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arxiv: 2606.23051 · v1 · pith:2G773XHAnew · submitted 2026-06-22 · ⚛️ physics.app-ph · cond-mat.mtrl-sci· cs.AI

Physics-governed executable modelling of triboelectric nanogenerators

Hongfa Zhao , Baiqiao Wang , Tiancong Zhao , Chun Jin , Hanlin Zhou , Mingrui Shu , Minyi Xu , Liwei Lin
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Wenbo Ding Zhong Lin Wang
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Pith reviewed 2026-06-26 06:10 UTC · model grok-4.3

classification ⚛️ physics.app-ph cond-mat.mtrl-scics.AI
keywords triboelectric nanogeneratorselectrostatic hierarchycharge-defined modellingTENG simulationphysics-governed frameworkexecutable modellingfinite geometry
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The pith

A charge-defined hierarchy unifies analytical and numerical models for triboelectric nanogenerators.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a charge-defined modelling framework for triboelectric nanogenerators that establishes a self-consistent electrostatic hierarchy. Triboelectric charges, pre-charging charges, and compensating electrode charges act as the defining state variables. This hierarchy links the analytical model for infinite plates with near-uniform fields to numerical methods needed for finite geometries with edge effects. Implemented as TENG-CLAW, it converts research requests into traceable simulations tied to explicit physical states, boundary conditions, and solver routes.

Core claim

Defining state variables exclusively via triboelectric charges, pre-charging charges and compensating electrode charges produces a self-consistent electrostatic hierarchy that unifies previously fragmented analytical, numerical and workflow approaches for TENGs.

What carries the argument

The self-consistent electrostatic hierarchy in which triboelectric charges, pre-charging charges and compensating electrode charges serve as defining state variables.

If this is right

  • The framework connects the infinite plate analytical limit for near-uniform fields with finite-geometry numerical formulations required for edge-dominated devices.
  • TENG-CLAW converts user-defined research requests into physically admissible simulation tasks.
  • Generated outputs are tied to explicit charge states, boundary conditions, solver routes and reusable artifacts across multiple workflow types.
  • This establishes a rigorous computational basis for interpreting TENG mechanisms and reproducible infrastructure for physics-guided device design.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The hierarchy could allow direct mapping of experimental outputs back to specific charge states for validation across device geometries.
  • Extending the state variables to time evolution might enable predictive simulation of dynamic TENG performance without separate models.
  • The approach may standardize comparisons between different TENG designs by holding the defining charge states fixed.

Load-bearing premise

That defining state variables exclusively via triboelectric charges, pre-charging charges and compensating electrode charges produces a hierarchy that is both self-consistent and sufficient to unify all previously fragmented approaches without introducing new inconsistencies.

What would settle it

A calculation showing that the hierarchy cannot reproduce the known analytical solution for the infinite plate limit, or a finite-geometry simulation where results deviate from the framework without being accountable by edge effects alone.

read the original abstract

Predictive modelling of triboelectric nanogenerators (TENGs) remains fragmented across analytical theories, finite-geometry solvers and disconnected simulation workflows. These disparate approaches must be unified into an executable framework to advance quantitative TENG research.Here we introduce a charge-defined modelling framework and implement it as TENG-CLAW, a physics-governed platform for traceable TENG simulation. The framework establishes a self-consistent electrostatic hierarchy in which triboelectric charges, pre-charging charges and compensating electrode charges serve as defining state variables.This hierarchy connects the infinite plate analytical limit for near-uniform fields with finite-geometry numerical formulations required for edge-dominated devices. Built on this basis, TENG-CLAW converts user-defined research requests into physically admissible simulation tasks, so that generated outputs are tied to explicit charge states, boundary conditions, solver routes and reusable artifacts across spatial, temporal, field-level, comparative and reporting workflows. This work establishes a rigorous computational basis for interpreting TENG mechanisms and provides reproducible research infrastructure for simulation and physics-guided device design.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper introduces a charge-defined modelling framework for triboelectric nanogenerators (TENGs), implemented as the TENG-CLAW platform. It establishes a self-consistent electrostatic hierarchy in which triboelectric charges, pre-charging charges and compensating electrode charges serve as defining state variables. This hierarchy is presented as connecting the infinite-plate analytical limit for near-uniform fields with finite-geometry numerical formulations, while converting user-defined requests into physically admissible simulation tasks that produce traceable outputs across multiple workflows.

