Selective Control of Novel TiO2 Nanorods: Excellent Building Blocks for the Electron Transport Layer of Mesoscopic Perovskite Solar Cells.

Novel TiO2 nanorods (NRs) with various lengths of 70-200 nm and uniform widths of 46-48 nm are selectively synthesized by a solvothermal reaction under a basic environment. The length of TiO2 NRs is reproducibly tuned by varying the concentration of tetramethylammonium hydroxide (TMAH), while the NRs in the pure anatase phase are grown in the [001] direction, caused by the preferential binding affinity of TMAH to the TiO2 (101) facet. TiO2 NRs of various lengths are then applied to form the electron transporting layer (ETL) of mesoscopic perovskite solar cells (PSCs). We found that PSC devices with NRs exhibit superior photovoltaic (PV) performance to those with conventional 46 nm-sized TiO2 nanoparticles (NP46). Particularly, the PSC with TiO2 NRs of 110 nm length (NR110) exhibits the optimum PV conversion efficiency (PCE): the average PCE is 22.64% with a VOC of 1.137 V, a JSC of 24.60 mA·cm-2, and a FF of 80.96%, while the champion PCE is 23.18%. In addition, the PSC with NR110 (PSC-NR110) reveals significantly improved long-term stability in air with a relative humidity of 40-50%. In 1000 h, its PCE is reduced by only 9% whereas that of PSC with NP46 decreases by 25%. The PSC properties analyzed by impedance spectroscopy and J-V curve measurements under dark conditions and at various light intensities provide evidence that PSC-NR110 has fewer defects and shows significantly reduced charge recombination. We discuss the advantages of NR structures in preparing the ETL of PSC devices and also explain why the charge recombination is suppressed.

Formation of Highly Efficient Perovskite Solar Cells by Applying Li-Doped CuSCN Hole Conductor and Interface Treatment.

Li-doped CuSCN films of various compositions were applied as hole-transporting material (HTM) for mesoscopic perovskite solar cells (PSCs). Those films of ~60 nm thickness, spin-coated on the perovskite layer, exhibit significantly higher crystallinity and hole mobility compared with the pristine CuSCN films. Among them, 0.33% Li-doped CuSCN (Li0.33:CuSCN) shows the best performance as the HTM of mesoscopic PSC. Furthermore, by depositing a slight amount of PCPDTBT over the Li0.33:CuSCN layer, the VOC was increased to 1.075 V, resulting in an average PCE of 20.24% and 20.65% for the champion device. These PCE and VOC values are comparable to those of PSC using spiro-OMETAD (PCE: 20.61%, VOC: 1.089 V). Such a remarkable increase can be attributed to the penetration of the PCPDTBT polymer into the grain boundaries of the Li0.33:CuSCN film, and to the interface with the perovskite layer, leading to the removal of defects on the perovskite surface by paving the non-contacting parts, as well as to the tight interconnection of the Li0.33:CuSCN grains. The PSC device with Li0.33:CuSCN showed a high long-term stability similar to that with bare CuSCN, and the introduction of PCPDTBT onto the perovskite/Li0.33:CuSCN further improved device stability, exhibiting 94% of the initial PCE after 100 days.

Oriented Crystal Growth during Perovskite Surface Reconstruction.

Surface passivation has become a key strategy for an improvement in power conversion efficiency (PCE) of perovskite solar cells (PSCs) since PSCs experienced a steep increase in PCE and reached a comparably matured point. Recently, surface passivation using a mixed salt of fluorinated alkyl ammonium iodide and formamidinium bromide demonstrated a remarkable improvement in both performance and stability, which can be tuned by the length of the alkyl chain. Nevertheless, the role of the alkyl chain in manipulating surface-limited crystal growth was not fully understood, preventing a further progress in interface control. In this study, we found that the length of the fluorine-substituted alkyl chain governed the crystal formation dynamics by manipulating surface tensions of different crystal orientations. The overall enhancement of the (001) plane, being the most favored, commonly resulted from the surface reformation of the perovskite film regardless of the chain length, while the highly oriented (001) over (111) was monitored with a particular chain length. The enhanced crystal orientation during surface recrystallization was responsible for the low trap density and thus effectively suppressed charge recombination at the interface, resulting in a considerable increase in open-circuit voltage and fill factor.

