Mechanical Energy Harvesting Performance of Ferroelectric Polymer Nanowires Grown via Template‐Wetting

Abstract Nanowires of the ferroelectric co‐polymer poly(vinylidenefluoride‐co‐triufloroethylene) [P(VDF‐TrFE)] are fabricated from solution within nanoporous templates of both “hard” anodic aluminium oxide (AAO) and “soft” polyimide (PI) through a facile and scalable template‐wetting process. The confined geometry afforded by the pores of the templates leads directly to highly crystalline P(VDF‐TrFE) nanowires in a macroscopic “poled” state that precludes the need for external electrical poling procedure typically required for piezoelectric performance. The energy‐harvesting performance of nanogenerators based on these template‐grown nanowires are extensively studied and analyzed in combination with finite element modelling. Both experimental results and computational models probing the role of the templates in determining overall nanogenerator performance, including both materials and device efficiencies, are presented. It is found that although P(VDF‐TrFE) nanowires grown in PI templates exhibit a lower material efficiency due to lower crystallinity as compared to nanowires grown in AAO templates, the overall device efficiency was higher for the PI‐template‐based nanogenerator because of the lower stiffness of the PI template as compared to the AAO template. This work provides a clear framework to assess the energy conversion efficiency of template‐grown piezoelectric nanowires and paves the way towards optimization of template‐based nanogenerator devices.


Introduction
Ferroelectric polymers [1][2][3] are of scientific and technological interest as,unlike typicalferroelectric ceramics,they are flexible,l ight-weight, bio-compatible,a nd low-temperature and solution-processable,a nd are attractive for usei np iezoelectric generators for mechanical energy harvesting. Ferroelectric/piezoelectric polymeric nanowires are commonly incorporated into "nanogenerators", [4][5][6] which have been found to outperform bulk or thin-film devices,and these have been attractingi ncreasing interest as energy solutions for small power devicess uch as portable electronics,w irelesss ensor nodes,b iomedical implants,a nd structural monitoring devices.T his interest is intensifiedb yc urrent technological trends such as the increasing prevalence of autonomous sensors,w hich have been predicted to riser apidly,f ueling the growth of the "Internet of Things" [7] linking everyday objects.
While there have been recentr eportso ff erroelectric polymers,s ucha sp olyamides (odd-numbered nylons), [8,9] having found applications in mechanical energy harvesting, polyvinylidine fluoride (PVDF) and its co-polymers have received by far the most interest for ferroelectric polymer nanogenerator applications [4,[10][11][12][13][14][15][16][17][18][19] due to their superiore lectromechanical properties.P VDF is af luoro-polymer knownt oe xhibit piezoelectricity since 1969 [20] and ferroelectricitys ince 1981. [21] PVDF consists of ac arbon backbonew ith each carbon in the chain alternatively binding two fluorineo rt wo hydrogen atoms oriented on opposite sides of the carbon chain. Thep iezoelectric properties of PVDF arise from the large difference in electronegativity between the fluorine and carbon atoms compared with the hydrogen atoms. This results in polar bonds and ar esulting dipole momentf rom the fluorine side of the chain towards the hydrogen side. [1,3,22] Chain conformations for differentc rystalline phaseso f PVDFa re shown in Figure 1a.T he b phase of PVDF is the all-trans phase (TTTT), which has the highest spontaneous polarization [22,23] and is thus desirable for piezoelectric applications.T his phase is more readily realized in P(VDF-TrFE), which is ac o-polymer consisting of polymer chainsa lternating non-periodically between vinylidene-fluoride (VDF)a nd trifluoro-ethylene (TrFE), [22,24,25] as shown in Figure 1b.W e have previously demonstrated that P(VDF-TrFE)n anowires grown via" template-wetting" showed enhanced crystallinity, Nanowireso ft he ferroelectric co-polymer poly(vinylidenefluoride-co-triufloroethylene) [P(VDF-Tr FE)] are fabricated from solution within nanoporous templates of both "hard" anodic aluminium oxide (AAO)a nd "soft" polyimide( PI) through af acile and scalable template-wettingp rocess.T he confined geometry afforded by the pores of the templates leads directly to highly crystalline P(VDF-TrFE) nanowires in am acroscopic "poled" state that precludes the need for external electrical poling procedure typically required for piezoelectric performance.T he energy-harvestingp erformanceo fn anogenerators based on these template-grown nanowires are extensively studied and analyzed in combination with finite element modelling. Both experimental results and computational models probingt he role of the templates in determiningo verall nanogenerator performance,i ncluding both materials and devicee fficiencies,a re presented. It is found that although P(VDF-TrFE) nanowires grown in PI templates exhibit al ower material efficiency due to lower crystallinity as comparedt on anowires grown in AAOt emplates,t he overall device efficiency was higher for the PItemplate-based nanogenerator because of the lower stiffness of the PI templatea sc ompared to the AAOt emplate.T his work provides ac lear framework to assess the energy conversion efficiency of template-grown piezoelectric nanowires and paves the way towards optimizationo ft emplate-based nanogenerator devices.
