Bending Potential Research Articles

Track-A-Worm 2.0: A Software Suite for Quantifying Properties of C. elegans Locomotion, Bending, Sleep, and Action Potentials.

Comparative analyses of locomotor behavior and cellular electrical properties between wild-type and mutant C. elegans are crucial for exploring the gene basis of behaviors and the underlying cellular mechanisms. Although many tools have been developed by research labs and companies, their application is often hindered by implementation difficulties or lack of features specifically suited for C. elegans. Track-A-Worm 2.0 addresses these challenges with three key components: WormTracker, SleepTracker, and Action Potential (AP) Analyzer. WormTracker accurately quantifies a comprehensive set of locomotor and body bending metrics, reliably distinguish between the ventral and dorsal sides, continuously tracks the animal using a motorized stage, and seamlessly integrates external devices, such as a light source for optogenetic stimulation. SleepTracker detects and quantifies sleep-like behavior in freely moving animals. AP Analyzer assesses the resting membrane potential, afterhyperpolarization level, and various AP properties, including threshold, amplitude, mid-peak width, rise and decay times, and maximum and minimum slopes. Importantly, it addresses the challenge of AP threshold quantification posed by the absence of a pre-upstroke inflection point. Track-A-Worm 2.0 is potentially a valuable tool for many C. elegans research labs due to its powerful functionality and ease of implementation.

Influence of fourth-order vibrational corrections on semi-experimental (reSE) structures of linear molecules.

Semi-experimental structures (reSE) are derived from experimental ground state rotational constants combined with theoretical vibrational corrections. They permit a meaningful comparison with equilibrium structures based on high-level abinitio calculations. Typically, the vibrational corrections are evaluated with second-order vibrational perturbation theory (VPT2). The amount of error introduced by this approximation is generally thought to be small; however, it has not been thoroughly quantified. Herein, we assess the accuracy of theoretical vibrational corrections by extending the treatment to fourth order (VPT4) for a series of small linear molecules. Typical corrections to bond distances are on the order of 10-5 Å. Larger corrections, nearly 0.0002 Å, are obtained to the bond lengths of NCCN and CNCN. A borderline case is CCCO, which will likely require variational computations for a satisfactory answer. Treatment of vibrational effects beyond VPT2 will thus be important when one wishes to know bond distances confidently to four decimal places (10-4 Å). Certain molecules with shallow bending potentials, e.g., HOC+, are not amenable to a VPT2 description and are not improved by VPT4.

The strongest dative bond in main-group compounds. Theoretical study of OAeF- (Ae = Be-Ba).

Quantum chemical calculations of the anions OAeF- (Ae = Be-Ba) have been carried out using ab initio methods at the CCSD(T)/def2-TZVPP level and density functional theory employing BP86 with various basis sets. The equilibrium structures have linear geometries for Ae = Be and Mg but they are strongly bent for Ae = Sr and Ba while the calcium species has a quasi-linear structure with a very low bending potential. The calculated bond dissociation energies suggest a record-high BDE of De = 144.08 kcal mol-1 for OBeF- at the CCSD(T)/def2-TZVPP level, which is the strongest BDE for a dative bond that has been found so far. The BDE of the heavier homologues have a continuously decreasing order for Ae with Be > Mg (113.01 kcal mol-1) > Ca (84.06 kcal mol-1) > Sr (72.06 kcal mol-1) > Ba (60.00 kcal mol-1). The calculation of the charge distribution reveals a significant charge donation OAe ← F- with a declining sequence for the heavier atoms Ae. The oxygen atom in OAeF- carries always a higher partial charge than the fluorine atom, which contradicts the standard electronegativities of the atoms. The surprising partial charges are explained with the bonding situation of the atoms in the actual electronic structure. The bonding analysis of the OAe-F- bonds using the EDA-NOCV method shows that the bonds have much more electrostatic character than the Ae-F- bonds in the diatomic anions. This finding is supported by the results of the LED partitioning approach. The dative interactions have three major and one minor component. The assignment of a quadruple bond for the heavier species with Ae = Ca, Sr, Ba is not reasonable. The driving force for the bent geometries is the accumulation of electronic charge in the lone-pair region at the Ae atoms, which enhances the electrostatic attraction with the other atoms. An adequate description of the bonding situation is given by the formula O--Ae+ ← F-.

Fulminic acid: a quasibent spectacle.

