Studies on the nonlinear piezoelectric response of polyvinylidene fluorideBernd R. Hahn Citation: Journal of Applied Physics 57, 1294 (1985); doi: 10.1063/1.334528 View online: http://dx.doi.org/10.1063/1.334528 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/57/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Piezoelectric responses in poly(vinylidene fluoride/hexafluoropropylene) copolymers Appl. Phys. Lett. 90, 242917 (2007); 10.1063/1.2748076 Nonlinear piezoelectricity in poly(vinylidene fluoride) J. Appl. Phys. 63, 1701 (1988); 10.1063/1.339905 Nonlinear dynamic response of piezoelectric polyvinylidene fluoride J. Appl. Phys. 51, 1860 (1980); 10.1063/1.327761 Piezoelectric relaxation in polyvinylidene fluoride J. Appl. Phys. 50, 3615 (1979); 10.1063/1.326310 Piezoelectricity and pyroelectricity in polyvinylidene fluoride J. Appl. Phys. 49, 4490 (1978); 10.1063/1.325454

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Studies on the nonnnear piezoe~ectric response of po~yvinyndene f~uoride Bernd R. Hahna)

Deutsches KunststojJ-Institut. Schlossgartenstr. 6 R. D-6100 Darmstadt. West Germany

(Received 15 August 1983; accepted for pUblication 31 July 1984)

Simple mechanical models can be useful in investigating the structural dependence of the piezoelectric activity of uniaxially oriented polyvinylidene fluoride. An experimentally observed. strong nonlinear relationship between the mechanical load and the transverse piezoelectric coefficient d32 is presented. This new behavior is discussed on the basis of a parallel arrangement of crystalline and amorphous regions perpendicular to the orientation axis. The coefficient d32

changes its sign also, the deformation being less than 3% in all cases. A mechanical series model is applied for the coefficient d31 whose behavior is very linear with the applied mechanical load. Furthermore, d32 shows a significant time dependence after a change in the mechanical load applied. These nonlinear effects depend upon structural features such as crystal perfection and were attributed. to processes occurring in the crystalline regions and in their interfaces with the amorphous surrounding, respectively. Also, the technical importance of these effects is obvious.

INTRODUCTION

Polyvinylidene fluoride (PVDF) is known for its piezo­and pyroelectric properties offering a wide variety oftechni­cal and scientific applications. 1.2 The piezo- and pyroelectric constants exceed the corresponding values of other known polymers by several orders of magnitude. It has been recog­nized that the mechanism responsible for these properties of polyvinylidene fluoride differs from the well-known mecha­nism of anorganic ferroelectrica. Over the last few years, a number of theoretical models have been proposed for the origin of the pyro- and piezoelectric properties ofpolyvinyli­dene fluoride. They seem to be successful at least on a semi­quantitative basis.3

-5

One crucial problem is the dependence of these particu­lar electrical properties on the structure of PVDF, whereas some structural features are unknown so far. This depen­dence is demonstrated by the dependence of the total polar­ization, which may be achieved during the poling procedure, on the structure, and by the absolute magnitude of the piezo­and pyroelectrical constants at constant polarization, which also depends on the structure.6 One can assume that the dis­tribution of the lamellae thickness,7 the degree of perfection of the two-phase structure,8 and the orientation of the chain elements in the amorphous regions9 ofPVDF are structural parameters, which also influence the electrical response and its temperature dependence. The largest values of the piezo­and pyroelectric coefficients are obtained for oriented. mate­rials (Fig. 1). Anisotropic structures necessarily result in an­isotropic mechanical properties, due to the specific arrange­ment of amorphous and crystalline regions within the material, relative to the direction in which the mechanical force acts. To a first approximation, highly oriented PVDF can be represented by a parallel arrangement of crystalline and amorphous regions in the direction perpendicular to the orientation axis and by a series model along the direction of the orientation. We thus expect the series model to hold for the piezoelectric coefficient d31 and the parallel model for

alPresent address: IBM world trade fellow. IBM. San Jose. California 95193.

the coefficient d32 (in a very simplified view). This paper is concerned with the temperature depen­

dence of d31 and d32, which is a direct consequence of the structural features discussed above. Above all, nonlinear properties will be discussed, which are displayed as the me­chanical offset stress increases. They are also related to the particular structure ofPVDF.

