How to handle Piezotech products?

Drying - Solvent Evaporation 

In order to get rid of any residual solvent and enhance film properties, a solvent evaporation step under atmospheric pressure or under vacuum can be carried out below the solvent’s boiling-point temperature. Evaporation strongly depends on evaporation facilities and air flow. It can thus be performed from room temperature to 140 °C, depending on the product grade.

Annealing

Annealing is a critical step to obtain the films with the best properties. It will control crystallization of the material and enhance electrical as well as mechanical properties.

For P(VDF-TrFE) copolymers

Annealing should be performed between the Curie temperature and the melting point, in the paraelectric phase, for 2-15 min. This corresponds to a 135-145 °C range. For Piezotech^® FC20, 80/20 P(VDF-TrFE), the 140-145 °C range is preferred.

For P(VDF-TrFE) copolymers, annealing should be performed in the paraelectric phase, as close as possible to the melting.

For P(VDF-TrFE-CTFE/CFE) terpolymers

Films may need to be annealed at an appropriate temperature during a variable time from 3 to 20 min, typically 5-15 °C below the melting point. A rapid annealing may be obtained on thin films using Infrared or Flash annealing.

In order to activate their piezoelectric and ferroelectric properties, P(VDF-TrFE) copolymers layers must be poled to orientate the C-F dipoles. Contact poling with top and bottom electrode, or non-contact Corona poling with only the bottom electrode can be carried out.

Typical process for contact poling

AC or DC volage can be applied, at room temperature, up to twice the coercive field: 100 V.µm^-1.

AC is advised with frequencies in the 0.1-10 Hz range.

Example of DC (blue) and AC (red) voltage ramps to pole a P(VDF-TrFE) layer

Example

An electric field is applied according to the following cycle:

• Voltage ramp: 0 V.µm^-1 to 100 V.µm^-1
• Frequency: 1 Hz (higher is possible)
• Number of cycles to reach 100 V.µm^-1: 15
• Signal wave form: Sinusoidal

Typical ferroelectric loop of a P(VDF-TrFE) copolymer poled at 100 V.µm^-1

Contact poling or Corona poling can be monitor by the current flowing through the P(VDF-TrFE) layer. 

Case of contact poling

For contact poling with AC voltage, the current between top and bottom electrodes is proportional to the sum of the resistive current, capacitive current and polarization current. After substracting the capacitive and resistive components of the raw current, polarization current can be extracted and after integration give the ferroelectric loop.

Charge sensors

Concepts: A charge sensor generates on its surface equal electric charges of opposite sign when it is stimulated by a mechanical force (piezoelectric effect) or a variation of temperature (pyro electric effect).

Equivalent diagrams: A piezo-, pyro- electric sensor can be modelled by one of the following equivalent diagrams:

Mode of operation: When using a piezo- pyro- electric sensor, the measured signal strongly depends on the conditions of experimentation. It is possible to measure a proportional signal, or to its derivate. The limit of these operation modes is given by the cut-off frequency of your instrumentation chain.

Signal conditioning

Direct connection: By connecting your sensor directly to your amplifier, oscilloscope, or DAC (data acquisition card) it must be kept in mind that external impedances may have a critical influence on the signal you will measure. In order to determine the said influences, the involved impedances (from the sensor, cable and measuring instrument input) are modelled as follows:

Equivalent diagram of a direct connection of a sensor

Further analysis of the diagram shows a high-pass filter behaviour, for which the cut-off frequency is given by:

When f >> fc, the measured signal is directly proportional to the generated charges:	When f << fc, the measured signal is proportional to the derivate:

Charge transducer

In order to drastically limit the influence of external impedances, the use of a charge transducer is recommended. The operating principle is based on the use of an external capacitor C to store the generated charges. A charge transducer may be also be called a charge-voltage converter.

Practical implementation of a charge-voltage transducer

As shown in the diagram, we consider the operational amplificator as ideal. The differential voltage between its inputs is null, so the current i generated by the sensor is driven to the feedback capacitor C. In order to prevent saturation of the output by parasitic influences, a parallel resistor R must be added to the feedback capacitor.

Such a circuit has a high-pass filter behaviour, for which the cut-off frequency is given by:

When f >> fc, the measured signal is directly proportional to the generated charges:	When f << fc, the measured signal is proportional to the derivate:

Deformation under electrical field

The deformation caused by the applied electric field can be defined by the simple formula:

S_i = d_3i.E

Where:

• S_i = Δx_i/x_i = ΔL/L represents the strain (relative deformation) of the sample in the x_i direction
• d_3i is the piezoelectric strain constant (in a perpendicular direction with respect to that of the applied electric field)

Example of an element with the following characteristics:

• Length: l = 1 cm
• Width: w = 2 mm
• Thickness: t = 9 µm
• Applied voltage: V = 200 V → E (electric field) = V/t
• (d₃₁, d^₃₂, d₃₃) = (11, 10, -30) pC.N^-1

The piezo strain constant d is given by:

d = strain developped/applied field = S/E

Sensors: Orders of Magnitude, Voltage generation

The electric field output (E) caused by an applied force can be defined by:

E = g_ij.σ_i

Where:

• σ_i is the applied mechanical stress (N.m^-2)
• g_ij is the piezoelectric voltage constant (Vm.Nm^-2)

g = electrical field developed/applied mechanical stress = E/σ

with g = d/ε = d/ε_rε₀

Example of an element with the following characteristics:

• Length: l = 2 cm
• Width: w =2 cm
• Thickness: t = 100 µm
• Compression 0.1 Bar → σ = -10000 N.m^-2
• (g₃₁, g₃₂, g₃₃) = (216, 19, -339) *10^-3 - Vm.Nm^-2

E = V₀/t = g₃₃.σ₃

V₀ = g₃₃.σ₃.t = 339 mV