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Polymer 54 (2013) 1709e1728

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Polymer

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Feature article

Novel polymer ferroelectric behavior via crystal isomorphism and thenanoconfinement effect

Lianyun Yang a, Xinyu Li b, Elshad Allahyarov c,d,e, Philip L. Taylor c, Q.M. Zhang b,**, Lei Zhu a,*

aDepartment of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH 44106-7202, USAbDepartment of Electrical Engineering, Pennsylvania State University, University Park, PA 16802, USAcDepartment of Physics, Case Western Reserve University, Cleveland, OH 44106-7079, USAd Institut für Theoretische Physik, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germanye Theoretical Department, Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13/19, 117419 Moscow, Russia

a r t i c l e i n f o

Article history:Received 29 November 2012Received in revised form13 January 2013Accepted 19 January 2013Available online 4 February 2013

Keywords:Crystal isomorphismNanoconfinement effectRelaxor ferroelectric behavior

* Corresponding author. Tel.: þ1 216 368 5861.** Corresponding author. Tel.: þ1 814 863 8994.

E-mail addresses: qxz1@psu.edu (Q.M. Zhang), lxz

0032-3861 � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.polymer.2013.01.035

Open access under CC B

a b s t r a c t

In contrast to the comprehensive understanding of novel ferroelectric [i.e., relaxor ferroelectric (RFE) andantiferroelectric] behavior in ceramics, RFE and double-hysteresis-loop (DHL) behavior in crystallineferroelectric polymers have only been studied in the past fifteen years. A number of applications such aselectrostriction, electric energy storage, and electrocaloric cooling have been realized by utilizing thesenovel ferroelectric properties. Nonetheless, fundamental understanding behind these novel ferroelectricbehaviors is still missing for polymers. In this feature article, we intend to unravel the basic physics viasystematic studies of poly(vinylidene fluoride-co-trifluoroethylene) [P(VDF-TrFE)]-based terpolymers,electron-beam (e-beam) irradiated P(VDF-TrFE) copolymers, and PVDF graft copolymers. It is found thatboth the crystal internal structure and the crystaleamorphous interaction are important for achievingthe RFE and DHL behaviors. For the crystal internal structure effect, dipole switching with reducedfriction and nanodomain formation by pinning the polymer chains are essential, and they can be ach-ieved through crystal repeating-unit isomorphism (i.e., defect modification). Physical pinning [e.g., inP(VDF-TrFE)-based terpolymers] induces a reversible, electric field-induced RFE4FE phase transitionand thus the DHL behavior, whereas chemical pinning [e.g., in e-beam irradiated P(VDF-TrFE)] results inthe RFE behavior. Finally, the crystaleamorphous interaction (or the nanoconfinement effect) results ina competition between the polarization and depolarization local fields. When the depolarization fieldbecomes stronger than the polarization field, a DHL behavior is observed. Obviously, the physics forferroelectric polymers is different from that for ceramics/liquid crystals and can be largely attributed tothe long-chain nature of semicrystalline polymers. This understanding will help us to design new fer-roelectric polymers with improved properties and/or better applications.

� 2013 Elsevier Ltd. Open access under CC BY-NC-ND license.

1. Novel ferroelectric polymers with different nonlineardielectric properties

Different from ceramic ferroelectrics, ferroelectric (FE) polymersrepresent a unique class of functional insulating materials due totheir long-chain rather than ionic-crystal nature. The advantages ofeasy processing and low cost have made them attractive for a varietyof practical applications. By definition, ferroelectricity refers to bothstructure and property aspects. Structure-wise, ferroelectric mate-rials must possess polar structures with spontaneous polarization.Property-wise, ferroelectric materials exhibit broad hysteresis loops

121@case.edu (L. Zhu).

Y-NC-ND license.

due to the existence of large spontaneous polarization (Fig. 1A andE). Here, D, the electric displacement, is the total charge densityinduced by applying an electric field (E) on a dielectric material,and is defined as D ¼ εE. In this equation, ε is the permittivity and isdefined as ε ¼ εrε0, where εr is the relative permittivity (or dielectricconstant) and ε0 is the permittivity of the vacuum. For linear di-electrics, the εr is a constant. For nonlinear dielectrics, the εr isa function of the electric field. Generally speaking, the electricalrelationship between D and E is similar to the mechanical relation-ship between strain and stress, respectively. It is this normal fer-roelectricity that makes ferroelectric polymers attractive for manyapplications such as nonvolatile memory [1e6] and transducers insensors and actuators [7e12]. In the other extreme case, when noferroelectric domains exist [e.g., in nonpolar polyethylene/poly-propylene or when dipoles cancel each other out, as in even-

Fig. 1. Schematic hysteresis loops for (A) normal ferroelectric, (B) paraelectric or dipolar glass or relaxor ferroelectric, (C) antiferroelectric, and (D) dielectric materials. From (D) to(A) the dielectric nonlinearity gradually increases. The bottom panel illustrates the ferroelectric domain structures of (E) normal ferroelectric, (F) relaxor ferroelectric, (G) dipolarglass, and (H) dielectric polymers. From (H) to (E) the domain size gradually increases.

L. Yang et al. / Polymer 54 (2013) 1709e17281710

numbered nylons], the polymers display linear electric polarization(i.e., D is a linear function as E; see Fig. 1D and H) [13]. The origin ofthe dielectric behavior lies in a simple fact that only electronic andatomic polarizations, rather than dipolar orientational, ionic, andinterfacial polarizations, work in the dielectric materials. In betweenthese two extreme cases, paraelectricity refers to the ability of polarmaterials with permanent dipoles to become polarized under anelectric field, but upon removal of the applied field the polarizationquickly returns to zero (the loop is similar to Fig. 1B) [13,14]. Froma structure point of view, paraelectric (PE) polymers should containpermanent dipoles but without any ferroelectric domains at zeroelectric field (similar to the case of dielectrics in Fig. 1H).

Recently, novel ferroelectric behaviors have emerged for ferro-electric polymers and have become increasingly attractive for newapplications such as electrostriction [9,15e26], electric energy stor-age [13,27e40], and electrocaloric cooling [41e53]. These includenarrow single (Fig.1B) and double (Fig.1C) hysteresis loop behaviors.For ceramics, these ferroelectric behaviors are not new and havebeen relatively well-understood. For example, it is known thatdecreasing the ferroelectric domain size to accommodate a few di-poles [i.e., nanodomains in relaxor ferroelectrics (RFE)] or just onedipole (i.e., dipolar glasses) will significantly mitigate the coopera-tive coupling among ferroelectric domains, resulting in a reductionof the spontaneous polarization and thus narrow single hysteresisloops [54,55]. For antiferroelectric (AFE) ceramics, double-hystere-sis-loops (DHLs) are observed due to reversible AFE4FE transitionsas the applied electric field reverses direction [56]. Nonetheless,these novel RFE and AFE ferroelectric behaviors are still rare (e.g., theRFE phase) or nonexistent (e.g., the AFE phase) in crystalline poly-mers. This can be attributed to the long-chain nature of ferroelectriccrystalline polymers. For example, nanodomain formation in close-packed long-chain polymer crystals is more difficult to achievethan that in compositionally disordered perovskite (ABO3) crystalscomposed of different ions on crystallographically equivalent sites,because ferroelectricity is achieved by 180�-flipping of permanentdipoles in the main-chain of ferroelectric polymers whereas fer-roelectricity can be easily achieved by displacement of the center iontowards eight corners of the tetragonal crystal structure of ceramicferroelectrics. As a result, the RFE behavior has only been reported

for electron-beam (e-beam) or g-ray irradiated poly(vinylidenefluoride-co-trifluoroethylene) [P(VDF-TrFE)] [16,17,22,25,26,57] andP(VDF-TrFE)-based terpolymers [21,22,25,58e64]. The long-chainnature of polymer crystals also makes the occurrence of theAFE/FE transition difficult, if not impossible. For example, in even-numbered nylons the hydrogen-bonded amide dipoles are arrangedin an AFE-like structure with an alternating up and down dipolarconfiguration in a long chain due to the zig-zag conformation of thealkane spacers [65,66]. It is impossible for every other hydrogen-bonded amide dipole to flip 180� and form a polar arrangement ina close-packed crystal. Therefore, it is important to understand thefundamental physics behind these novel ferroelectric behaviors forsemicrystalline polymers.

Fundamentally, most ferroelectric polymers are semicrystalline(note that we will not focus on ferroelectric liquid crystalline poly-mers in this feature article). For example, typical crystallinity forPVDF and its copolymers with chlorotrifluoroethylene (CTFE) andhexafluoropropylene (HFP) are below 50 wt.% primarily because ofstructural defects such as head-to-head/tail-to-tail (HHTT) sequence(usually 3e6 mol% by conventional radical polymerization) and/orcomonomers in the main chain [67]. For P(VDF-TrFE) and poly(VDF-co-tetrafluoroethylene) [P(VDF-TFE)] random copolymers, repeat-ing-unit isomorphism [65,68] takes place, because TrFE and TFE aresimilar in both chemical structure and size as VDF. Consequently, thecrystallinity significantly increases to >80 wt.%. Sometimes, whenannealed in the PE phase, the crystallinity of P(VDF-TrFE) can reachnearly 100 wt.% [69e71]. For these semicrystalline polymers, it isunderstandable that their ferroelectric properties are intimatelydependent upon both the internal crystal structure and the crystaleamorphous interaction (or the nanoconfinement effect [72,73]).Generally speaking, the crystalline structure is a major factor thataffects the ferroelectric behavior of polymers, whereas the nano-confinement effect is a less important factor.

2. Effect of crystal isomorphism on novel ferroelectricbehaviors of P(VDF-TrFE)-based copolymers

Before discussing ferroelectric behavior in P(VDF-TrFE)-basedrandom copolymers, it is necessary for us to understand the

L. Yang et al. / Polymer 54 (2013) 1709e1728 1711

normal ferroelectric behavior in terms of close-packing (or the areapacking density in the ab-plane; note that the molecular chain di-rection is along the c-axis) in PVDF crystals. For a b PVDF crystal, theaverage area packing density in the ab-plane is 82.6%, significantlyhigher than that (70%) for a nonpolar polyethylene crystal. As a zig-zag PVDF stem (contains perpendicular dipoles) inside a ferro-electric domain flips (at every rotation step of ca. 60� [74,75]) inresponse to an alternating field, it must experience significantintermolecular friction from its neighbors.We consider that it is thestrong intermolecular friction and large spontaneous polarizationthat prevent the easy rotation of PVDF chains inside the close-packed crystal. To achieve easy rotation of zig-zag PVDF chains, itis highly desirable to reduce intermolecular friction (by expandingthe interchain distance) and to decrease spontaneous polarization(by reducing the ferroelectric domain size).

