SELF-CHARGING DROPLET CAPACITOR FOR HARVESTING LOW-LEVEL AMBIENT ENERGY

A self-charging droplet capacitor for harvesting low-level ambient energy is provided. The capacitor includes a conductive liquid droplet, which is placed on a heterogeneous and hydrophobic surface of dielectric materials coated onto a conductive substrate. The substrate and the droplet, along with the dielectric materials in between, form a parallel-plate type capacitor. The droplet is free to move on the surface, and thus, provides a position-dependent variation of capacitance. The surface consists of two regions, each with a different material and thickness. The different strengths of solid-water contact electrification of the two materials give rise to a self-charging mechanism. The variation in thickness allows for the capacitance change required for energy harvesting.

FIELD OF THE DISCLOSURE

The present disclosure is related to energy harvesting devices.

BACKGROUND

There are plentiful and diverse energy sources in the ambient environment. In addition to the well-known types, i.e., energy from solar radiation, winds, ocean waves, etc., many other types of energy are abundant, and yet, largely untapped. For example, mechanical “free” energy is almost ubiquitous, as in human activities (such as walking) and vibrations of household appliances. As rapid technological advances continue to create new frontiers of electronic devices with ultra-low power consumption, interest in extracting this untapped mechanical energy has been growing as it holds great promise of evolving into an enabling technology for next-generation self-powered electronic systems.

Based on the energy transduction mechanism used, existing schemes can be categorized into three major groups, i.e., electromagnetic, piezoelectric, and electrostatic, each possessing unique advantages and challenges. Of particular interest is the electrostatic approach due to its advantages in, among others, efficiency, circuitry integration and device miniaturization. In an electrostatic device, energy is harvested through the external work done against the electrical field in a charged capacitor. It is normally realized by reducing the capacitance while keeping the charge intact. The higher the charge carried by the capacitor, the more effective it is.

In early studies, external power sources were widely used to provide the required charge. Lately, use of electrets has become the primary method for eliminating such cumbersome external power sources to improve device integration and performance. Due to environmental conditions, rapid loss of charge can occur in electrets, leading to performance degradation. More recently, contact electrification has received growing attention as a means to both provide and maintain the required charge in an electret. It allows the lost charge to be self-replenished when the device is in operation. However, as a spontaneous process, contact electrification only allows for a limited amount of charge refill, which limits the effectiveness of this method.

SUMMARY

A self-charging droplet capacitor for harvesting low-level ambient energy is provided. The capacitor includes a conductive liquid droplet, which is placed on a heterogeneous and hydrophobic surface of dielectric materials coated onto a conductive substrate. The substrate and the droplet, along with the dielectric materials in between, form a parallel-plate type capacitor. The droplet is free to move on the surface, and thus, provides a position-dependent variation of capacitance. The surface consists of two regions, each with a different material and thickness. The different strengths of solid-water contact electrification of the two materials give rise to a self-charging mechanism. The variation in thickness allows for the capacitance change required for energy harvesting.

In some embodiments, a device is fabricated with two or more droplet capacitors and one ceramic capacitor. Passive diode switches are used to enable reconfiguration of the connectivity of the capacitors, which leads to a geometrical growth of the energy in the system. With a 450 microliter (μL) water drop in each capacitor, the device can effectively harvest energy from low ambient vibrations. The energy harvested grows by 100 times within 11 cycles, sufficient to illuminate 30 light-emitting diodes (LEDs) connected in series.

An exemplary embodiment provides a self-charging droplet capacitor. The self-charging droplet capacitor includes a conductive substrate; a dielectric layer over the conductive substrate and forming a hydrophobic surface having a first region and a second region, wherein the first region and the second region of the dielectric layer have at least one of a difference in thickness or a difference in dielectric constant such that the first region has at least twice a capacitance of the second region; a conductive liquid droplet placed over the dielectric layer such that it is free to move on the hydrophobic surface; and an electrical lead in continuous contact with the conductive liquid droplet as it moves on the hydrophobic surface, wherein the electrical lead and the conductive substrate are coupled across a base capacitor such that the base capacitor is charged as the conductive liquid droplet moves from the first region to the second region and from the second region to the first region.

