The electronic behavior of a hydrogen electrolytic cell as a circuit element can be represented with a nonlinear V-I characteristic curve as shown schematically in Figure 1. The V-I curve shows that the total cell voltage E_e is the superposition of two separate voltages: (1) the practical decomposition voltage, E_d and (2) the additional applied voltage ΔE, which when superposed on E_d, yields the electrolytic current, I_e, ΔE is then identified with the electromotive force (emf) for conducting electrolytic current. Because the decomposition voltage E_d is a limit to the null-current static condition, it is identified with the barrier potential2345. For a cell undergoing electrolysis, the voltage source external to the cell must supply a voltage E_e,_,given by:

E_e= E_d +ΔE.　 (1)

When the current I_e flows, by the application of E_e, the product E_eI_e represents the total power that the power supply is required to provide. The value of this power is dependent on the value of E_d, as expressed by:

P = I_e (E_d +ΔE).　 (2)

The first term E_dI_e represents the power provided by the source to the current to overcome the barrier potential E_d before the cell conducts. The conventional electrolytic scheme with a single voltage source (SSE) requires the power given by Eq.(2).

The method of ESI-PSE shown in Figure 2a, supplies potentials to the electrodes in a dual manner. That is the superposition of voltages using two independent voltage sources; a bias-voltage source, which induces E_d at the cell electrodes (Step 1 in Figure 2b), and a dc power supply, which provides power to the cell (Step 2 in Figure 2b). These sources can act in parallel independently, and supply the cell electrodes with individual potentials, thus yielding a superposition such that the resulting voltage between the cell electrodes equals the magnitude of the algebraic sum of the individual potential, i.e.,E_d+ΔE ( Figure 2c).

The bias-voltage-source does not need to produce electrical current, but merely a static voltage because of the nullcurrent condition at E_d. The cell voltage E_eis the superposition of ΔE on E_d, and the entire corresponding electrolytic process is the superposition of the charge-transfer process where ΔE is applied (i.e., power is used) on the process of electrostatic energy creation where E_d is applied (i.e., power is not used). If the current 2F flows to produce 1 mole of H₂ and one-half mole of O₂, and because the current efficiency is known from experimental evidence to be nearly unity, the total power requirement for the ESI-PSE reduces to the generalized form for any given cell, regardless of E_d, temperature, pressure, composition of electrolyte solution and cell dimension:

P^* = 2F(E_e-E_d)=2FΔE. (3)

The bias voltage source PS1 is responsible for creating the electrostatic energy to place H₂O in the decomposition state. It is employed to induce potential E_d between the electrodes by means of the electrostatic induction, thereby making the electrodes bipolar. The system therefore consists of two circuits, Loop 1 and Loop 2. The total bias voltage is equally divided into E_d among the three channels, FG(+)-A, B-C and C-FG(-). Hence, E_d is induced as a floating potential on the cell electrodes with polarity as shown in Figure 2a. This system is able to prevent the two voltage sources from affecting each other. Because of the null-current condition, PS1 does not need to provide current, but merely induce a static voltage on the electrodes. The cell can now be replaced by an isolated circuit that contains an induced voltage source delivering an output voltage of E_d between the cell electrodes, A and C.　The performance of the cell can be explained through a series of steps. First, when PS1 output voltage V_PS = E_d, I = 0 (null point). Second, if V_PS is increased from the null point, an electrolytic current I = I_e flows owing to the total source voltage (emf) of ΔE =V_PS ‒ E_d. Hence, the two sources can be replaced by a single source that delivers ΔE. Furthermore, the voltage across the cell (cell voltage) is E_d + ΔE, as a result of the superposition of ΔE on E_d. If the current 2F flows to produce 1 mole of H₂ and one-half mole of O₂, and because the current efficiency is known from experimental evidence to be nearly unity, the total power requirement for ESI-PSE reduces to the generalized form given by Eq. (3) for any given cell, regardless of the decomposition voltage E_d, temperature, pressure, composition of electrolyte solution and cell dimension: In a typical cell system in which the cell is connected to a single voltage source (SSE), the power required to generate 1 mole H₂ is given by,

P^o = 2F(E_d +ΔE). (4)

To compare the power between two electrolytic schemes, we have the power ratio:

P^*/P^o =ΔE /(E_e+E_d). (5)

