Real Part Research Articles

Comparison of Approaches for Assessing Linearity of Impedance Measurements

There are two experimental methods available to assess the linearity of electrochemical impedance measurements. Observation of current as a function of potential, known as Lissajous plots, provides an instantaneous visual representation of the data.1 Deviation from an elliptical shape suggests a perturbation amplitude that is too large, resulting in nonlinear impedance data. A second approach is to measure, along with the fundamental, the higher harmonics of the measurement signal. Under potentiostatic control, the harmonics of current that exceed the noise level suggest nonlinear behavior. These harmonics may be expressed in terms of a frequency-dependent total harmonic distortion, THD, written as the ratio between the sum of the root mean square of the harmonic magnitude and fundamental frequency magnitude for electrochemical applications.The impedance was measured for a model system consisting of a Pt disk immersed in an electrolyte containing 0.01 M potassium ferricyanide, 0.01 M potassium ferrocyanide, and 1 M KCl. Measurements were performed using a Gamry Reference 3000 with THD measurement enabled and disabled. Low-frequency (10 mHz) Lissajous plots were recorded to facilitate comparison of the two methods for assessing linearity. The impedance measurements with THD enabled or disabled were in good agreement, including the frequency-dependent stochastic error structure, the shapes of Lissajous curves, and the values of the impedance. Both the low-frequency THD and the low-frequency Lissajous plots gave similar sensitivity to nonlinear behavior. Perturbation amplitudes of 1, 5, and 10 mV rms yielded elliptical Lissajous plots with THD values on the order of the background noise. Interestingly, the THD for the 10 mV perturbation was slightly above the background noise with a value of 0.01 (or 1 % of the fundamental). Perturbation amplitudes of 20, 60, and 100 mV rms yielded both non-elliptical Lissajous plots and low-frequency THD values much larger than the background noise.The regression of the measurement model 2 to the imaginary part of the impedance was applied to assess the consistency of the measured data to the Kramers-Kronig relations.3 Data measured at amplitudes of 1, 5, 10, and 20 mV rms were found to be consistent with the Kramers-Kronig relations, and data collected with amplitudes of 60 or 100 mV rms were found to be inconsistent with the Kramers-Kronig relations. As the measurement with a 20 mV rms amplitude was found to be nonlinear by observation of non-elliptical Lissajous plots and a THD of 4.2% at a frequency of 10 mHz, the post-measurement analysis of consistency with the Kramers-Kronig relations was found to be less sensitive than experimental observation of Lissajous plots and calculation of THD. Comparison of Lissajous plots to THD values suggests that experiments with THD less than 1% of the fundamental may be considered to be linear.

Positivity bounds on electromagnetic properties of media

We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from the external field). The equations of motion for the average electromagnetic field in a medium — the macroscopic Maxwell equations — can be derived from the in-in effective action and the effect of the medium is encoded in the electric and magnetic permeabilities ε(ω, |k|) and μ(ω, |k|). Microcausality implies analyticity of the retarded Green’s functions when the imaginary part of the 4-vector (ω, k) lies in forward light cone. With appropriate assumptions about the behavior of the medium at high frequencies one derives dispersion relations, originally studied by Leontovich. In the case of dielectrics these relations, combined with the positivity of the imaginary parts, imply bounds on the low-energy values of the response, ε(0, 0) and μ(0, 0). In particular the quantities ε(0, 0) – 1 and ε(0, 0) – 1/μ(0, 0) are constrained to be positive and equal to integrals over the imaginary parts of the response. We discuss various improvements of these bounds in the case of non-relativistic media and with additional assumptions about the UV behavior.

G band enhancement in ABt-twisted trilayer graphene

G band, originating from the in-plane vibrations of carbon atoms, is the main signature in Raman spectroscopy of graphene-based systems. It is often used to characterize the sample quality and obtain molecular vibration information. Here we investigate the Raman spectroscopy of ABt-twisted trilayer graphene (ABt-TTG) and observe two enhancement centers for the G band across samples with different twist angles. To understand the origin of these two enhancement centers, we theoretically calculate the G band intensity of ABt-TTG based on the continuum model. We find that the theoretical calculations exhibit two prominent peaks corresponding to the experimental observations after Fermi velocity corrections. We also investigated the real and imaginary parts of Raman resonances, respectively, and explained the origins of two enhancements of ABt-TTG. By using Raman spectroscopy, evolutions of band structures of ABt-TTG with respect to the twist angles can be characterized, which extends the potential applications of the Raman method in the investigation of electronic structures of graphene-based systems.