EXPERIMENT

The material used throughout our studies was PVDF X8N of Solvay (M" = 38 (00). Thin films, having a thick­ness of 50 pm, were obtained by extrusion. They were drawn at a temperature of 85 ·C up to a draw ratio A of 4 having a final thickness of 20 pm. Part of the drawn films were an­nealed with fixed ends at 120 and at 135·C for annealing times of 1 and 24 h, respectively. Aluminum electrodes were evaporated onto the films. The films were charged by corona poling, using an electrical field of 1.5 MV / cm. After the corona charging, the films were short circuited for 48 h in order to neutralize the surface charges. The size of the speci­men studied in piezoelectric measurements was usually 3X30mm.

3

! 1

P (draw axis)

/

2~m~ __________ -J

FIG. 1. Uniaxially oriented PVDF after poling. having a permanent dipole orientation inside the crystals along the 3 axis and a random dipole orienta­tion within the amorphous phase (schemel.

1294 J. Appl. Phys. 57 (4).15 February 1985 0021-8979/85/041294-05$02.40 © 1985 American Institute of Physics 1294 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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The piezoelectric constants were determined by means of a dynamic mechanical analyzer. The samples were sub­jected to a sinusoidal stress (15 Hz, 0.15 N). The charge re­sulting from the mechanical loading was measured in a short circuited arrangement. The static loading was varied at con­stant dynamic loading and at constant frequency. Thus the dependence of the piezoelectric coefficient on the static load­ing could be measured.

RESULTS AND DISCUSSION

Morphology

In order to understand the electrical properties, dis­cussed in the following, in detail, it is necessary to account for the structure of oriented polyvinylidene fluoride. It is known that the orientation of partially crystalline polymers results in the formation of a fibrillar structure lO as shown schematically in Fig. 2. To a first approximation, this struc­ture can be represented in terms of a series model of crystal­line and amorphous regions along the draw direction (1 axis).

Structural investigations employing small angle x-ray techniques have revealed that the structure along the draw direction consists of a periodic arrangement of amorphous and crystalline regions. Due to the differences in the electron density between the two phases, a discontinuous small angle scattering is observed (Fig. 3, curve A). No such discontin­uous scattering is observed in the direction perpendicular to the draw direction (Fig. 3, curve B). The particular structure, which is obtained for PVDF, depends strongly on the crystallization and annealing conditions as well as on the drawing conditions. lo These parameters influence, for in­stance, the long period L. A long period of about 100 A was obtained for the conditions mentioned above. The periodic arrangement of amorphous and crystalline regions (each having a thickness of about 50 A) will, of course, govern the mechanical and the electrical properties of the films in the draw direction, as wen as in the direction perpendicular to it.

The crystalline regions are characterized by a large elas­tic modulus in the draw direction since they contain fully extended chains in the f3 crystals in contrast to the amor­phous regions, which are characterized by coiled chain ele-

model: f d31 / amorphous phase)

r--~'---'

FIG. 2. Fibrillar structure of uniaxially -oriented PVDF and its representa­tion by a simple mechanical model.

