SUPHANNEEPONGKITWITOON

Electrostrictive (crystallization) fluoropolymers (co- and terpolymers).  Emphasis on the origin of the electromechanical response.

By  Suphannee Pongkitwitoon

Contents

1 Introduction

Ueda, T. and et al., 1997 [18] studied the actuation of elctrostrictive Poyurethane Elastomer (PUE) by applying electric field of direct current.  Then using laser position sensor measured the strain induced by the electric field.  They found that PUE, which had polyether as an elastomer, was inactive to electric field, whereas PUE, which had elastomer of polyester, was actively actuated by the field.  Additionally, the presence of this charging-discharging process plays an important role for electric actuation.  By increasing charging process, the action process of strain will be increased.  Since the strain is induced by charging process resulted in dipole orientation in polymeric chain, this also states that strain induced by electric field is converted into action process of elastomer leading to behavior of actuator with large strain.  This research concluded that the mechanism of actuation is deformation of polymer networks induced by the dipole orientation of electrically mobile element in PUE itself.  However, by attempts of containing better electromechanical properties of NASA [15] with large electric field – induced strain increasing the range of mechanical motion, the studying of electrostrictive polymers of flexible backbones and grafting crystalline groups by varying fraction of polymer phases, their molecular weights, and their thermal treatments are accomplished.

In attempts to significantly improve the electromechanical properties of electrostrictive copolymers, Cheng, Z. Y. and et al., 2001 [5] studied P(VDF/TrFE) with irradiation treatment and then gained polarization hysteresis very little at room temperature but very large electrostrictive strain from large anisotropic strain response along perpendicular to the polymer chain.  This work concluded that high strain and high electric modulus resulted in an improved electromechanical coupling factor.  Cheng, Z. Y., and et al., 1998 [20, 23] also mentioned about exceptionally response under external field of strain for P(VDF/TrFE) in 1998 [1], and under high mechanical stress in 1999.  Electrostrictive properties of P(VDF/TrFE) is studied by Cheng, Z. Y. and Xu, Heisheng, 2001 [20] and Hami, K. El and et al., 2001 [10].  Furthermore, in work of Buckley, G.S. and et al., 2001 [2], Cheng, Z. Y., and et al., 2002 [6], Cohen, Yoseph Bar, 1999 [8] and Kodama, H. and et al., 1997 [12], the structures of P(VDF/TrFE) was studied for understanding the most potential for achieving a large electrostrictive response, in which its own crystalline structures play a crucial role for developing the better electrostrictive behaviors.  However, the limitations of crystalline thickness, studied by Zhang, Q. M. and et al., 2001 [22], affected on electrostrictive behaviors of ferroelectric-polymers, especially in form of thin-films found in work of Urayama, Kenji and et al., 2000 [19].  Additionally, copolymer of P(VDF/TrFE) was studied by Casalini, R. and et al., 2001 [3] to improve electromechanical performance by chemical cross linking.  Eury, Sylvie and et al., 1999 [9] evaluated electrostrictive properties of low permittivity dielectrics required extremely sensitive instrumentation in terms of prediction of electrostriction coefficients.  Yimnirun, Rattikorn and et al., 1999 [21] studied the measurement methods of electrostriction for low permittivity dielectrics.  Heydt, R. and et al., 1998 [11] approached the design, performance and processing of an electrostrictive polymer films for acoustic actuator and for transducers in work of Cheng, Z. Y., and et al., 2002 [4].  Studies of applications of electrostrictive polymers obtained by Pelrine, Ronald and et al., 1998 [16] using for electronic actuators, by Kornbluh, Roy and et al. [13] utilizing for muscle actuators and artificial muscle in robot [14], by Zhang, Q. M., and et al., 1999 [24] and NASA [15] recently using for Aerospace in position control, Communication in optical switching and membranes, Propulsion in adjustable solar sails, Power generations in solar membrane reflectors, and High precision surfaces to correct surface deviations caused by thermal fluctuations and manufacturing tolerance/error, and Robotic devices.