Modeling of servo dynamic stiffness for multiple-periodic repetitive learning control system

Servo dynamic stiffness is a pivotal index in characterizing the rejecting performance for the exogenous periodic disturbances of the repetitive learning control system. In this paper, the mathematical modeling of the servo dynamic stiffness for the well-designed repetitive learning control system with multiple-periodic signals is studied by the frequency analysis method. To analysis the complex form of the servo dynamic stiffness, the magnitudes of the direct (real part) and quadrature (imaginary part) servo dynamic stiffness at harmonics of the disturbance are discussed based on the parameters of the repetitive learning controller. An illustrated example of the two linear servomotors with the mechanical coupling is given in this study. Computer simulation are presented to illustrate the effect of the proposed measurement method of the servo dynamic stiffness for the multiple-periodic repetitive learning control system. The proposed servo dynamic stiffness modeling can be used to accurate design the parameters of the repetitive learning control system, such that the batter control performance of the repetitive learning control system at most of the harmonics of the multi-periodic input signal can be achieved.

Complex conductivity as a tool to investigate the electrical behavior between graphene oxide and reduced graphene in supercapacitors: Correlation between the electrical properties

The storage mechanisms of solid-solid supercapacitors based on graphene oxide (rGO/GO/rGO) were explored by Zhang Q et al. (Zhang et al., 2014) [1], using Density Functional Theory (DFT) and Impedance Spectroscopy (EIS) to elucidate the unusual capacitive behavior of GO sandwich films. Their study revealed alternating charged layers without diffusion zones. Analysis of complex impedance (Z*) data, ranging from 10−3 to 3.106 Hz, was conducted using an equivalent circuit, though this was limited to Nyquist plot data.To further investigate charge storage mechanisms, the current study delved deeper into complex impedance (Z*) and conductivity (σ*). A theoretical approach identified relaxation processes in the imaginary parts of (Z″) and (σ'') across frequencies. Extrapolation up to 3.10^9 Hz and deconvolution confirmed three distinct relaxation processes in Z* and σ*, similar to Cole-Cole relaxation, which describes Maxwell-Wagner-Sillars (MWS) relaxation. This reflects local electrical interactions between active sites on molecular chains and counterions, creating induced dipolar moments or diffusion processes.The identified relaxations at low, medium, and high frequencies correspond well with DFT results, attributed to specific regions: graphene oxide (GO), the (rGO/GO) interface, and reduced graphene (rGO). Key parameters extracted from each relaxation, such as relaxation time, ionic strength, and conductivity values at different frequencies, showed good correlation. This approach, based on deep conductivity (σ*) analysis, effectively highlighted the charge conduction and storage mechanisms in rGO/GO/rGO supercapacitor films.

Real, imaginary and complex branches of Lamb waves in p-type piezoelectric semiconductor GaAs plate: Numerical and experimental investigation

First, we experimentally measure the concentration of holes of the piezoelectric semiconductor (PSC) Gallium arsenide (GaAs) material based on the Hall effect measurement. We then numerically calculate the Lamb wave characteristics in a p-type PSC GaAs plate using this measured value of the concentration of holes (estimated at approximately p0=3.5431×1025m−3). To guarantee the coupling effect that makes the Lamb wave a piezo-active wave, the GaAs crystal is oriented in a specific orientation of (110) plane. Ordinary differential equation (ODE) method is employed to calculate the dispersion curves, 3D view of the mechanical displacements, 3D view of the electric potential and 3D view of the concentrations of holes. Results show that the appearance of the complex branches of the Lamb modes coincides with the vanishing of the imaginary part of the wavevector (Im(k1)) to zero, which is a very remarkable finding that has not been discussed in previous studies. Meanwhile, these complex branches start exactly at the point of Zero-group-velocity (ZGV). Moreover, the present work highlights the hole drift characteristics of PSC GaAs and provides a critical comparative discussion with those published by (Zhu et al., 2018) for the PSC ZnO plate. Accordingly, the “Screening effect” phenomenon that is based on the positive holes in the negative electric potential region is discussed. The present results provide a theoretical and fundamental guidance on the development of smart devices based on the PSC GaAs material.

