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Investigation and modeling of various influencing factors on the dielectric breakdown strength of silicone elastomers
Materials Science & Engineering B 243 (2019) 65–70
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Materials Science & Engineering B journal homepage: www.elsevier.com/locate/mseb
Investigation and modeling of various influencing factors on the dielectric breakdown strength of silicone elastomers
T
⁎
Andreas Ziegmanna, , Claus Bernera, Dirk W. Schuberta,b a b
Institute of Polymer Materials, University Erlangen-Nürnberg, Martensstraße 7, 91058 Erlangen, Germany Keylab Advanced Fiber Technologies, Bavarian Polymer Institute, Dr.-Mack-Straße 77, 90762 Fürth, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Dielectric breakdown strength Silicone elastomer Barium titanate Electroactive polymer Dielectric elastomer
Dielectric elastomers are utilized as soft electroactive polymers for actuators, sensors or generator applications to transduce mechanical to electrical energy and vice versa. They are characterized by the ability to change shape while an electrical field is applied. Indeed, this effect is most significant for electrical fields near the electrical breakdown strength, therefore it is a limiting factor for application. This work investigates different factors influencing the dielectric breakdown strength of soft silicone elastomers such as the sample thickness, the force and the radius of the upper electrode, the filling degree and the size of air voids. It can be shown that the main influence is the compression of the sample, thus a novel master curve can be created and fitted by a semi empirical model function. Therefore a comparison of all different experimental set-ups is possible.
1. Introduction Electroactive polymers (EAP) can convert electrical to mechanical energy and vice versa, therefore they are a promising material class for application as artificial muscles. An important subgroup of EAPs are dielectric elastomer actuators (DEA) which have the advantage of low viscoelastic losses, high actuation strains and good actuation pressures [1]. One main drawback of DEAs is that high actuation strains are only achieved at very high voltages [2]. However, the voltage is limited by the dielectric breakdown strength (DBS) of the material and thus, the applied electric field has to be lower than the DBS. Furthermore, the DBS is an important material parameter e.g. for the applicability of lithium ion batteries [3]. Furthermore, from literature is known that the DBS is highly dependent on boundary conditions during measurement. The different influencing factors can be divided into two groups: intrinsic and extrinsic factors. Intrinsic factors are for example the thickness [4–7], the stiffness [6,8] and the degree of filling [9]. Defects in the dielectric, e. g. air voids in silicone elastomers, are another important intrinsic factor, as they often cause a breakdown. Other parameters like the electrodes [6], humidity [10], temperature [11], pre-stretch [6,12,5] and the force of the upper electrode [7] are extrinsic influences. However systematic studies do not yet exist. Most of these factors are discussed in the literature (see references above), sometimes even several factors [7]. But the authors conclude
⁎
that it is important to mention the experimental parameters in order to ensure comparability with other publications. In this work, different influencing factors such as the sample thickness, the size of air voids, the force and the radius of the upper electrode and the filling degree are evaluated and prioritized with respect to their significance. Finally a model is proposed to describe the DBS in dependence of the most relevant parameter, the compression of the sample, regardless of the boundary conditions. Furthermore, in order to reveal the influence of air voids on the DBS, we produced deliberately different sized air voids in the silicone elastomer and measured the corresponding DBS. 2. Materials The silicone elastomer used, ELASTOSIL P 7670, is industrially available from Wacker Chemie AG. It consists of polydimethylsiloxane (PDMS) and a two component system (A + B) with a mixing ratio of 1:1. The platinum catalyst leads to the addition curing of the room temperature vulcanizate. The material is filled with approximately 7.8 vol% silica [13] which yields a Shore A hardness of 7. Barium titanate with a particle size of < 3 μm was bought from Sigma-Aldrich. Laser diffraction revealed a particle size d90 of 3.12 ± 0.04 μm. We showed previously that the particle size in the silicone elastomer depends on the filling degree [13]. For the production of the samples components A and B were weighed in a ratio of 1:1 and mixed in a speedmixer DAC 150 SP from
Corresponding author. E-mail addresses: [email protected] (A. Ziegmann), [email protected] (D.W. Schubert).
https://doi.org/10.1016/j.mseb.2019.03.014 Received 17 April 2018; Received in revised form 11 January 2019; Accepted 21 March 2019 0921-5107/ © 2019 Elsevier B.V. All rights reserved.
Materials Science & Engineering B 243 (2019) 65–70
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Fig. 2. DBS E0 in dependence of the thickness d for a constant force F = 2 N and an electrode radius r = 15 mm. The power law fit is marked red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. Sketch of the experimental set-up.
Hauschild Engineering for 1 min at 1000 rpm. Afterwards the material was poured into a mould which was then evacuated in a desiccator. Samples with deliberate air voids were not evacuated. In order to decrease the vulcanization time the mould was placed in an oven for 1 h at 120°C. The samples filled with barium titanate are produced as follows. The barium titanate is added to component A and mixed for 8 min at 2000 rpm. During mixing heat is generated leading to the (pre-) vulcanization of the sample, therefore barium titanate is initially mixed only with component A. After evacuation the sample is cooled. Finally component B is added to the mixture and mixed for 1 min at 1000 rpm. After pouring into the mould and a subsequent evacuation the specimen is vulcanized at 120 °C for 1 h.
