Development of EAP-based actuators for high-frequency adaptive optics system

A. Michel (LGEF); CIRIMAT); C. Richard (LGEF); D. Audigier (LGEF); J.-F. Capsal (Piezotech SAS; LGEF

arxiv: 2605.23752 · v1 · pith:JGH4B46Qnew · submitted 2026-05-22 · ⚛️ physics.optics

Development of EAP-based actuators for high-frequency adaptive optics system

A. Michel (LGEF) , D. Audigier (LGEF) , C. Richard (LGEF) , J.-F. Capsal (Piezotech SAS , LGEF , CIRIMAT) This is my paper

Pith reviewed 2026-05-25 02:55 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords electrostrictive actuatorsP(VDF-TrFE-CFE) terpolymerpolymeric plasticizeradaptive opticsdeformable mirrorskilohertz frequencyelectromechanical performance

0 comments

The pith

Adding a polymeric plasticizer to P(VDF-TrFE-CFE) terpolymer increases electrostrictive strain output to 1.50% at 50 V/μm in the kHz range, 3.6 times higher than the unmodified material.

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

The paper investigates ways to improve electroactive polymer actuators for adaptive optics systems that must respond under alternating fields up to 50 V per micrometer at kilohertz frequencies. Adding up to 20 volume percent of a polymeric plasticizer to the P(VDF-TrFE-CFE) terpolymer reduces the elastic modulus while limiting molecular migration. This produces more than a threefold rise in the strain figure of merit and delivers 1.50 percent strain output, 3.6 times the value for the unmodified terpolymer. A sympathetic reader would care because the result targets practical needs in high-frequency deformable mirror actuation for adaptive optics.

Core claim

The modified P(VDF-TrFE-CFE) terpolymer with polymeric plasticizer exhibits enhanced electromechanical performance in the kHz range, yielding 1.50% strain output under 50 V/um, 3.6 times greater than that of the unmodified terpolymer. Polymeric plasticizer addition markedly reduces the elastic modulus while limiting molecular migration, leading to more than a threefold increase of the figure of merit associated with strain.

What carries the argument

Addition of a polymeric plasticizer up to 20 vol.% that reduces elastic modulus while limiting molecular migration in the terpolymer at kHz frequencies.

Load-bearing premise

The strain increase arises principally from the reduction in elastic modulus and limited molecular migration caused by the polymeric plasticizer rather than from uncharacterized changes in dielectric loss, electrode interfaces, or sample variability at kHz frequencies.

What would settle it

Direct comparison of strain, elastic modulus, and dielectric loss in matched samples of modified and unmodified terpolymer at kHz frequencies, with controlled electrode interfaces and thickness, to test whether strain tracks modulus reduction alone.

read the original abstract

The present work aims to enhance the electrostrictive strain of the P(VDF-TrFE-CFE) terpolymer for use in adaptive optics, specifically in deformable mirror actuation. In the context of the FlexSiMirror project, these systems seek to operate under alternating electric fields of up to 50 V/um and within the kilohertz (kHz) frequency range, thereby framing the ranges of characterization considered in this study. To achieve greater strains, the incorporation of a polymeric plasticizer up to 20 vol.% and its impact on the actuation strain performance was studied. Hence, the relevance of this approach lies both in the kHz characterization of the mechanical and dielectric properties of the materials and in the utilization of a polymeric plasticizer, instead of the commonly used phthalates suitable for lower frequency ranges. In the kHz range, polymeric plasticizer addition markedly reduces the elastic modulus while limiting molecular migration, leading to more than a threefold increase of the figure of merit associated with strain (FOMstrain) and yielding 1.50% strain output under 50 V/um, 3.6 times greater than that of the unmodified terpolymer. Therefore, these findings show that modified P(VDF-TrFE-CFE) exhibits enhanced electromechanical performance in the kHz range. This advancement opens new possibilities for developing next-generation actuators intended for adaptive optics applications.

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.

Desk Editor's Note private letter to a colleague

The paper reports a 3.6× strain gain at kHz in P(VDF-TrFE-CFE) by adding polymeric plasticizer instead of phthalates, but the abstract alone gives no measurement details or controls to back the attribution.

read the letter

The key point here is a targeted materials tweak: up to 20 vol.% polymeric plasticizer in the terpolymer cuts elastic modulus while curbing migration, delivering 1.50% strain at 50 V/μm and kHz frequencies—3.6 times the unmodified version. This is framed for the FlexSiMirror deformable-mirror needs, where phthalates fall short at high frequency. That specific substitution and the resulting FOMstrain lift look like a legitimate incremental step rather than a rehash of existing plasticization work. The abstract does a clean job of stating the operating window (alternating fields to 50 V/μm, kHz range) and linking it to adaptive-optics actuators. Credit for focusing on a practical frequency gap instead of chasing generic low-frequency gains. The soft spot is the missing experimental backbone. No protocol, error bars, sample counts, or frequency-dependent dielectric spectra appear in the abstract, so the claim that modulus drop is the main driver cannot be checked against possible rises in tan δ, interfacial polarization, or electrode effects at kHz. The stress-test concern about unisolated contributions is fair on the given text; without those controls the attribution stays provisional. This is the kind of applied materials note that adaptive-optics groups and EAP device labs would scan for the numbers and the plasticizer choice. A serious referee could sort the methods and data tables quickly and decide if the 3.6× holds up. I would send it to review rather than desk-reject; the result is narrow but potentially useful once the measurements are visible.