Push-Pull Carbazole-Based Dyes: Synthesis, Strong Ultrafast Nonlinear Optical Response, and Effective Photoinitiation for Multiphoton Lithography.

The present work reports on the ultrafast nonlinear optical (NLO) properties of a series of D-π-Α and D-A push-pull carbazole-based dyes and establishes a correlation between these properties and their efficiency for potential photonic and optoelectronic applications such as multiphoton lithography (MPL). The ultrafast NLO properties of the studied dyes are determined by two distinct experimental techniques, Z-scan and pump-probe optical Kerr effect (OKE), employing 246 fs laser pulses at 515 nm. The results indicate that chemical functionalization of the carbazole moiety with various strong electron-donating and/or electron-withdrawing groups, such as benzene, styrene, 4-bromostyrene, nitrobenzene, trimethyl isocyanurate, methyl, and indane-1,3-dione, can result in a controlled and significant enhancement of the NLO absorptive and refractive responses. In the context of potential applications, the efficiency of carbazole-based organic materials as photoinitiators (PIs) for MPL applications is demonstrated. The fabricated woodpile microstructure using chemically functionalized carbazole as a PI demonstrates improvements in both feature size and MPL efficiency compared to that using unfunctionalized carbazole as a PI. This is attributed to the efficient charge transfer resulting from chemical functionalization, which leads to a substantial increase (approximately 1 order of magnitude) in the values of the imaginary part of the second-order hyperpolarizability (Imγ) and the two-photon absorption cross section (σ). The achieved feature size of 280 nm is comparable to that obtained with other widely used PIs in MPL applications. Additionally, owing to the strong NLO properties of the studied functionalized carbazole, they could also be promising candidates for further applications in photonics and optoelectronics.

Theoretical investigation of optoelectronic properties in PbS/CdS core/shell spherical quantum dots under the effect of the electric field intensity, hydrogenic impurity and geometric parameters

In this paper, we theoretically investigated the combined effects of the external electric field (EF) strength and the geometric parameters on the linear, nonlinear and total dielectric functions as well as the effective dielectric function (DF) coefficients of PbS/CdS spherical core/shell quantum dots (CSQD) in the presence of the hydrogenic impurity located at the center. The subband energy eigenvalues and their corresponding wave functions are obtained by solving the time-independent Schrödinger equation and using the variational method (VM) in the framework of the effective mass approximation (EMA). The linear, nonlinear and total DF as well as the effective DF were discussed and evaluated under the influence of EF intensity, geometric parameters, the change of the number of quantum dots (QDs) per unit volume and optical intensity I based on the compact density matrix (CDM) approach. The obtained results show that the height peaks of the linear, nonlinear and Total DF as well as the effective DF coefficients increase and their resonant peak moves towards lower energies as the EF and geometric factors increase in both cases with and without considering the hydrogenic impurity effect. Furthermore, our findings show that the impact of optical intensity and the number of QDs per unit volume does not change the resonance peaks of imaginary parts of DF and effective DF but decreases their magnitudes. As a result, we believe that numerical results will present important developments and provide great contributions in designing new optoelectronic devices related to CSQD hetero-nanostructure.

Complex-valued multi-frequency electrical impedance tomography based on deep neural networks

The utilization of multi-frequency electrical impedance tomography (mfEIT), a non-invasive imaging technique, allows for the visualization of the conductivity distribution in biological tissues across different frequencies. However, the analysis of phase angle information within complex impedance remains a challenge, as most existing deep learning-based mfEIT algorithms are limited to real number processing. To mitigate this limitation, this study proposes a comlex reconstruction method which is inspired by the idea of combining deep learning with traditional reconstruction algorithm. It uses a spare Bayesian learning algorithm in the preprocessing stage that can perform complex arithmetic operations, and fully learns and makes use of the correlation between the real and imaginary parts to reconstruc the distribution of complex-valued conductivity in the measurement area. After that, an altered UNet network is used to further optimize the pre-reconstruction outcomes. The experimental outcomes validate the efficacy of the proposed algorithm in accurately reconstructing the complex-valued conductivity distributions of diverse biological tissues, such as potato and pig kidney, across different frequencies. Furthermore, the algorithm exhibits exceptional performance in mitigating the presence of image artifacts during the reconstruction process.

Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

The power of a macromolecular theory for the transport properties of a polymeric liquid increases with the number of analytical expressions for its most important material functions. In this work, we add another of these canonical function to our recent series of material function derivations for rotarance theory. By rotarance theory, we mean the explanation of the elasticity of polymeric liquids by use of (i) the diffusion equation to get the orientation distribution in Euler coordinates, and (ii) the integration in phase space using this distribution to get the target material function. In this paper, we target parallel superposition of oscillatory shear flow upon steady shear flow. We arrive at analytical expressions for both parts of the complex viscosity in parallel superposition. We find that these explain the classic experimental observations in parallel superposition: (a) the maximum in the real part of the complex viscosity, and (b) the negative values of minus its imaginary part, and (c) the independence of the steady mean shear stress from the superposed oscillation.

Magnetosonic shock waves in degenerate electron–positron–ion plasma with separated spin densities

This study investigates magnetosonic shock waves in a spin-polarized three-component quantum plasma using the quantum magnetic hydrodynamic model. We explore the influence of spin effects, specifically spin magnetization current and spin pressure, on shock wave behavior. Numerical analysis of the linear dispersion relation under varying parameters such as positron imbalance, spin polarization ratio, plasma beta, quantum diffraction, and magnetic diffusivity reveals differential impacts, with diffusion exerting significant influence on the plasma frequency. Our findings highlight the sensitivity discrepancy between the real and imaginary parts of the dispersion relation. Furthermore, nonlinear behavior of magnetosonic shock waves is examined via the Korteweg–de Vries–Burgers equation, showcasing transitions between oscillatory and monotonic wave patterns based on changes in dimensionless parameters. Notably, we observe the combined effects of spin-up and spin-down positrons with spin-up and spin-down electrons on shock wave dynamics, contributing to a deeper understanding of spin-plasma interactions with implications across various fields.

Study on human brain protection from electromagnetic radiation of mobile phone by plasma

The propagation characteristics of electromagnetic waves (EMW) in plasma with the plural dielectric properties (real and imaginary parts of the relative dielectric constant) were investigated in the virtual human brain (VHB) model by the full-wave solution. Simulation results indicate that the value of the electric and magnetic field amplitude of EMW with the frequency of 5 GHz and the value of specific absorption ratio within VHB can be reduced by more than 60% and 80%, respectively. After the secondary absorption of the plasma layer, the reflected wave amplitude is attenuated by 33.066 dB. The amplitude attenuation of EMW from 2.45 to 6 GHz can be exceeded 10 dB. Compared to the traditional absorbing materials for the electromagnetic protection, the plasma layer, as an absorbing medium, possesses wide frequency characteristics. These results have important reference value for reducing the high-frequency electromagnetic radiation to VHB.

A formulation of quantum fluid mechanics and trajectories

A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent Schrödinger equation, respectively, where the Schrödinger equation is in density matrix form. For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations of fluid mechanics, respectively. Generalizations of the energy and Euler equations are derived to obtain equations that are in the same form as they are in classical mechanics. The fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local variable mass. Over all space mass is conserved. The variable mass is a necessary condition for the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross flows are examined, where velocity directions are changed without changing the kinetic energy. For one-electron atoms, the velocity modification gives closed orbits for trajectories, and mass conservation, vortexes, and density stratification for fluid flows. For many body states, under certain conditions, and by hypotheses, Euler equations of orbital-flows are obtained. One-body Schrödinger equations that are a generalization of the Hartree–Fock equations are also obtained. These equations contain a quantum Coulomb’s law, involving the 2-body pair function of reduced density matrix theory that replace the charge densities.