where P is the probability of failure, E0 is the DBS at which 63.2 % of the samples break and m is the Weibull modulus which describes the reliability according to the reliability chart of Lanyi [15]. The distribution is narrower for a higher m thus the reliability increases, therefore high Weibull modulus values are desirable. In the results section the E0 values from the Weibull distribution are discussed, whereby the error bars are smaller than the symbol size. After the experiment the air entrapped samples were inspected in Keyence’s VHX-1000 light microscope to determine the diameter of the spherical void where the breakdown occurred. 4. Results and discussion
3. Experimental
First the intrinsic factors are discussed. The thickness dependency is shown in Fig. 2. These experiments were performed with a force of 2 N and a radius of 15 mm. The decrease in DBS with increasing thickness d is well known in the literature. A commonly used relation is a power law, like
The measurements were conducted on a custom made experimental set-up which can be seen in Fig. 1. The thickness of the specimen was measured with a dial gauge from HOLEX. The grounded electrode was planar with rounded edges and a radius of 25 mm. The upper electrode is hemispherical and in order to investigate the influence of the radius different radii were used (5 mm, 10 mm and 15 mm). The weight of the set-up is about 200 g. To achieve higher forces weights can be added to the cylinder holding the upper electrode, so in this case total weights of 500 g, 700 g and 1000 g can be used. This corresponds to the weight forces of approximately 2 N, 5 N, 7 N and 10 N. The voltage is increased by 2000 V/s until a breakdown or the maximum voltage of 40 kV DC is reached. At a critical current of 0.75 mA a breakdown is detected. For the application of the voltage a GLP2-CE from Schleich is used. Because of the low DBS of air the measurements were conducted in an isolating oil S3 ZX-I Dried from Shell in order to avoid a short circuit between the electrodes. Due to the very short measurement time ⩽20 s a swelling of the silicone elastomers can be neglected. Furthermore the measurements were performed in a grounded box for safety reasons. A minimum of 30 samples per experimental setting (in total 26) were measured, the corresponding breakdown voltage U and the measured thickness d at breakdown yield the electric DBS E:
E=
U d
E = kd−n
where E is the breakdown field, d is the thickness and k and n are two adjustable parameters, e.g. [4,16]. The decrease can be explained by the weakest link theory and the enlargement effect, because due to an increase in volume, the number and size of defects can increase and this in turn leads to an increased probability of breakdown [17,18]. Another intrinsic factor is the filling degree whose influence on the DBS is plotted in Fig. 3. These data points were measured with a force of 2 N, a radius of 10 mm and an initial thickness of 400 μm. It can be seen that the DBS increases with the filling level and at around 15 vol% a plateau is reached. In the literature the increase in DBS is mostly explained by an increase in Young’s modulus [7,19–21]. However the argumentation must be different. Due to the more compact polymer chains, trapping of charges can occur, which means that a higher voltage is required to destroy the sample [16]. Furthermore it is reported in the literature that the DBS of filled systems decreases again at higher filling levels. This can have several causes, such as the formation of agglomerates or a lack of interaction between matrix and filler [22–24]. In addition, an increase in filler particles increases the number of defects and the vacuoles on the surface of the particles, which leads to premature breakdown [13,24]. The greatest influence, however, is due to the difference in permittivity between the matrix and the filler. Due to the significantly higher permittivity of the particles than the matrix, the electrical field on the particle surface increases by up to a factor of three [18]. With the increase in the degree of filling, the number of
(1)
The resulting DBS of the 30 measured values is further analysed using the Weibull distribution, as recommended by the IEEE [14]: m
E P = 1 − exp ⎡−⎛ ⎞ ⎤ ⎢ ⎝ E0 ⎠ ⎥ ⎦ ⎣ ⎜
(3)
⎟
(2) 66
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Fig. 4. The three dashed lines correspond to the measured E0 from Weibull of the silicone elastomer without air inclusions (93 V/μm) which was measured with the same parameters, to E0 of the surrounding oil (22 V/μm) and to E0 of air (11 V/μm). As a further comparison the DBS of the material without deliberate voids is shown with open symbols. The samples were measured with a constant force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm. In order to avoid several voids over the thickness (see the two voids on the right in Fig. 6a) the deliberately created voids are intentionally large (left void in Fig. 6a), so that the influence of only one void can be evaluated. Furthermore it should be noted that no voids which have a larger diameter than the thickness of the silicone elastomer (400 μm) are closed. This is also possible for smaller pores, as only the largest diameter was measured in the light microscope. As expected, there is a decrease in strength due to the diameter of the air voids. This can be explained by the lower DBS of air compared to the silicone elastomer. At the same time the electric field in a void can increase by up to factor of 1.5, assuming that the permittivity of air is much lower than that of the matrix [18]. Thus, with ever-increasing inclusions, the DBS decreases further and further until it approaches the value of the surrounding oil. As the voids become smaller and smaller, the DBS increases sharply, before leading to an asymptote of the neat material without deliberate voids. We suggest a semi-empirical model to describe the DBS in dependence of the void diameter D. Coming from Eq. 1, the real electric field strength of the silicone elastomer ELSR can be described as:
Fig. 3. DBS E0 in dependence of the filling degree with barium titanate for the constant applied force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm.
particles increases and therefore also the number of increased electrical fields on the surface of the particles. This results in a higher probability of breakdown, similar to the enlargement effect [18,23,24]. Accordingly, there are several competing effects, with the two most important being the trapping of charges and the increases in field strength. In this case, an equilibrium of the two effects can be observed, as there is an apparent saturation of the curve. However, it is to be expected that the curve for larger filling degrees drops again and a possible maximum or rather sweet spot exists. For the sake of completeness it should be mentioned that with the selected materials it was unfortunately not possible to produce higher filled samples at the desired thicknesses without defects, so that these could not be tested. In order to investigate the influence of defects on the DBS, specimens with air inclusions were deliberately prepared. Subsequently, the diameter of the void responsible for the breakdown was determined in the light microscope. It is interesting to note that the breakdown always occurred at the largest void of the contact area, regardless of the concentration of defects. The dependence of the strength on the void diameter D is shown in
ELSR =
U U = d−D d 1−
(
D d
Eexp
=
) (
1−
D d
)
(4)
where Eexp equals the experimental DBS from Eq. 1. Since the DBS is a statistical process, we introduce breakdown probabilities which were estimated using the area of the void and the area of the silicone elastomer without voids. This results in a probability W0 for the silicone elastomer with voids and W1 for the silicone elastomer without voids:
W0 =
W1 =
D 2 2 2 R2
( )κ
D 2 R2 − 2 κ 2 R2
()
(5)
DK 2 ⎞ =1−⎛ ⎝ 2R ⎠
(6)
R corresponds to the radius of the upper electrode and κ is a probability factor. The sum of these probabilities is 1. Eqs. (4)–(6) make it possible to calculate the experimental DBS, which is made up of the strength of the pure silicone elastomer, that of silicone elastomer with deliberate voids and the corresponding probabilities.
D DK 2 ⎛ DK 2 ⎞ ⎤ ⎞ + 1−⎛ ⎞ Eexp = ELSR ⎡ ⎛1 − ⎞ ⎛ ⎢⎝ d ⎠ ⎝ 2R ⎠ ⎝ 2R ⎠ ⎠ ⎥ ⎝ ⎣ ⎦ ⎜
⎟
(7)
With this model it is possible to describe the material behavior with only one fit parameter κ , since all other parameters are given (ELSR , R, d). However, it is only valid for diameters < 400 μm which equals the initial thickness of the silicone elastomer, as otherwise a ternary system of silicone elastomer, air and oil is present. For larger voids a D−2 dependence is assumed, because of the increase of the area of the void at the edge of the silicone elastomer (see Fig. 5b). The lack of transition between the two areas can be explained by the possible penetration of oil at larger void diameters. As a result, the measurement results vary very widely, which leads to an error in the measurement results. Accordingly, the data can be described with the semi empirical equation suggested here. In comparison to the material without deliberate air inclusions, it is noticeable that the data for the pure material varies. For this reason, the data is evaluated using the Weibull distribution. However, after these samples were evacuated and no air voids were visible, other defects led to failure.
Fig. 4. DBS E in dependence of the diameter of air voids D for a constant applied force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm. The open symbols are the DBS of the silicone elastomer without voids. The red line corresponds to the semi-empirical model and the red dashed line to the assumed behaviour for big voids. The three black dashed lines correspond to the DBS of the pure material, the surrounding oil and the air according to Weibull. 67
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Fig. 5. Sketches of different sized voids in the silicone elastomer with a thickness d.