A direct measurement of power requires simultaneous direct measurements of voltage and current. However, in the above experimental setup, the electromotive force,ΔE, is determined as the change in voltage from the original value of E_d. To definitively verify the ESI-PSE scheme, it is necessary to test with a different scheme in which both the emf provided by the power supply and the current can be read directly on a voltmeter and an ammeter, respectively, enabling us to measure the power directly. This may be achieved by the double cell unit and external circuit shown in Figure 3a. This circuit consists of three pairs of electrodes and two equivalent cells, labeled Cell 1 and cell 2, which have the same physical size as the single cell. The outermost A-F pair represents the field generator electrodes connected to a bias voltage source, labeled PS1, which induces a bias potential at the inner electrodes by a mechanism similar to that in the previous case. The B-E middle pair is connected to another bias voltage source , labeled PS2, to impose a voltage opposing the voltage induced between B and E. Note that electrode B should be connected to thepositive output terminal of PS2 and electrode E to the negative output terminal. Hence, electrode B acts as the anode for Cell 1 and electrode E as the cathode for cell 2. The innermost C-D pair forms an open channel, and is connected to the third power supply, PS3, which provides the emf for electrolytic currents. Electrodes C and D acts as the cathode for cells 1 and 2, respectively. The polarity of the PS3 output terminal must be such that electrode C and D are connected to the negative and positive output terminals, respectively. Then, the loop, PS2(+)-B-C-PS3-D-E-PS2(—) forms the main electrolytic circuit. The performance of the cell can be explained through a series of steps. Step 1: When a voltage 2E_d is first induced between B and E by regulating the output voltage of PS1, while the voltage between C and D remains zero. A bias voltage, E_d, appears on both cells 1 and 2 (B-C and D-E), such that electrode B becomes positive with respect to electrode E. However, the innermost electrodes, C and D, are held at the same potential because electrons can move from D to C, passing through the supply PS3 (Figure 3b). Step 2: A counter bias voltage of 2E_d is then applied by the second bias voltage source, PS2, while the voltage between C and D remains zero, such that the counter voltage opposes the induced bias cell voltage between B and E. At this stage, both cells 1 and 2 are at E_d, while the voltage between C and D remains zero. Step 3: When the output voltage of PS3 rises from zero, the current begins to flow, as indicated by the arrows in Figure 3a. In this case, the voltages measured directly with a voltmeter between electrodes C and D are identified as the emf’ ‘s that conduct electrolytic current. The measured voltage gives the total source voltage (or emf) equal to the additional applied voltage, 2ΔE, in the electrolytic circuit as a result of potential superposition (Figure 3b). Thus, the product of the measured voltage and corresponding current yields the actual power provided by the source to the load. Step 4: To test the SSE mode in situ, this unit was converted into the SSE scheme by disconnecting PS1, PS2, and PS3, connecting the power supplies to Cells 1 and 2, respectively, and the V-I characteristics curve was measured for each cell.

The present cell shown in Figure 3a, was made of acrylic resin, contained six 62x40 mm electrodes, all 0.5 mm thick, made of rectangular stainless steel sheets. These were set in parallel and fixed to the side wall and the bottom of the tank. The electrodes formed two walls of a square channel, with insulators forming the other two walls. The distance between the cell electrodes was 20 mm. A diaphragm was not used to prevent a back reaction between hydrogen and oxygen because the present study was not concerned with current efficiency. The maximum voltage was applied to the field-generator electrodes so that if there were any opening in the inner cell electrode plates, an unexpected leakage of current would occur. An alkaline water electrolyte, H₂O-10%NaOH, at 300 K was selected for all tests.

The experimental results are shown inFigure 4. The values observed for the ESI-PSE appear somewhat dispersed. This may be because three voltage supply circuits are electrically floating. Figure 4b, is the V-I curves measured for both SSE and ESI-PSE modes. The current densities measured at A2 were plotted against circuit emf ; E_d was then determined to be 1.7 V by extrapolating the straight line to the voltage axis. In Figure 4a, the voltages between electrodes A-F, B-E and B-C were plotted as function of the cell voltage (emf ) measured between the electrodes C and D. The voltages E_A-F and E_B-E must remain constant as E_C-D changes, i.e., E_A-F=1.7x4=6.8 V and E_B-E=1.7x2=3.4 V, respectively. However, the measured values for E_B-E were higher than the theoretical line. E_B-C is theoretically related to E_{C-D (}negative value₎ by the equation, E_B-C=Ed—1/2E_C-D=1.7—1/2 E_C-D. Therefore, if E_C-D=0, E_B-C=E_d=1.7 V, and if E_C-D=—2.0 V, E_B-C=2.7 V.

Figure 5, shows the experimental power requirements for both ESI-PSE and SSE modes. The mutual consistency expressed by Eq.(5) with respect to the power requirements for both SSE and ESI-PSE mode can thus be established.

