Assessment of Tribological Properties of Ti3C2 as a Water-Based Lubricant Additive.

Water-based lubrication has attracted remarkable interest due to its environmental and economic advantages. However, practical applications of water-based lubrication are often limited, mainly because of low viscosity and corrosivity. The use of additives has been proposed to overcome these limitations. In this work, the tribological characteristics of titanium carbide (Ti3C2) MXenes, as additives for water-based lubrication, were systematically investigated for contact sliding between stainless steel under various normal forces and Ti3C2 concentrations. Both friction and wear were found to decrease with increasing Ti3C2 concentration up to 5 wt%, and then increased when the concentration was larger than 5 wt%. The results suggest that Ti3C2 flakes hindered direct contact, particularly at the edges of the contact interfaces. It was further shown that the agglomeration of Ti3C2 flakes may have reduced the hindering when an excessive amount of Ti3C2 (e.g., 7 wt%) was applied. The decreases in the friction coefficient and wear rate with 5 wt% of Ti3C2 concentration w approximately 20% and 48%, respectively. The outcomes of this work may be helpful in gaining a better understanding of the tribological properties of Ti3C2 as a feasible water-based lubrication additive.

Bundling of Collagen Fibrils Using Sodium Sulfate for Biomimetic Cell Culturing.

Collagen is the most abundant extracellular matrix protein. The concentrations, structural arrangement, and directionality of collagen depend on the type of tissue. Thick fibril bundles of collagen are observed in most collagenous tissues, including connective tissues, bones, and tendons, indicating that they play a critical role in many cell functions. In this study, we developed a new method to regulate collagen bundling without altering the protein concentration, temperature, or pH by using sodium sulfate to replicate bundled collagen fibrils found in vivo. Microstructure analysis revealed that both the thickness of the fibril bundles and the pore size of the matrix increased with the amount of sodium sulfate. In contrast, there was no significant change in the bulk mechanical stiffness of the collagen matrix. The modified collagen bundle matrix was used to investigate the responses of human cervical cancer cells by mimicking the extracellular environments of a tumor. Compared to the normal collagen matrix, cells on the collagen bundle matrix exhibited significant changes in morphology, with a reduced cell perimeter and aspect ratio. The cell motility, which was analyzed in terms of the speed of migration and mean squared displacement, decreased for the collagen bundle matrix. Additionally, the critical time taken for the peak turning angle to converge to 90° decreased, indicating that the migration direction was regulated by geometric cues provided by collagen bundles rather than by the intrinsic cell persistence. The experimental results imply that collagen bundles play an important role in determining the magnitude and direction in cancer cell migration. The proposed method of extracellular matrix modification can be applied to investigate various cellular behaviors in both physiological and pathological environments.

Effects of Interlayer Coupling and Band Offset on Second Harmonic Generation in Vertical MoS2/MoS2(1-x)Se2x Structures.

Noncentrosymmetric monolayers (MLs) of transition metal dichalcogenides (TMDCs) and their 3R-type vertical stacks provide an ideal platform for studying atomic-scale nonlinear light-matter interaction in terms of second harmonic generation (SHG). Unlike the case of MLs, SHG from artificial stacks can be nontrivially affected by interlayer coupling and band offset between the constituent MLs, where the latter occurs for band-gap-engineered vertical heterostructures (VHs). In order to study these effects, we produced different sets of 3R-type homobilayers (homo-BLs) and heterobilayers (hetero-BLs) composed of MoS2 and its ternary alloy MoS2(1-x)Se2x. We first investigated the impact of interlayer coupling on the SHG response across the A- and B-exciton resonances in the MoS2 homo-BLs. The coupling strength was varied by preparing (i) decoupled BLs (SiO2 intercalated), (ii) weakly coupled BLs (dry transferred), and (iii) strongly coupled BLs (postannealed) and monitored by photoluminescence, Raman, and reflectance difference spectroscopy, and atomic force microscopy. Unlike the decoupled BL, SHG in the coupled BLs cannot be explained by the simple square law in thickness due to coupling-induced band modification. The impact of exciton-resonance offset on SHG was also investigated in the hetero-BLs by controlling the Se concentration in MoS2xSe2(x-1). Although these VHs can significantly broaden the spectral range for efficient SHG by vertically superposing distinct resonances of the constituent MLs, coherent reinforcement of SHG cannot be achieved basically because of the π/2 phase difference between the on-resonance SHG field in one ML and the off-resonance SHG field in the other ML. Upon postannealing, however, the overlapping resonance regime exhibited unexpectedly high SHG enhancement. This may arise from the formation of the strong resonance when the VHs approach ideal 3R-type hetero-BLs. Our approach may be utilized for fully exploiting the TMDC VHs for highly efficient broadband SHG applications.