Almost of this paper is emphasis on electrostrictive fluoropolymer of Poly(vinylidene fluoride-trifluoroethylene) copolymers, P(VDF/TrFE) and their electromechanical properties.  According to briefly mentioning about the principle of electrical and conductive properties of polymers, the basic theoretical ideas are detailed by Scrosati, Bruno, 1993 [17] and Chilton, J.A. and Goosey, M.T., 1995 [7].  By gradient development, the topics were presented step by step from a structures and organization of electrostrictive Polymers in aspects of understanding the reasons how they behave as an electrostrictive polymer.  An approached mechanism and electrostrictive properties were detailed for understanding the potential of structures related to electromechanical properties and methods for measuring these properties.  Knowledge, learned from the above topics, leads to pragmatic manners of designs and processing for specific applications.

2 Structures and Organization of Electrostrictive Polymers

2.1 Network Structures of Electrostrictive Films

Since the electro-irradiated copolymers of vinylidene fluoride and trifluoroethylene have significant potential to achieve large electrostrictive responses [2].  By means of radiating, the principal effect of the radiation was mainly on network formation and such evidence brought methods to improve electromechanical properties of the materials [2, 7].  Since electron irradiation of P(VDF/TrFE) with high energy electrons or gramma rays induces a solid state, irreversible transformation of ferroelectric lattices to paraelectric phases, then the irradiation is attributed to crosslinking, chain scission, isomerization, bond rearangement with consequently effects on chemical and physical properties of these materials [2].  To understand the network structures of P(VDF/TrFE), Buckley, G. S. and Roland, C. M., 2001 [2] used techniques of two-solvent swelling for obtaining quantity of interaction parameters to enable to determine their crosslink densities along with a measure of degree of degradation accompanying radiolysis.  The copolymers were random copolymers of 68 mole% vinylidene fluoride and 32 mole% trifluoroethylene.  Irradiated film ~30 mm thick, prepared by curing under pressure 30 min at 180 °C, underwent with 2.6 MeV electrons at 98 ± 3 °C with maintaining stain at 450% by using 4%-10% dicumyl peroxide for chemically crosslinking.  Since networks of copolymers were chemically prepared from organic peroxide, then these networks were similar to the radiated crosslink materials both in the extent of degradation with respect to the Curie temperature and crystalline melting behaviors.  By using Flory-Rehner equation relates the number density of network chains, n, of functionality, f, to the volume reaction of that network at equilibrium swelling, n_R,

                                 (2-1) [2]

                                                                                                                                    (2-2) [2]

Plotting the relation between interaction coefficient and rhs from equation (2-2) as shown in Figure 2-1 [2] was calculated by equation (2-1) [2] to get crosslink density 0.75 ± 0.17 per 100 eV displayed in the inset of this Figure 2-1.  These crosslink lead to network formation, ionizing radiation even though there exist some evidences, causing such as side reactions of scissions, rearrangement, isomerization, cyclization within polymer chains.  These side reactions affect on physical properties for instance chain scission reduces stiffness and strength, while cyclization and isomerization perturb steric regularities which reduce crystallinity, attributing to diminish electromechanical properties [2, 7].  However, these transient crystalline polymers can survive for hours comparatively much longer than most side reactions are very fast.   Additionally, high ionization potential with low polarizability of the C-F bonding of fluoropolymers brings very long lifetimes up to five years [2] for fluoro-radicals.  These evidences are particularly susceptible to degradation when exposed to ionizing radiation [2].  Thus degradation can be quantified by analyzing the soluble fraction of P(VDF/TrFE) after network formation with considering production of an insoluble gel as a yield of its crosslinks.  For the above reasons, Buckley, G.S. and Roland, C. M., 2001 [2] and Cheng, Z. Y. and et al., 2002 [7] proposing the main objective of crosslinking P(VDF/TrFE) is for developing of better electromechanical properties with large electrostrictive strain under irradiating electron beam.  The large electromechanical coupling factors and properties results from crosslinks reducing the interaction between dipoles in the crystalline domains and then suppressing the degree of crystallization , which reduces the capacity of polarization of the copolymers [2].

