Why Hydrogen Energy andFuel Cell!

Changes in temperature, sea level and Northern Hemisphere snow cover Source: IPCC.

Reason for this is Green House Gas (GHG) Emission

Global anthropogenic GHG emissions Source: IPCC

Open-ended energy systems: GHG emission

Quality of Life vs. Energy Usage

Trend in Crude Discoveries, Consumption and Price with Time

Crude oilDiscoveries Year G

bbl/Year1960 60

1980 30

2000 10

2020 5

Crude oilConsumption Year X 10 19 J

/year

1960 25

1980 120

2000 160

2020 200

Crude Oil Price Year US$ / bbl(5.74 GJ)

Note: crude priceis highlyfluctuating in lastfew years.2008/09 - US$142 / bbl. In2010, US$ 65 /bbl

1960 20

1980 55

2000 30

2020 ?

bbl: barrels of oil equivalent

Look for Alternatives !

Natural Gas Biomass Solar Water Nuclear

H2

Generation Transportation Storage Dispensing Fuel cell

Energy Consumption in Different Types of Passenger Cars

Type Energy consumption, kJ/km

Well-to-tank

Tank-to-wheel

Well-to-wheel

Gasoline ICE 694 2777 3471

Diesel ICE 377 2314 2691

CNG ICE 423 2834 3257

H2 ICE 1424 2136 3560

Gasoline ICE-HEV 479 1915 2394

Diesel ICE-HEV 251 1543 1794

CNG-ICE-HEV 241 1615 1856

H2 ICE-HEV 1102 1653 2755

H2 FC 771 1157 1928

H2 FC-HEV 740 1111 1851

Carbon Dioxide Emission From Different Types of Passenger Cars

Fuel Cell Makes Sense

Closed Hydrogen Energy System: Min GHG Emission

Fuel Cell

History, Principle & Overview of Fuel Cells

Fuel cell is a device that takes fuel as input and produces electricity as output Converts chemical energy of raw materials into electrical energy Different from battery - A fuel cell will keep on producing electricity as long as fuel is

available Similar to a chemical factory which transforms raw material(fuel) into final product

(electricity)

A simple fuel cell

Electrochemical half reactions of a H2-O2 fuel cell:

Electrons transferred from the fuel travel through the external circuit (thus constituting an

electric current) and do useful work before they complete the reaction Spatial separation achieved by an electrolyte, a material which allows ions to flow but not

electrons

Fig: A simple fuel cell with platinum electrodes dipped in sulphuric acid ( an aqueousacidic electrolyte)

Basic fuel cell operations

1. Reactant transport2. Electrochemical reaction3. Ionic and electronic conduction4. Product removal

Advantages

More efficient than combustion engines – directly convert chemical energy to electricalenergy

Mechanically ideal – no moving parts , good reliability, long lasting systems Clean and silent operation Easy independent scaling between power (determined by fuel cell size) and capacity (

determined by fuel availability)

Disadvantages

Cost – a major issue Fuel availability and storage Durability under stop-start cycles Low volumetric power densities as compared to batteries and combustion engines

Power density comparison of various technologies

Fuel cell and Hydrogen economy :

H2 fuel cells coupled with electrolyzers and renewable energy conversion technologies provide acompletely closed loop, pollution free energy economy. A schematic of this scheme is shown in fig1.4.

Types of fuel cells

Classification based on type of electrolyte

1. Phosphoric acid fuel cell (PAFC)2. Polymer electrolyte membrane fuel cell (PEMFC)3. Alkaline fuel cell (AFC)4. Molten carbonate fuel cell (MCFC)5. Solid oxide fuel cell (SOFC)

Major fuel cell technologies

PEMFC PAFC AFC MCFC SOFC

Electrolyte PolymerMembrane Liq.H3PO4immobilized Liquid KOH

ImmobilizedMoltencarbonate Ceramic

Chargecarrier H+ H+ OH- CO3

2- O2-

OperatingTemperature 800C 2000C 60-2000C 6500C 650-

10000C

Catalyst Platinum Platinum Platinum Nickel Perovskites

FuelCompatibility

H2,methanol H2 H2 H2 ,CH4 H2 ,CH4,CO

Different Types of Fuel Cells

Basu, S. (Ed.) Recent Trends in Fuel Cell Science and Technology, Springer (2007)

Fuel Cell Component

Schematic of Proton Exchange Membrane Fuel Cell

Note the flow of fuel,oxidant, products, ions and electrons through the differentcomponents of PEMFC

Polymer Electrolyte Membrane Fuel Cell

Basu, S. (Ed.) Recent Trends in Fuel Cell Science and Technology, Springer (2007)

Fuel cell performance

Fuel cell performance can be assessed by current-voltage curves. i-V curves show the voltage output of a fuel cell for a given current load. Ideal fuel cell performance is dictated by thermodynamics Real fuel cell performance is always less than ideal fuel cell performance due to losses. The major types of loss are :

1. Activation loss (losses due to electrochemical reaction)

2. Ohmic loss (losses due to ionic and electronic conduction)3. Concentration loss (losses due to mass transport)

Combined fuel cell i-V and power density curve

Fuel cell power density increases with increasing current density, Reaches a maximum,and then falls at still higher current densities.

Fuel cells are designed to operate at or below the power density maximum. At current densities below the power density maximum, voltage efficiency improves but

power density falls. At current densities above the power density maximum, both voltage efficiency and power

density fall.

Fuel Cells – Types and Chemistry

Alkaline fuel cell (AFC)

Anode (Pt/C)

Cathode (Pt/C)

First used in space shuttle by NASA 60% efficiency between 150 – 200 deg C operating temp. Electrode poisoning is observed in presence of OH-

Proton Exchange Membrane Fuel Cells (PEMFC)

Anode (Pt/C):

Cathode (Pt/C):

Uses a solid polymer electrolyte, usually perfluorosulfonic acid (nafion) membrane. Membrane electrode assembly (MEA ) consists of the anode, cathode, proton exchange

membrane (PEM) and gas diffusion layers (GDLs). Nafion allows transport of protons while blocks electrons. Membrane should remain hydrated for efficient transport of protons, and hence PEMFCs

can’t be operated at higher temperatures Electrode poisoning in presence of OH-

Phosphoric Acid Fuel Cell (PAFC)

Operating principle is similar to that of a PEMFC Phosphoric acid is the electrolyte used, which conducts protons and has good thermal

stability Operating temperature varies between 175 – 200 deg C Used for heavy vehicles such as buses and trucks

Direct Alcohol Fuel Cell (DAFC)

Anode (Pt/C)

Cathode (Pt/C) Uses lighter alcohols such as methanol or ethanol instead of hydrogen Can be operated at lower temperatures; 40 – 80 deg C Might be useful for future portable devices such as laptops, calculators

Molten Carbonate Fuel Cell (MCFC)

Anode (Ni)

Cathode (NiO2)

Molten carbonate salt is used as electrolyte Operates at higher temp., around 650 deg C Hydrocarbons can also be used as fuel, where internal reforming produces H2

Schematic of MCFC

Note the flow of fuel,oxidant, products, ions and electrons through the differentcomponents of MCFC

Solid Oxide Fuel Cell (SOFC)

Anode (Ni/YSZ)

Cathode (Perovskite/LaMnO3)

Uses hard ceramic electrolyte crystal lattice Operates at higher temp.; 750 – 1000 deg C O2- migrates through crystal at this high temp. High efficiency upto 60% can be reached Natural gas can be used as a fuel due to internal reforming at this temp.