1295 J. Appl. PhyS., Vol. 57. No.4. 15 February 1985

1000

\ \ \ \

PVDF

A{JJ) \ 8(1) \

\ ,

o , 8 U ffi ~

scattering angle ~ ,ea 1m radJ

FIG. 3. Angular dependence of the scattered intensity obtained by small­angle x-ray scattering (SAXS) for a uniaxially oriented PVDF sample paral­lel (curve A) and perpendicular (curve B) to the draw (1 axis).

ments and by a low extensional modulus (Y~ ::::: 200 GPa, Yf ;::: 1 GPa).4 Thus we expect that a deformation along the draw direction results predominantly in an extension of the amorphous regions. If, however, a stress is applied perpen­dicular to the draw direction, we expect that both the crys­talline regions and the amorphous regions are deformed in a similar way for geometric reasons. In addition, we know that the elastic moduli of the amorphous phase and the crystal­line phase perpendicular to the chain direction are of the same order of magnitude (Y~ ;::: 10 GPa, y~;::: 1 GPa).4

Temperature dependence of d31 and d32

The piezoelectric response is governed by the mechani­cally induced changes of the distribution of the mechanical and electrical fie1ds within the amorphous and crystalline regions. The change of the distribution win be a function of the direction of the external mechanical loading relative to the draw direction. In addition, we expect that the change of the distribution depends strongly on the temperature. The transition from the glassy state to the equilibrium fluid state results in strong variations of the mechanical properties of the amorphous regions and thus in strong variations of the total mechanical properties of the films predominantly along the draw direction. This point of view is in agreement with the experimental results as can be seen in Fig. 4. d32 does not depend on the temperature as strongly as the coefficient d31

does. I I It is obvious that the strong increase of d31 with increas­

ing temperature, particularly in the temperature range above - 40 ·C , is directly related to the occurrence of the glass transition around - 40 DC. No influence of the glass transition on the transverse coefficient d32 is observed. This coefficient is strongly determined by the mechanical proper­ties of the crystalline regions in the direction perpendicular to the chain direction (e direction) due to the particular mor­phology of the films.

The influence of the amorphous phase on the absolute value of the piezoelectric coefficients is demonstrated by the much 1arger absolute value of the piezoelectric coefficient d31 as compared to d32. Conclusively, the interaction and contribution of different structural elements to the piezoe-

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5

PVDF strptched ()..::4)

. . . . ~ ..•

............

.A7 ..... . . . . . . . .

v= 75Hz

t=Q75N

......... -.-..~ ~2~0~~--~80~~---4~0~~--~0--~--4~0~~~80

Temperature [oG;

FIG. 4. Temperature dependence of the piezoelectric coefficients d31 and d32 for uniaxially oriented PVDF.

lectric response seems to be separated very wen in different directions of molecular orientation as far as highly oriented PVDF is concerned.

Linearity of d31

The systematic deviations observed for the temperature dependence of the coefficients d31 and d32 due to anisotropy of the structure of PVDF suggest looking for other struc­ture-dependent properties of the piezoelectric response. We were interested, in particular, in the linearity of the piezoe­lectric response, that is, in the dependence of the piezoelec­tric coefficients d31 and d32 on the external average mechani­cal. stress-the offset stress 0"0'

In order to study this property, we applied a total stress 0", consisting of a large constant stress 0"0 and a small sinu­soidal stress 0" _ either along direction one or two of the film. We measured the piezoelectric coefficient d31 and d32 in the same way as described above.

Anorganic piezoelectric materials are usually charac­terized by a linear electrical response, even if the mechanical loading is varied over several orders of magnitude. This is a requirement necessary for the application of these materials

~ ~~30r-~--~~--~~~~--~~--~~

...... c: 25 PVDF stretched 12111m), annealed (7h,720 ·C)

,~ ~I-.-.-.-.-·-··--=---!~--! .g20

~ 75 .~ ~ 70 u 9(}/70 stretched

F.. ::o.15N

v::75Hz WIdth: 5mm

..!;!! Q) S[:--·-·-·-·-·-_·-·_-~ .S! 0::

80/20 stretched Ol--"--·~-·--·--·-o 7 2 3 4 5

Static Load [N}

FIG. 5. Linearity of the piezoelectric coefficient d31 in dependence of the static load applied (I N corresponds to a static stress of9.5 X I(t N/m2) for PVDF and PVDF IPMMA blends containing 10 and 20 wt. % PMMA (all samples have been drawn to a dmw ratio of 4).

