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2.3 Temperature dependence of triboelectricity Power density (mW/m2) 220 200 180 160 140 120 100 80 A. 600 Voltage (normalized) Actual distribution of ions N2 q q N1 q q q q 23 Net charge distribution q q Q = q(N1 - N2) 3.0 2.5 2.0 1.5 1.0 0.5 C. 00 100 200 Temperature (K) 400 500 D.00 50 100 150 200 250 Temperature (K) 300 350 400 450 50 100 150 200 Temperature (K) 250 300 350 B. Voltage (V) 1800 1600 1400 1200 1000 800 600 400 200 300 Al PTFE Cu Cooling stage Su et al. Wen et al. Figure 2.5: A: Picture of the actual ion distribution and the net charge distribution. The ratio of the number of particles on the two levels N2/N1 is given by the Boltzmann factor. B: Plot of the triboelectric power density as a function of temperature from experiments with triboelectric generators using Al and PTFE as contact materials. Our Schottky model is fitted to data points from Su et al. [34] using the least square function in gnuplot yielding a separation energy corresponding to the temperature E/kB = 451 K. C: Plot of normalized voltage as a function of temperature from Wen et al. [35]. We have fitted our model to data to find E/kB = 374 K. Between 200 K and 300 K Wen et al. found a large peak that, however, was not reproduced by Su et al. or by Lu et al. shown above. The four highest data points in the peak are excluded from fit. D: Plot of voltage as a function of temperature from Lu et al.[36]. Our model is fitted to data. We found for this fit E/kB = 269 K. The capacitor voltage is given by U = Q/C where C = ε0A/d is the capacitance so qN 2 U = C 1+e−E/kBT −1 . (2.29) The energy of a capacitor is W = Q2/(2C). The power density P = Wf/A becomes q = ion with charge q Lu et al. N2q2f 2 2 P = 2CA 1+e−E/kBT −1 , (2.30) where f is the charging/discharging frequency. The power density P is thus pro- portional to the frequency while the maximum output power from the device to thePDF Image | Nanomechanics Quantum Size Effects, Contacts, and Triboelectricity
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