Schematic of SOFC

Note the flow of fuel,oxidant, products, ions and electrons through the differentcomponents of SOFCRegenerative Fuel Cells (RFC)

Water is electrolysed using solar cell Solar energy can be stored as hydrogen, which can be used during night Can be useful for space applications Electrolyser:

Electrolyser:

Anode (Pt/C):

Cathode (Pt/C):

Alkaline fuel cell (AFC)

The working principle of an alkaline fuel cell is shown schematically in fig. 1. The alkaline fuel cellgenerally operates on hydrogen and oxygen gases. The solution of potassium hydroxide in water isused as the electrolyte. At the anode, hydrogen gas reacts with the OH- ions to produce water andelectrons. Electrons generated at the anode conduct through a load connected to an externalcircuit and migrate towards cathode.

Fig.1. Alkaline fuel cell

These electrons at cathode react with oxygen and water to produce hydroxyl ions, which diffusethrough the electrolyte and reaches anode. The reactions in the AFC are given below

The efficiency of an alkaline fuel cell is about 60% (4) when the operating temperature is about150 oC to 200 oC. Alkaline fuel cell was first used by NASA in Apollo space shuttle. It was fuelledby hydrogen and oxygen for the power generation while the astronauts used the reaction by-product, water for drinking purposes. The typical life of a 2 KW AFC is about 5000 hrs. Theelectrode gets eventually poisoned in the presence of OH- and carbonate is formed in the presenceof CO2 in air. Because of these reasons, AFC faces tremendous challenges for itscommercialization. The problem of alkaline electrolyte is handled by replacing it withperfluorosulphonic acid membrane, which is discussed in the next section. However, there exists apossibility of poisoning the anode catalyst and the formation of carbonates in the presence of CO2(5). This problem is tackled by re-circulating the electrolyte after removing the carbonate and theheat of reaction. Recently, many investigators (6) are looking at the possibility of using alcohol asfuel directly feeding it to alkaline fuel cell to generate power.

Proton Exchange Membrane Fuel Cells (PEMFC)

The proton exchange membrane (PEM) fuel cell as shown in fig. 2, uses a solid polymer electrolyte(perfluorosulphonic acid membrane) in the form of a thin, permeable sheet for the transport ofproton (7). Generally, platinum, Pt-black or Pt/Ru catalyst is used as anode and cathode catalystsrespectively.

Fig. 2. Proton exchange membrane fuel cell

The proton exchange membrane is sandwiched between anode and cathode catalyst, which ispasted on gas diffusion layer made of carbon cloth or paper. The composite structure of gasdiffusion layer, anode, proton exchange membrane, cathode and gas diffusion layer is known asmembrane electrode assembly (MEA) and is the heart of polymer electrolyte membrane fuel cell.Gas diffusion layer works as substrate for catalyst and ensure the proper distribution of reactantsover the catalyst. Hydrogen molecules are stripped at the anode electrode-catalyst into electronsand protons (H+). Electrons are collected at low resistance material, which helps to conduct theelectrons from the fuel cell to the outer circuit. This low resistance material is known as the bipolarplate made of graphite and it has channels to supply the reactants over the diffusion layer both onthe anode and cathode sides (Fig 2). The protons permeate through membrane and reachescathode side, where it reacts with oxygen and conducted electrons from the outer circuit toproduce water. The proton exchange membrane made of perfluorosulphonic acid allows proton topass through it and restricts the passage of electrons. The migration of proton in membrane ispromoted by sulphonate group present in polytetrafluoroethylene membrane structure through theformation of hydronium ion. Thus, the membrane needs to be hydrated for efficient transport ofproton in the form hydronium ion. Moreover, the PEM fuel cell cannot be operated above 80oCbecause of the water loss from the membrane and subsequent poor conduction of proton. Thereaction scheme for proton exchange membrane is shown below:

Phosphoric Acid Fuel Cells (PAFC)

The reactions occurring on the anode and cathode are similar to PEMFC as given in equations 4 to6. A PAFC as shown in fig. 3 consists of an anode and a cathode made of finely dispersed platinumcatalyst on carbon and the electrolyte is housed in silicon carbide structure.

Fig.3. Phosphoric acid fuel cell

The electrolyte is an inorganic acid, concentrated phosphoric acid (100%), which is like themembranes in PEMFC, conducts proton. Phosphoric acid (H3PO4) is the only common inorganicacid that has enough thermal stability, and very low volatility (150oC) to be considered as anelectrolyte for fuel cells (8). The pure 100% phosphoric acid has a freezing point of 42oC, whichrestricts the operation below this temperature. The operating temperature of the PAFC is in therange of 175oC to 200oC. This was the most commercially developed fuel cell at one point of time.However, the advancement of PEMFC decreased its value in the market. The phosphoric acid fuelcell can be used in large vehicles, such as buses and trucks.

Direct Alcohol Fuel Cells (DAFC)

The direct alcohol fuel cell (DAFC) is a variant of PEM cell. The direct alcohol fuel cell uses lighteralcohols like methanol or ethanol instead of hydrogen gas. The alcohols dissociate to electrons,hydrogen ions and carbon dioxide at the anode. The positively charged hydrogen ions diffuse fromanode to cathode through the polymer electrolyte membrane and electrons migrate toward thecathode through an external circuit. At the cathode, the electrons, hydrogen ions and oxygen fromthe air react to form water. The reactions involved in direct methanol fuel cell are shown below(9):

The direct alcohol fuel cells are operated at lower temperature (40 oC - 80oC) and thought to bepower source in future for portable equipments like laptop, calculator etc.

Molten Carbonate Fuel Cells (MCFC)

The schematic diagram of a molten carbonate fuel cell is shown in fig.4. The molten carbonate fuelcell uses a molten carbonate salt as the electrolyte (10).

Fig.4. Molten carbonate fuel cell

The anode process involves a reaction between hydrogen and carbonate ions to form water andcarbon dioxide while releasing electrons at the anode. The electrons migrate towards cathodethrough the load connected to an external circuit. The cathodic process involves oxygen andcarbon dioxide from the oxidant stream with electrons to produce carbonate ions. The need forcarbon dioxide in the oxidant stream requires a system for collecting the carbon dioxide from theanode exhaust and mixing it with the cathode feed stream. The reactions occur at 650 oC whensalts melt and conduct carbonate ions from the cathode to the anode. The reactions in the moltencarbonate fuel cell are given below:

Solid Oxide Fuel Cells (SOFC)

The schematic diagram of a solid oxide fuel cell is shown in fig. 5. Solid oxide fuel cells work ateven higher temperatures than molten carbonate fuel cells. A solid oxide fuel cell (SOFC) uses a

hard ceramic electrolyte crystal lattice instead of a liquid and operates at temperatures of 750oC to1000oC (10).