Nonmagnetic Metal Plate Thickness Measurement Algorithm Based on Inductance Imaginary Part Slope

Nonmagnetic Metal Plate Thickness Measurement Algorithm Based on Inductance Imaginary Part Slope

Investigation of the impact of non-magnetic Si element addition and heat treatment on the electromagnetic wave absorption properties of medium entropy FeCoNiSi alloy particles

Based on chemical liquid phase reduction and high temperature annealing, the effects of non-magnetic Si element addition and heat treatment regime on the microstructure, magnetic properties, and electromagnetic wave absorption properties of medium entropy alloy particles FeCoNiSi were studied. The results show that the prepared Fe1Co0.8Ni1Six alloy particles have a spherical structure, and with the increase of Si content, the particle size continuously decreases, with the average particle size decreasing from 150 to 200 nm to 20-50 nm. After high temperature annealing, the alloy particles undergo some agglomeration and growth. The as-prepared Fe1Co0.8Ni1Six alloy particles exhibit an amorphous state, and crystallization occurs during high temperature annealing, but the increase in Si element content has a certain inhibitory effect on the crystallization of the alloy particles. With the increase of Si element content and annealing temperature, the specific saturation magnetization intensity of the material shows a decreasing trend, while the residual magnetism and coercivity show an increasing trend. With the increase of Si element content, the real and imaginary parts of the permeability change alternately in different frequency ranges. The magnetic loss mechanism for the three alloy particles was eddy current loss in the frequency ranges of 10-14GHz and 16.5-18GHz. With the increase of Si element content, the magnetic loss shows an increasing trend, and the impedance matching shows a decreasing trend. The Fe1Co0.8Ni1Si0.5 alloy particle sample has the maximum reflection loss |RLmax| of 28.2 dB at thickness of 2.3 mm, and the Fe1Co0.8Ni1Si0.7 alloy particle sample has an effective absorption bandwidth of 1.7GHz at thickness of 1.9 mm. Eddy current loss was the main magnetic loss mechanism for Fe1Co0.8Ni1Si0.6 alloy particles under 400 °C and 600 °C annealing conditions, and for Fe1Co0.8Ni1Si0.7 alloy particles under 600 °C annealing conditions. With the increase of annealing temperature, the fluctuation of dielectric loss with frequency decreases in the low frequency range, and increases in the high frequency range, while annealing reduces the fluctuation of magnetic loss with frequency. Under 400 °C annealing conditions, the attenuation constant of the three alloy particles was lower than that of the unannealed alloy particles, and under 600 °C annealing conditions, the attenuation constant of Fe1Co0.8Ni1Si0.5 alloy particles in the frequency range of 6-15GHz was higher than that of unannealed and 400 °C annealed alloy particles, and that of Fe1Co0.8Ni1Si0.6 alloy particles in the frequency range of 7-14GHz was higher than that of unannealed and 400 °C annealed alloy particles. High temperature annealing was not able to effectively improve the impedance matching performance of Fe1Co0.8Ni1Six alloy particles. The maximum reflection loss |RLmax| of Fe1Co0.8Ni1Si0.6 alloy particles under 600 °C annealing conditions was 37.8 dB.

Radiation and reaction at one loop

We study classical radiation fields at next-to-leading order using the methods of scattering amplitudes. The fields of interest to us are sourced when two massive, point-like objects scatter inelastically, and can be computed from one-loop amplitudes. The real and imaginary parts of the amplitudes play important but physically distinct roles in the radiation field. We argue that the imaginary part captures the effects of radiation reaction. This aspect of radiation reaction is directly linked to cuts of one-loop amplitudes which expose Compton trees. We also discuss the fascinating interplay between renormalisation, radiation reaction and classical field theory from this perspective.

Effect of Manganese Oxide Doping of Tin Oxide Thin Films on the Optical and Structural Properties

Tin oxide pure and manganese oxide doped (SnO2:Mn2O3) films were grown on a glass substrate in vacuum by pulsed laser deposition (PLD) technique (using Nd: YAG Laser) at different ratios of Mn2O3 (0, 3, 5, 7, 9) % wt. The structural and optical properties were studied. The X-ray diffraction (XRD) studies showed the structure nature of the films to be polycrystalline and rutile tetragonal. The optical transmittance spectra and optical constants of the prepared thin films, such as extinction coefficient (k), refractive index (n), and real (εr) and imaginary parts (εi) of the dielectric constant, were investigated. The values of the energy band gap increased from 3.5 eV to 3.55 eV with increasing the doping concentration.

