Bending States Research Articles

Preparation and thermal properties of biomimetic polymer-based flexible ultra-thin flat heat pipe

Inspired by the structure of the human spine, a flexible ultra-thin flat heat pipe featuring a biomimetic human spine design has been devised. This flat heat pipe, equipped with a biomimetic human spine structure, is capable of undergoing repeated bending at large angles. An experimental study was conducted to investigate the primary influencing factors. The results revealed that the optimal liquid filling ratio for the flexible ultra-thin flat heat pipe is 0.3. The dip angle is positively correlated with the heat transfer performance of the flexible ultra-thin flat heat pipe, and the bending angle is negatively correlated with the heat transfer performance of the flexible ultra-thin flat heat pipe. The maximum thermal conductivity of the flexible ultra-thin flat heat pipe can reach 1457.68 W/(m·K). The flexible ultra-thin flat heat pipe with liquid filling rate of 0.3 and bending angle of 0 degree has the fastest start-up speed. A visualized experimental platform was further designed to observe the internal flow of the working fluid within the flexible ultra-thin heat pipe in various bending states. The visual experimental results demonstrate that bending initiates the premature condensation of steam within the flexible section, and the condensed working medium subsequently generates resistance to the flow of subsequent steam, leading to an inability for the latter to be smoothly transported to the condensing section, thereby creating a vicious cycle.

Designing self-cleaning & flexible multifunctional wearable heater

Wearable fabric heater has aroused wide concern in personalized temperature regulation. However, it is still challenging to develop multifunctional wearable heater with multimodal & fast thermal response, good flexibility, strong abrasion, excellent washability, good antibacterial performance, and recyclability. To accomplish these properties, a self-cleaning & flexible multifunctional wearable heater is designed by spraying mixture of Ti3C2Tx MXene/ZnO composite and PDMS on cotton fabric (CF-MZP). The designed CF-MZP fabric heater shows high photothermal/electrothermal/synergistic conversion properties and fast thermal response (just 30 s). Furthermore, the CF-MZP fabric possesses excellent superhydrophobic and self-cleaning properties that endow the heater with strong abrasion, excellent washability, and good antibacterial performance. Interestingly, the CF-MZP heater also exhibits good breathability, durability and flexible performance, which is demonstrated as a flexible wearable heater attached to knuckle position of a human body, showing steady temperature of around 50.9 °C at a voltage of 3 V or about 80.5 °C upon NIR lamp (0.2 W cm-2) irradiation, either relaxed and bending (90° or 180°) states. Furthermore, the CF-MZP heater can be recycled by separating ordinary oil-water mixture and high viscous heavy oil. Consequently, the designed CF-MZP fabrics provide a good perspective application in self-cleaning, recycled, and flexible wearable heaters.

An Ultra-Thin Multi-Band Logo Antenna for Internet of Vehicles Applications

In this paper, an ultra-thin logo antenna (LGA) operating in multiple frequency bands for Internet of Vehicles (IoVs) applications was proposed. The designed antenna can cover five frequency bands, 0.86–1.01 GHz (16.0%) for LoRa communication, 1.3–1.36 GHz (4.6%) for GPS, 2.32–2.71 GHz (16.3%) for Bluetooth communication, 3.63–3.89 GHz (6.9%) for 5G communication, and 5.27–5.66 GHz (7.1%) for WLAN, as the simulation indicated. The initial antenna started with a modified coplanar waveguide (CPW)-fed circular disk monopole radiator. To create extra current paths and further excite other modes, the disk was hollowed out into the shape of the car logo of the Chinese smart EV brand XPENG composing four rhombic parasitic patches. Next, four triangular parasitic patches were inserted to improve the impedance matching of the band at 5.6 GHz. Finally, four metallic vias were loaded for adjusting resonant points and the return loss reduction. Designed on a flexible substrate, the antenna can easily bend to a certain degree in complex vehicular communication for IoV. The measured results under horizontal and vertical bending showed the LGA can operate in a bending state while maintaining good performance. The proposed LGA addresses the issue of applying one single multi-band antenna to allow vehicles to communicate over several channels, which relieves the need for a sophisticated antenna network.