2.1. PE behavior in P(VDF-TrFE) random copolymers

As mentioned above, P(VDF-TrFE) random copolymers demon-strate type-2 repeating-unit isomorphism [7], because the twohomopolymers have different crystal structures (PVDF has fourorthorhombic crystal structures (see Fig. 4 in Ref. [13]) and PTrFEhas a hexagonal crystal structure [76]). Consequently, both theinterchain distance and overall crystallinity increase as comparedwith the homopolymers. For example, the (110/200) d-spacing(d110/200) is 4.42 �A for the low temperature FE phase in a P(VDF-TrFE) 50/50 (mol/mol) random copolymer, and it is larger thanthe d110/200 of 4.26 �A for the b PVDF crystal. However, the averagearea packing density in the ab-plane for the low temperature FEphase is 78.0%, not much lower than that (82.6%) for PVDF. There-fore, normal ferroelectric behavior with a broad hysteresis loop isstill observed for the low temperature FE phase, although switchingof zig-zag P(VDF-TrFE) chains becomes easier. The d110/200 for thehigh-temperature PE phase of P(VDF-TrFE) 50/50 increases to4.86 �A, and the average area packing density in the ab-plane de-creases to ca. 70%, significantly lower than those for both b PVDFand low temperature FE P(VDF-TrFE) crystals. As a result, the dipoleand chain flipping become much easier for the high-temperaturePE phase of P(VDF-TrFE). This is exactly observed in a DeE loopstudy in a recent report (see Fig. 2) [77]. At 100 �C [above the Curietemperature (TC) at 64 �C], narrow single loops with minimumhysteresis are observed for the high-temperature PE phase ata poling frequency of 1000 Hz (Fig. 2D). This is drastically differentfrom the open loops observed for the low temperature FE phase ata poling frequency of 1000 Hz at 25 �C (Fig. 2A).

Moreover, the ferroelectric behavior of the high-temperature PEphase is dependent upon poling frequency (as is the low temper-ature FE phase). The hysteresis loops gradually open up as thepoling frequency decreases from1000 Hz to 1 Hz (Fig. 2DeF). This issomewhat inconsistent with the definition of the PE phase; how-ever, it can be explained by the schematic illustration in Fig. 2G.Below the TC, large ferroelectric domains having a large sponta-neous polarization exist in the sample (Fig. 2G a). Above the TC,these ferroelectric domains completely disappear with randomlymixed TG (T is trans and G is gauche) and TTTG conformations inP(VDF-TrFE) chains (Fig. 2G b). However, applying a high enoughelectric field will induce both nucleation and growth of ferroelectricdomains (Fig. 2G cee). This is confirmed by the field-dependentFourier transform infrared (FTIR) results in Fig. 2H. Below the TC,the long T sequence in the FE phase is evidenced by the absorptionpeak at 507 cm�1. Above the TC, the mixed TG and TTTG con-formation in the PE phase is evidenced by a broadband at 514 cm�1.Upon application of an electric field of 50 MV/m, a shoulder startsto appear at 507 cm�1, suggesting the nucleation and growth offerroelectric domains with a long T sequence in the chain. On

further increasing the electric field to 125 MV/m, the 507 and514 cm�1 bands merge into one centered at 510 cm�1. As shown inFig. 2G, the high-frequency poling induces nucleation of nanosizedferroelectric domains (nanodomains) within the weakly interactiveparaelectric matrix (Fig. 2G e). Consequently, narrow single hys-teresis loops with minimal spontaneous (or remanent) polarizationare achieved. Upon decreasing the poling frequency to 1 Hz,nanodomains grow into relatively large ones (Fig. 2G d and c), andthus open ferroelectric loops with relatively large spontaneous (orremanent) polarization are observed.

Frequency-dependent dipole switching is also reflected in thebroadband dielectric spectroscopy (BDS) results for a uniaxiallystretched P(VDF-TrFE) 50/50 film during the first and second heatingcycles under different frequencies (Fig. 3). During the first heatingcycle (Fig. 3A and B), the glass transition temperature (Tg) is observedaround �20 �C at 1 Hz and it increases with increasing poling fre-quency. Meanwhile, a broad Curie transition is observed for 1 Hz,starting around 35 �C and showing a relatively sharp peak at 80 �C.This result corresponds well with the differential scanning calo-rimetry (DSC) result in Fig. 3H, where two Curie transitions are seenat 50 and 80 �C, respectively. After heating to 100 �C and cooling backto �50 �C, the history of mechanical stretching on the Curie transi-tion is removed. Subsequent BDS results during the second heatingcycle are shown in Fig. 3C and D. In addition to the frequency-dependent glass transition peak, a relatively sharp Curie transitionpeak is observed at 65 �C for 1 Hz and it gradually broadens andshifts to higher temperatures upon increasing the poling frequency.Comparing the BDS results during the first and second heating cy-cles, we infer that the TC must be domain size dependent. On onehand, uniaxial stretching enhances the crystal orientation withenlarged domain size in some P(VDF-TrFE) crystallites, becausea higher TC is observed at 80 �C relative to 64 �C seen during thesecond heating (see Fig. 3H). On the other hand, some crystallites aretorn apartwith a decreased domain size, and thus the TC decreases to50 �C correspondingly. A similar domain size dependence for TC hasalso been reported in the literature [67,71,78]. Namely, large domainsresulted in a higher TC and small domains resulted in a lower TC. Theactivation energies (Ea) for both amorphous (from the glass transi-tion in Fig. 3D) and crystalline (from the Curie transition in Fig. 3C)dipole relaxations can be obtained from Arrhenius plots of log(peakfrequency) versus 1/T (see Fig. 3E). From the linear regionswhere theArrhenius equation applies, the activation energies for the amor-phous and crystalline dipoles are found to be 0.57 and 7.4 eV,respectively. Obviously, it is muchmore difficult to switch crystallinedipoles than amorphous ones for semicrystalline ferroelectric poly-mers. The nonlinear part for the amorphous dipoles in Fig. 3E can beexplained by the reduced mobility near Tg (i.e., the WLF equationapplies instead), whereas the high-frequency nonlinearity for thecrystalline dipoles may be attributed to the fact that crystalline di-poles cannot follow the electric field at such high frequencies.

From Fig. 3AeD, upturns in both εr0 and εr

00 are observed athigh temperatures (>80 �C) and low frequencies. These εr

0 and εr00

upturns can be explained by enhanced loss from impurity ions inthe sample (i.e., from suspension polymerization) as temperatureand poling time increase, since the slope in the double-log plot ofthe εr

00 at low frequencies is nearly �1 [79]. In a recent report, wedemonstrate that a parts-per-million (ppm) or even sub-ppm levelof impurity ions in PVDF can cause significant increases in bothεr

0 and εr00 [80]. Evidence of impurity ion relaxation is demon-

strated in εr0 and εr

00 as a function of frequency at different tem-peratures (see Fig. 3F and G). At low temperatures, there is noupturn in εr

0 and only a weak peak in εr00 at low frequencies. On

increasing temperature, theweak peak in εr00 gradually increases its

intensity and shifts to higher frequencies. Finally, above 75 �C thelow-frequency loss in εr

00 becomes so large that an increase in εr0 is

Fig. 2. Bipolar hysteresis DeE loops for a uniaxially stretched P(VDF-TrFE) 50/50 film (draw ratio ¼ 300%) in the PE and FE phases at 100 and 25 �C, respectively: (A and D) 1000 Hz,(B and E) 10 Hz, and (C and F) 1 Hz. The poling field (a sinusoidal waveform) starts at 25 MV/m and increases at increments of 25 MV/m. (G) Schematic illustration of theferroelectric-to-paraelectric Curie phase transition and electric field-induced ferroelectric domain nucleation/growth and corresponding ferroelectric behaviors in the paraelectricphase. Dark blue arrows represent large dipoles in the zig-zag stems in the ferroelectric crystal (light blue rectangle) or domains (light blue ovals). Orange double arrows representweak dipoles in the paraelectric crystal (light green rectangles). (H) FTIR spectra of ferroelectric and paraelectric P(VDF-TrFE) 50/50 under different electric fields at 24 and 100 �C,respectively. (Reproduced and adapted with permission from Ref. [77].)

L. Yang et al. / Polymer 54 (2013) 1709e17281712

also observed. Meanwhile, a broad dipole relaxation is seen at highfrequencies and the peak gradually shifts to higher frequencieswith increasing temperature. From the plot of log(peak frequency)versus 1/T obtained from εr

00 in Fig. 3G (data not shown), an Ea of ca.0.3 eV is determined for the dipoles, which is similar to the value of0.57 eV obtained for amorphous dipoles in Fig. 3E. Therefore, thehigh-frequency relaxation should be attributed to amorphousdipoles.

2.2. DHL behavior in P(VDF-TrFE)-based terpolymers

On the basis of the high-temperature PE behavior of P(VDF-TrFE), we have learned that expanded interchain distance andnanodomains with reduced spontaneous polarization are critical toreduce intermolecular friction and speed up dipole flipping in fer-roelectric crystals. This knowledge is helpful for the design and

development of novel ferroelectric polymers. To further expand theinterchain distance, an even larger comonomer than TrFE needs tobe incorporated into the P(VDF-TrFE) random copolymers. Possiblecandidates are vinyl chloride (VC), 1,1-chlorofluoroethylene (CFE),chlorodifluoroethylene (CDFE), chlorotrifluoroethylene (CTFE), andhexafluoropropylene (HFP) [58]. Intriguingly, direct copoly-merization of VDF with these comonomers most likely will notresult in the formation of repeating-unit isomorphism because oftheir large sizes. For example, CTFE repeating units are mostlyexcluded from the PVDF crystals in P(VDF-CTFE) and no expansionof the interchain distance is observed experimentally [27,73].Therefore, presence of TrFE in PVDF is important for the thirdcomonomer to be incorporated in the crystal and further expandthe interchain distance.

