h - Dipartimento di Scienze Chimiche



h - Dipartimento di Scienze Chimiche
A.A. 2015/2016 Materiali Inorganici
Prof. Antonella Glisenti
Department of
Chemical Sciences
University of Padova
FC performance
Gibbs free energy and Nerst potential
Ideal performance
Cell efficiency
Actual performance
FC Performance variables
Rendimento Termodinamico
Massimo rendimento: Carnot = (T2-T1)/T2
(Ciclo di Carnot)
Massimo lavoro ottenibile: LMAX = Carnot Q
Termodinamica delle FC
Per una reazione l’energia scambiata:
U = Q - LMAX
U = Q - (Lmecc+ Lel)
(q = nF F = eN = 1.602 10-19 C
6.023e23 = 96488 C)
E = differenza di potenziale
H = U + PV
Lel = nFE
U = Q – (PV + VP) - nFE
H = Q - nFE
(energia disponibile dalla reazione)
G = H - TS
TS = Q
H - G = TS
(calore ceduto all’ambiente, calore perso)
G = - nFE
Cell Efficiency
Thermal efficiency of a fuel conversion device = amount of useful
energy produced relative to the change in enthalpy, ∆H, between the
product and feed streams.
Ideal efficiency of a FC, operating reversibly:
H - TS
Therm =
Per la reazione:
H2 + ½ O2 = H2O
Therm =
Therm =
- 228.61
= 0.945
Gas a fine reazione
Therm =
- 237.19
= 0.83
Liquido a fine reazione
H2 fuelled cells
H2 + ½ O2  H2O
Efficiency often expressed in terms of the ratio of the operating cell
voltage (< Vid for losses) to the ideal cell voltage.
Thermal efficiency of a H2/O2 FC in terms of the actual cell voltage
(considering the complete fuel reaction):
 =
Useful energy
0.83 Vactual
Useful power
0.83 Vcelll
Vactual Corrent
Videal Corrent/0.83
=0.675 x Vcell
 = 0.675 x V
Gibbs Free Energy and Nerst Potential
Per la reazione generica:
α A + β B →  C+ δ D
Indicando con G°A, G°B, G°C, G°D le energie libere molari standard
delle specie A,B,C,D :
∆G° =  G°C + δ G°D - α G°A - β G°B
G°I = energia libera molare per la specie e alla temperatura T.
All’equilibrio G = 0
Poiché G = -nFE
Ideal Performance
The Nerst potential gives the ideal open circuit cell potential
(= upper limit achievable)
Electrochemical reactions in fuel cells
Ideal Performance
Fuel Cell Reactions and the Corresponding Nernst Equations
E° (298K) for a H2/O2 fuel cell = 1.18 V with gaseous water product.
Influenza della Temperatura
H2/O2 Potenziale ideale di cella in funzione della temperatura
(298 K)
Cell type
Ideal voltage
(353 K)
(373 K)
(478 K)
(923 K)
(1073 K)
(1373 K)
Influence of reactant concentrations and type
 Less concentrated reagents = correction of the Nerst potential (as
much as 250 mV in higher-temperature cells).
 The ideal performance of a FC depends on the electrochemical
H2 + ½ O2  H2O
CO + ½ O2  CO2
CH4 + 2 O2  2H2O + CO2
Direct oxidation on CO and CH4 = minor reactions
CO + H2O  H2 + CO2
CH4 + 2 H2O  4H2 + CO2
• The driving force for anodic oxidation of CO and CH4 is lower (higher
open circuit voltage of the hydrogen oxidation).
• The kinetics of hydrogen oxidation on the anode are significantly
faster than that of CO or CH4 oxidation.
• Surface area and active surface sites available.
• Mass-transfer.
Cell Energy Balance
The cell energy balance states that the enthalpy flow of the
reactants entering the cell will equal the enthalpy flow of the
products leaving the cell plus the sum of three terms:
(1) The net heat generated by physical and chemical processes within
the cell
(2) The dc power output from the cell
(3) The heat loss from the cell to its surroundings
The energy balance varies for the different types of cells because of
the differences in reactions that occur according to cell type.
A typical energy balance determines the cell exit temperature
knowing the reactant composition, the feed stream temperatures, H2
and O2 utilization, the expected power produced, and a percent heat
Graph showing the voltage for a
typical low temperature, air
pressure, FC
Graph showing the voltage
for a typical air pressure FC
operating at about 800°C.
Phenomena contributing to irreversible losses
 Activation-related losses. Kinetic aspects. Activation energy of
the electrochemical reactions at the electrodes; depend on the
reactions, the electro-catalyst material and microstructure, reactant
activities (and hence utilization), and weakly on current density.
 Ohmic losses. Ionic resistance in the electrolyte and electrodes,
electronic resistance in the electrodes, current collectors and
interconnects, and contact resistances.
Ohmic losses are proportional to the current density, depend on
materials selection and stack geometry, and on temperature.
 Mass-transport-related losses. Finite mass transport limitations
rates of the reactants; depend strongly on the current density,
reactant activity, and electrode structure.
 Fuel crossover and internal currents. Energy loss resulting from
waste of fuel passing through the electrolyte, electron conduction
through the electrolyte.
Activation related losses
 In low and medium temperature FCs activation overvoltage is the
most important cause of irreversible voltage drop
 It occurs mainly at the cathode (the activation overvoltage of both
electrodes is important in cells using fuels other than hydrogen)
a A + b B …. → g G + h H ….
Velocità di reazione = k [A]m[B]n ….
Costante di velocità = k
Ordine globale di reazione = m + n + ….
