Lower Free Energy Barrier Research Articles

Enhanced Water Nucleation and Growth Based on Microdroplet Mobility on Lubricant-Infused Surfaces.

Lubricant-infused surfaces (LISs) can promote stable dropwise condensation and improve heat transfer rates due to a low nucleation free-energy barrier and high droplet mobility. Recent studies showed that oil menisci surrounding condensate microdroplets form distinct oil-rich and oil-poor regions. These topographical differences in the oil surface cause water microdroplets to rigorously self-propel long distances, continuously redistributing the oil film and potentially refreshing the surface for re-nucleation. However, the dynamic interplay between oil film redistribution, microdroplet self-propulsion, and droplet nucleation and growth is not yet understood. Using high-speed microscopy, we reveal that during water condensation on LISs, the smallest visible droplets (diameter: ∼1 μm, qualitatively representing nucleation) predominantly emerge in oil-poor regions due to a lower nucleation free-energy barrier. Considering the significant heat transfer performance of microdroplets (<10 μm) and transient characteristic of microdroplet movement, we compare the apparent nucleation rate density and water collection rate for LISs with oils of different viscosities and a solid hydrophobic surface at a wide range of subcooling temperatures. Generally, the lowest lubricant viscosity leads to the highest nucleation rate density. We characterize the length and frequency of microdroplet movement and attribute the nucleation enhancement primarily to higher droplet mobility and surface refreshing frequency. Interestingly and unexpectedly, hydrophobic surfaces outperform high-viscosity LISs at high subcooling temperatures but are generally inferior to any of the tested LISs at low temperature differences. To explain the observed nonlinearity between LISs and the solid hydrophobic surface, we introduce two dominant regimes that influence the condensation efficiency: mobility-limited and coalescence-limited. We compare these regimes based on droplet growth rates and water collection rates on the different surfaces. Our findings advance the understanding of dynamic water-lubricant interactions and provide new design rationales for choosing surfaces for enhanced dropwise condensation and water collection efficiencies.

Metal-free catalysis for the reaction of nitrogen dioxide dimer with phenol: An unexpected favorable source of nitrate and aerosol precursors in vehicle exhaust

Atmospheric reaction mechanism and dynamics of phenol with nitrogen dioxide dimer were explored by the density functional theory and high-level quantum chemistry combined with statistical kinetic calculations within 220–800 K. The nitric acid and phenyl nitrite, the typical aerosol precursors, are the preponderant products because of the low formation free energy barrier (∼8.7 kcal/mol) and fast rate constants (∼10−15 cm3 molecule−1 s−1 at 298 K). Phenyl nitrate is the minor product and it would be also formed from the transformation of phenyl nitrite in NO2-rich environment. More importantly, kinetic effects and catalytic mechanism of a series of metal-free catalysts (H2O, NH3, CH3NH2, CH3NHCH3, HCOOH, and CH3COOH) on the title reaction were investigated at the same level. The results indicate that CH3NH2 and CH3NHCH3 can not only catalyze the title reaction by lowering the free energy barrier (about 1.4–6.5 kcal/mol) but also facilitate the production of organic ammonium nitrate via acting as a donor-acceptor of hydrogen. Conversely, the other species are non-catalytic upon the title reaction. The stabilization energies and donor-acceptor interactions in alkali-catalyzed product complexes were explored, which can provide new insights to the properties of aerosol precursors. Moreover, the lifetime of phenol determined by nitrogen dioxide dimer in the presence of dimethylamine may compete with that of determined by OH radicals, indicating that nitrogen dioxide dimer is responsible for the elimination of phenol in the polluted atmosphere. This work could help us thoroughly understand the removal of nitrogen oxides and phenol as well as new aerosol precursor aggregation in vehicle exhaust.

Discovering Catalytic Reaction Networks Using Deep Reinforcement Learning from First-Principles.