In this study, we use a P(VDF-TrFE-CFE) 59.2/33.6/7.2 terpol-ymer as an example to study the ferroelectric behavior after further

Fig. 3. Broadband dielectric spectroscopy results for a uniaxially stretched P(VDF-TrFE) 50/50 film (draw ratio ¼ 300%) during (A and B) the first and (C and D) the second heatingcycles, respectively. (A and C) and (B and D) show the real ðεr 0Þ and imaginary ðεr 00Þ relative permittivity as a function of temperature at various frequencies. (E) Arrhenius plots (log fversus 1/T) for amorphous and crystalline dipoles. (F and G) εr 0 and εr

00 as a function of frequency at different temperatures. (H) DSC first heating, first cooling, and second heatingcurves for the uniaxially stretched P(VDF-TrFE) 50/50 film.

L. Yang et al. / Polymer 54 (2013) 1709e1728 1713

enlarging the interchain distance. At this CFE composition (7.2 mol%), the low temperature FE phase has been successfully convertedinto an RFE phase [60]. A hot-pressed film of this terpolymer isuniaxially stretched in the RFE phase at 10 �C to a draw ratio of400%. Upon mechanical stretching, a certain amount of FE phase isdeveloped, and this is reflected in the first heating curve in DSC(Fig. 4) and the two-dimensional (2D) wide-angle X-ray diffraction(WAXD) pattern in Fig. 5A. Note that the existence of an FE phase inultrathin P(VDF-TrFE-CFE) LangmuireBlodgett (LB) films is alsoreported previously [81]. From Fig. 4, two TCs are observed witha weak peak at 27 �C and another peak at 49 �C. After melt-recrystallization, only one broad TC is seen at 22 �C for the secondheating (Fig. 4). The TC at 49 �C can be attributed to the Curie

-50 -25 0 25 50 75 100 125 150-2

0

2

4

6

15°C

27°C 49°C

97°C

123°C

Hea

t flo

w (W

/g)

Temperature (°C)

1st heating 1st cooling 2nd heating

exo

22°C

P(VDF-TrFE-CFE) 59.2/33.6/7.2

Fig. 4. DSC first heating, first cooling and second heating curves for a uniaxiallystretched P(VDF-TrFE-CFE) 59.2/33.6/7.2 terpolymer film. The stretching is performedat 10 �C and the draw ratio is 400% with a drawing rate of 12 mm/min. The heating andcooling rates are 10 �C/min.

transition for the stretch-induced FE phase and the low tempera-ture TC is attributed to the Curie transition for the RFE phase. Notethat mechanical stretching results in a larger ferroelectric domainsize and thus a slightly higher TC at 27 �C for the terpolymer.

Crystal orientations in the uniaxially stretched P(VDF-TrFE-CFE) terpolymer film during the first and second heating cyclesare shown in Fig. 5. From the 2D WAXD pattern in Fig. 5A, both(110/200) reflections from the stretch-induced FE and RFE phasesare seen on the equator and the (001)FE and (002)RFE reflectionsare seen on the meridian. The corresponding one-dimensional(1D) WAXD profiles on both equator and meridian during thefirst heating cycle are shown in Fig. 5C. At �38 �C, the (110/200)RFE reflection is seen at 4.81 �A, which is similar to the (110/200)PE reflection (4.86�A) of the P(VDF-TrFE) 50/50 [77]. The (110/200)FE reflection appears as a shoulder at 4.57 �A. As the temper-ature increases to 47 �C, both (110/200)FE and (001)FE reflectionsdisappear, which corresponds to the DSC results in Fig. 4. The(110/200)RFE reflection continuously shifts to lower q values andfinally the (110/200)PE d-spacing increases to 4.98�A at 90 �C. Afterthe first heating cycle, the stretch-induced FE phase disappearsand 1DWAXD profiles during the second heating cycle are shownin Fig. 5D. Upon increasing the temperature, the (110/200)reflection continuously shifts to lower q values, and correspond-ingly the d-spacing increases from 4.84 �A at �38 �C to 4.98 �A at90 �C. Regardless of the (110/200) d-spacing changes, the (002)reflection remains constant at 27.4 nm�1 (d-spacing of 2.29 �A). Incontrast with the DSC study, there is no obvious transition for the(110/200) [and the (002)] reflections during the RFE/PE Curietransition in the second heating cycle (see Fig. S1A in the Sup-plementary material). We consider that the heating rate of 10 �C/min is so fast that the transition cannot be observable in X-raydiffraction.

In addition to DSC and WAXD, FTIR is another useful techniqueto detect chain conformation changes for semicrystalline polymers.The FTIR results for the uniaxially stretched P(VDF-TrFE-CFE) ter-polymer film during the first and second stepwise heating cyclesare shown in Fig. 6. From the first heating cycle (Fig. 6A), the long Tsequence for the stretch-induced FE phase is evidenced by ab-sorption bands at 507, 848, and 1287 cm�1 [82,83]. Note that all

Fig. 5. 2DWAXD patterns of (A) as-stretched and (B) 90 �C-annealed uniaxially stretched P(VDF-TrFE-CFE) terpolymer films (draw ratio¼ 300%). The bottom panel shows 1DWAXDprofiles for the equator and meridian reflections during (C) the first and (D) the second heating cycles. The heating rate is 10 �C/min and each curve is 5 �C apart with the lasttemperature being 90 �C. The inner two weak and diffuse rings belong to the Kapton� tapes used to encapsulate the sample.

Fig. 6. FTIR spectra for the uniaxially stretched P(VDF-TrFE-CFE) terpolymer film during (A) the first and (B) the second heating cycles. The spectra are collected during a stepwiseheating process with steps of 5 �C. All curves are overlaid for clarity.

L. Yang et al. / Polymer 54 (2013) 1709e17281714

Fig. 7. (A and C) Real ðεr 0Þ and (B and D) imaginary ðεr 00Þ relative permittivity as a function of temperature under different frequencies for the uniaxially stretched P(VDF-TrFE-CFE)terpolymer film during (A and B) the first and (C and D) the second heating cycles. (E and G) εr 0 and (F and H) εr 00 as a function of frequency at different temperatures for theuniaxially stretched P(VDF-TrFE-CFE) terpolymer film during (E and F) the first and (G and H) the second stepwise heating cycles.

L. Yang et al. / Polymer 54 (2013) 1709e1728 1715

trans conformation can be obtained for the P(VDF-TrFE-CFE) ter-polymers due to the presence of VDF to relieve the steric hindrancecaused by the large Cl atoms in the CFE units. Upon increasing thetemperature to 45 �C, the band at 507 cm�1 (the second dashed linefrom the right) gradually disappears and a new doublet band at514/527 cm�1 appears, indicating the FE/PE transition. The bandat 848 cm�1 decreases its intensity and the band at 1287 cm�1

disappears. Meanwhile, another doublet band at 605/614 cm�1

becomes more pronounced. Note that the absorption bands at 514/527 and 605/614 cm�1 can be assigned to mixed TG and TTTGconformations [67]. After cooling from 90 to �40 �C (Fig. 6B), thestretch-induced FE phase disappears, because the bands at 507,848, and 1287 cm�1 become weaker and the bands at 514/527 and605/614 cm�1 become stronger. Intriguingly, two bands at 772 and

Fig. 8. Bipolar hysteresis loops for the uniaxially stretched P(VDF-TrFE-CFE) terpolymer fi

respectively. The poling frequency is 10 Hz. Bipolar hysteresis loops under different frequencfield (triangular waveform) starts at 25 MV/m with a stepwise increase of 25 MV/m except

800 cm�1 become much more pronounced, and they are assignedto the T3G sequence for the g PVDF crystal [84]. Therefore, a short Tsequence (i.e., nanodomains) is resulted for the RFE P(VDF-TrFE-CFE). This is possibly attributed to the random sequence of CFEalong the chain [i.e., 14 repeating units of VDF/TrFE per CFE unit].During the second heating cycle (Fig. 6B), although there is noobvious change for bands at 514/527, 605/616, and 848 cm�1 in thevicinity of the RFE/PE transition at 22 �C, the bands at 772 and800 cm�1 clearly decrease their intensities. This indicates the dis-appearance of nanodomains with a short T3G sequence above theTC at 22 �C.

The dynamic dielectric properties of the uniaxially stretchedP(VDF-TrFE-CFE) terpolymer film during the first and secondheating cycles are studied by BDS. As shown in Fig. 7, both the glass

lm (draw ratio ¼ 300%) at (A) �25 �C, (B) 0 �C, (C) 25 �C, (D) 50 �C, and (E) 65 �C,ies at 25 �C are also shown: (F) 1000 Hz, (G) 100 Hz, (C) 10 Hz, and (H) 1 Hz. All polingfor those at 1000 Hz.

L. Yang et al. / Polymer 54 (2013) 1709e17281716

and Curie transitions for the amorphous and crystalline dipoles areseen during heating for εr

0 and εr00 as a function of temperature.

For example, during the first heating cycle, the Tg and TC areobserved at �11 and 39 �C (10 Hz), respectively, and they graduallyincrease with increasing the frequency (Fig. 7B). During the secondheating cycle (note that the FE phase is eliminated after the firstheating to 90 �C), the Tg and TC are seen at �17 and 12 �C (10 Hz),respectively, and both values increase with increasing the fre-quency (Fig. 7D). The high TC at 39 �C during the first heating isattributed to the stretch-induced FE phase, whereas the low TC at12 �C during the second heating is attributed to the RFE phase. FromFig. 7B and D, we can see that the frequency dependence(Ea ¼ 0.6 eV) of the Tg is stronger than that (Ea ¼ 6.7 eV) for the TC,indicating again that amorphous dipoles are easier to switch thancrystalline dipoles at low electric fields. The high-temperature(>50 �C) and low-frequency (<1 kHz) upturns in the εr

00 in Fig. 7Band D are attributed to the impurity ion relaxation, as revealed bythe frequency scans for the first and second heating cycles (Fig. 7EeH). In Fig. 7E and G, upturns in the εr

0 are observed at low

Fig. 9. Bipolar hysteresis loops for the 70 �C-annealed uniaxially stretched P(VDF-TrFE-CFE) tThe poling frequency varies from left to right: (A, E, I, M) 1000 Hz, (B, F, J, N) 100 Hz, (C, Gbreakdown and thus no results for 1 Hz bipolar poling are obtained. All poling field (trian1000 Hz.

frequencies (<1 Hz) and high temperatures (>50 �C). Meanwhile,in Fig. 7F and H upturns in the εr

00 in the double-log plot showa slope of ca. �1, clearly indicating the loss from impurity ions[79,80,85]. At high frequencies, a decrease in the εr

0 and a broadpeak in the εr

00 can be attributed to the relaxation of amorphousdipoles. At intermediate frequencies, plateaus in the εr

0 areobserved in Fig. 7E and G. For the first heating, the maximum valuein the plateau εr

0 is observed for 50 �C, whereas during the secondheating it is observed for 25 �C. This is because the TC is 49 �C for thestretch-induced FE phase during the first heating and the TC is 22 �Cfor the RFE phase during the second heating.