Figure 2-1 : Relationship between interaction coefficient, rhs, and crystalline density [2]

2.2 Critical Thickness and Layer Thinning Effects

Furthermore, Cheng, Y. Z. and et al., 2002 [7] found that irradiation not only reduces crystallinity in copolymer films but also produces significant changes in ferroelectric to paraelectric phase transition behaviors.  On the other hand, irradiation leads to a reduction in the polar domain size, attributing to lower a critical size into a few nanometers with threshold of instability of the macroscopic ferroelectric state and transforming in structures of the crystalline regions in the copolymer from a polar all trans ferroelectric into a nonpolar state trans-gauche conformation.  This result brought the way to approach how thin of layer should be in works of Zhang, Q. M. and et al., 2001 [23] and Urayama, Kenji and et al., 2000 [20].  Caused by kinetics of crystalline process, the decrease of dielectric constant in thin films of P(VDF/TrFE) copolymer reduces the thickness of the films depending on crystal orientation [23].  Therefore a change in the average crystal orientation in copolymer films at thickness near 100 nm may also be an original for dropping of the dielectric constant along that thickness as shown in Figure 2-2.  In a work of Urayama et al. [20] the dielectric and ferroelectric properties of copolymer remarkably depend on layer thickness, especially in case of less than a few hundred nanometers thick.  Thus meaningful conclusion of thinning of layers affect on changes in morphology, crystallinity and chain orientation in spin-coated layers but the layer thinning is not consequently reducing its dimensionality [20, 23].  Furthermore, the orientation of crystallites is preferable to be aligned parallel to film surface and such limited pattern of thin layer might also alter the dielectric constant of crystalline phase by decreasing thickness [20].

Figure 2-2 : Thickness relates to Dielectric constant in work of Zhang et al., 2001 [23].

2.3 Annealing Effects on Crystalline Structures Induced-Switching Properties

Relationship of annealing on structures of copolymers, crystalline and thickness studied by Kadama et al., 1997 [13] was shown that annealing at broadly distribution range of Curie point around 120-130 °C resulted in increasing of crystallinity from 50%-80%, whereas annealing at 130-145 °C caused remarkably growing in crystalline lamellae, regularly aligning parallel to film surface, and then yielding larger thickness from 20 nm to 70 nm.  With the large nucleation growth process, observed transient switching properties were consistent occurring along the time [13].

3 Electromechanical Properties of Electrostrictive Polymers

The attempts to improve the electromechanical properties of P(VDF/TrFE) copolymers in works of Cheng et al., 2001 [5] are particularly obtaining obvious results such as in electrostrictive strain, polarization hysteresis, huge anisotropic, longitudinal and transverse strain responses, high elastic energy density including modulus, and mechanical load capacity under high energy electron irradiation treatment.  By using electromechanical coupling factors, characterizations of frequencies required to maintain high strain response was quantitative near 100 kHz [5, 24].  The reasons, supporting the excellent behaviors of P(VDF/TrFE) in manners of  exceptionally high electrostrictive responding under electron irradiation, suggested by Zhang et al., 1993 [24] that irradiation breaks up the coherent polarization domains of all-trans chains in normal ferroelectric properties into nanopolar regions in nanometer size levels, and then transforms these all-trans chains into trans- and gauche- bonding, as being relaxor ferroelectric materials.  Therefore, these transformation brings the expanding and contracting of the polar-regions under external electron fields.  The effects of electron fields, coupling with the large difference in the lattice strain between these polar and nonpolar phases, generate the ultrahigh strain [24, 23].

Casalini, R. and Roland C. M., 2001 [3] improve the electromechaical performance of P(VDF/TrFE) copolymers by using chemical crosslinking.  By means of curing copolymers with an organic peroxide within combination of a free-radical trap, followed by crystallization, the ferroelectric networks exhibit a high electrostrictive response.  At low frequency of electric field, significantly high longitudinal strain was obtained at 12%, which its magnitude was larger than the best results of previous reporting more than twice.

Furthermore, studies ferroelectric and electromechanical properties of terpolymers by Xu, Haisheng et al., 2001 [21] exhibited little of polarized hysteresis loops and high electrostrictive strain at room temperature.  Behaviors of dielectric and polarization of terpolymers are ferroelectric relaxor.  Revealed by x-ray and Fourier transform infrared, the random incorporation of bulky chlorotrifluoroethylene (CTFE) termonomers within polymer chains causes disordering of the ferroelectric phases.  The CTFE acts as random defect fields, which randomize the inner- and intra- chain polar coupling, therefore resulting in the observed ferroelectric relaxor behaviors.