Enhanced Phase Stability of Compressive Strain-Induced Perovskite Crystals.

Control of strain in perovskite crystals has been considered as an effective strategy to ensure the phase stability of perovskite films where a compressive strain is particularly preferred over a tensile strain due to a lowered Gibbs free energy by the unit cell contraction effect. Here we adapt the strategy of strain control into perovskite solar cells in which the compressive strain is applied by utilizing a thermal expansion difference between the perovskite film and an adjacent layer. Poly(4-butylphenyldiphenylamine), with a higher thermal expansion coefficient compared to that of perovskite, is employed as a substrate for perovskite crystal growth at 100 °C, followed by cooling to room temperature. The applied compressive strain at the interface, as a result of a greater contraction of the polymer compared to the perovskite film, is confirmed by grazing incidence X-ray diffraction showing a red peak shift with increasing secondary angle. The compressive strain-induced perovskite film shows relatively constant absorbance spectra as a function of time. In the meantime, the absorbance spectra of a film without strain control exhibit a gradual decay with developing an Urbach tail. Importantly, the effect of strain engineering is remarkably prominent in the long-term photovoltaic performance. The photocurrent drops by 41% over 911 h without controlling strain, which is significantly improved by employing compressive strain, showing only a 6% drop in photocurrent from a shelf-stability test without encapsulation. It is also noted that an S-shaped kink appears in the current-voltage curves since 579-h-long storage for the device without strain control, leading to unreliable and overestimated fill factor and conversion efficiency. On the other hand, a 16% increase in fill factor with a stable performance is derived over 911 h from the compressive strain-induced device.

Increase in Photocurrent Density of WO3 Photoanode by Placing a Layer of an Ordered Array of Mesoporous WO3 Micropillars on Top of a WO3 Sheet Layer.

A facile stamping method was developed to assemble ordered arrays of mesoporous WO3 micropillars with uniform sizes, shapes, and lengths on F-doped tin oxide glass. Using this method, a series of WO3 heterostructural bilayer photoanodes consisting of an array of m-µm long ordered mesoporous WO3 micropillars at the top and the n-µm thick mesoporous WO3 plain sheet layer at the bottom (denoted as m/n) were prepared. Among them 2.5/7.5 displayed a steady state photocurrent density of 3.6 mA cm-2 at 1.23 V (vs RHE) under AM 1.5 (1 Sun), which is much higher than that of the plain 10-µm thick WO3 sheet (2.5 mA cm-2). This phenomenon occurs owing to the following six benefits: increases in charge carrier density, number of photogenerated electron, charge collection rate, thermodynamic feasibility for the vectorial charge transport from the outermost layer of the photoanode to the inner layer, the surface hydrophilicity, and the decrease in charge transfer resistance.

Controllable synthesis and self-template phase transition of hydrous TiO2 colloidal spheres for photo/electrochemical applications.

Hydrous TiO2 colloidal spheres (HTCS) derived from the direct precipitation of titanium alkoxides have attracted continuous interests since 1982. Entering the 21st century, rapid progress in the development of structure-directing agents (SDAs) have enabled reproducible and size-controllable synthesis of highly uniform HTCS with diameters in the nano- to micro-meter range. The availability of various HTCS provides versatile self-templating platforms for the targeted synthesis of nanoporous TiO2 and titanate spheres with tunable composition, crystallographic phases, and internal structures for a variety of advanced photo/electrochemical applications. This review provides a historical overview for the evolution of HTCS, along with an insightful discussion for the formation mechanism of self-assembly of HTCS during the sol-gel process. Key synthetic parameters including SDA, solvent, reaction temperature and water dosage are discussed for the size and morphology control of HTCS with predictable textural properties. Then, we describe the synthetic strategies of nanoporous TiO2 and titanate spheres using various HTCS as self-templates. Here, the focus lies on the interactions between TiO2 nanobuilding blocks with precursors or media at the solid/liquid and solid/solid interfaces, the concurrent phase transitions, and the microstructural and morphological evolutions. Selective formation of crystal phase and internal structures (e.g., solid, hollow, core-shell, yolk-shell) are discussed by manipulating the crystallization kinetics. To further elucidate the composition-structure-property-performance relationship for the resulting nanoporous TiO2 and titanate spheres, their applications in photo(electro)catalysis, mesoscopic solar cells, and lithium-ion batteries are scrutinized. Finally, we share opinions on key challenges and perspectives for the future controllable preparation, formation mechanisms, and applications of HTCS and their crystalline derivatives.

