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    Polymer-based nanopiezoelectric generators for energy harvesting applications S. Crossley, R. A. Whiter and S. Kar-Narayan* Energy harvesting from ambient vibrations originating from sources such as moving parts of machines, fluid flow and even body movement, has enormous potential for small power applications, such as wireless sensors, flexible, portable and wearable electronics, and biomedical implants, to name a few. Nanoscale piezoelectric energy harvesters, also known as nanogenerators (NGs), can directly convert small scale ambient vibrations into electrical energy. Scavenging power from ubiquitous vibrations in this way offers an attractive route to provide power to small devices, which would otherwise require direct or indirect connection to electrical power infrastructure. Ceramics such as lead zirconium titanate and semiconductors such as zinc oxide are the most widely used piezoelectric energy harvesting materials. This review focuses on a different class of piezoelectric materials, namely, ferroelectric polymers, such as polyvinlyidene fluoride (PVDF) and its copolymers. These are potentially superior energy harvesting materials as they are flexible, robust, lightweight, easy and cheap to fabricate, as well as being lead free and biocompatible. We review some of the theoretical and experimental aspects of piezoelectric energy recovery using Polymer-based NGs with a novel emphasis on coupling to mechanical resonance, which is relevant for efficient energy harvesting from typically low frequency (,1 kHz) ambient vibrations. The realisation of highly efficient and low cost piezoelectric polymer NGs with reliable energy harvesting performance could lead to wide ranging energy solutions for the next generation of autonomous electronic and wireless devices. Keywords: Energy harvesting, Nanogenerators, Polymers, Piezoelectric This paper is part of a special issue on Smart Materials Introduction Harvesting energy from ambient sources in our environment has generated tremendous interest1–3 as it offers a fundamental energy solution for small power applications including, but not limited to, ubiquitous wireless sensor nodes, portable, flexible and wearable electronics, biomedical implants and structural monitoring devices. As an example, consider that the number of smart devices linking everyday objects via the ‘Internet of Things’ is set to increase at an enormously rapid rate. These devices will be small in size and in many cases embedded, and will wirelessly provide useful data that will make our lives easier, better and more energy efficient. The only sustainable way to power them is using ambient energy harvesting that lasts through the lifetime of the product. Hence, there is a pressing need for commercially viable small scale energy harvesters that can operate in any environment. In this regard, photovoltaic cells, for example, have generated significant interest as they have been shown to achieve the Department of Materials Science, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, UK *Corresponding author, email sk568@cam.ac.uk highest power density per unit area,1,2 albeit under relatively intense sunlight (y20 mW cm23). This precludes applications that require operation indoors, at night or embedded within opaque structures (e.g. sensors within building walls, medical implants in the human body, etc.). Ambient vibrations, on the other hand, are ubiquitously available and easily accessible, originating from ever present sources such as moving parts of machines, fluid flow and even body movements (e.g. walking/running as shown in Fig. 1). The available energy density from typical random vibrations in the frequency range of a few Hz to tens of kHz is significant (y0?01–10 mW cm23),1,2 highlighting the enormous potential of vibration-based energy harvesting. In this regard, piezoelectric materials are capable of directly converting mechanical vibrations into electrical power, and are well suited for microscale device applications. In particular, nanoscale piezoelectric energy harvesters, or nanogenerators (NGs), are capable of converting ambient vibrations that are typically small (Table 1) into electrical energy,4 thus paving the way for the realisation of the next generation of self-powered devices, with profound implications in far-reaching areas such as biomedicine, robotics, environmental monitoring, resource management and sustainable development. ß 2014 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 14 April 2014; accepted 7 July 2014 DOI 10.1179/1743284714Y.0000000605 Materials Science and Technology 2014 VOL 30 NO 13a 1613 Crossley et al. Polymer-based nanogenerators for energy harvesting 1 Energy harvesters have been suggested for embedding in footwear, where they may be subjected to accelerations of up to 100 m s22 at a frequency of