1296 J. Appl. Phys., Vol. 57, No.4, 15 February 1985

~ ~~Q751----~----~--~----~--~----~--~

1:: .9:! .U

PVDF IsotropIc (47I1m)

~ ~ Ql0 __ -e_-._e-___ - _______ --_·

G

~ u 0.05

~ ~

F..=0.7SN v = 15Hz

width:5mm

.Q) ~ ~~--~----~2----~3----~4----~5----~6-----7

Static Load [N]

FIG. 6. Linearity of the piezoelectric coefficient d31 in dependence of the static load applied for isotropic PVDF. The I axis corresponds to the direc­tion of film extrusion [I N ~4.3 X 106 (N/m2~J.

in technical parts such as force transducers. We expect PVDF to behave linearly, if the deformation due to the ap­plied stress is well within the range of the elastic mechanical response, that is, for deformations not exceeding 3% for short loading times. Above this value, structural changes can be expected to happen.

It is, therefore, not surprising that for small deforma­tions along the draw direction a linear piezoel.ectric response is displayed. The coefficient d31 is thus independent of the mechanical stress, as can be seen in Fig. 5. A similar result was obtained for uniaxially stretched blends of PVDF and PMMA containing 10 and 20 wt. % PMMA. The drawn films of these blends are known to display structures which are similar to these of pure PVDF.6

•12 We can thus conclude

that a deformation of the amorphous phase in oriented par­tially crystalline PVDF and blends of PVDF with PMMA win result in a linear response of the material, provided that the total deformation is small.

Studies on isotropic PVDF films revealed that these films are also characterized by a linear piezoelectric response (Fig.6).

Nonlinearity of dn

A rather surprising behavior is displayed by the piezoe­lectric coefficient d32 (Fig. 7) as a function of the total applied stress. This coefficient is strongly nonlinear. It even changes the sign with increasing stress. This behavior turned out to be reversible. In order to study the reversibility, tbe same basic sample was stretched to break several times. In each case, the remaining part of the sample was used for the subse­quent deformation cycle. The final. sample obtained in this way showed the same nonlinear response as the original sam­ple. The only difference was that the absolute value of the piezoelectric coefficient decreased slightly with increasing number of deformation cycles.

The total deformation was kept below 3% in all cases. The nonlinearity of the electrical response is not caused by a nonlinearity of the macroscopic Young modulus, since we observed that the Young modulus Yz is not changed signifi­cantly if the sample is subjected to the same conditions as given above for the determination of the nonlinearity of the

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PVOF

" sfN!fched f22/J.m) 1.5 0,\

~'.0 ."." \\ "OPl ",,0\ F.. =o.15N

II = 15Hz

~ 0.5 • \ .S!! \ \

widfh6mm

. It! \ :t:: 0 r-----'--~~\ 4-'---'---1

~ \ \ \ \

1;-0.5 \\

~ -1.0 • 1"run \.~ o ·;rdrun ~ . l-~ \

-2.00 2 3 I. 5 6

Static Load IN]

FIG. 7. Nonlinearity of the transverse piezoelectric response (dd for an uniaxially oriented PVDF sample in dependence ofthe static load applied in a first and in a second run [1 N~9.l X 10<1 (N/m')].

electrical response (Fig. 8). We also investigated the nonlin­ear behavior as a function of the structure of the films. For this purpose, the perfection of the crystalline regions was varied by changing the thermal treatment of the material (Figs. 9 and 10). The only influence observed was that the differences in the electrical response between different defor­mation cycles were diminished as the quality of the crystal­line regions increased, whereas the nonlinearity was only slightly reduced.

The difference in the electric response observed for the directions 1 and 2 of the films has to originate from the parti­cular structure of these films. We know that d31 is mainly determined by a deformation of the amorphous regions, whereas d32 depends also on the deformation of the crystal­line regions perpendicular to the c-direction. In this case, the deformation in the crystals may be large, due to the small extensional moduli of the crystals in the a and b direction.4

0/---0 -----.--. ___ D___ __.