Significance. If the claimed self-consistent hierarchy and executable implementation hold, the work would provide a unified physics-governed basis for TENG simulation, addressing fragmentation across analytical theories, numerical solvers and disconnected workflows, and supplying reproducible infrastructure for mechanism interpretation and device design.

minor comments (1)
  1. The supplied text consists only of the abstract; no equations, boundary conditions, derivations, data, error analysis or implementation details are available to verify whether the hierarchy supports the unification claim or remains free of new inconsistencies.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for reviewing our manuscript on the charge-defined electrostatic hierarchy and TENG-CLAW platform. The recommendation is listed as uncertain, yet the report contains no specific major comments to address point by point. We remain available to respond to any detailed concerns the referee may wish to raise.

Circularity Check

0 steps flagged

No significant circularity; derivation chain not reducible from supplied text

full rationale

The abstract and high-level description introduce a charge-defined framework with triboelectric, pre-charging and compensating electrode charges as state variables, claiming a self-consistent hierarchy that unifies analytical and numerical approaches. No equations, boundary conditions, derivations, fitted parameters, or self-citations appear in the provided material. Without explicit steps that reduce outputs to inputs by construction (e.g., no fitted ratios renamed as predictions or ansatzes smuggled via self-citation), the central claim cannot be shown to be circular. The unification is presented as a modeling choice rather than a mathematical identity forced by prior definitions. This is the expected honest non-finding for an abstract-only view of a computational framework paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms or invented entities; the central claim rests on the unverified assertion that the listed charge types form a complete defining hierarchy.

pith-pipeline@v0.9.1-grok · 5745 in / 1100 out tokens · 29197 ms · 2026-06-26T06:10:27.930196+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

61 extracted references · 12 canonical work pages

  1. [1]

    A droplet -based electricity generator with high instantaneous power density

    Xu, W., et al. A droplet -based electricity generator with high instantaneous power density. Nature 578, 392-396 (2020)

    2020

  2. [2]

    Transcutaneous ultrasound energy harvesting using capacitive triboelectric technology

    Hinchet, R., et al. Transcutaneous ultrasound energy harvesting using capacitive triboelectric technology. Science 365, 491-494 (2019)

    2019

  3. [3]

    Wireless and battery-free implantable sensing technologies for translatable bioelectronics

    Meng, X., et al. Wireless and battery-free implantable sensing technologies for translatable bioelectronics. Nat. Sens. 1, 290-304 (2026)

    2026

  4. [4]

    Biomimetic multimodal tactile sensing enables human-like robotic perception

    Li, S., et al. Biomimetic multimodal tactile sensing enables human-like robotic perception. Nat. Sens. 1, 52-62 (2026)

    2026

  5. [5]

    Wang, Z. L. From contact electrification to triboelectric nanogenerators. Rep. Prog. Phys. 84, 096502 (2021)

    2021

  6. [6]

    Zhao, H. , et al. Flexible nanogenerators for intelligent robotics: design, manufacturing, and applications. Int. J. Extrem. Manuf. 7, 022012 (2024)

    2024

  7. [7]

    Wang, Z. L. The expanded Maxwell’s equations for a mechano -driven media system that moves with acceleration. Int. J. Mod Phys B 37, 2350159 (2023)

    2023

  8. [8]

    & Wang, Z

    Cheng, T., Shao, J. & Wang, Z. L. Triboelectric nanogenerators. Nat. Rev. Methods Primers 3, 39 (2023)

    2023

  9. [9]

    Xiang, H., Peng, L., Yang, Q., Wang, Z. L. & Cao, X. Triboelectric nanogenerator for high -entropy energy, self -powered sensors, and popular education. Sci. Adv. 10, eads2291 (2024)

    2024

  10. [10]

    & Liu, Y

    Chen, X., Han, C., Wen, Z. & Liu, Y . Theoretical boundary and optimization methodology of contact -separation triboelectric nanogenerator. Appl. Mater. Today 29, 101685 (2022)

    2022

  11. [11]

    L., Deane, J

    Bulathsinghala, R. L., Deane, J. H. & Dharmasena, R. I. G. The Distance‐ Dependent Electric Field Theory for Sliding Mode Triboelectric Nanogenerators. Adv. Energy Mater. 15, 2403853 (2025)

    2025

  12. [12]

    Theoretical study of contact-mode triboelectric nanogenerators as an effective power source

    Niu, S., et al. Theoretical study of contact-mode triboelectric nanogenerators as an effective power source. Energy Environ. Sci. 6, 3576 (2013)

    2013

  13. [13]