Ferroelectric behavior of the uniaxially stretched P(VDF-TrFE-CFE) terpolymer film is studied by DeE hysteresis loop tests. Typ-ical hysteresis loops at different temperatures are shown inFig. 8AeE. Below the TC (49 �C) of the stretch-induced FE phase,open loops with a sense of double hysteresis are observedwhen thepoling field is above 75 MV/m. At 50 �C, the RFE phase has alreadytransformed into a PE phase and the stretch-induced FE phasegradually disappears. As a result, slim loops with a weak sense of

erpolymer film at (AeD) �25 �C, (EeG) 0 �C, (IeL) 25 �C, and (MeO) 50 �C, respectively., K, O) 10 Hz, and (D, H, L) 1 Hz. Note that at 50 �C, the 70 �C-annealed film is easy togular waveform) starts at 25 MV/m with increments of 25 MV/m except for those at

L. Yang et al. / Polymer 54 (2013) 1709e1728 1717

double hysteresis are observed above 75 MV/m, similar to thehysteresis loops for P(VDF-TrFE) at 100 �C (see Fig. 1E). When thetemperature increases to 65 �C, the center portions of the hysteresisloops gradually open up with an ellipsoidal shape. This can beattributed to the enhanced impurity ion loss and electronic con-duction at elevated temperatures, consistent with the BDS resultsin Fig. 7EeF [80,85]. Frequency-dependent hysteresis loops for theuniaxially stretched P(VDF-TrFE-CFE) at 25 �C are shown in Fig. 8Cand FeH. Upon increasing the poling frequency to 1000 Hz, themaximum D (Dmax) decreases and loops display more double hys-teresis. However, broad loops are still observed because the samplecontains certain FE phase.

After annealing the uniaxially stretched P(VDF-TrFE-CFE) ter-polymer film at 70 �C for 1 h, the stretch-induced FE phase disap-pears and the sample contains 100% RFE phase. Temperature-dependent hysteresis loops at various poling frequencies are shownin Fig. 9. At �25 �C, double loops with significant hysteresis andremanent polarization are observed upon decreasing the polingfrequency to below 100 Hz. At 1000 Hz, the crystalline dipolescannot follow the electric field and less hysteresis is seen. The largehysteresis can be attributed to the larger domain size in the RFEphase when the temperature is sufficiently low. When increasingthe temperature to 0 and 25 �C, the hysteresis in the DeE loopscontinuously decreases due to a continuous decrease in the domainsize and an increase in the interchain distance. At 25 �C, a signifi-cant amount of RFE phase should transform into the PE phase.Therefore, the remanent polarization reduces to nearly zero andtypical DHLs are observed. The double hysteresis should be causedby the electric field-induced (RFE/PE)/FE phase transition uponpoling and the FE/(RFE/PE) phase transition upon removing thefield, because the FE phase is observed after mechanical stretching.Currently, we do not have unambiguous evidence of the FE phaseduring the in-situ electric poling process. In the future, we will usetime-resolved polarized FTIR [86] to investigate dipole flipping andphase transitions in uniaxially stretched P(VDF-TrFE-CFE) terpol-ymer films. At 50 �C (above the TC at 22 �C), the sample becomes100% PE phase. As a result, narrow hysteresis loops are observed at

Fig. 10. Schematic representations of physical (temporary) and chemical (permanent) pinniand e-beam crosslinked P(VDF-TrFE) copolymers. l1, l2, and l3 are average interchain distancerespectively. The orange-red and blue ovals with arrows in them represent dipolar TrFE and tinside the crystal.

1000 Hz, similar to the DeE loops at 1000 Hz for the P(VDF-TrFE)film in the PE phase (see Fig. 2D). Upon decreasing the frequency,a sense of double hysteresis is observed at high fields. This againcan be attributed to some FE domain formation within the PEmatrix at high enough electric poling fields.

After annealing the uniaxially stretched P(VDF-TrFE-CFE) film inthe PE phase at 70 �C, the overall crystallinity increases and the filmappears to be much more brittle. As a result, the film quality de-creases, resulting in a significant reduction in breakdown strength.Therefore, it is difficult to obtain a full set of DeE loops at 1 Hzpoling frequency at 70 �C.

The physical origin for the DHLs observed for P(VDF-TrFE-CFE)terpolymers is explained in the top panel of Fig. 10. In the firststep, pre-expansion of the interchain distance in PVDF crystals byTrFE via repeating-unit isomorphism is important, namely, l2 > l1where l1 and l2 are interchain distances in PVDF and P(VDF-TrFE)crystals, respectively. This first step expansion of interchain dis-tance makes it possible to further incorporate the even larger thirdcomonomer, such as VC, CFE, CDFE, and CTFE, into the isomorphiccrystalline structure. A good example for this effect is to compareP(VDF-CTFE) with P(VDF-TrFE-CTFE). For P(VDF-CTFE), the CTFErepeating units are too large to be effectively incorporated ina PVDF crystal. As a result, most CTFE units are repelled from thePVDF crystal and no RFE behavior can be observed in P(VDF-CTFE)[27,73]. However, CTFE can be effectively incorporated intoa P(VDF-TrFE) crystal, leading to an RFE behavior [58,87]. Theincorporation of the even larger third comonomer further expandsthe interchain distance, namely, l3 > l2, where l3 is the interchaindistance of the terpolymer crystal. Note that HFP cannot be effec-tively incorporated into P(VDF-TrFE) to form the RFE phase becausethe HFP unit is too large [88]. Meanwhile, these larger comonomerscan effectively pin the P(VDF-TrFE) chains, if they are randomlydistributed along the chain. For example, in the P(VDF-TrFE-CFE)59.2/33.6/7.2 terpolymer, on average two neighboring CFE unitscan pin about 14 VDF/TrFE repeating units. This pinning will allowthe in-between P(VDF-TrFE) chains to rotate more freely because ofthe increased interchain distance. However, these CFE units can

ng in laterally expanded P(VDF-TrFE) crystals, namely, P(VDF-TrFE)-based terpolymerss in PVDF, P(VDF-TrFE), and P(VDF-TrFE)-based terpolymers or e-beamed P(VDF-TrFE),he third comonomer with larger sizes. The green bars represent the chemical crosslinks

L. Yang et al. / Polymer 54 (2013) 1709e17281718

only provide temporary physical pinning. When the poling elec-trical field becomes high enough, dipoles start to switch becausethe CFE unit also has a dipole moment. Consequently, the highelectric field will generate FE domains within the RFE matrix.However, these FE domains should beweaker than those formed bymechanical stretching because they can transform back to the RFEphase after a decrease in the poling field. We speculate that theelectric field-induced FE domains in the terpolymer may be justlarge enough so that significant hysteresis is observed duringRFE4FE transitions.

2.3. Narrow single hysteresis loop behavior in e-beam irradiatedP(VDF-TrFE) copolymers

From the above discussion, it would be better to permanentlypin P(VDF-TrFE) chains in the crystal in order to avoid hysteresisduring the RFE4FE transitions. One effective way is to chemicallycrosslink the P(VDF-TrFE) crystal with an optimized crosslinkingdensity (see the bottom panel in Fig. 10). Nonetheless, effectiveways to crosslink polymer crystals via chemical reactions have notyet been possible because polymer crystals, being of greater densitythan the amorphous phase, do not allow penetration of cross-linking agents such as molecular radicals into them. Instead, ion-izing radiation, such as e-beam [16,89,90], g-ray [91,92], and protonradiation [23,93e95], have been used to crosslink PVDF and PVDF-based copolymer crystals. Intriguingly, only P(VDF-TrFE) crystalsare found to be susceptible to ionizing radiation, and in this case theinterchain distance gradually increases with increasing irradiationdose. PVDF and other PVDF-based copolymer crystals do not showsimilar changes in the crystalline phase upon ionizing irradiation[89,90]. This must be attributed to the special reactivity of TrFE toionizing irradiation. For example, upon e-beam irradiation the TrFEunits can transform into >CHeCF3 groups, as evidenced by high-temperature (170 �C) solid-state 19F NMR [96,97], although thedetailed transformation mechanism is still unclear. Note that thetemperature for the solid-state NMR study has to be above the Tm ofP(VDF-TrFE) crystals. Otherwise, the 19F signals inside the crystalscannot be obtained due to the lowmobility of the crystalline nuclei.Therefore, it is fairly difficult to determine explicitly what hashappened inside P(VDF-TrFE) crystals after ionizing radiation.However, we consider that the P(VDF-TrFE) crystals must beinternally crosslinked. These internal chemical crosslinks not onlyexpand the interchain distance, but also permanently pin theP(VDF-TrFE) chains in between. As a result, easy dipole rotation,nanodomains and thus narrow hysteresis loops will be achieved.