Operational and environmental conditions regulate the frictional behavior of two-dimensional materials.

The friction characteristics of single-layer h-BN, MoS2, and graphene were systematically investigated via friction force microscopy measurements at various operational (e.g., normal force and sliding speed) and environmental (e.g., relative humidity and thermal annealing) conditions. The low friction characteristics of these single-layer materials were clearly observed from the normal force-dependent friction results, and their interfacial shear strengths were further estimated using a Hertz-plus-offset model. In addition, speed-dependent friction characteristics clearly demonstrated two regimes of friction as a function of sliding speed - the first is the logarithmic increase in friction with sliding speed regime at sliding speeds smaller than the critical speed and the second is the friction plateau regime at sliding speeds greater than the critical speed. Fundamental parameters such as effective shape of the interaction potential and its corrugation amplitude for these single-layer materials were characterized using the thermally-activated Prandtl-Tomlinson model. Moreover, friction of single-layer h-BN, MoS2, and graphene was found to increase with relative humidity and decrease with thermal annealing; these trends were attributed to the diffusion of water molecules to the interface between the single-layer materials and their substrates, which leads to an increase in the puckering effect at the tip-material interface and interaction potential corrugation. The enhanced puckering effect was verified via molecular dynamics simulations. Overall, the findings enable a comprehensive understanding of friction characteristics for several classes of two-dimensional materials, which is important to elucidate the feasibility of using these materials as protective and solid-lubricant coating layers for nanoscale devices.

Layer-by-layer thinning of MoS2 via laser irradiation.

Layer-by-layer thinning of molybdenum disulfide (MoS2) via laser irradiation was examined using Raman spectroscopy and atomic force microscopy. In particular, the effects of number of layers, laser conditions, and substrate were systematically identified. The results demonstrated the presence of nanoparticles on the MoS2 at sufficient laser treatment conditions prior to layer-by-layer thinning. The volume of nanoparticles was found to increase and then decrease as the number of MoS2 layers increased; the non-monotonic trend was ascribed to changes in the thermal conductivity of the film and interfacial thermal conductance between the film and substrate with number of layers. Moreover, the volume of nanoparticles was found to increase as the magnification of the objective lens decreased and as laser power and exposure time increased, which was attributed to changes in the power density with laser conditions. The effect of substrate on nanoparticle formation and layer-by-layer thinning was investigated through a comparison of freestanding and substrate-supported MoS2 subjected to laser irradiation; it was illustrated that freestanding films were thinned at lower laser powers than substrate-supported films, which highlighted the function of the substrate as a heat sink. For conditions that elicited thinning, it was shown that the thinned areas exhibited triangular shapes, which suggested anisotropic etching behavior where the lattice of the basal plane was preferentially thinned along the zigzag direction terminated by an Mo- or S-edge. High-resolution transmission electron microscopy of freestanding MoS2 revealed the presence of a 2 nm thick amorphous region around the laser-treated region, which suggested that the crystalline structure of laser-treated MoS2 remained largely intact after the thinning process. In all, the conclusions from this work provide useful insight into the progression of laser thinning of MoS2, thereby enabling more effective methods for the development of MoS2 devices via laser irradiation.

Effect of tip shape on nanomechanical properties measurements using AFM.