Another exemplary embodiment provides a self-charging device. The self-charging device includes a base capacitor; a first droplet capacitor; a second droplet capacitor, wherein each of the first droplet capacitor and the second droplet capacitor is configured to produce a positive charge in a first state and a negative charge in a second state; and solid state switching elements coupling the first droplet capacitor and the second droplet capacitor to the base capacitor such that the positive charge and the negative charge produced by the first droplet capacitor and the second droplet capacitor control the solid state switching elements and charge the base capacitor.

DETAILED DESCRIPTION

A self-charging droplet capacitor for harvesting low-level ambient energy is provided. The capacitor includes a conductive liquid droplet, which is placed on a heterogeneous and hydrophobic surface of dielectric materials coated onto a conductive substrate. The substrate and the droplet, along with the dielectric materials in between, form a parallel-plate type capacitor. The droplet is free to move on the surface, and thus, provides a position-dependent variation of capacitance. The surface consists of two regions, each with a different material and thickness. The different strengths of solid-water contact electrification of the two materials give rise to a self-charging mechanism. The variation in thickness allows for the capacitance change required for energy harvesting.

In some embodiments, a device is fabricated with two or more droplet capacitors and one ceramic capacitor. Passive diode switches are used to enable reconfiguration of the connectivity of the capacitors, which leads to a geometrical growth of the energy in the system. With a 450 microliter (μL) water drop in each capacitor, the device can effectively harvest energy from low ambient vibrations. The energy harvested grows by 100 times within 11 cycles, sufficient to illuminate 30 light-emitting diodes (LEDs) connected in series.

Embodiments described herein provide a droplet variable capacitor, which self charges each time the droplet moves across a hydrophobic surface while simultaneously varying the capacitance. An energy harvesting device can be fabricated with multiple such capacitors. When driven by an external excitation, the device switches between two configurations, allowing a positive feedback mechanism to be established, which drives the energy stored in the device to grow exponentially. Semiconductor diodes are used to provide automatic switching without the need for mechanical switches. The self-charging effect produces sufficient energy for the initial operation of semiconductor diodes, which allows for continuous energy harvesting in the successive cycles. Using a water drop of 450 μL, the capacitor self charges by 3.8 nanocoulombs (nC) when the drop moves across the surface. Within 11 energy harvesting cycles, a 100-fold increase in energy stored in the system has been observed, from 0.027 μJ to 2.7 μJ. A device with two 450 μL water drops can produce sufficient energy to illuminate 30 green LEDs connected in series.

A. Materials and Methods

FIG.1Ais a schematic diagram of an exemplary self-charging droplet variable capacitor10according to embodiments described herein in an initial, uncharged state.FIG.1Bis a schematic diagram of the self-charging droplet variable capacitor10ofFIG.1Ain a first transition state.FIG.1Cis a schematic diagram of the self-charging droplet variable capacitor10ofFIG.1Ain a charged state.FIG.1Dis a schematic diagram of the self-charging droplet variable capacitor10ofFIG.1Ain a second transition state.

FIGS.1A-1Dfurther illustrate the working principle of the self-charging droplet variable capacitor10(e.g., part or all of an energy harvesting capacitive device). As in a traditional capacitor, the droplet variable capacitor10includes two electrodes with dielectric materials in between. One of the electrodes is made from a solid, conductive material (e.g., doped silicon in the illustrated example, though any conductive material may be used), which may also serve as the substrate of the device (e.g., a conductive substrate12). A movable, conductive droplet14is used as the other electrode. The mobility of the conductive droplet14allows for a position-dependent variation of capacitance.

In the illustrated embodiment, a dielectric layer16is composed of a passivation layer18(e.g., a layer of tantalum pentoxide) coated with a heterogeneous surface20. The heterogeneity involves two aspects, each serving a distinct purpose. The heterogeneous surface20contains two regions22,24of different thicknesses and materials. In an exemplary aspect, a first region22is thinner (resulting in a higher capacitance) and second region24is thicker. The variation in thickness allows the capacitance to change with the position of the conductive droplet14. In some embodiments, the capacitance in the first region22is at least twice the capacitance of the second region24to improve energy harvesting of the droplet variable capacitor10. The material difference (e.g., polytetrafluoroethylene (PTFE) for the first region22and CYTOP for the second region24) allows for self-charging as a result of contact electrification. Some embodiments may use a common dielectric material with a varied thickness, which may require treatment of the surfaces in the first region22and the second region24to facilitate contact electrification.