Fig. 8. DBS E0 in dependence of the compression d 0/ d . The lines are the fit from Eq. (8), where the solid line corresponds to a free n and the dashed line n = 1.
Fig. 6. DBS E0 in dependence of the force of the upper electrode for different electrode radii and an initial thickness of 400 μm.
Table 1 Parameters of the compression model without exponent. Parameter
Value
Std. dev.
unit
E0, start E0, saturation a
51.7 488 0.12 0.9796
4.9 30 0.02
V/μ m V/μ m –
adj. R2
Table 2 Parameters of the compression model with exponent. Parameter
Value
Std. dev.
unit
E0, start E0, saturation a n
12.9 674 0.14 0.7 0.9819
9.6 86 0.03 0.2
V/μ m V/μ m – –
adj. R2
Fig. 7. DBS E0 in dependence of the radius of the upper electrode for different forces and an initial thickness of 400 μm.
an initial sample thickness of 400 μm. It can be seen that for increasing forces the DBS increases as well. This can also be explained by the trapping of charges, because a higher compression leads to a decrease in the free volume and thus more tightly packed polymer chains [16]. The compression also results in some of the defects being squeezed out of the measuring area and thus no longer contributing to the strength, which increases accordingly. Therefore stronger electric fields are necessary to destroy the sample.
For the sake of completeness, it should also be noted that partial discharges can occur in filled systems as well as in the case of defects due to local field strength increases, which can result in a significant shortening of the lifetime. These have no influence on the measurement of short-term strength, so they are neglected in this work [18]. The first extrinsic factor discussed is the applied force of the upper electrode. The influence on E0 is plotted in Fig. 6 for different radii and
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Acknowledgement
In Fig. 7 the influence of the radius of the curvature is shown for different applied forces at a sample thickness of 400 μm. The same trend as in Fig. 6 with regard to the applied force can be seen. However the radius also changes the DBS. With a decrease in the radius the contact area between electrode and sample decreases, leading to higher stresses and thus to a greater compression of the sample. This compression again leads to a hindrance of the spreading of a conductive path which would yield a breakdown. The analysis of these influencing factors (sample thickness, size of air voids, force and radius of the upper electrode and the filling degree) demonstrate a strong influence of the compression. In Fig. 8 the DBS in dependence of the compression (d 0/ d ) is plotted for all different experimental set-ups, but without deliberate voids, where d 0 is the starting thickness and d is the thickness at breakdown. The standard deviation for higher compressions is large because the samples are close to the measurement limit of the dial gauge (10 μm), therefore the calculated error propagation leads to larger errors. It can be seen that the DBS ranges between 50 V/μm for a compression of 1.36 and 431 V/μm for a compression of 19.35. This is an increase by a factor of 8.7 for the same material, dependent only on the compression. In this way, it is possible to adjust the strength of a material specifically through compression. The great influence of compression can be explained, as mentioned above, by the trapping of charges and the compression of voids. A comparison with the literature shows that the compression has a similar influence on DBS as the pre-strain [12,25–27]. There, the increase in DBS is justified by a shift in electromechanical instabilities towards higher electric fields [28–31]. This may also be the case with compressed specimens, as both pre-stretching and compression exert a transverse force on the specimen, resulting in a decrease in thickness. Furthermore all data points fall on one curve (master curve) and the data could be fitted with the following equation:
The authors would like to thank Harald Rost for the construction of the experimental set-up. References [1] R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-speed electrically actuated elastomers with strain greater than 100%, Science 287 (5454) (2000) 836–839, https:// doi.org/10.1126/science.287.5454.836 URLhttp://science.sciencemag.org/ content/287/5454/836. [2] M. Hodgins, S. Seelecke, Systematic experimental study of pure shear type dielectric elastomer membranes with different electrode and film thicknesses, Smart Mater. Struct. 25 (9) (2016) 095001, https://doi.org/10.1088/0964-1726/25/9/095001. [3] G. Wu, Z. Jia, H. Cheng, Yonghong Chengand Zhang, X. Zhou, H. Wu, Easy synthesis of multi-shelled zno hollow spheres and their conversion into hedgehog-like zno hollow spheres with superior rate performance for lithium ion batteries, Appl. Surf. Sci. 464 (2019) 472–478, https://doi.org/10.1016/j.apsusc.2018.09.115. [4] G. Chen, J. Zhao, S. Li, L. Zhong, Origin of thickness dependent dc electrical breakdown in dielectrics, Appl. Phys. Lett. 100 (22) (2012) 222904, https://doi. org/10.1063/1.4721809 URLhttps://doi.org/10.1063/1.4721809. [5] D. Gatti, H. Haus, M. Matysek, B. Frohnapfel, C. Tropea, H.F. Schlaak, The dielectric breakdown limit of silicone dielectric elastomer actuators, Appl. Phys. Lett. 104 (5) (2014) 52905, https://doi.org/10.1063/1.4863816. [6] S. Zakaria, P.H.F. Morshuis, M.Y. Benslimane, L. Yu, A.L. Skov, The electrical breakdown strength of pre-stretched elastomers, with and without sample volume conservation, Smart Mater. Struct. 24 (5) (2015) 55009, https://doi.org/10.1088/ 0964-1726/24/5/055009. [7] B. Chen, M. Kollosche, M. Stewart, J. Busfield, F. Carpi, Electrical breakdown of an acrylic dielectric elastomer: effects of hemispherical probing electrode’s size and force, Int. J. Smart Nano Mater. 6 (4) (2016) 290–303, https://doi.org/10.1080/ 19475411.2015.1130974. [8] M. Kollosche, H. Stoyanov, H. Ragusch, S. Risse, A. Becker, G. Kofod, Electrical breakdown in soft elastomers: Stiffness dependence in un-pre-stretched elastomers, in: 2010 10th IEEE International Conference on Solid Dielectrics (ICSD), pp. 1–4. https://doi.org/10.1109/ICSD.2010.5568259. [9] P. Kim, N.M. Doss, J.P. Tillotson, P.J. Hotchkiss, M.