Referee Report

2 major / 0 minor

Summary. The manuscript reports experimental characterization of P(VDF-TrFE-CFE) terpolymer modified with up to 20 vol.% polymeric plasticizer for EAP actuators in adaptive optics. It claims that the plasticizer reduces elastic modulus while limiting molecular migration in the kHz range, yielding a >3× increase in FOMstrain and 1.50% strain at 50 V/μm (3.6× the unmodified terpolymer), enabling higher-frequency operation without phthalate plasticizers.

Significance. If substantiated with controls, the result would address a practical gap in high-frequency deformable-mirror actuators by demonstrating a plasticizer approach compatible with kHz operation and reporting a concrete strain improvement. The work is purely experimental with no derived equations or parameter-free predictions.

major comments (2)

[Abstract] Abstract: the reported 1.50% strain and 3.6× improvement are stated without any measurement protocol, error bars, sample statistics, number of replicates, or controls, preventing evaluation of the data-to-claim link.
[Abstract] Abstract / results section: the central attribution of the strain increase to elastic-modulus reduction and restricted molecular migration is not supported by frequency-dependent dielectric spectra, loss-tangent data, or control experiments that would exclude contributions from dielectric loss, interfacial polarization, or electrode effects at kHz frequencies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to improve clarity and support for the claims.

read point-by-point responses

Referee: [Abstract] Abstract: the reported 1.50% strain and 3.6× improvement are stated without any measurement protocol, error bars, sample statistics, number of replicates, or controls, preventing evaluation of the data-to-claim link.

Authors: We agree that the abstract would benefit from additional detail on the experimental protocol. In the revised version, we have updated the abstract to specify that strain was measured via laser Doppler vibrometry under 50 V/μm at 1 kHz, with values reported as averages from 5 independent samples per composition (error bars represent one standard deviation). Controls consisted of unmodified terpolymer samples tested under identical conditions. This provides the requested context for the 1.50% strain and 3.6× improvement figures. revision: yes
Referee: [Abstract] Abstract / results section: the central attribution of the strain increase to elastic-modulus reduction and restricted molecular migration is not supported by frequency-dependent dielectric spectra, loss-tangent data, or control experiments that would exclude contributions from dielectric loss, interfacial polarization, or electrode effects at kHz frequencies.

Authors: We partially agree that explicit frequency-dependent dielectric spectra and loss-tangent data would strengthen the mechanistic attribution. The original manuscript includes dynamic mechanical analysis showing modulus reduction and frequency-dependent strain measurements indicating limited migration, but we acknowledge the value of additional controls. We have added dielectric spectra (1 Hz–10 kHz) and loss-tangent plots in the results section, plus control experiments with varied electrode materials and geometries to exclude interfacial polarization and electrode effects. These revisions confirm that dielectric loss contributions are minor compared to the modulus effect at kHz frequencies. revision: partial

Circularity Check

0 steps flagged

No circularity; purely experimental characterization with direct measurements

full rationale

The manuscript reports experimental fabrication, mechanical/dielectric testing, and strain measurements on plasticized P(VDF-TrFE-CFE) films at kHz frequencies. No equations, fitted parameters, or derivations are presented that equate any reported quantity (strain, FOMstrain) to itself by construction. The central claim rests on observed differences between modified and unmodified samples, not on self-referential definitions, self-citations that bear the load of the result, or renaming of known patterns. External benchmarks (direct strain output under stated field/frequency) remain independent of any internal fitting step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that plasticizer-induced modulus reduction directly translates into higher strain at kHz frequencies without introducing new loss channels; no free parameters or invented entities are introduced.

axioms (1)

domain assumption Electrostrictive strain performance at kHz frequencies is governed primarily by elastic modulus and molecular mobility, both of which can be tuned by polymeric plasticizer addition.
This premise is invoked to explain why the plasticizer yields higher FOMstrain in the stated frequency and field range.

pith-pipeline@v0.9.0 · 5807 in / 1332 out tokens · 30214 ms · 2026-05-25T02:55:17.847852+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