In some examples, the two regions22,24have similar dielectric constants. As used herein, materials with a “similar” dielectric constant refers to any two or more materials having dielectric constant values within a tolerance of ±5% of each other. In the illustrated embodiment, the first region22is formed from PTFE and the second region24is formed from CYTOP (e.g., with PTFE and CYTOP having a similar dielectric constant of2). The capacitance is thus primarily determined by the thickness of the dielectric layer16. The effect of contact electrification between water and CYTOP is much weaker than that between water and PTFE. In some embodiments, the difference in dielectric constant between the first region22may be larger (e.g., to have a planar surface, the dielectric constant in the first region22may be twice the dielectric constant in the second region24).

The resulting surface charge densities of the two regions22,24are significantly different. Such a difference in surface charge density creates a self-charging mechanism for the droplet variable capacitor10. Without loss of generality, it can be assumed the conductive droplet14is initially on PTFE with both electrodes grounded (FIG.1A). The device can be modeled as a charge source powering two capacitors connected in series. One of the capacitors, referred to as the intrinsic capacitor Cintrherein, is established at the liquid-solid interface in a similar manner as an electrical double-layer due to the surface charge, while the other, referred to as the droplet capacitor C herein, is established due to the electrodes and dielectric layers.

In the initial state, the intrinsic capacitance Cintris charged due to the surface charge while the droplet capacitor C is neutral. When the conductive droplet14moves across the surface to the CYTOP region, the lower surface charge density of the CYTOP surface induces a discharging current from the intrinsic capacitor Cintr, which charges the droplet capacitor C (FIG.1B) until the conductive droplet14is completely on the CYTOP surface (FIG.1C).

If the conductive droplet14then moves backward toward the PTFE side, the higher surface charge density on the PTFE surface will lead to discharging of the droplet capacitor C and charging of the intrinsic capacitor Cintr(FIG.1D) until the conductive droplet14is completely in the PTFE region and the initial state is restored (FIG.1A). It is thus reasonable to model the entire device as one capacitor, which acquires a certain amount of positive charge when the conductive droplet14moves from the first region22(e.g., the PTFE region) to the second region24(e.g., the CYTOP region) and the same amount of negative charge when the conductive droplet14moves from the second region24to the first region22.

In an exemplary aspect, the conductive droplet14is encapsulated in the droplet variable capacitor10by sidewalls26made from an appropriate material (e.g., an insulating material such as acrylic). The conductive droplet14may further be encapsulated by a lid (not shown) such that the conductive droplet14resides (and moves freely) within an air cavity. The conductive droplet14may be any conductive liquid or gel, such as water, a liquid metal (e.g., mercury, caesium, rubidium, francium, gallium, alloys of these, etc.), a liquid conductive polymer, and so on.

A self-charging variable capacitor10according toFIGS.1A-1Dwas fabricated on a doped silicon substrate that was coated with300nanometer (nm)-thick tantalum pentoxide (Ta2O5). The doped silicon substrate functioned as a fixed electrode for the device. The Ta2O5coating provided necessary insulation to avoid the device being shorted due to possible pin holes in the hydrophobic coatings. The thicknesses of PTFE and CYTOP coatings were approximately 0.8 microns (μm) and 19.5 μm, respectively. A water drop of a volume of 450 μL was used as the conductive droplet14(e.g., movable electrode). The corresponding capacitance was measured directly to be C=2.77 nanofarads (nF) when the water drop was on PTFE and C′=0.13 nF when it was on CYTOP.

A. Energy Harvesting Mechanism

It has been shown that proper, repetitive reconfiguration of a system of variable capacitors induces positive feedback on the electric energy stored in the system. Such a snowball effect is beneficial to scavenging low-level energy from the ambient environment.

