Insights into the Morphotropic Phase Boundary in Ferroelectric

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Insights into the Morphotropic Phase Boundary in Ferroelectric Polymers from the Molecular Perspective Yang Liu,† Bing Zhang,‡ Aziguli Haibibu,† Wenhan Xu,† Zhubing Han,† Wenchang Lu,‡ J. Bernholc,‡ and Qing Wang*,† †

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Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, United States S Supporting Information *

ABSTRACT: Significantly enhanced electromechanical responses are inherent to piezoelectric materials at the morphotropic phase boundary (MPB). Here we reveal that conformational competition between the trans-planar and 3/1-helical phases of poly(vinylidene fluoride− trifluoroethylene) P(VDF-TrFE) occurs intramolecularly rather than intermolecularly to induce the formation of MPB. We attribute significantly enhanced piezoelectric properties observed near MPB to the polarization rotation between energetically degenerate trans-planar and 3/1-helical phases. Our results offer design principles to search for new MPB polymers from a molecular perspective.

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INTRODUCTION Morphotropic phase boundary (MPB) refers to a region of coexisting phases or an intermediate low-symmetry phase in the phase diagram of piezoelectrics, which separates two competing phases with distinct symmetries.1 Realizing MPB usually requires a flat energy surface between different symmetries, which facilitates polarization rotation and thus induces a large piezoelectric response.2−4 In general, symmetry breaking across the boundary is necessary, and crystallography is, therefore, crucial in the design of MPB in perovskite piezoelectrics.3,5 Almost all existing MPBs occur in inorganic ceramics and crystals, except for a newly discovered phase boundary in a narrow composition range of ferroelectric P(VDF-TrFE) copolymers.6 Realizing MPB in organic materials not only greatly widens this well-established physical concept but also opens a completely new avenue to the polymers with greatly increased piezoelectric responses. However, the general principles for designing MPB in piezoelectric polymers remain lacking. On the one hand, physical properties of polymers depend on the arrangement of constituent monomers at the single chain scale. On the other hand, it is challenging to reach a reasonable crystal description of polymers based on current diffraction techniques, which yield quite a high disagreement factor (∼10%−30%) in structural refinements of ferroelectric polymers,7−9 in contrast to inorganic ceramics and crystals. Indeed, polymer crystallography corresponds to the ideal condition because polymers never have a perfect crystal structure due to inherent structural defects and complex morphology.10 Therefore, a more practical paradigm in piezoelectric polymers is to focus on the constituent monomers and microstructures11,12 instead of the crystallo© XXXX American Chemical Society

graphic structures. In this work, we investigate the mechanisms of MPB formation in ferroelectric polymers from a molecular perspective, with focus on identifying the most promising avenues for the design of new MPB piezoelectric polymers.

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RESULTS AND DISCUSSION The significant change in the preferred chain conformation of P(VDF-TrFE) occurs near MPB, as revealed in our previous work.6 Specifically, when the VDF content decreases, a structural evolution from the trans-planar phase (all-trans conformation) to the 3/1-helical phase [(TG)3 or (TG̅ )3 conformation, T, trans; G, gauche] occurs. In the transition region between 49 mol % ⩽ VDF ⩽ 55 mol %, competing ferroelectric and relaxor properties6 occur simultaneously. This picture suggests that the phase boundary occurs within a single molecular chain6 (Figure 1a). However, it is still unclear whether the phase boundary can happen intermolecularly between polymer chains with distinct conformations (Figure 1b). To fundamentally answer this question, we choose copolymer/terpolymer blends as a platform. Ferroelectric copolymer P(VDF-TrFE) 65/35 mol % with a ground-state conformation of all trans and relaxor terpolymer P(VDF-TrFECFE) 61.5/30.3/8.2 mol % (CFE: chlorofluoroethylene) adopting a 3/1-helical conformation just like P(VDF-TrFE) relaxor compositions6 (VDF < 49 mol %) are selected. Given that both polymers do not cocrystallize,13 we can create a mixture of the trans-planar and 3/1-helical phases in polymer Received: February 6, 2019 Revised: March 17, 2019