Mechanoreception of pneumatic soft robotic finger without tactile sensor based on dual-position feature

Purpose Mechanoreception is crucial for robotic planning and control applications, and for robotic fingers, mechanoreception is generally obtained through tactile sensors. As a new type of robotic finger, the soft finger also requires mechanoreception, like contact force and object stiffness. Unlike rigid fingers, soft fingers have elastic structures, meaning there is a connection between force and deformation of the soft fingers. It allows soft fingers to achieve mechanoreception without using tactile sensors. This study aims to provide a mechanoreception sensing scheme of the soft finger without any tactile sensors. Design/methodology/approach This research uses bending sensors to measure the actual bending state under force and calculates the virtual bending state under assumed no-load conditions using pressure sensors and statics model. The difference between the virtual and actual finger states is the finger deformation under load, and its product with the finger stiffness can be used to calculate the contact force. There are distinctions between the virtual and actual finger state change rates in the pressing process. The difference caused by the stiffness of different objects is different, which can be used to identify the object stiffness. Findings Contact force perception can achieve a detection accuracy of 0.117 N root mean square error within the range of 0–6 N contact force. The contact object stiffness perception has a detection average deviation of about 15%, and the detection standard deviation is 10% for low-stiffness objects and 20% for high-stiffness objects. It performs better at detecting the stiffness of low-stiffness objects, which is consistent with the sensory ability of human fingers. Originality/value This paper proposes a universal mechanoreception method for soft fingers that only uses indispensable bending and pressure sensors without tactile sensors. It helps to reduce the hardware complexity of soft robots. Meanwhile, the soft finger no longer needs to deploy the tactile sensor at the fingertip, which can benefit the optimization design of the fingertip structure without considering the complex sensor installation. On the other hand, this approach is no longer confined to adding components needed. It can fully use the soft robot body’s physical elasticity to convert sensor signals. Essentially, It treats the soft actuators as soft sensors.

Sequence-specific dynamic DNA bending explains mitochondrial TFAM’s dual role in DNA packaging and transcription initiation

Mitochondrial transcription factor A (TFAM) employs DNA bending to package mitochondrial DNA (mtDNA) into nucleoids and recruit mitochondrial RNA polymerase (POLRMT) at specific promoter sites, light strand promoter (LSP) and heavy strand promoter (HSP). Herein, we characterize the conformational dynamics of TFAM on promoter and non-promoter sequences using single-molecule fluorescence resonance energy transfer (smFRET) and single-molecule protein-induced fluorescence enhancement (smPIFE) methods. The DNA-TFAM complexes dynamically transition between partially and fully bent DNA conformational states. The bending/unbending transition rates and bending stability are DNA sequence-dependent—LSP forms the most stable fully bent complex and the non-specific sequence the least, which correlates with the lifetimes and affinities of TFAM with these DNA sequences. By quantifying the dynamic nature of the DNA-TFAM complexes, our study provides insights into how TFAM acts as a multifunctional protein through the DNA bending states to achieve sequence specificity and fidelity in mitochondrial transcription while performing mtDNA packaging.

Experimental investigation on lateral resistance capacity enhancement effect of a self-centering shape factor in self-centering pier systems

In self-centering (SC) pier systems, a rocking interface is typically employed at the bottom of a pier to achieve a gap-opening mechanism. However, compared with the full-section bending state of the bottom section of a ductile pier (DP), the local compressive state of the rocking interface in the SC pier inevitably leads to a significant reduction in the lateral resistance capacity. Although a prestressing tendon (PT) force can improve the lateral resistance capacity, it also induces local damage. Moreover, its enhancement effect is limited, particularly in the case of a column with a high axial compression ratio. Therefore, this study proposes an innovative measure to significantly improve the hysteretic performance of an SC pier without inducing additional damage, which is to raise the location of the rocking interface. First, the SC shape factor ξSC is innovatively defined to quantify the above-mentioned measure, and its working mechanism is investigated in detail in this study. Second, a high-lateral-resistance SC pier system (HLRSCP), which applies the concept of ξSC, is proposed and introduced for its advantages. Third, hysteretic tests of the DP and HLRSCP with high axial compression ratios are performed and analyzed. Finally, the enhancement effect of ξSC on the lateral resistance capacity is parametrically examined using a finite element model, and the feasible region of ξSC is inferred and presented. The results validate the effectiveness and feasibility of the concept of the SC shape factor in improving the hysteretic performance of the SC pier system.