Fig.5. Solid oxide fuel cell

Today's technology employs several ceramic materials as the active SOFC components. The anodeis typically formed from an electronically conducting nickel/yttria-stabilised zirconia (Ni/YSZ)cermet (ie, a ceramic/metal composite). The cathode is based on a mixed (ie, both electronic andionic) conducting perovskite, lanthanum manganate (LaMnO3). Yttria-stabilised zirconia (YSZ) isused for the ion-conducting electrolyte. At this high operating temperature, oxygen ions migratethrough the crystal lattice. As hydrogen is passed over the anode, oxide ions moves across theelectrolyte to oxidize the fuel. The oxygen is supplied, usually from air, at the cathode. Electronsgenerated at the anode travel through an external load to the cathode, completing the circuit.Oxygen combines with electrons at cathode to form oxide ions, thus completing the reaction.These cells can reach efficiencies of around 60% and expected to be used for combined heatingand power purposes. They can be used potentially for providing auxiliary power in vehicles. Themain advantage of SOFC is possibility of internal reforming at 750oC - 1000oC and hence naturalgas can be used as fuel in SOFC. The following reactions occur at the SOFC electrodes:

Regenerative Fuel Cells (RFC)

In this type of fuel cells water is electrolyzed with the help of electricity from solar photovoltaic cell

to produce hydrogen and oxygen gases and utilizing these gases in the PEM fuel cell to generateelectricity (11). This technology is useful in space application. Further, using this technology solarenergy can be stored in the form of hydrogen energy and it will be of use in the night when solarphotovoltaic would not work. Fig. 6 depicts the concept of a regenerative fuel cell.

Fig. 6. Regenerative fuel cell system

The following reactions describe the water splitting process inside the electrolyser:

Fuel Cells Thermodynamics

Internal energy

The energy associated with microscopic movement and interaction between particles on theatomic and molecular scale.

Entropy is determined by the number of possible microstates accessible to a system (thenumber of possible ways of configuring a system)

For an isolated system

S = k log Ω

S:total entropy of the system;

K:Boltzmann’s constant;

O:number of possible microstates accessible to the system

First law

The law of conservation of energy

d (Energy) univ = d(Energy) system +d (Energy) surrounding = 0d (Energy) system = -d (Energy) surrounding

Energy transfer between a closed system and its surrounding via heat(Q) and work (W)

dU = dQ –dW

Positive work is defined as work done by the system on the surroundings If there is onlymechanical work done by a system( eg. Expansion of a system by dV against a pressure, P)

(dW)mechanical=pdVdU = dQ –dW

Second law

In a system, a process that occurs will tend to increase the total entropy of the universe.

dSuniv>=0

For a reversible transfer of heat at contant pressure

dS=dQrev/T

H2-O2 Fuel Cell

H2+1/2 O2 ---> H2O ; ΔGrxn=-273 kJ/mol H2

eg 5 mole of O2 is reacted , the extrinsic Gibbs free energy change

Some Important terms

Standard State

Because most thermodynamic quantities depend on T and p, we need a reference statecalled as a standard state.

Room temperature(298.15K) and Pressure 1 bar=100kPa

Standard state condition are designated by a superscript zero,

Reversibility

Reversible implies equilibrium E represents a reversible fuel cell voltage and V represents an operational (

nonreversible ) fuel cell voltage

Heat Potential of a Fuel

dH=TdS+Vdp

for a constant pressure process

dH=TdS = dU+dW

Calculating Reaction Enthalpies

:: enthalpy required to form 1 mole of chemical species ‘i’ at STP from thereference species

Work potential of a fuel: Gibbs free energy

G=H-TS

dG = dH – TdS

Relationship between Gibbs free energy and Electrical Work

Relationship between Gibbs free energy and voltage

Potential of a system to perform electrical work is measured by voltage (electricalpotential)

Electrical work done by moving a charge Q ( coulombs) through an electricalpotential difference E(volts), Welec

Welec=EQ

If the charge is carried by electrons

Q = NF n: number of moles of electrons transferred ; F: Faraday constant

H2-O2 Fuel Cell

Relationship between Gibbs free energy and Electrical Work

Standard Electrode Potentials: computing reversible voltage

Standard state electrode potential is standard state reversible voltages of variouselectrochemical half reactions relative to the hydrogen reduction reaction.

Predicting reversible voltage of a fuel cell under non-standard-state conditions

Reversible voltage variation with temperature

For molar reaction quantities

Defining ET as the reversible cell voltage at T At cinstant p,

Reversible voltage variation with pressure

Reversible voltage variation with concentration

Fuel cell efficiency

Ideal efficiency of a fuel cell is limited by ΔG Real efficiency is lower than ideal efficiency because of non-ideal irreversible process

Ideal reversible fuel cell efficiency

If work is extracted from a chemical reaction,

For a fuel cell, the maximum amount of energy available to do work is given by Gibbs freeenergy. Thus the reversible efficiency of a fuel cell is

At room temperature, H2-O2 Fuel Cell

HHV:Higher heating value

H2-O2 fuel cell, if H2O(l) is product, it is HHV. If H2O(g) is product, it is LHV. Efficiency iscalculated based on HHV

Comparison with conventional heat/expansion engine

Real fuel cell efficiency

Two main reasons for decrease in fuel cell efficiency:

Voltage losses Fuel utilization

Voltage efficiency of the fuel cell

Ratio of the real operating voltage of the fuel cell (V) to the thermodynamically reversiblevoltage of the fuel cell (E)

Operating voltage depend on the current (i) drawn from the fuel cell: The lighter the current load, the lower the voltage Fuel cell are most efficient at low load

Fuel utilization efficiency of the fuel cell

Ratio of the fuel need by the cell to generate electric current and the total products to thefuel cell.

The supply of fuel to a fuel cell is adjusted to the current FC is always supplied with just a bit more fuel than it need at any load

Nernst Equation AnalysisIn a hydrogen-oxygen fuel cell system, water is produced as the final product. With purehydrogen and oxygen at standard conditions, i.e. 1 atm and 298 K, the reversible cellpotential obtained is 1.229 V. This is the maximum voltage that can be withdrawn from thissystem. However, in reality the feed streams, i.e. hydrogen and oxygen are often diluted forseveral reasons. For example, air can be used as a source of oxygen, which also containsnitrogen. Similarly, the products from water gas shift reaction (CO2 + H2) can be used as asource for hydrogen. Additionally, pure hydrogen and oxygen can be used at differentpressures and temperatures. Therefore, there is a need to understand the dependency of thereversible cell potential on the concentration of various species. In order to build arelationship between the cell potential and concentration of different species, we firstrecollect the concept of chemical potential learnt in thermodynamics. Chemical potentialmeasures the change in the Gibbs free energy of a system with change in chemistry of thesystem. It is defined for each species in the system. Chemical potential for a species i inphase a can be related to the Gibbs free energy change as follows

.................................................................................(1)

where μiα is the chemical potential of species i in phase a and measures the

change in the Gibbs free energy of the system with infinitesimal change in the number ofmolesof species i, while temperature, pressure and the moles of other species are heldconstant. Also, from thermodynamics the chemical potential of a species i, can be related toits concentration through activity, a –

.................................................................................(2)

where is the chemical potential of species i at standard conditions, i.e. 1 atm and 298K; ai denotes the activity of species i. The activity of species is a function of its chemicalnature. In other words the activity of a chemical species depends on the chemical nature ofthe species. The following table lists the activity of species depending on their chemicalnature.

Chemical Nature Activity

Ideal gas

ai=pi/po; where pi and p0 are respectivelythe partial pressure of species i and thestandard state pressure, i.e. 1 atm. Forexample, activity of nitrogen (N2) in air at1 atm would be partial pressure of N 2 inair. Since air approximately contains 78 %N2(by volume), the activity of N 2 wouldbe 0.78 for 1 atm air pressure. However, ifthe air pressure is increased to 2 atm, theN2pressure increases proportionally andhence the activity is doubled, i.e. 1.56.

Nonideal gasai=γi (pi/po); where γi is an activitycoefficient, while p i and p 0 have the samemeanings as defined for the case of an

ideal gas.γi is the measure of deviationfrom ideal behavior (0 < γi < 1). Thetheories are available fromthermodynamics to quantify γi. Please notethat while calculating the activity of N 2above, we assumed the ideal gas case.However, nonideal behavior of N 2 and airwould decrease the activity.

