behaviors, and functions of the confined water are mainly summarized through several common low-dimensional water formats in the fields of solid/air-water interface, nanochannel confinement, and biological hydration layer. These researches indicate that the unusual behaviors of the confined water depend strongly on the confinement size and the interaction between the molecules and confining surface. These diverse properties of confined water open a new door to materials science and may play an important role in the future development of biology.

Confinement-Controlled Aqueous Chemistry within Nanometric Slit Pores

In this Focus Review, we put the spotlight on very recent insights into the fascinating world of wet chemistry in the realm offered by nanoconfinement of water in mechanically rather rigid and chemically inert planar slit pores wherein only monolayer and bilayer water lamellae can be hosted. We review the effect of confinement on different aspects such as hydrogen bonding, ion diffusion, and charge defect migration of H⁺(aq) and OH^-(aq) in nanoconfined water depending on slit pore width. A particular focus is put on the strongly modulated local dielectric properties as quantified in terms of anisotropic polarization fluctuations across such extremely confined water films and their putative effects on chemical reactions therein. The stunning findings disclosed only recently extend wet chemistry in particular and solvation science in general toward extreme molecular confinement conditions.

Nonlocal Dielectric Response of Water in Nanoconfinement

Recent experiments reporting a very low dielectric permittivity for nanoconfined water have renewed the interest in the structure and dielectric properties of water in narrow gaps. Here, we describe such systems with a minimal Landau-Ginzburg field theory composed of a nonlocal bulk-determined term and a local water-surface interaction term. We show how the interplay between the boundary conditions and intrinsic bulk correlations encodes the dielectric properties of confined water. Our theoretical analysis is supported by molecular dynamics simulations and comparison with the experimental data.

Dielectric Behavior near a Spherical Ion

The dielectric response of a polar solvent to an ion is analyzed in terms of the bound charge, the net charge that accumulates near the ion as a consequence of the inhomogeneous polarization of the surrounding solvent. We demonstrate that the total bound charge arising in a full molecular treatment is identical to the total bound charge from standard continuum theory. In continuum theory, the bound charge resides in an infinitely thin layer, while in a molecular description the bound charge is spread over a region of finite width. Near simple atomic ions, the width of the bound charge distribution is roughly 1.3 nm. By simulating a sequence of ion charges from 0.1 to 2 e, where e is the magnitude of the electron charge, we analyze the applicability of linear response theory, which has been used by several authors. With increasing charge, the nonlinear response extends to an increasing distance from the ion. However, outside the region containing bound charge, the response is linear and in accord with continuum theory. Previous attempts to assign a dielectric constant to a solvent in the interfacial region are analyzed.

Anomalous dielectric response of nanoconfined water

In order to develop a microscopic level understanding of the anomalous dielectric properties of nanoconfined water (NCW), we study and compare three different systems, namely, (i) NCW between parallel graphene sheets (NCW-GSs), (ii) NCW inside graphene covered nanosphere (NCW-Sph), and (iii) a collection of one- and two-dimensional constrained Ising spins with fixed orientations at the termini. We evaluate the dielectric constant and study the scaling of ε with size by using linear response theory and computer simulations. We find that the perpendicular component remains anomalously low at smaller inter-plate separations (d) over a relatively wide range of d. For NCW-Sph, we could evaluate the dielectric constant exactly and again find a low value and a slow convergence to the bulk. To obtain a measure of surface influence into the bulk, we introduce and calculate correlation lengths to find values of ∼9 nm for NCW-GS and ∼5 nm for NCW-Sph, which are surprisingly large, especially for water. We discover that the dipole moment autocorrelations exhibit an unexpected ultrafast decay. We observe the presence of a ubiquitous frequency of ∼1000 cm^-1, associated only with the perpendicular component for NCW-GS. This (caging) frequency seems to play a pivotal role in controlling both static and dynamic dielectric responses in the perpendicular direction. It disappears with an increase in d in a manner that corroborates with the estimated correlation length. A similar observation is obtained for NCW-Sph. Interestingly, one- and two-dimensional Ising model systems that follow Glauber spin-flip dynamics reproduce the general characteristics.

Comment on "investigation of dielectric constants of water in a nano-confined pore" by H. Zhu, F. Yang, Y. Zhu, A. Li, W. He, J. Huang and G. Li, RSC Adv., 2020, , 8628

Zhu et al. recently reported the spatially resolved dielectric profile and value of the average static dielectric constant of water confined inside a silica nanopore. However, the authors neglected the inherent anisotropy and non-local nature of the dielectric response under confinement. Neglect of these important issues produces erroneous results and vastly underestimates the average values. We demonstrate the correct way to incorporate the anisotropy and to obtain the average dielectric constant of cylindrically nanoconfined dipolar fluids. Use of the correct theoretical formalism expectedly shows convergence of the calculated dielectric response to the bulk value with increasing the nanopore size. On the contrary, the equation used by Zhu et al. fails to exhibit the convergence of the same. Instead, decreases as the nanopore size is gradually increased.