y1?2 Hz (Table 1) Piezoelectric NGs were first demonstrated using ZnO nanowires3,5,6 by Wang and co-workers, whose pioneering work demonstrated the feasibility of this technology in powering commercial light emitting diodes,7 liquid crystal displays8 and devices for wireless data transmission.9 Subsequent NGs based on nanowires of PbZrxTi12xO3,10–12 GaN13 and BaTiO314–16 have all revealed promising energy harvesting performance. However, these NGs are still far from being commercially viable due to issues relating to reliability, robustness and performance optimisation that are yet to be addressed.17 Ferroelectric polymers, for example polyvinylidene fluoride (PVDF) and its copolymers, are potentially superior energy harvesting materials due to their flexibility, robustness, low weight and ease and low cost of fabrication, as well as being lead free and biocompatible. In addition, nanowires of ferroelectric polymers are of particular interest due to the enhancement of the desired piezoelectric crystalline phase in confined geometries18,19 and due to the size dependent and confinement induced enhancement of electromechanical properties common to all piezoelectric nanowires.20 Figure 2 shows the number of publications on piezoelectric NGs since 2007. While there has been a steady increase in the number of reported papers in this field, thus far there have been relatively few reports on Polymer-based NGs which presently are almost exclusively based on PVDF and its copolymers.21–25 Often the yield and ultimately efficiency of the reported PVDF based NGs are limited by the complex fabrication techniques used, which will be addressed in this review. Furthermore, NGs based on other ferroelectric polymers such as polyamides (odd-numbered nylons)26 and polyureas27 have rarely been attempted. While these polymers have lower piezoelectric coefficients than PVDF and its copolymers, they possess certain advantages such as better temperature stability, wider temperature range of operation and the possibility of fabrication on semiconductor substrates using vapour deposition techniques,28 all of which may be vital in certain applications. Polymers versus ceramics Table 2 provides relevant materials properties of a selection of piezoelectric materials. It can be seen that while ceramics possess larger piezoelectric coefficients than polymers, they also possess higher elastic moduli and are hence stiffer than polymers making them less sensitive to small vibrations and more prone to stress failure.17 Another advantage of piezoelectric polymers is that their acoustic impedance is lower than that of ceramics and more closely matched to that of water or air implying that sonic vibrations would be more effectively transmitted in common ambient environments.29 The lower density, r, of piezoelectric polymers could prove attractive for applications where weight of the NG may be an issue. The resonance frequency of NGs is an important device parameter that determines the operating fre- quency range and can be instrumental in the optimisa- tion of energy harvesting performance. However, it has so far been largely overlooked and is rarely considered in the literature. It is important to note that analytical expressions of normal vibrational modes are only possible for certain high symmetry geometries. For the case of a large flat disc of thickness L, the period of the fundamental ‘thickness’ mode (Fig. 3) is approximated by half the time taken for an acoustic wave to propagate through the disc, yielding an expression for thickness mode frequency ft: 1 Y !1=2 ft~ 2L 3rð1{2nÞ (1) Here the square root is an expression for the reciprocal acoustic velocity in terms of elastic constants Y (Young’s modulus) and n (Poisson’s ratio). For a typical thickness L y60 mm, ft lies in the tens of MHz range for most materials (Table 2), which is much higher than the typically low frequencies associated with ambient vibrations (,1 kHz). Reports of NGs with sub-kHz resonance frequencies in BaTiO3 nanowires have exploited a geometry in which only a small fraction of the device mass is piezoelectric.15,16 In most reported NG device geometries, the energy harvesting performance is not optimised as the NG is operated at frequencies far from resonance, and is thus an issue that we aim to highlight in this review. Table 1 Selection of suggested sources of mechanical vibration for energy harvesting (compilation: Beeby and White39) Source Approx. frequency/Hz Approx. RMS acceleration/m s22 Human ankle during walk 1.2 Mains powered compressor 50 Car cabin 40 Car wheel axle 16 Static building 10 100 0.25 0.05 2 0.1 1614 Materials Science and Technology 2014 VOL 30 NO 13a Crossley et al. Polymer-based nanogenerators for energy harvesting 2 Publications as a function of year on labelled topics: compiled via topic searches on Reuters Web of Science Theoretical background In