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<p>The determination of transient changes in bulk resistance under applied electric fields is essential for evaluating surface conductivity in dielectric materials. Theoretical approaches can provide valuable insights into voltage propagation by analyzing temporal variations in the bulk response. However, due to the lack of a detailed and accurate understanding of the mechanisms governing resistance changes under external electric fields, the applicability of existing models remains limited. In this work, an improved model based on Rall’s biophysical-mathematical framework for neurons is presented and experimentally validated. Hydroxyapatite (HA), the primary mineral constituent of human bone and teeth, has attracted considerable interest as a pseudocapacitive electrode material for supercapacitors owing to its structural stability, abundant electroactive sites, and favorable ion transport properties, making it an attractive model system for evaluating the proposed approach. HA was subjected to thermal and electrical stimulation in the 250–1500&#xa0;V range at 1000&#xa0;°C. The comparative analysis between the theoretical model and experimental results demonstrates that our theoretical framework provides a robust basis for predicting electric current behavior in HA under externally applied voltages. Its applicability remains valid under real-world conditions, including the effects of diffusion and geometric factors. The proposed model demonstrates superior performance compared with recently reported deterministic and stochastic dielectric models.</p> Graphical abstract <p></p>

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A bulk-surface continuum model for voltage propagation in dielectric materials

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月27日

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  • Manuel Rivas,
  • Lourdes Franco,
  • Luis J. del Valle

摘要

The determination of transient changes in bulk resistance under applied electric fields is essential for evaluating surface conductivity in dielectric materials. Theoretical approaches can provide valuable insights into voltage propagation by analyzing temporal variations in the bulk response. However, due to the lack of a detailed and accurate understanding of the mechanisms governing resistance changes under external electric fields, the applicability of existing models remains limited. In this work, an improved model based on Rall’s biophysical-mathematical framework for neurons is presented and experimentally validated. Hydroxyapatite (HA), the primary mineral constituent of human bone and teeth, has attracted considerable interest as a pseudocapacitive electrode material for supercapacitors owing to its structural stability, abundant electroactive sites, and favorable ion transport properties, making it an attractive model system for evaluating the proposed approach. HA was subjected to thermal and electrical stimulation in the 250–1500 V range at 1000 °C. The comparative analysis between the theoretical model and experimental results demonstrates that our theoretical framework provides a robust basis for predicting electric current behavior in HA under externally applied voltages. Its applicability remains valid under real-world conditions, including the effects of diffusion and geometric factors. The proposed model demonstrates superior performance compared with recently reported deterministic and stochastic dielectric models.

Graphical abstract