FIG.2Ais an equivalent circuit diagram of a three-capacitor self-charging device28according to embodiments described herein.FIG.2Bis a first configuration of the three-capacitor self-charging device28ofFIG.2Ain which a first self-charging variable capacitor10a(having a first capacitance C1) and a second self-charging variable capacitor10b(having a second capacitance C2) are connected in series.FIG.2Cis a second configuration of the three-capacitor self-charging device28ofFIG.2Ain which the first self-charging variable capacitor10aand the second self-charging variable capacitor10breduce in capacitance and are connected in parallel.

The self-charging device28includes the first self-charging variable capacitor10a, the second self-charging variable capacitor10b, and a fixed base capacitor C0interconnected by solid state switching elements (e.g., D1, D2, D3). In this regard, the self-charging device28ofFIGS.2A-2Ccan be switched between parallel and series configurations to facilitate self-charging. In each configuration, the electric current flows in a fixed direction. In the first configuration (FIG.2B), the current flows from the base capacitor C0to the variable capacitors10a(with capacitance C1) and10b(with capacitance C2), which are connected in series. In the second configuration (FIG.2C), the variable capacitors are connected in parallel with the capacitances being reduced by external work, i.e., C′1<C1and C′2<C2. In this configuration, the current flows from the first variable capacitor10a(with capacitance C′1) and the second variable capacitor10b(with capacitance C′2) to the base capacitor C0.

It is thus possible to use solid state switching elements, such as diodes or transistors, instead of mechanical switches to provide the required switching during reconfiguration provided that the required voltages to turn the solid state switching elements on (e.g., forward biases in the case of diodes) can be achieved. This also provides improved integration between the design of the energy harvester (e.g., the self-charging variable capacitors) and the supporting circuit.

In an exemplary aspect, the first self-charging variable capacitor10ais connected (e.g., directly connected) to a first node of the base capacitor C0and the second self-charging variable capacitor10bis connected (e.g., directly connected) to a second node of the base capacitor C0. A first switching element (e.g., first diode D1) is coupled between the first self-charging variable capacitor10aand the second self-charging variable capacitor10b(e.g., with the anode of the first switching element connected to the first self-charging variable capacitor10a). In this regard, the first self-charging variable capacitor10ais coupled between the first node of the base capacitor C0and the first switching element (first diode D1), and the second self-charging variable capacitor10bis coupled between the second node of the base capacitor C0and the first switching element (first diode D1).

A second switching element (second diode D2) is coupled between the second node of the base capacitor C0and a node between the first self-charging variable capacitor10aand the first switching element (e.g., such that the cathode of the second diode D2is connected to the anode of the first diode D1). A third switching element (third diode D3) is coupled between the first node of the base capacitor C0and a node between the second self-charging variable capacitor10band the first switching element (e.g., such that the anode of the third diode D3is connected to the cathode of the first diode D1).

The basic switching mechanism is described as follows. It should be understood that while the mechanism is discussed with respect to diodes as switching elements, other solid state switching elements may be used, including diodes (e.g., standard diodes, Schottky diodes, Zener diodes, PIN diodes, etc.), transistors (e.g., bipolar transistors, field effect transistors, etc.), thyristors, etc., and combinations thereof. When the voltage across the base capacitor C0is sufficiently greater than the sum of those across the first self-charging variable capacitor10aand the second self-charging variable capacitor10b, the first diode D1is on whereas the second diode D2and the third diode D3are both off due to being reverse biased. Thus, the current flows from the base capacitor C0to the first self-charging variable capacitor10aand the second self-charging variable capacitor10bas shown inFIG.2B. The current stops after the system reaches equilibrium.

The capacitances of the first self-charging variable capacitor10aand the second self-charging variable capacitor10bare then reduced to C′1<C1and C′2<C2, respectively, due to the external energy input (e.g., from motion or vibration of the self-charging device28). As a result, the voltages respectively across the first self-charging variable capacitor10aand the second self-charging variable capacitor10bincrease while the total charge remains the same. Such increase in voltage creates a forward bias for both the second diode D2and the third diode D3while keeping the first diode D1off. If there is sufficient amount of charge, the increase of voltages will be large enough to turn on the second diode D2and the third diode D3to allow a current to flow from the first self-charging variable capacitor10aand the second self-charging variable capacitor10bto the base capacitor C0as shown inFIG.2C. Note that the circuit model shown inFIGS.2A-2Ccan be extended to include any number of variable capacitors as demonstrated in Section III.C (FIGS.4and5).