order to make the link between piezoelectric materials properties and energy harvesting performance, we review fundamental piezoelectric theory as well as a simple theoretical model of an inertial generator. Piezoelectricity relates to the electric displacement D (surface charge per unit area) induced in a material by an applied stress T. In three dimensions, stress is described by two vectors, applied force Fi and the normal to the area upon which the force acts Aj. Stress, F/A, is thus a second rank tensor Tij whose diagonal elements represent ‘normal’ stress and off-diagonal elements represent shear stress. Electric displacement and electric field are vectors Di and Ej respectively, and the permittivity, eij5D/E, is represented by a second rank tensor. Taking T and E as independent variables, D is specified by D~dT zeE (2) where d is the piezoelectric constant of the material and is represented by a third rank tensor. Strain S is a second rank tensor specified by S~sT zdt E (3) where dt is the transpose of d, and s is elastic compliance represented by a 4th-rank tensor. We are usually spared from having to work with these tensors in full as static equilibrium requires Tij5Tji, Sij5Sji and sijkl5sijlk5 sjikl5sjilk, leading to the accessible ‘Voigt notation’,30 where 363 second rank tensors are represented as 166 matrices, 36363 third rank tensors are represented as 366 matrices and 3636363 fourth rank tensors are represented as 666 matrices (Fig. 4). Furthermore, the ‘matter’ tensors s, d and e are required by Neumann’s Table 2 For common ceramic, single crystal and polymer materials, we tabulate room temperature bulk Young’s modulus Y, Poisson’s ratio n, piezoelectric matrix elements d33 and d31, electromechanical coupling factors k33 and k31, density r, Curie temperature TC, acoustic impedance Z0, dielectric constant e and thickness-mode resonance frequency ft. Z0 evaluated as [rY(122n)]1/2 (taking n50?33 where experimental value unavailable). Resonance frequency calculation ft (via equation (1)): the sample was assumed to be of thickness 60 mm. TC for polymers can be difficult to measure due to the competing process of melting Parameter Units PbTi0?48Zr0?52O3 BaTiO3 (single BaTiO3 ZnO (single P(VDF-TrFE) (ceramic) crystal) (ceramic) crystal) PVDF 78-22 Nylon-11 Polyurea Y n d33 d31 k33 k31 r TC Z0 e ft Refs GPa pC N21 pC N21 58 0.34 223 293.5 0.67 kg m23 uC MRayl MHz 7500 386 20.8 1180 24 31, 53 64 0.33 85.6 234.5 0.56 6020 130 19.5 4600 27 54, 55 112 0.31 191 279 0.49 5720 130 27.0 2000 35 56 139 0.33 12.3 25.12 0.466 5704 27.9 11.26 40 57 2.1 3.1 0.44 235 239 28 15–30 0.1 1800 80 3.2 10–15 15 46, 58 0.2 1900 y70 2.4 15–20 10 46, 59 1.5 2.2 3 1100 95 1.3 4 10 60, 61 10 0.08 1450 .100 1.8 4 10 27, 62 Materials Science and Technology 2014 VOL 30 NO 13a 1615 Crossley et al. Polymer-based nanogenerators for energy harvesting 3 Illustration of thickness and membrane vibrational modes of thin piezoelectric disc Principle30 to show the same symmetry as the crystal structure. This means that for materials with low anisotropy, or polycrystalline solids with many randomly oriented grains, the elastic compliance tensor may be specified with just two parameters, e.g. Y and n.30 A material must possess at least one unique direction in order to be piezoelectric.31 For uniaxial systems such as many ferroelectrics, the z axis is conventionally aligned with the polar direction, such that the piezoelectric d33 coefficient describes the electrical response to a normal stress along the polar direction. This does not 4 a Voigt notation for representation of piezoelectric constant d, a third-rank tensor. The elements of d specify the relationship between the unique elements of stress T and strain S (top), and electric field E and electric displacement D (left). b Schematic showing the shear and transverse elements of stress S acting on a cube of material imply that the remaining d coefficients are zero, as a stress along some other direction is still capable of producing a strain along the polar direction. However, the d33 coefficient is a reasonable comparator of the magnitude of the piezoelectric effect in uniaxial systems. Small values of e coefficients will favour large open circuit voltages for a given value of d33. Piezoelectric materials for devices must be prepoled, usually via application of a field larger than the coercive field EC31,32 whose value is determined by energetic barriers to domain wall motion, such as pinning against defects. Because domain thermodynamics is a strong function of geometry and temperature, EC varies significantly with both for a given material. Its value can be less than 1 kV cm21 in some single crystals close to the Curie temperature TC, but usually increases at lower T and for thinner samples, and can be more than 1000 kV cm21 in many ferroelectric polymers. Thus, poling is often performed at