Determining the reaction pathways, which is central to illustrating the working mechanisms of a catalyst, is severely hindered by the high complexity of the reaction and the extreme scarcity of the data. Here, we develop a novel artificial intelligence framework integrating deep reinforcement learning (DRL) techniques with density functional theory simulations to automate the quantitative search and evaluation on the complex catalytic reaction networks from zero knowledge. Our framework quantitatively transforms the first-principles-derived free energy landscape of the chemical reactions to a DRL environment and the corresponding actions. By interacting with this dynamic environment, our model evolves by itself from scratch to a complete reaction path. We demonstrate this framework using the Haber-Bosch process on the most active Fe(111) surface. The new path found by our framework has a lower overall free energy barrier than the previous study based on domain knowledge, demonstrating its outstanding capability in discovering complicated reaction paths. Looking forward, we anticipate that this framework will open the door to exploring the fundamental reaction mechanisms of many catalytic reactions.

Effect of Graphene on Ice Polymorph

Recently, ice with stacking disorder structure, consisting of random sequences of cubic ice (Ic) and hexagonal ice (Ih) layers, was reported to be more stable than pure Ih/Ic. Due to a much lower free energy barrier of heterogeneous nucleation, in practice, the freezing process of water is controlled by heterogeneous nucleation triggered by an external medium. Therefore, we carry out molecular dynamic simulations to explore how ice polymorphism depends on the lattice structure of the crystalline substrates on which the ice is grown, focusing on the primary source of atmospheric aerosols, carbon materials. It turns out that, during the nucleation stage, the polymorph of ice nuclei is strongly affected by graphene substrates. For ice nucleation on graphene, we find Ih is the dominant polymorph. This can be attributed to structural similarities between graphene and basal face of Ih. Our results also suggest that the substrate only affects the polymorph of ice close to the graphene surface, with the preference for Ih diminishing as the ice layer grows.

Synergistic Effect of Atomically Dispersed Ni-Zn Pair Sites for Enhanced CO2 Electroreduction.

Dual-atom catalysts have the potential to outperform the well-established single-atom catalysts for the electrochemical conversion of CO2 . However, the lack of understanding regarding the mechanism of this enhanced catalytic process prevents the rational design of high-performance catalysts. Herein, an obvious synergistic effect in atomically dispersed Ni-Zn bimetal sites is observed. In situ characterization combined with density functional theory (DFT) calculations reveals that heteronuclear coordination modifies the d-states of the metal atom, narrowing the gap between the d-band centre (εd ) of the Ni (3d) orbitals and the Fermi energy level (EF ) to strengthen the electronic interaction at the reaction interface, resulting in a lower free energy barrier (ΔG) in the thermodynamic pathway and a reduced activation energy (Ea ) as well as fortified metal-C bonding in the kinetic pathway. Consequently, a CO faradaic efficiency of >90% is obtained across a broad potential window from -0.5 to -1.0V (vs RHE), reaching a maximum of 99% at -0.8V, superior to that of the Ni/Zn single-metal sites.

Two-Step Crystal Nucleation Is Selected Because of a Lower Surface Free Energy Barrier

Two-Step Crystal Nucleation Is Selected Because of a Lower Surface Free Energy Barrier

Regulating polysulfide intermediates by ultrathin Co-Bi nanosheet electrocatalyst in lithium−sulfur batteries

The practical application of lithium–sulfur (Li–S) batteries is hindered by the nonconductivity of sulfur, sluggish reaction kinetics and polysulfide shuttling. The liquid lithium polysulfide intermediates, connecting the Li–S battery electrochemical reaction of sulfur to Li2S, play a decisive role on battery performance. Herein, Co-Bi nanosheets intimately grown on reduced graphene oxides (Co-Bi/rGO) composite has been reported for the first time to regulate the polysulfide intermediates. The Co-Bi could not only chemically trap polysulfides but also propel the acceleration of polysulfide conversion enabled by a lower free energy and decomposition energy barrier in Li–S reaction process. Therefore, the Co-Bi/rGO–S cathode delivers a high capacity of 1334 mAh g–1 at 0.2 C, impressive rate performance up to 8 C, outstanding cycling stability over 500 cycles at 1 C, and remarkable areal capacity of 8.3 mAh cm–2 with a high sulfur mass loading of 9.5 mg cm–2. The chemical binding strength, the Gibbs free energy and the energy barrier for transition state from theoretical calculations give a deep insight of polysulfide regulation by Co-Bi.