 Maggiore è k maggiore è la velocità
 La concentrazione dei reagenti può influenzare la velocità di reazione
Dr. Antonella Glisenti - Dip. Scienze Chimiche - Università degli Studi di Padova
Fattore d’urto
- Ea/RT
Energia di attivazione
Costante di velocità
 > Energia di attivazione > effetto della temperatura
Phenomena contributing to irreversible losses:
activation losses
Activation Losses: slow electrode kinetics; are the result of complex
surface electrochemical reaction steps, each of which have their own
reaction rate and activation energy.
Usually, the rate parameters and activation energy of one or more
rate-limiting reaction steps control the voltage drop.
Heterogeneous reaction
It is possible to approximate the voltage drop due to activation
polarization by a semi-empirical equation, called the Tafel equation.
V =
 nF
 = electron transfer coefficient of the
reaction at the electrode
i0 = exchange current density.
Tafel Plots
Tafel plots: a visual understanding of the activation polarization of a
FC. They are used to measure the exchange current density, given by
the extrapolated intercept at ηact = 0 and the transfer coefficient
(from the slope).
This simplified description
did not try to describe:
absorption of reactant
electrons, desorption of
product species, and the
nature of the electrode
For a FC which has
no losses at all except for the activation
V = E – Aa ln ( i ) – Ac ln ( i )
 A is higher for a slow
electrochemical reaction
The constant i0 is higher
if the reaction is faster.
 i0 = current density at
which the overvoltage
begins to move from zero
Tafel plots for slow and fast
electrochemical reactions
Exchange current density
zero current density the
reaction is taking place all the time
but the reverse reaction is also
taking place
2 O2 + 4e- + 4H+  2H2O
2O2 + 4e- + 4H+
 At
 There is a continual
backwards and forwards
flow of electrons from and
to the electrolyte.
This current density is the
exchange current density
> Current density = the
surface of the electrode
is more “active”.
Graph of cell voltage against current density, assuming losses are due only to
the activation overvoltage at one electrode, for three different values of
exchange current density i0.
Activation Voltage Drop
 i0 is much smaller for oxygen electrode (10-8 A/cm2) – the
overvoltage at the anode is negligible compared to that of the
cathode (for hydrogen FCs)
 i0 cathode = 0.1 mA/cm2
 i0 anode = 200 mA/cm2
Catalytic effect
Raising the cell temperature
Using more effective catalysts
Increasing the roughness of the electrodes
Increasing the reactant concentration
Increasing the pressure
Ohmic Polarization
Ohmic losses = resistance to flow of ions in the electrolyte +
resistance to flow of electrons through the electrode.
< electrode separation, > electrolyte ionic conductivity = < Ohmic losses
ohm = i R
i = current flowing through the cell,
R = total cell resistance = Relectronic + Rionic+ Rcontact
Any of these components can dominate the ohmic resistance, depending
on the cell type: for SOFCs: the ionic resistance in planar electrolytesupported; electronic bulk resistance in tubular; contact resistances in
planar thin-electrolyte
Area Specific Resistance
(ASR = ohmic resistance normalized by the active cell area Ωcm2)
function of the cell design, material choice, manufacturing technique,
and, because material properties change with temperature, operating
ASR is a key performance parameter, especially in HTFC, where the
ohmic losses often dominate the overall polarization of the cell.
Ohmic Polarization
 Electrodes with the highest possible conductivity
 Electrolyte with the highest possible conductivity
 Electrolyte as thin as possible
 Good design and use of appropriate materials for
the bipolar plates or cell interconnects
Mass Transport Losses
As a reactant is consumed at the electrode by electrochemical
reaction, it is often diluted by the products, when finite mass
transport rates limit the supply of fresh reactant and the evacuation
of products. As a consequence, a concentration gradient is formed
which drives the mass transport process.
With purely gas-phase reactants and products (such as an SOFC),
gas diffusion processes control mass transfer.
 In other cells, multi-phase flow in the porous electrodes can have a
significant impact (e.g. in PEFC).
 In hydrogen fuel cells, the evacuation of product is often more
limiting than the supply of fuel, given the difference between the
diffusivities of hydrogen and water (vapor).
Mass Transport Losses
The Nernst equation for the reactant species at equilibrium
conditions, or when no current is flowing, is
When current is flowing, the surface concentration becomes less
than the bulk concentration, and the Nernst equation becomes
The potential difference (ΔE) produced by a concentration change at
the electrode is called the concentration polarization:
Mass Transport Losses: the Nerstian drop
If this loss is the only one:
V = E + B ln
E = 1.2 V
B = 0.016 V, 0.200 V
il = 1000 mA
B = Type of FC, operating state, operating conditions …
 Hydrogen supplied from reformers
 Air cathode: air not well circulated
 Mass transport problems for nitrogen left behind
Summing Cell Voltage
V = E – Aa ln ( i ) – Ac ln ( i ) – (i+in) r + B ln
E = reversible open circuit voltage
in = internal and fuel crossover
equivalent current density
A = slope of the Tafel line
io = exchange current density at
the cathode/anode
B = constant in the mass transfer overvoltage equation
il = limiting current density at the electrode with the lowest limiting
current density
r = area specific resistance.
Vcell  modifications to
 Fuel cell design (electrode structures, electro-catalysts, more
conductive electrolyte, thinner cell components, etc.).
 System Design
 Operating
conditions (e.g., higher gas pressure, higher
temperature, change in gas composition to lower the gas impurity
 Compromises
stability/durability of cell components, cost
J. Larminie, A. Dicks; Fuel Cell Systems Explained – Wiley 2000

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