Dilute solution

ai=ci/co; where ci and c0 are respectivelythe molar concentration of species i andthe standard state concentration, i.e. 1 M(1 mol/L). For example, the acitivity of Na+ ions in 0.1 M NaCl is 0.1. However, theactivity of Na + ions in 0.1 M Na2 SO4wouldbe 0.2, since 1 mol of Na2SO4 gives 2moles of Na+ ions

(Na2SO4 -------> 2Na+ + SO42-)

Nonideal solution

ai=γi(ci/co); where γi is an activitycoefficient, used to measure the deviationfrom ideal behavior. As already discussed,0 <γi < 1 and therefore, the activitycalculated assuming a nonideal behavior ofa species is low compared to that of idealbehavior.

Pure components

ai=1; i.e. the activity of the purecomponents can be taken as unity. Forexample the activity of pure aluminum inan aluminum electrode is 1. Also, theactivity of liquid water is taken as unity.

Table 1. Activity of species depending on their chemical natureTherefore, in order to calculate the Gibbs free energy change of the total system, thecontributions from all species are added –

(UsingEquation 1)

(Using Equation2)...............................................................(3)

For hydrogen-oxygen fuel cell system, we have the following overall reaction –

It should be noted that the above reaction can be written in

the following manner too – However, the totalGibbs free energy change calculated for this system would be different for the above tworeactions. This is due to the difference in stoichiometric coefficients of H2, O2 and H2O in thetwo reactions. Therefore, it becomes necessary to work with molar Gibbs free energychange,Δg' which is defined on a per mole basis and is therefore intrinsic, i.e. independent ofthe quantity of the system. For our case, the molar Gibbs free energy change for the

formation of water is -237 kJ/mol H2at standard temperature and pressure. However, if 10moles of O2 reacted then the total Gibbs free energy change is given by

Hence, on a molar basis for species H2, the molar Gibbs free energy change for this reactioncan be calculated from the chemical potentials of various species participating in the reaction–

.....................................................................(4)Using Equations 2 and 4, we have –

where ; is the Gibbs free change for the reaction atstandard conditions, i.e. 1 atm and 298 K.

...............................................................................................(5)The amount of Gibbs free energy change (Δg'rxn) can be related to the electrical work by –

.........................................................(6)where n is the number of moles of electron transferred, F is Faraday’s constant and Ecell isthe potential difference across the cell. It should be noted that the value of n is 2 in our case,since for every one mole of water formed, 2 moles of electrons are transferred. UsingEquations 5 and 6, we get –

As we discussed previously, the activities of H2 and O2 can be replaced by their respectivepartial pressure assuming ideal behavior. This assumption leads to

.............................................................................................(7)The above relation clearly shows the dependency of reversible cell potential on the partialpressures of H2 and O2 and is known as the Nernst Equation. In general for any arbitrarynumber of products and reactants, we have –

...........................................................................................(8)where vi denotes the stoichiometric coefficient of ith species involved in the chemicalreaction. For example, in our case the stoichiometric coefficient of O2 is 1/2. The Nernstequation relates the reversible cell potential to the effective concentrations of various speciesand is therefore, a very significant result. In case of a hydrogen-oxygen fuel cell system, wehave n = 2 and hence –

This expression gives the maximum theoretical voltage across the cell at a particulartemperature and pressure. This theoretical voltage is also known as the open circuit voltage(OCV), i.e. the voltage observed when no current is drawn from the cell. When the activitiesif H2 and O2 are both unity, i.e. the partial pressure of both H2 and O2 is 1 atm, it can beeasily seen that the expression reduces to –

Both the proton exchange membrane fuel cell (PEMFC) and the solid oxide fuel cell (SOFC)use hydrogen and oxygen as the feed streams, however, the OCV observed is different for thetwo. This is due to the difference in operating temperatures of PEMFC and SOFC. While theoperating temperature range for a PEMFC is 40 to 100°C, the SOFCs are operated at veryhigh temperatures ranging from 750-1000°C. It should be noted that the temperaturedependency of the OCV is not that straightforward as indicated by the Nernst equation andone needs to be careful in analyzing those results. This is because the E0 cell value is also afunction of temperature, i.e. changes with change in temperature. The E0 cell decreases withincrease in temperature. Therefore, at standard pressure conditions, pH2 = pO2=1 atm, theOCV of a SOFC is lower than that of a PEMFC.

PartialPressure

ofH 2(atm)

PartialPressure

ofO2(atm)

OpenCircuitVoltage

(V)

DifferencebetweenOCV and

E0 cell(mV)

1 1 1.229 0

1 2 1.233 4

1 3 1.236 7

1 4 1.238 9

1 5 1.239 10

2 2 1.242 13

3 3 1.250 21

4 4 1.256 27

5 5 1.260 31

2 1 1.238 9

3 1 1.243 14

4 1 1.247 18

5 1 1.250 21

Table 2. OCV (at standard temperature condition, i.e. T = 298.15 K) vs. partial pressures ofH2 and O2as calculated by Nernst Equation As seen from the values in the table, the OCVincreases slightly with increase in pressure of hydrogen and/or oxygen. However, it can beseen that the OCV difference is not very significant even after reaching higher pressures, i.e.5 atm H2 and O2, only 31 mV voltage difference is observed. Nernst equation also shows thatpotential difference can be generated with the same redox couple by having differentconcentrations of species at the anode and the cathode side. This type of arrangement isknown as a concentration cell. For example, voltage can be obtained from a hydrogenconcentration cell where the anode and the cathode are maintained at different partialpressures of hydrogen. For a hydrogen concentration cell, the following reactions take place –

1. At anode : H2 ------> 2H+ + 2e- ; E0a = 0.0 V vs. NHE2. At cathode :2H+ + 2e- --- --> H2 ; E0c = 0.0 V vs. NHE3. Overal : H2 ----------> H2 ; E0cell = E0c - E0a = 0 V

Fig.1. A schematic representation of a hydrogen concentration cellWe can write the following Nernst equation for this hydrogen concentration cell –

where (aH2)cathode and (aH2)anode are the activities of H2 at the cathode and anode siderespectively. Assuming ideal gas behavior, and replacing the activities of H2 by its partialpressure, we get –

where (PH2)cathode and (PH2)anode are the partial pressures of H2 at the cathode and anode siderespectively. Replacing the values of E0cell (= 0 V), n (= 2), R (= 8.314 J/(mol-K)), T (=298.15 K), F (= 96500 C/mol) and (say), in the above equation we get –

Therefore, for Ecell (or OCV) to be positive, Q should be less than unity. In otherwords, (PH2)cathode< (PH2)anode The variation in values of OCV with different values of Q hasbeen listed in Table 3. This clearly shows that OCV increases with decrease in the value ofQ.

OCV(V) Q

0 1

0.059 10-2

0.118 10-4

0.177 10-6

0.236 10-8

0.295 10-10

0.354 10-12

Table 3. Variation in OCV with QThis hydrogen concentration cell can produce decent voltage without oxygen and thereforecan be used in outer space where oxygen unavailable.

Electrode potential and Electrochemical Potential

It is the electromotive force of a cell built of two electrodes:

Suppose,

on the left-hand side (LHS) is the standard hydrogen electrode (SHE, EH2/H+ = 0.0 V) , and on the right-hand side (RHS) is the electrode the potential of which is being defined.

Note, by convention potential of SHE is zero. We will discuss about SHE in detail little later.