B. Device Implementation

FIG.3Ais a schematic diagram of an exemplary three-capacitor self-charging device28according to embodiments described herein in an initial, uncharged state.FIG.3Bis a schematic diagram of the three-capacitor self-charging device28ofFIG.3Aafter transition of the conductive droplet14from the first region (PTFE) of the dielectric layer to the second region (CYTOP).FIG.3Cis a schematic diagram of the three-capacitor self-charging device28ofFIG.3Aafter transition of the conductive droplet14back to the first region (PTFE).

As an example,FIGS.3A-3Cshow the working principle of an embodiment involving two self-charging droplet variable capacitors10a,10band one fixed capacitor. In an exemplary aspect, each droplet variable capacitor10a,10bincludes an electrical lead30in continuous contact with the conductive liquid droplet14as it moves on the dielectric surface. The electrical lead30may, for example, be a wire running through the air cavity of the conductive droplet14, or it may be a conductive material deposited over a lid and/or sidewall of the air cavity.

Depending on the positions of the conductive droplets14, the system can be switched between two configurations: the first configuration, in which both conductive droplets14are on the surface of the thinner, PTFE region with diodes connected such that if the first diode D1is on, both the second diode D2and the third diode D3will be off, and hence the first self-charging variable capacitor10aand the second self-charging variable capacitor10bare connected in series; and the second configuration, in which both conductive droplets14are on the surface of the thicker, CYTOP region. In this configuration, if both the second diode D2and the third diode D3are on, the first diode D1will be off, and thus, the first self-charging variable capacitor10aand the second self-charging variable capacitor10bare connected in parallel.

Without loss of generality, it is assumed in the initial state, the system is in the first configuration and both conductive droplets14are grounded so that there is no unbalanced charge in the conductive droplets14(FIG.3A). There is no initial charge in the base capacitor C0. An external excitation drives the conductive droplets14to move toward the CYTOP region. If the self-charging effect is sufficiently strong, the second diode D2and the third diode D3will be on while the first diode D1will be off due to the reverse bias. The system is switched to the second configuration. Charge will flow to the base capacitor C0as shown inFIG.3B.

The base capacitor C0is now charged. The external excitation (e.g., a motion or vibration of the self-charging device28) then drives the conductive droplets14back to the PTFE region. The first diode D1is turned on while the second diode D2and the third diode D3are off. The system is in the first configuration again. Charge flows from the base capacitor C0to the conductive droplets14as shown inFIG.3C.

The work done by the external excitation is converted to electrical energy, which is stored in the capacitors. If the excitation is periodic such that the conductive droplets14are driven to continuously move between the two surface regions, it is possible for the electrical energy to grow exponentially because of the positive feedback resulting from the continuous switching of the system between two configurations.

Using the equivalent circuit model shown inFIGS.2A-2C, the energy harvesting process can be quantitatively analyzed. Here a device composed of a base capacitor C0and an arbitrary number (n>1) of variable capacitors is considered. For simplicity, the following assumptions are made: (1) all variable capacitors are identical, i.e., C1=C2= . . . Cn=C, C′1=C′2= . . . C′n=C′; (2) the motion induced self-charging effect imposes a fixed amount of charge,Qself, to each conductive droplet14, and (3) the conductive droplets14are driven by an external excitation to repetitively move across the two regions on the surface in the same manner.

It is noted that the reverse biases on the diodes can be significantly different, and thus, the number of diodes required for each configuration to avoid diode breakdown can be different. Therefore, it is further assumed that the total forward bias on the diodes for the first configuration is VF1and that for the second configuration is VF2. An energy harvesting cycle is defined as the time required for the conductive droplets14to complete a single round-trip on the surface, within which the system completes reconfiguration twice and is in the configuration of the initial state. The end of the ith cycle is also the start of the i+1th cycle. It can be shown that the total charge in the system follows

where α=C0/C′, β=C/C0, Qt(w)(i)(w=1,2) is the charge in the system for each configuration in the ith cycle, Qζ(w)is the amount of charge from the combined effect of the diodes and self-charging capacitors, i.e.,

It can be shown that

The total charge in the system will grow exponentially.

