Effects of Solvent Polarity on Li-ion Diffusion in Polymer Electrolytes: An All-Atom Molecular Dynamics Study with Charge Scaling

Conductivity and Diffusivity of Ions in Aqueous MgCl2 from Equilibrium and Nonequilibrium Simulations

Advanced electrochemical energy storage technologies require new electrolytes to be considered, so efficient computational characterization of ionic conductivity in a range of systems is of importance. In this manuscript we compare different equilibrium (EMD) and nonequilibrium molecular dynamics (NEMD) simulation algorithms to determine ionic conductivities. Aqueous magnesium ion batteries utilizing magnesium chloride as the electrolyte are a promising alternative to conventional lithium-ion batteries, so we focus on magnesium chloride electrolytes to demonstrate our results. We show the importance of accounting for ionic correlations and find that NEMD algorithms can provide more efficient calculations of ionic conductivity than EMD algorithms when ionic correlations need to be accounted for. In contrast, diffusivities and Nernst-Einstein conductivities can be determined more efficiently with EMD algorithms in the highly conductive systems considered here. We also demonstrate that the alignment of the water molecules due to the applied field in NEMD simulations is small at typical field strengths and has no impact on the calculated conductivities. Comparison of the results for the conductivity of different ions and their coupling provides insight into how force fields might be improved.

To Hop or Not to Hop: Unveiling Different Modes of Ion Transport in Solid Polymer Electrolytes through Molecular Dynamics Simulations

Although the basic modes of ion transport in solid polymer electrolytes (SPEs) are already classified and well-described, their distribution in typical polymer electrolytes is not clear and neither are the effects on the distribution by different degrees of ion-ion and ion-polymer interactions. Here, the ion-transport mechanisms in poly(ethylene oxide) are studied along with poly(ε-caprolactone) at different molecular weights and LiTFSI salt concentrations using molecular dynamics simulations. Through tracking of the cation coordination changes, three transport mechanisms are categorized, i.e., ion hopping, continuous motion (successive exchange of the coordination sphere), and vehicular transport. The observed dominant transport mechanism is in all cases continuous motion, which changes from polymer-mediated to anion-mediated with increasing salt concentration, while polymer-mediated vehicular transport is not observed to be a major contributor to cation transport. In both systems, ion hopping is also essentially absent, as can be expected in systems with strong ion-polymer interactions. The results illustrate how the usual description of ion transport in polymer electrolytes as coupled to segmental motions is too simplistic to catch the full essence of the ion-transport phenomena, whereas the frequently used notion of "ion hopping" in the majority of cases is incorrect for SPEs.

Nanocrystals with Aggregate Anionic Structure Enable Ion Transport Decoupling of Chain Segment Movement in Poly(ethylene oxide) Electrolytes

All-solid-state polymer electrolytes are promising for lithium batteries, but Li+ transport in these electrolytes relies on amorphous chain segment movement, leading to low Li+ mobility and poor mechanical strength. Here we propose a novel Li+ transport mechanism mediated by PEO3:LiBF4 nanocrystals (NCPB) with the aggregate (AGG) anionic structure, which enables a change from amorphous to crystalline phase dominated ion transport in all-solid-state PEO/LiBF4 electrolyte. Experiments and simulations reveal that the interaction between Li+ and F in NCPB with AGG anionic structure simultaneously restricts anion transport and reorients anions within the free volume of NCPB, resulting in a three-coordination intermediate to facilitate Li+ transport. The unique Li+ transport mechanism through NCPB makes the PEO/LiBF4 electrolyte with a high Li+ transference number (0.73) and remarkably increased mechanical strength (storage modulus >100 MPa) at 45 °C. As a result, the Li|LiFePO4 batteries with the ultrathin self-supported PEO/LiBF4 electrolyte (10 μm) exhibit significantly improved cycle life (97 % @ 468 cycles) compared to those with PEO/LiTFSI electrolyte (failed @ 68 cycles). This work demonstrates a novel ion transport mechanism for achieving selective and rapid Li+ transport.