3.1 Ferroelectric-Paraelectric Phase Transformation

Transforming ferroelectric phase into paraelectric phase was associated with very large lattice strain, proposed by Cheng et al., 2001 [5].  From low temperature ferroelectric phase to high temperature paraelectric phase, lattice strain of highly aligned copolymers with higher crystallinity can be translated into very large macroscopic strain as a thermal strain when going through phase transition as shown n Figure 3-1.  The expected high field induced lattice strain at phase transformation can be controlled by external field of both electric and mechanical fields [5].

Figure 3-1 : Lattice strains were related to temperatures [5].

3.2 Electromechanical Properties

                By using high energy electron irradiation, the ferroelectric phase at room temperature enable to be converted into a macroscopically paraelectric like phase as reference [5].  Furthermore, very sharp dielectric constant peak from the phase transforming found in previous works can be remarkably broadened and then moved into near room temperature.  Additionally, polarization hysteresis can be eliminated by means of high energy electron irradiation to gain very high electrostrictive responses [5].

Figure 3-2 : Polarization hysteresis eleiminated by irradiation with high electron field [5].

3.2.1 Elecrtostrictive Strian and Electromechanical Coupling Factors at Low frequency

Longitudinal strain with thickness changes of films, induced by applied electric fields, exhibited little polarization in Figure 3-3 (a) because of the electrostrictive natures of the strain response as confirming in Figure 3-4 [5].

Figure 3-3 : Longitudinal strain related to polarization and temperature [5].

Furthermore, there is no significant difference [5] between strain of stretched and unstretched films under high field as shown in Figure 3-3 (b).  Temperature dependence of field induced strain in Figure 3-3 (c) showed remaining nearly particularly constant [5].  These evidence can help to optimize reducing polarization to obtain high electrostrictive strain [5].

Figure 3-4 : Field induced strain plotted versus the square of field induced polarization [5].

            There exists large anisotropic strain in P(VDF/TrFE) copolymers both along and perpendicular to chain direction [5].  Thus transverse strain, associated with changing of length of film under electric field, of irradiated copolymers can be controlled over large range by varying film processing [5].  Transverse strain of unstretched films is relatively small with amplitude of ratio between transverse and longitudinal strain at less than 0.33 [5].  With such feature, there remain attractions to utilizing in some devices such as thickness mode of ultrasonic transducers [5], electroimechanical actuators and sensors [8].  Since very weak transverse electromechanical response with respect to longitudinal one significantly affects on reduction of lateral influence of thickness resonance, which improve thickness transducer performance [5, 8], then this feature results in improving of thickness strain response.  On the contrary, for stretched films, a transverse strain (S₁) along the stretching direction was very large, whereas the transverse strain perpendicular to oriented direction was much smaller than longitudinal strain as following Figure 3-5 [5].     

Figure 3-5 : Amplitude of transverse strain in comparison between of along and perpendicular to stretching direction vs. longitudinal strain [5].

Relationship between polarization and electromechanical responses was considered as a coupling factor (k₃₃) for unstretched and stretched films in Figure 3-6.  The results showed evidence of single crystal of copolymers and very high transverse coupling factor of irradiated film much more than unirradiated one [5] as in Figure 3-6.

Figure 3-6 : Electromechanical coupling factors of irradiated stretched and unstretchd films.

3.2.2 High Frequency Strain Response and Electromechanical Resonance Behaviors

Irradiated copolymer exhibits behaviors of ferroelectric relaxor, having strong dielectric dispersion at near room temperature [5].  Electrostrictive strain, closely related to polarization responses, is induced by high frequency field higher than strain is generated by low frequency [5].  Longitudinal strain of unstrethed films depends on frequency of filed according to Figure 3-7 [5] even though strain level remains nearly constant at around room temperature [5].

Figure 3-7 : Frequency dependent longitudinal strain for unstretchedly irradiated films [5]

Additionally, Yong’s modulus, elastic compliance (s₁₁₊), and electromechanic resonance, along stretched direction, are increased with higher frequency of the field as Figure 3-8 [5].

Figure 3-8 : Mechanical resonance response along stretching direction with higher frequency field [5].

3.3 Mechanical Load Effect on Electrostrictive Strain

Under constant electric field, transverse strain increases with initial load and then reaches the maximum at particular tensile stress at around 20 MPa [5].  The further increase of the load reduces filed induced strain, but however, the strain generated by field is still be the same as without load as Figure 3-9.  These evidences indicate the high load capacity of materials.