Atomic force microscopy (AFM)-based indentation has been widely used to understand mechanical properties in conjunction with surface topography and structure at the nano-scale. In this work, nanomechanical properties of three different specimens were determined using four different AFM probes with spherical and flat-ended tips and conical tips with rounded apexes, to provide useful information for probe selection and for better interpretation of force-indentation data. These probes were modeled as a sphere, flat punch, and hyperboloid, respectively, after careful characterization to determine the elastic modulus based on contact models. Polyacrylic acid, polyvinylidene fluoride, and styrene-butadiene rubber were used as specimens. The results showed that the probe with a flat-ended tip was prone to misalignment between the flat end of the tip and specimen surface, which caused that the force-indentation data could not be interpreted using the contact model due to imperfect contact. Also, hysteresis was consistently observed in force-indentation data for the probes with a spherical tip and conical tips with rounded apexes, likely due to friction. This further resulted in significant differences in the elastic moduli of the specimens as large as 22-100% as determined from extension and retraction curves. The elastic moduli approximated by the mean of those from the extension and retraction curves generally agree with those from the instrumented indentation. Considering the uncertainties associated with the modeling of tip shape and force and indentation measurements, the probe with relatively large tip radius (e.g., ∼30 nm) was recommended for more accurate measurement for the specimen with a few GPa elastic modulus. Furthermore, the difference between elastic moduli determined from extension and retraction curves was found to increase as the ratio of contact stiffness to flexural stiffness of the AFM probe decreased. The outcome of this work is expected to provide useful information for obtaining accurate mechanical property measurements using an AFM based on a better understanding of the interaction between AFM probe and specimen.

Surface Properties of Laser-Treated Molybdenum Disulfide Nanosheets for Optoelectronic Applications.

Transition metal dichalcogenide two-dimensional materials have attracted significant attention due to their unique optical, mechanical, and electronic properties. For example, molybdenum disulfide (MoS2) exhibits a tunable band gap that strongly depends on the numbers of layers, which makes it an attractive material for optoelectronic applications. In addition, recent reports have shown that laser thinning can be used to engineer an MoS2 monolayer with specific shapes and dimensions. Here, we study laser-thinned MoS2 in both ambient and vacuum conditions via confocal µ-Raman spectroscopy, imaging X-ray photoelectron spectroscopy (i-XPS), and atomic force microscopy (AFM). For low laser powers in ambient environments, there is insufficient energy to oxidize MoS2, which leads to etching and redeposition of amorphous MoS2 on the nanosheet as confirmed by AFM. At high powers in ambient, the laser energy and oxygen environment enable both MoS2 nanoparticle formation and nanosheet oxidation as revealed in AFM and i-XPS. At comparable laser power densities in vacuum, MoS2 oxidation is suppressed and the particle density is reduced as compared to ambient. The extent of nanoparticle formation and nanosheet oxidation in each of these regimes is found to be dependent on the number of layers and laser treatment time. Our results can shed some light on the underlying mechanism of which atomically thin MoS2 nanosheets exhibit under high incident laser power for future optoelectronic applications.

Interfacial Strength and Surface Damage Characteristics of Atomically Thin h-BN, MoS2, and Graphene.

Surface damage characteristics of single- and multilayer hexagonal boron nitride (h-BN), molybdenum disulfide (MoS2), and graphene films were systematically investigated via atomic force microscopy (AFM)-based progressive-force and constant-force scratch tests and Raman spectroscopy. The film-to-substrate interfacial strengths of these atomically thin films were assessed based on their critical forces (i.e., the normal force where the atomically thin film was delaminated from the underlying substrate), as determined from progressive-force scratch tests. The evolution of surface damage with respect to normal force was further investigated using constant-force tests. The results showed that single-layer h-BN, MoS2, and graphene strongly adhere to the SiO2 substrate, which significantly improves its tribological performance. Moreover, defect formation induced by scratch testing was found to affect the topography and friction force differently prior to failure, which points to distinct surface damage characteristics. Interestingly, the residual strains at scratched areas suggest that the scratch test-induced in-plane compressive strains were dominant over tensile strains, thereby leading to buckling in front of the scratching tip and eventually failure at sufficient strains. These trends represent the general failure mechanisms of atomically thin materials because of a scratch test. As the number of layers increased, the tribological performances of atomically thin h-BN, MoS2, and graphene were found to significantly improve because of an increase in the interfacial strengths and a decrease in the surface damage and friction force. In all, the findings on the distinctive surface damage characteristics and general failure mechanisms are useful for the design of reliable, protective and solid-lubricant coating layers based on these materials for nanoscale devices.

Growth and Simultaneous Valleys Manipulation of Two-Dimensional MoSe2-WSe2 Lateral Heterostructure.

