Series Resistance Constant

For low HF concentrations in the order of 0.1%, the behavior of the interface is not oscillation, but rather resonant if the potential is set to a fixed value and time is allowed for stabilization, a steady-state constant current is finally reached. Addition of a series resistor in the order of 1 kD crrf2 leads to sustained potentiostatic oscillations [Ch5], For higher HF concentrations of about 2-5% aqueous HF, the system is self-oscillating, if the series resistivity of the electrolyte itself is not electronically compensated. For even higher concentrations the periodicity is lost and... 

Galvanostatic evaluation is often conducted at current densities of about 10-50 mA/cm2 and capacitances in the range of 1 F/cm2 can be easily achieved. The discharge time is approximately 100-200s for a 2V range. A good series resistance is below 1 Q cm2 in organic electrolytes (a time constant of about 1 s). An important component of the series resistance may be the interfacial resistance between the current collector and the active mass. 

FIGURE 11.2 Charging and discharging voltage profile of a DLC when the current is constant. The profile is almost linear. When the current is switched on or off, a voltage step due to the current in the series resistance is observed. 

The capacitance and the series resistance have values which are not constant over the frequency spectrum. The performances may be determined with an impedance spectrum analyzer [70], To take into account the voltage, the temperature, and the frequency dependencies, a simple equivalent electrical circuit has been developed (Figure 11.10). It is a combination of de Levie frequency model and Zubieta voltage model with the addition of a function to consider the temperature dependency. 

The capacitor voltage, U can be measured only across the capacitance and the series resistance taken together. At time zero, there is an instantaneous voltage drop due to the current in the series resistance, Rs /TO). The discharging process across a load resistance, R, has then a time constant (Equation 11.9). 

FIGURE 11.17 BCAP0350 lifetime experiment. The capacitance and series resistance are recorded as a function of the duration of a constant voltage polarization of 2.5 VDC and a constant temperature of 50°C. 

Consider the situation under potentiostatic conditions. Here, the potential control takes care that the sum of the potential drop across the double layer, DL, and through the electrolyte up to the position of the RE (and possibly additional external series resistances) is constant, i.e. that U = DL + I Rn or / = (U - DL)/Rn. Rn is the sum of the uncompensated cell resistance and possible external resistances and I the total current through the cell. Hence, a perturbation of a state on the NDR branch towards larger values of Dl causes, on the one hand, a decrease of the faradaic current If, and, on the other hand, a decrease of the current through the electrolyte, I. The charge balance through the cell, which can be readily obtained from the general equivalent circuit of an electrochemical cell (Fig. 8), tells us whether the fluctuation is enhanced or decays ... 

Fig. 8. General equivalent circuit of an electrochemical cell. C double layer capacitance qSDL potential drop across the double layer Zp faradaic impedance Rij series resistance (comprising the uncompensated ohmic cell resistance and all external resistances). V is a potentiostatically fixed voltage drop. (It differs from the potentiostatically applied voltage by the constant potential drop across the RE see footnote 3).

The pump has a throttling valve that relates pressure drop to flow rate Q as follows Ap (throttling) = 15(g/500)2. The temperature varies from 20 to 27°C (68 to 80.6°F). A series of constant-pressure tests yielded the data on aav and (1 — eav) shown in Fig. 14.4, aav being the average specific filtration resistance and eav the average porosity of the cake. Find cake thickness as a function of time. 

Completing a circuit and measuring the current that flows on contact or separation can quantify the transfer of electrons [2]. A typical result on contact electrification is shown in Figure 24.3. The time constants associated with the current peaks can be adjusted by inserting a series resistance in the measurement circuit. In real time, the equilibration of surface state electrons occurs instantaneously. In these experiments, the plasma polymer of tetrafluoroethylene (TFE) was deposited on two different substrate, nylon film and polished brass, and the contact and separation currents were measured with a (uncoated) brass probe... 

The series resistance was determined mainly by the resistance of the electrodes, that is 20 2 for ITO, or 50 2 for Au. Other resistances in series with the sample had negligible values. Therefore, the RC time constant was estimated to be less than 5 nsec. Such a short charging time is necessary to observe the EL spikes, as will be shown below. 

As was shown by Hills and Djordjevic (1968), it is reasonable to assume that except at extremely high frequencies, Co is negligible under the selected experimental conditions. The rate constant k in Eq. (8.61) will be very high at elevated temperatures and therefore is assumed to be negligible. An analysis based on these approximations gives the series resistance component (the bridge arrangement allowed the series component of the unknown to be measured) of the cell impedance as... 

Series resistance (12) RC time constant (m/sec) Energy in spark gap (J)... 

In the first series of tests (Figure 12), the storage capacitor was kept constant at 2800 pF and the RC time constant of the spark electrical circuit was increased from approximately 0.1 psec to 40 msec by increasing in increments the series resistance from approximately 1 G, to 15 Mfl. The energy level at the 50% firing point was used as a measure of sensitivity. As can be seen in Figure 12, the energy decreases from 8 X W J to a minimum of 6.5 X IO" J as the RC time constant is increased from 0.1 psec to some value between 0.1 and 1... 

As mentioned in the introduction, the electrical nature of a majority of electrochemical oscillators turns out to be decisive for the occurrence of dynamic instahilities. Hence any description of dynamic behavior has to take into consideration all elements of the electric circuit. A useful starting point for investigating the dynamic behavior of electrochemical systems is the equivalent circuit of an electrochemical cell as reproduced in Fig. 1. The parallel connection between the capacitor and the faradaic impedance accounts for the two current pathways through the electrode/electrolyte interface the faradaic and the capacitive routes. The ohmic resistor in series with this interface circuit comprises the electrolyte resistance between working and reference electrodes and possible additional ohmic resistors in the external circuit. The voltage drops across the interface and the series resistance are kept constant, which is generally achieved by means of a potentiostat. 

Performance and Diode Parameters. For finding the optimum absorber composition, organic solar cells of the type A with various [CuPc] [C60] ratios were prepared at a non-optimised substrate temperature. The Eff behaviour with the absorber composition (Fig. la) is dominated by the behaviour of the Jso and FF [4], In the compositional range investigated, 0.2 < [CuPc]/([CuPc] + [C60]) < 0.8, the devices V00 is almost constant taking values of about 400 mV (not shown). An efficiency of 1.6% is achieved in Fig. la at a [CuPc] [C60] composition of about 1 1 (by weight) [4], The diode quality factor, n. of the devices decreases from 2.6-2.7 at the either minimum of CuPc or C6o content to 1.8 at 1 1 absorber composition. At the same time, the OSCs series resistance decreases almost symmetrically from 0.34-0.38 Q x cm2 at a content of 17% of either CuPc or C to -0.2 Q x cm2 at an identical content of CuPc and C6o-... 

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