    Dharmasena, R. D. I. G. , et al. Triboelectric nanogenerators: providing a fundamental framework. Energy Environ. Sci. 10, 1801-1811 (2017)

    2017

  14. [14]

    & Wang, Z

    Shao, J., Willatzen, M., Shi, Y . & Wang, Z. L. 3D mathematical model of contact-separation and single -electrode mode triboelectric nanogenerators. Nano Energy 60, 630-640 (2019)

    2019

  15. [15]

    Z., Adams, S., Long, J

    Hasan, S., Kouzani, A. Z., Adams, S., Long, J. & Mahmud, M. P. Comparative study on the contact -separation mode triboelectric nanogenerator. J. Electrostatics 116, 103685 (2022)

    2022

  16. [16]

    & Wang, Z

    Niu, S. & Wang, Z. L. Theoretical systems of triboelectric nanogenerators. Nano Energy 14, 161-192 (2015)

    2015

  17. [17]

    & Wang, Z

    Shao, J., Willatzen, M. & Wang, Z. L. Theoretical modeling of triboelectric nanogenerators (TENGs). J. Appl. Phys. 128, 111101 (2020)

    2020

  18. [18]

    & Silva, S

    Dharmasena, R., Jayawardena, K., Mills, C., Dorey, R. & Silva, S. A unified theoretical model for Triboelectric Nanogenerators. Nano Energy 48, 391-400 (2018)

    2018

  19. [19]

    & Wang, Z

    Luo, J. & Wang, Z. L. Recent progress of triboelectric nanogenerators: From fundamental theory to practical applications. EcoMat 2, e12059 (2020)

    2020

  20. [20]

    Kim, S., Han, J. W. & Chung, J. A Unified Enhanced Quasi‐Electrostatic 3D Charge Model for Accurate Prediction and Design Optimization of Contact‒ Separation Triboelectric Nanogenerators. Adv. Mater. Technol. 10, 70003 (2025)

    2025

  21. [21]

    Doganay, D. , et al. Triboelectric nanogenerators from fundamentals to applications. Nano Energy 138, 110825 (2025)

    2025

  22. [22]

    Quasi-electrostatic three-dimensional charge model for contact- separation triboelectric nanogenerator

    Chen, X., et al. Quasi-electrostatic three-dimensional charge model for contact- separation triboelectric nanogenerator. Nano Energy 111, 108435 (2023)

    2023

  23. [23]

    & Shi, J

    Liu, W. & Shi, J. A dynamics model of triboelectric nanogenerator transducers. Nano Energy 89, 106479 (2021)

    2021

  24. [24]

    Theoretical Modeling of Triboelectric Receiver transducer for Mechanic-Electrical Transformations

    Chang, H., et al. Theoretical Modeling of Triboelectric Receiver transducer for Mechanic-Electrical Transformations. Nano Energy 129, 110039 (2024)

    2024

  25. [25]

    & Liu, L

    Su, Y ., Yin, D., Zhao, X., Hu, T. & Liu, L. Exploration of advanced applications of triboelectric nanogenerator-based self-powered sensors in the era of artificial intelligence. Sensors 25, 2520 (2025)

    2025

  26. [26]

    & Wang, Z

    Zhang, Z., Shao, J., Nan, Y ., Willatzen, M. & Wang, Z. Theory and shape optimization of acoustic driven triboelectric nanogenerators. Mater. Today Phys. 27, 100784 (2022)

    2022

  27. [27]

    Theoretical modeling of contact -separation mode triboelectric nanogenerators from initial charge distribution

    Zhao, H., et al. Theoretical modeling of contact -separation mode triboelectric nanogenerators from initial charge distribution. Energy Environ. Sci. 17, 2228- 2247 (2024)

    2024

  28. [28]

    Zhao, H. , et al. Theoretical analysis of triboelectric nanogenerators: Charge mechanisms, energy conversion, and multifunctional applications. Nano Energy 144, 111382 (2025)

    2025

  29. [29]

    Zhang, H. a. Y ., Linjie and Quan, Liwei and Zheng, Xianglong. Theories for triboelectric nanogenerators: A comprehensive review. Nanotechnol. Rev. 9, 610-625 (2020)

    2020

  30. [30]

    & Satyanaryana, B

    Roopa, J., Swathi, H., Geetha, K. & Satyanaryana, B. Modeling and simulation of triboelectric nanogenerator for energy harvesting using COMSOL Multiphysics® and optimization on thickness of flexible polymer. Mater. Today Proc. 48, 702-705 (2022)