Using general computational chemistry strategy to unravel the reactivity of emerging pollutants: An example of sulfonamide chlorination

Increasing number of emerging pollutants in environments requires an effective approach which can facilitate the prediction of reactivity and provide insights into the reaction mechanisms. Computational chemistry is exactly the tool to fulfill this demand with its good performance in theoretical investigation of chemical reactions at molecular level. In this study, chlorination of sulfonamide antibiotics is used as an illustration to present a systematic strategy demonstrating how computational chemistry can be applied to investigate the reaction behavior of emerging pollutants. Sulfonamides is a class of micropollutants that contain the common structure of 4-aminobenzenesulfonmaide while differ in their heterocycles. Based on the calculated conceptual DFT indices, the reactive sites of sulfonamide are successfully predicted, which locate on their common structure of 4-aminobenzenesulfonmaide. Therefore, all sulfonamides follow the similar reaction pathway. Product identification by LTQ-Orbitrap MS further verifies the in silico prediction. Three critical pathways are discovered, i.e., S-N bond cleavage, Cl-substitution onto aniline-N, and the following rearrangement to lose -SO2- group, among which Cl-substitution is the key step due to its lowest free energy barrier. Heterocycles impact the reaction rate by affecting the electronic density of aniline group. In general, the more electron-donating the heterocycle is, the more readily sulfonamides to be chlorinated.

Identifying active sites of boron, nitrogen co-doped carbon materials for the oxygen reduction reaction to hydrogen peroxide

The electrochemical synthesis of hydrogen peroxide (H2O2) from two-electron oxygen reduction reaction (2e- ORR) is a promising alternative for producing chemicals on demand, but its widespread application is still hampered by the low efficiency. Here, we successfully prepared a boron and nitrogen co-doped porous carbon (B/NC) aerogel with a tunable B, N co-doped configuration by the gelation of PVA-graphene, borax and PANI, followed by pyrolysis. Due to a hierarchical porous structure and optimized B, N co-doping, B/NC aerogel showed an excellent electrocatalytic performance for H2O2 production in alkaline solution with a high H2O2 selectivity (94.16%) at positive applied potential (0.6 V vs. RHE), superior than most of the other reported electrocatalysts. Density functional theory (DFT) calculations reveal that the hexagonal boron nitride (hBN) coupled with neighboring pyridinic-N species act as the active sites to lower free energy barrier for formation of HOO* intermediate, thus facilitating H2O2 production. Practically, B 2p electron plays an important role for the adsorption of HOO* intermediates. B and Nco-doping into carbon materials provides an effective and facile method to reasonably construct carbon-based catalysts for electroreduction of O2 to H2O2.

Elucidating the Dual Mode of Action of Dipeptidyl Enoates in the Inhibition of Rhodesain Cysteine Proteases.

A computational study of the two possible inhibition mechanisms of rhodesain cysteine protease by the dipeptidyl enoate Cbz-Phe-Leu-CH=CH-CO2 C2 H5 has been carried out by means of molecular dynamics simulations with hybrid QM/MM potentials. The low free energy barriers confirm that the Cys25 residue can attack both Cβ and C1 atoms of the inhibitor, confirming a dual mode of action in the inhibition of the rhodesain by enoates. According to the results, the inhibition process through the Cys25 attack on the Cβ atom of the inhibitor is an exergonic and irreversible process, while the inhibition process when Cys25 attacks on the C1 atom of the inhibitor is and exergonic but reversible process. The interactions between the inhibitor and rhodesain suggest that P2 is the most important fragment to consider in the design of new efficient inhibitors of rhodesain. These results may be useful for the design of new inhibitors of rhodesain and other related cysteine proteases based on dipeptidyl enoates scaffolds.

Modulating Electronic Structure of an Au‐Nanorod‐Core–PdPt‐Alloy‐Shell Catalyst for Efficient Alcohol Electro‐Oxidation

