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www.advancedsciencenews.com www.aem-journal.com Figure3. a)Showstherelativepermittivity(er)ofPTFEsheetasthefunctionoftemperature ranging from 20 to 150 C as its test frequency is 120 Hz. b) The charging for a capacitor (50 V, 2 mF) with the load resistance R (510 V) at various temperatures within 300 s. The inset shows the Schematic circuit diagram of TENG for charging a capacitor through a full- bridge rectifier. c–f) Finite-element simulation about the space potential distribution of TENG and its color gradient bar with different potential values under different temperatures: c) 20 C, d) 20 C, e) 60 C, and f) 150 C. The up-plate is Al elctronde, the down-plate is PTFE sheet. The deeper red color (or blue color) is, the more positive (or negative) the space potential is. density and relative permittivity of PTFE on the charge density of PTFE surface. Due to the principle of charge conservation, the same amount of positive charges will be induced on the Al electrode when two materials contact together. Therefore, we can calculate the electric surface density (sAl) on the Al electron, Z lt sAl 1⁄4 spðxÞdx 0 1 1⁄4ðfPfAlÞðeN"tÞ1=2 1e ð2Þ Then, the quantity of charges DQAl could be described by, DQAl 1⁄4 SsAl 1 1⁄4SðfPfAlÞðeN"tÞ1=2 1e ð3Þ We assumed the electric charges on the Al electrode will transfer totally through external circuit to form short circuit current, so the amount of transferred charges (DQsc) can be described by 1 DQsc 1⁄4 QAl 1⁄4 SðfP fAlÞðeN"tÞ1=2 1 e ð4Þ To our best knowledge, the work function of Al and PTFE is 4.30 and 5.75 eV, respectively.[37] By quantitatively fitting the experimental data, we can obtain a nonlinear fitting equation of the relative permittivity of PTFE, as shown in Equation 5 and its numerical fitted curve is shown in Figure 4a. er 1⁄4 5:86037 108 T 3 þ 8:38492 106T2 7:02889 104T þ 2:05 ð5Þ contact electrification is given by Chowdry and Westgate,[36] The amount of transferred charges (DQsc) are influenced by the temperature-induced changes of relative permittivity and effective traps density N"t from the Equation 4. First of all, only the temperature effect on relative permittivity of PTFE was taken into regarded and the influence of effective traps density N"t on (DQsc) was ignored, we take N"t 1⁄4 1:3 105=ðcm3 eVÞ. Therefore, from Equations 4 and 5, the relationship between DQsc and T could be described by DQsc 1⁄4 28:747 ð5:86037 108T3 þ 8:38492 106T2 7:02889 104T þ 2:05Þ12 109C ð6Þ From Equation 6, the relation curve between the transferred charges and temperature can be achieved by taking N" t 1⁄4 1:3 105 =ðcm3 eV Þ shown in Figure 4b, which is basically accordant with the measurement of short-circuit transferred charges. The difference of theoretical calculation and experimental measure- ment of transferred charges may be the temperature-induced sPðxÞ1⁄4q2N"tVðxÞ1⁄4qN"tðfAl fPÞexpðxÞ lt ð1Þ lt1⁄4 e 1n2 q 2 N" t where, V(x) is the electric potential on the PTFE sheet, lt is the Debye length, q is the electron charge, the sp is the volume charge density of PTFE, N"tð=cm3 eVÞ is the volume defects density in unit energy. Here, the term defect is referred to those effective traps that can be occupied by electrons. The ФAl and Фp are the work function of the Al and PTFE, respectively. The chosen model, in this paper, is a simple and approximate model, that is, suitable for this paper to explain the effect of defect Adv. Eng. Mater. 2017, 00, 1700275 1700275 (4 of 8) © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimPDF Image | Temperature Effect on Performance of Triboelectric Nanogenerator
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