Mesoporous WO3/TiO2 spheres with tailored surface properties for concurrent solar photocatalysis and membrane filtration.

The strategical integration of membrane water filtration with semiconductor photocatalysis presents a frontier in deep purification with a self-cleaning capability. However, the membrane fouling caused by the cake layer of the reclaimed TiO2 nanoparticles is a key obstacle. Herein, mesoporous WO3/TiO2 spheres (∼450 nm in diameter) consisting of numerous self-assembled WO3-decoated anatase TiO2 nanocrystallites are successfully prepared via a facile wet-chemistry route. The decoration of monolayered WO3 significantly affects the surface, photocatalytic, and optical properties of original mesoporous TiO2 spheres. XRD and Raman analyses show the presence of monolayered WO3 suppresses the crystal growth of TiO2 during the calcination process, significantly improves the surface acidity, and causes an obvious red shift in absorption edge. These favorable textural properties, coupling the enhanced interfacial charge carrier separation, render mesoporous WO3/TiO2 spheres with a superior photocatalytic activity in degradation of methylene blue under UV, visible, and solar light irradiations. The optimal molar ratio of W/Ti is examined to 6%. The synthesized mesoporous WO3/TiO2 spheres also show much higher flux during membrane filtration in both dead-end and cross-flow modes, suggesting a promising photocatalyst for concurrent membrane filtration and solar photocatalysis.

Remarkable variation of visible light photocatalytic activities of M/Sn0.9Sb0.1O2/TiO2 (M=Au, Ag, Pt) heterostructures depending on the loaded metals.

Sn0.9Sb0.1O2/TiO2 (ATO/TiO2) heterostructure is a potential visible light photocatalysts that function via an inter-semiconductor hole-transport mechanism. Herein we selectively deposited Au, Ag, or Pt onto the ATO surface of ATO/TiO2 to investigate charge-trapping behaviors of the noble metals and their effects on photocatalytic performance. We observed that Pt deposition greatly enhanced the photocatalytic activity whereas effects of Au or Ag depositions were not significant. The result of spectroscopic analysis also indicates that Pt is the most effective in scavenging the electrons from the ATO CB. Particularly, Pt/ATO/TiO2 (ATO:TiO2 = 15:85 in weight) produced CO2 of 42 ppmv in 2 h, which is 16 times and 4.8 times that of bare ATO/TiO2 and nitrogen-doped TiO2, respectively. Pt deposition on the ATO seems to suppress two independent charge recombination pathways, that is, recombination of electron-hole pairs in ATO and electron transport from the ATO CB to TiO2 VB.

Controllable Synthesis and Crystallization of Nanoporous TiO2 Deep-Submicrospheres and Nanospheres via an Organic Acid-Mediated Sol-Gel Process.

Although considerable progress has been achieved in the preparation of uniform hydrous TiO2 spheres (HTS) through the sol-gel process, there is plenty of room left in tailoring the size and morphology of HTS on the deep-submicron scale or even nanoscale since the diameters of the so far reported HTS are mostly on the (sub)micron scale (0.3-1.2 µm). Here, we develop a novel titanium tetraisopropoxide (TTIP)-organic acid (OA)-acetonitrile (ACN)-methanol (MeOH)-H2O system, which facilitates the control of nanoporous HTS to the range of 50-300 nm. The synthetic parameters including OA, (co-)solvent, concentration of precursor, and reaction temperature are comprehensively optimized, aiming at reproducible preparation and precise size control. Among the various OAs, n-valeric acid presents the best capability in controlling the spherical morphology and size uniformity. The synthesized amorphous HTS containing numerous micropores and mesopores show excellent hydrothermal stability and offer suitable self-template for the subsequent synthesis of mesoporous anatase TiO2 spheres (MAT) with a large surface area of 99.1 m2/g. The obtained TiO2 deep-submicrospheres and nanospheres with tunable sizes show great potential in various research fields.

Highly efficient adsorptive removal of sulfamethoxazole from aqueous solutions by porphyrinic MOF-525 and MOF-545.