AbstractDirect alcohol fuel cells (DAFCs) utilize alcohol electro‐oxidation reactions (AORs) to provide electricity, where catalysts with optimal electronic structures are required to accelerate sluggish AORs. Herein, an electrocatalyst with an Au‐nanorod core and a PdPt‐alloy shell is designed. Its electronic structures are modulated through epitaxial growth of a PdPt‐alloy shell on the Au‐nanorod core, which exhibits a tensional strain effect and atomic steps. Three key problems of AORs are solved with this catalyst, including poor adsorption of alcohols on the catalyst, CO poisoning of the catalyst, and a high free energy barrier for the AORs. Taking methanol electro‐oxidation reaction (MOR) as an example, this catalyst shows 9.4 times higher mass activity than the market‐available Pt/C catalyst. Theoretic simulations prove that this catalyst has a low free energy barrier for the MOR, and strong adsorption of methanol but weaker adsorption of carbonaceous intermediates. The reasons behind this are the stretched geometric structure of the PdPt (100)‐alloy shell and the optimized electronic structure of catalytic sites on the catalyst surface. Meanwhile, efficient electro‐oxidation of ethanol, ethylene glycol, and glycerol is realized. This work paves the way to design and synthesize universal and efficient AOR catalysts for the construction of high‐performance DAFCs.

Photocatalytic conversion of CO to fuels with water by B-doped graphene/g-C3N4 heterostructure

Photocatalytic reduction of carbon monoxide (CO) is a promising route to the production of high-value chemicals and fuels, as a supplement to high energy-input Fischer-Tropsch synthesis (FTS) and a key step in direct photo/electro-reduction CO2 to multi-carbon products. However, many current research efforts for high-efficiency FTS/CO2 reduction mainly focus on the metal-based catalysts, while metal-free and solar-driven photocatalysts are rarely explored. Here, by means of Lewis acid sites, a metal-free composite photocatalyst for CO reduction, namely boron (B) doped-graphene/g-C3N4 heterostructure, is proposed. First-principles calculations show that the dopants (B) as catalytic sites can effectively capture and activate CO molecules and reduce CO to CH3OH and CH4 in different doping content. It is worth noting that C2 products, i.e., C2H5OH, can be produced with low free energy barriers on para-doped graphene/g-C3N4. Meanwhile, the competitive hydrogen evolution reaction (HER) can be greatly suppressed, leading to the high selectivity of CO reduction. Moreover, the formation of a built-in electric field in heterostructure enhances the separation of photogenerated electrons and holes, which further accelerates the transmission of photogenerated electrons to the catalytic sites and improves the reaction efficiency. Overall, this work not only proposes a new strategy from a new perspective to solve problems of high energy consumption and low selectivity of FTS, but also provides a tandem strategy to solve problems of CO2 to multi-carbon products.

Cell-Penetrating Peptides: Correlation between Peptide-Lipid Interaction and Penetration Efficiency.

Cell-penetrating peptides are used in the delivery of peptides and biologics, with some cell-penetrating peptides found to be more efficient than others. The exact mechanism of how they interact with the cell membrane and penetrate it, however, remains unclear. This study attempts to investigate the difference in free energy profiles of three cell-penetrating peptides (TAT, CPP1 and CPP9) with a model lipid bilayer (DOPC) using molecular dynamics pulling simulations with umbrella sampling. Potential mean force (PMF) and free energy barrier between the peptides and DOPC are determined using WHAM analysis and MM-PBSA analysis, respectively. CPP9 is found to have the smallest PMF value, followed by CPP1 and TAT, consistent with the experimental data. YDEGE peptide, however, does not give the highest PMF value, although it is a non-cell-permeable peptide. YDEGE is also found to form water pores, alongside with TAT and CPP9, suggesting that it is difficult to distinguish true water pore formation from artefacts arising from pulling simulations. On the contrary, free energy analysis of the peptide-DOPC complex at the lipid-water interface with MM-PBSA provides results consistent with experimental data with CPP9 having the least interaction with DOPC and lowest free energy barrier, followed by CPP1, TAT and YDEGE. These findings suggest that peptide-lipid interaction at the lipid-water interface has a direct correlation with the penetration efficiency of peptides across the lipid bilayer.

