Strong Internal Electric Field Research Articles

Construction of 2D/2D Pd Metallene/COFs System with Strong Internal Electric Field for Outstanding Solar Energy Photocatalysis

Construction of 2D/2D Pd Metallene/COFs System with Strong Internal Electric Field for Outstanding Solar Energy Photocatalysis

Z-Scheme Heterojunction of Hierarchical Cu2S/CdIn2S4 Hollow Cubes to Boost Photoelectrochemical Performance.

The exaltation of light-harvesting efficiency and the inhibition of fast charge recombination are pivotal to the improvement of photoelectrochemical (PEC) performance. Herein, a direct Z-scheme heterojunction is designed of Cu2S/CdIn2S4 by in situ growth of CdIn2S4 nanosheets on the surface of hollow CuS cubes and then annealing at 400°C. The constructed Z-scheme heterojunction is demonstrated with electron paramagnetic resonance and redox couple (p-nitrophenol/p-aminophenol) measurements. Under illumination, it shows the photocurrent 6 times larger than that of hollow Cu2S cubes, and affords outstanding PEC performance over the known Cu2S and CdIn2S4-based photocatalysts. X-ray photoelectron spectroscopy and density functional theory results demonstrate a strong internal electric field formed in Cu2S/CdIn2S4 Z-scheme heterojunction, which accelerates the Z-scheme charge migration, thereby promoting electron-hole separation and enhancing their utilization efficiency. Moreover, the hollow structure of Cu2S is conducive to shortening the charge transport distance and improving light-harvesting capability. In proof-of-concept PEC application, a PEC detection method for miRNA-141 based on the sensitivity of benzo-4-chloro-hexadienone to light absorption on Cu2S/CdIn2S4 modified electrode is developed with good selectivity and a limit of detection of 32 aM. This work provides a simple approach for designing photoactive materials with highly efficient PEC performance.

Engineering an A-D-A structure to enhance internal electric fields in silica-PDI-decorated vertical graphene for efficient photocatalytic oxidation

Efficient charge separation and transfer are crucial for elevating photocatalytic oxidation, and designing a photocatalyst structure with strong internal electric fields (IEF) hold promise for addressing the issue. Herein, we synthesized a silica-PDI (silica-perylene diimides) decorated vertical graphene (s-PDI@VG) architecture with an Acceptor-Donor-Acceptor (A-D-A) structure. The A-D-A configuration facilitated electron transfer from tertiary N-atom to perylene tetracarboxylic dianhydride (PTCDA) and flower-like vertical graphene (VG), resulting in a larger molecular dipole moment of s-PDI@VG compared to PTCDA and s-PDI. Consequently, an IEF with 7.5 times higher than PTCDA and 4.8 times higher than s-PDI was built, which is beneficial for photogenerated charge separation. Additionally, the valence band (VB) of s-PDI@VG deepened from 1.43 eV to 1.62 eV, enabling it to afford a strong oxidation potential. As a proof-of-concept, the 3D s-PDI@VG photocatalyst demonstrated favorable persulfate (PMS) activation and pollutant adsorption, resulting in 1.6 times higher photogenerated holes based on LSCM results. This photocatalyst also achieved 98.2 % mineralization of high-ionization-potential (h-IP) organics within 30 min. This work offers insights into a novel photocatalytic oxidation strategy with high mineralization by engineering A-D-A structure and enhancing the IEF strength of photocatalyst molecules.

Promoting photothermal catalytic N2 reduction through dynamic mass transfer and accelerated charge transfer dynamics

The effective adsorption and mass transfer of N2 at the catalytic active site, along with efficient photogenerated charge transfer at the interface are the prerequisites for the photothermal catalysis N2 reduction. Here, the hydrophobic-hydrophilic biphasic heterojunction Bi2WO6/ Bi2Sn2O7 (BWSO-20) was prepared by solvothermal method, and a strong interfacial internal electric field (IEF) was formed. The effects of N2 dynamic mass transfer and interface charge transfer kinetics on the performance of photothermal catalytic N2 reduction (PTC-NRR) was investigated. The results from in-suit DRIFTS, DFT, and molecular dynamics simulations (MD) indicated that a biphasic structure enhanced the dynamic mass transfer of N2 in the hydrophobic phase (BSO) and H2O in the hydrophilic phase (BWO) simultaneously. Additionally, the IEF that accelerates the transfer kinetics of photo-generated charges. Therefore, more photo-generated electrons and holes could transfer to the surface of the hydrophobic/hydrophilic phase catalyst and undergo redox semi-reactions with N2 and H2O. The PTC-NRR reached 366.1 μmoL·g−1 when using BWSO-20 without adding sacrificial agent. This work provides a new way to achieve efficient photothermal N2 reduction based on the interfacial charge transfer kinetics accelerated by the interfacial internal electric field and the dynamic mass transfer enhanced by hydrophobic – hydrophilic two-phase heterojunction.