The metal-organic frameworks MOF-525 and MOF-545 comprised of Zr-oxide clusters and porphyrin moieties in different geometries were synthesized solvothermally and applied for the adsorptive removal of the broadly used organic contaminant sulfamethoxazole (SMX) from water. Both MOFs were found highly efficient for the adsorption of SMX with the maximum adsorption capacities of 585 and 690 mg/g for MOF-525 and MOF-545, respectively. The latter value is the highest adsorption capacity reported so far for the adsorption of SMX molecules on any adsorbent. The adsorption equilibrium could be modeled successfully by the Langmuir model, which showed close to matching with the experimental data. Their adsorption equilibriums were attained within 120 and 30 min for MOF-525 and MOF-545, respectively. MOF-545 with mesopores demonstrated superior adsorption kinetics to MOF-525 with micropores, and the simulation by the pseudo-second-order kinetic model indicated ca. 20 times faster adsorption by MOF-545 than MOF-525. Both showed pH-dependent adsorption of SMX with a gradual reduction at high pH due to the repulsion between negatively charged adsorbent and SMX. The adsorption of SMX conducted over a group of representative MOFs with different physicochemical properties and detailed characterization confirmed that the high adsorption capacity of the porphyrin MOFs is achieved by H-bonding between the SMX molecule and the N-sites of the porphyrin units in the MOFs, π-π interaction, and the high surface area. The adsorbents were easily regenerated by simple washing with acetone and reusable with >95% efficiency during 4 repeated adsorption-desorption cycles.

Silicotungstate, a Potential Electron Transporting Layer for Low-Temperature Perovskite Solar Cells.

Thin films of a heteropolytungstate, lithium silicotungstate (Li4SiW12O40, termed Li-ST), prepared by a solution process at low temperature, were successfully applied as electron transporting layer (ETL) of planar-type perovskite solar cells (PSCs). Dense and uniform Li-ST films were prepared on FTO glass by depositing a thin Li-ST buffer layer, followed by coating of a main Li-ST layer. The film thickness was controlled by varying the number of coating cycles, consisting of spin-coating and thermal treatment at 150 °C. In particular, by employing 60 nm-thick Li-ST layer obtained by two cycles of coating, the fabricated CH3NH3PbI3 PSC device demonstrates the photovoltaic conversion efficiency (PCE) of 14.26% with JSC of 22.16 mA cm-2, VOC of 0.993 mV and FF of 64.81%. The obtained PCE is significantly higher than that of the PSC employing a TiO2 layer processed at the same temperature (PCE = 12.27%). Spectroscopic analyses by time-resolved photoluminescence and pulsed light-induced transient measurement of photocurrent indicate that the Li-ST layer collects electrons from CH3NH3PbI3 more efficiently and also exhibits longer electron lifetime than the TiO2 layer thermally treated at 150 °C. Thus, Li-ST is considered to be a promising ETL material that can be applied for the fabrication of flexible PSC devices.

Dual-Function Au@Y2O3:Eu3+ Smart Film for Enhanced Power Conversion Efficiency and Long-Term Stability of Perovskite Solar Cells.

In the present study, a dual-functional smart film combining the effects of wavelength conversion and amplification of the converted wave by the localized surface plasmon resonance has been investigated for a perovskite solar cell. This dual-functional film, composed of Au nanoparticles coated on the surface of Y2O3:Eu3+ phosphor (Au@Y2O3:Eu3+) nanoparticle monolayer, enhances the solar energy conversion efficiency to electrical energy and long-term stability of photovoltaic cells. Coupling between the Y2O3:Eu3+ phosphor monolayer and ultraviolet solar light induces the latter to be converted into visible light with a quantum yield above 80%. Concurrently, the Au nanoparticle monolayer on the phosphor nanoparticle monolayer amplifies the converted visible light by up to 170%. This synergy leads to an increased solar light energy conversion efficiency of perovskite solar cells. Simultaneously, the dual-function film suppresses the photodegradation of perovskite by UV light, resulting in long-term stability. Introducing the hybrid smart Au@Y2O3:Eu3+ film in perovskite solar cells increases their overall solar-to-electrical energy conversion efficiency to 16.1% and enhances long-term stability, as compared to the value of 15.2% for standard perovskite solar cells. The synergism between the wavelength conversion effect of the phosphor nanoparticle monolayer and the wave amplification by the localized surface plasmon resonance of the Au nanoparticle monolayer in a perovskite solar cell is comparatively investigated, providing a viable strategy of broadening the solar spectrum utilization.