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DOI: 10.1021/acs.jpcc.9b01220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. (a−i) Electric field induced strain in the blends with various compositions, measured by a 1 Hz triangular waveform of a bipolar electric field at room temperature. The blend corresponds to a mixture of ferroelectric copol-ymer P(VDF-TrFE) 65/35 mol % and relaxor terpolymer P(VDF-TrFE-CFE) 61.5/30.3/8.2 mol %. The dashed line in part i indicates the strain enhancement with increasing terpolymer content. Figure 1. Ball-and-stick model corresponding to MPB formation: (a) intramolecularly within a single molecular chain and (b) intermolecularly between mixed chains with the all-trans and 3/1 helical conformations. For simplicity, the model is illustrated using the structure of PVDF.

electric properties.1−5 Consequently, our finding suggests that MPB takes place via competition between the trans-planar and 3/1-helical configurations in single chains (Figure 1a). The strain-field responses at high fields provide further evidence of the absence of MPB in the blends (Figure 2i). It can be seen in Figure 2i that the strain-field curve in P(VDF-TrFE) is characterized by a typical butterfly characteristic of normal ferroeleciticy.14,15 With terpolymer faction increasing, the butterfly shape gradually smears out and finally evolves into a shape with nearly no peaks for the blend containing only P(VDF-TrFE-CFE) in which electrostriction plays a dominant role.17 In addition, as the fraction of terpolymer increases, the strain magnitude at 100 MV m−1 increases dramatically especially at high terpolymer factions (>50%). Such monotonic strain increase indicates no coupling between different chains with the trans-planar and 3/1-helical conformations in the blends, which adds more evidence of the absence of MPB in the blends. In addition, we find that the polarization−electric field hysteresis loops gradually evolve from normal ferroelectric with nonzero remnant polarization to relaxor with a slim shape as the terpolymer content increases (Figure S3), which is consistent with the strain evolution at 100 MV m−1 (Figure 2i). We further show that the change of terpolymer structure [i.e., P(VDF-TrFE-CTFE) 61.8/30.4/7.8 mol %, CTFE = chlorotrifluoroethylene] in the blends does not change the whole picture. The strain responses at both low (Figure 3a) and high fields (Figure 3b) both indicate the piezoelectric-toelectrostrictive evolution with the decrease of the terpolymer content. It is found that the critical terpolymer concentration for such evolution here is about 80%, which is slightly larger compared to the case (70%) with P(VDF-TrFE-CFE). Additionally, we have also studied other blends by changing the copolymer composition [i.e., P(VDF-TrFE) 55/45 mol %]. The results all show no evidence of MPB occurring in these blends. Consequently, the absence of phase boundary in a

blends, in which the fraction of the 3/1-helical phase can be tuned by simply changing the volume ratio between copolymer and terpolymer, i.e., Co/Ter. If the MPB comes from mixed chains of two competing conformations in P(VDF-TrFE), the blends here can provide nearly the same conditions as those anticipated in P(VDF-TrFE) near the MPB. Specifically, the increase of the terpolymer faction in polymer blends may correspond to the decrease of VDF content in P(VDF-TrFE). This platform can, therefore, help to identify the dominant mechanisms responsible for driving the MPB formation in P(VDF-TrFE)s. We first present our electric-field-induced strain data in the copolymer/terpolymer blends at a low field of 25 MV m−1 and a high field of 100 MV m−1, which are summarized in Figure 2a−i. It is shown that the strain response evolves from a linear curve (Co/Ter = 100/0; Figure 2a) to a parabolic type (Co/ Ter = 0/100; Figure 2h), as the terpolymer fraction increases. Typically, the changes in the field direction cause a strain sign change in a ferroelectric copolymer (i.e., Co/Ter = 100/0; Figure 2a) and the slope corresponds to the longitudinal piezoelectric coefficient d33 (refs 14. and 15). The quadratic behavior in Figure 2f−h is indicative of electrostriction, the sign of which does not depend on the field direction.16 We find that |d33| decreases continuously with the increase of terpolymer faction (Figure 2a−d), and there is a critical terpolymer content of 70% (Co/Ter = 30/70; Figure 2e) above which electrostriction becomes dominant. Typically, relaxors at small electric fields cannot have piezoelectricity because they are macroscopically paraelectric. In this case, they only exhibit electrostriction (Figure 2h). This evidence explicitly rules out the MPB formation in blends, the presence of which inherently results in significantly enhanced piezoB

DOI: 10.1021/acs.jpcc.9b01220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 4. Schematic of the 3/1-helical (a) and trans planar (b) conformations. The green arrows correspond to the projections of the −CF2 dipole directions on planes defined by the CF2 groups. The red arrows indicate the net polarization direction. The right panels are the side views of 3/1-helical and all-trans conformations where the yellow arrows indicate the directions of in-plane polarization.

very close to each other near MPB. The nearly vanishing barrier6 maximizes the flexibility of polarization rotation between the two phases and thus enhances the piezoelectric properties. The polarization is unlikely to rotate directly by 90° from Figure 4a to 4b. Instead, the polarization rotation is probably realized via successive local bond rotations. The detailed rotation path under electric field can be investigated via ab initio calculations20−22 and possibly diffraction refinements.