with an et polarizationa long the length of the nanowires causing them to be "self-poled". [10,26] Theo bserved preferential crystallization behavior had earlier been attributed to preferential nucleation and growth from the pore walls during templatei nfiltration. [12,15] In ref. [26],t he self-poled nature of the nanowires was explored in detail, revealing similar physical properties as electricallypoled thin-film samples of the same material. In the same study,p iezoresponse force microscopy (PFM) was used to establish self-poling in the nanowires,w hich was otherwisen ot observed in an unpoled as-grownf ilm. This is therefore particularly advantageous for piezoelectric applicationsi nvolving template-grown P(VDF-TrFE) nanowires whereby an external electric poling field is not required.
Te mplate-wetting is as imple and scalable nanowire fabrication methodt hat involves the infiltration of ap olymer melt or solution into an anoporous template, [12,13,15,17,[27][28][29][30] followed by solidification or solvent evaporation giving rise to nanowires or nanotubes formed within the template.T his processr elies on the high surface energy of the template walls,a si nfiltration is predominantly driven by the difference in surface energy between pore walls and infiltrating polymer. We have previously shown that template-wetting can be used to achieve self-poled P(VDF-TrFE) nanowires grown within both hard anodic aluminiumo xide (AAO) templates (Youngsm odulus Y % 122 GPa [31] ), as well as soft polyimide( PI) templates (Y % 3GPa [32,33] ), wheret he choice of template material was shown to play ar ole in determining the crystallinity of the nanowires. [26] Here,w er eporto nt he energy-harvesting performance of nanogenerators that have been assembled from P(VDF-TrFE) nanowires embedded in both AAOa nd PI templates in order to ascertain the role played by the templatei nd eterminingn anogenerator output performance.I mportantly,w epresent detailed computational modelling of these template-based nanogenerators to assess the performance of the P(VDF-TrFE) nanowires within the nanogenerator devicesa nd, in particular,t od etermine their electromechanical conversion efficiency andr elevant nanogeneratorf igures of merit. [6] Our studies pave the way for deviceo ptimizationi nvolving any combination of template and ferroelectric/piezoelectric nanowire material, and ar eliable means to predict mechanical energy-harvesting performance at the nanogenerator design stage.

