Nanogenerator

A Nanogenerator is a type of technology that converts mechanical/thermal energy as produced by small-scale physical change into electricity. A Nanogenerator has three typical approaches: piezoelectric, triboelectric, and pyroelectric nanogenerators. Both the piezoelectric and triboelectric nanogenerators can convert mechanical energy into electricity. However, pyroelectric nanogenerators can be used to harvest thermal energy from a time-dependent temperature fluctuation.
"Nanogenerators are referred as a field that uses displacement current as the driving force for effectively converting mechanical energy into electric power/signal, disregarding if nanomaterials are used or not."
Theory of nanogenerators from Maxwell's equations.
Maxwell's equations have the following basic forms:
formula_1 (1.1)
formula_2 (1.2)
formula_3 (1.3)
formula_4 (1.4)
where the displacement current, formula_5, was first introduced by Maxwell in 1861 to satisfy the continuity equation for electric charges. The electric displacement vector D is given by formula_6, and for an isotropic dielectric medium, formula_7, thus formula_8 . The displacement current density is presented as
formula_9 (2.1)
Recently, the Maxwell's equations have been expanded to calculate the power output of nanogenerators. An additional term Ps was first added into D by Wang in 2017, where Ps is "the polarization created by the electrostatic surface charges owing to mechanical triggering, different from the electric field induced medium polarization P. The D" can be rewritten as formula_10, so the displacement current density is obtained by
formula_11 (2.2)
Then the Maxwell's equations can be expanded as
formula_12 (3.1)
formula_2 (3.2)
formula_3 (3.3)
formula_15 (3.4)
These equations are the cornerstones for deriving the output characteristics of nanogenerators, from which the output current and voltage, and the related electromagnetic radiation of a nanogenerator have all been derived.
General theory for the polarization "P"s.
The polarization Ps created by the electrostatic surface charges can be expressed by the following equation, when defining the charge density function "σs"(r,"t") on the media surface by a shape function of "f"(r,"t")=0.
formula_16 (4)
where the delta function "δ"("f"(r,"t")) is introduced to confine the media shape. Through solving the scalar electric potential formula_17 from the surface charges
formula_18 (5)
the Ps can be obtained by
formula_19
This indicates that the output energy per cycle E can be calculated as the encircled area of the closed loop in the V–Q curve, and all V-Q cycles are named as ‘cycles for energy output’ (CEO).
By periodic transformation between in load and short circuit conditions, cycles for maximum energy output can be obtained. When the load equals infinite, the V-Q becomes a trapezoid shape, the vertices of which are determined by the maximum short-circuit transferred charge QSC,max, and the maximum output energy can be calculated as:
formula_20 formula_21
For the TENG operating in CMEO with inﬁnite load resistance, the period T includes two parts of time. One part is from the relative motion in TENG, and the other part is from the discharging process in short-circuit condition. The breakdown effect is widely existing in triboelectric nanogenerators, which will seriously affects the effective maximized energy output, Eem.
Therefore, the average output power P at CMEO considering the breakdown effect should satisfy:
formula_22
Where v is the average velocity value of the relative motion in TENG, which depends on the input mechanical motions. In this equation, formula_23 is the only term that depends on the characteristics of the TENG itself.
The energy-conversion efﬁciency of the TENG can be expressed as (at CMEO with R=∞ considering breakdown effects):
formula_24
Here F stands for the average dissipative force during the operation of the TENG. This force can be frictional force, air resistance force or others. stands for the average dissipative force during the operation of the TENG. This force can be frictional force, air resistance force or others.
Therefore, it can be concluded that the term formula_23 determines both the average power and the energy-conversion efﬁciency from the characteristics of TENG itself. Eem contains QSC,max that is proportional to the triboelectriﬁcation area A. Therefore, to exclude the effect of the TENG size on the output energy, the area A should be placed in denominator of this term and then the term formula_26 determines the merits of TENG. QSC,max, VOC,max and V max’ are all proportional to the surface charge density σ. Therefore, Eem is proportional to the square of the surface charge density σ. Then, a dimensionless structural FOM (FOMS) of TENG can be defined, as the factor only depends on the structural parameters and xmax:
formula_27
Here ε0 is the permittivity of the vacuum. This structural FOM represents the merit of the TENG from the structural design. And then the performance FOM (FOMP) of TENG can be deﬁned as:
formula_28
Here,
formula_29
which is the only component related to the material properties. The FOMP can be considered as the universal standard to evaluate varieties of TENGs, since it is directly proportional to the greatest possible average output power and related to the highest achievable energy-conversion efﬁciency, regardless of the mode and the size of the TENG.
Standardized Method for Output Capacity Assessment.
With the breakdown effect considered, a standardized method is proposed for output capability assessment of nanogenerators, which can experimental measure the breakdown limit and Eem of nanogenerators. 
Former studies on the theoretical model implies that TENG can be considered as a voltage source combining with a capacitor in series, of which the capacitance varies during operation. Based on the capacitive property, the assessment method is developed by charging the target TENG (TENG1) at different displacement x to measure the breakdown condition. Another TENG (TENG2) is added as the high-voltage source to trigger the target TENG to approach the breakdown condition. Switch 1 (S1) and switch 2 (S2) are used to enable different measurement steps. 