Confinement-Induced Enhancement of Parallel Dielectric Permittivity: Super Permittivity Under Extreme Confinement

Enhancement of parallel (x-y plane) dielectric permittivity of confined fluids has been shown previously. However, a theoretical model that explains this enhancement is lacking thus far. In this study, using statistical-mechanical theories and molecular dynamics simulations, we show an explicit relation between the parallel dielectric permittivity, density variations, and dipolar correlations for protic and aprotic fluids confined in slit-like channels. We analyze the importance of dipolar correlations on enhancement of parallel dielectric permittivity inside large channels and extreme confinements. In large channels, beyond the interfacial region, dipolar correlations exhibit bulk-like behavior. Under extreme confinement, the correlations become stronger to the extent that they give rise to a giant increase in the parallel dielectric permittivity. This sudden increase in dielectric permittivity can be a signature of a liquid transition into higher-ordered structures and has important consequences for understanding ion transport, molecular dissociation, and chemical reactions inside nanoconfined environments.

Water Layer at Hydrophobic Surface: Electrically Dead but Dynamically Alive?

The origin of the anomalous low value of the static dielectric constant (SDC) of confined water has been addressed and unearthed. While the low value is partly due to the different dielectric boundaries, a significant role is played by the "electrically dead layer" (EDL). As the observed dielectric constant is the harmonic mean of the grid-wise SDCs, the first layer, having the smallest SDC, makes a disproportionately large contribution. This enhanced contribution, in turn, arises from the orientationally ordered surface water molecules. They exhibit reduced fluctuations in collective dipole moment, as the molecules remain partly caged due to water-surface interactions. This phenomenon is found to be universal. We study the structure and dynamics of the water molecules which characterize the EDL. We demonstrate that while the EDL remains alive at a molecular level, with a finite residence time, it displays time scales not substantially different compared to the distant water layers.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

This Review explores the dynamic behavior of water within nanopores and biological channels in lipid bilayer membranes. We focus on molecular simulation studies, alongside selected structural and other experimental investigations. Structures of biological nanopores and channels are reviewed, emphasizing those high-resolution crystal structures, which reveal water molecules within the transmembrane pores, which can be used to aid the interpretation of simulation studies. Different levels of molecular simulations of water within nanopores are described, with a focus on molecular dynamics (MD). In particular, models of water for MD simulations are discussed in detail to provide an evaluation of their use in simulations of water in nanopores. Simulation studies of the behavior of water in idealized models of nanopores have revealed aspects of the organization and dynamics of nanoconfined water, including wetting/dewetting in narrow hydrophobic nanopores. A survey of simulation studies in a range of nonbiological nanopores is presented, including carbon nanotubes, synthetic nanopores, model peptide nanopores, track-etched nanopores in polymer membranes, and hydroxylated and functionalized nanoporous silica. These reveal a complex relationship between pore size/geometry, the nature of the pore lining, and rates of water transport. Wider nanopores with hydrophobic linings favor water flow whereas narrower hydrophobic pores may show dewetting. Simulation studies over the past decade of the behavior of water in a range of biological nanopores are described, including porins and β-barrel protein nanopores, aquaporins and related polar solute pores, and a number of different classes of ion channels. Water is shown to play a key role in proton transport in biological channels and in hydrophobic gating of ion channels. An overall picture emerges, whereby the behavior of water in a nanopore may be predicted as a function of its hydrophobicity and radius. This informs our understanding of the functions of diverse channel structures and will aid the design of novel nanopores. Thus, our current level of understanding allows for the design of a nanopore which promotes wetting over dewetting or vice versa. However, to design a novel nanopore, which enables fast, selective, and gated flow of water de novo would remain challenging, suggesting a need for further detailed simulations alongside experimental evaluation of more complex nanopore systems.

How different are the dynamics of nanoconfined water?

We unravel the combined effects of confinement and surface interactions by studying the position dependent, time-resolved dynamic response functions in nano-containers of different shapes. Spectroscopic signatures are additionally studied through solvation dynamics by placing ionic and dipolar probes at varying distances from the enclosing surface. We find that the confined water molecules exhibit exotic dynamical features and stark differences from that in the bulk liquid. We employ atomistic molecular dynamics simulation to obtain the solvation time correlation function, non-Gaussian parameter, and non-linear response function that reveal the existence of heterogeneous and non-exponential dynamics with a strong sensitivity to both the size and the shape of the enclosure. Importantly, the slower long-time decay constant exhibits a non-monotonic spatial dependence. The initial ultrafast component is reminiscent of the same in the bulk, but it is found to have a different origin in the present systems. We perform shell-wise analyses to understand the microscopic origin of these observations and the range of the propagation of the surface induced effects.