Selective Oxidizing Gas Sensing and Dominant Sensing Mechanism of n-CaO-Decorated n-ZnO Nanorod Sensors.

In this work, we investigated the NO2 and CO sensing properties of n-CaO-decorated n-ZnO nanorods and the dominant sensing mechanism in n-n heterostructured one-dimensional (1D) nanostructured multinetworked chemiresistive gas sensors utilizing the nanorods. The CaO-decorated n-ZnO nanorods showed stronger response to NO2 than most other ZnO-based nanostructures, including the pristine ZnO nanorods. Many researchers have attributed the enhanced sensing performance of heterostructured sensors to the modulation of the conduction channel width or surface depletion layer width. However, the modulation of the conduction channel width is not the true cause of the enhanced sensing performance of n-n heterostructured 1D gas sensors, because the radial modulation of the conduction channel width is not intensified in these sensors. In this work, we demonstrate that the enhanced performance of the n-CaO-decorated n-ZnO nanorod sensor is mainly due to a combination of the enhanced modulation of the potential barrier height at the n-n heterojunctions, the larger surface-area-to-volume ratio and the increased surface defect density of the decorated ZnO nanorods, not the enhanced modulation of the conduction channel width.

Morphology and Optical Properties of Bare and Silica Coated Hybrid Silver Nanoparticles.

Owing to their wide applications in the field of optoelectronics, photonics, catalysis, and medicine; plasmonic metal nanoparticles are attaining considerable interest nowadays. The optical properties of these metal nanoparticles depend upon their size, shape, and surrounding medium. The present work studies the morphology and optical properties of bare silver nanoparticles and silica coated hybrid silver nanoparticles. Aqueous phase mediated synthesis and water-in-oil microemulsion mediated synthesis are two different wet chemical routes employed for nanosynthesis. Direct coating of silica is performed in water-in-oil microemulsion on pre-synthesized silver nanoparticles using tetraethyl orthosilicate as silica precursor. This study shows that using different wet chemical routes the size of the synthesized nanoparticles could be tuned. In addition, using reverse micelles as nanoreactors, the thickness of the silica shell around the core silver nanoparticles could be significantly controlled. Further, the optical properties of silver nanoparticles could be adjusted through the size and the surface coating.

Vertically aligned nanostructured TiO2 photoelectrodes for high efficiency perovskite solar cells via a block copolymer template approach.

We fabricated perovskite solar cells with enhanced device efficiency based on vertically oriented TiO2 nanostructures using a nanoporous template of block copolymers (BCPs). The dimension and shape controllability of the nanopores of the BCP template allowed for the construction of one-dimensional (1-D) TiO2 nanorods and two-dimensional (2-D) TiO2 nanowalls. The TiO2 nanorod-based perovskite solar cells showed a more efficient charge separation and a lower charge recombination, leading to better performance compared to TiO2 nanowall-based solar cells. The best solar cells employing 1-D TiO2 nanorods showed an efficiency of 15.5% with VOC = 1.02 V, JSC = 20.0 mA cm(-2) and fill factor = 76.1%. Thus, TiO2 nanostructures fabricated from BCP nanotemplates could be applied to the preparation of electron transport layers for improving the efficiency of perovskite solar cells.

Novel Carbazole-Based Hole-Transporting Materials with Star-Shaped Chemical Structures for Perovskite-Sensitized Solar Cells.

Novel carbazole-based hole-transporting materials (HTMs), including extended π-conjugated central core units such as 1,4-phenyl, 4,4'-biphenyl, or 1,3,5-trisphenylbenzene for promoting effective π-π stacking as well as the hexyloxy flexible group for enhancing solubility in organic solvent, have been synthesized as HTM of perovskite-sensitized solar cells. A HTM with 1,3,5-trisphenylbenzene core, coded as SGT-411, exhibited the highest charge conductivity caused by its intrinsic property to form crystallized structure. The perovskite-sensitized solar cells with SGT-411 exhibited the highest PCE of 13.00%, which is 94% of that of the device derived from spiro-OMeTAD (13.76%). Time-resolved photoluminescence spectra indicate that SGT-411 shows the shortest decay time constant, which is in agreement with the trends of conductivity data, indicating it having fastest charge regeneration. In this regard, a carbazole-based HTM with star-shaped chemical structure is considered to be a promising candidate HTM.

