STRC Piezo Voltage Budget PVDF-TrFE
A PVDF-TrFE nanofilm (100 nm) deposited on the tectorial-membrane undersurface generates a useful voltage across the OHC apical membrane ONLY if deposited at bundle-scale curvature (R ≤ 100 nm) — i.e., conformally on OHC-adjacent surfaces, not as a macroscopic sheet on the TM. At R = 1 µm (naive macroscopic deposition), the capacitive divider delivers only 3.6 mV at 60 dB — below the 10 mV prestin activation threshold.
Physics — per-unit-area capacitive divider
Piezo film generates open-circuit voltage V_oc from stress σ = E·ε, where ε is bending strain. The OHC membrane is a parallel capacitor (C_mem) connected to the piezo film (C_film). V_wall (what prestin sees) = V_oc × C_film / (C_mem + C_film). Transfer efficiency η = C_film / (C_mem + C_film) — grows with thinner film, higher permittivity.
Specific membrane capacitance C_spec = 9 mF/m² = 0.9 µF/cm² (standard OHC value). PVDF-TrFE with 100 nm thickness, ε_r = 10: C_film = 8.8·10⁻¹² · 10 / 10⁻⁷ = 0.88 mF/m² per unit area. Transfer η ≈ 0.09.
Results (Phase 1 at 60 dB SPL)
| Scenario | V_oc | η | V_wall | Min SPL to activate |
|---|---|---|---|---|
| PVDF-TrFE 100 nm R=1 µm (macroscopic) | 40.7 mV | 0.090 | 3.6 mV ❌ | 70 dB |
| PVDF-TrFE 100 nm R=100 nm (bundle-scale) | 407 mV | 0.090 | 36.4 mV ✅ | 50 dB |
| Terpolymer P(VDF-TrFE-CFE) 100 nm R=1 µm | 13.6 mV | 0.330 | 4.5 mV ❌ | 70 dB |
| PLLA 100 nm R=1 µm | 90.4 mV | 0.029 | 2.6 mV ❌ | 75 dB |
Dominant lever: bending radius R. V_oc scales inversely with curvature — 10× smaller R gives 10× more voltage. Going from macroscopic TM deposition (1 µm curvature) to bundle-scale (100 nm curvature) gives a 10× V_wall boost, moving the system from 70 dB activation threshold to 50 dB.
Engineering levers (60 dB PVDF-TrFE, thickness × curvature sweep)
- Thickness: thinner films improve η (more C_film) but reduce V_oc ∝ thickness → net wash above ~50 nm
- Curvature radius: dominant lever; smaller R = more voltage per acoustic cycle
- Higher-permittivity materials (terpolymer ε_r ≈ 50) improve η 3–4× but cost V_oc
- Heat dissipation: negligible regardless of design (~10⁻¹⁴ W per patch)
Updated hypothesis framing
Piezoelectric amplification is physics-viable at 60 dB SPL only with nanoscale-conformal film deposition — the delivery problem is harder than simple “drop it on the TM.” Feasible via:
- Functionalised nanoparticles capturing to OHC-adjacent surfaces (anti-prestin antibody, A666 peptide)
- Fallback: macroscopic TM coating + 70 dB hearing-aid operating regime (higher but clinically feasible for Misha)
Phase 1 gate: conditional pass. Proceed to Phase 2 (frequency response + strain model sensitivity — see STRC Piezo Frequency Response Bundle Mechanics) with two variants: bundle-scale conformal (primary) and macroscopic TM + 70 dB fallback.
Files / Models
~/STRC/models/piezo_voltage_budget.py— voltage-budget script (per-unit-area capacitive divider)~/STRC/models/piezo_voltage_budget_results.json— thickness × curvature × material sweep~/STRC/models/piezo_voltage_budget.png— 6-panel figure
Connections
[part-of]STRC Piezoelectric TM Bioelectronic Amplifier — parent hypothesis[see-also]STRC Piezo Frequency Response Bundle Mechanics — Phase 2 strain-model + audiogram sweep[see-also]Prestin and OHC Electromotility — the 10 mV prestin threshold is the design constraint[applies]Misha — therapy target; his 70 dB hearing-aid output provides fallback operating regime