elevated temperatures or by cooling through TC under field. Materials with an EC exceeding their dielectric strength can sometimes still be poled by placing them, unelectroded, in an electrical corona.33 Interestingly, PVDF nanowires have been shown to exhibit ‘self-poling’ when grown by the process of template wetting18,19,34–38 in nanoporous templates due to confinement induced preferential orientation18,19 of the crystal lamellae. Modal dynamics are of central importance when considering harvester geometries as the amount of energy that can be harvested depends on (1) the forces that are applied to the harvester due to ambient vibrations; (2) the degree of coupling between these forces and the natural vibrational modes of the harvester; and (3) the degree of coupling between these natural vibrational modes and the piezoelectric tensor of the harvester. A variety of sources for vibrational energy harvesting have been suggested39 with typical frequencies ranging in the sub-kHz range (Table 1). For example, walking can generate accelerations of order 100 ms22 at the ankle at a frequency of order 1 Hz while vibrational spectra from machinery typically show a series of peaks in the sub-kHz regime of order 0?1– 1 ms22 (Fig. 5 shows the frequency dependent acceleration obtained from a vacuum pump). To analyse the response of a piezoelectric energy harvester, we consider the Williams and Yates model40 (Fig. 6, cartoon in lower left), where the harvester is regarded as a mass m coupled via a spring of stiffness k to a large external structure of displacement y(t). In this inertial generator model, the displacement of the harvester with respect to the external structure is given by z(t). Energy dissipation is assumed to be via viscous damping with coefficient b52(fezfp)[mk]1/2, where the dimensionless quantities fe and fp represent the damping terms due to harvesting (piezoelectric transduc- tion in this specific case, although the exact transduction 1616 Materials Science and Technology 2014 VOL 30 NO 13a Crossley et al. Polymer-based nanogenerators for energy harvesting 5 RMS acceleration as function of frequency for a mains-powered vacuum pump (Edwards E2M8): measured with an attached accelerometer (Bruel and Kjaer DeltaTron 4517) and lock-in amplifier (Signal Recovery 7265); mechanical coupling to 50 Hz mains is apparent mechanism is irrelevant) and parasitic loss respectively. The equation of motion is given by m :z:ðtÞzbz:ðtÞzkzðtÞ~{m :y:ðtÞ (4) Note that fe may be controlled by varying the degree of impedance matching of the electrical load to the harvester. Furthermore, f5fezfp51 is the condition for critical damping. For each Fourier component y(t)5Y0eivt, z(t)52mv2R(v)y(t), where R(v)51/(k2mv2zibv) is the complex response function of the harvester which describes the phase and amplitude of the response z relative to the driving force 2my¨(t). We may rewrite R(v) in terms of f and the natural frequency of the harvester vn5(k/m)0?5 RðvÞ~ À 1Á=m v2n{v2 z2ifvvn (5) Rearranging to evaluate |R(v)|: jR(v)j~ð1=mÞ ÀvÀv2n{2n{vv2Á22Áz{ð22iffvvvvnnÞ2 hÀ v2n{v2 Á2zð2fvvn Þ2i1=2 ~ð1=mÞ " À v2n {v2 Á2zð2fvvn Þ2 #1=2 (6) 1 ~~ð8><>:1=hm1{Þ ðÀvv=2nv{1n=Þv2À2imÁ222zzv½4n2ðÁ2fðfvv=vvnnÞ2ފ29>=>;1=2 Figure 6a shows mv2|R(v)| as a function of frequency for a range of damping coefficients f and resonance frequencies vn. The factor of mv2 ensures that the y axis is dimensionless, and thus represents the relative acceleration response to an applied periodic acceleration, or the relative displacement response of an applied periodic displacement. Although the bandwidth of |R(v)| increases with increasing f, the value of |R(v)| decreases with increasing f for all values of v (Fig. 6a). There is a stationary point of |R(v)| near vn which vanishes for f.1, i.e. for overdamped systems. The bandwidth of |R(v)| increases with vn (Fig. 6a). The instantaneous harvested power P(v,t), is given by the product of the velocity, z˙(t)5ivz(t), and the resulting damping force of the harvesting process, 2fe[mk]1/2z˙(t), yielding Pðv,tÞ~{2fev2½mkŠ1=2zðtÞ2 ~2fev6m5=2k1=2Y02RðvÞ2e2ivt (7) The time-averaged power P(v) is given by half the modulus of the instantaneous power, i.e. PðvÞ~fev6m5=2k1=2Y02RðvÞ2e2ivt ~fev6m5=2k1=2Y02jRðvÞj2 ~ h1{fðevv=6vvn{nÞ24im2z1=2½k21f=ð2vY=02vnފ2 ~ h1{ðvm=fveYnÞ022ðiv2z=v½n2Þf3ðvv3=vnފ2 (8) Equation (8) is the expression derived in the original paper of Williams and Yates,40 and led to a conclusion that harvested power at resonance varies as v3. However, this would imply that an ambient vibration at high frequencies is as likely to show a magnitude of Y0 as one at low frequencies. In fact, as was noted by Roundy and Zhang,41 vibrational energy is proportional Materials Science and Technology 2014 VOL 30 NO 13a 1617 Crossley et al. Polymer-based nanogenerators for energy harvesting 6 (Lower left cartoon) Generic vibrational energy