50 nm sized spherical TiO2 nanocrystals for highly efficient mesoscopic perovskite solar cells.

Single crystalline TiO2 nanoparticles (NPs) with spherical morphology are successfully synthesized by a hydrothermal reaction under basic conditions. TiO2 NPs, selectively controlled to the sizes of 30, 40, 50, and 65 nm, are then applied to a mesoporous photoelectrode of CH3NH3PbI3 perovskite solar cells. In particular, a spherical TiO2 NP of 50 nm size (NP50) offers the highest photovoltaic conversion efficiency (PCE) of 17.19%, with JSC of 21.58 mA cm(-2), VOC of 1049 mV, and FF of 0.759 while the enhancement of PCE mainly arises from the increase of VOC and FF. Furthermore, the fabricated photovoltaic devices exhibit reproducible PCE values and very little hysteresis in their J-V curves. Time-resolved photoluminescence measurement and pulsed light-induced transient measurement of the photocurrent indicate that the device employing NP50 exhibits the longest electron lifetime although the electron injection from perovskite to TiO2 is less efficient than the devices with smaller TiO2 NPs. The extended electron lifetime is attributed to the suppression of electron recombination due to optimized mesopores generated by the spherical NP50.

Room temperature, ppb-level NO2 gas sensing of multiple-networked ZnSe nanowire sensors under UV illumination.

Reports of the gas sensing properties of ZnSe are few, presumably because of the decomposition and oxidation of ZnSe at high temperatures. In this study, ZnSe nanowires were synthesized by the thermal evaporation of ZnSe powders and the sensing performance of multiple-networked ZnSe nanowire sensors toward NO2 gas was examined. The results showed that ZnSe might be a promising gas sensor material if it is used at room temperature. The response of the ZnSe nanowires to 50 ppb-5 ppm NO2 at room temperature under dark and UV illumination conditions were 101-102% and 113-234%, respectively. The responses of the ZnSe nanowires to 5 ppm NO2 increased from 102 to 234% with increasing UV illumination intensity from 0 to 1.2 mW/cm(2). The response of the ZnSe nanowires was stronger than or comparable to that of typical metal oxide semiconductors reported in the literature, which require higher NO2 concentrations and operate at higher temperatures. The origin of the enhanced response of the ZnSe nanowires towards NO2 under UV illumination is also discussed.

14.8% perovskite solar cells employing carbazole derivatives as hole transporting materials.

Three novel carbazole-based molecules have been synthesized and successfully applied as hole-transporting materials (HTMs) of CH3NH3PbI3-based perovskite solar cells. In particular, the perovskite cell with SGT-405, having a three-arm-type structure, exhibited a remarkable photovoltaic conversion efficiency (PCE) of 14.79%.

Effects of functionalization of TiO2 nanotube array sensors with Pd nanoparticles on their selectivity.

This study compared the responses of Pd-functionalized and pristine titanate (TiO2) nanotube arrays to ethanol with those to acetone to determine the effects of functionalization of TiO2 nanotubes with Pd nanoparticles on the sensitivity and selectivity. The responses of pristine and Pd-functionalized TiO2 nanotube arrays to ethanol gas at 200 °C were ~2877% and ~21,253%, respectively. On the other hand, the responses of pristine and Pd-functionalized TiO2 nanotube arrays to acetone gas at 250 °C were ~1636% and 8746% respectively. In the case of ethanol sensing, the response and recovery times of Pd-functionalized TiO2 nanotubes (10.2 and 7.1 s) were obviously shorter than those of pristine TiO2 nanotubes (14.3 and 8.8 s), respectively. In contrast, in the case of acetone sensing the response and recovery times of Pd-functionalized TiO2 nanotubes (42.5 and 19.7 s) were almost the same as those of pristine TiO2 nanotubes (47.2 and 17.9 s). TiO2 nanotube arrays showed the strongest response to ethanol and Pd functionalization was the most effective in improving the response of TiO2 nanotubes to ethanol among six different types of gases: ethanol, acetone, CO, H2, NH3 and NO2. The origin of the superior sensing properties of Pd-functionalized TiO2 nanotubes toward ethanol to acetone is also discussed.