Combined classification and regression inverse kinematics modeling for overall shape prediction of soft manipulators

In helping astronauts perform tasks, soft manipulators offer the advantages of softness, lightness, low cost, and interaction safety to interact with. However, modeling their inverse kinematics through traditional methods is subject to truncation errors, complex derivations and inexpressibility equations, owing to geometric singularities. Furthermore, facing the future control requirement for multiple major feature points on manipulators, most neural network approaches that solve the drive space only by the inverse solution of the end task space, cannot obtain the inverse kinematics solutions of all feature points, due to their including redundancy (the dimension n of the drive space of feature points is larger than that of the end task space). Therefore, this paper proposes a method combining classification and regression based on multi-layer perceptron for inverse kinematic modeling, namely the IK-MLP-CR method, with the bending states classified and the whole manipulator shape predicted, greatly reducing the amount of training data and training time. Finally, the performance evaluation of the proposed model is validated through the simulation and ground microgravity experiments. Results show that using the IK-MLP-CR method results in a successful grasping rate of over 97%, and that the trend of the experimental bending conforms to physical motions under different pressures.

Highly Efficient Organic Light–Emitting Diode Using DNA as Scattering Layer

AbstractHerein, an organic light–emitting diode (OLED) is fabricated with increased luminous efficiency and biocompatibility by topographic DNA film. In addition to the natural abundance and biocompatibility of DNA, its semi‐flexible characteristics facilitated the emergence of the liquid crystal phase, allowing the formation of a periodic wavy undulation structure by applying shear force. The resultant zigzag structure possesses sufficient periodicity and roughness, enhancing the effective scattering of emitted light. Furthermore, the DNA‐coated red OLED demonstrates cell proliferative effects and exhibits high electrical and thermal stability even in a bent state, suggesting its potential application in attachable OLED‐based light therapy.

Vibrational Relaxation of D2O Induced by Collision with He: A Rigid Bender Close Coupling Study.

The vibrational relaxation of the first excited bending state of D2O induced by collision with He is studied at the close coupling level and using the Rigid Bender approximation. A new 4D potential energy surface is calculated and reported for this system. It is then used to determine the low-lying bound states of the D2O-He van der Waals complex and to perform scattering calculations. Collision rates are determined for pure rotational transitions as well as for rovibrational transitions within the first excited bending state. The results are compared with those obtained for the collision of D2O with other noble gases such as Ne and Ar. We also analyse the differences observed with respect to the H2O+He collisions and compare our results with experiment.

Flexible staircase triboelectric nanogenerator for motion monitoring and gesture recognition

Triboelectric sensors, which are used in human-computer interaction and condition monitoring, have attracted tremendous scientific interest owing to their broad applicability, high energy utilization, and high accuracy detection. Here, a staircase-style flexible triboelectric sensor assembled by the antimony-doped tin oxide (ATO) functionalized flexible polyvinylidene fluoride polymer (PVDF) composite film is first proposed for gesture recognition and human motion detection. The modified composite film ATO/PVDF with high polarization and large permittivity improves the electrical output of the triboelectric nanogenerator (TENG). Compared with the pure PVDF, the modified PVDF film-based TENG could substantially enhance power density by 11.5 times. The peak voltage and power density of the flexible staircase-style TENG achieve 70 V and 0.58 W/m2, respectively. The flexible triboelectric sensor can be attached to the finger or wrist to obtain movement information through positive/negative signals. A set of rules between gestures and corresponding letters and numbers is defined and a gesture recognition system using deep learning algorithms is developed. The flexible triboelectric sensor realizes human body part bending, gesture, and motion state recognition, offering potential solutions and novel possibilities in smart sensing and human-computer interaction.

Torsion and bending sensing based on the specklegrams from a coupled few-mode multi-core fiber

A novel optical torsion and bending dual-parameter sensor based on the detection of a coupled few-mode multi-core fiber (FM-MCF) specklegrams is proposed and experimentally demonstrated. A 3-mm-long multimode fiber (MMF) is used to couple the light from the injection single mode fiber into all cores of the FM-MCF, and thus the fiber structure is formed by the ultra-short MMF and FM-MCF. The specklegrams of the FM-MCF can be detected and segmented to infer the change of the FM-MCF. The torsion angle of 0-360° of the FM-MCF can be determined accurately by detecting the overall rotation angles of the specklegrams. And since the modes in each core of the FM-MCF are strongly coupled and the mode interference is highly sensitive to external disturbance, bending sensing based on the analysis of sub-specklegrams from each outer core is verified within the curvature range of 2.57–12.83 m−1 with the help of deep learning. Furthermore, based on a dual-output layer classification network, the capability of the sensor for torsion and bending sensing simultaneously is tested. The recognition accuracy for 36 combinations of 4 torsion angles and 9 bending states are 100% and 97.12%, respectively. The sensor here proposed has the advantages of low cost, simple structure, ease of interrogation and good accuracy.