harvester, after Williams and Yates.40 a Response function R(v) for various resonance frequencies vn (top) and dimensionless transduction damping coefficients f. b Normalised time-averaged power P(v) for various vn and dimensionless damping coefficients fe. The parasitic contribution to f, fp is zero. c–g For vn/2p510 Hz, normalised P(v) is plotted for various fe and fp. The plot legend is common to b 1618 Materials Science and Technology 2014 VOL 30 NO 13a Crossley et al. Polymer-based nanogenerators for energy harvesting 7 Resonance frequency measurement. Acoustic excitation is denoted by curly arrows, and electrical excitation by straight arrows. a A transducer is used to excite a sample acoustically, and the transmitted response is detected by a second transducer. The sample need not be piezoelectric. b A piezoelectric sample is excited electrically and the acoustic response measured by a transducer. c A transducer is used to excite a piezoelectric sample acoustically, and the electrical response of the sample is measured to the magnitude of acceleration A05v2Y0, so it is more appropriate to express equation (8) in terms of A0 PðvÞ~ h1{ðmvf=evAn20Þð2vi2=zvn½Þ23fvðv{=1vnފ2 (9) Figure 6b shows P(v)/[mA02] as a function of frequency for a range of transduction damping coefficients fe, as well as vn, with parasitic damping fp set to zero. It can be seen that the maximum power is always extracted from vibrations near vn. Power at vyvn increases with vn but decreases with fe. For v..vn, power varies as v22 and increases with fe and vn. For v,,vn, power varies as v2, and increases with fe, but decreases with vn. Bandwidth increases with fe and vn. Figure 6c–g show P(v)/[mA02] as a function of frequency for vn/2p fixed at 10 Hz, and fe and fp being varied. Addition of a parasitic fp reduces power for vyvn, but has little effect on power away from resonance. The main conclusions to be drawn from Fig. 6 are: (i) a harvester must have resonance modes near an ambient vibration in order for a significant proportion of available power to be harvested (ii) large values of fe are favourable for broadband applications, i.e. cases where a harvester is not tuned to a specific and non-varying frequency. For on-resonance applications an optimal value of fe is expected, which should be determined experimentally. Resonance modes The natural frequencies of the harvester may be obtained via measurement, calculation (for certain high-symmetry geometries) or modelling using finite element analysis (FEA).42 There are a number of ways to measure the natural frequencies of a harvester experimentally. As a piezoelectric material under an applied AC voltage dissipates the maximum amount of energy at mechanical resonance, a peak in the dielectric loss tangent tan d may be observed at the natural frequency. It is straightforward to measure tan d at frequencies from y100 Hz to y100 kHz using an impedance bridge, but sensitivities are often too low in the important sub-kHz regime particularly if the piezoelectric coupling to those modes is small. High quality commercial impedance analysers can be used up to y100 MHz with special fixtures. Resonances which are purely electrical in nature can also manifest in a frequency scan of tan d, and it is not always straightforward to distinguish between electrical and acoustic features in the spectra. The acoustic response of the sample may be measured directly by mechanically coupling it to an external transducer of known characteristics (Fig. 7a). The sample can be excited by a second transducer (Fig. 7a) or via its own piezoelectric response (Fig. 7b). A third possibility is to excite a sample acoustically and measure the piezoelectric response (Fig. 7c). The set-up shown in Fig. 7a has the advantage that vibrational modes weakly coupled to the piezoelectric tensor can be probed. The type of transducer would depend on the frequency range being probed, typically a permanent magnet shaker at sub-kHz frequencies, and a piezoelectric actuator at higher frequencies. In order to measure a full range of vibrational modes, it would be necessary to repeat these experiments for different sample orientations. The use of AC techniques involving lock-in amplifiers would prove useful in extracting small signals of a given frequency from a noisy background. For a full modal resolution, it may be necessary to perform high speed imaging of the sample under excitation. This can be performed optically or, for microscopic samples, via electron microscopy.43 While Table 2 indicates that ‘thickness’ mode resonances are often at frequencies far from those at which ambient vibrations occur, it may be possible to excite ‘membrane’ modes (Fig. 3) that show natural frequencies Materials Science and Technology 2014 VOL 30 NO 13a 1619 Crossley et al. Polymer-based nanogenerators for energy harvesting K u~F (10) In practice it is usual to define