Inhomogeneity of Interfacial Electric Fields at Vibrational Probes on Electrode Surfaces

Electric fields control chemical reactivity in a wide range of systems, including enzymes and electrochemical interfaces. Characterizing the electric fields at electrode-solution interfaces is critical for understanding heterogeneous catalysis and associated energy conversion processes. To address this challenge, recent experiments have probed the response of the nitrile stretching frequency of 4-mercaptobenzonitrile (4-MBN) attached to a gold electrode to changes in the solvent and applied electrode potential. Herein, this system is modeled with periodic density functional theory using a multilayer dielectric continuum treatment of the solvent and at constant applied potentials. The impact of the solvent dielectric constant and the applied electrode potential on the nitrile stretching frequency computed with a grid-based method is in qualitative agreement with the experimental data. In addition, the interfacial electrostatic potentials and electric fields as a function of applied potential were calculated directly with density functional theory. Substantial spatial inhomogeneity of the interfacial electric fields was observed, including oscillations in the region of the molecular probe attached to the electrode. These simulations highlight the microscopic inhomogeneity of the electric fields and the role of molecular polarizability at electrode-solution interfaces, thereby demonstrating the limitations of mean-field models and providing insights relevant to the interpretation of vibrational Stark effect experiments.

Giant Axial Dielectric Response in Water-Filled Nanotubes and Effective Electrostatic Ion-Ion Interactions from a Tensorial Dielectric Model

Molecular dynamics simulations in conjunction with effective medium theory are used to investigate dielectric effects in water-filled nanotubes. The resulting effective axial dielectric constant shows a divergent increase for small nanotube radii that depends on the nanotube length, while the effective radial dielectric constant decreases significantly for thin nanotubes. By solving Poisson's equation for an anisotropic dielectric medium in cylindrical geometry, we show that the axial ion-ion interaction depends for small separations primarily on the radial dielectric constant, not on the axial one. This means that electrostatic ion-ion interactions in thin water-filled nanotubes are on the linear dielectric level significantly enhanced due to water confinement effects at small separations, while at large separations the outside medium dominates. If the outside medium is metallic, then the ion-ion interaction decays exponentially for large ion separation.

Water in Carbon Nanotubes: Pronounced Anisotropy in Dielectric Dispersion and Its Microscopic Origin

We report a remarkable anisotropy in the dielectric properties of water under cylindrical nanoconfinements in carbon nanotubes (CNTs). We employ linear response theory and use a new relation to define and calculate the two distinct eigenvalues of the dielectric tensor, namely, the axial (ε_z) and perpendicular (ε_x/y) components. We discover that not just the dielectric tensor but dielectric relaxation also exhibits strong anisotropy. The present study reveals that the parallel (ε_z) and the orthogonal (ε_x/y) components approach the bulk value in an opposite manner when the diameter of the CNT is increased. Rather unexpectedly, the polarization fluctuations remain quenched in the perpendicular direction even for the largest systems studied. The microscopic origin of the observed anisotropy is attributed to the propagation of surface effects into the confined liquid.

Effect of Hydrogen Bonds on the Dielectric Properties of Interfacial Water

The dielectric constant for water is reduced under confinement. Although this phenomenon is well known, the underlying physical mechanism for the reduction is still in debate. In this work, we investigate the effect of the orientation of hydrogen bonds on the dielectric properties of confined water using molecular dynamics simulations. We find a reduced rotational diffusion coefficient for water molecules close to the solid surface. The reduced rotational diffusion arises due to the hindered rotation away from the plane parallel to the channel walls. The suppressed rotation in turn affects the orientational polarization of water, leading to a low value for the dielectric constant at the interface. We attribute the constrained out-of-plane rotation to originate from a higher density of planar hydrogen bonds formed by the interfacial water molecules.

One-Dimensional Confinement Inhibits Water Dissociation in Carbon Nanotubes

The effect of nanoconfinement on the self-dissociation of water constitutes an open problem whose elucidation poses a serious challenge to experiments and simulations alike. In slit pores of width ≈1 nm, recent first-principles calculations have predicted that the dissociation constant of H₂O increases by almost 2 orders of magnitude [ Muñoz-Santiburcio and Marx, Phys. Rev. Lett. 2017 , 119 , 056002 ]. In the present study, quantum mechanics-molecular mechanics simulations are employed to compute the dissociation free-energy profile of water in a (6,6) carbon nanotube. According to our results, the equilibrium constant K_w drops by 3 orders of magnitude with respect to the bulk phase value, at variance with the trend predicted for confinement in two dimensions. The higher barrier to dissociation can be ascribed to the undercoordination of the hydroxide and hydronium ions in the nanotube and underscores that chemical reactivity does not exhibit a monotonic behavior with respect to pore size but may vary substantially with the characteristic length scale and dimensionality of the confining media.

Nanoconfinement in Slit Pores Enhances Water Self-Dissociation

We investigate the self-dissociation of water that is nanoconfined between the sheets of a realistic layered mineral, FeS mackinawite, as well as between Lennard-Jones walls via ab initio simulations. By comparing it with the same reaction in bulk water under various thermodynamic conditions, we show that such strong two-dimensional confinement between hard surfaces greatly enhances the self-dissociation process of water-thus increasing its ionic product K_{w} due to nanoconfinement. In addition to providing free energies, we analyze in detail the underlying dielectric properties in terms of dipole moment distributions, and thus the polarity of the liquid, as well as local polarization fluctuations as quantified by dielectric tensor profiles perpendicular to the lamella.