In this study, a hot-pressed P(VDF-TrFE) 50/50 film (ca. 60e80 mm) is uniaxially stretched to a draw ratio of 400% at a draw

Fig. 11. DSC thermograms of the e-beam irradiated uniaxially stretched P(VDF-TrFE) 50/540 Mrad, and (C) 60 Mrad. The heating and cooling rates are 10 �C/min.

rate of 12 mm/min at room temperature. Afterwards, the film isannealed in the PE phase at 100 �C for 2 h to achieve a high crys-tallinity of >85 wt.% (determined by WAXD and DSC), followingprevious efforts to achieve single crystal-like P(VDF-TrFE) crystals[69]. The final film thickness is about 20e23 mm. The uniaxiallystretchedP(VDF-TrFE) 50/50film is then subjected tohigh-energye-beam irradiation at 70 �C for 20, 40, and 60Mrad at a dose rate of ca.1 Mrad/min. The DSC results for these e-beam irradiated P(VDF-TrFE) 50/50 samples are shown in Fig. 11. After e-beam irradiationat 20Mrad (Fig.11A), both TC (47 �C,weak and broad) and Tm (143 �C,sharp) decrease as compared to the TC (64 �C) and Tm (157 �C) for thepristine P(VDF-TrFE) 50/50 copolymer (see Fig. 3H). The reduced TCmay be attributed to reduced ferroelectric domain size after e-beamirradiation. However, the reduction inTm (14 �C) ismuch larger thanthat (4.1 �C) for a biaxially oriented PVDF film (12 mm thick) that hasbeen e-beam irradiated at 105 �C for 20 Mrad (see Fig. S2 in theSupplementary material and Ref. [90]). For the biaxially orientedPVDF film, the slight decrease in Tm is attributed to the reducedlateral crystallite size but not necessarily to the crystalline lamellarthickness decrease because the lamellar thickness (10e20 nm) isless susceptible to e-beam irradiation than the lateral size. Weconsider that e-beam irradiation causes permanent changes in theP(VDF-TrFE) crystal, converting the TrFE units into chemical cross-links. These structural defects substantially decrease the Tm after e-beam irradiation for P(VDF-TrFE). Upon melt-recrystallization, theTC for the e-beam irradiated P(VDF-TrFE) 50/50 at 20Mrad becomesmore obvious at 55 �C, which is slightly increased as comparedwiththe TC at 47 �C for the as-irradiated sample. This can be explained byan increase in the ferroelectric domain size after exclusion ofcrosslinked defects from the crystal through melt-recrystallization.Meanwhile, the lamellar thickness may decrease due to crosslinks,and the Tm therefore decreases to 139 �C. Upon increasing the ra-diation dose to 40 and 60 Mrad, respectively, the TC disappearsduring the first heating (Fig. 11B and C), consistent with previousresults [17,98]. The reason for the disappearance of TC for theseirradiated samples may be attributed to the second-order phasetransition, and this will be discussed later. Meanwhile, the Tmvaluescontinuously decrease significantly. For example, at 40 Mrad the Tmis 129 �C (a 28 �C decrease), and at 60 Mrad the Tm is 116 �C (a 41 �Cdecrease). After melt-recrystallization, obvious but broad Curietransitions reappear, and the TC values decrease with increasing thee-beam dose; 45 �C for the 40 Mrad dosed sample and 41 �C for the60 Mrad dosed sample.

From previous work on e-beam irradiated P(VDF-TrFE) [16,17], itis known that the disappearance of TC after e-beam irradiationabove 40 Mrad at 70 �C can be attributed to the formation of theRFE phase. However, the structure of the RFE phase in e-beam

0 during the first heating, first cooling, and second heating cycles: (A) 20 Mrad, (B)

L. Yang et al. / Polymer 54 (2013) 1709e1728 1719

irradiated P(VDF-TrFE) is still not well-understood. From the abovethree e-beam irradiated samples, the 20 Mrad sample still possessan FE phase, and its electrical property is typically ferroelectric atroom temperature (see Fig. S3 in the Supplementary material).Meanwhile, we observe that the ferroelectric properties of the 40and 60Mrad samples are quite similar (see Fig. S4 in the Supportingmaterial for the ferroelectric properties of the 40 Mrad sample).Therefore, we use the 60 Mrad sample for investigation by WAXD.Fig. 12A shows the 2D WAXD pattern for the e-beam irradiated(60 Mrad) uniaxially stretched P(VDF-TrFE) 50/50 film. The sharp(110/200)RFE reflection is seen on the equator and the broad(002)RFE reflection is on the meridian, indicating long-range orderin the lateral direction and disorder along the chain direction(similar to the arrangement of the rotator phases in oligo-alkanesand polyethylene at high pressures [99]). The d-spacing of the(110/200) reflection is 4.80 �A at �38 �C and it continuously in-creases with increasing temperature (Fig. 12C), whereas the (002)reflection keeps constant at 2.3�A.When the temperature is at 123e128 �C, the (110/200) d-spacing increases to 5.0 �A. During the first

Fig. 12. 2D WAXD patterns of (A) as-irradiated (60 Mrad) and (B) melt-recrystallized P(VDuniaxially stretching to a 400% draw ratio followed by annealing at 100 �C for 2 h. The bottomfirst and (D) the second heating cycles. The heating rate is 10 �C/min and each curve is 5 �C athe Kapton� tape used to encapsulate the sample.

heating process, again there is no obvious first-order transitionobserved in the WAXD profiles in Fig. 12C (also see Fig. S1B in theSupplementary material). After heating to 150 �C, the (110/200)reflection on the equator completely disappears, leaving an iso-tropic amorphous halo centered at 5.3 �A. Intriguingly, the (002)reflection on the meridian does not disappear, but transforms intoa weak halo centered at 2.3 �A (see Fig. S5 in the Supplementarymaterial). We consider that the chain orientation in the moltenstate does not completely disappear but is somewhat “locked in” bye-beam crosslinking. This result also indirectly proves that theP(VDF-TrFE) crystals are crosslinked by e-beam irradiation. Theweak halo at 2.3 �A should represent the average spacing along the“frozen” chain direction with random T and G conformations. Aftermelt-recrystallization, the 2D WAXD pattern is shown in Fig. 12B.The overall crystallinity (determined by DSC) for the recrystallizedsample substantially decreases to 38 wt.% due to the crosslinking,as compared to 60 wt.% for the as-irradiated sample. The d-spacingof the (110/200)RFE decreases to 4.73 �A at �38 �C. Meanwhile,crystal orientation is largely preserved due to the “frozen” oriented

F-TrFE) 50/50 film irradiated at 60 Mrad. Before irradiation, the film was obtained bypanel shows 1DWAXD profiles for the equator and meridian reflections during (C) the

part with the last temperature being 150 �C. The inner two weak/diffuse rings belong to

L. Yang et al. / Polymer 54 (2013) 1709e17281720

chains as mentioned above. Upon the second heating, completemelting of the crystals is observed above 130 �C, where the (110/200) reflection at 4.96 �A disappears on the equator and the (002)reflection on the meridian transforms into a weak halo at 2.3 �A.Again, no obvious first-order transition is observed from theWAXDprofiles in Fig.12D (see Fig. S1B in the Supplementarymaterial). Weconclude that WAXD is not sensitive enough to detect details ofcrystal structure and chain conformation in the RFE phase.

We then utilize FTIR to study the chain conformation in the RFEphase of the e-beam irradiated (60 Mrad) uniaxially stretchedP(VDF-TrFE) 50/50 film, and the results are shown in Fig. 13 for thefirst and second heating cycles. At �40 �C in the first heating cycle(Fig. 13A), the absorption bands for long T sequences are seen at475, 510, and 848 cm�1, and the bands for short T and TG sequencesare observed at 526 and 615 cm�1, respectively. The coexistence ofboth long and short T sequences indicates that the RFE phase hasa disordered crystalline structure. However, the peak intensity ofthe 510 cm�1 band is stronger than that of the 615 cm�1 band,indicating that the ferroelectricity dominates in the sampleat �40 �C. Upon increasing temperature, the bands at 475, 510, and848 cm�1 for the long T sequence gradually decrease in intensity,whereas the band at 526 cm�1 for the short T sequence graduallygrows in intensity. Above 50e60 �C, the band at 526 cm�1 becomesstronger than that at 510 cm�1. Finally, at 120 �C all the crystalsmelt; however, there are no noticeable changes in the FTIR spec-trum as compared to the spectra just before crystal melting. Thisoccurs because before melting, the crystals are so defective that thechains have already predominantly adopted the TG conformation,which is not much different from that in the melt. After melt-recrystallization and cooling to �40 �C (Fig. 13B), the long Tsequence band at 510 cm�1 becomes much sharper and the short Tsequence band at 526 cm�1 becomes weak. This is consistent withthe DSC results that more ferroelectricity is developed with the TCat 41 �C after melt-recrystallization for the irradiated sample (seeFig. 11C). Upon increasing the temperature to 45 �C, the short Tsequence band at 526 cm�1 starts to grow, corresponding well totheweak Curie transition at 41 �C in DSC (Fig.11C). Finally, at 120 �Call the crystals melt, but no significant change in the FTIR spectra isseen before and after the crystal melting. From these FTIR results,we see that all changes are quite subtle because the RFE phasealready contains a disordered crystal structure with a significantamount of short T and TG sequences. Melt-recrystallization willlargely expel the structural defects such as crosslinks from thecrystals, resulting in a significant decrease in the overall crystal-linity and enhanced ferroelectricity (possibly due to enlarged fer-roelectric domains). Comparing the e-beam irradiated (60 Mrad)

Fig. 13. FTIR spectra for the e-beam irradiated (60 Mrad) uniaxially stretched P(VDF-TrFE) 510 min) cycles. The spectra are collected during a stepwise heating process from �40 to 12

P(VDF-TrFE) 50/50 copolymer with the P(VDF-TrFE-CTE) 59.2/33.6/7.2 terpolymer, we see no bands for the T3 sequence at 772 and800 cm�1. We speculate that the molar content of the structuraldefects (crosslinks) may be lower than that (7.2 mol%) of CFE in theterpolymer. As a result, long T sequences rather than the T3sequence are adopted for the e-beam irradiated P(VDF-TrFE).Nonetheless, this needs further investigation.

The dynamic dielectric behavior of the e-beam irradiated(40 Mrad) uniaxially stretched P(VDF-TrFE) 50/50 film during thefirst and second heating cycles are studied by BDS. Note that theuniaxially stretched film with 40 Mrad irradiation exhibits similarferroelectric properties to the film with 60 Mrad irradiation.Therefore, we use the 40 Mrad film as an example here. As shownin Fig. 14, both the glass transition and Curie transition for theamorphous and crystalline dipoles are seen during heating forεr

0 and εr00 as a function of temperature. For example, during the

first heating cycle, the Tg and TC are observed at �10 and 31 �C(1 Hz) in the εr

00 plot, and they gradually increase with increasingfrequency (Fig. 14B). During the second heating cycle after melt-recrystallization, the Tg and TC are seen at �20 and 40 �C (1 Hz)in the εr

00 plot, and both values increase with increasing frequency(Fig. 14D). Before melt-recrystallization, the RFE/PE Curie tran-sitions under various frequencies appear to be broad in the εr

0

plot (Fig. 14A) and weak in the εr00 plot (Fig. 14B) for the as-

irradiated film. After melt-recrystallization, the FE/PE Curietransitions become sharper in the εr

0 plot (Fig. 14C) and muchmore pronounced in the εr

00 plot (Fig. 14D). Similar results havebeen reported in the literature [100,101]. This clearly indicatesthat certain ferroelectricity is regained for the melt-recrystallizedfilm due to the exclusion of structural defects (mostly likelychemical crosslinks) outside the P(VDF-TrFE) crystals. The high-temperature (>50 �C) and low-frequency (<1 kHz) upturns inthe εr

00 in Fig. 14B and D again are attributed to the impurity ionrelaxation, as revealed by the frequency scans for the first andsecond heating cycles (Fig. 14EeH). In Fig. 14E and G, upturns inthe εr

0 are observed at low frequencies (<1 Hz) and high tem-peratures (>75 �C). Meanwhile, in Fig. 14F and H upturns in theεr

00 in the double-log plot show a slope of ca. 1, clearly indicatingthe migrational loss from impurity ions [80,85]. At high fre-quencies, a decrease in εr

0 and a broad peak in εr00 can be

attributed to the relaxation of amorphous dipole. At intermediatefrequencies, plateaus in εr

0 are observed in Fig. 14E and G. Forboth the first and second heating cycles, the maximum plateau εr

0

values are observed at 50 �C, because the TCs are fairly close(around 31e40 �C) for the as-irradiated and melt-crystallizedfilms.