non-zero K coefficients for adjacent nodes only. A diagonal mass matrix M for the nodes is also defined via r and internodal volumes. The natural frequencies and associated vibrational modes are given by the eigenvalues and eigenvectors of the following equation.44 À{v2 M à zK à Á~0 (11) 8 FEA mesh of subsection of nanowires in a matrix (Abaqus): FEA can be used to resolve vibrational eigenmodes in the technologically crucial sub-kHz range. For a circular disc of negligible thickness, these modes may be solved using Bessel functions. However, the coupling to the piezoelectric tensor is likely weaker than a thickness mode operating with the polar direction out of plane. In FEA a 3D model of the harvester is constructed out of N nodes with 3D displacements (un,vn,wn) where n,N. The force on the nodes is similarly denoted (Fun,Fvn,Fwn). The nodal displacement of the entire model may be described by a (3N)-element long vector u5(u1, v1, w1, u2, v2, w2, …, uN, vN, wN), with the nodal force vector F similarly defined. The space between nodes is filled with elements which are assigned material properties such as density r, elastic compliance s, and if piezoelectricity is to be explicitly modelled, the piezoelectric and permitivity coefficients. Knowledge of s for each element allows an approximate linear relationship between each and every component of u and F to be defined, forming a large (3N)6(3N) ‘stiffness matrix’ K which satisfies Once the eigenmodes are determined, it is possible to resolve the corresponding macroscopic piezoelectric coupling factors from the knowledge of the piezoelectric tensor of each FEA element. One of the disadvantages of this type of FEA is that every feature of the model must necessarily be ‘meshed’ with nodes. This makes it difficult to explicitly model macroscopic samples with nanoscale structural features such as a large assembly of NGs, as the number of nodes required becomes unfeasibly large. In order to model such a device, it is necessary to first ascertain appropriate ‘average’ material properties for the regions containing nanowires. This may be attempted via a secondary FEA model focussing on a small section containing a manageable number of NGs (Fig. 8). Overall, this type of analysis allows for a deeper understanding and better control of the frequency dependent energy harvesting performance of NGs, which has implications for materials selection and device design. Fabrication and characterisation of Polymer-based piezoelectric NGs Polymer-based NGs represent a relatively small proportion of the total research on NGs (Fig. 2), and are almost exclusively based on PVDF which was discovered to be piezoelectric in 1969.45 The polymer chains are polarisable because of the highly electronegative 9 Structure of a and b phases of PVDF: only b phase is piezoelectric due to the all-trans configuration 1620 Materials Science and Technology 2014 VOL 30 NO 13a Crossley et al. Polymer-based nanogenerators for energy harvesting 10 a PVDF nanowire fabrication by electrospinning and b PVDF nanowire fabrication by nanoporous anodised aluminium oxide (AAO) template wetting:38 thin layer of silver is deposited in Step (ii) before infiltration of PVDF solution in Step (iii) to allow for selective etching with ferric nitrate in step (iv) that serves to remove PVDF film formed on surface of template onto which PVDF solution was dropped fluorine atoms (Fig. 9). Piezoelectricity is strongest in the ferroelectric all-trans b phase (Fig. 9), but it is the a phase which typically forms in the absence of strain.46 The b phase is promoted by straining to many tens of %, or via an electric field-induced transformation under fields of order 1000 kV cm21, at elevated temperatures. PVDF and related copolymers, such as poly(vinylidene flouride-trifluoroethylene) [P(VDF-TrFE)] and poly (vinylidene flouride-trifluoroethylene-chlorofluoroethylene) [P(VDF-TrFE-CFE)], have attracted a lot of attentions in the previous decades as they combine piezoelectricity with a Young’s modulus much lower than typical ceramics (Table 2). Additionally, they are biocompatible, cheap, mechanically robust and chemically stable, making them particularly attractive for applications in NGs. PVDF nanowires are typically fabricated using an electrospinning process. Electrospinning involves the use of a large voltage (typically tens of kV) to counteract the surface tension of a droplet of molten or dissolved PVDF, causing a thin stream of liquid to be ejected from the droplet, which subsequently solidifies.47 Under optimised conditions, this can result in wires with diameters of order 100–1000 nm to be deposited on a substrate held at zero potential at some distance from the droplet. The droplet forms a shape known as a Taylor cone, and its mass is typically maintained from a reservoir inside a syringe (Fig. 10a). The ferroelectric b phase is