under consideration that lne::T . 2:303loge::T;R . 8:3145J=eK? moleT; F . 8:3145
Ws=eK?moleT; F . 96485 As=equiv:; thusR=F . 0:02569V ? equiv: ? mole 1.
The lead-acid battery may be taken as an example: In the usually applied
concentration range, diluted H2SO4 is dissociated mainly into Ht and HSO 4
ions.
Only about 1% of the H2SO4 molecules dissociate into 2 ?Ht and SO2 4 . In
consideration of the actual state of dissociation, the laptop computer batteries can be written
Pb t PbO2 t 2 ?Ht t 2 ?HSO 4
, 2 ? PbSO4 t 2 ?H2O e9T
The free enthalpy of this reaction is DG . 372:6 kJ. When this value is inserted into
Eq. (5) the standard value of the equilibrium voltage results:
Uo;s . 1:931V e10T
which applies for aHt ; aHSO4 , and aH2O . 1 mole=L and is approached by an acid of
the density 1:066 g= cm3 or a concentration of about 1.083 mole/L e&10 wt%T.
Table 1.1 shows battery systems, their cell reaction, nominal voltage Uo and
theoretical specific energy that is derived by the above thermodynamic laws, and in
Column 9 the actually reached specific energy. The Sony VGP-BSP9 battery systems, listed in
the lines 11 and 12 in Table 1.1, will be treated in Chapter 10, the zinc/bromine
system in Section 1.8.5.
Note: Actually not the true equilibrium voltage but only the open circuit voltage can be
measured with lead-acid batteries. Due to the Sony VGP-BPS10 secondary reactions of
hydrogen and oxygen evolution and grid corrosion, mixed potentials are established at
both electrodes, which are a little different from the true equilibrium potentials (cf. Fig.
1.18). But the differences are small and can be ignored.
Figure 1.2 Equilibrium cell voltage of the lead-acid battery referred to, acid density, and
acid concentration in wt% H2SO4.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
The thermodynamic data also determine the Dell XX327
coefficient of the
equilibrium cell voltage or electrode potential according to the relation
dUo
dT .
DS
n ? F e13T
In Sony VGP-BPS13AS
practice this coefficient usually can be neglected, since it is small and
concealed by other effects that far more strongly depend on temperature.
The specific energy (Column 8 in Table 1.1) results from division of the energy
that can be drawn from the cell eUo ? n ? FT by the weight of the reacting components.
The discrepancy between the theoretical value and that in practice (Column 9) is
caused by all the passive components that are required in an actual cell or battery.
1.3.2.1 Single Electrode Potential
Thermodynamic calculations are always based on an electrochemical cell reaction,
and the derived voltage means the voltage difference between two electrodes. The
voltage difference between the electrode and the electrolyte, the ‘absolute potential’,
cannot exactly be measured, since potential differences can only be measured
between two electronic conductors (2). ‘Single electrode potential’ always means the
cell voltage between this electrode and a reference electrode. To get a basis for the
electrode-potential scale, the zero point was arbitrarily equated with the potential of
the standard hydrogen electrode (SHE), a hydrogen electrode under specified
conditions at 25 8C (cf. Ref. 3).
In battery practice, hydrogen reference electrodes are not used. They are not
only difficult to handle, but include in addition the risk of contamination of the
battery’s electrodes by noble metals like platinum or palladium (4). Instead, a
IBM 40Y6799
of reference electrodes are used, e.g. the mercury/mercurous sulfate
reference electrode eHg=Hg2SO4T in lead-acid batteries, and the mercury/mercuric
oxide reference electrode (Hg/HgO) in alkaline solutions (e.g. Ref. 5). In lithium ion
batteries with organic electrolyte the electrode potential is mostly referred to that of
the Sony VGP-BPS21 electrode (cf. Chapter 18).
1.3.3 Current Flow, Kinetic Parameters, and Polarization
When current flows, the Vostro 1500 Battery
cell reaction must occur at a corresponding rate. This means
that electron transfer has to be forced into the desired direction, and mass transport
is required to bring the reacting substances to the electrode surface or carry them
away. To achieve this current flow, additional energy is required. It finds its
expression in overvoltages, i.e. deviations from the equilibrium voltage (sometimes
denoted as ‘irreversible entropy loss’ T? DSirr). Furthermore, current flow through
conducting elements causes ohmic voltage drops. Both mean irreversible energy loss
and corresponding heat generation, caused by current flow.