0/50 film during (A) the first and (B) the second heating (after annealing at 115 �C for0 �C with each curve 5 �C apart. All curves are overlaid for clarity.

Fig. 14. (A and C) Real ðεr 0Þ and (B and D) imaginary ðεr 00Þ relative permittivity as a function of temperature under different frequencies for the e-beam irradiated (40 Mrad)uniaxially stretched P(VDF-TrFE) 50/50 film during (A and B) the first and (C and D) the second heating (i.e., after melt-recrystallization) cycles. (E and G) εr 0 and (F and H) εr 00 asa function of frequency at different temperatures for the e-beam irradiated (40 Mrad) uniaxially stretched P(VDF-TrFE) 50/50 film during (E and F) the first and (G and H) the secondstepwise heating (i.e., after melt-recrystallization) cycles.

L. Yang et al. / Polymer 54 (2013) 1709e1728 1721

Temperature-dependent ferroelectric properties of the e-beamirradiated (60 Mrad) uniaxially stretched P(VDF-TrFE) 50/50 filmare studied by DeE loop measurements, and the results are shownin Fig. 15. At �25 �C, the DeE loops are relatively open, and this canbe attributed to the slightly increased domain size at such a lowtemperature. On increasing temperature, the hysteresis in DeEloops gradually decreases and the most narrow hysteresis loopsare observed at 25 �C.When the temperature increases to 50 �C, theDeE loops start to open up again, especially at 1 Hz. Finally, thehysteresis loops substantially open up for 1 Hz at 75 �C. The openedloops at high temperatures and low frequencies can be attributed toenhanced ion migrational loss and/or dc conduction in the sample[80,85]. For all these temperatures, the Dmax slightly increases withdecreasing poling frequency; however, the loop shape does notchange much except for 1 Hz at 75 �C.

This temperature-dependent RFE behavior can be explainedusing the schematic representation in the bottom panel of Fig. 10.We hypothesize that the inclusion of TrFE is critical for e-beaminduced crosslinking inside the crystals, because PVDF and itsother copolymers do not show the RFE behavior even after e-beamirradiation. After high-energy e-beam irradiation, the crystal isinternally crosslinked and this is important for the appearance ofthe RFE behavior. When the crosslinking density is low (e.g.,20 Mrad at 70 �C), the sample is still ferroelectric with a decreasedTC (see Fig. 11A). When the crosslinking density increases toa critical value (e.g., with 40 and 60 Mrad irradiation at 70 �C), thetrue RFE behavior can be achieved without any observation of TC(see DSC curves during the first heating in Fig. 11B and C). Weconsider that the Curie transition has become a second-ordertransition. The crosslinking of both amorphous and crystallinephases has prevented detailed structural analyses of what hashappened in the crystal. However, the crosslinks inside the crystalpermanently pin P(VDF-TrFE) chains with suitable segmentallengths, resulting in nanodomains (see the bottom panel ofFig. 10). Therefore, the pinned P(VDF-TrFE) chains in betweenbehave like torsional springs and the conventional ferroelectric-to-paraelectric Curie transition is effectively prohibited. Mean-while, the interchain distance is also enlarged, as evidenced by theWAXD study in Fig. 12. On applying an external electric field, the

dipoles in the pinned P(VDF-TrFE) chains can rotate more freely.Due to the tendency of permanent pinning and enlarged inter-chain distance to reduce the dipoleedipole interaction, the fer-roelectric domains must be small in both directions perpendicularand parallel to the chains. It is these nanodomains with easyrotating main-chain dipoles that result in a true RFE behavior (i.e.,narrow single hysteresis loops) in e-beam irradiated P(VDF-TrFE).Due to the lack of effective experimental methods to determinethe size and shape of ferroelectric domains at the nanoscale, weresort to computer simulation to “visualize” these nanodomainslater. Finally, when the crosslinking density is too high in thecrystal, P(VDF-TrFE) chains will be permanently locked in and thedipole switching will be lost as observed in previous reports[16,17]. Although the chemical pinning effectively eliminated theTC in the sample, the size of these nanodomains may still betemperature-dependent. At low temperatures (e.g., �25 �C), thenanodomains appear larger and thus the DeE loops become broad(see Fig. 15AeD). As the size of nanodomains gradually decreases,narrow hysteresis loops are observed (e.g., at 0e50 �C). On furtherincreasing the temperature, the mobility of P(VDF-TrFE) chainsbecomes so high that both impurity ion loss and dc conductionsignificantly increase, as discussed above. As a result, the DeEloops will eventually broaden at high temperatures and lowfrequencies.

Aftermelt-recrystallizationof the e-beam irradiated P(VDF-TrFE)films, structural defects (i.e., the pinning points) will be largelyexcluded from the crystals. As a result, certain ferroelectricity isrestored, as proven by the reappearance of TC during the secondheating cycles in DSC (see Fig. 11B and C). The reappearance offerroelectricity after melt-recrystallization results in broader DeEhysteresis loops, as shown in Fig. 16 [101]. Before melt-recry-stallization, typical RFE behavior is observed for the e-beam irradi-ated uniaxially stretched P(VDF-TrFE) 65/35 films with differentdoses; 60, 85, and 100Mrad (1.2 MeV e-beam irradiation at 100 �C).After melt-recrystallization, the DeE loops broaden with anincreased Dmax. The lower Dmax for the e-beam irradiated P(VDF-TrFE) films suggests fewer polarizable VDF/TrFE dipoles and thussmaller domains due to the chemical pinning (or crosslinks) insidethe crystals.

Fig. 15. Bipolarhysteresis loops for the e-beamirradiated (60Mrad)uniaxiallystretchedP(VDF-TrFE)50/50film (drawratio¼400%) atdifferent temperatures: (AeD)�25 �C, (EeH)0 �C,(IeL) 25 �C, (MeP) 50 �C, and (QeT) 75 �C. The poling frequencies decrease from left to right: (A, E, I, M, Q) 1000 Hz, (B, F, J, N, R) 100 Hz, (C, G, K, O, S) 10 Hz, and (D, H, L, P, T) 1 Hz,respectively. All poling field (a triangular waveform) starts at 25 MV/mwith step increments of 25 MV/m except those at 1000 Hz.

L. Yang et al. / Polymer 54 (2013) 1709e17281722

2.4. Computer simulation of nanodomains in pinned PVDF chains

As we mentioned above, it is not possible to visualize ferro-electric domains, especially nanodomains, using current exper-imental techniques. To understand the nature of nanodomains andtheir relationship to RFE behavior, we have performed fully atom-istic simulations of pinned zig-zag PVDF chains in a crystal withenlarged lateral unit cell dimensions (i.e., ax and by). In this mo-lecular dynamics simulation, all the two-body, three-body, andfour-body interaction constants depend on the type of atoms

involved in the interaction. These parameters, as well as the van derWaals interaction parameters and the atomic partial charges, aretaken from the force-field developed for PVDF polymers [102]. Thelong-range electrostatic interactions between charged particles arehandled using the standard Lekner summation algorithm [103].The initial configuration is a zero-temperature crystal with all transchains running parallel to each other along the z-axis (Fig. 17A).Note that the unit cell c-axis is along the chain direction or the z-axis. Each chain contains 30 e(CH2CF2)e repeating units. There arein total 144 such chains, corresponding to 72 PVDF ab-cells in the xy

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100

P (m

C/m

2 )

E (MV/m)

100 Mrad R ecrysta llized

C

Fig. 16. Bipolar hysteresis loops for e-beam irradiated uniaxially stretched P(VDF-TrFE) 65/35 films before (blue) and after (red) melt-recrystallization: (A) 60 Mrad, (B) 85 Mrad, and(C) 100 Mrad. The poling frequency is 10 Hz with a triangular waveform. (Reproduced and adapted with permission from Ref. [101]. Copyright 2005 American Institute of Physics.)

L. Yang et al. / Polymer 54 (2013) 1709e1728 1723

plane. The end CH2 and CF2 groups are elastically attached to thesurfaces of two parallel walls separated by a distance, D ¼ 30cz. Onthe surface of the left wall placed at z ¼ 0 nm, all the fixed CH2groups are oriented in such a way that their H atoms point in thenegative direction of the x-axis. Correspondingly, the F atoms of thefixed CF2 groups on the surface of the right wall, placed at z ¼ D,point along the positive direction of the x-axis. Such a firm fixing ofboth chain ends mimics the chemical crosslinks in the e-beamirradiated P(VDF-TrFE) crystal and prevents their rotation aroundthe z-axis near the walls. During the initial stage of the simulation,the system is gradually raised from zero to room temperature in 6consecutive runs at increments of 50 K. In each run the system isequilibrated for 20 ps. Once the system temperature reaches 300 K,simulation data, such as the positions of atoms, their velocities, and

Fig. 17. Simulation results for the time evolution of a layered domain morphology in a PVDThe unit cell of the PVDF crystal is enlarged about four times in both x and y directions to ax ¼10, 50, 100, 200, and 250 ps. The domains with dipoles in the upward direction are showcorresponds to the dipole amplitude of 0 D whereas red color corresponds to 2.1 D. Empty re(KeO) show domain structures for the middle layer at a simulation time of 300 ps. Succesimulation boxes have dimensions of 21.0 � 24.0 � 7.68 nm3.

the forces acting on them, are stored at time intervals of 1 ps forprocessing later.