• 1M run

·rrUl'l

~.--Q-- -........----. a~_a

F..=0,15N II = 15Hz

..,Kith 5.7mm

2 3 I, 5 IS Static Load IN)

FIG. 8. Young's modulus Y2 of uniaxially oriented PVDF (poled) in depen­dence of the static load applied [1 N corresponds to a static stress of]07 (N/ m 2

)].

1297 J. Appl. Phys., Vol. 57, No.4, 15 February 1985

1.5

\{§1.o.

~ ~ 0.5

~ ~ a

It! -0.5 ~ u

.!!! a ~ -1.

.~ ct: -1.5

PVDF

stretched.ofll"l«Jled f1h, 120"C). 23jlm

• ,s'run a~run

F.. =0.15N v = 15Hz

width.' 6mm

..... ~ .... :+, ...• ~\

"~"'. \\

(''I-.. froctu,.~:

-2.0 o.L---'"--2-'--~3~--'"I,--5'--~6---'7

Static Load IN)

FIG. 9. Nonlinearity of dJ2 for uniaxially oriented PVDF which has been annealed with fixed ends (1 h, 120 'C) before poling. The load dependence is shown for different TUns using the remaining rest after fracture.

I t is therefore reasonable to attribute the nonlinearity of the piezoelectrical response to the properties of the crystal­line regions and to interface effects, respectiVely.

Films having a small biaxial component

For comparison, it is tempting to study a uniaxially ori­ented PVDF which contains a small biaxial component. Such a small biaxial component can be induced, for instance, by stretching a polymer film uniaxially on a roller machine, because lateral shrinkage is partly inhibited during the stretching procedure.

The Kureha KF Piezo Film is supposed to have such a small biaxial component, at least for stiffness reasons. There­fore, the differences in the structural features along the 1 direction as compared to the 2 direction are not as significant as in a purely uniaxially-oriented film lik.e they have been shown in Figs. 1-10.

FIG. 10. Nonlinearity of d32 for uniaxially oriented PVDF having a higher degree of crystal perfection than the samples shown in Figs. 7 and 9. Sample has been annealed (24 h, 135 'C) with fixed ends before poling.

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Kureha Piezo Film 30/Jm

I • 8 B • .. . . o •

o • . • • I , , I

F.. = Ol5N II = 15Hz

width' 56mm length : 35 mm

I :i ..!l..aD D a aDD a a-.

FIG. 11. Nonlinearity of d)2 for a uniaxially oriented PVDF film having a small biaxial component (Kureha Piezo Film, 30pm), [1 N~5.95 X 10" (NI m2)J.

We observed that the piezoelectric coefficients of the Kureha films are less nonlinear as compared to the case of the uniaxially drawn films described above. Figure 11 repre­sents the experimental results. A nonlinear behavior is still displayed. It is observed, however, that a constant coefficient is obtained, as the stress surpasses a limited range of stresses. In addition, no change of sign takes place. Furthermore, it is obvious that the differences in the electrical response ob­served for different cycl:es of mechanical loading are small.

Time dependence of d32

The nonlinear behavior of the coefficient d32 of the uniaxially drawn films depend on the time, as becomes ob­vious from the results shown in Fig. 12. Figure 12 displays the coefficient d32 of the Kureha Piezo Film as a function of the time, following a stepwise increase of the mechanical load of 10 N. We used a constant dynamic load with an amplitude of 0.15 N. The coefficient decays from 4.05 (pCI N) to 1.6 (pC/N) immediately after the load step is applied. At constant stress it increases again as a function of the time. n displays a value of about 3.2 after 16 h. If the constant stress of 10 N is removed at this particular time, we observe nearly the same value for d32 as before the stepwise increase of the stress. This indicates that under these circumstances, reversible as well as irreversible processes occur in the material governing the piezoelectrical properties. The irre­versible flow of the material at constant stress is too small in order to account for the time dependence of the electrical response.

