High Performance Coils and Yarns of Polymeric Piezoelectric Nanofibers

Transcription

1 Supplementary Information High Performance Coils and Yarns of Polymeric Piezoelectric Nanofibers Mahmoud Baniasadi 1, Jiacheng Huang 1, Zhe Xu 1, Salvador Moreno 1, Xi Yang 2, Jason Chang 3, Manuel Angel Quevedo-Lopez 2, Mohammad Naraghi 4, and Majid Minary-Jolandan 1,5* 1Department of Mechanical Engineering, 2 Department of Materials Science and Engineering, 3Department of Bioengineering, 5 UT Dallas NanoTech Institute, University of Texas at Dallas, 8 W. Campbell Rd, Richardson, TX 758 4Department of Aerospace Engineering, 3141 TAMU College Station, TX *Corresponding Author. majid.minary@utdallas.edu Figure S1 Piezoelectric characterization of electrospun nanofibers. (A) Shows the experimental setup including a flexure stage controlled by a step-motor controller to flex the ribbon sample and a digital multimeter to register the generated electric charges. (B) and (C) show side-view of the ribbon sandwiched between two aluminum contacts and Kapton tape in (B) flexed and (C) relaxed states, respectively. 1

2 Figure S2 Optical microscope image of individual PVDF-TrFE nanofibers on the substrate for PFM experiments. 2

3 Figure S3 (A)-(D) SEM micrographs of a ribbon (membrane) with aligned nanofibers shown in different magnifications. 3

4 A B C Fabricated DC motor coil Electrospun ribbon Weight Twisted yarn to coil Figure S4 Fabrication of yarns and coils from electrospun ribbons through twisting using a DC electric motor. (A) A pre-twist ribbon with a hanging weight at one end. (B) A ribbon fully twisted to yarn form and partially twisted to coil form (bottom section). The inset shows the zoomed-in view of the twisted part to coil form. (C) A several centimeter-long coil with uniform coils along its length. 4

5 Figure S5 SEM micrographs of a coil fabricated from an aligned ribbon shown in different magnifications. The coil has an outer diameter of ~295 µm. 5

6 Figure S6 SEM micrographs of a yarn fabricated from an aligned ribbon shown in different magnifications. The yarn has a diameter of ~185 µm. 6

7 Figure S7 (A)-(D) SEM micrographs of a coil fabricated from a random ribbon shown in different magnifications. 7

8 Figure S8 Tensile experiment results in terms of specific stress vs. strain for (A) ribbon, (B) yarn, and (C) coil samples fabricated from random nanofibers. 8

9 Table S1 Failure strain (%), specific strength, and the gravimetric toughness for the samples with (A) aligned, and (B) random nanofibers. Table A Sample # of turns/mm Failure Strain (%) Specific Strength (MPa/g/cm 3 ) Toughness (J/g) Coil Coil Coil Coil Coil Coil Coil Coil Yarn Yarn Yarn Yarn Yarn Ribbon-1 N/A Ribbon-2 N/A Ribbon-3 N/A Ribbon-4 N/A Ribbon-5 N/A Sample Table B # of turns/mm Failure Strain (%) Specific Strength (MPa/g/cm 3 ) Toughness (J/g) Rope Rope Rope Yarn Yarn Ribbon-1 N/A Ribbon-2 N/A Ribbon-3 N/A

10 Theoretical analysis of the electrostatic interaction between nanofibers A single piezoelectric nanofiber with the assigned coordinate system is shown in Figure S9. Figure S9 Single nanofiber with the assigned coordinate system. PVDF belongs to the orthorhombic structure in polar point group mm2 1. The relation between polarity and applied mechanical stress for this symmetry group can be written as: P1 P 2 P 3 d31 d 32 d 33 d 24 d T 12 (1) For an applied stress along Z1-direction, 11, we have P3 d31 11, and other polarizations are zero. Hence, under an axial stress, polarization normal to the axis of the nanofiber will result in surface charges density of σe equal to d13 σ11. For adjacent nanofibers that are favorably poled (poled in the same direction), the surface charges will look as shown in Figure S1. Figure S1 Interaction of two nanofibers with surface charges generated from piezoelectric effect (Length of the nanofiber junction is L). 1