    2022

  31. [31]

    Yin, P., Tang, L., Li, Z., Guo, H. & Aw, K. C. Circuit representation, experiment and analysis of parallel -cell triboelectric nanogenerator. Energy Convers. Manage. 278, 116741 (2023)

    2023

  32. [32]

    Rehman, H. U. , et al. Density functional theory investigation on triboelectric nanogenerator: A comprehensive review. Sens. Actuators, A 393, 116866 (2025)

    2025

  33. [33]

    & Ding, W

    Wang, B., Zhao, H., Jin, C., Xu, Y . & Ding, W. Ionic-electrostatic modeling of solid-liquid triboelectric nanogenerators. Iontronics 2, 17 (2026)

    2026

  34. [34]

    & Ventura, J

    Callaty, C., Gonçalves, I., Rodrigues, C. & Ventura, J. Modeling the performance of contact -separation triboelectric nanogenerators. Curr. Appl. Phys. 50, 100-106 (2023)

    2023

  35. [35]

    & Ou-Yang, W

    Chen, X., Wu, H., Li, J., Chen, X. & Ou-Yang, W. The space tribo-charge region and equivalent charge plane model in triboelectric nanogenerators. J. Mater. Chem. A 13, 22517-22526 (2025)

    2025

  36. [36]

    & Zhang, Z

    Ye, Z., Liu, S., Wang, W. & Zhang, Z. Full-response triboelectric nanogenerator modeling and sensing framework: Zero state and zero input in synergy. Device 3, 100872 (2025)

    2025

  37. [37]

    Zhou, H. , et al. Computer aided design automation for triboelectric nanogenerators. Nano Energy 118, 108963 (2023)

    2023

  38. [38]

    Li, W. , et al. Research advances in triboelectric nanogenerators based on theoretical simulations. Nano Energy 127, 109724 (2024)

    2024

  39. [39]

    & Vivekanandan, S

    Karthikeyan, V . & Vivekanandan, S. Optimising the materials for triboelectric nanogenerator to harvest the wrist pulse signal: a numerical study using the finite element method. RSC Adv. 15, 43357-43365 (2025)

    2025

  40. [40]

    R., Jayapalan, B

    Kannabiran, K., Mohamed Rabi, B. R., Jayapalan, B. & Palani, L. T. Harnessing energy from low -frequency and low -amplitude vibrating sources using triboelectric nano generator. Appl. Phys. A 131, 316 (2025)

    2025

  41. [41]

    Wang, S. , et al. Maximum surface charge density for triboelectric nanogenerators achieved by ionized-air injection: methodology and theoretical understanding. Adv. Mater. 26, 6720-6728 (2014)

    2014

  42. [42]

    & Dharmasena, R

    Meng, S., McErlain -Naylor, S. & Dharmasena, R. Wearable triboelectric nanogenerators for biomechanical sensing. Nano Energy, 111412 (2025)

    2025

  43. [43]

    & Mao, Y

    Zhang, B., Ren, T., Li, H., Chen, B. & Mao, Y . Recent progress of nature materials based triboelectric nanogenerators for electronic skins and human – machine interaction. Adv. Energy Sustainability Res. 5, 2300245 (2024)

    2024

  44. [44]

    & Wen, Z

    Zhang, L., Liu, Y ., Sun, X. & Wen, Z. Advances in triboelectric nanogenerators in acoustics: Energy harvesting and Sound sensing. Nano Trends 8, 100064 (2024)

    2024

  45. [45]

    Recent advances in mechanical vibration energy harvesters based on triboelectric nanogenerators

    Du, T., et al. Recent advances in mechanical vibration energy harvesters based on triboelectric nanogenerators. Small 19, 2300401 (2023)

    2023

  46. [46]

    Hasan, M. A. M., Zhu, W., Bowen, C. R., Wang, Z. L. & Yang, Y . Triboelectric nanogenerators for wind energy harvesting. Nat. Rev. Electr. Eng. 1, 453-465 (2024)

    2024

  47. [47]

    Salman, M., Sorokin, V . & Aw, K. Systematic literature review of wave energy harvesting using triboelectric nanogenerator. Renew. Sustain. Energy Rev. 201, 114626 (2024)

    2024

  48. [48]

    Zhao, H. , et al. Dual‐tube helmholtz resonator‐based triboelectric nanogenerator for highly efficient harvesting of acoustic energy. Adv. Energy Mater. 9, 1902824 (2019)

    2019

  49. [49]

    simulate the transferred charge and current of this contact –separation device under sinusoidal motion

    Zhao, H. , et al. Underwater wireless communication via TENG -generated Maxwell’s displacement current. Nat. Commun. 13, 3325 (2022). Acknowledgements This work was supported by National Key R&D Program of China ( Grant No. 2024YFB3816000), Shenzhen Science and Technology Program ( Grant Nos. KJZD20240903100905008 and JCYJ20240813111910014), Guangdong Inn...