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

Breaking through the bending limit of Al-alloy tubes by cryogenic effect controlled mechanical properties and friction behaviours

Aluminium alloy (Al-alloy) tubes, especially large-diameter thin-walled tubes with a tough bending radius, have been widely utilised in different industrial clusters owing to their high strength-to-weight ratio and good corrosion resistance. However, achieving such extreme specifications is challenging because severe and nonuniform bending deformation may cause tension and compression instabilities, such as overthinning, cracking, and wrinkling. Considering possible improvements in mechanical properties and friction behaviours of Al-alloy at cryogenic temperature (CT), the cryogenic bending potential of the 6061-O tubes with an extreme ratio of D/t of 89 (diameter/wall thickness) was explored at different deformation temperatures, including room temperature (RT) 20 °C, −60 °C, −120 °C, and −180 °C. First, the cryogenic mechanical properties and friction behaviour of the tubes were characterised. It was found that the overall mechanical properties of the Al-alloy tube were improved because of sub-grain formation and a more uniform distribution of dislocations at CT. The coefficient of friction between the tube and tooling exhibited a varying degree of reduction owing to the sensitivity of the tubes and the lubricant to CT. Subsequently, an innovative experimental platform for cryogenic bending was designed, and a finite element model of cryogenic bending was established. Third, cryogenic tube bendability and mechanism were explored. It was found that 6061-O tube formability can be effectively improved by cryogenic bending; however, there is no monotonic relationship between the bendability improvement and temperature decrease. The temperature to obtain the best bendability is −60 °C, at which the average wrinkle height is decreased by 81.4 %, and the average wall thickness reduction rate is reduced by 23.8 %. The bending limit represented by the bending radius is reduced from a 3.0D bending radius at RT to 1.0D at −60 °C, which is realised by the different or even opposite effects of the mechanical properties of tubes and the friction coefficient between the multiple contact interfaces on wall thinning and wrinkling.

Additively Manufactured Porous Filling Pneumatic Network Actuator

This research project investigated the additive manufacturing of pneumatic actuators based on the principle of droplet dosing using an Arburg Freeformer 300-3X 3D printer. The developed structure consists of a porous inner filling and a dense, airtight chamber. By selectively varying the filling densities of the porous inner filling, different membrane deflections of the actuator were achieved. By linking the actuators, a pneumatic network actuator was developed that could be used in endorobotics. To describe the membrane deflection of an additively manufactured pneumatic actuator, a mathematical model was developed that takes into account the influence of additive manufacturing and porous filling. Using a dedicated test rig, the predicted behavior of the pneumatic actuators was shown to be qualitatively consistent. In addition, a pneumatic network actuator (PneuNet) with a diameter of 17 mm and a height of 76 mm, consisting of nine chambers with different filling densities, could be bent through 82° under a pressure of 8 bar. Our study shows that the variation of filling densities during production leads to different membrane deflections. The mathematical model developed provides satisfactory predictions, although the influence of additive manufacturing needs to be determined experimentally. Post-processing is still a necessary step to realize the full bending potential of these actuators, although challenges regarding air-tightness remain. Future research approaches include studying the deflection behavior of the chambers in multiple directions, investigating alternative materials, and optimizing the printing process to improve mechanical properties and reliability.

Empirical rovibronic energy levels of C3

ABSTRACT The carbon trimer, C 3 also known as propadienediylidene, is a quasi-linear molecule with an unusual electronic structure and a very flat bending potential in its ground electronic state. C 3 is an important species in astrophysics and carbon plasmas. Observed transition wavenumbers within and between the X ~ 1 Σ g + and A ~ 1 Π u states of C 3 are extracted from 21 papers and then subjected to a Measured Active Rotational-Vibrational Energy Levels (MARVEL) analysis: a corrected list of 4940 transitions are inverted to yield 1887 empirical energy levels. Uncertainties for these levels are determined using a newly implemented bootstrap method. These levels will provide input for developing a full spectroscopic model for C 3 which can used to generate a line list for the X ~ 1 Σ g + and A ~ 1 Π u states.