The covalently bonded in-plane heterostructure (HS) of monolayer transition-metal dichalcogenides (TMDCs) possesses huge potential for high-speed electronic devices in terms of valleytronics. In this study, high-quality monolayer MoSe2-WSe2 lateral HSs are grown by pulsed-laser-deposition-assisted selenization method. The sharp interface of the lateral HS is verified by morphological and optical characterizations. Intriguingly, photoluminescence spectra acquired from the interface show rather clear signatures of pristine MoSe2 and WSe2 with no intermediate energy peak related to intralayer excitonic matter or formation of MoxW(1-x)Se2 alloys, thereby confirming the sharp interface. Furthermore, the discrete nature of laterally attached TMDC monolayers, each with doubly degenerated but nonequivalent energy valleys marked by (KM, K'M) for MoSe2 and (KW, K'W) for WSe2 in k space, allows simultaneous control of the four valleys within the excitation area without any crosstalk effect over the interface. As an example, KM and KW valleys or K'M and K'W valleys are simultaneously polarized by controlling the helicity of circularly polarized optical pumping, where the maximum degree of polarization is achieved at their respective band edges. The current work provides the growth mechanism of laterally sharp HSs and highlights their potential use in valleytronics.

Quantitative Assessment of Friction Characteristics of Single-Layer MoS2 and Graphene Using Atomic Force Microscopy.

Atomically thin layered materials such as MoS2 and graphene have attracted a lot of interest as protective coating layers for micro- and nano-electromechanical devices based on their superior mechanical properties and chemical inertness. In this work, the frictional characteristics of single layer MoS2 and graphene prepared by the mechanical exfoliation method were quantitatively investigated using atomic force microscopy. The results showed that both MoS2 and graphene exhibited relatively low friction forces of 1-3 nN under normal forces ranging from 1 to 30 nN. However, a higher increase in the friction force as the normal force increased was observed in the case of MoS2. The differences in the adhesion characteristics and mechanical properties of atomically thin layered materials may influence the puckering of the layer, which in turn influences the frictional behavior.

Laser-Induced Particle Adsorption on Atomically Thin MoS2.

Atomically thin molybdenum disulfide (MoS2) shows great potential for use in nanodevices because of its remarkable electronic, optoelectronic, and mechanical properties. These material properties are often dependent on the thickness or the number of layers, and hence Raman spectroscopy is widely used to characterize the thickness of atomically thin MoS2 due to the sensitivity of the vibrational spectrum to thickness. However, the lasers used in Raman spectroscopy can increase the local surface temperature and eventually damage the upper layers of the MoS2, thereby changing the aforementioned material properties. In this work, the effects of lasers on the topography and material properties of atomically thin MoS2 were systematically investigated using Raman spectroscopy and atomic force microscopy. In detail, friction force microscopy was used to study the friction characteristics of atomically thin MoS2 as a function of laser powers from 0.5 to 20 mW and number of layers from 1 to 3. It was found that particles formed on the top surface of the atomically thin MoS2 due to laser-induced thermal effects. The degree of particle formation increased as the laser power increased, prior to the thinning of the atomically thin MoS2. In addition, the degree of particle formation increased as the number of MoS2 layers increased, which suggests that the thermal behavior of the supported MoS2 may differ depending on the number of layers. The particles likely originated from the atmosphere due to laser-induced heating, but could be eliminated via appropriate laser powers and exposure times, which were determined experimentally. The outcomes of this work indicate that thermal management is crucial in the design of reliable nanoscale devices based on atomically thin MoS2.

Quantitative assessment of contact and non-contact lateral force calibration methods for atomic force microscopy.

Atomic Force Microscopy (AFM) has been widely used for measuring friction force at the nano-scale. However, one of the key challenges faced by AFM researchers is to calibrate an AFM system to interpret a lateral force signal as a quantifiable force. In this study, five rectangular cantilevers were used to quantitatively compare three different lateral force calibration methods to demonstrate the legitimacy and to establish confidence in the quantitative integrity of the proposed methods. The Flat-Wedge method is based on a variation of the lateral output on a surface with flat and changing slopes, the Multi-Load Pivot method is based on taking pivot measurements at several locations along the cantilever length, and the Lateral AFM Thermal-Sader method is based on determining the optical lever sensitivity from the thermal noise spectrum of the first torsional mode with a known torsional spring constant from the Sader method. The results of the calibration using the Flat-Wedge and Multi-Load Pivot methods were found to be consistent within experimental uncertainties, and the experimental uncertainties of the two methods were found to be less than 15%. However, the lateral force sensitivity determined by the Lateral AFM Thermal-Sader method was found to be 8-29% smaller than those obtained from the other two methods. This discrepancy decreased to 3-19% when the torsional mode correction factor for an ideal cantilever was used, which suggests that the torsional mode correction should be taken into account to establish confidence in Lateral AFM Thermal-Sader method.