As a result, the HP DV6000 Battery
U under current flow is reduced on discharge or
increased secondary cell on charge compared to the equilibrium value Uo. The
difference U Uo, when measured as deviation from cell voltage, comprises:
1. The overvoltage, caused by electrochemical reactions and concentration
deviations on account of transport phenomena.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
2. The ohmic voltage drops, caused by the electronic as well as the ionic
currents in the conducting parts including the electrolyte.
The sum of both is Dell Latitude D600 Battery called polarization, i.e.
polarization . overvoltage t ohmic voltage drops e14T
The quantity determined in practice is always polarization. Overvoltage can only be
separated by special electrochemical methods.
1.3.3.1 Courses of the Reaction
Various possibilities exist for the combination of reaction steps, and only some of
them will briefly be described. Usually the reaction path consists of a number of
reaction steps that precede or follow the acer laptop battery charge transfer step as indicated in
Fig. 1.3. The slowest partial step of this chain is decisive for the rate of the overall
reaction. As a consequence, 6 cell acer battery, or even limitations of the reaction rate,
often are not caused by the electron-transfer step itself, but by preceding or following
steps.
Some of these steps include mass transport, since the reaction would soon come
to a standstill, if ions would no longer be available at the surface of the electrode or if
reaction products would not be cleared away and would block the reacting surface.
For this reason, migration and diffusion influence the kinetic parameters.
In a number of electrode reactions, the reaction product is dissolved. This
applies, for example, to some metal electrodes, like 9 cell acer battery, lithium, cadmium, and also
to lead. For the acer 5100 battery, the low solubility of cadmium hydroxide eCdeOHT2T and
Figure 1.3 Course of an electrochemical reaction. Charge transfer often can only occur with
adsorbed species, then adsorption/desorption steps are included. Furthermore, chemical
reactions may precede or follow the electron transfer step.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
lead sulfate ePbSO4T causes precipitation of the formed new compound, as
illustrated for the lead-acid system in Fig. 1.4.
During discharge, lead ions ePb2tT are dissolved at the negative electrode. A
corresponding number of electrons is removed from the electrode as negative charge.
The solubility of the Pb2t ions is, however, limited to about 10 6 mole=dm3 in the
presence of HSO 4
or SO2 4 ions (sulfuric acid, cf. Eq. (10)). As a consequence, the
dissolved Pb2t ions form lead sulfate ePbSO4T on the electrode surface immediately
after the dissolution process, mostly within the pore system of the active material.
The discharging reaction at the positive electrode proceeds in a similar manner:
bivalent lead ions ePb2tT are formed by the reduction of tetravalent lead ions ePb4tT acquiring two electrons. The Pb2t ions also dissolve and immediately form lead
sulfate ePbSO4T. In addition, water is formed at the positive electrode during
discharging, because oxygen ions eO2 T are also released from the lead dioxide
ePbO2T that combine with the protons eHtT of the dilute sulfuric acid to H2O
molecules.
During charging of the battery, these reactions occur in the opposite direction,
as indicated by the double-line arrows in Fig. 1.4. Lead (Pb) and lead dioxide ePbO2T are formed from lead sulfate ePbSO4T.
The electrochemical reaction, the transfer step, can only take place where
electrons can be supplied or removed, which means that this conversion is not
possible on the surface of the lead sulfate, as lead sulfate does not conduct electric
current. For this reason, the Pb2t ions must be dissolved and transported by
migration or diffusion to the conductive electrode surface (lead or lead dioxide).
The solubility of the acer 5050 battery products is a very important parameter for
electrode reactions that occur via dissolution of the reactants, as the example shown
Figure 1.4 Reaction steps in the lead-acid battery. Double-lined arrows mark the charging
reaction.
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in Fig. 1.4. If the product of the discharge is highly soluble, during discharge the
electrode will to a large extent be dissolved and will lose its initial structure. This
leads to problems during recharge because the redeposition of the material is favored
where the concentration of the solution has its highest value. As a consequence, the
structure of the electrode will be changed as demonstrated in the upper row of Fig.
1.5.