Effect of gradient microstructure on the bendability of AZ31 alloy sheet

Extensive researches have elucidated the pronounced benefits of gradient microstructures for the mechanical properties of metallic materials. However, the ramifications of gradient microstructures on formability, particularly regarding their effects on bendability, remain inadequately understood. In this work, the effects of gradient microstructure on the bendability of AZ31 Mg alloy sheet are systematically investigated by comparing the microstructure evolution and strain distribution in the sheets with uniform microstructure (grain size = 12.8 µm and 91.3 µm) and gradient microstructure (grain size = 11.5–75.4 µm). The results show that the bendability of the sheet with gradient microstructure is significantly improved when the fine grains (FGs) are placed at the outer side (TBE-FG sample) and the bendability is increased by 93.1% compared to the sample with fine and uniform microstructure (CE-FG sample). With coarse grains (CGs) placed at the inner side, the strain at the compressive region of the TBE-FG sample is higher than its counterparts, while the tensile strain at the extended region is lowest among the four samples. Quasi-in-situ bending experiments reveal that the CGs at the inner side of the TBE-FG sample undergo more twinning. Moreover, the increment of residual dislocation density at the outer side of the TBE-FG sample is lower than those of other samples, which extends the bending potential. This work provides a novel perspective to improve the bendability of the Mg alloy sheet.

Enhancing Tubular Bending Precision Using Torch-assisted Softening Technique


 
 
 
 
 
 Abstract: This study presents a novel approach to improve the precision of tubular bending processes. By integrating a torch burner into the conventional manual bending tool, a method was developed to soften the workpiece prior to bending, effectively reducing defects attributed to forced bending. The research includes manual calculations and SolidWorks simulations for comparative analysis. The proposed tool design, utilizing a 40 mm x 40 mm x 700 mm L-profile iron frame with ASTM A36 material, demonstrated successful bending of pipes with ∅ outside 25 mm and ∅ inside 20 mm, achieving a seamless 180° bend from the initial 0° position. The results highlight enhanced bending accuracy and underline the potential of torch-assisted bending for broader applications in fabrication and manufacturing processes.
 Highlight:
 
 nnovative Integration: Integration of a torch burner with a manual bending tool for enhanced precision in tubular bending processes.
 Defect Reduction: Softening the workpiece before bending reduces defects associated with forced bending, ensuring higher quality outcomes.
 Comprehensive Analysis: The study employs both manual calculations and SolidWorks simulations for a thorough comparative analysis, validating the proposed approach's efficacy.
 
 Keyword: Precision Improvement, Tubular Bending, Torch-Assisted Softening, Defect Reduction, SolidWorks Simulation
 
 
 
 
 

A multiscale framework for modeling fibrin fiber networks: Theory development and validation

Fibrin fibers and fibrin network, the key structural components of blood clots, are imperative for maintaining the functionality of blood clots in hemostasis and wound healing. Although extensive experimental investigations have lent valuable insights into the link between structure of fibrin network and the mechanical behavior of the blood clots, there is a lack of approaches to systematically quantify how the alterations in the microstructure of fibrin network dictate its mechanical responses to various external loadings. Such quantitative knowledge is essential for understanding the mechanism underlying thromboembolism, a pathological condition that could trigger life-threating events, such as pulmonary embolism. Herein, we present a multiscale framework for modeling a fibrin fiber network constructed by individual fibrin fibers. First, we develop a mechanical model for fibrin fibers using constitutive equations to capture both the tensile and bending behaviors of individual fibrin fibers. In particular, we propose an equation to describe the radial packing structure of protofibrils in the fibrin fiber cross-section, through which we can incorporate the microscopic variables, i.e., protofibril density, fiber radius, and the stiffnesses of αC-regions and fibrin protofibrils, into the derivation of a bending potential for the fibrin fiber model. With this derived bending potential, we show that the computed bending stiffness and persistence lengths of the fibrin fiber model are consistent with those reported in prior experimental studies. Next, we use the mechanical model of fibrin fibers to inform the parameters in a coarse-grained particle-based model for simulating fibrin network. Our simulation results show that the stress-strain relationships computed from fibrin network model when under tension, shear, and compression, align with experimental results, demonstrating the validity and capability of the proposed multiscale framework in modeling the mechanical responses of the fibrin network under various external loadings.

Internal Electric Field-Modulated Charge Migration Behavior in MoS2 /MIL-53(Fe) S-Scheme Heterojunction for Boosting Visible-Light-Driven Photocatalytic Chlorinated Antibiotics Degradation.