This paper suggests that the electric power and hydrogen energy can be produced in the absence of external energy. However, it must be noted that this generation system does not have any relation to a perpetual motion machine. The origin of the net electric power extracted from the generation cycle is “zero power input” electrostatic energy which is created and stored in the electrolytic cell due to an intrinsic coulombic force at the decomposition voltage during electrolysis. It is then essential to prove the existence of this kind of energy.

Figure 8 is the schematics representing the performance of electrochemical cells in which there are always ionic flows by migration. In these cells, the electrons flowing in the external circuits are prohibited to enter the electrolyte, so that the energy source for migration of ions in the electrolyte is the electrostatic field strength established by time-invariable potential difference between the electrodes.

As shown in Figure 1a, electrically isolated electrodes bring the surface charge, Q.

The thermodynamic equilibrium conditions for the electrostatic field system shown in Figure 1a, are determined by the Gibbs phase rule6. It fixes the number of intensive variables to establish the equilibrium. If the electrostatic field strength E is included in the independent variables, the number of degrees of freedom is given by f=c+3‒p, where c and p, are respectively the number of components and phases. If f is considered for the H₂O-KOH solution (alkaline-water electrolyte used in the water electrolytic cell), c = 3 and p = 1, then f = 5. It follows that if T, P, N_H and N_K (N: mole fraction) are kept constant, the internal energy U becomes a function of E alone; fixing E within the stability range of the solution fixes its equilibrium state.

The electrochemical system involving electrodes separated by an ionic solution electrolyte stores energy without consuming power, but only if the potential between electrodes is maintained constant. In addition, the ionic current in the electrolyte solution is driven by the electrostatic field free of power and expressed as a function of the electrostatic field strength, (∂φ/∂x)78. The ionic current flows under the influence of an electric field created by the potential difference between the electrodes. The current I due to the migration of charged species j in the bulk region of a linear mass-transfer system having a cross-sectional area A can generally be expressed as:

I_j= |z_j|FAu_jC_j(∂φ/∂x), (9)

where z_j is the charge number for species j, F is the Faraday constant, u_j is the mobility of species j, C_j is the concentration of j, and (∂φ/∂x) represents the electric field strength. Non-electrical term associated with the diffusion was omitted, because the concentration gradient is very small in the bulk solution 8. The fact that the energy storage and the ionic current in the electrolyte does not require power, but only constant electrode potential leads to the principle of the internal self-sustainability for the electrostatic energy.

The main point of the ESI-PSE is the “zero power input” electrostatic energy. This type of energy is observed in the FC (Figure 8c). The FC is able to function exclusively under the zero power input electrostatic energy. When the H₂-O₂ fuel is applied to the respective electrodes, a constant FC voltage appears between the electrodes, which creates a current flowing through a load located outside the cell. This current generates power in this load using the total energy of the fuel. The energy of the fuel is thus completely converted into power in the load outside the cell. There is then no power inside the cell. This indicates that the spontaneous transfer of ions inside the cell is a power-free phenomenon. No power is required for this kinetic process. This is evidences for the existence of “zero power input” electrostatic energy. For this reason, the electrostatic energy is identified as internally created energy. For the process shown in Figure 2c, the power supply located outside the cell does not need to provide power, but only a static voltage to the electrodes. Therefore, the electrostatic energy is free of power.

The quantity of the energy created in the medium between the electrodes by a constant electrostatic field formed at an inter-electrode voltage, v , equals the energy stored in the medium by the process of charging a capacitor at the same voltage, because both cases are performed at the same constant electrostatic field strength vector, E, thus the same equilibrium state is attained as indicated by the phase rule. The energy, W, stored in the system connected to a voltage source is expressed by:

W = ʃQdv = (1/2)vQ, (10)

using the relation Q=Cv where Q is the charge built up on the electrodes, and C is the capacitance. If we add the relations, v=EL, Q=DA and LA=V, and make use of D=εE, where D is the electric displacement vector and ε is the permittivity, then the Eq.(9) becomes:

W = VεE²/2. (11)

The energetically self-sustaining power generation system is based on this electrodynamic energy which is spontaneously created in an electrolytic cell.

To identify the energy, W, obtained in this manner as a part of the equilibrium internal energy of the system in the electrostatic field, its thermodynamic expression must include the term, VεE²/2. The internal energy of an ionic solution, U, is a function of the thermodynamic factors of the system and is expressed as

U=U ( S, V, n_j, D ), (12)

where S is the entropy; V is the volume; n_j, the number of moles of the ionic species j. An infinitesimal change in U from this state is

dU=TdS–PdV+Σμ_jdn_j+(VE/2)dD, (13)

where μ_j is the chemical potential of the ionic species j. The last term on the right was deduced from the relation 9101112:

(∂U/∂D)_S,V,nj=VE /2. (14)

It represents variations in U resulting from variations in the electrostatic field. Because T, P, μ_j, and E are constant, one may write Eq. (13) in the integrated form:

U=TS‒PV+Σμ_jn_j+VεE²/2. (15)

The integrated quantity of U includes the last term, VεE²/2, then, in the presence of the electrostatic field, the energy increase is thermodynamically favorable; so the energy creation is a consequence of the tendency of the system to approach an equilibrium state.