Ferroelectric polarization-electric field promoted S-scheme CdSe/BaxSr1-xTiO3 for highly efficient solar hydrogen evolution

Coupling the ferroelectric polarization and internal electric field to realize effective separation and migration of photogenerated charges is highly attractive for accomplishing efficient photocatalytic hydrogen production. In this work, an internal electric field modulated S-scheme heterostructure was fabricated by depositing CdSe on ferroelectric BaxSr1-xTiO3 (BxST) through an in-situ growth method. Because of the oriented powerful electron transport driven by the strong spontaneous polarization and internal electric field, the as-synthesized CdSe/BxST heterojunctions demonstrated excellent solar to H2 performance. Without the addition of noble metal cocatalyst, 7% CdSe/B0.8ST exhibited a H2 evolution rate of 1971.8 µmol g-1 h−1 with an apparent quantum yield of 12.1% at 365 nm. Moreover, the obtained heterojunction catalysts exhibit good stability after 12 h continuous irradiation. This work provides a viable strategy on the utilization of ferroelectric polarization and internal electric field strategy to promote charge transfer and separation of S-scheme photocatalysts.

Photocatalytic degradation of iohexol by photo-driven double Z heterojunction photocatalyst under strong internal electric field in synergy with peroxymonosulfate (PMS)

This paper describes the preparation of a double Z heterojunction photocatalyst, g-C3N4/Bi2O2CO3/MnWO4 (CBCM), with a potent internal electric field using the hydrothermal method. The degradation efficiency can be further improved by combining photocatalytic technology with activated persulfate (PMS) technology. The synthesis of CBCM-7 was validated through XRD and TEM analyses, while XPS provided evidence of electron transfer and the establishment of heterojunctions within its structure. Additionally, PL, PC, and EIS measurements underscored CBCM-7′s proficient rate of photogenerated charge separation and robust charge transfer properties. The experimental results showed that the photocatalytic degradation of the iodinated contrast agent was substantially enhanced by this catalyst coupled with PMS. The degradation rate of Iohexol was up to more than 90 % within 40 min. After the completion of the recycling experiment, the degradation efficiency of this system remained above 80 %. Mechanistic analyses, including EPR tests, indicate that the main active groups generated by the degradation of this dual Z-scheme heterostructured photocatalyst coupled with activated PMS were superoxide radicals and hydroxyl radicals.

High Sensitive and Stable UV-Vis Photodetector Based on MoS2/MoO3 vdW Heterojunction.

The development of new high-performance photodetectors (PDs) is currently focused on achieving small size, low power consumption, low cost, and large bandwidth. Two-dimensional (2D) materials and heterostructures offer promising approaches for the future development of optoelectronic devices. However, there has been limited research on 2D wide-bandgap semiconductor heterostructures. In this study, we successfully constructed a MoS2/MoO3 vdW heterojunction PD. This PD exhibited excellent response and significant photovoltaic behavior in the ultraviolet (UV) to visible (Vis) range. Under 365 nm UV light and 1 V bias voltage, the PD demonstrated a high responsivity of 645 mA/W, a high specific detectivity of 8.98 × 1010 Jones, and fast response speeds of 55.9/59.6 ms. At 0 V bias voltage, the responsivity reached as high as 157 mA/W. Furthermore, the PD exhibited remarkable stability in its performance. These outstanding characteristics can be attributed to the strong internal electric field created by the type II heterojunction structure and the chemical stability of the materials. This work opens a route for the application of 2D wide-bandgap semiconductor materials in optoelectronic devices.