Understanding Ion Transport in Alkyl Dicarbonates: An Experimental and Computational Study

In an effort to improve safety and cycling stability of liquid electrolytes, the use of dicarbonates has been explored. In this study, four dicarbonate structures with varying end groups and spacers are investigated. The effect of these structural differences on the physical and ion transport properties is elucidated, showing that the end group has a significant influence on ion transport. The solvation structure and ion transport in the dicarbonates are compared to those of the linear carbonates dimethyl carbonate (DMC) and diethyl carbonate (DEC). Although the carbonate coordination numbers (CN) are similar in the different systems, the CN from the anion is higher in dicarbonate electrolytes. At low salt concentrations, rapid solvent exchange is observed in the DMC- and DEC-containing systems, transitioning to a more correlated ion transport at high salt concentration. In contrast, the exchange of solvents around lithium ions (Li+) is limited in the dicarbonate systems regardless of the salt concentration, with only one carbonate group from each molecule participating in the coordination. In addition, according to the molecular dynamics simulations, Li+ mainly moves together with coordinating dicarbonate molecules and anion(s).

Charge Scaling in Classical Force Fields for Lithium Ions in Polymers

Polymer electrolytes are of interest for applications in energy storage. Molecular simulations of ion transport in polymer electrolytes have been widely used to study the conductivity in these materials. Such simulations have generally relied on classical force fields. A peculiar feature of such force fields has been that in the particular case of lithium ions (Li+), their charge must be scaled down by approximately 20% to achieve agreement with experimental measurements of ion diffusivity. In this work, we present first-principles calculations that serve to justify the charge-scaling factor and van der Waals interaction parameters for Li+ diffusion in poly(ethylene glycol) (PEO) with bistriflimide (TFSI-) counterions. Our results indicate that a scaling factor of 0.79 provides good agreement with DFT calculations over a relatively wide range of Li+ concentrations and temperatures, consistent with past reports where that factor was adjusted by trial and error. We also show that such a scaling factor leads to diffusivities that are in quantitative agreement with experimental measurements.

Molecular dynamics simulation of salt diffusion in constituting phosphazene-based polymer electrolyte

A growing demand to visualize polymer models in liquid poses a computational challenge in molecular dynamics (MD) simulation, as this requires emerging models under suitable force fields (FFs) to capture the underlying molecular behaviour accurately. In our present study, we have employed TIP3P potential on water and all atomistic optimized potentials for liquid simulations FFs to study the liquid electrolyte behavior of phosphazene-based polymer by considering its potential use in lithium-ion polymer batteries. We have explored the polymer's local structure, chain packing, wettability, and hydrophobic tendencies against the silicon surface using a combination of a pseudocontinuum model in MD simulation, and surface-sensitive sum frequency generation (SFG) vibrational spectroscopy. The finding yields invaluable insights into the molecular architecture of phosphazene. This approach identifies the importance of hydrophobic interactions with air and hydrophilic units with water molecules in understanding the behavior and properties of phosphazene-based polymers at interfaces, contributing to its advancements in materials science. The MD study uniquely captures traces of the polymer-ion linkage, which is observed to become more pronounced with the increase in polymer weight fraction. The theoretical observation of this linkage's influence on lithium-ion diffusion motion offers valuable insights into the fundamental physics governing the behavior of atoms and molecules within phosphazene-based polymer electrolytes in aqueous environments. Further these predictions are corroborated in the molecular-level depiction at the air-aqueous interface, as evidenced from the OH-oscillator strength variation measured by the SFG spectroscopy.The fundamental findings from this study open new avenues for utilizing MD simulation as a versatile methodology to gain profound insights into intermolecular interactions of polymer. It could be useful in the application of biomedical and energy-related research, such as polymer lithium-ion batteries, fuel cells, and organic solar cells.

Salt Effects on the Mechanical Properties of Ionic Conductive Polymer: A Molecular Dynamics Study

Functional polymers can be used as electrolyte and binder materials in solid-state batteries. This often requires performance targets in terms of both the transport and mechanical properties. In this work, a model ionic conductive polymer system, i.e., poly(ethylene oxide)-LiTFSI, was used to study the impact of salt concentrations on mechanical properties, including different types of elastic moduli and the viscoelasticity with both nonequilibrium and equilibrium molecular dynamics simulations. We found an encouragingly good agreement between experiments and simulations regarding Young's modulus, bulk modulus, and viscosity. In addition, we identified an intermediate salt concentration at which the system shows high ionic conductivity, high Young's modulus, and short elastic restoration time. Therefore, this study laid the groundwork for investigating ionic conductive polymer binders with self-healing functionality from molecular dynamics simulations.