-J. Pan, S.R. Marder, J. Li, J.P. Calame, J.W. Perry, High energy density nanocomposites based on surfacemodified BaTiO(3) and a ferroelectric polymer, ACS Nano 3 (9) (2009) 2581–2592, https://doi.org/10.1021/nn9006412. [10] J. Schmid, Influence of absolute humidity on the electrical breakdown in air, Eur. Trans. Electrical Power 2 (5) (1992) 327–334, https://doi.org/10.1002/etep. 4450020511. [11] L. Liu, H. Chen, J. Sheng, J. Zhang, Y. Wang, S. Jia, Effect of temperature on the electric breakdown strength of dielectric elastomer, Proc. SPIE 9056 (2014), https://doi.org/10.1117/12.2044910 9056-9056-9. [12] G. Kofod, P. Sommer-Larsen, R. Kornbluh, R. Pelrine, Actuation response of polyacrylate dielectric elastomers, J. Intell. Mater. Syst. Struct. 14 (12) (2003) 787–793, https://doi.org/10.1177/104538903039260. [13] A. Ziegmann, D.W. Schubert, Influence of the particle size and the filling degree of barium titanate filled silicone elastomers used as potential dielectric elastomers on the mechanical properties and the crosslinking density, Mater. Today Commun. 14 (2018) 90–98, https://doi.org/10.1016/j.mtcomm.2017.12.013. [14] IEEE Guide for the Statistical Analysis of Electrical Insulation Breakdown Data, IEEE Std 930-2004 (Revision of IEEE Std 930–1987), 2005, 0_1–41. [15] F.J. Lanyi, P. Kunzelmann, D.W. Schubert, Novel chart for representation of material performance and reliability, Macromol. Symp. 365 (1) (2016) 194–202, https://doi.org/10.1002/masy.201650010. [16] K.H. Oh, C.K. Ong, B.T.G. Tan, C. Le Gressus, G. Blaise, Variation of trapping/detrapping properties as a function of the insulator size, J. Appl. Phys. 74 (3) (1993) 1960–1967, https://doi.org/10.1063/1.354780. [17] J. Oesterheld, Dielectrisches Verhalten von Silikonelastomer-Isolierungen bei hohen elektrischen Feldstärken, Dissertation, Technische Universität, Dresden. [18] A. Küchler, Hochspannungstechnik, 1st Edition, Springer, Berlin and Heidelberg and New York, 2005. [19] L. Yu, S. Vudayagiri, S. Zakaria, M.Y. Benslimane, A.L. Skov, Filled liquid silicone rubbers: possibilities and challenges, p. 90560S.https://doi.org/10.1117/12. 2044565. [20] S. Vudayagiri, S. Zakaria, L. Yu, S.S. Hassouneh, M. Benslimane, A.L. Skov, High breakdown-strength composites from liquid silicone rubbers, Smart Mater. Struct. 23 (10) (2014) 105017, https://doi.org/10.1088/0964-1726/23/10/105017. [21] L. Yu, A.L. Skov, Silicone rubbers for dielectric elastomers with improved dielectric and mechanical properties as a result of substituting silica with titanium dioxide, Int. J. Smart Nano Mater. 6 (4) (2016) 268–289, https://doi.org/10.1080/ 19475411.2015.1119216. [22] S. Liu, S. Xiu, B. Shen, J. Zhai, L. Kong, Dielectric properties and energy storage densities of poly(vinylidenefluoride) nanocomposite with surface hydroxylated cube shaped Ba0.6Sr0.4TiO3 nanoparticles, Polymers 8 (12) (2016) 45, https://doi. org/10.3390/polym8020045. [23] Y. Hao, X. Wang, K. Bi, J. Zhang, Y. Huang, L. Wu, P. Zhao, K. Xu, M. Lei, L. Li, Significantly enhanced energy storage performance promoted by ultimate sized ferroelectric BaTiO3 fillers in nanocomposite films, Nano Energy 31 (2017) 49–56, https://doi.org/10.1016/j.nanoen.2016.11.008. [24] Z.-M. Dang, J.-K. Yuan, S.-H. Yao, R.-J. Liao, Flexible nanodielectric materials with
n
d E0 = (E0, saturation − E0, start ) ⎡1 − exp ⎛−a ⎛ 0 − 1⎞ ⎞ ⎤ + E0, start ⎢ ⎠ ⎠⎥ ⎝ ⎝d ⎣ ⎦ ⎜
⎟
(8)
where E0, saturation (saturation value), E0, start (DBS at no compression), a and n are fitting parameters. The fit was performed once with fixed n = 1 (dashed line in Fig. 8) and with a free n (solid line), because the former describes the data well for larger compressions and the latter describes the data better for very small compressions. Nevertheless, both fits have a similar adjusted R2 . Tables 1 and 2 show the resulting fit parameters. With this equation it is possible to compare the DBS of a material regardless of the reported experimental set-up and therefore regardless of the experimenter/work group. Furthermore, the E0, start fit parameter allows one to estimate the DBS for no compression. It is also shown that the addition of barium titanate (red data points) has the same effect as the compression of the neat silicone elastomer, in contrast to Fig. 3. Consequently, the increase in Young’s modulus by the addition of filler has the same effect as an increase through compression, or in other words the addition of barium titanate. 5. Conclusions Various influencing factors (thickness, filling degree, defects, electrode radius and force of the upper electrode) on the DBS of silicone elastomers were investigated, revealing that all effects can be reduced to the influence of compression and the corresponding reduction of voids. Thus a model and a master curve of the dielectric strength depending on the compression of the specimen could be created. Additionally it becomes apparent to adjust the DBS of a material and otherwise to compare the measured DBS of different experimental setups and working groups with each other. In order to further improve the model, especially for high deformations, a dial gauge with a measuring resolution smaller than 10 μm should be used in the future. 69
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[25]
[26]
[27]
[28]
elastomers, Phys. Rev. Lett. 118 (2017) 078001, https://doi.org/10.1103/ PhysRevLett. 118.078001. [29] D. De Tommasi, G. Puglisi, G. Zurlo, Electromechanical instability and oscillating deformations in electroactive polymer films, Appl. Phys. Lett. 102 (2013) 011903, https://doi.org/10.1063/1.4772956. [30] D. De Tommasi, G. Puglisi, G. Zurlo, Inhomogeneous deformations and pull-in instability in electroactive polymeric films, Int. J. Non Linear Mech. 57 (2013) 123–129, https://doi.org/10.1016/j.ijnonlinmec.2013.06.008. [31] R.W. Ogden, G. Saccomandi, I. Sgura, On worm-like chain models within the threedimensional continuum mechanics framework, Proc. R. Soc. Lond. Ser. A 462 (2006) 749–768, https://doi.org/10.1098/rspa.2005.1592.