Detailed process flow of this method, including an experiment part and a data analysis part. First of all, it is critical to keep the surface charge density identical as reflected by QSC,max, to ensure the consistency of measurement at different x. Thus in Step 1, S1 was turned on and S2 was turn off to measure QSC,max; if QSC,max is lower than the expected value, additional triboelectrification process is conducted to approach that. And then in Step 2, x was set into a certain value, and the short-circuit charge transfer QSC(x) at a certain x was measured by coulometer Q1. In step 3, S1 was turned off, S2 was turn on, and then the TENG2 was triggered to supply high-voltage output for TENG1. The charge flowing into TENG1 and the voltage across TENG1 was measured at the same time, in which the charge was measured by coulometer Q2, and the voltage was obtained by multiplying the resistance R with the current flowing through it as measured by current meter I, as detailed in Methods. The turning points obtained in this (Q, V) were considered as the breakdown points. And then, if x<xmax, the process was repeated starting from step 1 with an increased x, until xmax was achieved to finish the experimental measurement part. For the data analysis part, first, C(x) was calculated from the slope of the linear part in the measured (Q, V), by considering it as the non-breakdown part. And then, the first turning point (Qb(x), Vb (x)) was determined at the variant R2 value by linearly fitting C(x), which was considered as the threshold breakdown point. Finally, for any x∈[0, xmax], all the (Qb(x), Vb (x)) can be transferred into (QSC(x)- Qb(x), Vb (x)) as the breakdown points plotted in the V-Q cycle to calculate Eem of TENG.
Pyroelectric nanogenerator.
A pyroelectric nanogenerator is an energy harvesting device converting the external thermal energy into an electrical energy by using nano-structured pyroelectric materials. Usually, harvesting thermoelectric energy mainly relies on the Seebeck effect that utilizes a temperature difference between two ends of the device for driving the diffusion of charge carriers. However, in an environment that the temperature is spatially uniform without a gradient, such as in the outdoors, the Seebeck effect cannot be used to harvest thermal energy from a time-dependent temperature fluctuation. In this case, the pyroelectric effect has to be the choice, which is about the spontaneous polarization in certain anisotropic solids as a result of temperature fluctuation. The first pyroelectric nanogenerator was introduced by Prof. Zhong Lin Wang at Georgia Institute of Technology in 2012. By harvesting the waste heat energy, this new type of nanogenerator has the potential applications such as wireless sensors, temperature imaging, medical diagnostics, and personal electronics.
Mechanism.
The working principle of pyroelectric nanogenerator will be explained for 2 different cases: the primary pyroelectric effect and the secondary pyroelectric effect.
The working principle for the first case is explained by the primary pyroelectric effect, which describes the charge produced in a strain-free case. The primary pyroelectric effect dominates the pyroelectric response in PZT, BTO, and some other ferroelectric materials. The mechanism is based on the thermally induced random wobbling of the electric dipole around its equilibrium axis, the magnitude of which increases with increasing temperature. Due to thermal fluctuations under room temperature, the electric dipoles will randomly oscillate within a degree from their respective aligning axes. Under a fixed temperature, the total average strength of the spontaneous polarization form the electric dipoles is constant, resulting in no output of the pyroelectric nanogenerator. If we apply a change in temperature in the nanogenerator from room temperature to a higher temperature, the increase in temperature will result in that the electric dipoles oscillate within a larger degree of spread around their respective aligning axes. The total average spontaneous polarization is decreased due to the spread of the oscillation angles. The quantity of induced charges in the electrodes are thus reduced, resulting in a flow of electrons. If the nanogenerator is cooled instead of heated, the spontaneous polarization will be enhanced since the electric dipoles oscillate within a smaller degree of spread angles due to the lower thermal activity. The total magnitude of the polarization is increased and the amount of induced charges in the electrodes are increased. The electrons will then flow in an opposite direction.
For the second case, the obtained pyroelectric response is explained by the secondary pyroelectric effect, which describes the charge produced by the strain induced by thermal expansion. The secondary pyroelectric effect dominates the pyroelectric response in ZnO, CdS, and some other wurzite-type materials. The thermal deformation can induce a piezoelectric potential difference across the material, which can drive the electrons to flow in the external circuit. The output of the nanogenerator is associated with the piezoelectric coefficient and the thermal deformation of the materials. The output current I of the pyroelectric nanogenerators can be determined by the equation of I=pA(dT/dt), where p is the pyroelectric coefficient, A is the effective area of the NG, dT/dt is the rate of change in temperature.
Applications.
Pyroelectric nanogenerator is expected to be applied for various applications where the time-dependent temperature fluctuation exists. One of the feasible applications of the pyroelectric nanogenerator is used as an active sensor, which can work without a battery. One example has been introduced by Professor Zhong Lin Wang's group in 2012 by using a pyroelectric nanogenerator as the self-powered temperature sensor for detecting a change in temperature, where the response time and reset time of the sensor are about 0.9 and 3 s, respectively. In general, the pyroelectric nanogenerator gives a high output voltage, but the output current is small. It not only can be used as a potential power source, but also as an active sensor for measuring temperature variation.