Results and Discussion
P(VDF-TrFE) nanowires,o fd iameter 200 nm and lengths % 60 mma nd % 20 mm, were fabricated within AAOa nd PI templates,r espectively, via template-wetting as describedi n detail in previousw ork. [10] Thep ore sizes are nominally identical in both of these templates,a lthough the AAOt emplates have higher porosity than the PI templates.F igure 2a shows  scanningelectron microscopy (SEM) imageso ft he bare templates prior to infiltration of the polymer to form nanowires, while Figure 2b show photographs of nanogenerators based on the respective AAOa nd PI templates that were assembled by sputteringe lectrodes onto both sides and attaching wires for electricala ccess. Energy-harvesting measurements were carried out in ab espoke setup (previously described in ref. [10]) used to test the nanogenerator output performancei nr esponse to ap eriodic mechanical impacting excitation havingf requency ranging from 5-25 Hz,a nd at ac onstant driving amplitude of 2mm. Ty pical output voltage waveforms as measured for the AAO-based and PI-based nanogenerators at different frequenciesa re shown in SupportingI nformation S1. The output poweri sm easured across as eries of load resistances to determinet he maximum power output across an impedance-matched load. Figure 3s hows ar epresentative graph depicting the variationo fr oot mean square( RMS) voltage and power density of an AAO-and PI-based device being impacted at 25 Hz, respectively,a safunctiono fl oad resistance,w here the power is determined by the square of the RMS voltage divided by the resistance.T he RMS voltage values were determined from device output signals each of at least 5s in duration for at least three devices prepared with identical methods.C urrent and voltage output from different devices successfully prepared with identical methods had standard errors of % 6% or less.P eaks in the power output for matched impedance loads were observed as expected,a nd have been reported for other energyh arvesting piezoelectric devices using PVDF-based polymers. [34] The load that gives the maximump ower output was found to decrease slightly with frequency and to be slightly less for the polyimided evices compared with the AAOd evices.T his varies from 40-20 MW for an AAOd evice and 20-10 MW for apolyimided evice (see Supporting Information S2). Figure 4s hows ap lot of peak power density for AAOa nd PI devicesa safunction of frequency.T he peak output power density is higher in the PI-based device than that of an AAO-based deviced espite there being less piezoelectric material present as ar esult of the relative thicknesses and porosity of the templates.T his is due to the fact that AAOi s significantly stiffer than PI, which resultsi nf ar less strain and effectives tress in the P(VDF-TrFE) nanowires within an AAOd evice compared to within aPId evice.
In order to comparet he performanceo ft he two different template-based devicesa nd the template-grown P(VDF-Tr FE) nanowires themselves,t he devicea nd materiale fficiency,a nd stress and strain figures of merit, h T and h S , [6] provide the most meaningful metrics. In order to determine these values,the mechanical input energy must be considered for the device as aw hole,w hile for the material efficiency, only the component of the input energy that contributes to stress/strain in the P(VDF-TrFE) nanowires themselves is relevant.T oa chieve this,w eu se computational modellingo f the devicesf or further analysis and comparison.
Form odelling the piezoelectric energy-harvesting devices, af inite element method (FEM)w as used, which is aw ell-established technique for modelling 3D systems of arbitrary ge-  ometry and has been previously used to model piezoelectric nanostructures. [35][36][37] Modelling was carried out within the softwarep ackage COMSOL Multiphysics5.2. Due to the scale mismatch between the macroscopic devices and their nanoscale features,m odellingo facomplete device was computationally impossible due to the required number of elements to adequately mesh the geometry.T he approach taken was therefore to model small areas of ad evice containing a manageable number ( 61) of full-length nanowires and to determine the potential difference created across the nanowires for ag iven stress applied to the device.G iven the restriction on the area of devicet hat could be modelled, this approachb enefits from the fact that the nanowires act as parallel capacitors in the device geometry. [36] This means that as tress applied uniformly across the top surface of the device,a sw as the case in our energy harvestingm easurement setup,t he potential difference across each nanowire is the same and that of as ingle nanowire is the same as the device as aw hole.T he results from the model could be compared with peak open-circuit voltage measurements of the devicesf or different mechanical input frequencies (associated with different peak stresses). This approach of calculating applied stress and/or strain from open-circuit voltage has been used analytically in otherr eportedw ork on piezoelectric energy-harvestingd evices. [35,37] From the stress and strain calculated by the model, the strain energy of the nanowires can be calculated and then compared with the measured electrical energy output, in order to determine the material energy conversion efficiency of the respective templategrown P(VDF-TrFE) nanowires,aswella sh T and h S . [6] Ad etailed descriptiono ft he modela nd parameters used is provided in Supporting InformationS 3. Thev alues of the piezoelectric constant and Young'sm odulus of the P(VDF-Tr FE) nanowires used in the model had been directly determined using piezoresponse force microscopy (PFM) and quantitative nanomechanical mapping (QNM), respectively, as reported previously. [26,38] Open-circuit voltage measured using the energy harvestings et-up was used in conjunction with the FEM models to determine applied axial stresses (see SupportingT able S3). Figure 5s hows examples of the electrical potential distributioni nn anowires within models of an AAOa nd PI-basedd evicef or the samel evel of mechanical excitation.