FIG.4is an equivalent circuit diagram of a four-capacitor self-charging device28according to embodiments described herein. The four-capacitor embodiment includes three self-charging variable capacitors10a,10b,10cand a base capacitor C0connected with six switching elements in a manner similar to the three-capacitor embodiment ofFIGS.2A-2CandFIGS.3A-3C. That is, in the first configuration, the first self-charging variable capacitor10a, the second self-charging variable capacitor10b, and a third self-charging variable capacitor10care connected in series across the base capacitor C0. In the second configuration, the first self-charging variable capacitor10a, the second self-charging variable capacitor10b, and the third self-charging variable capacitor10care connected in parallel with each other and the base capacitor C0.

FIG.5is an equivalent circuit diagram of a five-capacitor self-charging device28according to embodiments described herein. The five-capacitor embodiment includes four self-charging variable capacitors10a,10b,10c,10dand a base capacitor C0connected with nine switching elements in a manner similar to the three-capacitor embodiment ofFIGS.2A-2CandFIGS.3A-3C. That is, in the first configuration, the first self-charging variable capacitor10a, the second self-charging variable capacitor10b, the third self-charging variable capacitor10c, and a fourth self-charging variable capacitor10dare connected in series across the base capacitor C0. In the second configuration, the first self-charging variable capacitor10a, the second self-charging variable capacitor10b, the third self-charging variable capacitor10c, and the fourth self-charging variable capacitor10dare connected in parallel with each other and the base capacitor C0.

FIG.6Ais a graphical representation of an output voltage of a self-charging variable capacitor as the conductive droplet moves from the first region (PTFE) to the second region (CYTOP) of the dielectric layer.FIG.6Bis a graphical representation of an output voltage of a self-charging variable capacitor as the conductive droplet moves from the second region (CYTOP) to the first region (PTFE) of the dielectric layer.FIGS.6A and6Bshow the electrical outputs of a self-charging variable capacitor with a 450 μL water drop. A voltage was applied to the variable capacitor when the water drop was on one side and the voltage was measured after the water drop was moved across the junction to the other surface.

FIG.6Ashows the results obtained when the voltage was applied when the water drop was on PTFE. The results for the case where the voltage was applied when the water drop was on CYTOP are shown inFIG.6B. In both cases, the measured voltages VOand applied voltages VIshow a strong linear relationship, indicating a stable capacitance variation. When the applied voltage is zero, i.e., VI=0 V, the capacitor self-charges to 29.1 V (or 3.8 nC) when the water drop moves from the PTFE surface to CYTOP. This can provide sufficient initial voltage bias for diodes to conduct forward.

The ratio between the measured capacitances, i.e., C/C′=21.31, is much larger than the slope of the linear relationship (17.09) shown inFIG.6A. This indicates that not all the charge moved along with the water drop when it moved from PTFE to CYTOP. The charge remaining on the surface after the water drop had moved away can be calculated using the measured capacitances and the data shown inFIG.6A.

FIG.7is a graphical representation of charge remaining on the first region (PTFE) when the conductive droplet moves to the second region (CYTOP) as inFIG.6A. Such left-over charge can be modeled using a parasite capacitor connected in parallel to the self-charging variable capacitor. Its value can be calculated to be Cp=0.64 nF for the PTFE side. When the applied charge is more than 17 nC, which is equivalent to approximately 6 V of voltage applied to the water drop when it is on PTFE, the parasite capacitance starts to show nonlinearity and increase with the applied charge. Such parasite capacitance for the CYTOP side is negligible because the slope shown inFIG.6Bis the same as the ratio between the two capacitances, i.e., C′/C=0.047.