Chemically bonded CdS/Bi2MoO6 Z-scheme heterojunction synergises with strong internal electric field for photocatalytic CO2 reduction

Constructing strong interfacial electric fields to enhance the surface charge transport kinetics is an effective strategy for promoting CO2 conversion. Herein, we present the fabrication of CdS-Bi2MoO6 Z-scheme heterojunctions with a robust internal electric field (IEF) using an in situ growth technique, establishing chemical bonding between the components. The IEF at the interface can offer an impetus for the segregation and transportation of photogenerated carriers, while the Cd-O chemical bonding mode acts as a rapid conduit for these carriers, thereby reducing the charge transfer distance. As a result, the Z-scheme charge transfer is accelerated due to the synergistic influence of these two factors. Therefore, the optimized CdS/Bi2MoO6 Z-scheme heterojunction possesses significantly enhanced dynamic carrier mobility, thus promoting the conversion of CO2 to CO without the need for additional co-catalysts or sacrificial agents. This optimization yields a remarkable CO selectivity of up to 97%. Meanwhile, the expedited Z-scheme charge transfer mechanism is validated through X-ray photoelectron spectroscopy, Kelvin probe force microscopy, and in situ diffuse reflectance infrared Fourier transform spectroscopy.

Enhancing the near-infrared upconversion photocatalytic activity of ZnO/Bi3Ti2O8F:Yb3+, Er3+ by modulating the internal electric field through Z-scheme heterojunction construction

Exploring strategies to improve the near-infrared response of photocatalysts is an urgent challenge that can be overcome by utilizing upconversion (UC) luminescence to enhance photocatalysis. This paper reports the fabrication of a ZnO/Bi3Ti2O8F:Yb3+, Er3+ (ZnO/BTOFYE) Z-scheme heterojunction based on a Bi3Ti2O8F:Yb3+, Er3+ (BTOFYE) UC photocatalyst via electrostatic self-assembly. Fermi energy difference at the interface of BTOFYE and ZnO generates a strong internal electric field (IEF) in the Z-scheme heterojunction, offering a novel charge transfer mode that promotes carrier transfer and separation while retaining the strong redox capability. These results are confirmed through in situ X-ray photoelectron spectroscopy, in situ Kelvin probe force microscopy, electron spin resonance, and density functional theory calculations. In addition, the effect of the IEF on the UC luminescence process of Er3+ enhances the luminescence intensity, considerably improving the UC utilization efficiency. The optimal ZnO/BTOFYE degrades 64 % of ciprofloxacin in 120 min, which is 2.3 times more than that degraded by BTOFYE. Overall, the results of this study offer a reference for the rational development of high efficiency UC photocatalysts by generating IEF in Z-scheme heterojunctions.

Photothermal flows activated CsPbBr3 ⊆ Pb-TCPP S-scheme heterojunction: In-situ converted interface for robust CO2 reduction coupling with benzylamine oxidation

By the self-sacrificial conversion approach, the perovskite CsPbBr3 nanocrystals (CPB NCs) are impregnated from a lead-porphyrin metal–organic frameworks (Pb-TCPP). Such rational design not only shapes the firm heterojunction to optimize interface electronic environment and rapid reaction kinetics. The difference on Fermi level between the parent Pb-TCPP and derived CPB dramatically could trigger electron transfer, generating a strong internal electric field. The S-scheme heterojunction not only contributes to promote the photogenerated electron transfer separation, but also endows its excellent photothermal properties, which in turn improve the reoxidation ability of the heterojunction. In-situ experimental characterization and theoretical calculations unveil electron-rich CPB acts as the CO2 activation sites and the Pb-TCPP side plays a vital role in benzylamine (BA) oxidation. The as-transferred 0.1CPB ⊆ Pb-TCPP delivers the outperformed photochemical property with a yield rate of 143.3 μmol·g−1·h−1 of CO and 18.6 μmol·g−1·h−1 of CH4, and BDA productive rate of 21.4 mmol·g−1·h−1. This work puts forward to a luxurious booster to interface phase conversion and photothermal effect in the photosynthetic fields.