ECell =Eeft - Erigh =0- Eright=- Eelectrode

Thus, if the potential of RHS electrode is positive then Ecell is negative and if it is negative Ecell ispositive. Instead of writing LHS and RHS electrode based on the positive side or negative side ofEH2/H+ = 0.0 V, an electrode is named positive (anode) or negative (cathode) electrode.

By convention:

ECell= (ECathode -EH2/H+)- (EAnode- EH2/H+)

ECell= ECathode- EAnode

Standard electrode potential ( E°), is the measure of individual potential of a reversibleelectrode at standard state.

The basis for an electrochemical cell is always a redox reaction which can be broken down into twohalf-reactions: oxidation at anode (loss of electron) and reduction at cathode (gain of electron).Electricity is generated due to electric potential difference between two electrodes. This potentialdifference is created as a result of the difference between individual potentials of the two metalelectrodes with respect to the electrolyte.

Although the overall potential of a cell can be measured, there is no simple way to accuratelymeasure the electrode/electrolyte potentials in isolation. The electric potential also varies withtemperature, concentration and pressure. Since the oxidation potential of a half-reaction is thenegative of the reduction potential in a redox reaction, it is sufficient to calculate either one of thepotentials. Therefore, standard electrode potential is commonly written as standard reductionpotential.

Calculation of standard electrode potential

The reference electrode; chosen by convention, is the standard hydrogen electrode (SHE):Pt/H2 (a=1)/H+(a=1)

It’s potential (electrostatic standard) is taken as 0.0 V at all temperature. Similarly, the standardelectromotive force (EMF) of the half –reactions:

2H++2e- <------->H2 ....................... E0=0.0 V

Half cell potentials can be determined by measuring them in whole cells against the SHE. Forexample, in the system shown in figure 1, measurement of the standard electrode potential ofelement Ag

Pt/H2 (a=1)/H+ (a=1)// Ag+ (a=1)/Ag

the cell potential is 0.799 V and silver is positive. Thus the standard potential of the Ag+/Agcouple is 0.799 V vs. SHE.

Standard electrode potential table/Electrochemical series

It is the lists of the all the elements of redox couple according to the magnitude of the electrodepotential [1, 2]. It compares the standard-state reversible voltages of various electrochemical halfcell reactions relative to the hydrogen reduction reaction. The example shows some of the extremevalue of standard cell potential for some elements based on the ranking:

Cathode(Reduction)Half-Reaction

StandardPotentialE° (volts)

Li++(aq) + e- ->Li(s) -3.04

K+(aq) + e- ->K(s) -2.92

Ca2+(aq) + 2e- ->Ca(s) -2.76

Na+(aq) + e- ->Na(s) -2.71

Al3+(aq) + e- ->Al(s) -1.66

Ti2+(aq) + 2e- -> -1.63

Ti(s)

Mn2+(aq) 2e- ->Mn(s) -1.18

Zn2+(aq) + 2e- ->Zn(s) -0.76

Cr3+(aq) + 3e- ->Cr(s) -0.71

Fe2+(aq)+ 2e- ->Fe(s) -0.44

Co2+(aq) + 2e- ->Co(s) -0.28

Ni2+(aq) + 2e- ->Ni(s) -0.25

Sn2+(aq) + 2e- ->Sn(s) -0.14

Fe3+(aq) + 3e- ->Fe(s) -0.04

2H+ +2e- -> H2 (g) 0.00

Cu2+(aq) + 2e- ->Cu(s) 0.34

Ag+(aq) + e- ->Ag(s) 0.80

Pt+2(aq) + 2e- ->Pt(s) 0.20

Cl2 (g) +2e- -> 2C- 0.36

Au3+(aq) + 3e- ->Au(s) 1.56

F2(g) + 2e- -> 2F-

(aq) 2.87

Table 1. Electrochemical series (at 298 K)

To access complete electrochemical series, please refer [1, 2]. The most negative electrodepotential represents the strongest reducing agent and the most positive represents the strongestoxidizing agent. Apart from the quantitative information given by the electrochemical series, it alsogives the qualitative information e.g. if the two electrochemical couples brought into contact thenreaction will proceed in such a manner that the oxidizing member of the couple having higherelectrode potential with the reducing member of the couple having electrode potential isthermodynamically favored .

Example:

Consider the Fe+2-H+ reaction couple from the electrochemical series. Because the hydrogenreduction reaction has a larger electrode potential compared to the iron reduction reaction (0 V > -0.44 V), the net reaction occur as [3]:

Iron would go through oxidation reaction in redox couple with hydrogen reduction reaction. Thusthe iron reduction as listed in the table is reversed in the form of oxidation reaction and thepotential sign us changed from –ve to +ve (+0.44 V). This is the thermodynamically spontaneousreaction direction under standard state conditions as Eo= +ve. Thus the reaction would take placespontaneously with the generation of 0.44 V if we consider a fuel cell constructed in such amanner. If Eo = -ve, then we would have applied potential so that the reaction would take placeforward direction as shown above and we generally call the process as electrolysis.

Instead of Fe ----> Fe+2 + 2e (Eo = 0.44 V), if we consider Cu2+(aq) + 2e ---->Cu(s) (Eo = 0.34V), then hydrogen reduction reaction would have not taken place spontaneously but in reverseddirection i.e., hydrogen oxidation reaction (H2 ----->2H+ + 2e; Eo = - 0.0 V). Eo of the combinedoxidation and reduction couple would have been 0.34 V resulting spontaneous reaction in theforward direction.

Dominance diagram

There is ambiguity in the arrangement of the some elements in electrochemical series because itmay form different redox couples, e.g. iron can exists in Fe3+, Fe2+ form.

Fe3+(aq)+3e- <---->Fe E0=-0.04 VFe2+ (aq)+2e- <------>Fe E0=-0.44 V

Iron can exists in different forms Fe3+(aq), Fe2+(aq), Fe(s), which depends on the potential theyhave been exposed. Figure 2 shows the dominance diagram of Fe. It shows which isthermodynamically dominant species at any particular potential. The horizontal lines correspond tothe standard potentials of electrode reactions:

Fe3+(aq)+e<----->Fe2+(aq) E0=0.771 VFe2+(aq)+2e-<---->-Fe(s) E0=-0.44 V

Figure 2. Dominance diagram for element iron. The horizontal lines correspond to thestandard potentials of electrode reactions:

Fe3+ (aq)+e-Fe2+(aq) and Fe2+ (aq)+2e-<------>Fe(s)

The diagram reveals that when a potential of 0.0 V is applied to the iron containing solution eitherby electrode or by any other more concentrated redox couple then iron will exists in the Fe2+ form[2].

Example:

a) Let us consider Fe3+/Fe2+ -Cu2+/Cu reaction couple. Fe3+ reduction reaction has the higherpotential as compared to the Cu2+ reduction reaction (0.771 V > 0.34 V). So copper would gothrough the oxidation reaction in redox couple with the iron reduction reaction and the net reactionwould occur as:

which thermodynamically favorable reaction(E0>0) with generation of 0.431 V.

b) Consider Fe2+/Fe – Cu2+/Cu reaction couple. Since copper reduction potential is higher ascompared to the iron reduction potential (0.34 V > -0.44 V), so iron would go through oxidationreaction in the redox couple with copper reduction reaction.The net reaction occurred as:

which thermodynamically favorable reaction (E0>0) with generation of 0.78 V.

