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## Viscoelastic properties of cellular polypropylene ferroelectrets

- Viscoelastic properties of cellular polypropylene ferroelectrets (PP FEs) were studied at low frequencies (0.3–33 Hz) by dynamic mechanical analysis and at high frequencies (250 kHz) by laser Doppler vibrometry. Relaxation behavior of the in-plane Young’s modulus (Y´ 11~1500 MPa at room temperature) was observed and attributed to the viscoelastic response of polypropylene matrix. The out-of-plane Young’s modulus is very small (Y´33≈0.1 MPa) at low frequencies, frequency- and stress-dependent, evidencing nonlinear viscoelastic response of PP FEs. The highfrequency mechanical response of PP FEs is shown to be linear viscoelastic with Y´33≈0.8 MPa. It is described by thickness vibration mode and modeled as a damped harmonic oscillator with one degree of freedom. Frequency dependence of Y*33 in the large dynamic strain regime is described by the broad Cole-Cole relaxation with a mean frequency in kHz range attributed to the Dynamics of the air flow between partially closed air-filledViscoelastic properties of cellular polypropylene ferroelectrets (PP FEs) were studied at low frequencies (0.3–33 Hz) by dynamic mechanical analysis and at high frequencies (250 kHz) by laser Doppler vibrometry. Relaxation behavior of the in-plane Young’s modulus (Y´ 11~1500 MPa at room temperature) was observed and attributed to the viscoelastic response of polypropylene matrix. The out-of-plane Young’s modulus is very small (Y´33≈0.1 MPa) at low frequencies, frequency- and stress-dependent, evidencing nonlinear viscoelastic response of PP FEs. The highfrequency mechanical response of PP FEs is shown to be linear viscoelastic with Y´33≈0.8 MPa. It is described by thickness vibration mode and modeled as a damped harmonic oscillator with one degree of freedom. Frequency dependence of Y*33 in the large dynamic strain regime is described by the broad Cole-Cole relaxation with a mean frequency in kHz range attributed to the Dynamics of the air flow between partially closed air-filled voids in PP FEs. Switching-off the relaxation contribution causes dynamic crossover from the nonlinear viscoelastic regime at low frequencies to the linear viscoelastic regime at high frequencies. In the small strain regime, contribution of the air flow seems to be insignificant and the power-law response, attributed to the mechanics of polypropylene cell walls and closed air voids, dominates in a broad frequency range. Mechanical Relaxation caused by the air flow mechanism takes place in the sound and ultrasound frequency range (10 Hz–1MHz) and, therefore, should be taken into account in ultrasonic applications of the PP FEs deal with strong exciting or receiving signals.…