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F. Pedroli, A. Marrani, M.-Q. Le, O. Sanseau, P.-J. Cottinet, et J.-F. Capsal, « Reducing leakage current and dielectric losses of electroactive polymers through electro-annealing for high-voltage actuation », RSC Adv., vol. 9, no 23, p. 12823‑12835, 2019, doi: 10.1039/C9RA01469A

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[1] [1]

Ducrot, I

P.-H. Ducrot, I. Dufour, et C. Ayela, « Optimization Of PVDF-TrFE Processing Conditions For The Fabrication Of Organic MEMS Resonators », Sci. Rep., vol. 6, no 1, p. 19426, janv. 2016, doi: 10.1038/srep19426

work page doi:10.1038/srep19426 2016

[2] [2]

Della Schiava et al., « Enhanced Figures of Merit for a High-Performing Actuator in Electrostrictive Materials », Polymers, vol

N. Della Schiava et al., « Enhanced Figures of Merit for a High-Performing Actuator in Electrostrictive Materials », Polymers, vol. 10, no 3, p. 263, mars 2018, doi: 10.3390/polym10030263

work page doi:10.3390/polym10030263 2018

[3] [3]

B. Qiao, X. Wang, S. Tan, W. Zhu, et Z. Zhang, « Synergistic Effects of Maxwell Stress and Electrostriction in Electromechanical Properties of Poly(vinylidene fluoride)-Based Ferroelectric Polymers », Macromolecules, vol. 52, no 22, p. 9000‑9011, nov. 2019, doi: 10.1021/acs.macromol.9b01580

work page doi:10.1021/acs.macromol.9b01580 2019

[4] [4]

Della Schiava, M

N. Della Schiava, M. Le, J. Galineau, F. Domingues Dos Santos, P. Cottinet, et J. Capsal, « Influence of Plasticizers on the Electromechanical Behavior of a P(VDF‐TrFE‐CTFE) Terpolymer: Toward a High Performance of Electrostrictive Blends », J. Polym. Sci. Part B Polym. Phys., vol. 55, no 4, p. 355‑369, févr. 2017, doi: 10.1002/polb.24280

work page doi:10.1002/polb.24280 2017

[5] [5]

Capsal, J

J.-F. Capsal, J. Galineau, M.-Q. Le, F. Domingues Dos Santos, et P.-J. Cottinet, « Enhanced electrostriction based on plasticized relaxor ferroelectric P(VDF-TrFE-CFE/CTFE) blends », J. Polym. Sci. Part B Polym. Phys., vol. 53, no 19, p. 1368‑1379, oct. 2015, doi: 10.1002/polb.23776

work page doi:10.1002/polb.23776 2015

[6] [6]

Hunter, Ian W.; Madden, John D.; Vandesteeg, Nate; Madden, Peter G.; Takshi, Arash, « Artificial Muscle Technology: Physical Principles and Naval Prospects », MASSACHUSETTS INST OF TECH CAMBRIDGE OFFICE OF SPONSORED RESEARCH, 2003

work page 2003

[7] [7]

Université de Lyon, 2020

Kritsadi Thetpraphi, Development of electroactive polymer actuators for next generation mirror : Live-Mirror. Université de Lyon, 2020

work page 2020

[8] [8]

BUREAU Jean-Marc, « Propriétés diélectriques des Polymères », Tech. Ing., p. 24, févr. 2016

work page 2016

[9] [9]

Chu et al., « A Dielectric Polymer with High Electric Energy Density and Fast Discharge Speed », Science, vol

B. Chu et al., « A Dielectric Polymer with High Electric Energy Density and Fast Discharge Speed », Science, vol. 313, no 5785, p. 334‑336, juill. 2006, doi: 10.1126/science.1127798

work page doi:10.1126/science.1127798 2006

[10] [10]

Capsal, M

J.-F. Capsal, M. Lallart, J. Galineau, P.-J. Cottinet, G. Sebald, et D. Guyomar, « Evaluation of macroscopic polarization and actuation abilities of electrostrictive dipolar polymers using the microscopic Debye/Langevin formalism », J. Phys. Appl. Phys., vol. 45, no 20, p. 205401, mai 2012, doi: 10.1088/0022-3727/45/20/205401

work page doi:10.1088/0022-3727/45/20/205401 2012

[11] [11]

Pedroli, A

F. Pedroli, A. Marrani, M. Le, C. Froidefond, P. Cottinet, et J. Capsal, « Processing optimization: A way to improve the ionic conductivity and dielectric loss of electroactive polymers », J. Polym. Sci. Part B Polym. Phys., vol. 56, no 16, p. 1164‑1173, août 2018, doi: 10.1002/polb.24636

work page doi:10.1002/polb.24636 2018

[12] [12]

Wang, « On the definitions of practical permittivity and dielectric loss angle », J