From the above two reactions it shows that the Fe2+ is the thermodynamically dominant species

Electrochemical potential

It is a thermodynamic measure that combines the concepts of energy stored in the form ofchemical potential and electrostatics. An electrochemical potential difference will inherently providethe driving force for both the transport of charge (electro migration) and the transport of mass(diffusion) by an ion (an ion having both charge and mass will obviously transport both by itsmovement).

Figure 3 shows a hydrogen concentration cell. Hydrogen fuel compartment maintained at apressure of 50 atm whereas the other compartment maintained at a pressure of 10-8 atm. Atroom temperature, we can generate almost 0.287 V due to a difference in hydrogen concentration.A voltage develops due to the difference in the chemical potential of both sides. Due to chemicalpotential gradient, some hydrogen decomposes on the platinum catalyst to protons and electrons.The protons transport to the other compartment via electrolyte and combines with the electrons onthe platinum catalyst to reproduce hydrogen gas. If two platinum electrodes are not connectedthen on the fuel side excess electrons will accumulated while electrons will be depleted on thevacuum side, setting up an electrical potential gradient. This further retards the flow of hydrogenand at equilibrium chemical potential gradient exactly balance by the electrical potential gradient.The concept of chemical and electrical potentials offsetting one another to maintainthermodynamic equilibrium is summarized by the electrochemical potential [3].

In generic terms, electrochemical potential is the mechanical work done in bringing 1 mole of anion from a standard state to a specified concentration and electrical potential. Also it is the partialmolar Gibbs energy of the substance at the specified electric potential, where the substance is in a

specified phase. Electrochemical potential can be expressed as [1].

Where, i is the species, zi is the charge number, F is the Faraday’s constant, Φa is the electricalpotential experienced by the species i.

The term zi FΦa is the electrical potential energy per mole of species i in phase a

The term called chemical potential

Where, ni is the no. of moles of i in phase a. Thus, the electrochemical potential would be

Where, is the electrochemical free energy and Φa is the electrical potential experienced by thespecies i.

Properties of electrochemical potential

For an uncharged species

For any substance: For a pure phase at unit activity (e.g. solid Zn, AgCl, Ag, or H2 at unit fugacity

):

For a electron in a meta(z=-1)l . Activity effects can be neglectedbecause the electron concentration never changes appreciably.

For equilibrium of species i between phases a and ß :

Formulation of cell potential

For a reaction at equilibrium

We can derive the Nernst equation from the basis of electrochemical potential. For deriving it weshould also include the change in electrochemical potential for the electrons as they move fromanode to cathode. Solving for the difference in the electrical potential for the electrons at thecathode versus the anode (Δ φ e- )) gives the cell potential E[3].

Consider the H2 –O2 fuel cell reaction

At equilibrium

But,

Expanding the above equation, we get

Thus we arrive

which is the Nernst equation of the cell.

References

1. Bard J. Allen, Faulkner R. Larry, “Electrochemical methods- Fundamentals andApplications, second addition, 2006

2. Keith B. Oldham, Jan C. Myland, Alan M. Bond, Electrochemical Science and Technology,John Wiley and Sons, 2012

3. Ryan P. O'Hayre, Suk-Won Cha, Whitney Colella and Fritz B. Prinz, Fuel cell fundamentals,John Wiley and Sons, 2006

Activation over-potentialElectrochemical Reactions

Electrochemical reactions are redox (reduction-oxidation) reactions that involve transfer of free electrons at the interface of an electron conductor(e.g. metal surface) and an ionic conductor (e.g. electrolyte). Such reactions are either driven by externally applied voltage or voltage may becreated by the electro-chemical reaction that occurs spontaneously. The branch of science dealing with electrochemical reactions iselectrochemistry. One point may be noted that in chemical reactions no transfer of electrons take place whereas in electrochemical reactions involvetransfer of free electrons.Since electrochemistry deals with the transfer of charge between and electrode and a chemical species in an electrolyte, electrochemical processesare necessarily heterogeneous.For example

H2<-->2H++2e-...................................................................................................................(1)

In (1) above reaction, electron transfer takes place at the interface between the electrode (e.g. Pt) and an electrolyte (e.g. H2SO4 in water).Electrochemical reactions are heterogeneous because H+ cannot exist inside the electrode and free electrons cannot exist inside the electrolyte.Hence, it is a heterogeneous reaction.

Figure 1: Electrochemical reaction at the electrode-electrolyte interface showing heterogeneous nature of the reaction

Any electrochemical cell has two electrodes called the anode, where oxidation takes place and the cathode, where reduction takes place. Thesereactions occurring at the anode and cathode are called half-cell reactions which together constitute the full electrochemical cell.

Understanding Potential

A general electrochemical reaction can be displayed as follows:

Oxspecies+e- <--->Respecies.....................................................................................................(2)

Where Oxspecies and Respecies are the oxidized and reduced form of the same chemical entity. Voltage (potential) is a measure of electron energy. Bymanipulating the voltage in an electrochemical reaction, course of above reaction can be influenced. For example, if the potential in above reactionis made more negative than the equilibrium potential, then reaction will be biased in the forward direction. On the other hand, if the electrodepotential is made relatively more positive than the equilibrium potential, the reaction will be biased in the reverse direction. Thus, voltage applied toan electrochemical cell decides the course a reaction will take.

Activation Energy

For any reaction to occur spontaneously, the change in Gibbs energy should necessarily be negative. Even if the Gibbs free energy decreases fromreactants to products, the reaction rates are finite because of impedance which is known as activation barrier (Figure 2). This impedance is a barrierthat needs to be overcome for the chemical reaction to occur (please go to module 5 in-situ analyses for electrochemical impedance analyses).Lower the activation energy, easier it is for reactants to convert from reactants to products. Transition state theory states that only a species inactivated state can undergo transition from reactant to product. Hence, it is necessary to first overcome the activation energy before conversion intoproducts.

Figure 2: Gibbs Energy change for an electrochemical reaction. Activation barrier makes the reaction rate finite.

Thermodynamic treatment from statistical mechanics tells that probability of finding a species in an activated nature is exponentially dependant onthe size of the activation barrier:

....................................................................................................(3)

Where P* is the probability of finding a reactant species in the activated state, ?G1 is the energy barrier (energy gap between the reactants and theactivated species), T is temperature (K) and R is the universal gas constant.

Reaction Rate

For any chemical reaction, it is not just the product that is important but also the rate at which it forms. Therefore, we need to find out the reactionrate in the forward direction. This can be understood and calculated as follows:

The reaction rate is the number of reactant species available to participate in the reaction multiplied by the probability that they will be found in theactivated state (because, only these will participate in the reaction) multiplied by the rate at which these transform into the final products. As such,reaction rate is given by:

u1=CRtP*....................................................................................................(4)

Where, u1 is the reaction rate in the forward direction, CR is the reactant surface concentration (mol/cm2) and t is the transformation rate fromactivated state to final products. However, this is still not the net reaction rate, because the reverse reaction is happening too.

Net Reaction Rate

The net rate of reaction is given by:

Net rate = forward rate – reverse rate

u=u1-u2....................................................................................................(5)

Where, u is the net rate of reaction and ??2 is the rate of reaction in reverse direction. Quite intuitively, the net reaction rate can be given as

....................................................................................................(6)

Where, t2 and ΔG2 are the transformation rate and activation barrier for the reverse direction and CP is the product surface concentration.

Gibbs energy change for the entire reaction can be given as

....................................................................................................(7)

Using equation 7 to substitute ΔG2 in equation 6 , the net reaction rate can be given as:

.........................................................................................(8)

Exchange Current Density

Now, we know that current is charge transferred per unit time.