Unveiling the structural and optoelectronic properties of (P, Bi, Sb)-doped GaAs by first- principles calculations

In this work, we investigate the influence of M substitutions (M = P, Bi, and Sb) on the structural, electronic, and optical properties of gallium arsenide, GaM x As1-x for x=0,0.25,0.50,0.75,1.0 using density functional theory (DFT). We have observed that the cubic symmetry of the semiconductors in conserved, and lattice constants show a linear behavior with dopant concentration, according to Vegard’s law. Specifically, the lattice constants increased for Bi and Sb dopants, whilst decreased for P dopants. Furthermore, the bulk modulus decreased with an increase in M-concentration for all M-doped systems. The energy analysis showed that the P-doped system was the most stable system. In terms of the electronic band structure, all M-doped compounds exhibited a direct electronic band gap. The P-doped system showed a wide band gap, while the Sb-doped systems displayed a narrow band gap, both compared to pristine GaAs. The Bi-doped system showed metallic-like behavior. To gain insights into the linear optical properties of the GaM x As1-x compounds, we calculated the real and imaginary parts of the dielectric function, as well as other optical parameters such as the absorption coefficient, refractive index, extinction coefficient, and reflectivity. The results showed that P doping leads to a blue-shift in the optical absorption coefficient, while Bi and Sb doping lead to a red-shift. These findings provide valuable theoretical insights for the potential application of GaM x As1-x semiconductors in photovoltaics and optoelectronic devices.

Ray tracing through absorbing dielectric media in the Schwarzschild spacetime

Abstract General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the Drude model. When absorption is included the eikonal becomes complex, with the imaginary part related to the absorption along a ray between emission and observation points. We extend results from the literature to include dispersion in the index of refraction. The complex Hamiltonian splits into a real part that describes the equations of motion and a constraint equation that governs the momentum loss in the system. We work in coordinates which are fully real, with a real metric in physical spacetime. We assume the dust and plasma distributions of the Drude matter to coincide and vary as a power-law $1/r^h$. We find that transmission requires $h>1$, otherwise exponential absorption occurs along ray paths. We use ray-tracing through strongly absorbing matter near the surface of the compact star, as well as specializing to a point-lens in the weak-field limit with weakly absorbing matter to generate potentially observable light curves for distant observers. In the appropriate limits, our theory reproduces results from the literature.

Hydrogen production and spin-orbit interaction in blue phosphorene and janus transition metal dichalcogenides vdw heterostructures: A first-principles study

Accumulating lamination of weak attractive interactions is a crucial process for strategically altering the physical features of materials, which is an essential step in crafting cutting-edge functional electronic applications. In this study, we explore the electronic, Rashba spin splitting, optical, and photocatalytic properties of novel vdW heterostructure comprising blue phosphorene (P(blue)) and Janus monolayers (JTMDCs) like JMXY (Mo, W/X = S, Se; Y = Te) using first-principles calculations. We study two different stacking arrangements as Model-I and Model-II, which arise from the alternating order of chalcogen atoms at opposite surfaces in the Janus monolayer. AIMD simulations confirm the geometric stability of P(blue)-JMXY heterostructures at room temperature. All the investigated vdW heterostructures exhibit indirect bandgap and both models have Type-II band alignment calculated by weighted band alignment. Rashba spin splitting is observed in P(blue)-JMXY heterostructures, where Bader charge and work function analyses show that JMXY donates electrons to P(blue). Moreover imaginary part of the dielectric ε2(ω) function indicates that excitons predominantly govern energy conversions in visible and infrared regions. Furthermore, the promising photocatalytic activity of P(blue)-JMXY vdW heterostructures for water splitting under acidic conditions (pH=0) is demonstrated, with Model-I P(blue)-JMoSeTe and P(blue)-JWSeTe, as well as Model-II P(blue)-JMoSTe and P(blue)-JWSeTe vdW heterostructures being particularly noteworthy.