11 The electrostatic interactions between nanofibers can be estimated by treating the building blocks shown in Figure S1 as a parallel plate capacitor. Based on the principle of virtual work, the electrostatic shear force between nanofibers, Fe, can be calculated as the derivative of the electrostatic energy stored in the electric field between the nanofibers, Ue, with respect to a virtual sliding displacement between the fibers. The latter can be expressed as the change in the overlap area between the nanofibers per unit of the equivalent contact width, w (w is measured normal to plane). Therefore, Fe is estimated as: F e 2 e wg U 1 (2) L 2 where g and ɛ are the distance between nanofibers, and the absolute permittivity of the void (air) between nanofibers, respectively. In (2), the surface charge density, σe (= d13 σ11), is only a function of the piezoelectric coefficient of the nanofibers and the internal stress in the nanofibers. Therefore, in the limit of very small gaps (compared to contact width and length) the electrostatic shear force is independent of the overlap length. Hence, the work required to break nanofibers junction in shear, Ue, (subscript e stands for electrostatic) is: L 1 e Lgw 1 d13 11 VV 1 11 d13 e 1 e e F Tot U F dx F L v V (3) where L is the overlap length between nanofibers, VV is the volume of the void, which is equal to L g w. Vv in (3) is replaced with its equivalent value based on the total volume of the yarn, VTot, and the volume fraction of the nanofibers, vf ( 1 V v V ). This energy is V F Tot stored as the electrostatic energy in the void between the nanofibers. A comparison can be 11

12 drawn between the electrostatic energy stored in between the nanofibers and the elastic energy stored within the nanofibers. The latter is estimated as U result, it can be shown that: Ealstic 2.5 v F V Tot E. As a 2 Ue Ed13 1 vf (4) U v Elastic F The dimensionless parameter, Ed 2 13 structural parameters such as void density is included in, is a property of piezoelectric materials (the 1 vf vf ), which relates the energy stored in the electrostatic fields of piezoelectrically induced charges to elastic energy stored in the material. As such, this parameter can be considered a figure of merit for mechanical to electrostatic energy conversion in elastic piezoelectric materials with brick-and-mortar type structures. The volume fraction of the nanofiber (vf) can be calculated from the effective area of the yarns. The effective area of the yarns can be calculated by dividing the linear density of the yarns by its density, based on (5). λ ( g / m) ρ( g / m ) A eff. = 3 (5) where λ is the linear density of the yarns (weight/length) and ρ is the density of polymer. The linear density is defined as the weight per unit length of the yarn. This definition of the effective area takes into account the voids in the yarn s cross-section between the nanofibers. The effective diameter is, then, calculated by assuming a circular cross-section with an area of Aeff. 12

13 The porosity of the yarns can be defined as: A eff 1, A apparent (6) where the volume fraction is v 1. The Aapparent can be obtained from the SEM images assuming a circular cross section. F 13

14 Polarization (C/cm 2 ) Voltage (V) Fig S11 Acquired ferroelectric polarization of PVDF-TrFE nanofiber ribbons. 14

15 Current (na) Calculation of the elastic energy and electric charge from the PVDF-TrFE sample in flexure experiment time (s) Figure S12 Acquired current from the PVDF-TrFE ribbons. The strain energy was calculated by modeling the PVDF-TrFE sample as a beam under bending deformation. In this case, the elastic energy density is 2. The strain was estimated from the beam bending as, where h is the thickness of the PVDF ribbon and R is the radius of the curvature during the stroke of the stage. Based on the length of the sample and the stroke of the stage, R was estimated to be ~ 11.9 mm. With sample thickness h=12 µm, the strain equation yields a.5 strain at the top and bottom layer of the PVDF ribbon. E= 1.4 GPa was assumed for PVDF-TrFE. This results in a strain energy density of J/m 3. The elastic energy for a single nanofiber can be calculated by multiplying the strain energy density with the volume of a single nanofiber, based on the average diameter of the nanofibers. Since the current was acquired from only the top and bottom nanofibers in the ribbon based on the electrode connection, this number was 15

16 multiplied by the estimated number of nanofibers in the width of the ribbon at the top and bottom surfaces, using the width of the ribbon and the diameter of an average nanofiber. Electric charge generation obtained by integration of the area under the voltage and current signals (Figs. 3B and S12), which was averaged over 18 peaks (Table S2). The final efficiency was calculated to be. This is a rather small efficiency; however our system was not necessarily optimized for power efficiency, rather for demonstration of the effect of piezoelectric charges on mechanical properties. By improving the quality of the contacts to collect more of the generated current, higher efficiencies can be obtained. In particular by making the ribbon thinner, higher efficiency may be achieved. 16

17 Table S2 Electric energy for 18 peaks of stroke for the PVDF-TrFE sample. Peak # electric energy (J) E E E E E E E E E E E E E E E E E E-12 17

18 References (1) Newnham, R. E., Properties of Materials: Anisotropy, Symmetry,Structure. Oxford University Press: 25. (2) Chang, C. E.; Tran, V. H.; Wang, J. B.; Fuh, Y. K.; Lin, L. W., Direct-Write Piezoelectric Polymeric Nanogenerator with High Energy Conversion Efficiency.Nano Lett.,21, 1,