Open-circuit voltages

Open-circuit voltage can be defined thermodynamically through the change in the Gibbs free energy of reaction. Consider again Eq. (1.11)  

The Gibbs free energy change at constant temperature and pressure (AG)j p equals the sum of the chemical potentials fij of a species 

The chemical potential of a species of activity aj is related to its standard chemical potential fij by 

For simplicity s sake we leave out the indication in Eq. (2.42) for constant temperature and pressure, but the restriction still applies  

3 V is an empirical factor, mainly caused by the dark current-voltage curve of the device, which is determined by the ideality factor n and the reverse dark current. 

Follovdng the discussion, in order to improve Voc, the design rule of new materials is to maximize the energy difference between the HOMO level of the donor and the LUMO level of the acceptor, more specifically, to make the HOMO level of polymers deeper and LUMO level of fullerene derivatives shallower. 

As described in Section 1.2.3.2, the reversible cell potential or Nemst voltage of a hydrogen fuel cell can be expressed as Equation 1.45. This value is what we call the theoretical OCV, and it is affected by both the temperature and the pressure. 

The theoretical OCV has the same value as the reversible eell potential. However, even when no current is drawn from a fuel cell, there is irreversible voltage loss, which means that the actual values of the OCV are always lower than the theoretically expected values. To date, a quantitative explanation for such OCV behavior has not been clear in the literature. One explanation attributes this behavior to H2 crossover and/or internal current, as described in the fuel cell book written by Larminie and Dicks [26]. A mixed potential [121-124] has also been widely used to interpret the lower OCV. The combined effects of fuel crossover, internal short, and parasitic oxidation reactions occurring at the cathode are the source of the difference between the measured open circuit cell voltage and the theoretical cell potential. Therefore, the actual OCV is expressed as 

In general, the mixed potential is composed of both the cathodic O2/H2O reaction potential 

The local electrochemical reaction on the Pt surface creates a Pt-0 surface coverage of 30%, and the remaining 70% remains as pure Pt. At steady-state mixed potential, a complete layer of Pt-0 can never be achieved in order to keep the reaction of Pt to Pt-0 continued due to the diffusion of Pt-O into the bulk metal. The reported mixed cathode potential is around 1.06 V (vs. SHE) at standard conditions (25 °C, 1 atm) with an O2 partial pressure dependence of 15 mV atm [124, 125]. 

Another OCV loss is caused by the crossover of fuel through the electrolyte. Ideally the electrolyte allows the transport of only ions. In reality, however, some fuel permeates across the membrane from the anode to the cathode. In addition, some direct transfer of electrons across the membranes can occur and cause electronic short. A fuel loss due to crossover leads to a current loss. The current loss associated with an electrical short is generally small (ca. few milli-amperes) relative to the typieal operating current of a fuel cell, and therefore is not a significant source of current inefficiency. However, these effects have a significant effect on the OCV of the cell. This is particularly true of a low-temperature cell, in which activation losses are considerable [126]. 

It is convenient to consider the mass of data available for silicon and GaAs MIS cells in terms of the four factors, open circuit voltage V, short circuit current density J, fill factor FF, and ef iciency r). Pulfrey has comparea values of these parameters obtained by numerous workers who have made cells based on both majority and minority carrier tunnelling. Before considering the results for the min MIS and layer cells.ayer cells in more detail let us summarise the current position for the four parameters. 

Owing to the fact that the commonly used thermal oxidation process leads to silicon rich layers at the silicon - insulator boundary and a consequent increased number of donor states in this region, cells made using n type silicon suffer from an unfavourable decrease in band bending. This results in n-type substrates leading to cells having reduced values of usually 450 mV as shown in table 2. 

Type Substrate n Resistivity Orientation (fi. cm) Barrier Metal Oxidation Method Voc (mV) Reference 

The exception for n-type substrates occurs when deposited SiO is used - in this case the silicon rich layer is not present giving rise to a more favourable distribution of surface states and a value of n 1.34. 

In order to profit from the properties of the silicon rich oxide layer, p-type substrates are used. In this case significantly higher values of V 500 - 600 mV have been reported using Al, 

---

Open circuit voltage is the voltage across the terminals of a cell or battery when no external current flows. It is usually close to the thermodynamic voltage for the system. 

Likewise, the battery voltage is increased from its open circuit voltage on charge. 