Taking into account the effect of parasite capacitance and defining δ=Cp/C, the amount of charge in the system follows

where

represents the effect of the parasitic capacitance,

In this evaluation, the ratio between the maximum and minimum capacitances of the variable capacitors is kept constant. Under this condition, {circumflex over (γ)} reaches the maximum value when α=β=√{square root over (C/C′)}. For the prototype devices used in this evaluation, the optimal value of C0is 0.60 nF and the maximum growth rate is {circumflex over (γ)}max=1.33.

B. Energy Harvesting Performance

Dividing both sides by Ct(w), Equation 2 can be converted into a voltage expression as follows

where Ct(1)=C0+C/2 and Ct(2)=C0+2C′.

FIG.8Ais a graphical representation of voltage accumulation of an embodiment of the self-charging device in the first configuration and the second configuration.FIG.8Bis a graphical representation of harvested energy of the embodiment of the self-charging device in the first configuration and the second configuration.FIGS.8A and8Bshow the results obtained when the self-charging device is driven by an external excitation. The device was slowly rocked by ±8° so that the two water drops synchronously moved across the junction repetitively. An electrometer is connected to the base capacitor C0to continuously measure the growth of voltage.

The first cycle started with both water drops on PTFE and the system was in the first configuration with charge neutralized. When water drops moved from PTFE to CYTOP, the second diode D2and the third diode D3were turned on due to capacitor self-charging while the first diode D1was reverse biased. The system was then switched to the second configuration so that charge flew to the base capacitor C0with the voltage settling at 8 V. The water drops were then driven back towards PTFE. The first diode D1was turned on due to the charge carried by the water drops while the second diode D2and the third diode D3were off due to the reverse bias. The system was switched back to the first configuration with the voltage across the base capacitor C0settling at 1 V.

Continued excitation of the device created a positive-feedback mechanism, which drove the voltage to 53 V in just a few cycles. The fitted growth rate, {circumflex over (γ)}, is 1.33 when the measured voltages from the first configuration are used. It is 1.30 when the voltages from the second configuration are used. The experimental results agree very well with the theoretical value 1.33. As the electrical potential of variable capacitors on the PTFE side exceeds 6 V, the growth rate starts to reduce due to the nonlinearity and the increase in parasite capacitance. This leads to slower growth of voltages.FIG.8Bshows the harvested energy in the prototype device. The energy increased by 100 times, from 0.027 μJ to 2.7 μJ in the first configuration, within 11 cycles.

FIG.9Ais a schematic diagram of an embodiment of the self-charging device28with two 450 μL water drops illuminating 30 LEDs connected in series under a 3 hertz (Hz) vibration.FIG.9Bis a time history of voltages across the base capacitor C0of the self-charging device28ofFIG.9A. Such low-frequency vibrations can be found in many human activities, such as walking. After a few seconds, the voltage output reached a sufficiently high value to illuminate 30 green LEDs, as shown inFIG.9B.

C. Harvesting Energy with Additional Resistive Loads

During the reconfiguration process, electrical currents are generated when charge redistributes among the capacitors. Embodiments of the self-charging device described herein can be used to harvest energy from such flow of charge through a resistive load. For example, a resistive load RLcan be connected between the base capacitor C0and the variable capacitors.

FIG.10Ais an equivalent circuit diagram of an embodiment of the self-charging device28used for energy harvesting with a resistive load.FIG.10Bis a graphical representation of energy harvested per cycle by the self-charging device28ofFIG.10A. Note that the final state of the device at the end of each reconfiguration process is path independent, therefore, the resistive load does not alter the exponential growth of charge or the energy stored in the device.

Numerical simulations have been conducted with using different levels of resistive load to evaluate the potential of harvesting energy through transient currents. For simplicity, the internal resistance of the device has been assumed to be negligible. The total energy dissipated through the resistive load during a complete reconfiguration process, i.e., the first configuration switching to the second configuration or vice versa, has been calculated through numerical integration. The results obtained respectively with resistive loads of 1 megaohm (MΩ) and 1 kilohm (kΩ) are shown inFIG.10B. It is seen that the energy harvested through a resistive load grows exponentially with the number of cycles. The harvested energy when the device is switched from the first configuration to the second configuration is significantly more than that from the opposite reconfiguration. The level of resistive load slightly impacts the amount of energy harvested—a higher resistive level yields slightly more energy.