high permittivity for power energy storage, Adv. Mater. (Deerfield Beach, Fla.) (25(44), 2013,) 6334–6365, https://doi.org/10.1002/adma.201301752. J. Huang, S. Shian, R.M. Diebold, Z. Suo, D.R. Clarke, The thickness and stretch dependence of the electrical breakdown strength of an acrylic dielectric elastomer, Appl. Phys. Lett. 101 (12) (2012) 122905, https://doi.org/10.1063/1.4754549. J.-S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (25) (2006) 7727–7751, https://doi.org/10.1016/j. ijsolstr.2006.03.026. C. Jordi, A. Schmidt, G. Kovacs, S. Michel, P. Ermanni, Performance evaluation of cutting-edge dielectric elastomers for large-scale actuator applications, Smart Mater. Struct. 20 (7) (2011) 075003 . G. Zurlo, M. Destrade, D. DeTommasi, G. Puglisi, Catastrophic thinning of dielectric
70
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Materials Science & Engineering B journal homepage: www.elsevier.com/locate/mseb
Investigation and modeling of various influencing factors on the dielectric breakdown strength of silicone elastomers
T
⁎
Andreas Ziegmanna, , Claus Bernera, Dirk W. Schuberta,b a b
Institute of Polymer Materials, University Erlangen-Nürnberg, Martensstraße 7, 91058 Erlangen, Germany Keylab Advanced Fiber Technologies, Bavarian Polymer Institute, Dr.-Mack-Straße 77, 90762 Fürth, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Dielectric breakdown strength Silicone elastomer Barium titanate Electroactive polymer Dielectric elastomer
Dielectric elastomers are utilized as soft electroactive polymers for actuators, sensors or generator applications to transduce mechanical to electrical energy and vice versa. They are characterized by the ability to change shape while an electrical field is applied. Indeed, this effect is most significant for electrical fields near the electrical breakdown strength, therefore it is a limiting factor for application. This work investigates different factors influencing the dielectric breakdown strength of soft silicone elastomers such as the sample thickness, the force and the radius of the upper electrode, the filling degree and the size of air voids. It can be shown that the main influence is the compression of the sample, thus a novel master curve can be created and fitted by a semi empirical model function. Therefore a comparison of all different experimental set-ups is possible.
1. Introduction Electroactive polymers (EAP) can convert electrical to mechanical energy and vice versa, therefore they are a promising material class for application as artificial muscles. An important subgroup of EAPs are dielectric elastomer actuators (DEA) which have the advantage of low viscoelastic losses, high actuation strains and good actuation pressures [1]. One main drawback of DEAs is that high actuation strains are only achieved at very high voltages [2]. However, the voltage is limited by the dielectric breakdown strength (DBS) of the material and thus, the applied electric field has to be lower than the DBS. Furthermore, the DBS is an important material parameter e.g. for the applicability of lithium ion batteries [3]. Furthermore, from literature is known that the DBS is highly dependent on boundary conditions during measurement. The different influencing factors can be divided into two groups: intrinsic and extrinsic factors. Intrinsic factors are for example the thickness [4–7], the stiffness [6,8] and the degree of filling [9]. Defects in the dielectric, e. g. air voids in silicone elastomers, are another important intrinsic factor, as they often cause a breakdown. Other parameters like the electrodes [6], humidity [10], temperature [11], pre-stretch [6,12,5] and the force of the upper electrode [7] are extrinsic influences. However systematic studies do not yet exist. Most of these factors are discussed in the literature (see references above), sometimes even several factors [7]. But the authors conclude
⁎
that it is important to mention the experimental parameters in order to ensure comparability with other publications. In this work, different influencing factors such as the sample thickness, the size of air voids, the force and the radius of the upper electrode and the filling degree are evaluated and prioritized with respect to their significance. Finally a model is proposed to describe the DBS in dependence of the most relevant parameter, the compression of the sample, regardless of the boundary conditions. Furthermore, in order to reveal the influence of air voids on the DBS, we produced deliberately different sized air voids in the silicone elastomer and measured the corresponding DBS. 2. Materials The silicone elastomer used, ELASTOSIL P 7670, is industrially available from Wacker Chemie AG. It consists of polydimethylsiloxane (PDMS) and a two component system (A + B) with a mixing ratio of 1:1. The platinum catalyst leads to the addition curing of the room temperature vulcanizate. The material is filled with approximately 7.8 vol% silica [13] which yields a Shore A hardness of 7. Barium titanate with a particle size of < 3 μm was bought from Sigma-Aldrich. Laser diffraction revealed a particle size d90 of 3.12 ± 0.04 μm. We showed previously that the particle size in the silicone elastomer depends on the filling degree [13]. For the production of the samples components A and B were weighed in a ratio of 1:1 and mixed in a speedmixer DAC 150 SP from
Corresponding author. E-mail addresses: [email protected] (A. Ziegmann), [email protected] (D.W. Schubert).
https://doi.org/10.1016/j.mseb.2019.03.014 Received 17 April 2018; Received in revised form 11 January 2019; Accepted 21 March 2019 0921-5107/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 2. DBS E0 in dependence of the thickness d for a constant force F = 2 N and an electrode radius r = 15 mm. The power law fit is marked red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 1. Sketch of the experimental set-up.
Hauschild Engineering for 1 min at 1000 rpm. Afterwards the material was poured into a mould which was then evacuated in a desiccator. Samples with deliberate air voids were not evacuated. In order to decrease the vulcanization time the mould was placed in an oven for 1 h at 120°C. The samples filled with barium titanate are produced as follows. The barium titanate is added to component A and mixed for 8 min at 2000 rpm. During mixing heat is generated leading to the (pre-) vulcanization of the sample, therefore barium titanate is initially mixed only with component A. After evacuation the sample is cooled. Finally component B is added to the mixture and mixed for 1 min at 1000 rpm. After pouring into the mould and a subsequent evacuation the specimen is vulcanized at 120 °C for 1 h.