Figure 3. (a) Electric field induced strain in the blends with various compositions at (a) 25 MV m−1 and (b) 100 MV m−1. The blend corresponds to a mixture of ferroelectric copolymer P(VDF-TrFE) 65/35 mol % and relaxor terpolymer P(VDF-TrFE-CTFE) 61.8/ 30.4/7.8 mol %. The dashed line in part a indicates the piezoelectricto-electrostrictive evolution.

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simple chain mixture of different conformations suggests designing MPB on the intrachain scale. Finally, we address the general molecular route to possible MPB in piezoelectric polymers. To rapidly search for potential MPB polymers, we first require that a candidate polymer exhibits a rich crystalline phase diagram, as defined by its crystalline chain conformations.11,12 A rotation of covalent bonds could lead to interconversion between conformational isomers, which could generate two nearly energetically degenerate phases. In most cases, different crystalline phases correspond to different crystallographic structures in ferroelectric polymers,12 which naturally meets the requirement of symmetry breaking between different crystalline phases. Inspired by these considerations, we provide deeper insights into significantly enhanced piezoelectric responses observed at MPB in terms of the polarization rotation mechanism1−5 between the competing trans-planar and 3/1-helical phases. To give a more general picture from the single chain scale, here we consider a single PVDF chain containing separated 3/1-helical (Figure 4a) and trans-planar (Figure 4b) parts. For the case of P(VDF-TrFE), the substitution of some H atoms by some F atoms leading to different chain tacticity of P(VDF-TrFE)6 can be further included while the conformational disorder due to stereoirregularity of the −CHF− functional group can also be added.6,18,19 The 3/1-helical conformation possesses components of the dipole moment both parallel and perpendicular to the chain axis, and the net polarization direction is along the chain axis (Figure 4a). In contrast, the net polarization in the all-trans conformation is normal to the chain axis (Figure 4b). The chain consists of two segments with different polarization directions. The conformational evolution from the trans-planar to 3/1-helical type occurs in the same chain (Figure 1a), and the energies of the trans-planar and 3/1-helical segments are

CONCLUSIONS We show that MPB arises from conformational competition on a single molecular chain scale. A rather flat energy landscape between two nearly energetically degenerate crystalline phases enables easy rotation of polarization, which explains the remarkably enhanced piezoelectric properties near MPB.6 The basic principles uncovered in this work indicate that MPB may be a general phenomenon occurring for ferroelectric polymers with multiple single-chain crystalline conformations. We hope that our findings will accelerate the exploration of new MPB piezoelectric polymers for flexible, wearable, and biocompatible devices and applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b01220. Polymer synthesis and blend preparation, electromechanical characterization, and additional experimental data (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(Q.W.) E-mail: [email protected]. ORCID

Wenhan Xu: 0000-0002-4347-2601 J. Bernholc: 0000-0002-9981-8851 Qing Wang: 0000-0002-5968-3235 Notes

The authors declare no competing financial interest. C

DOI: 10.1021/acs.jpcc.9b01220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

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(21) Ranjan, V.; Yu, L.; Nardelli, M. B.; Bernholc, J. Phase equilibria in high energy density PVDF-based polymers. Phys. Rev. Lett. 2007, 99, 047801. (22) Bystrov, V. S.; Paramonova, E. V.; Bdikin, I. K.; Bystrova, A. V.; Pullar, R. C.; Kholkin, A. L. Molecular modeling of the piezoelectric effect in the ferroelectric polymer poly(vinylidene fluoride) (PVDF). J. Mol. Model. 2013, 19, 3591−3602.

ACKNOWLEDGMENTS We acknowledge the support of ONR (N000141612082 and N000141612459).

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DOI: 10.1021/acs.jpcc.9b01220 J. Phys. Chem. C XXXX, XXX, XXX−XXX