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

To calculate the open circuit voltage of the lead—acid battery, an accurate value for the standard cell potential, which is consistent with the activity coefficients of sulfuric acid, must also be known. The standard cell potential for the double sulfate reaction is 2.048 V at 25 °C. This value is calculated from the standard electrode potentials for the (Pt)H2 H2S04(yw) PbS04 Pb02(Pt) electrode 1.690 V (14), for the Pb(Hg) PbS04 H2S04(yw) H2(Pt) electrode 0.3526 V (19), and for the Pb Pb2+ Pb(Hg) 0.0057 V (21). 

Table 1 gives the calculated open circuit voltages of the lead—acid cell at 25°C at the sulfuric acid molalities shown. The corrected activities of sulfuric acid from vapor pressure data (20) are also given. 

The temperature dependence of the open circuit voltage has been accurately determined (22) from heat capacity measurements (23). The temperature coefficients are given in Table 2. The accuracy of these temperature coefficients does not depend on the accuracy of the open circuit voltages at 25°C shown in Table 1. Using the data in Tables 1 and 2, the open circuit voltage can be calculated from 0 to 60°C at concentrations of sulfuric acid from 0.1 to 13.877 m. 

Open-circuit voltage ratio test for slip-ring motors 11/264... 

Time constant for open circuit voltage (when motor control will use delayed transfer to alternate sources on voltage loss). This value must include the effect of any capacitors applied on the load side of the motor controller. 

When lithium ions become sufficiently mobile due to heating, they migrate from the anode to the cathode with the reactions shown in Fig. 5.24 and produce open circuit voltages of about 2.5 V under ideal conditions. In... 

Typical dimensions for the /5-alumina electrolyte tube are 380 mm long, with an outer diameter of 28 mm, and a wall thickness of 1.5 mm. A typical battery for automotive power might contain 980 of such cells (20 modules each of 49 cells) and have an open-circuit voltage of lOOV. Capacity exceeds. 50 kWh. The cells operate at an optimum temperature of 300-350°C (to ensure that the sodium polysulfides remain molten and that the /5-alumina solid electrolyte has an adequate Na" " ion conductivity). This means that the cells must be thermally insulated to reduce wasteful loss of heat atjd to maintain the electrodes molten even when not in operation. Such a system is about one-fifth of the weight of an equivalent lead-acid traction battery and has a similar life ( 1000 cycles). 

Short circiiit Open circuit Voltage source Current source... 

Secondary Voltage of Wound-Rotor Motors. The secondary voltage of wound-rotor motors is the open-circuit voltage at standstill, measured across the slip rings, with rated voltage applied on the primary winding. 

There is experimental consensus on the most important parameters of singlelayer polymer photovoltaic devices, the short circuit current / , the open circuit voltage V c, and the filling factor FF. From these parameters the efficiencies of PPV based devices were typically calculated to be around 0.1% under monochromatic low light intensities. Efforts to extend the classical semiconductor picture of... 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

Friend et at. studied the influence of electrodes with different work-functions on the performance of PPV photodiodes 143). For ITO/PPV/Mg devices the fully saturated open circuit voltage was 1.2 V and 1.7 V for an ITO/PPV/Ca device. These values for the V c are almost equal to the difference in the work-function of Mg and Ca with respect to 1TO. The open circuit voltage of the ITO/PPV/A1 device observed at 1.2 V, however, is considerably higher than the difference of the work-function between ITO and Al. The Cambridge group references its PPV with a very low dark carrier concentration and consequently the formation of Schottky barriers at the PPV/Al interface is not expected. The mobility of the holes was measured at KT4 cm2 V-1 s l [62] and that for the electrons is expected to be clearly lower. 

Table 2. Open-circuit voltage (OCV) and polarization (P) at 1.00 mA per 100 mg sample in 9 mol L1 KOH solution ...

Corrosion of the positive grid [Eq. (28)1 occurs equivalent to about 1 mA/lOOAh at open-circuit voltage and intact passivation layer. It depends on electrode potential, and is at minimum about 40-80mV above the PbS04/Pb02 equilibrium potential. The corrosion rate depends furthermore to some extent on alloy composition and is increased with high anti-monial alloys,... 

Disintegration of the Oxide Layer at Open-Circuit Voltage... 

At open-circuit voltage, no anodic current flow through the positive electrode occurs that can oxidize the PbO (or PbO x) layer, but the corrosion reaction... 

---