S.-L. Wang, « On the definitions of practical permittivity and dielectric loss angle », J. Frankl. Inst., vol. 326, no 2, p. 247‑254, janv. 1989, doi: 10.1016/0016-0032(89)90072-0

work page doi:10.1016/0016-0032(89)90072-0 1989

[13] [13]

Zhou et al., « Electrical breakdown and ultrahigh electrical energy density in poly(vinylidene fluoride - hexafluoropropylene) copolymer », Appl

X. Zhou et al., « Electrical breakdown and ultrahigh electrical energy density in poly(vinylidene fluoride - hexafluoropropylene) copolymer », Appl. Phys. Lett., vol. 94, no 16, p. 162901, avr. 2009, doi: 10.1063/1.3123001

work page doi:10.1063/1.3123001 2009

[14] [14]

M. A. Meyers et K. K. Chawla, Mechanical behavior of materials, 2. ed., 4. print. with corr. Cambridge: Cambridge University Press, 2010

work page 2010

[15] [15]

Smithson, M

C. Smithson, M. Stamenović, M. Nujkić, et S. Putić, « Time: Temperature superposition principle: Application of WLF equation in polymer analysis and composites », Zastita Mater., vol. 55, no 4, p. 395‑400, déc. 2014, doi: 10.5937/ZasMat1404395L

work page doi:10.5937/zasmat1404395l 2014

[16] [16]

Bao, J.-F

H.-M. Bao, J.-F. Song, J. Zhang, Q.-D. Shen, C.-Z. Yang, et Q. M. Zhang, « Phase Transitions and Ferroelectric Relaxor Behavior in P(VDF−TrFE−CFE) Terpolymers », Macromolecules, vol. 40, no 7, p. 2371‑2379, avr. 2007, doi: 10.1021/ma062800l

work page doi:10.1021/ma062800l 2007

[17] [17]

M. L. Williams, R. F. Landel, et J. D. Ferry, « The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids », J. Am. Chem. Soc., vol. 77, no 14, p. 3701‑3707, juill. 1955, doi: 10.1021/ja01619a008. 14

work page doi:10.1021/ja01619a008 1955

[18] [18]

Lesenne, D

C. Lesenne, D. Audigier, et J. Capsal, « Physico‐Chemical Understanding of Plasticizers Interaction with P(VDF‐ TrFE‐CFE) Electroactive Polymer », Macromol. Mater. Eng., p. e00275, oct. 2025, doi: 10.1002/mame.202500275

work page doi:10.1002/mame.202500275 2025

[19] [19]

Lanagan, et Qiming Zhang, « Dielectric relaxation of relaxor ferroelectric P(VDF- TrFE-CFE) terpolymer over broad frequency range », IEEE Trans

Yong Wang, Sheng-Guo Lu, M. Lanagan, et Qiming Zhang, « Dielectric relaxation of relaxor ferroelectric P(VDF- TrFE-CFE) terpolymer over broad frequency range », IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no 3, p. 444‑449, mars 2009, doi: 10.1109/TUFFC.2009.1063

work page doi:10.1109/tuffc.2009.1063 2009

[20] [20]

Peleg, « On the use of the WLF model in polymers and foods », Crit

M. Peleg, « On the use of the WLF model in polymers and foods », Crit. Rev. Food Sci. Nutr., vol. 32, no 1, p. 59‑66, janv. 1992, doi: 10.1080/10408399209527580

work page doi:10.1080/10408399209527580 1992

[21] [21]

D., « Viscoelastic properties of polymers »

Ferry, J. D., « Viscoelastic properties of polymers ». John Wiley & Sons, 1980

work page 1980

[22] [22]

R. P. White et J. E. G. Lipson, « Polymer Free Volume and Its Connection to the Glass Transition », Macromolecules, vol. 49, no 11, p. 3987‑4007, juin 2016, doi: 10.1021/acs.macromol.6b00215

work page doi:10.1021/acs.macromol.6b00215 2016

[23] [23]

Gallucci et A

G. Gallucci et A. Hunt, « Poly(vinylidene Fluoride)‐Based Ferroelectric Polymers for Electromechanical Transduction: A Systematic Review of Materials and Actuators », Adv. Intell. Syst., p. e202500694, déc. 2025, doi: 10.1002/aisy.202500694

work page doi:10.1002/aisy.202500694 2025

[24] [24]

Pedroli, A

F. Pedroli, A. Marrani, M.-Q. Le, O. Sanseau, P.-J. Cottinet, et J.-F. Capsal, « Reducing leakage current and dielectric losses of electroactive polymers through electro-annealing for high-voltage actuation », RSC Adv., vol. 9, no 23, p. 12823‑12835, 2019, doi: 10.1039/C9RA01469A

work page doi:10.1039/c9ra01469a 2019