Thes train energy of an isotropic material, W S ,i sg iven by Equation (1), [39,40] where A is the cross-sectional area, L is the length (thickness) of the material, T is the stress and S is the strain. Forc alculation of the strain energy of one of the devices,t he polydimethylsiloxane (PDMS) layers coatingt he top and bottom electrode surfacesn eeded to be considered in addition to then anowire filled nanoporous template. The total strain energy of ad evice for each impactc ycle, W D S , was given by the summation of the strain energies of the template( W T S ), nanowires (W NW S ), and PDMSl ayers (W PDMS S ), as shown in Equation (2).
Thecombined strain energyofthe nanowire-filled nanoporous template is given by Equation (3) where A T is the crosssectional area of the filled template, L T is the thickness of the template (also equal to the length of the nanowires), T axial is the peak axial applied stress,a nd S axial is the peak axial strain given by Equation (4) where Y NW and Y T aret he Youngsm oduli of nanowires and template,r espectively, and p T is the porosity of the template.
Forc alculation of W PDMS S ,t he axial strain in the PDMS layers, S PDMS ,n eeded to be considered. As the PDMSl ayers were mechanically connected in series with the filled template (unlike the template and nanowires,w hich were mechanically connected in parallel) S PDMS differs from S axial .B ecause the PDMSlayers were thin and adhered to the electroded templates urface,t he lateral strain of the PDMSw as confined by the lateral strain in the template. S PDMS was therefore taken to be given by Equation (5) by equatingt he two lateral strains through introduction of the Poisson's ratios of the templatea nd PDMS, n T ,a nd n PDMS . W PDMS S could therefore then be given by Equation (6), where L PDMS is the thickness of aP DMSl ayer and taking into account that there are two PDMSl ayers.F rom Equation (2), Equation (3) and Equation (6), W D S may therefore be given by Equation (7).
To determinet he material energy conversion efficiency of the piezoelectric nanowires within ad evice,t he strain energy of just the nanowires, W NW S ,n eeded to be calculated. This is given by Equation (8) where A NW is the cross-sectional area of the active nanowires determinedf rom the electrode area and the porosity of the template.
Thee lectrical energy generated by ad evice with each impact, W E ,w as determined from the integral of the product of current I and voltage V with respectt ot ime t for one impactc ycle,w here I and V were measured across an impedance-matched load for maximum power output. Fore ach frequency and device,t ype values of W E were determined by averaging over calculation from at least 30 cycles. From values of W E ,d evice and material efficiencies, c D and c NW , [6] could then be determined using Equations (9) and (10), respectively.
Thep redictive capability of the model was tested for a range of experimental parameters,a se xplained in Supporting Information S4. Table 1s hows values of W NW S , W E ,a nd c NW determined from the model in conjunction with experimental results for AAOa nd PI devices.T he values of c NW for P(VDF-TrFE) were seen to be consistent for each device type with average values of 7.1 %a nd 6.4 %f or AAO-and PI template-based devices,r espectively.N oc lear frequency dependence was seen,w hich is expected for this device geometry [6] where the frequencies used are far from expected resonances and therefore this furtherv alidatest he deter-mined values. Importantly,al ower value of c NW for P(VDF-Tr FE) nanowires grown in PI templates relative to those grown in AAOt emplates is consistentw ith materials characterizationt hat was carried out and detailed in previous work, [26] where lower crystallinity was reportedf or nanowires grown in PI templates as compared to those grown in AAO templates.T he FEM analysis described here can be easily extendedt oo ther template-grown polymeric materials [8,41] for energy harvestingapplications. Interestingly,a verage values of c D for AAOand PI devices were found to be 0.10 %a nd 0.75 %, respectively,e ven thought he PI template-grown P(VDF-TrFE) nanowires showed al ower c NW as compared to AAOt emplate-grown nanowires.T his could be attributed to the higher stiffness of the AAOt emplate as comparedt ot he PI template,w hich meantt hat al arger fractiono ft he input mechanical energy was lost to deforming the AAOt emplatet han the PI template leading to overall lower device efficiency.I nb oth cases the nanogenerator device design resulted in c D being low compared to c NW ,w hich represents at heoretical limit of c D for ag iven material. Additionally,f igures of merit h T and h S , [6] were also determined,w ith values of 0.18 GJ m À3 and 28.4 pJ m À3 Pa À2 for the P(VDF-TrFE) nanowires fabricated in AAOt emplates and valueso f0 .16 GJ m À3 and 25.6 pJ m À3 Pa À2 for P(VDF-TrFE) nanowires fabricated in PI templates.I np ractice other considerations of device design need to however be considered to allow adequatei ntegration, robustness,and reliability of devices.