promoted by a combination of the large electric fields applied during the electrospinning process, and the inherent mechanical stretching. While this method is Materials Science and Technology 2014 VOL 30 NO 13a 1621 Crossley et al. Polymer-based nanogenerators for energy harvesting 11 SEM images of a a partially etched P(VDF-TrFE) nanowire filled AAO template revealing forest of nanowires and b, c single template grown P(VDF-TrFE) nanowire of length 60 mm and diameter 200 nm, collected on Si substrate after dissolution of AAO template commonly used, it involves complex equipment and high voltages, and often suffers from poor control of nanowire size and alignment. An alternative fabrication process is via template wetting18,19,34–38 whereby dissolved or molten PVDF is soaked into a nanoporous templates (Fig. 10b). During the process of nanowire formation, the PVDF is subjected to substantial stresses which result in preferential formation of the ferroelectric b phase.18,19,34–38 Suitable templates include anodised aluminium oxide (AAO) that are available commercially with a range of sizes, pore diameters and pore densities. A typical geometry for nanowire fabrication is a disc of y2 cm2 area and 60 mm thickness.38 AAO is amorphous and has substantially lower stiffness than crystalline Al2O3 (Table 3). The lower stiffness of AAO coupled with the template porosity results in the templates being macroscopically quite flexible and can be readily bent by hand. Furthermore, it is possible to free the nanowires from the templates via a selective etch in phosphoric acid. Track-etched polycarbonate membranes can also be employed as templates with lower stiffness constants (Table 3) that may be favourable in certain applications. PVDF samples show enough microscopic ordering to possess certain characteristic Bragg reflections, which are typically weaker and more diffuse than those seen in ceramic or single crystal samples. It is therefore straightforward to ascertain which phases of PVDF are present in significant quantities, using X-ray diffraction with standard Bragg Brentano optics. Differential scanning calorimetry gives a measure of the latent heat of any phase transitions of the PVDF, such as those occurring near the Curie temperature of y80uC. This gives information about the phases present and level of crystallinity, which is important in determining the piezoelectric properties of materials. Infrared spectroscopy, typically Fourier transform infrared spectroscopy, is a standard tool which probes the vibrational modes of individual monomers in the sample. Atomic force microscopy and scanning electron microscopy are usually the most convenient methods to directly visualise nanowires (Fig. 11). Energy conversion efficiency The definition of NG efficiency most relevant to applications is the energy recovered divided by the available energy in the excitational vibration. While such a figure of merit would reflect both electrical and mechanical coupling to acoustic vibrations, it is not in common usage. Instead, the efficiency of a NG is usually defined as the electrical energy recovered divided by the strain energy applied to the NG during a mechanical cycle, which neglects the mechanical–mechanical coupling term. The electrical energy recovered, which will be maximised for an impedance matched load,17,48 is straightforward to measure by integration of V(t)I(t) (where V, I and t are voltage, current and time respectively). The strain energy applied to the sample can be estimated as 0?5STv50?5S2Yv, where v is the NG Table 3 For materials used for nanoporous templates, we tabulate room temperature elastic and dielectric properties (see Table 2 caption for symbol definitions) Parameter Y n r Z0 e ft Refs Units GPa kg m23 MRayl MHz Al2O3 (single crystal) 530 0.24 4000 36.8 11.5 77 55 Al2O3 (ceramic) 377 0.24 3950 30.9 65 55 Al2O3 (amorphous) 122 3100 19.4 52 63 Polycarbonate 2.3 0.37 1200 1.7 3 13 64 1622 Materials Science and Technology 2014 VOL 30 NO 13a Crossley et al. Polymer-based nanogenerators for energy harvesting volume and S can be determined experimentally. Efficiency, while an important NG performance parameter, has rarely been quantified in literature. Notably, the study of Chang et al.49 measured an average value of 12?8%, in electrospun PVDF nanowires, which is extremely promising given that the efficiency of PVDF films measured in the same work was less than 2?6%. This increase was attributed to a reduction in the barrier to domain wall motion in the case of the nanowire. A comparable efficiency of 11% was recently reported in self-poled template grown P(VDF-TrFE)38 which was attributed to improved crystallinity achieved as a result of template-induced confinement. Efficiencies of up to 30% have been reported in individual ZnO nanowires probed by AFM.3 There remains plenty of scope in understanding and optimizing