The dependence of the equilibrium voltage on the sony VGP-BPS9/S of dissolved
components is given by the Nernst equation (Eq. (8)), and reads for the lead-acid
battery as an example:
Uo . 1:931 t 0:0592 ? log
aHt ? aHSO 4
aH2O
V e11T
Equation (11) shows that the TOSHIBA PABAS057
cell voltage depends only on the acid
concentration. It is independent of the present amount of lead, lead dioxide or lead
sulfate, as long as all three substances are available in the electrode. (They are in
solid state and per definition their activity is 1mole/L.) The result of this equation is
plotted in Fig. 1.2.
In battery practice, mostly the approximation is used:
Equilibrium cell voltage . acid density ein g= cm3 or kg=dm3T t 0:84 e12T
Fig. 1.2 shows that the Sony VGP-BPS8
curve and the Latitude D610 Battery
formula coincide quite
well.
Connected to the shape change is a further drawback of the high solubility,
namely the tendency that during recharging the precipitated material forms dendrites
that may penetrate the separator and reach the opposite electrode, thus gradually
establishing a short circuit.
A typical example of this situation is the zinc electrode, which allows only
limited discharge/charge cycles. Zinc electrodes are therefore not used in commercial
secondary batteries, with the exception of the rechargeable alkaline zinc manganese
dioxide battery (RAM) (6) which is a battery of low initial cost, but also limited cycle
life.
The metallic lithium electrode is another example where cycling causes
problems due to its high solubility that causes shape change (cf. Chapter 18 and the
lithium-ion system in Fig. 1.7).
Extremely low solubility of the reaction products leads to a more or less dense
covering layer (lower row in Fig. 1.5), and when the formed substances do not
conduct electrons, like the PbSO4 in Fig. 1.4, the discharge reaction comes to a halt
as soon as the passivating layer is completed. Thus only a thin layer of the active
material reacts. To encounter such a passivation, the active material in technical
electrodes, e.g. lead and cadmium electrodes, are used as a spongy structure that has
Figure 1.5 Effect of the solubility of the reaction products on electrode structure when the
discharging/charging mechanism occurs via the dissolved state.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
a large surface area on the order of m2/g. The advantage of the low solubility is that
the products of the reaction are precipitated within the pores of the active material,
close to the place of their origin, and the structure of the electrode remains nearly
stable. Nevertheless, a gradual disintegration of the active material is observed after
a certain number of charge/discharge cycles.
A quite different course takes the reaction in the nickel-hydroxide electrode
that is employed in nickel/cadmium, nickel/hydrogen, and nickel/metal hydride
batteries as the positive one. This mechanism is illustrated in Fig. 1.6. Here the
reaction product is not dissolved, but the nickel ions are oxidized or reduced while
they remain in their crystalline structure (that of course undergoes certain changes).
To preserve electrical neutrality, a corresponding number of Ht ions (protons) must
migrate into the crystal lattice during the discharge, which means reduction of Ni3t
or Ni4t ions into Ni2t ions. When the nickel electrode is charged (oxidized), these
protons have to leave the crystal lattice. Otherwise, local space charges would
immediately bring the reaction to a standstill. The comparatively high mobility of
the small Ht ions allows such migration, but requires a large surface area of the
active material to keep the penetration distance low.
Here oxidation and reduction occur within the solid state, and it depends on
the potential of the electrode how far the material is oxidized. A consequence in
battery practice is that full capacity of this electrode is only reached at a sufficient
high end of charge voltage. Float charging at a comparatively low voltage, as it is
normal for standby applications, does not preserve full capacity and requires regular
equalizing charges or corresponding oversizing of the battery.
Figure 1.6 Simplified charge and discharge mechanism of the nickel-hydroxide electrode
with simultaneous release and absorption of protons (Ht ions) and incorporation of a small
amount of potassium ions eKtT.
Copyright . 2003 by Expert Verlag. All Rights Reserved.
Another reaction mechanism that in a certain aspect resembles to the above
one characterizes lithium-ion batteries (cf. Chapter 18). The course of the cell
reaction is illustrated in Fig. 1.7
In such a acer 3680 battery, a carbon electrode that forms layers and allows intercalation
of Li ions is combined with a positive electrode of a metal oxide that also intercalates
the small Lit ions into a layered structure (mainly LixCO2, LixNiO2, or LixMn2O4).
These positive electrodes intercalate the lithium when discharged, i.e. the
lithium-filled material characterizes the discharged state of the positive electrode,
and the Lit ions compensate for a corresponding reduction of the metal ions
eMe4t t x ? e ) Mee4 xTtT. The (simplified) cell reaction is
Charging?