where P is the probability of failure, E0 is the DBS at which 63.2 % of the samples break and m is the Weibull modulus which describes the reliability according to the reliability chart of Lanyi [15]. The distribution is narrower for a higher m thus the reliability increases, therefore high Weibull modulus values are desirable. In the results section the E0 values from the Weibull distribution are discussed, whereby the error bars are smaller than the symbol size. After the experiment the air entrapped samples were inspected in Keyence’s VHX-1000 light microscope to determine the diameter of the spherical void where the breakdown occurred. 4. Results and discussion
3. Experimental
First the intrinsic factors are discussed. The thickness dependency is shown in Fig. 2. These experiments were performed with a force of 2 N and a radius of 15 mm. The decrease in DBS with increasing thickness d is well known in the literature. A commonly used relation is a power law, like
The measurements were conducted on a custom made experimental set-up which can be seen in Fig. 1. The thickness of the specimen was measured with a dial gauge from HOLEX. The grounded electrode was planar with rounded edges and a radius of 25 mm. The upper electrode is hemispherical and in order to investigate the influence of the radius different radii were used (5 mm, 10 mm and 15 mm). The weight of the set-up is about 200 g. To achieve higher forces weights can be added to the cylinder holding the upper electrode, so in this case total weights of 500 g, 700 g and 1000 g can be used. This corresponds to the weight forces of approximately 2 N, 5 N, 7 N and 10 N. The voltage is increased by 2000 V/s until a breakdown or the maximum voltage of 40 kV DC is reached. At a critical current of 0.75 mA a breakdown is detected. For the application of the voltage a GLP2-CE from Schleich is used. Because of the low DBS of air the measurements were conducted in an isolating oil S3 ZX-I Dried from Shell in order to avoid a short circuit between the electrodes. Due to the very short measurement time ⩽20 s a swelling of the silicone elastomers can be neglected. Furthermore the measurements were performed in a grounded box for safety reasons. A minimum of 30 samples per experimental setting (in total 26) were measured, the corresponding breakdown voltage U and the measured thickness d at breakdown yield the electric DBS E:
E=
U d
E = kd−n
where E is the breakdown field, d is the thickness and k and n are two adjustable parameters, e.g. [4,16]. The decrease can be explained by the weakest link theory and the enlargement effect, because due to an increase in volume, the number and size of defects can increase and this in turn leads to an increased probability of breakdown [17,18]. Another intrinsic factor is the filling degree whose influence on the DBS is plotted in Fig. 3. These data points were measured with a force of 2 N, a radius of 10 mm and an initial thickness of 400 μm. It can be seen that the DBS increases with the filling level and at around 15 vol% a plateau is reached. In the literature the increase in DBS is mostly explained by an increase in Young’s modulus [7,19–21]. However the argumentation must be different. Due to the more compact polymer chains, trapping of charges can occur, which means that a higher voltage is required to destroy the sample [16]. Furthermore it is reported in the literature that the DBS of filled systems decreases again at higher filling levels. This can have several causes, such as the formation of agglomerates or a lack of interaction between matrix and filler [22–24]. In addition, an increase in filler particles increases the number of defects and the vacuoles on the surface of the particles, which leads to premature breakdown [13,24]. The greatest influence, however, is due to the difference in permittivity between the matrix and the filler. Due to the significantly higher permittivity of the particles than the matrix, the electrical field on the particle surface increases by up to a factor of three [18]. With the increase in the degree of filling, the number of
(1)
The resulting DBS of the 30 measured values is further analysed using the Weibull distribution, as recommended by the IEEE [14]: m
E P = 1 − exp ⎡−⎛ ⎞ ⎤ ⎢ ⎝ E0 ⎠ ⎥ ⎦ ⎣ ⎜
(3)
⎟
(2) 66
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Fig. 4. The three dashed lines correspond to the measured E0 from Weibull of the silicone elastomer without air inclusions (93 V/μm) which was measured with the same parameters, to E0 of the surrounding oil (22 V/μm) and to E0 of air (11 V/μm). As a further comparison the DBS of the material without deliberate voids is shown with open symbols. The samples were measured with a constant force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm. In order to avoid several voids over the thickness (see the two voids on the right in Fig. 6a) the deliberately created voids are intentionally large (left void in Fig. 6a), so that the influence of only one void can be evaluated. Furthermore it should be noted that no voids which have a larger diameter than the thickness of the silicone elastomer (400 μm) are closed. This is also possible for smaller pores, as only the largest diameter was measured in the light microscope. As expected, there is a decrease in strength due to the diameter of the air voids. This can be explained by the lower DBS of air compared to the silicone elastomer. At the same time the electric field in a void can increase by up to factor of 1.5, assuming that the permittivity of air is much lower than that of the matrix [18]. Thus, with ever-increasing inclusions, the DBS decreases further and further until it approaches the value of the surrounding oil. As the voids become smaller and smaller, the DBS increases sharply, before leading to an asymptote of the neat material without deliberate voids. We suggest a semi-empirical model to describe the DBS in dependence of the void diameter D. Coming from Eq. 1, the real electric field strength of the silicone elastomer ELSR can be described as:
Fig. 3. DBS E0 in dependence of the filling degree with barium titanate for the constant applied force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm.
particles increases and therefore also the number of increased electrical fields on the surface of the particles. This results in a higher probability of breakdown, similar to the enlargement effect [18,23,24]. Accordingly, there are several competing effects, with the two most important being the trapping of charges and the increases in field strength. In this case, an equilibrium of the two effects can be observed, as there is an apparent saturation of the curve. However, it is to be expected that the curve for larger filling degrees drops again and a possible maximum or rather sweet spot exists. For the sake of completeness it should be mentioned that with the selected materials it was unfortunately not possible to produce higher filled samples at the desired thicknesses without defects, so that these could not be tested. In order to investigate the influence of defects on the DBS, specimens with air inclusions were deliberately prepared. Subsequently, the diameter of the void responsible for the breakdown was determined in the light microscope. It is interesting to note that the breakdown always occurred at the largest void of the contact area, regardless of the concentration of defects. The dependence of the strength on the void diameter D is shown in
ELSR =
U U = d−D d 1−
(
D d
Eexp
=
) (
1−
D d
)
(4)
where Eexp equals the experimental DBS from Eq. 1. Since the DBS is a statistical process, we introduce breakdown probabilities which were estimated using the area of the void and the area of the silicone elastomer without voids. This results in a probability W0 for the silicone elastomer with voids and W1 for the silicone elastomer without voids:
W0 =
W1 =
D 2 2 2 R2
( )κ
D 2 R2 − 2 κ 2 R2
()
(5)
DK 2 ⎞ =1−⎛ ⎝ 2R ⎠
(6)
R corresponds to the radius of the upper electrode and κ is a probability factor. The sum of these probabilities is 1. Eqs. (4)–(6) make it possible to calculate the experimental DBS, which is made up of the strength of the pure silicone elastomer, that of silicone elastomer with deliberate voids and the corresponding probabilities.
D DK 2 ⎛ DK 2 ⎞ ⎤ ⎞ + 1−⎛ ⎞ Eexp = ELSR ⎡ ⎛1 − ⎞ ⎛ ⎢⎝ d ⎠ ⎝ 2R ⎠ ⎝ 2R ⎠ ⎠ ⎥ ⎝ ⎣ ⎦ ⎜
⎟
(7)
With this model it is possible to describe the material behavior with only one fit parameter κ , since all other parameters are given (ELSR , R, d). However, it is only valid for diameters < 400 μm which equals the initial thickness of the silicone elastomer, as otherwise a ternary system of silicone elastomer, air and oil is present. For larger voids a D−2 dependence is assumed, because of the increase of the area of the void at the edge of the silicone elastomer (see Fig. 5b). The lack of transition between the two areas can be explained by the possible penetration of oil at larger void diameters. As a result, the measurement results vary very widely, which leads to an error in the measurement results. Accordingly, the data can be described with the semi empirical equation suggested here. In comparison to the material without deliberate air inclusions, it is noticeable that the data for the pure material varies. For this reason, the data is evaluated using the Weibull distribution. However, after these samples were evacuated and no air voids were visible, other defects led to failure.
Fig. 4. DBS E in dependence of the diameter of air voids D for a constant applied force of 2 N, an electrode radius of 10 mm and an initial thickness of 400 μm. The open symbols are the DBS of the silicone elastomer without voids. The red line corresponds to the semi-empirical model and the red dashed line to the assumed behaviour for big voids. The three black dashed lines correspond to the DBS of the pure material, the surrounding oil and the air according to Weibull. 67
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Fig. 5. Sketches of different sized voids in the silicone elastomer with a thickness d.