Ion Transport in Polymer Electrolytes: Building New Bridges between Experiment and Molecular Simulation

ConspectusPolymer electrolytes constitute a promising type of material for solid-state batteries. However, one of the bottlenecks for their practical implementation lies in the transport properties, often including restricted Li+ self-diffusion and conductivity and low cationic transference numbers. This calls for a molecular understanding of ion transport in polymer electrolytes in which molecular dynamics (MD) simulation can provide both new physical insights and quantitative predictions. Although efforts have been made in this area and qualitative pictures have emerged, direct and quantitative comparisons between experiment and simulation remain challenging because of the lack of a unified theoretical framework to connect them.In our work, we show that by computing the glass transition temperature (Tg) of the model system and using the normalized inverse temperature 1000/(T - Tg + 50), the Li+ self-diffusion coefficient can be compared quantitatively between MD simulations and experiments. This allows us to disentangle the effects of Tg and the polymer dielectric environment on ion conduction in polymer electrolytes, giving rise to the identification of an optimal solvating environment for fast ion conduction.Unlike Li+ self-diffusion coefficients and ionic conductivity, the transference number, which describes the fraction of current carried by Li+ ions, depends on the boundary conditions or the reference frame (RF). This creates a non-negligible gap when comparing experiment and simulation because the fluxes in the experimental measurements and in the linear response theory used in MD simulation are defined in different RFs. We show that by employing the Onsager theory of ion transport and applying a proper RF transformation, a much better agreement between experiment and simulation can be achieved for the PEO-LiTFSI system. This further allows us to derive the theoretical expression for the Bruce-Vincent transference number in terms of the Onsager coefficients and make a direct comparison to experiments. Since the Bruce-Vincent method is widely used to extract transference numbers from experimental data, this opens the door to calibrating MD simulations via reproducing the Bruce-Vincent transference number and using MD simulations to predict the true transference number.In addition, we also address several open questions here such as the time-scale effects on the ion-pairing phenomenon, the consistency check between different types of experiments, the need for more accurate force fields used in MD simulations, and the extension to multicomponent systems. Overall, this Account focuses on building new bridges between experiment and simulation for quantitative comparison, warnings of pitfalls when comparing apples and oranges, and clarifying misconceptions. From a physical chemistry point of view, it connects to concentrated solution theory and provides a unified theoretical framework that can maximize the power of MD simulations. Therefore, this Account will be useful for the electrochemical energy storage community at large and set examples of how to approach experiments from theory and simulation (and vice versa).

Synergistic theoretical and experimental study on the ion dynamics of bis(trifluoromethanesulfonyl)imide-based alkali metal salts for solid polymer electrolytes

Model validation of a well-known class of solid polymer electrolyte (SPE) is utilized to predict the ionic structure and ion dynamics of alternative alkali metal ions, leading to advancements in Na-, K-, and Cs-based SPEs for solid-state alkali metal batteries. A comprehensive study based on molecular dynamics (MD) is conducted to simulate ion coordination and the ion transport properties of poly(ethylene oxide) (PEO) with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt across various LiTFSI concentrations. Through validation of the MD simulation results with experimental techniques, we gain a deeper understanding of the ionic structure and dynamics in the PEO/LiTFSI system. This computational approach is then extended to predict ion coordination and transport properties of alternative alkali metal ions. The ionic structure in PEO/LiTFSI is significantly influenced by the LiTFSI concentration, resulting in different lithium-ion transport mechanisms for highly concentrated or diluted systems. Substituting lithium with sodium, potassium, and cesium reveals a weaker cation-PEO coordination for the larger cesium-ion. However, sodium-ion based SPEs exhibit the highest cation transport number, indicating the crucial interplay between salt dissociation and cation-PEO coordination for achieving optimal performance in alkali metal SPEs.