Tunable Nano-Bending Structures of Loosened/Tightened Lassos with Bi-Stable Vibration-Induced Emissions for Multi-Manipulations of White-Light Emissions and Sensor Applications.

The first tunable nano-bending structures of [1]rotaxane containing a single-fluorophoric N,N'-diphenyl-dihydrodibenzo[a,c]phenazine (DPAC) moiety (i.e., [1]RA) are developed as a loosened lasso structure to feature the bright white-light emission [CIE (0.27, 0.33), Φ = 21.2%] in THF solution, where bi-stable states of bending and twisted structures of DPAC unit in [1]RA produce cyan and orange emissions at 480 and 600nm, respectively. With acid/base controls, tunable loosened/tightened nano-loops of corresponding [1]rotaxanes (i.e., [1]RA/[1]RB) can be achieved via the shuttling of macrocycles reversibly, and thus to adjust their respective white-light/cyan emissions, where the cyan emission of [1]RB is obtained due to the largest conformational constraint of DPAC moiety in its bending form of [1]RB with a tightened lasso structure. Additionally, the non-interlocked analog M-Boc only shows the orange emission, revealing the twisted form of DPAC fluorophore in M-Boc without any conformational constraint. Moreover, the utilization of solvents (with different viscosities and polarities), temperatures, and water fractions could serve as effective tools to adjust the bi-stable vibration-induced emission (VIE) colors of [1]rotaxanes. Finally, tuning ratiometric emission colors of adaptive conformations of DPAC moieties by altering nano-bending structures in [1]rotaxanes and external stimuli can be further developed as intelligent temperature and viscosity sensor materials.

Fabrication of highly flexible, wearable, free-standing symmetric supercapacitors with high voltage operation enabled by hierarchical graphene/cerium oxide/polypyrrole hybrid films

Flexible, free-standing supercapacitors play a significant role in the development of future wearable energy storage devices. Herein, we successfully fabricated the highly flexible and free-standing graphene/cerium oxide/polypyrrole hybrid films by thermal reduction of graphene oxide (GO) followed by the sol–gel synthesis of CeO2 and then the addition of PPy. By regulating oxygen functional groups in GO, the electronic conductivity and electroactive sites of the hybrid films are significantly controlled, leading to enhanced energy storage capability. Finally, a symmetric flexible supercapacitor (FSC) device was developed using the prepared films as electrodes. Resulting, the integrated symmetric GO-400/CeO2/PPy FSC manifests excellent areal capacitance of 49.0 mF cm−2 at 1 mA cm−2, with a durability of 83.1 % over 10,000 cycles. Specifically, the FSC exhibited capacitance retention of 77.2 % after 10,000 cycles under bending state with exceptional rate ability. Meanwhile, an impressive energy density of 19.69 µW h cm−2 was attained at a power density of 0.85 mW cm−2. Evidently, the synergistic interactions between GO and PPy nanosheets, along with CeO2 favour the rapid electron movement of electrode material for next-generation wearable, portable electronics.

Layer‑by‑layer assembled binder-free hydrated vanadium oxide-acetylene black electrode for flexible aqueous zinc ion battery