Fig. 8. DBS E0 in dependence of the compression d 0/ d . The lines are the fit from Eq. (8), where the solid line corresponds to a free n and the dashed line n = 1.
Fig. 6. DBS E0 in dependence of the force of the upper electrode for different electrode radii and an initial thickness of 400 μm.
Table 1 Parameters of the compression model without exponent. Parameter
Value
Std. dev.
unit
E0, start E0, saturation a
51.7 488 0.12 0.9796
4.9 30 0.02
V/μ m V/μ m –
adj. R2
Table 2 Parameters of the compression model with exponent. Parameter
Value
Std. dev.
unit
E0, start E0, saturation a n
12.9 674 0.14 0.7 0.9819
9.6 86 0.03 0.2
V/μ m V/μ m – –
adj. R2
Fig. 7. DBS E0 in dependence of the radius of the upper electrode for different forces and an initial thickness of 400 μm.
an initial sample thickness of 400 μm. It can be seen that for increasing forces the DBS increases as well. This can also be explained by the trapping of charges, because a higher compression leads to a decrease in the free volume and thus more tightly packed polymer chains [16]. The compression also results in some of the defects being squeezed out of the measuring area and thus no longer contributing to the strength, which increases accordingly. Therefore stronger electric fields are necessary to destroy the sample.
For the sake of completeness, it should also be noted that partial discharges can occur in filled systems as well as in the case of defects due to local field strength increases, which can result in a significant shortening of the lifetime. These have no influence on the measurement of short-term strength, so they are neglected in this work [18]. The first extrinsic factor discussed is the applied force of the upper electrode. The influence on E0 is plotted in Fig. 6 for different radii and
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Acknowledgement
In Fig. 7 the influence of the radius of the curvature is shown for different applied forces at a sample thickness of 400 μm. The same trend as in Fig. 6 with regard to the applied force can be seen. However the radius also changes the DBS. With a decrease in the radius the contact area between electrode and sample decreases, leading to higher stresses and thus to a greater compression of the sample. This compression again leads to a hindrance of the spreading of a conductive path which would yield a breakdown. The analysis of these influencing factors (sample thickness, size of air voids, force and radius of the upper electrode and the filling degree) demonstrate a strong influence of the compression. In Fig. 8 the DBS in dependence of the compression (d 0/ d ) is plotted for all different experimental set-ups, but without deliberate voids, where d 0 is the starting thickness and d is the thickness at breakdown. The standard deviation for higher compressions is large because the samples are close to the measurement limit of the dial gauge (10 μm), therefore the calculated error propagation leads to larger errors. It can be seen that the DBS ranges between 50 V/μm for a compression of 1.36 and 431 V/μm for a compression of 19.35. This is an increase by a factor of 8.7 for the same material, dependent only on the compression. In this way, it is possible to adjust the strength of a material specifically through compression. The great influence of compression can be explained, as mentioned above, by the trapping of charges and the compression of voids. A comparison with the literature shows that the compression has a similar influence on DBS as the pre-strain [12,25–27]. There, the increase in DBS is justified by a shift in electromechanical instabilities towards higher electric fields [28–31]. This may also be the case with compressed specimens, as both pre-stretching and compression exert a transverse force on the specimen, resulting in a decrease in thickness. Furthermore all data points fall on one curve (master curve) and the data could be fitted with the following equation:
The authors would like to thank Harald Rost for the construction of the experimental set-up. References [1] R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-speed electrically actuated elastomers with strain greater than 100%, Science 287 (5454) (2000) 836–839, https:// doi.org/10.1126/science.287.5454.836 URLhttp://science.sciencemag.org/ content/287/5454/836. [2] M. Hodgins, S. Seelecke, Systematic experimental study of pure shear type dielectric elastomer membranes with different electrode and film thicknesses, Smart Mater. Struct. 25 (9) (2016) 095001, https://doi.org/10.1088/0964-1726/25/9/095001. [3] G. Wu, Z. Jia, H. Cheng, Yonghong Chengand Zhang, X. Zhou, H. Wu, Easy synthesis of multi-shelled zno hollow spheres and their conversion into hedgehog-like zno hollow spheres with superior rate performance for lithium ion batteries, Appl. Surf. Sci. 464 (2019) 472–478, https://doi.org/10.1016/j.apsusc.2018.09.115. [4] G. Chen, J. Zhao, S. Li, L. Zhong, Origin of thickness dependent dc electrical breakdown in dielectrics, Appl. Phys. Lett. 100 (22) (2012) 222904, https://doi. org/10.1063/1.4721809 URLhttps://doi.org/10.1063/1.4721809. [5] D. Gatti, H. Haus, M. Matysek, B. Frohnapfel, C. Tropea, H.F. Schlaak, The dielectric breakdown limit of silicone dielectric elastomer actuators, Appl. Phys. Lett. 104 (5) (2014) 52905, https://doi.org/10.1063/1.4863816. [6] S. Zakaria, P.H.F. Morshuis, M.Y. Benslimane, L. Yu, A.L. Skov, The electrical breakdown strength of pre-stretched elastomers, with and without sample volume conservation, Smart Mater. Struct. 24 (5) (2015) 55009, https://doi.org/10.1088/ 0964-1726/24/5/055009. [7] B. Chen, M. Kollosche, M. Stewart, J. Busfield, F. Carpi, Electrical breakdown of an acrylic dielectric elastomer: effects of hemispherical probing electrode’s size and force, Int. J. Smart Nano Mater. 6 (4) (2016) 290–303, https://doi.org/10.1080/ 19475411.2015.1130974. [8] M. Kollosche, H. Stoyanov, H. Ragusch, S. Risse, A. Becker, G. Kofod, Electrical breakdown in soft elastomers: Stiffness dependence in un-pre-stretched elastomers, in: 2010 10th IEEE International Conference on Solid Dielectrics (ICSD), pp. 1–4. https://doi.org/10.1109/ICSD.2010.5568259. [9] P. Kim, N.M. Doss, J.P. Tillotson, P.J. Hotchkiss, M.