Ion Solvation Cage Structure in Polymer Electrolytes Determined by Combining X-ray Scattering and Simulations

Solvation structure plays a crucial role in determining ion transport in electrolytes. We combine wide-angle X-ray scattering (WAXS) and molecular dynamics (MD) simulation to identify the solvation cage structure in two polymer electrolytes, poly(pentyl malonate) (PPM) and poly(ethylene oxide) (PEO) mixed with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt. As the salt concentration increases, the amorphous halo in the pure polymers is augmented by an additional peak at low scattering angles. The location of this peak and its height are, however, different in the two electrolytes. By decoupling the total intensity into species contributions and mapping scattering peaks to position-space molecular correlations, we elucidate distinct origins of the additional peak. In PPM, it arises from long-range charge-ordering between solvation cages and anions, while in PEO it is dominated by correlations between anions surrounding the same cage. TFSI- ions are present in the PPM solvation cage, but expelled from the PEO solvation cage.

Enabling selective zinc-ion intercalation by a eutectic electrolyte for practical anodeless zinc batteries

Two major challenges hinder the advance of aqueous zinc metal batteries for sustainable stationary storage: (1) achieving predominant Zn-ion (de)intercalation at the oxide cathode by suppressing adventitious proton co-intercalation and dissolution, and (2) simultaneously overcoming Zn dendrite growth at the anode that triggers parasitic electrolyte reactions. Here, we reveal the competition between Zn²⁺ vs proton intercalation chemistry of a typical oxide cathode using ex-situ/operando techniques, and alleviate side reactions by developing a cost-effective and non-flammable hybrid eutectic electrolyte. A fully hydrated Zn²⁺ solvation structure facilitates fast charge transfer at the solid/electrolyte interface, enabling dendrite-free Zn plating/stripping with a remarkably high average coulombic efficiency of 99.8% at commercially relevant areal capacities of 4 mAh cm^-2 and function up to 1600 h at 8 mAh cm^-2. By concurrently stabilizing Zn redox at both electrodes, we achieve a new benchmark in Zn-ion battery performance of 4 mAh cm^-2 anode-free cells that retain 85% capacity over 100 cycles at 25 °C. Using this eutectic-design electrolyte, Zn | |Iodine full cells are further realized with 86% capacity retention over 2500 cycles. The approach represents a new avenue for long-duration energy storage.

Molecular-Level Insight into Charge Carrier Transport and Speciation in Solid Polymer Electrolytes by Chemically Tuning Both Polymer and Lithium Salt

The advent of Li-metal batteries has seen progress toward studies focused on the chemical modification of solid polymer electrolytes, involving tuning either polymer or Li salt properties to enhance the overall cell performance. This study encompasses chemically modifying simultaneously both polymer matrix and lithium salt by assessing ion coordination environments, ion transport mechanisms, and molecular speciation. First, commercially used lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt is taken as a reference, where F atoms become partially substituted by one or two H atoms in the -CF₃ moieties of LiTFSI. These substitutions lead to the formation of lithium(difluoromethanesulfonyl)(trifluoromethanesulfonyl)imide (LiDFTFSI) and lithium bis(difluoromethanesulfonyl)imide (LiDFSI) salts. Both lithium salts promote anion immobilization and increase the lithium transference number. Second, we show that exchanging archetypal poly(ethylene oxide) (PEO) with poly(ε-caprolactone) (PCL) significantly changes charge carrier speciation. Studying the ionic structures of these polymer/Li salt combinations (LiTFSI, LiDFTFSI or LiDFSI with PEO or PCL) by combining molecular dynamics simulations and a range of experimental techniques, we provide atomistic insights to understand the solvation structure and synergistic effects that impact macroscopic properties, such as Li⁺ conductivity and transference number.

Carbonyl-Containing Solid Polymer Electrolyte Host Materials: Conduction and Coordination in Polyketone, Polyester, and Polycarbonate Systems

Research on solid polymer electrolytes (SPEs) is now moving beyond the realm of polyethers that have dominated the field for several decades. A promising alternative group of candidates for SPE host materials is carbonyl-containing polymers. In this work, SPE properties of three different types of carbonyl-coordinating polymers are compared: polycarbonates, polyesters, and polyketones. The investigated polymers were chosen to be as structurally similar as possible, with only the functional group being different, thereby giving direct insights into the role of the noncoordinating main-chain oxygens. As revealed by experimental measurements as well as molecular dynamics simulations, the polyketone possesses the lowest glass transition temperature, but the ion transport is limited by a high degree of crystallinity. The polycarbonate, on the other hand, displays a relatively low coordination strength but is instead limited by its low molecular flexibility. The polyester performs generally as an intermediate between the other two, which is reasonable when considering its structural relation to the alternatives. This work demonstrates that local changes in the coordinating environment of carbonyl-containing polymers can have a large effect on the overall ion conduction, thereby also showing that desired transport properties can be achieved by fine-tuning the polymer chemistry of carbonyl-containing systems.