Multi-resistive reduced graphene oxide diode with reversible surface electrochemical reaction induced carrier control.

The extended application of graphene-based electronic devices requires a bandgap opening in order to realize the targeted device functionality. Since the bandgap tuning of pristine graphene is limited to 360 meV, the chemical modification of graphene is considered essential to achieve a large bandgap opening at the expense of electrical properties degradation. Reduced graphene oxide (RGO) has attracted significant interest for fabricating graphene-based semiconductors since it has several advantages over other forms of chemically modified graphene; such as tunable bandgap opening, decent electrical properties, and easy synthesis. Because of the reduced bonding nature of RGO, the role of metastable oxygen in the RGO matrix is recently highlighted and it may offer emerging ionic devices. In this study, we show that multi-resistivity RGO/n-Si diodes can be obtained by controlling the RGO thickness at a nanometer scale. This is made possible by (1) a metastable lattice-oxygen drift within bulk RGO and (2) electrochemical ambient hydroxyl (OH) formation at the RGO surface. The effect demonstrated in a p-RGO/n-Si heterojunction diode is equivalent to electrochemically driven reversible electronic manipulation and therefore provides an important basis for the application of O bistability in RGO for chemical sensors and electrocatalysis.

Cell spreading and proliferation in response to the composition and mechanics of engineered fibrillar extracellular matrices.

The extracellular matrix (ECM) consists of a complex mixture of biochemical and physical stimuli that together regulate cell behavior. In this study, we engineer a model ECM consisting of fibrillar Type-1 collagen plus fibronectin that allows systematic examination of the effects of matrix composition and mechanics on cells. On this combined protein matrix, cells exhibit intermediate degrees of spreading and proliferation compared to their responses on collagen or fibronectin alone. Adhesion to the combination matrix could be blocked by peptides containing the sequence arginine-glycine-aspartic acid (RGD) and by antibodies against α1 integrin, suggesting cell-matrix engagement was mediated by a combination of integrin receptors that recognize fibronectin and collagen. Regardless of integrin engagement, cells were sensitive to the mechanical properties of the combination ECM, suggesting that cells could process biochemical and mechanical cues simultaneously and independently.

Note: Lateral force microscope calibration using multiple location pivot loading of rectangular cantilevers.

This note outlines a calibration method for atomic force microscope friction measurement that uses the "pivot" method of [Bogdanovic et al., Colloids Surf. B 19, 397 (2000)] to generate optical lever sensitivities for known torque applied to rectangular cantilevers. We demonstrate the key calibration parameter to be a linear function of the position at which it is determined along the length of the cantilevers. In this way the optical lever system can be calibrated for cantilever torque by applying loads at locations along the length of a cantilever, away from the integrated tip, so that issues such as tip damage or interference can be avoided.

Nanomechanical properties of thin films of type I collagen fibrils.

The mechanical cues that adherent cells derive from the extracellular matrix (ECM) can effect dramatic changes in cell migration, proliferation, differentiation, and apoptosis. Model ECMs composed of collagen fibrils formed from purified collagen are an important experimental system to study cell responses to mechanical properties of the ECM. Using a self-assembled model system of a film composed of 100-200 nm diameter collagen fibrils overlaying a bed of smaller fibrils, we have previously demonstrated changes in cellular response to systematically controlled changes in mechanical properties of the collagen. In this study, we describe an experimental and modeling approach to calculate the elastic modulus of individual collagen fibrils, and thereby the effective stiffness of the entire collagen thin film matrix, from atomic force microscopy force spectroscopy data. These results demonstrate an approach to the analysis of fundamental properties of thin, heterogeneous, and organic films and add further insights into the mechanical and topographical properties of collagen fibrils that are relevant to cell responses to the ECM.

Lateral force calibration: accurate procedures for colloidal probe friction measurements in atomic force microscopy.