Conclusions
Te mplate-wetting has been shown to be an attractive fabrication method for ferroelectric/piezoelectric polymeric nanowires due to its simplisticn ature that is not reliant on complicated set-ups and the use of high temperatures and/or pressures. Importantly,t he realization of self-poled nanowires [8,10] through this method makes it particularly attractive in nanogeneratora pplications.I nt his work, we presented a combination of experimental results and computational modelling to determine primarily the role playedb yt he template in the energy-harvesting performanceofP(VDF-TrFE) nanowires fabricated within them via template-wetting. While we had previously shown that the choice of template material determines the crystallinity of the ferroelectric polymer nanowires fabricated within the template, [26] here we have shownh ow this also affects the piezoelectric energy-harvesting capability of the nanowires.I tw as shown, both through directm easurements of electrical output in response to periodic impactinga sw ell as through finitee lement modelling of the nanowire-filled template-based nanogenerator devices, that AAOt emplate-grown P(VDF-TrFE) nanowires had highere nergyc onversion efficiency than their PI templategrown counterparts,b ecause of greater crystallinity.H owever, the overalld evice efficiency was higher for the PI template-based device due to the lower stiffness of the PI template as compared to AAOt emplate.T he computational models developed in this work can be easily applied to any

Experimental Section
Thet wo types of commercial nanoporous templates used in this work were AAOt emplates (Anapore,W hatman) and PI tracketched templates (ipPore,i t4ip), both with nominal pore diameter of % 200 nm. TheA AO templates were % 60 mmt hick and % 25 mm in diameter, with nominal porosity of % 50 %, while the polyimide templates were % 15 mmt hick with nominal porosity of % 15.7 %. TheP It emplates were purchased in the form of A4 sheets and cut to tiles typically of size 20 mm 20 mm for this work.
To produce the solutions in the template-wetting process, P(VDF-TrFE) in powder form with am olar composition of 70:30 of VDF:TrFE (Piezotech, France) was dissolved in methyl ethyl ketone (MEK) (Sigma-Aldrich), sonicated for % 60 min, and then drop-cast onto the templates.I tw as found that for the AAOa nd PI templates using solutions with ac oncentration of 10 %a nd 6% by weight, respectively,a nd ah ot plate temperature of 60 8Ci nb oth cases resulted in the formation of nanowires completely filling the length of the template pores. Piezoelectric energy harvesting nanogenerators were assembled from as-grown P(VDF-TrFE) nanowire-filled AAOa nd PI templates.P rior to the polymer infiltration of the templates,athin film of platinum of thickness % 100 nm was sputter coated (Emitech k550) on the bottom side of the template.F ollowing polymer nanowire infiltration from the opposite side and subsequent removal of the residual polymer film as previously described, a thin film of platinum ( % 100 nm) was deposited on the on top resulting in forming two electrodes on either side of the template contacting the enclosed nanowires.Ashadow mask was used during sputter coating of the platinum electrodes,w hich defined the effective area of the device;t his also prevented the platinum coating to the edge of the template,w hich in turn prevented electrical shorting of the device.T hin copper wires were then attached to each platinum layer using silver conductive paint (H K Wentworth) to allow for electrical access to the nanogenerator. Forp rotection and to assist in stress being applied evenly across the devices during operation, the devices were coated in polydimethylsiloxane (PDMS).