Segmental Motion Adjustment of the Polycarbonate Electrolyte for Lithium-Metal Batteries

Carbonyl oxygen atoms are the primary active sites to solvate Li salts that provide a migration site for Li ions conducting in a polycarbonate-based polymer electrolyte. We here exploit the conductivity of the polycarbonate electrolyte by tuning the segmental motion of the structural unit with carbonyl oxygen atoms, while its correlation to the mechanical and electrochemical stability of the electrolyte is also discussed. Two linear alkenyl carbonate monomers are designed by molecular engineering to combine methyl acrylate (MA) and the commonly used ethylene carbonate (EC), w/o dimethyl carbonate (DMC) in the structure. The integration of the DMC structural unit in the side chain of the in situ constructed polymer (p-MDE) releases the free motion of the terminal EC units, which leads to a lower glass-transition temperature and higher ionic conductivity. While pure polycarbonates are normally fragile with high Young's modulus, such a prolonged side chain also manipulates the flexibility of the polymer to provide a mechanical stable interface for Li-metal anode. Stable long-term cycling performance is achieved at room temperature for both LiFePO₄ and LiCoO₂ electrodes based on the p-MDE electrolyte incorporated with a solid plasticizer.

Structure and Diffusion of Ionic PDMS Melts

Ionic polymers exhibit mechanical properties that can be widely tuned upon selectively charging them. However, the correlated structural and dynamical properties underlying the microscopic mechanism remain largely unexplored. Here, we investigate, for the first time, the structure and diffusion of randomly and end-functionalized ionic poly(dimethylsiloxane) (PDMS) melts with negatively charged bromide counterions, by means of atomistic molecular dynamics using a united atom model. In particular, we find that the density of the ionic PDMS melts exceeds the one of their neutral counterpart and increases as the charge density increases. The counterions are condensed to the cationic part of end-functionalized cationic PDMS chains, especially for the higher molecular weights, leading to a slow diffusion inside the melt; the counterions are also correlated more strongly to each other for the end-functionalized PDMS. Temperature has a weak effect on the counterion structure and leads to an Arrhenius type of behavior for the counterion diffusion coefficient. In addition, the charge density of PDMS chains enhances the diffusion of counterions especially at higher temperatures, but hinders PDMS chain dynamics. Neutral PDMS chains are shown to exhibit faster dynamics (diffusion) than ionic PDMS chains. These findings contribute to the theoretical description of the correlations between structure and dynamical properties of ion-containing polymers.

Toward Bottom-Up Understanding of Transport in Concentrated Battery Electrolytes

Bottom-up understanding of transport describes how molecular changes alter species concentrations and electrolyte voltage drops in operating batteries. Such an understanding is essential to predictively design electrolytes for desired transport behavior. We herein advocate building a structure-property-performance relationship as a systematic approach to accurate bottom-up understanding. To ensure generalization across salt concentrations as well as different electrolyte types and cell configurations, the property-performance relation must be described using Newman's concentrated solution theory. It uses Stefan-Maxwell diffusivity, ij , to describe the role of molecular motions at the continuum scale. The key challenge is to connect ij to the structure. We discuss existing methods for making such a connection, their peculiarities, and future directions to advance our understanding of electrolyte transport.

Electric-Field-Induced Spatially Dynamic Heterogeneity of Solvent Motion and Cation Transference in Electrolytes

While electric fields primarily result in migration of charged species in electrolytic solutions, the solutions are dynamically heterogeneous. Solvent molecules within the solvation shells of the cation will be dragged by the field while free solvent molecules will not. We combine electrophoretic NMR measurements of ion and solvent velocities under applied electric fields with molecular dynamics simulations to interrogate different solvation motifs in a model liquid electrolyte. Measured values of the cation transference number (t_{+}^{0}) agree quantitatively with simulation-based predictions over a range of electrolyte concentrations. Solvent-cation interactions strongly influence the concentration-dependent behavior of t_{+}^{0}. We identify a critical concentration at which most of the solvent molecules lie within solvation shells of the cations. The dynamic heterogeneity of solvent molecules is minimized at this concentration where t_{+}^{0} is approximately equal to zero.