Although the lattice constants of the pure b-phase unit cell areax ¼ 0.85 nm, by ¼ 0.491 nm, and cz ¼ 0.256 nm, other values withenlarged by, but with a fixed by/ax ratio are also considered in oursimulations. We find that increasing the separation distance be-tween chains, while keeping the geometry of the crystal intact,strongly affects the average dipole moment of the sample and re-duces the strength of Coulomb correlations between aligned di-poles. When the separation distance becomes greater than therange of the van derWaals interaction, the chains no longer feel thesteric hindrance of their neighbors. As a consequence, the dipoles ineach chain can respond more readily to temperature fluctuations.Our simulation results (not shown here) indicate that at smaller

F crystal with all trans chains along the z-axis sandwiched between two parallel walls.3.5 nm and by ¼ 2.0 nm. (AeJ) show the morphology at simulation times of 1, 2, 3, 4, 5,

n in colors from blue to red, corresponding to different dipole amplitudes. Blue colorgions represent the domains with their dipole moments down (or negative amplitude).ssive images show dipole strength varying from 0 to 2 D with 0.5 D increments. All

L. Yang et al. / Polymer 54 (2013) 1709e17281724

separations, i.e., by < 1 nm, the average dipole moment of a systemhaving chains with 100 repeating units decreases only slightly fromits zero-temperature value of 2.1 D to 1.8 D. At larger separations,the average dipole moment drops sharply, and the uniform dipoleorientation found in the b-form unit cell is absent in regions faraway from both walls.

In a preliminary simulation, we set by at 0.6, 1.2, and 2.0 nm,respectively, while keeping the ratio of by/ax fixed as in the b-form.For by ¼ 0.6 nm, no dipole rotation is observed for simulation timesup to 500 ps. For by ¼ 1.2 nm, strong chain aggregation leads toa non-uniform density distribution in space. When by ¼ 2 nm, nochain aggregation is observed and a unique nanodomain structureevolves from a single well-aligned domain (see Fig. 17AeJ). Within10 ps, tiny domains with different dipole orientations start toappear and continue to grow in size with increasing time. Beyond50 ps, it is found that an isolated middle section of the simulatedsystem keeps the dipole moment oriented upward, while the re-gions between the walls and the middle section change theirdipolar orientation from the upward direction to the downwarddirection. Up to 300 ps, the nanodomain morphology with fourlayers (note that the left and right layers at the wall are consideredas one full layer) seems to become stable. We consider that thelayered domain structure must be dictated by the two confiningwalls. Each nanodomain layer has a length of about 7e8 repeatingunits. The lateral dimension of these layered nanodomains is por-trayed in Fig. 17KeO by showing the dipole amplitudes in themiddle, upward-oriented region at a simulation time of 300 ps.Upon increasing the threshold amplitude of the displayed dipolemoment from 0 to 2 D in 0.5 D increments, the lateral dimension ofthe nanodomains gradually decrease from bicontinuous to moreisolated. If we use an amplitude of 1.5 D (Fig. 17N) for the domainsize analysis, the average lateral dimension is about 2e4 unit cells.

It is noticed that the chain separation distances employed in thesimulation are set at unrealistically large in order to achieve thedevelopment of nanodomains. The necessity to consider such ex-tremes arises from the limitations encountered in performing fullyatomistic simulations. With simulated times of even 500 ps,insufficient molecular realignment would be observed at smallerseparations. Consequently, we are obliged to compensate byspeeding up the relaxation processes artificially. If unlimited com-puter time were available, one might expect to see, in systems withonly a 12% expansion of the interchain distance, the type ofbehavior we find at a 400% increase in separation. We are currently

Fig. 18. Schematic illustrations of (A) an electrically polarized ferroelectric PVDF crystal (ferroelectric P(VDF-TrFE) crystal by a thin layer of polystyrene (PS, in green color) under a pothe dipole moment or the external electric field E0. Both polarization and depolarization fie2011 American Chemical Society.)

exploring other avenues by which the simulation may be accel-erated in order to obtain more realistic results.

3. Effect of crystaleamorphous interaction on novelferroelectric behaviors (the nanoconfinement effect)

As mentioned above, most ferroelectric polymers are semi-crystalline (we have not focused on ferroelectric liquid crystalpolymers [104] in this article). In addition to the more importanteffect of the internal crystal structure, the interactions that occur atthe interface between the crystalline and amorphous regions canalso affect the ferroelectric properties of polymers. We call this thenanoconfinement effect. In a recent perspective article [13], wehave already discussed this nanoconfinement effect and here wewill briefly review our conclusions.

In a simple case, a semicrystalline ferroelectric polymer can berepresented by the serial capacitor model shown in Fig. 18A. In thismodel, a ferroelectric polymer (e.g., PVDF) crystal is sandwichedbetween two amorphous layers, which are in direct contact withtwo metal electrodes. The chain direction is perpendicular to theexternal field. Upon application of an external electric field (E0)above the coercive field (Ec), dipoles in the ferroelectric PVDFcrystal will align along the field direction, creating a local depola-rization field (Edepol) in the crystal, as shown in Fig. 18A [105,106]:

Edepol ¼Pinε0

(1)

where Pin is the polarization inside the ferroelectric crystal due tothe electrically aligned dipoles. Meanwhile, a compensation po-larization (Pcomp) in the amorphous PVDF at the crystaleamorphous interface will form outside the ferroelectric crystal.Note that Pin may not equal Pcomp, especially during a dynamicpoling process. Based on the serial capacitor model in Fig. 18A, thelocal polarization field for the ferroelectric crystal is imposed fromthe charges on the electrodes and can be defined as [105,106]:

Epol ¼Dε0

¼ Q þ Pcomp

ε0(2)

where Q is the charge density in a vacuum capacitor, i.e., Q ¼ ε0E0.Dipole switching depends on the local electric field in the crystal

(EL,cryst), which has at least three sources of contribution; i) Epol

blue rectangles) sandwiched between two amorphous layers and (B) a nanoconfinedling electric field. The folded chain direction in the lamellar crystals is perpendicular tolds are shown in the schemes. (Reproduced with permission from Ref. [72]. Copyright

L. Yang et al. / Polymer 54 (2013) 1709e1728 1725

(positive) ii) Edepol (negative) and iii) other contributions from di-poles nearby [105,107]. Note that there should not be contributionfrom both amorphous layers to the local field inside the crystal. Ifwe consider that contribution from nearby dipoles in the crystalcan cancel out [105,107], we may assume that the contribution (iii)can be neglected. Then, the local electric field largely depends onthe competition between Epol (orQþ Pcomp) and Edepol (or Pin). Upona forward poling (to the positive direction), Q þ Pcomp is larger thanPin and thus Epol will be higher than Edepol. Crystalline dipoles willbe polarized along the external electric field direction. Uponreverse poling (to the negative direction), two scenarios can takeplace. First, if Q þ Pcomp is larger than Pin as both Edepol and Epoldecrease with the external field, the Epol will be higher than theEdepol and the normal ferroelectric behavior with a single polingprocess will be resulted. Second, if Pin is higher than Qþ Pcomp, thenEdepol will be greater than Epol at a certain point. As a result, fullyaligned dipoles/domains will become less stable than they are ina situation where part of mobile (or reversible) dipoles/domainsreverts to the opposite direction, resulting in a minimum (or evennet zero) remanent polarization. Therefore, the DHL behavior witha two-step poling process will be obtained [38,72]. Finally, ina recent report we observe that there are a certain amount ofreversible dipoles/domains in P(VDF-HFP) (and also PVDF), inaddition to irreversible ones [108]. These reversible (or mobile)dipoles/domains can relax (i.e., randomize) within a few ms uponremoving the poling electric field. As a result, the same dischargedenergy density will be obtained regardless of how fast the sample ischarged and discharged up to 1000 Hz. From the above discussionof the internal crystal structure effect, we consider that even inclose-packed PVDF and its copolymer crystals, a certain number ofnanodomains may still exist depending on the crystallite size andpoling condition. These nanodomains should be fairly mobile orreversible because of small spontaneous polarization. If the amountof these reversible nanodomains is high enough (e.g., close to 50%),a minimum remanent polarization will be achieved around E ¼ 0,resulting in a two-step poling process or the DHL behavior.

On the basis of the above discussion, the DHL behavior can beachieved by either increasing the Pin or decreasing the Pcomp, ora combination of both. Generally speaking, it is relatively difficult to

Fig. 19. (Top) Synthesis of P(VDF-TrFE-CTFE)-g-PS graft copolymer from the P(VDF-TrFE-CTF(A) and (B) Bipolar DeE hysteresis loops for uniaxially stretched P(VDF-TrFE) 93/7 and P(VDThe DeE loop for the graft copolymer at a poling field of 150 MV/m. Two-step poling procespermission from Ref. [72]. Copyright 2011 American Chemical Society.)

increase the Pin, because the dipole moment per repeating unit isfixed by the covalent bonds. On the contrary, reducing the Pcomp iseasier and can be effectively used to obtain the DHL behavior. Forexample, the average dipole moment per repeating unit for theamorphous P(VDF-TrFE) is lower than that for the amorphousPVDF. The Pcomp for P(VDF-TrFE) therefore should be lower thanthat for PVDF. This explains why the DHL behavior is often observedfor P(VDF-TrFE) (especially with relatively high TrFE contents)rather than PVDF at certain poling electric fields [5,109e115].Nonetheless, the DHL behavior in P(VDF-TrFE) is not stable. Afterrepeated electric poling (e.g., 5e10 times), the double hysteresiseventually disappears and is replaced by the single normal ferro-electric loop [111,113]. This can be explained by the growth ofnanodomains into large domains and thus an increase in Pcompupon repeated electric poling in P(VDF-TrFE) samples.