Hence, if Q (coulomb) is the charge transferred in time t (sec), then the current is given by the relation

...................................................................................................(9)

If an electrochemical reaction results in the transfer of n electrons, then

.................................................................................................(10)

Where, F is the Faraday's constant and is the rate of electrochemical reaction (mol s-1).From above relation, the forward current density can beexpressed as

....................................................................................................(11)

Similarly, the reverse current density can be given as

....................................................................................................(12)

Note that i is current and j is current density. Since electrochemical reaction takes at the interface of electrolyte-electrode, it is wise to express interms of current density than simply current. Also note that at equilibrium, there is no net current density. That is, the forward and reverse currentdensities should be equal. This current density at equilibrium is known as the exchange current density. At this point, no net current is extractedfrom the cell under operation.

Butler-Volmer Equation:

Generally, in an electrochemical cell, we aim to get some useful net current from the cell under operation. For this, it is important to deviate fromequilibrium, where the energies of the reaction are balanced. For this, we need to understand the equilibrium state of a reaction by analyzing theenergies of the system. For understanding this approach, we can take the earlier example only (Equation 1)

One of the steps involved here is the chemi-desorption of the adsorbed hydrogen on the catalyst surface (denoted by cat below)

cat-H --> cat+e++H+

As shown in Figure 3 (a), the chemical free energy of the above reaction step decreases as the distance from the interface (catalyst-hydrogen)increase. But, the electrical energy increases (Figure 3 (b)) as the distance from in interface increases (development of charge ensues with e-accumulating up at the electrode and H+ in the electrolyte. This charge accumulation continues till the resultant potential difference (ΔΦ)

counterbalances the difference in free energies between the reactant and product state.

The combined effect of these two energies can be seen in figure 3 (c) where the net effect leads to equal forward and reverse reaction rates.

This build up of the charge, ΔΦ neutralizes the difference between the two reaction rates by decreasing the activation energy barrier for the reversereaction and increasing the activation energy barrier for the forward reaction rate. As such, while the forward reaction rate decreases, the reversereaction rate increases. This makes it difficult to extract a net current from the cell.

Now, it can be stated that

...................................................................................................(13)

We know that the sum of interfacial electric potential difference at anode and cathode yield the overall thermodynamic equilibrium voltage. Theseanode and cathode interfacial potentials are called Galvani potentials. The exact magnitude of these Galvani potentials is not known.

We had earlier studied that voltage plays a crucial role in deciding the course of a reaction. This is because charged species are involved in the

reaction and this free charge species are sensitive to voltage which changes the free energy of these species upon bringing up a change in thevoltage. As a result, this changes the size of the activation barrier. Now, voltage will play a crucial role in extracting a net current from theelectrochemical reaction.

Reducing the Galvani potential at both anode and cathode reduces the forward reaction activation barrier and at the same time, increases thereverse reaction activation barrier. This results into a net forward reaction and hence, a net current can be obtained from the electrochemical cell.

By looking at the figure 4(b), it can be seen that if the Galvani potential is reduced by a value of η, the forward reaction activation barrier is reducedby αηFη and the reverse reaction activation barrier is increased by (1-α)ηFη (figure 4(c)). Here, α is called the charge transfer coefficient and itdenotes how a change in Galvani potential changes the activation barrier for forward and reverse reactions thus producing a net cell current.

We already know that at equilibrium, the current density is given by the exchange current density. Moving away from equilibrium and taking intoaccount the changes in activation barrier, the new current densities can be written as follows:

...................................................................................................(14)

...................................................................................................(15)

The net current j is therefore,j1-j2 (subtracting eq. 15 from 14)

...................................................................................................(16)

We also need to take into account the change in reactant and product surface concentration; owing to change in voltage that changes the reactionrate. This change in concentration can be taken care of by introducing actual surface concentrations CR* and CP*. Accordingly, eq. (16) becomes:

...................................................................................................(17)

Where, j0 is the current density measured at surface concentrations CR and CP. Eq. 17 is called the Butler-Volmer equation and denotes therelationship between current density, surface concentration and activation voltage loss in an electrochemical loss. We can conclude from the aboveequation that the current density increases exponentially with activation over-voltage (η).

Activation Over-potential

Activation over-potential represents the voltage that is sacrificed to overcome the activation barrier to extract a net current from an electrochemicalreaction. The over-potential is the extra voltage needed to reduce the energy barrier of the reaction (usually the rate determining step) so that thereaction proceeds at a desired rate. Thus, higher is the voltage sacrificed, higher is the current density obtained.

The magnitude of this activation loss is governed by reaction kinetic parameters and j0. Having a high j0 is highly favored. This can also be shownfrom Figure 5, which shows the plot for cell voltage versus current density.

Figure 5: Voltage versus current density at different exchange current densitiesTafel Equation

The Butler–Volmer equation (17) often is quite complex to deal with owing to its exponential nature. Thus, it creates unnecessarily complicationswhich can be resolved by making some simplifications under certain conditions. We consider here two cases:

1.η is very small: For small ? (less than 15 mV at room temperature), a Taylor series expansion of the Butler-Volmer equation (17) yields:

..........................................................................................................(18)

Approximation being made here is that ex˜1+x for small values of x. Eq. 18 displays linear relationship between current density and over-potentialfor small disturbances from equilibrium.

2. η is very large: When η is very large (> than 50-100 mV at room temperature), only the forward reaction rate contributes significantly to currentdensity. In other words, the reaction becomes irreversible and the eq. 17 is simplified to :

.........................................................................................................(19)

Solving for η yields,

.........................................................................................................(20)

A plot of η and ln (j) should be a straight line with intercept as - RT/anF ln(j0 ) with slope RT/aNF . Eq. 20 is known as the Tafel equation.

Tafel equation is important to calculate transfer coefficient a and exchange current density j0 from the slope and intercept as shown in figure 6.

Figure 6: plot of activation over-potential and current density. At low over-potential, Tafelequation deviates from its linear nature.

Concentration Polarization

Transport processes in fuel cells:

By this time, we are aware that in fuel cells the following processes occur simultaneously.

Mass Transport Heat Transport Momentum Transport Charge (electron and ion) Transport

All these processes are very complex and have interlinkages and dependencies to each other asper the scheme shown.

These transport processes of the fuel cell are equally important and responsible for the desiredoutput of an efficient fuel cell. The understanding of all the above processes in a fuel cell requiresthe knowledge of multicomponent, multiphase, and multidimensional transport processes.

The basic knowledge may be gathered from the fundamental books on heat transfer, masstransfer, fluid mechanics, and mass transfer. However, here we would like to present a simplisticview of the essential knowledge required to understand the fuel cell.Objective of this section is tomake you understand the various transport processes and their impact on the fuel cell.

Revisiting some of the basic concepts:

Consider a mixture of volume V, containing N different species. The concentration of a species imay be described by anyone of the following ways,

molar concentration(Ci)

Where, ni represents the number of moles of species i in the mixture and

Mass concentration(ρi)

Where, mi represents the number of moles of species i in the mixture and

Where, Wi represents the molecular weight of species i in the mixture.

Mole fraction(Xi)

Where C is total molar concentration.

Mass fraction(Yi)

Where is the total mass concentration.

Concept of Average and Diffusion Velocity:

Vi is the velocity (absolute) of different species with respect to the stationary coordinate.

The average velocity of the species in the mixture can be defined as:

Mass- average velocity (v)

Thus the mass-average velocity is averaged by the proportional amount of mass of each species inthe mixture.