Energetically self-sustaining energy cycles to produce electric power and hydrogen have been investigated on the basis of ESI-PSE. The system concepts are shown in Figure 9.　The electric power generation system is a combined energy cycle consisting of the H₂O=H₂+1/2O₂ reduction reaction performed by the ESI-PSE and the H₂+1/2O₂=H₂O oxidation reaction performed by the fuel cell. Part of the power delivered by the fuel cell is returned to the electrolytic cell and the remainder represents the net power output. In the hydrogen generation system, part of the hydrogen delivered from the EC is returned to the FC to generate power, and the remainder represents the net hydrogen output.

Major components of the generation system are a fuel cell stack (FC stack), an ESI-PSE cell stack (EC stack). The FC stack converts the pure stoichiometric H₂-O₂ fuel provided by the EC stack into electricity. In addition to cycling the generated power, H₂O, which contains heat from the exothermic reaction in the FC stack, is transferred to the EC stack to be used in its endothermic reaction. The solid polymer membrane electrolyte (PEM) are used for both fuel cell and ESI-PSE water electrolytic cell for the reason of its solid structure and its ability to operate at high current densities. The cell electrodes normally consist of a current collector, gas diffusion electrode and catalyzer electrode. Because these components are electrically conductive, the field generators can induce potentials on the inner electrodes. The EC cells are assumed to use in the bipolar configuration shown in Figure 6. The approach to optimizing the generation system and designing the system to be compact is of preferential importance. The PEM generation system is essentially an energy cycle with close conjunction of two electrochemical devices. It is important to note that with respect to the structure, the PEM EC cell must be identical with the typical PEM FC cell which has established feasibility so far. Both the FC and EC stacks must be constructed in the same form of a bipolar series connection. Only the number of cells connected in series may be different from each other.

This power generation cycle functions with zero energy input, so that the ordinary definition of energy efficiency is not applicable to the present case. Therefore, the power cycle efficiency was defined as the ratio ξ_p of the net power extracted from the generator, P_net, to the power produced by the pure stoichiometric H₂-O₂ fuel in the FC, P_f:

ξ_p = P_net/ P_f. (16)

If the voltage efficiency of FC, η, is the ratio of practical output voltage to the standard output voltage, then for 1 mole H₂,

P_f = 2FηE_f^o. (17)

where E_f^o is the standard output voltage of FC. Mass balance in the cycle requires equality of the electrolytic and galvanic currents. If the current efficiency is assumed to be unity, then Eq.(3) is subtracted from Eq.(17) to yield the theoretical net power output of the cycle,P_net . Hence, the cycle power efficiency is rearranged in the form:

ξ_p = P_net/ P_f = 1—ΔE / ηE_f^o. (18)

The hydrogen cycle efficiency,ξ_H, is defined as the ratio of the net hydrogen output rate from the hydrogen generator, M_net, to the total hydrogen generation rate from the ESI-PSE EC, M_T.If welet M_r be the recycling rate of hydrogen from the ESI-PSE EC to the FC to produce power, then

ξ_H=M_net /(M_r+M_net)=(M_T—M_r)/M_T (19)

The FC provides power, 2FηE_f^o, per 1 mole of H₂. It can then provide power, 2FM_rηE_f^o, per M_r moles of H₂. This power is recycled to the EC stack to generate hydrogen. In the ESI-PSE EC stack, the power given by Eq.(3) is used to generate 1 mole of H₂, so that when the power, 2M_rηE_f^o, is applied, the number of H₂ moles produced can be described as,

M_r+M_net= 2FM_rηE_f^o/2FΔE=M_rηE_f^o/ΔE. (20)

Hence, M_net is given by,

M_net=M_r(ηE_f^o/ΔE—1) (21)

Therefore, the hydrogen cycle efficiency is expressed in the same form as Eq.(18):

ξ_H=M_net /(M_r+M_net) ₌(1—ΔE/ηE_f^o) (22)

In Figure 10, the cycle efficiencies were plotted as function of ΔE for the ESI-PSE EC and η for the FC. Typical ΔE and η values for the commercial PEM EC and PEM FC are reported to be 0.21 V and 0.8, respectively13; corresponding power and hydrogen cycle efficiencies are near to 80%.