Inadequate photo-generated charge separation, migration, and utilization efficiency limit the photocatalytic efficiency. Herein, a MoS2 /MIL-53(Fe) photocatalyst/activator with the S-scheme heterojunction structure is designed and the charge migration behavior is modulated by the internal electric field (IEF). The IEF intensity is enhanced to 40mV by modulating band bending potential and the depletion layer length of MoS2 . The photo-generated electron migration process is boosted by constructing the electron migration bridge (Fe-O-S) and modulating the IEF as the driving force, confirmed by the density functional theory calculation. Compared with the pristine materials, the photocurrent density of MoS2 /MIL-53(Fe) is significantly enhanced 27.5 times. Contributed by the visible-light-driven cooperative catalytic degradation and the high-efficiency direct photo-generated electron reduction dichlorination process, satisfactory chlorinated antibiotics removal and detoxification performances are achieved. This study opens up new insights into the application of heterojunctions in photocatalytic activation of PDS in environmental remediation.

Mode selectivity of dynamically induced conformation in many-body chainlike bead-spring models.

We consider conformation of a chain consisting of beads connected by stiff springs, where the conformation is determined by the bending angles between the consecutive two springs. Stability of a conformation is determined intrinsically by a potential energy function depending on the bending angles. However, effective forces induced by excited springs can change the stability, and a conformation can stay around a local maximum or a saddle of the bending potential. A stabilized conformation was named the dynamically induced conformation in a previous work on a three-body system [Y. Y. Yamaguchi etal., Phys. Rev. E 105, 064201 (2022)2470-004510.1103/PhysRevE.105.064201]. A remarkable fact is that the stabilization by the spring motion depends on the excited normal modes, which depend on a conformation. We extend analyses of the dynamically induced conformation in many-body chainlike bead-spring systems. Simple rules are that the lowest-eigenfrequency mode contributes to the stabilization and that the higher the eigenfrequency is, the more the destabilization emerges. We verify theoretical predictions by performing numerical simulations.

Filler-induced heterogeneous nucleation of polymer crystals investigated by molecular dynamics simulations

Filler particles are known to act as nucleants for polymer crystallisation yet the connection between the filler surface properties and polymer crystallisation are not well understood. In this work, molecular dynamics simulations were used to investigate homogeneous and heterogeneous polymer nucleation and crystallisation using a generic linear bead–spring polymer model with a bond bending potential. The polymer systems were equilibrated at high temperature and then cooled at a constant rate. Without a surface present, polymers with stiff chains were found to crystallise more readily than more flexible polymers. The degree of crystallinity was estimated based on the mass fraction of straight chain segments which we equate to stem mass fraction. At a temperature Tc a sharp increase in density, radius of gyration and stem mass fraction occurred. After cooling, the systems were reheated and some systems showed hysteresis with a sharp decrease in these properties occurring upon melting at Tm>Tc. For slower heating rates, crystal growth occurred during heating from between the glass transition temperature, Tg, and Tc until just before melting at Tm. The presence of an isotropic surface was found to promote crystallisation in flexible systems that did not crystallise in the bulk, where the stem mass fraction and Tc increased with the interaction strength between the surface and the polymer beads. Changes in Tc and degree of crystallinity with cooling rate are consistent with experimental observations. This model captures polymer crystallisation phenomena and provides insight into heterogeneous nucleation, demonstrating that strong interfacial interactions promote crystallisation, thus aiding the choice or design of nucleants for control of polymer crystallisation and microstructure.

Effect of Confinement and Coulomb Interactions on the Electronic Structure of the (111) LaAlO3/SrTiO3 Interface.

A tight binding supercell approach is used for the calculation of the electronic structure of the (111) LaAlO3/SrTiO3 interface. The confinement potential at the interface is evaluated solving a discrete Poisson equation by means of an iterative method. In addition to the effect of the confinement, local Hubbard electron-electron terms are included at the mean-field level within a fully self-consistent procedure. The calculation carefully describes how the two-dimensional electron gas arises from the quantum confinement of electrons near the interface due to the band bending potential. The resulting electronic sub-bands and Fermi surfaces show full agreement with the electronic structure determined by angle-resolved photoelectron spectroscopy experiments. In particular, we analyse how the effect of local Hubbard interactions change the density distribution over the layers from the interface to the bulk. Interestingly, the two-dimensional electron gas at the interface is not depleted by local Hubbard interactions which indeed induce an enhancement of the electron density between the first layers and the bulk.