the parameters that govern energy conversion efficiency in Polymer-based NGs. In practice, the overall energy conversion efficiency of a given NG would also depend on the efficiency of the additional electrical circuitry required to convert the typically AC output of a piezoelectric NG (in response to periodic vibrations) into a DC power supply as required by most electronic devices. This circuitry also involves voltage step-up/step-down capability as well as impedance matching control for optimal power transfer from NG to the device being powered. Examples of such circuits can be found in Ref. 39 and can be adapted to specific applications. Power conditioning and management circuity contribute to the overall efficiency of NG devices and thus forms an important aspect of practical power generation using piezoelectric NGs. Outlook Piezoelectric polymers can be exploited in NGs for applications in vibrational energy harvesting due to their flexibility, robustness, low densities, biocompatibility, ease and scalability of fabrication. While the majority of studies focus on NGs based on piezoelectric ceramics due to their higher piezoelectric coefficients, reliable and durable performance at a low cost and in a variety of environments may be more readily achieved in Polymerbased NGs. However, a quantitative comparison of the performance across various reported Polymer-based NGs is difficult as data on important device parameters, such as strain rates and/or energy conversion efficiency, are not often available. The reported literature in this respect focuses primarily on PVDF-based NGs as this family of polymers shows the highest piezoelectric coefficients among known ferroelectric polymers.27 However, ferroelectric polymers such as polyamides and polyureas may also be exploited in NGs for applications where PVDF or its copolymers may be unsuitable, for e.g. at temperatures higher than the melting point (y100uC). In terms of NG device fabrication and optimisation, computational modelling could prove useful in designing NGs for application in specific frequency ranges in line with available ambient vibrations. In addition, NGs involving geometries other than that of nanowires may be useful for resonance mode matching, for e.g. as in the case of the recently reported mesoporous sponge-like PVDF NG.50 Traditional fibre producing techniques such as electrospinning are currently being fine tuned and scaled up to address increasing demands for high quality polymer nanowires.51 An electrospinning technique was recently used to deposit nanowires of poly(vinylidene fluoridehexafluoropropylene) [P(VDF-HFP)] nanofibers doped with silver nanoparticles. It was found that the addition of silver nanoparticles enhanced the piezoelectric phase formed and hence the output power of the nanogenerator fabricated using these nanowires.65 More recently, cost effective and scalable techniques such as template wetting18,19,34–38 have been demonstrated to produce self-poled piezoelectric nanowires for applications in NGs. Sponge-like NGs fabricated by Mao et al.50 represent an advance in terms of NG device design and performance. Additionally, physical vapour deposition techniques may be adapted for processing potentially promising piezoelectric polymers such as odd numbered nylons.28 There is a steadily increasing interest in the field of Polymer-based NGs (Fig. 2) which is witnessing exciting new developments in terms of materials processing, device fabrication and measurement techniques.17,52 At the same time, issues relating to NG performance need to be addressed through experimentation and numerical modelling as the commercial realisation of Polymer-based NGs would ultimately depend on advances in materials and device engineering, as well as on fundamental understanding of the factors that govern energy harvesting performance in these devices. Polymer-based NGs stand to benefit from the tremendous momentum in the related fields of microelectromechanical systems, nanofabrication and processing technologies, themselves driven by diverse scientific and industrial interest. These NGs could have a significant role to play in the development of self-powered devices with far-reaching implications in the area of sustainability, for example via smart resource management schemes using wireless sensors. Acknowledgements We thank Dave Ritchie and Vijay Narayan for experimental support. SKN is grateful for support from the Royal Society through a Dorothy Hodgkin Fellowship. This work was supported by the EPSRC Cambridge NanoDTC (EP/G037221/1). References 1. S. Roundy, E. Leland, J. Baker, E. Carleton, E. Reilly, E. Lai, B. Otis, J. Rabaey, P. Wright and V. Sundararajan: ‘Improving power output for vibration-based energy scavengers’, Perv. Comput., 2005, 4, 28. 2. K. A. Cook-Chennault, N. Thambi and A. M. 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