The Piezoelectric Effect

 

Materials which generate an electric potential in response to mechanical stress  are considered to be piezoelectric materials. Such materials will also change shape when an electric field is applied to them. The effect is schematically represented in the following diagram.

                                                        Image:SchemaPiezo.gif

Figure 1. A schematic diagram which shows a sample of piezoelectric material (gray) being subject to stress (arrows); the resultant voltage is registered on the volt meter. 1

The piezoelectric effect was discovered and studied in the late 19th century by Pierre Curie and his brother Jacquez Curie and has been observed in a wide range of materials such as quartz (SiO2),  Rochelle Salt (Potassium sodium tartrate, NaKC4H4O6), barium titanate (BiTiO3) and lithium niobate (LiNbO3). It has also been observed in biological materials such as  bone, tendons, sugar,dentin, wood and skin. Note that most of these biological materials are polymeric . There are also a number of man made polymeric materials which exhibit the effect, most importantly the subject of our case study,  PVDF.  The basic discovery of piezoelectric behavior in PVDF was made by Kawaii in 1969. In all of piezoelectric materials it appears that there is a separation of charge which generates a net dipole at a site in the material. The nature of one type of site in a piezoelectric can be visualized by considering the lattice of  Pb(TiO2),  pictured below.1

                                                           

In this representation one sees that the center of positive charge (Ti4+ is slightly displaced (upward) relative to the center of negative charge at the center of the oxygen octahedron.  The vector P in the above diagram points in the direction of the net dipole resulting from the displacement of charge.

Piezoelectric Exercise I

The dipoles in macroscopic sample of material can have random orientations in which case the material has no net moment. This situation is pictured in (1) below.

 

                                                   

Figure 3. Different align domains.

Applying a strong electric field under the appropriate conditions (temperature, pressure, etc)  can produce alignment of the dipoles as schematically pictured in (2) and (3) above. The oriented dipolar domains pictured above can loose their structure at high temperature, with wear etc. Poled ferroelectric materials form materials which are piezoelectric; that is they produce a voltage when stressed. Conversely,  when a voltage is applied to a sample of  piezoelectric material that sample changes shape.  The voltage which develops in a piezoelectric are due to the formation of net positive and negative charges on the surface of the material when it a sample of it is stressed..  Pyroelectric materials create a voltage when their temperature is changed, Pyroelectric materials are piezoelectric but the converse is not always true. PVDF is both pyroelectric and piezoelectric with both effects arising out of the ferroelectric properties of the poled polymer. Note that the voltage effect observed with piezoelectric materials is transient and is absent if there is no stress on the material.

 

It is important to keep in mind some of the important attributes of  piezoelectric PVDF as one thinks about building sensors. PVDF films develop a surface charge only when the when the film is stressed, the voltage difference of the surfaces can be quite large but any current that can be collected and made to flow through an external circuit is quite small.  Exerting stress on a relatively thin PVDF film causes  changes in all dimensions of the film. Thus, the simple compression model which is employed in the calculations which follow is very much an approximation The pyroelectric and piezoelectric properties of  PVDF are useful in sensor applications; the deformation of PVDF under an applied voltage can be used in industrial and medical actuator applications. The theory and properties of  ferroelectric, piezoelectric and pyroelectric  materials receive considerable attention in  advanced solid state physics courses.

 

Piezoelectric materials have been used in a wide range of applications including quartz watches, solid state gas lighters,  medical ultrasound imagers, sound systems, and microfluidic pumps.  A published pump design is pictured below.

 

                                                Image

 

Fig. 4. (a) Schematic drawing of the fabricated microfluidic pump using P(VDF-TrFE) as the active polymer material. The planar pump operation is based on the rectifying action realized using the two nozzle/diffuser structures. (b) Cross-sectional view of the nozzle"diffuser pump along the line A"A shown in (a). The unimorph structure is electroded only in the pump chamber area with two 20 μm thick PVDF active layers bonded onto a 40 μm thick inactive layer. The PVDF diaphragm covers the entire device however, it only actuates in the pump chamber region where the electrodes are present (c) 3D view of the rectangular nozzle/diffuser elements with labels of the various parameters characterizing the nozzle/diffuser structures. Two different nozzle/diffusers with W1 = 295 and W2 = 713 μm and W1 = 197 and W2 = 603 μm, respectively, with θ = 10" have been characterized.

Electroactive polymer based microfluidic pump

Feng Xia, Srinivas Tadigadapa and Q.M. Zhang ,
Department of Electrical Engineering and Materials Research Institute, The Penn State University, University Park, PA 16802, USA
Received 28 March 2005;  revised 16 June 2005;  accepted 16 June 2005.  Available online 24 August 2005.
Sensors and Actuators A: Physical
Volume 125, Issue 2, 10 January 2006, Pages 346-352

The properties of piezoelectric materials can be expressed mathematically. The material in the appendix (link below) provides a demonstration of mathematical modeling of piezoelectric phenomena.

Piezoelectric Appendix

 

References

1. Piezoelectricity.  http://en.wikipedia.org/wiki/Piezoelectricity

 


Valid HTML 4.01 Transitional