Research ArticleAPPLIED SCIENCES AND ENGINEERING

Optimization principles and the figure of merit for triboelectric generators

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Science Advances  15 Dec 2017:
Vol. 3, no. 12, eaap8576
DOI: 10.1126/sciadv.aap8576
  • Fig. 1 Triboelectric charge generation.

    Two materials with different work functions φw exchange electrons when brought into contact, generating surface charges. Rubbing is not essential as long as intimate contact is made. When the two materials separate, an electrostatic voltage is produced, which establishes a force to move the charges back if there is any conducting path. When at least one of the materials is not conductive at the surface, surface charges remain after the separation.

  • Fig. 2 Principles for optimizing triboelectric generation.

    (A) Schematic of a typical triboelectric generator (contact-separation mode). The dielectric maintains a surface charge throughout the cycle. When the moving electrode pulls away from the dielectric and enlarges the air gap (left), charge separation builds a potential that drives some of the charge to the stationary electrode. A load resistor is placed between the electrodes to produce work from this charge motion. The moving electrode cycles back and forth, producing an alternating current. The mechanical motion is characterized by an angular frequency ω. (B) A device circuit scheme where the device 1/RC is maintained close to ω. The device 1/Cdevice is large, making the relative fluctuation in 1/Ctotal = 1/Cair + 1/Cdevice smaller. A large load resistance is used to compensate for the large 1/Cdevice. (C) A device circuit scheme where overall matching is poor. 1/Cdevice is small, resulting in a large fluctuation in 1/RC. (D) The charge deposited in the stationary electrode. The good matching case (blue) resembles a sinusoid, whereas the poor matching case (red) is highly distorted. (E) The overall current decreases with larger 1/Cdevice because of the requirement of a larger load resistor. (F) The time-averaged power is optimized with a balance of both good matching and current. Power is generally higher with good matching rather than with high current.

  • Fig. 3 Analysis of the ideal model in steady state with dimensionless parameters.

    (A) Power map for the two device parameters R* and 1/C*. The color represents the dimensionless power per cycle Embedded Image. Restricted optimization of power for a given 1/C* (solid line) and a given R* (dashed line) is shown, and the two coincide at the global optimum condition (green dot). Two example suboptimal conditions (red dot, poor matching case; blue dot, good matching case) are indicated. (B) V* (= I* R*), (C) I*, and (D) P* curves for the global optimum condition and two suboptimal conditions indicated in (A). It is seen that the poor matching condition (red lines) produces highly distorted curves with low power, whereas the good matching condition (blue lines) shows characteristics as good as the global optimum condition (green lines).

  • Fig. 4 The influence of parasitic capacitance.

    (A) Decrease in the maximum obtainable power with increasing dimensionless parasitic capacitance Embedded Image. (B) Shift in the optimum R* (solid line) and 1/C* (dashed line) condition with the presence of Embedded Image.

  • Fig. 5 Model fitting to experimental data from Niu et al. (19).

    (A) Power change with respect to load resistance. Experimental data sets consist of driving conditions with average speeds of 0.08 m/s (black circles), 0.04 m/s (blue circles), and 0.02 m/s (red circles). Solid lines are from the ideal model by assuming a fixed 1/C* = 0.07, which determines the shape of the curve. The scaling of the model curve to real dimensions was determined by fitting due to the lack of experimental details in the study of Niu et al. (19). (B) The change of maximum power (left axis) and optimum resistance (for a fixed device capacitance; right axis) with respect to the average driving speed. The curves represent the expected scaling behavior of maximum power (Embedded Image, Eq. 7) and optimum load resistance (∝ 1/ω for fixed xmax;, Eq. 3) from the ideal model.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaap8576/DC1

    fig. S1. Circuit model diagrams of triboelectric generators.

    fig. S2. Transient characteristics of the ideal model.

    fig. S3. One-dimensional projections of the steady-state dimensionless power output.

    fig. S4. The influence of parasitic capacitance on device characteristics.

    fig. S5. Comparison of the output power and mechanical work input.

  • Supplementary Materials

    This PDF file includes:

    • The Ideal Model
    • Parasitic Capacitance Model
    • Power Output vs. Work Input
    • fig. S1. Circuit model diagrams of triboelectric generators.
    • fig. S2. Transient characteristics of the ideal model.
    • fig. S3. One-dimensional projections of the steady-state dimensionless power output.
    • fig. S4. The influence of parasitic capacitance on device characteristics.
    • fig. S5. Comparison of the output power and mechanical work input.

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