Dilute polymer solutions under shear flow: Comprehensive qualitative analysis using a bead-spring chain model with a FENE-Fraenkel spring

Although the nonequilibrium behavior of polymer solutions is generally well understood, particularly in extensional flow, there remain several unanswered questions for dilute solutions in simple shear flow, and full quantitative agreement with experiments has not been achieved. For example, experimental viscosity data exhibit qualitative differences in shear-thinning exponents, the shear rate for the onset of shear-thinning, and high-shear Newtonian plateaus depending on polymer semiflexibility, contour length, and solvent quality. While polymer models are able to incorporate all of these effects through various spring force laws, bending potentials, excluded volume (EV) potentials, and hydrodynamic interaction (HI), the inclusion of each piece of physics has not been systematically matched to experimentally observed behavior. Furthermore, attempts to develop multiscale models (in the sense of representing an arbitrarily small or large polymer chain) which can make quantitative predictions are hindered by the lack of ability to fully match the results of bead-rod models, often used to represent a polymer chain at the Kuhn-step level, with bead-spring models, which take into account the entropic elasticity. In light of these difficulties, this work aims to develop a general model based on the so-called FENE-Fraenkel spring, originally formulated by Larson and co-workers [J. Chem. Phys. 124 (2006)], which can span the range from rigid rod to traditional entropic spring, as well as include a bending potential, EV, and HI. As we show, this model can reproduce, and smoothly move between, a wide range of previously observed polymer solution rheology in shear flow.

Modelling realistic 3D deformations of simple epithelia in dynamic homeostasis

The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue’s shape must remain relatively unchanged. Simple epithelial tissues occur in various structures throughout the body, such as the endothelium, mesothelium, linings of the lungs, saliva and thyroid glands, and gastrointestinal tract. Despite the prevalence of simple epithelial tissues, there are few models which accurately describe how these tissues maintain a stable structure.Here, we present a novel, 3D, deformable, multilayer, cell-centre model of a simple epithelium. Cell movement is governed by the minimisation of a bending potential across the epithelium, cell–cell adhesion, and viscous effects. We show that the model is capable of maintaining a consistent tissue structure while undergoing self renewal. We also demonstrate the model’s robustness under tissue renewal, cell migration and cell removal. The model presented here is a valuable advancement towards the modelling of tissues and organs with complex and generalised structures.

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics.

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C5H9) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to Trot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N - 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40-90 #/cm-1) in the critical regime (ρ ≈ 100 #/cm-1) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C2 symmetry double minimum 1D energy surface over a C2v transition state. The inversion barrier [Vbarrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a "deceleration" of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding "acceleration" of IVR processes in linear hydrocarbons.

A computational study of mechanical and electrical properties of zigzag graphene nanoribbon force sensor

Force sensors have many applications in new technologies such as robotic systems, medical tools and electronics. Therefore, it is necessary to make high sensitivity force sensors. Nanomaterials are very useful for making these sensors. In this paper, we study the mechanical and electrical properties of zigzag graphene nanoribbon force sensor by classical molecular dynamics (MD) with reactive force field (Reaxff) and density functional based tight binding (DFTB) combined with non-equilibrium Green's function (NEGF) method. Our results show that the bending angle, potentials energy, bond energy and deflection distance increase with increasing external force, while distance between tip and nanoribbon and electrical conductivity decrease. In addition, to study the electrical properties of force sensor, we calculated the local density of states (LDOS), density of states (DOS) and transmission spectrum. Our results show that these quantities change by external force. So we can measure them to judge the operation of sensor.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water.

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

Linear bounded potential model for semiconductor band bending

We propose a simple but unexplored model for the semiconductor band bending with the aim to obtain a relatively simple expression to calculate the energy spectrum for the confined levels and the analytical expressions for wave-functions. This model consists of a linear potential but it is bounded or trimmed in energy unlike the well known wedge potential (WP) model. We present exact solutions for this potential in the frame of the effective mass approximation and they are valid for electron or hole confinement potential. This model provides a more adequate physical scenario than the WP since it takes into account the charge balance involved in the band bending potential. These results allow to treat confined potential problems as in the case of a two-dimensional electron gas in a simplified way. We discuss the application of this approximation to the recombination time of electrons an holes and for the Franz–Keldysh effect.