Vanadium oxides are potential positive electrode materials for aqueous zinc ion batteries (ZIBs) owing to their advantages of high theoretical capacity, low cost, and so on. Developments of methods for preparing binder-free vanadium oxide electrodes on a large scale and further investigation of their Zn2+ storage mechanisms are essential for expanding their uses in large-scale energy storage systems and wearable electronics. In this work, binder-free electrodes with hydrated vanadium oxide (V2O5·nH2O, denoted as VOH)-acetylene black (AB) on carbon cloth (VOH-AB/CC) are fabricated by a simple and scalable method which combined low-temperature hydrothermal treatment with layer-by-layer drop/spray-coating process. The AB can greatly improve the electrical conductivity of VOH, thereby enhancing the electrochemical performance. The as-prepared electrode with 20 wt% of AB (VOH-AB2/CC) delivers a high capacity of 280 mA h g−1 at 1 A/g and a good rate capability of 205 mA h g−1 at 4 A/g, which is better than many of the reported binder-free vanadium base electrodes. Besides, excellent cycling performance with 89 % retention rate after 3000 cycles at 4 A/g is achieved on the VOH-AB2/CC electrode. Furthermore, a storage mechanism of Zn2+/H+/H2O insertion accompanied by the formation of basic zinc salt precipitate during the discharging process is proposed by the aid of ex-situ XRD and XPS techniques. Additionally, the flexible Quasi-Solid-State ZIB constructed using VOH-AB/CC as positive electrode can work well at different bending states and two ZIBs connected in series can lighten a light-emitting diode even under bending state. This work provides a low-cost, time-saving, environmental-friendly and scalable method to fabricate binder-free hydrated vanadium oxide electrodes for flexible aqueous ZIBs.

Flexible piezoelectric pressure sensor based on BaTiO3-CNT/RTV composite film with filter paper microstructures for monitoring hand motions

Flexible piezoelectric sensors are widely used in various applications such as physiological signal monitoring and human-computer interaction. The present study introduces a BaTiO3-CNT/RTV piezoelectric sensor fabricated using a filter paper template. It incorporates micro-scale fiber stacking and a 1% CNT doping in the microstructure, resulting in a notable enhancement of sensor sensitivity, increasing it from 0.07 V N−1 to 0.69 V N−1, representing an almost tenfold improvement. Furthermore, the study investigates the influence of affecting factors like the flexible substrate of the sensing film, thickness, and mass fractions of various materials on the output voltage. The sensor exhibits superior characteristics such as good repeatability under 5000 cyclic loads, high elongation at break, fast response (80 ms) and recovery times (90 ms), and good linearity. It also demonstrates outstanding sensitivity (12 mV/10°) when monitoring different finger bending states, enabling real-time, sensitive, and reliable hand motion tracking. This sensor holds promising prospects for future developments in the fields of intelligent grasping and sign language translation.

Bendable, lamellar MXene membrane electrodes with diverse diffusion pathways for potential application in miniaturized capacitive deionization devices

Flexible devices have shown great application potential in portable and miniaturized devices. However, work on flexible electrodes for capacitive deionization (CDI) has not been well developed due to the issues of desalination property, processability, and availability under actual bending conditions. Herein, we constructed a kind of flexible lamellar MXene membrane by assembling Ti3C2Tx sheets with both crumpled and perforated structures and studied their desalination performance in conventional planar and bent configurations. The crumpled and perforated features in Ti3C2Tx (C-P-TC) nanosheets could optimize the in-plane and out-of-plane diffusion channels of the stacked samples, respectively, effectively improving the accessibility of membranes. As a result, the desalination performance of such C-P-TC electrodes was superior to that of those assembled from crumpled or perforated sheets alone. Significantly, this flexible C-P-TC electrode still showed excellent performance at real bend deformation, which possessed not only almost the same CDI capacity as the traditional planar configuration but also good cycling stability. This work not merely proposes an alternative strategy to improve the CDI performance of lamellar MXene electrodes by regulating the nanostructures of channels but also confirms their effective deionization ability under real bent state, greatly facilitating the potential use of flexible electrodes in miniaturized CDI devices.

Transport studies in piezo-semiconductive ZnO nanotetrapod based electronic devices

ZnO nanotetrapods (ZnO NTs) with a non-centrosymmetric crystal structure consisting of four 1-D arms interconnected together through a central crystalline core, introduce interesting piezoelectric semiconducting responses in nanorods in the bent state. Considering the widespread applications of nanotetrapods in semiconductor devices, it becomes very crucial to establish a coupled model based on piezoelectric and piezotronic effects to investigate the carrier transport mechanism, which is being reported here in detail for the first time. In this work, we established a multiphysics coupled model of stress-regulated charge carrier transport by the finite element method (FEM), which considers the full account of the wurtzite (WZ) and zinc blende (ZB) regions as well as the spontaneous polarization dependence and the dependence of the material properties on the arm orientation. It is discovered that the forward gain of ZnO NT in the lateral force working mode is almost 50 % higher than that in the nanorod or in the normal force working mode while the reverse current is reduced to negligible. Through the simulation calculations and corresponding analysis, it is confirmed that the developed piezoelectric polarization charges are able to regulate the transport and distribution of carriers in ZnO crystal, which lays a theoretical foundation for the application of piezo-semiconductive ZnO NT devices in advanced technologies.