In silico Probing Ca2+ And Zn2+ Permeable Transmembrane 4Aβ1-42 Barrel

Alzheimer’s disease is known as one of the most popular forms of dementia affecting numerous people worldwide. The Amyloid beta (Aβ) peptides form to oligomeric conformations that cause the intracellular Ca2+ and Zn2+ abnormality leading to the death of neuron cells. The failure of AD therapy targeting Aβ oligomers probably caused by misunderstanding the ions transport through transmembrane Aβ (tmAβ) ion-like channel since Aβ oligomers transiently exist in a mixture order of Aβ oligomers. The high-resolution of tmAβ peptides are thus unavailable until the date. Fortunately, computational approaches are able to complement the missing experimental structures. The transmembrane 4Aβ1-42 (tm4Aβ1-42) barrel, one of the most neurotoxic elements, was thus predicted in the previous work. Therefore, in this context, the Ca2+/Zn2+ ions transport through the tm4Aβ1-42 barrel was investigated by using the fast pulling of ligand (FPL) and umbrella sampling (US) methods. Good consistent results were obtained implying that Ca2+ ion transport through tm4Aβ1-42 barrel with a lower free energy barrier compared with Zn2+ ion. The obtained results about Ca2+/Zn2+ transport across tmAβ1-42 barrel probably enhances the AD therapy

N-Heterocyclic Carbenes–Cu

The electronic structures of N-heterocyclic carbenes (NHC) imidazolinylidene, thiazolinylidene, imidazolylidene, thiazolylidene, and 1,2,4-triazolylidene and their complexes with cuprous halides (CuX, X = Cl, Br, I) were investigated theoretically at the B3LYP/def2-SVP level. In contrast to other NHCs, imidazolylidene and 1,2,4-triazolylidene do not dimerize owing to the negligible coefficient of the vacant p-orbital at the carbene centre in their respective LUMOs. This is further supported by their greater thermodynamic and kinetic stabilities revealed by greater activation free energies and smaller standard free energies for their dimerization. Second-order perturbation interactions in the natural bond orbital (NBO) analysis of the NHCs indicate that six π electrons are delocalized in imidazolylidene, thiazolylidene, and 1,2,4-triazolylidene, conferring aromatic character and thereby enhancing their thermodynamic stability. NBO analysis reveals the existence of effective back bonding from a d orbital of Cu to the NHC, increasing the Wiberg bond index of the C–Cu bond to ~1.5. Owing to the large electronic chemical potential (μ) and high nucleophilicity indices, NHCs are able to transfer their electron density effectively to the cuprous halides having low μ values and high electrophilicity indices to yield stable NHC–CuI complexes. Large values of the Fukui function f(r) at the carbene centre of the NHCs and Cu atom of the NHC–CuI complexes indicate their softness. Imidazolylidene was found to be the softest, rationalizing wide use of this class of NHCs as ligands. The coordination of the NHCs to cuprous halides is either barrierless or has a very low activation free energy barrier. In the A3 reaction wherein NHC–Cu(I) complexes are used as catalyst, the reaction of NHC–CuI with phenylacetylene changes the latter into acetylide accompanied by raising the energy level of its HOMO considerably compared with the level of the uncomplexed alkyne, making its reaction with benzaldehyde barrierless.

Multi-phase-field simulation of microstructure evolution in metallic foams

This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field approach. The model allows to naturally account for the effect of additives which prevent two gas bubbles from coalescence. By applying a non-merging criterion to the phase fields and at the same time raising the free energy penalty associated with additives, it is possible to completely prevent coalescence of bubbles in the time window of interest and thus focus on the formation of a closed porous microstructure. On the other hand, using a modification of this criterion along with lower free energy barriers we investigate with this model initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions.

Density functional theory study of nitrogen-doped graphene as a high-performance electrocatalyst for CO2RR

Metal-free catalysts for the CO2 reduction reaction (CO2RR) is a research hotspot to enhance CO2 utilization as a way to counteract global warming. Nitrogen-doped graphene attracts attention because of the abundance of nitrogen and promising catalytic performance of graphene. In this work, we investigated various N-doped configurations and their corresponding catalytic abilities for CO2RR to ethanol via spin-polarized density functional theory (DFT) computations. The final results indicate that site 43 of binary-N-doped graphene had high CO2RR activity, stable adsorption of reactants, and good activation of CO2. The catalysis process demonstrated features of low free energy barriers in the rising stage and obvious facilitation of the potential-limiting step. Compared with a catalyst-free process, it can effectively improve the reaction activity. The results provide theoretical guidance for the design and preparation of high-performance CO2RR catalysts.