To achieve stable DHLs, we propose to confine PVDF or P(VDF-TrFE) crystals with a thin layer of low polarizability polymer suchas polystyrene (PS) to purposely reduce Pcomp and limit domaingrowth upon repeated poling (see Fig. 19B) [13,72]. In detail, PS sidechains are grafted from a P(VDF-TrFE-CTFE) 88.2/7.7/3.5 terpolymerusing atom transfer radical polymerization (ATRP) [116], followingan established method in literature (see the top panel of Fig. 19)[117]. The last step dechlorination by n-Bu3SnH is conducted toavoid crosslinking of the graft copolymer under further thermaltreatments. The PS content is determined to be 14 wt.%, corre-sponding to 3.2 styrene repeating units per PS graft and each main-chain contains 47 PS side chain. A P(VDF-TrFE) 93/7 (mol/mol)copolymer is used as a control to comparewith the graft copolymer.P(VDF-TrFE) 93/7 and P(VDF-TrFE-CTFE)-g-PS(14%) films areobtained by hot-pressing at 240 �C followed by uniaxial stretchingat 110 �C. The 2D XRD patterns in the insets of Fig. 19A and Bindicate that the chains in the P(VDF-TrFE) crystals are parallel tothe stretching direction. Bipolar DeE hysteresis loops for P(VDF-TrFE) 93/7 and P(VDF-TrFE-CTFE)-g-PS(14%) are shown in Fig. 19Aand B, respectively, and a clear difference is seen. For P(VDF-TrFE)93/7, DHLs are seen at the poling field below 200 MV/m, abovewhich only normal ferroelectric loops are seen. Note that these lowfield DHLs are unstable and will disappear after repeated poling aswe mentioned above. For P(VDF-TrFE-CTFE)-g-PS(14%), DHLs are

E) terpolymers using atom transfer radical polymerization followed by dechlorination.F-TrFE-CTFE)-g-PS(14%) films. Corresponding 2D XRD patterns are shown as insets. (C)ses are shown to explain the competition between the Edepol and Epol. (Reprinted with

L. Yang et al. / Polymer 54 (2013) 1709e17281726

seen at the poling field up to 400 MV/m. These DHLs are stable andcan survive hundreds of poling cycles (data not shown).

The observed DHL behavior in P(VDF-TrFE-CTFE)-g-PS (14%)can be explained using the model in Figs. 18B and 19C. After thecrystallization-induced microphase separation, a low polarizabilityPS-rich interfacial layer confines (or insulates) the ferroelectricP(VDF-TrFE) crystal. As a result, the Pcomp in P(VDF-TrFE-CTFE)-g-PS(14%) greatly decreases, as compared with that in P(VDF-TrFE)(nearly 40% at 400 MV/m). A typical DHL with the remanentelectric displacement, Drem w 0, at a poling field of 150 MV/m isshown in Fig. 19C. Two steps during the reverse poling process areobserved. During the first step, Q þ Pcomp < Pin and thusEpol < Edepol. The reversible dipoles/domains will revert back to theopposite direction, resulting in nearly zero net dipole moment.During the second step, Q þ Pcomp > Pin and thus Epol > Edepol. Thedipoles/domains will be aligned along the reverse field direction.Due to the nanoconfinement effect, no growth of reversiblenanodomains is allowed. Therefore, the DHL behavior becomesstable.

4. Concluding remarks and outlook

Ferroelectrics and dielectrics represent two extremes of elec-trical properties for insulating materials. By gradually decreasingthe nonlinearity, novel ferroelectric behaviors such as narrow sin-gle (or the RFE) and DHL behaviors can be achieved. The key is tointroduce one or more permanent dipoles in a small ferroelectricdomain (or nanodomain) with enhanced dipole reversibility, sur-rounded by a weakly interacting matrix. In other words, nano-domains can decrease the spontaneous (or remanent) polarization,and then enhanced dipolar reversibility can reduce polarizationhysteresis.

From the above studies of P(VDF-TrFE)-based terpolymers ande-beam irradiated copolymers, we learn that these novel ferro-electric properties can be successfully achieved via careful tailoringof both the crystal internal structure and the crystaleamorphousinteraction (the nanoconfinement effect) in semicrystalline poly-mers (note that dipolar glass and liquid crystal polymers are notconsidered in this feature article). In general, the effect of crystalinternal structure is more important than the nanoconfinementeffect, and can be effectively achieved by repeating-unit iso-morphism and by pinning inside the crystal. The effect ofrepeating-unit isomorphism is to increase the interchain distancefor dipole flipping with reduced friction in the crystal, whereaspinning will limit the domain size and provide the pinning force forfast dipole reversal. Pinning can be either physical (i.e., temporary)or chemical (i.e., permanent). For physical pinning, the RFE phase isstable at low electric fields and will transform into an FE phase athigh electric fields. Reversible RFE4FE phase transitions asa function of electric field result in a DHL behavior. This is exactlywhat is observed for P(VDF-TrFE)-based terpolymers. For chemicalpinning, the isomorphic crystal needs to be crosslinked in the solid-state (or in-situ) to achieve the permanent pinning force forreversible dipole switching. Nonetheless, in-situ crosslinking offerroelectric polymer crystals has been difficult to achieve exceptby the use of ionization radiations such as high-energy e-beam, g-ray, and proton irradiations. Once the material is properly cross-linked with an appropriate length in between neighboring cross-linking points, nanodomain and dipole reversibility (i.e., the RFEbehavior) can be obtained. This is observed for e-beam irradiatedP(VDF-TrFE) crystals. The nanoconfinement effect, in general, is lessimportant for novel ferroelectric behaviors in semicrystalline fer-roelectric polymers. Nonetheless, by manipulation of the crystaleamorphous interface to reduce the Pcomp, a two-step dipole rever-sal (i.e., DHL) behavior is observed due to a stronger Edepol than Epol.

This has been seen in a P(VDF-TrFE-CTFE)-g-PS(14%) graftcopolymer.

What we have learned in this work will stimulate several newresearch directions. First, the consequences of nanodomain andpinning should be applicable to other ferroelectric polymers, suchas odd-numbered nylons, polyurethanes, and polyureas. The key isto achieve repeating-unit isomorphism and pinning of the ferro-electric crystal. Second, other in-situ crystal crosslinking mecha-nisms, which will not involve ionizing radiation, should be pursued.For example, UV-induced topochemical polymerization has beenused to achieve solid-state crosslinking of diacetylene crystals[118,119]. If this concept can be employed for ferroelectric polymercrystals, UV-crosslinking will be much more appealing for practicalapplications. Third, a combination of both crystal internal structureand nanoconfinement effects will be able to produce double loopswith minimum hysteresis. This is more desirable for high-energydensity/low-loss electric energy storage [13]. All these opportu-nities make ferroelectric polymers attractive for new and betterapplications.

Acknowledgments

LZ and QMZ thank the Army Research Office (ARO, W911NF-11-1-0534) for supporting this work. LZ also acknowledges supportfrom the Office of Naval Research (ONR, N00014-05-1-0338) andNational Science Foundation (NSF, DMR-0907580). PLT acknowl-edges support from the Petroleum Research Fund of the AmericanChemical Society (PRF# 51995-ND7). The authors are indebted toProfessors Donald Schuele and Jerome Lando at Case WesternReserve University and Professor Takeo Furukawa at Tokyo Uni-versity of Science for helpful discussions.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.polymer.2013.01.035.

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Lianyun Yang was born in Jilin Province, China. Heobtained his B.S. degree in polymer chemistry at Universityof Science and Technology of China in 2009. Currently, heis a Ph.D. candidate in the Department of MacromolecularScience and Engineering at Case Western Reserve Univer-sity. His current research interest focuses on novel ferro-electric polymers as high-k/low-loss dielectrics for energystorage applications.

L. Yang et al. / Polym1728

Xinyu Li obtained a B.E. degree in Department of MaterialsScience and Engineering, Tsinghua University, Beijing,China in 2009. Presently, he is pursuing a Ph.D. degree inthe Department of Electrical Engineering at the Pennsyl-vania State University. His current research focuses on thedevelopment of organic materials exhibiting novel elec-trical properties, especially giant electrocaloric response,as well as the design of solid-state cooling devices basedon the electrocaloric effect.

Elshad Allahyarov is currently a researcher at the PhysicsDepartment of Case Western Reserve University. He alsoholds scientific positions as a researcher at the Institute forTheoretical Physics II in Heinrich-Heine University of Dus-seldorf, Germany, and as a senior researcher in the Theo-retical Department of the Institute for High Temperaturesof Russian Academy of Sciences in Moscow, Russia. Hereceived his M.S. degree in Theoretical Physics in 1988from Moscow State University, Russia. He obtained hisPh.D. degree in Theoretical Physics in 1995, and his Doctorof Sciences (Habilitation) degree in Theoretical Physics in2005, both from Russian Academy of Sciences. His researchinterest includes the physics of soft matter, nucleation

problems in dense systems, morphological changes in ionomers under external fields,

the role of Coulomb correlations in colloidal and biophysical systems, and energy stor-age in charged polymers.

Philip L. Taylor is Distinguished University Professor andPerkins Professor of Physics and Macromolecular Scienceand Engineering at Case Western Reserve University. Hereceived his B.Sc. degree in Physics in 1959 from King’sCollege, London, and his Ph.D. in Theoretical Physics in1963 from the University of Cambridge. He has held vis-iting positions at the Universities of Bonn, Manchester,Utrecht, Cambridge, Oregon, and Washington. He is a Fel-low of the American Physical Society and of the AmericanAssociation for the Advancement of Science. His researchinterests include theoretical and simulation studies of theelectrical and thermodynamic properties of polymers andliquid crystals.

4 (2013) 1709e1728

Qiming Zhang is currently Distinguished Professor ofElectrical Engineering and Materials Science and Engi-neering at Penn State University. The research areas in hisgroup include fundamentals and applications of novelelectronic and electroactive materials. Research activitiesin his group cover actuators, sensors, transducers, di-electrics and charge storage devices, polymer thin filmdevices, polymer MEMS, electrocaloric effect and solid-state cooling devices and electro-optic and photonic de-vices. He has over 340 publications and 10 patents in theseareas. He is the recipient of the 2008 Penn State Engineer-ing Society Premier Research Award and a Fellow of IEEEand a Fellow of APS.

Lei Zhu is currently an Associate Professor of Macro-molecular Science and Engineering at Case WesternReserve University. He received his B.S. degree in MaterialsChemistry in 1993 and M.S. degree in Polymer Chemistryand Physics in 1996 from Fudan University. He earned hisPh.D. degree in Polymer Science in 2000 from the Uni-versity of Akron. After two-year post-doctoral experienceat University of Akron, he joined Institute of Materials Sci-ence and Department of Chemical, Materials and Biomo-lecular Engineering at University of Connecticut, as anAssistant Professor. In 2009, he moved to Case WesternReserve University. He is recipient of National ScienceFoundation (NSF) Career Award, 3M Non-tenured Faculty

Award, and DuPont Young Professor Award. His research interests include high-k pol-

ymer and polymereinorganic hybrid materials for electrical applications, developmentof artificial antibody as nanomedicines, and supramolecular self-assembly of supermo-lecules and polymers. He is author and co-author of w100 refereed journal publica-tions and 5 book chapters.