The colloidal probe technique for atomic force microscopy (AFM) has allowed the investigation of an extensive range of surface force phenomena, including the measurement of frictional (lateral) forces between numerous materials. The quantitative accuracy of such friction measurements is often debated, in part due to a lack of confidence in existing calibration strategies. Here we compare three in situ AFM lateral force calibration techniques using a single colloidal probe, seeking to establish a foundation for quantitative measurement by linking these techniques to accurate force references available at the National Institute of Standards and Technology. We introduce a procedure for calibrating the AFM lateral force response to known electrostatic forces applied directly to the conductive colloidal probe. In a second procedure, we apply known force directly to the colloidal probe using a precalibrated piezo-resistive reference cantilever. We found agreement between these direct methods on the order of 2% (within random uncertainty for both measurements). In a third procedure, we performed a displacement-based calibration using the piezo-resistive reference cantilever as a stiffness reference artifact. The method demonstrated agreement on the order of 7% with the direct force methods, with the difference attributed to an expected systematic uncertainty, caused by in-plane deflection in the cantilever during loading. The comparison establishes the existing limits of instrument accuracy and sets down a basis for selection criteria for materials and methods in colloidal probe friction (lateral) force measurements via atomic force microscopy.

The relative roles of collagen adhesive receptor DDR2 activation and matrix stiffness on the downregulation of focal adhesion kinase in vascular smooth muscle cells.

Cells within tissues derive mechanical anchorage and specific molecular signals from the insoluble extracellular matrix (ECM) that surrounds them. Understanding the role of different cues that extracellular matrices provide cells is critical for controlling and predicting cell response to scaffolding materials. Using an engineered extracellular matrix of Type I collagen we examined how the stiffness, supramolecular structure, and glycosylation of collagen matrices influence the protein levels of cellular FAK and the activation of myosin II. Our results show that (1) cellular FAK is downregulated on collagen fibrils, but not on a non-fibrillar monolayer of collagen, (2) the downregulation of FAK is independent of the stiffness of the collagen fibrils, and (3) FAK levels are correlated with levels of tyrosine phosphorylation of the collagen adhesion receptor DDR2. Further, siRNA depletion of DDR2 blocks FAK downregulation. Our results suggest that the collagen receptor DDR2 is involved in the regulation of FAK levels in vSMC adhered to Type I collagen matrices, and that regulation of FAK levels in these cells appears to be independent of matrix stiffness.

The treatment of collagen fibrils by tissue transglutaminase to promote vascular smooth muscle cell contractile signaling.

The enzyme tissue transglutaminase 2 (TG2) appears to play an important role in several physiological processes such as wound healing, the progression of cancer and of vascular disease. Additionally, TG2 has been proposed as a means of stabilizing collagen extracellular matrix (ECM) scaffolds for tissue engineering applications. In this report, we examined the effect of TG2 treatment on the mechanical properties of the ECM, and associated cell responses. Using a model ECM of fibrillar collagen, we quantitatively examined vascular smooth muscle cell (vSMC) response to untreated, or TG2 treated collagen. We show that cells respond to TG2 treated collagen with increased spreading, an increase in contractile response as indicated by elevated F-actin polymerization and myosin light chain phosphorylation, and increased proliferation, without apparent changes in integrin specificity or matrix topography. Comparative atomic force microscopy loading studies indicate that TG2 treated fibrils are 3 times more resistant to shearing force from an AFM tip than untreated fibrils. The data suggest that TG2 treatment of collagen increases matrix mechanical stiffness, which apparently alters the contractile and proliferative response of vSMC.

Accurate noncontact calibration of colloidal probe sensitivities in atomic force microscopy.

The absolute force sensitivities of colloidal probes comprised of atomic force microscope, or AFM, cantilevers with microspheres attached to their distal ends are measured. The force sensitivities are calibrated through reference to accurate electrostatic forces, the realizations of which are described in detail. Furthermore, the absolute accuracy of a common AFM force calibration scheme, known as the thermal noise method, is evaluated. It is demonstrated that the thermal noise method can be applied with great success to colloidal probe calibration in air and in liquid to yield force measurements with relative standard uncertainties below 5%. Techniques to combine the electrostatics-based determination of the AFM force sensitivity with measurements of the colloidal probe's thermal noise spectrum to compute noncontact estimates of the displacement sensitivity and spring constant are also developed.