A novel photoelectrochemical aptasensor based on 3D flower-like g-C3N4/BiOI p-n heterojunction for the sensitive detection of kanamycin

BackgroundKanamycin (KAN) residues in animal-derived foods continuously enter the human body, which will pose serious threats to human health such as hearing loss, nephrotoxicity and other complications. Therefore, to sensitively detect KAN residues by a reliable technology is extremely urgent in food quality and safety. Compared with traditional methods being limited by cost and complexity, photoelectrochemical (PEC) biosensors benefit from some merits such as rapid response, excellent sensitivity and good stability. In this study, the construction of a highly efficient PEC platform to realize KAN residues detection is discussed. ResultsHerein, a novel p-n heterojunction consisting of flower-like BiOI microspheres and graphite carbon nitride (g-C3N4) nanoflakes was developed to establish a PEC aptasensor for KAN detection at 0 V. The prepared g-C3N4/BiOI heterostructure showed not only significantly enhanced PEC activity due to the larger specific surface area but also greatly increased charge separation efficiency owing to the strong internal electric field. Meanwhile, using g-C3N4/BiOI as a highly efficient photoactive material for binding amine-functionalized aptamers to capture KAN, the photocurrent signals showed a ‘turn off’ mode to achieve the sensitive detection of KAN. The proposed PEC aptasensor exhibited linear response for KAN from 5 × 10−9 to 3 × 10−7 mol L−1 with a low detection limit of 1.31 × 10−9 mol L−1, and satisfactory recoveries (97.44–107.38 %) were obtained in real food samples analysis. SignificanceThis work presented a novel p-n heterojunction-based PEC aptasensor with strong selectivity and stability, rendering it allowed to detect KAN in animal-derived foods including milk, honey and pork. Additionally, the detection range satisfied the MRLs for KAN specified by the national standards, demonstrating the potential application for food analysis. The study provides a new insight into the development of efficient and practical biosensors for antibiotic residues detection.

Enhancement of H2O2 generation rate in porphyrin photocatalysts via crystal facets regulation to create strong internal electric field

Enhancement of H2O2 generation rate in porphyrin photocatalysts via crystal facets regulation to create strong internal electric field

Internal electric field-modulated dual S-scheme ZnO@Co3O4/CsPbBr3 nanocages for highly active and selective photocatalytic CO2 reduction

The rational design of a step-scheme (S-scheme) heterojunction with strong internal electric field (IEF) and high redox capacity is a promising strategy for photocatalytic CO2 reduction reaction (CO2RR). However, the precise process of charge transport on the multi-interfaces remains a great challenge. Herein, a dual S-scheme heterojunction constructed in the ZnO@Co3O4/CsPbBr3 hierarchical nanocage was prepared for enhancing CO2RR activity. Without sacrificial agent and photosensitizer, the optimal photocatalyst exhibits a competitive CH4 yield rate of 238.8 μmol g−1h−1 with high selectivity (90.9%), affording an apparent quantum efficiency of 4.6 % at 400 nm, outperforming most previously comparable photocatalysts. In situ X-ray photoelectron spectroscopy (in situ XPS), photoelectrochemical measurement and theoretical calculation verifies the dual S-schematic charge-transport pathway. The remarkably improved performance in CO2RR is due to the rapid charge separation through O-Co-Br bridge driven by the strong internal electric field. This research furnishes a new insight to reveal dynamic charge transfer mechanism for CO2 conversion applications.

Polar topological bubbles in (K,Na)NbO3-based single crystals via synergetic phase and defect engineering

The investigations of polar topological conformations have become one of the hotspots due to their multitudinous physical properties and potential applications in emerging electronic devices. However, constructing polar topologies in bulk form is exceedingly challenging. In this study, bubble domains with different polar topologies, including flux-closure and half-closure, are successfully achieved in Cu-doped (K,Na)(Nb,Ta)O3 single crystals by elaborately adjusting the phase structure and defect dipoles. The coexistence of orthorhombic and tetragonal phases results in a flattened free energy landscape, while the presence of a high concentration of defect dipoles in local regions leads to the generation of the strong internal electric field, further modifying the energy profile. The interplay of various types of energies gives rise to the smooth rotation of the polar vectors, facilitating the formation of topological structures. These findings provide a practical method for constructing topological bubble domains in bulk materials, thereby enriching the understanding of the physical properties arising from topological structures.