In a very simple view, the observation that d32 is stress dependent and becomes negative when a certain stress level is exceeded can be interpreted as mainly reversible depolar­ization which is mechanically induced. A negative value for d32 win be obtained as soon as overall polarization (about 4.3 /lCI cm2

) is starting to become reduced when the mechanical stress continues to increase. There are basically two different mechanisms which may account for the phenomena de­scribed above:

(1) overall sample size effect due to changes in mechani­cal properties like in poisson ratios effecting the dipole den-

1296 J. Appl. Phys., Vol. 57. No.4. 15 February 1965

'@3.4

~ . _ 30

.~

.g 26 .... . (IJ

8 .~ 2. ~

Kureho Piezo Film 3OJJf'(t

tir:I •

...

........ .. ./ .... F_= 015N

v :15Hz width: 5.6mm

length : 34.5mm

"1 __ I.B ;efore testing d32(05NJ = 4.05 ":

:. offer testing d32105NJ = 3.70 ~ I~L-________ ~ ________ ~ ________ ~~ ____ --J

01 1.0 10 100 1000 Time/min]

FIG. 12. Time dependence of d)2 after a load step of 10 N in the static load applied and the values of d)2 determined before and after testing (Kureha Piezo Film) [1 N ~ 5.95 X 10" (N/m2)].

sity, and/or (2) intrinsic effect related to changes in dipole orienta­

tion. We tend to favor the second mechanism since measure­

ments using different frequencies for testing those nonlinear effects clearly show relaxationlike behavior giving relaxa­tion times and energies similar to those expected for single extended chains rotating in the PVDF crysta1.6 A mechani­cal stress perpendicular to the chain axis therefore might change the angular orientation distribution of the chain stems carrying the dipole moments, accounting for the changes in polarization mentioned above. If this holds true, one would have a new very sensitive tool to study chain rota­tion in polymers like PVDF experimentally. Studies are cur­rently under way in order to elucidate the phenomena pre­sented above in further detail.

ACKNOWLEDGMENTS

The author gratefully acknowledges the help of Dr. J. H. Wendorff during preparation of the manuscript and ex­perimental help by R. Gerhard-Multhaupt during the poling experiments.

I A. I. Lovinger, in Developments in Crystalline Polymers 1, edited by D. C. Bassett (Applied Science, London, 1982).

2G. M. Sessler, J. Acoust. Soc. Am. 70, 1596 (1981). 3M. G. Broadhurst, G. T. Davis, J. E. McKinney, and R. D. Collins, J. Appl. Phys. 49, 4992 (1978).

4K. Tashiro, M. Kobayashi, H. Tadokoro, and E. Fukada, Macromole­cules 13, 691/1980).

'Yo Wada and R. Hayakawa, Ferroelectrics 32, 115 (1981). 6B. R. Hailn, thesis, Technical University of Darmstadt, West Gennany, May 1983.

7J. M. Schultz, J. S. Lin. R. W. Hendricks, R. R. Lagasse, and R. G. Kepler, J. AppJ. Phys. 51, 5508 (1980).

8K, Nakagawa and Y. Ishida, J. Poiym. Sci. Polym. Phys. Ed. 11, 1503 (1973).

·S. Tasaka and S. Miyata, Ferroelectrics 32, 17 (1981). lOA. Peterlin, in Structure and Properties of Oriented Polymers, edited by I.

M. Ward (Applied Science, London, 1975). IIp. T. A. Klaase and J. van Turnhout, in Proceedings of the Third Interna­

tioMI Conference on Dielectric Materials, Measurements, and Applica­tions, lEE Conf. Pub\.171 (lEE, Birmingham, England, 1979), pp. 411-414.

126. R. Hahn and J. H. Wendorft'(unpublished).

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