Silk fibroin and sericin polymer blends for sustainable battery separators

Natural polymers are a promising alternative for reducing the environmental impact of batteries. For this reason, it is still necessary to study their behavior and implement its use in these devices, especially in separator membranes. This work reports on new separator membranes based on silk fibroin (SF) and silk sericin (SS) prepared by salt leaching method. The effect of the different SS relative content on the physiochemical properties of the membranes and on the electrochemical performance of the corresponding batteries with lithium iron phosphate (LFP) as cathodes has been reported. It is observed that the increasing of SS content leads to a decrease of the overall crystallinity of the membranes. All SF/SS membranes presented a well-defined porosity above 75% with a uniform distribution of interconnected micropores. The electrolyte uptake and the ionic conductivity are dependent on the relative SS content. The addition of 10 wt% of SS into SF membranes, induce a high ionic conductivity of 4.09 mS.cm^-1 and high lithium transference number (0.52), due to the improvement of the Li⁺ ions conduction paths within the blended structure. Charge/discharge tests performed in Lithium/C-LFP half-cells reveal a discharge capacity of 85 mAh.g^-1 at 2C after 100 cycles for batteries with a SF/SS separator, containing a 10 wt% of SS, which suggests a stabilizing effect of Sericin on discharge capacity. Further, a 50% and 35% of capacity of retention and capacity fade, respectively, is observed. The presented SF/SS membrane show high electrochemical stability, being suitable for implementation in a next generation of sustainable battery systems. This could allow the SS valorization considering that 150,000 tons of SS are abandoned each year, reducing the contamination of environmental effluents.

The solvation structure, transport properties and reduction behavior of carbonate-based electrolytes of lithium-ion batteries

Despite the extensive employment of binary/ternary mixed-carbonate electrolytes (MCEs) for Li-ion batteries, the role of each ingredient with regards to the solvation structure, transport properties, and reduction behavior is not fully understood. Herein, we report the atomistic modeling and transport property measurements of the Gen2 (1.2 M LiPF₆ in ethylene carbonate (EC) and ethyl methyl carbonate (EMC)) and EC-base (1.2 M LiPF₆ in EC) electrolytes, as well as their mixtures with 10 mol% fluoroethylene carbonate (FEC). Due to the mixing of cyclic and linear carbonates, the Gen2 electrolyte is found to have a 60% lower ion dissociation rate and a 44% faster Li⁺ self-diffusion rate than the EC-base electrolyte, while the total ionic conductivities are similar. Moreover, we propose for the first time the anion–solvent exchange mechanism in MCEs with identified energetic and electrostatic origins. For electrolytes with additive, up to 25% FEC coordinates with Li⁺, which exhibits a preferential reduction that helps passivate the anode and facilitates an improved solid electrolyte interphase. The work provides a coherent computational framework for evaluating mixed electrolyte systems.

The different roles of the anion, cyclic and linear carbonates, and additive in mixed-carbonate electrolytes are revealed. The anion–solvent exchange mechanism and factors influencing the solid electrolyte interphase (SEI) formation are deciphered.

Importance of the Ion-Pair Lifetime in Polymer Electrolytes

Ion pairing is commonly considered as a culprit for the reduced ionic conductivity in polymer electrolyte systems. However, this simple thermodynamic picture should not be taken literally, as ion pairing is a dynamical phenomenon. Here we construct model poly(ethylene oxide)-bis(trifluoromethane)sulfonimide lithium salt systems with different degrees of ion pairing by tuning the solvent polarity and examine the relation between the cation-anion distinct conductivity σ+-d and the lifetime of ion pairs τ+- using molecular dynamics simulations. It is found that there exist two distinct regimes where σ+-d scales with 1/τ+- and τ+-, respectively, and the latter is a signature of longer-lived ion pairs that contribute negatively to the total ionic conductivity. This suggests that ion pairs are kinetically different depending on the solvent polarity, which renders the ion-pair lifetime highly important when discussing its effect on ion transport in polymer electrolyte systems.