Novel A–D–A Type Naphthalenediimide Supramolecule for H2O2 Photosynthesis with Solar‐to‐Chemical Conversion 1.03%

AbstractOrganic supermolecules have shown great promise for photocatalytic hydrogen peroxide (H2O2) production. However, the limitation of intramolecular charge separation efficiency is still a crucial scientific problem. In this study, a novel acceptor–donor–acceptor (A–D–A) type naphthalenediimide supramolecule (SA‐NDI) is successfully designed for overcoming fundamental issues in organic supermolecule. Composed of one electron‐rich core (naphthalenediimide) and two electron‐poor units (aminopyridine), the supramolecule possesses strong intramolecular charge transfer ability. Meanwhile, the SA‐NDI has an obviously stronger internal electric field, which is 2.83 times higher than that of D–A type supramolecule. The A–D–A type SA‐NDI efficiently accelerates charge separation, so that the intramolecular electron quickly migrates to the acceptor for a two‐electron oxygen reduction reaction. The SA‐NDI supramolecule shows excellent H2O2 accumulation ability (13.7 mm) and stable cyclic time above 120 h. Meanwhile, the catalyst exhibits a superior solar‐to‐chemical conversion efficiency of 1.03% under simulated solar irradiation. This work provides an entirely new idea to design an organic supramolecule with an efficient intramolecular charge transfer monomer.

Construction of a bifunctional BiVO4 based S-scheme heterojunction for enhancing photothermal-photocatalytic oxygen generation and benzaldehyde production

In order to address the main challenges in photocatalysis, such as the recombination of photo-generated carriers and the limited absorption range of light, a successful strategy was developed by creating a photothermal-photocatalytic S-scheme heterojunction through the combination of CdS nanoparticles with BiVO4 nanorods. XPS analysis, as well as SPV results, revealed the establishment, direction, and strength of the internal electric field (IEF) in the created CdS/BiVO4 heterojunction. Due to the matched band structure and the strong IEF, the heterojunction followed the S-scheme transfer mode under light, inducing the strong redox ability and fast separation of photo-generated carriers. Besides that, the heat generated by incorporating a photothermal-effect during illumination also helped to boost the photocatalytic reaction. As a result, the engineered CdS/BiVO4 heterojunction exhibited an impressive benzaldehyde production of 17.45 mmol g−1·h−1, approximately four times higher than that of pure BiVO4 (3.70 mmol g−1·h−1). Furthermore, the oxygen evolution rate of the CdS/BiVO4 heterojunction was 3146.68 µmol·g−1, much higher than that of BiVO4 (1042.98 µmol·g−1). This study introduces a novel approach to overcome the fundamental obstacles in semiconductor photocatalysis, paving the way for enhanced overall performance.

Self-Powered UV Photodetector Construction of the P(EDOS-TTh) Copolymer-Modified ZnO Nanoarray.

To solve the problem that zinc oxide nanorods (ZnO NRs)-based self-powered ultraviolet (UV) photodetectors cannot obtain both higher responsiveness and shorter response time, P(EDOS-TTh) was prepared using 3,4-ethylenedioxyselenphene (EDOS) and terthiophene (TTh) as copolymers, which modify the ZnO NRs surface, and the ZnO/P(EDOS-TTh) P-N junction self-powered UV device is assembled. The effect of the number of electrochemical polymerization cycles on the UV photodetection performance of ZnO/P(EDOS-TTh) P-N heterojunction was studied by adjusting the number of electrochemical polymerization cycles at the monomer molar ratio of 1:1. Benefiting from the enhanced built-in electric field of the ZnO/P(EDOS-TTh) interface, balancing photogenerated carriers, and charge separation and transport. The results show that the contact between N-type ZnO NRs and P-type P(EDOS-TTh) is best when the number of polymerization cycles is 3, due to the fact that EDOS-TTh and ZnO NRs form excellent P-N heterojunctions with strong internal electric fields, and the devices show good pyroelectric effect and UV photodetection performance. Under 0 V bias and 0.32 mW/cm2 UV irradiation, the responsivity (R) of ZnO/P(EDOS-TTh) reaches 3.31 mA/W, the detectivity (D*) is 7.25 × 1010 Jones, and the response time is significantly shortened. The rise time is 0.086 s, which exhibited excellent photoelectric properties and stability. UV photodetection performance with high sensitivity and fast response time is achieved.