Figure 3-9 : The transverse strain at different tensile stress along drawing direction [5].

3.3.1 High Electrostrictive Stain under High Mechanical Stress

The electric field induced stain in the electron irradiated P(VDF/TrFE) copolymers generates the high electrostrictive strain even under high mechanical stress [1] because electrostrictive coupling of local polarization was changed with stress.  Transverse strain at different tensile stress under a constant electric field initially increases with the load and reaches into maximum at about 20 MPa of tensile stress.  The one of important results is generated strain under high tensile stress of 45 MPa nearly the same as that without load according to Figure 3-10 [1].

Figure 3-10 : Effect of tensile stress on electric field induced transverse strain (S₁) [1].

Even though longitudinal strain as a function of hydrostatic pressure [1] was not changed much with pressure at low frequency, however, it was dramatically increased with the pressure at high field as following Figure 3-11 [1].  By considering the electrostrictive coupling of local polarization with stress in ferroelectric structures [1], these experiments clearly demonstrated that the elctrostrictive copolymers have a high load capacity and this maintains their strain level even under very high electromechanical load.

Figure 3-11 : Effect of hydrostatic pressure on electric field induced longitudinal strain [1].

Since relaxor ferroelectric characteristics, using by simple Smolensky model, can be regarded as consisting of local polar-regions [1] with different Curie points over broad temperature ranges, the transverse and longitudinal strains under stress at field range from low to high are temperature dependent as shown in Figure 3-12 and 3-13 [1].

Figure 3-12 : Temperature dependence transverse strain [1]

Figure 3-13 : Temperature dependence longitudinal strain [1]

The results obtained from Bharti et al., 1999 [1] clearly indicated that electric field induced strain was came from its local polarization itself.  Variations of field induced strain with stress were indeed related to natures of electrostrictive properties and temperature along with the following equation:

                                             (3-1)

4 Electrostriction Measurements

4.1 Quantity and Prediction of Electrostrictive Properties

The evaluation of electrostrictive properties in term of mathematical models is presented in Eury, Sylvie and et al., 1999 [10].  Furthermore determining the quantity of the properties of low permittivity dielectric requires extremely sensitive instrumentation.  Then modification the instrument and some equations can approach the measurement of this properties [10].  By means of changing in capacitance of order of 10^-6 and coupling two lock-in amplifiers to detect in-phase cyclic uniaxial stress on materials, extensive electrostriction data along with ferroelectric soft copolymer composites are verified linear relationship between electrostriction coefficient (Q) and the ratio of elastic compliance to dielectric permittivity [10].  These methods lead to an effective way to predict the electrostrictive properties of materials.

The proposed equations of electrocstricton effects were derived and expressed following;

                                                           (4-1) [10]

                      (4-2) [10]

            The prediction of electrostrictive coefficients under electric field, in which cations and anions of crystal structure were displaced in opposite directions by an amount of Dr, may express as the following equations [10].  Such displacement is responsible for electric polarization, dielectric permittivity and electrostrictive strain.  Additionally, large strain compliance in solid state introduces large changes in dielectric stiffness and anhormonic potentials.  For obtaining better expression, the relationships, correlated between electrostrictive properties and dielectric stiffness, h, were related to stress, X in equation (4-3) [10].

                                                      (4-3) [10]

4.2 Measurement of Electrostrictive Properties

By using modified single beam interferometer, Yimnirun, Rattikorn and et al., 1999 [22] are capable of measurement in level of sub-angstrom resolution in displacement.  Furthermore, modified Morley’s type instrument was used to determine very small change in path length of interference fringe intensity of electrostriction coefficient of low permittivity [22].  

Two approached techniques, using for determining electrostriction coefficients, of modified Michelson-Morley interferometer, in Figure 4-1, and dynamic compressometer, in Figure 4-2, are able to effectively measure strain induced in applied field or polarization by direct effect for prior method and gain change in permittivty under stress by converse effect for later method [22].

Figure 4-1 : Modified interferometer [22]

Figure 4-2 : Compressometer [22]

5 Design and Performance of Elecrostrictive Polymers

6 Applications and Trends of Electrostrictive Polymers

7 Conclusion and Discussion

Reference:

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