-J. Pan, S.R. Marder, J. Li, J.P. Calame, J.W. Perry, High energy density nanocomposites based on surfacemodified BaTiO(3) and a ferroelectric polymer, ACS Nano 3 (9) (2009) 2581–2592, https://doi.org/10.1021/nn9006412. [10] J. Schmid, Influence of absolute humidity on the electrical breakdown in air, Eur. Trans. Electrical Power 2 (5) (1992) 327–334, https://doi.org/10.1002/etep. 4450020511. [11] L. Liu, H. Chen, J. Sheng, J. Zhang, Y. Wang, S. Jia, Effect of temperature on the electric breakdown strength of dielectric elastomer, Proc. SPIE 9056 (2014), https://doi.org/10.1117/12.2044910 9056-9056-9. [12] G. Kofod, P. Sommer-Larsen, R. Kornbluh, R. Pelrine, Actuation response of polyacrylate dielectric elastomers, J. Intell. Mater. Syst. Struct. 14 (12) (2003) 787–793, https://doi.org/10.1177/104538903039260. [13] A. Ziegmann, D.W. Schubert, Influence of the particle size and the filling degree of barium titanate filled silicone elastomers used as potential dielectric elastomers on the mechanical properties and the crosslinking density, Mater. Today Commun. 14 (2018) 90–98, https://doi.org/10.1016/j.mtcomm.2017.12.013. [14] IEEE Guide for the Statistical Analysis of Electrical Insulation Breakdown Data, IEEE Std 930-2004 (Revision of IEEE Std 930–1987), 2005, 0_1–41. [15] F.J. Lanyi, P. Kunzelmann, D.W. Schubert, Novel chart for representation of material performance and reliability, Macromol. Symp. 365 (1) (2016) 194–202, https://doi.org/10.1002/masy.201650010. [16] K.H. Oh, C.K. Ong, B.T.G. Tan, C. Le Gressus, G. Blaise, Variation of trapping/detrapping properties as a function of the insulator size, J. Appl. Phys. 74 (3) (1993) 1960–1967, https://doi.org/10.1063/1.354780. [17] J. Oesterheld, Dielectrisches Verhalten von Silikonelastomer-Isolierungen bei hohen elektrischen Feldstärken, Dissertation, Technische Universität, Dresden. [18] A. Küchler, Hochspannungstechnik, 1st Edition, Springer, Berlin and Heidelberg and New York, 2005. [19] L. Yu, S. Vudayagiri, S. Zakaria, M.Y. Benslimane, A.L. Skov, Filled liquid silicone rubbers: possibilities and challenges, p. 90560S.https://doi.org/10.1117/12. 2044565. [20] S. Vudayagiri, S. Zakaria, L. Yu, S.S. Hassouneh, M. Benslimane, A.L. Skov, High breakdown-strength composites from liquid silicone rubbers, Smart Mater. Struct. 23 (10) (2014) 105017, https://doi.org/10.1088/0964-1726/23/10/105017. [21] L. Yu, A.L. Skov, Silicone rubbers for dielectric elastomers with improved dielectric and mechanical properties as a result of substituting silica with titanium dioxide, Int. J. Smart Nano Mater. 6 (4) (2016) 268–289, https://doi.org/10.1080/ 19475411.2015.1119216. [22] S. Liu, S. Xiu, B. Shen, J. Zhai, L. Kong, Dielectric properties and energy storage densities of poly(vinylidenefluoride) nanocomposite with surface hydroxylated cube shaped Ba0.6Sr0.4TiO3 nanoparticles, Polymers 8 (12) (2016) 45, https://doi. org/10.3390/polym8020045. [23] Y. Hao, X. Wang, K. Bi, J. Zhang, Y. Huang, L. Wu, P. Zhao, K. Xu, M. Lei, L. Li, Significantly enhanced energy storage performance promoted by ultimate sized ferroelectric BaTiO3 fillers in nanocomposite films, Nano Energy 31 (2017) 49–56, https://doi.org/10.1016/j.nanoen.2016.11.008. [24] Z.-M. Dang, J.-K. Yuan, S.-H. Yao, R.-J. Liao, Flexible nanodielectric materials with
n
d E0 = (E0, saturation − E0, start ) ⎡1 − exp ⎛−a ⎛ 0 − 1⎞ ⎞ ⎤ + E0, start ⎢ ⎠ ⎠⎥ ⎝ ⎝d ⎣ ⎦ ⎜
⎟
(8)
where E0, saturation (saturation value), E0, start (DBS at no compression), a and n are fitting parameters. The fit was performed once with fixed n = 1 (dashed line in Fig. 8) and with a free n (solid line), because the former describes the data well for larger compressions and the latter describes the data better for very small compressions. Nevertheless, both fits have a similar adjusted R2 . Tables 1 and 2 show the resulting fit parameters. With this equation it is possible to compare the DBS of a material regardless of the reported experimental set-up and therefore regardless of the experimenter/work group. Furthermore, the E0, start fit parameter allows one to estimate the DBS for no compression. It is also shown that the addition of barium titanate (red data points) has the same effect as the compression of the neat silicone elastomer, in contrast to Fig. 3. Consequently, the increase in Young’s modulus by the addition of filler has the same effect as an increase through compression, or in other words the addition of barium titanate. 5. Conclusions Various influencing factors (thickness, filling degree, defects, electrode radius and force of the upper electrode) on the DBS of silicone elastomers were investigated, revealing that all effects can be reduced to the influence of compression and the corresponding reduction of voids. Thus a model and a master curve of the dielectric strength depending on the compression of the specimen could be created. Additionally it becomes apparent to adjust the DBS of a material and otherwise to compare the measured DBS of different experimental setups and working groups with each other. In order to further improve the model, especially for high deformations, a dial gauge with a measuring resolution smaller than 10 μm should be used in the future. 69
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[25]
[26]
[27]
[28]
elastomers, Phys. Rev. Lett. 118 (2017) 078001, https://doi.org/10.1103/ PhysRevLett. 118.078001. [29] D. De Tommasi, G. Puglisi, G. Zurlo, Electromechanical instability and oscillating deformations in electroactive polymer films, Appl. Phys. Lett. 102 (2013) 011903, https://doi.org/10.1063/1.4772956. [30] D. De Tommasi, G. Puglisi, G. Zurlo, Inhomogeneous deformations and pull-in instability in electroactive polymeric films, Int. J. Non Linear Mech. 57 (2013) 123–129, https://doi.org/10.1016/j.ijnonlinmec.2013.06.008. [31] R.W. Ogden, G. Saccomandi, I. Sgura, On worm-like chain models within the threedimensional continuum mechanics framework, Proc. R. Soc. Lond. Ser. A 462 (2006) 749–768, https://doi.org/10.1098/rspa.2005.1592.
high permittivity for power energy storage, Adv. Mater. (Deerfield Beach, Fla.) (25(44), 2013,) 6334–6365, https://doi.org/10.1002/adma.201301752. J. Huang, S. Shian, R.M. Diebold, Z. Suo, D.R. Clarke, The thickness and stretch dependence of the electrical breakdown strength of an acrylic dielectric elastomer, Appl. Phys. Lett. 101 (12) (2012) 122905, https://doi.org/10.1063/1.4754549. J.-S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (25) (2006) 7727–7751, https://doi.org/10.1016/j. ijsolstr.2006.03.026. C. Jordi, A. Schmidt, G. Kovacs, S. Michel, P. Ermanni, Performance evaluation of cutting-edge dielectric elastomers for large-scale actuator applications, Smart Mater. Struct. 20 (7) (2011) 075003 . G. Zurlo, M. Destrade, D. DeTommasi, G. Puglisi, Catastrophic thinning of dielectric
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