Special role of indium nitride in the properties of related compounds and quantum structures

This Review provides a thorough description of the experimental progress on the InN family and other relevant compounds. Although InN is of great interest, many of its properties are not well understood and are still puzzling researchers with a number of unexpected effects. These include a surprisingly small energy gap, sensitivity to applied pressure in terms of lattice stability, and poor miscibility with compounds with smaller lattice parameters, such as GaN and AlN. Special features of InN under pressure are highlighted, such as the effect of conduction band filling and the strong pressure dependence of the effective mass. Several negative and positive effects due to the presence of In have been observed. We highlight their implications for InN-based alloys and quantum structures, which are crucial materials in modern optoelectronics (light emitting diodes and laser diodes). These effects include In clustering, large piezoelectricity resulting in strong internal electric fields that reduce the optical gain in nitride heterostructures, and difficulties in growing high-In superlattices and other quantum structures. All of these effects pose challenges that need to be addressed. We show that theoretical explanations allow for the clarification of puzzling experimental observations. Discussed are (i) a reformulation of the rule describing the bandgap dependence on pressure in all III–V semiconductors; (ii) the very large bandgap curvatures in nitride alloys; and (iii) the discrepancies between theory and experiment in the optical emission from InN/GaN superlattices, leading to the conclusion that epitaxial growth of high In content InxGa1−xN (x > 0.3) quantum wells on GaN is not possible.

Novel 2D/2D S-scheme heterojunction photocatalyst for peroxymonosulfate activation enables ciprofloxacin ultrafast degradation: High-efficiency photogenerated carrier transport

Organic pollutants, such as ciprofloxacin (CIP), are ubiquitously detected in wastewater. However, their removal remains a challenge for conventional wastewater treatment technologies. Photocatalysis and peroxymonosulfate activation coupling are considered a promising strategy for the removal of recalcitrant organic pollutants. However, identifying optimal photocatalysts that can effectively couple with peroxymonosulfate activation and induce synergistic degradation of organic pollutants remains a challenge to be addressed. In this work, a novel S-scheme inorganic–organic heterojunction BiVO4/Cu-TCPP (BC) was fabricated. In situ X-ray photoelectron spectrum showed that the strong internal electric field of the S-scheme heterojunctions enabled efficient carrier transport. The generated photogenerated electrons could activate the peroxymonosulfate, which further promoted the separation of the carriers. The BC-vis-peroxymonosulfate system achieved 93.1% ciprofloxacin removal in 10 min with apparent rate constants k of 0.2426 min−1, which is larger than most reported peroxymonosulfate systems. Electron paramagnetic resonance spectra and liquid chromatography mass spectrometry demonstrated that the synergistic coupling of S-scheme heterojunction with peroxymonosulfate activation significantly improved the catalytic activity of the reaction system and enabled rapid CIP removal via both radical and nonradical pathways. The BC-vis-peroxymonosulfate system demonstrated ultra-fast removal of other quinolone antibiotics and organic pollutants and strong environmental adaptability under various conditions, suggesting its great potential for practical application. This study provides new insights for the design of efficient S-scheme heterojunction coupled peroxymonosulfate activation for environmental remediation.

Modulating interface internal electric field for efficient charge separation in Co3O4/M-TiO2 p-n junction

The practical application of photocatalysis in water purification is restricted by the high electron-hole recombination efficiency. Herein, a Co3O4/M-TiO2 p-n composite catalyst with internal electric field (IEF) modulation was constructed. Because of the large number of oxygen vacancies (OVs) within Co3O4/M-TiO2, which could redistribute extra electrons to adjacent Co sites through the strong electron absorption effect of Co. Consequently, the charge distribution at the interface of Co3O4/M-TiO2 have been changed, forming positive and negative charge regions on M-TiO2 and Co3O4, respectively. Compared with Co3O4/P25, the amount of OVs in Co3O4/M-TiO2 is significantly increased, making the charge distribution at the interface more uneven and resulting in a significantly increased IEF intensity of Co3O4/M-TiO2 by 1.9 times. A series of photoelectric chemical experiments showed that driven by powerful IEF, the photogenerated electron-hole separation efficiency of Co3O4/M-TiO2 is significantly improved. In the photocatalysis-peroxymonosulfate (PMS) oxidation coupling system, Co3O4/M-TiO2 achieved high efficiency degradation of tetracycline hydrochloride (93.6 %) within 30 min, and a synergistic degradation mechanism of photocatalysis and PMS oxidation was proposed. This study provides a novel perspective on the construction of heterojunctions possessing strong internal electric fields.