Mechanistic Insights into the Conversion of Biorenewable Levoglucosanol to Dideoxysugars

A molecular understanding of the conversion of biorenewable threo- and erythro-levoglucosanol (LGOL) to 3,4-dideoxysugars in aqueous medium is provided based on first-principles simulations. The synthetic importance of this transformation is that these intermediates can be quantitatively hydrogenated to (S,S)/(S,R) hexane-1,2,5,6-tetrol (tetrol), whose stereochemistry depends on which dideoxy sugar intermediates are formed during LGOL conversion. The thermodynamic and kinetic feasibility of the acetal (R₂C(OR)₂) hydrolysis in LGOL is investigated via computing the free energy profile. In aqueous medium, the rate-determining step of LGOL hydrolysis is the protonation of the anhydro-bridge oxygen atom of LGOL concurrent with ring opening, yielding the cyclic forms of 3,4-dideoxymannose (DDM) and 3,4-dideoxyglucose (DDG) from threo- and erythro-LGOL, respectively. The measured activation energies of LGOL hydrolysis are 20.5 and 23.6 kcal/mol for DDM and DDG formation, respectively. These values are in agreement with the computed protonation free energies of 17.1 and 18.2 kcal/mol, respectively. Based on the simulations, a Bronsted base-catalyzed isomerization from DDG or DDM to 3,4-dideoxy fructose (DDF) is preferred with lower apparent activation free energy barriers compared to the acid-catalyzed isomerization. In summary, this study provides mechanistic information about the conversion of the biomass-derived anhydro-sugar LGOL to 3,4-dideoxy sugars, which are precursors to renewable high-value chemicals.

Conventional Molecular Dynamics and Metadynamics Simulation Studies of the Binding and Unbinding Mechanism of TTR Stabilizers AG10 and Tafamidis

Amyloid transthyretin (ATTR) amyloidosis is a widespread and fatal systemic amyloidosis characterized by the misfolding and amyloid aggregation of transthyretin (TTR). Studies suggest that dissociation of the TTR tetramer is the key step for its misfolding. Because of the importance of tetramer dissociation on ATTR amyloidosis, many TTR stabilizers have been discovered to stabilize the tetramer structure. This paper describes the application conventional molecular dynamics and metadynamics simulations to investigate the binding and unbinding mechanisms of two TTR stabilizers, including AG10 and tafamidis. AG10 has been granted an orphan drug designation by the U.S. Food and Drug Administration (FDA), and tafamidis was the first FDA-approved treatment for ATTR cardiomyopathy. The conventional molecular dynamics simulations reveal that both AG10 and tafamidis can stabilize the TTR tetramer through different mechanisms. AG10 stabilizes TTR tetramer by forming H-bonds with S117 to mimic the protective effect of T119M. Tafamidis stabilizes the tetramer by forming H-bond with S52 in the flexible CD loop to increase its structural stability. Despite the strong binding affinity of tafamidis, the free-energy surface constructed from metadynamics simulation suggests that tafamidis unbinds more readily than AG10 with lower free-energy barriers between the binding state and other intermediates. Finally, by performing pharmacophore analysis, we found two common important moieties of the studied compounds for their binding on the pockets, which can provide valuable guidance for future lead compounds' optimization in designing drugs for ATTR amyloidosis.

Fingerprints of relaxor ferroelectrics: Characteristic hierarchical domain configurations and quantitative performances

Ferroelectrics’ structure-property relationships are of guiding significance in high-performance material designing and usually clarified from the aspect of symmetries, which is arduous and costly. On the principle of convenience, here, the concept that domains can provide a brandnew nondestructive and fast way for this relationship clarification is demonstrated. Utilizing scanning probe microscopy, quantitative original local elastic/piezoelectric/ferroelectric performances of various characteristic domain configurations are directly investigated in relaxor ferroelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals. Among them, the polygonal lamellar domains with coexistence of straight c, a and c/a walls in the at-morphotropic phase boundary composition, own high surface effective Young's modulus (average values close to 160 GPa), strong original average local piezoresponse (8.5 pm) and effective longitudinal piezoelectric response (d33, 14 pm V−1), together with ease of electrical switching. Low free energy barrier and strong piezoelectric anisotropy contribute intrinsically to these better functionalities. Higher and easier domain wall motion, larger ratio of c+/c− domains, and larger depolarization and elastic energies stemmed from larger domain width/size act as extrinsic factors. These results help to understand relaxor ferroelectrics comprehensively and provide a reference of domain-based structure selection for better material design.