    2022

  50. [50]

    Zhao, H. , et al. Theoretical modeling of contact -separation mode triboelectric nanogenerators from initial charge distribution. Energy Environ. Sci. 17, 2228 - 2247 (2024). https://doi.org/10.1039/d3ee04143c

    work page doi:10.1039/d3ee04143c 2024

  51. [51]

    Theoretical study of contact-mode triboelectric nanogenerators as an effective power source

    Niu, S., et al. Theoretical study of contact-mode triboelectric nanogenerators as an effective power source. Energy Environ. Sci. 6, 3576 (2013). https://doi.org/10.1039/c3ee42571a

    work page doi:10.1039/c3ee42571a 2013

  52. [52]

    Wang, Z. L. The expanded Maxwell’s equations for a mechano -driven media system that moves with acceleration. Int. J. Mod Phys B 37, 2350159 (2023). https://doi.org/10.1142/S021797922350159X

    work page doi:10.1142/s021797922350159x 2023

  53. [53]

    Wang, Z. L. On Maxwell's displacement current for energy and sensors: the origin of nanogenerators. Mater. Today 20, 74 -82 (2017). https://doi.org/10.1016/j.mattod.2016.12.001

    work page doi:10.1016/j.mattod.2016.12.001 2017

  54. [54]

    & Kim, J.-B

    Kim, S., Ha, J. & Kim, J.-B. Calculation of polarization and bound charge density inside a dielectric material in triboelectric nanogenerators: Analytical and numerical study. Eur. Phys. J. Plus 131, 382 (2016). https://doi.org/https://doi.org/10.1140/epjp/i2016-16382-1

    work page doi:10.1140/epjp/i2016-16382-1 2016

  55. [55]

    Harrington, R. F. Matrix methods for field problems. Proc. IEEE 55, 136 -149 (1967). https://doi.org/10.1109/PROC.1967.5433

    work page doi:10.1109/proc.1967.5433 1967

  56. [56]

    & Glisson, A

    Rao, S., Wilton, D. & Glisson, A. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propag. 30, 409 -418 (1982). https://doi.org/10.1109/TAP.1982.1142818

    work page doi:10.1109/tap.1982.1142818 1982

  57. [57]

    Generation of finite difference formulas on arbitrarily spaced grids

    Fornberg, B. Generation of finite difference formulas on arbitrarily spaced grids. Math. Comp. 51, 699 -706 (1988). https://doi.org/10.1090/S0025-5718-1988- 0935077-0

    work page doi:10.1090/s0025-5718-1988- 1988

  58. [58]

    Zhao, H. , et al. Underwater wireless communication via TENG -generated Maxwell’s displacement current. Nat. Commun. 13, 3325 (2022). https://doi.org/10.1038/s41467-022-31042-8

    work page doi:10.1038/s41467-022-31042-8 2022

  59. [59]

    Dual‐tube helmholtz resonator‐based triboelectric nanogenerator for highly efficient harvesting of acoustic energy

    Zhao, H., et al. Dual‐tube helmholtz resonator‐based triboelectric nanogenerator for highly efficient harvesting of acoustic energy. Adv. Energy Mater. 9, 1902824 (2019). https://doi.org/10.1002/aenm.201902824

    work page doi:10.1002/aenm.201902824 2019

  60. [60]

    Vicinagearth1(1) (2024)

    Li, X., Wang, S., Zeng, S., Wu, Y . & Yang, Y . A survey on LLM-based multi-agent systems: workflow, infrastructure, and challenges. Vicinagearth 1, 9 (2024). https://doi.org/https://doi.org/10.1007/s44336-024-00009-2

    work page doi:10.1007/s44336-024-00009-2 2024

  61. [61]

    Nechvatal, J. , et al. Report on the development of the Advanced Encryption Standard (AES). J. Res. Natl. Inst. Stand. Technol. 106, 511 (2001). https://doi.org/10.6028/jres.106.023

    work page doi:10.6028/jres.106.023 2001