Highly tri-heteroatom doped porous carbon for aqueous and flexible quasi-solid-state zinc-ion hybrid supercapacitors

Porous carbon, a promising low-cost cathode material for zinc-ion hybrid supercapacitors (ZHSCs), is plagued by inferior hydrophilicity and insufficient active sites during charge/discharge process. Herein, a highly tri-heteroatom co-doped porous carbon material (HSACNS0.5) was prepared from the pyrolysis of Humulus scandens combining heteroatom doping. The high oxygen, nitrogen and sulfur content (total about 29.2 %) combining superior specific surface area (1505.9 m2 g−1) and hierarchical porous structure leads to superior wettability and abundant active sites, resulting in rapid kinetic behaviors and considerable ions adsorption capacity. Furthermore, the high content of heteroatoms provides extra pseudocapacitance. Consequently, the aqueous ZHSC based on HSACNS0.5 displays an excellent specific capacitance of 414.4 F g−1 at 0.5 A g−1, and energy density of 187.4 Wh kg−1 at a power density of 810 W kg−1. Moreover, the HSACNS0.5 cathode based flexible quasi-solid-state ZHSC operates well at different bending states. Even at a high mass loading of 17.3 mg cm−2, the ZHSC shows cycling stability and a superior areal capacitance of 4.27 F cm−2.

Multifunctional fiber-shaped flexible wearable strain sensor with high sensitivity and wide sensing range for detecting autonomous driving technology in automobiles

Flexible strain sensors have developed rapidly and shown enormous application prospects in human motion detection, intelligent robots, and other fields in recent years. However, developing satisfactory strain sensors that meet the requirements of high sensitivity, wide detection range and prominent durability remains a significant challenge. Herein, we developed a flexible and wearable multifunctional fiber-shaped carbon black (CB) and thermoplastic polyurethane (TPU) strain sensor (defined as CTSS) by combining wet spinning and ultrasound. The CTSS possesses characteristics of lightweight, wide sensing range (>390 %), high sensitivity (up to 1414), short response and recovery time (200 ms), ultralow detection limit (0.005 % strain) and good durability. These advantages endow the CTSS with good capability to monitor complicated human activities efficiently (e.g., joint bending, facial expression and breathing). CTSS can also clearly distinguish different bending states. It was then used to monitor the steering of a car in real-time, proving its tremendous potential as high performance flexible electronics device. CTSS is then encapsulated with Ecoflex (E-CTSS) as a single packaged fiber, exhibiting good triboelectric nanogenerator (TENG) performance, with a maximum output voltage beyond 12V for a single packaged fiber, and can maintain stable output. Indicating that E-CTSS has self powered sensing capability.

Influence of cladding tube structure on transmission characteristics of negative curvature terahertz fiber

A novel type of polarization negative curvature terahertz fiber has been designed, which has a cladding region composed of two long semi-circular cladding tubes in the horizontal direction and four long semi-elliptical cladding tubes in the oblique direction. The optimal fiber dimensions are determined to investigate the internal relationship between polarization characteristics and fiber cladding structure. The transmission performances of the negative curvature fiber are investigated by varying the thickness of fiber cladding tubes and adjusting the structural characteristics of cladding tubes in different directions. Relatively good transmission performances can be obtained with a cladding tube thickness of 80 μm. The birefringence can be stably maintained at the order of 10−4, and the confinement loss of the x-polarized mode at 2.55 THz is 0.036 dB cm−1. Moreover, the dispersion coefficient of the two polarized modes is stable between ±0.6 ps (THz·cm)−1 in the 2.3–2.6 THz band. The bent performance of the designed fiber at 2.52 THz is also discussed. The results show that the fiber has low bending sensitivity, and can still maintain excellent birefringence and low confinement loss in the bending state. For the y polarization, the birefringence can be basically stabilized at the order of 10−4 within a bending radius of 10–60 cm.