Mass- average velocity (v*)

Thus the molar-average velocity is averaged by the proportional amount of moles of each speciesin the mixture.

It is to be noted that diffusion is the relative motion of a species with respect to the averagemotion of a mixture as a whole. Thus,

Mass- average velocity

Mass- average velocity

Bulk motion: v or v* Diffusion: vi or vi*

Therefore, the total mass flux and total molar flux of the species i relative to the stationarycoordinate become,

Diffusion Law:

Consider a typical case of a fuel cell, which has a non-reacting mixture containing two species i,&j. The rate of mass transfer for species i diffusing through j follows Fick’s Law. For unidirectionalflux in x-direction,

The above equation is the Fick’s Law in terms of mass flux and conveys that the diffusion massflux arises from the mass concentration gradient. The negative sign shows that the diffusion flux isin the direction of decreasing concentration.In a similar way, the equation can be written for themolar concentration gradient,

The proportionality constant Dij is called binary diffusivity, or the diffusion coefficient of the species

i with respect to species j. The unit of diffusivity is m2/s.

Table:A few relevant values (approx.) of binary coefficient required in fuel cell are shown in tableat 25o C and 1 atm. Pressure.

Species i Speciesj Dij(m2/s)

H2 (g) Air (g) 0.41 X 10-4

O2 (g) Air (g) 0.21 X 10-4

C2H5OH(l) H2O(l) 0.12 X 10-8

CO2 (g) H2O(l) 0.20 X 10-8

CO2 (g) H2O(l) 0.24 X 10-8

O2 (g) H2O(l) 0.63 X 10-8

N2 (g) H2O(l) 0.26 X 10-8

Now, we would see that the momentum and heat transport laws are very similar to the masstransport and equivalent laws are Newton’s Law and Fourier Law, respectively. Consider a flowsituation where the flow is over a solid surface (x-z plane) in an orderly (laminar) and smoothmanner in the x-direction, the velocity, temperature and concentration of species i changes in they-direction.

Note: The reader may get the details in any standard book on fluid mechanics, heat transfer, andmass transfer.

Newton's Law of Viscossity (momentum transport)

Where Md,y is the the momentum flux , v is the kinematic viscosity (m2/s) and vX is the velocity inx-direction.

The Fourier law can be represented by the following equation for the heat transfer in the y-direction,

Fourier's Law

Where, qy is the heat flux, α is the thermal diffusivity (m2/s). These transport properties arerelated to each other by some non-dimensional ratios.After this brief discussion on the transportproperties, we will now focus on concentration polarization in the fuel cell.

Polarization: Activation PolarizationOhmic PolarizationConcentration Polarization

Recall that during the explanation of the activation polarization, we have assumed that theconcentration of the reactant is constant and independent of the cell current density. However, inreal situation when we draw the current, the concentration of the reactant decreases at thereaction site. Once the concentration of the reactant decreases, the low availability of the reactantat the reaction site leads to the reduction of corresponding voltage. If we further keep on drawingthe current the reactant concentration depleted and at a certain current the cell voltage dropsdown to zero voltage. This maximum current is known as the limiting current.

The reactant does not continued to be transported to the reaction site because of limitation of thecertain processes. A few major processes include the slow diffusion in the gas phase in theelectrode pores (problem aggravates in case of flooded electrode), slow diffusion of the productthrough reactant from the active sites and vice-versa. These losses are known as reaction losses.Moreover, the concentration of the reactant decreases along the flow channel from inlet to outlet,which adds to the increases in the voltage loss. The combined effect of the Nernst loss andreaction loss is known as concentration loss or concentration polarization.

Concentration loss = Nernst loss + reaction loss

Quantifying Concentration Polarization

The quantification of the concentration polarization may be done by simplified or by rigorousengineering approach. In this NPTEL course we will be limited to the simplified approach only.

Consider an electrode prepared with backing layer and catalyst layer. It may be assumed that thecatalyst layer is very thin as compared to the backing layer. Thus the thickness of the catalystlayer may be considered negligible. The reactant concentration at the inlet is considered to be Co.We know that the reactant is transported from the flow channel through convection and to theelectrode by diffusion. If the concentration of reactant at the end of the backing layer is Cc, and atthe surface of the electrode is Ce, the rate of the mass transfer at steady-state can be calculatedas shown below.

The mass transfer rate from flow channel to the electrode surface through convection is,

Where N is the mass transfer rate (mol/s), A is the electrode area and hmis the mass transfercoefficient.

Similarly, the mass transfer rate from electrode surface to the catalyst surface by diffusion is,

Where, Deff is the effective diffusion coefficient as the diffusion will be from the porous media.

In case of a porous electrode with porosity of φ and without any water flooding Deff will be definedby the Bruggmann’s correlation

At steady state these mass transfer rates will be same thus eliminating Ce from the above twoequation,

Where, R is the total mass transfer resistant of the reactant to the catalyst layer.

By this time, we know that due t the different resistances the rate of mass transfer of the reactantto the catalyst site or reaction site is N. once the reactant is reached to the reaction site theelectrochemical reaction will occur which result in the current and we are aware that the currentgeneration and the rate of reactant transport is linked by the Faraday’s law,

Where, J is Current Density.

On substituting the value of rate of mass transfer (N) in the above equation,

Thus by the above relation we can find out that the current density is proportional to the reactantconcentration difference in the inlet and the catalyst layer as well as the concentration of the inletconcentration of the reactant. Here we can see that if the current density increases, Cc will reduceand at the maximum current density the value of Cc becomes zero.Therefore, the maximumpossible current density (limiting current density; JL) when all the reactant supplied to the catalystlayer is consumed by the electrochemical reaction, can be found out at Cc = 0,

It can be emphasized at this moment that the limiting current at a particular design and operatingcondition is fixed at a certain value. However, by improving the design and operating conditionsthe limiting current may be improved by analyzing the above equation. Increase in mass transfercoefficient (hm) will improve JL: How to improve the mass transfer coefficient? The flow conditionsmust be improved in the flow channel.

Increase in effective diffusivity (Deff) will improve JL: Issues of design and operating condition! Theeffective diffusivity is the function of temperature and porosity of the electrode (or gas diffusionlayer) and thus can be improved by these improving these factors.On combining J and JL,

It is very interesting relation and can easily provide the real concentration of the reactant at thecatalyst surface if the current density and limiting current density are known for a particular fuelcell at the operating conditions. The above equation may be rearranged to,

Now, to quantify the concentration overpotential, consider Nernst equation for a single reactantspecies,

If the reactant concentration at the inlet and at the catalyst surface if same then the cell voltage(E) will be maximum (EO). Thus,

A few points must be noted for the previous equation,

1. The equation is valid at higher current densities.2. Reactant transport should be the rate limiting process.3. The pores of the gas diffusion layer are assumed to be free of water droplets.4. Other physico-chemical processes are ideal and do not affect the system considered.

Note: Detailed knowledge of the concentration polarization in terms of individual mass transportinto the fuel channel, diffusion of the reactant from the fuel channel to the interface of gasdiffusion layer and catalyst layer, and diffusion of the reactant into the catalyst layer (for high andlow current densities), removal of the product from the reaction sites etc. All these processes canevaluated with the complex mathematics along with various co-relations. These processes arebeyond the scope of the NPTEL course.

Ohmic Overpotential

In a typical operation of a fuel cell, the electrons flow through the external load while the ionsmove across the electrolyte to complete the whole circuit. Therefore, ion transport across theelectrolyte is essential for current flow. The current can be related to the charge on the ionstransported through the electrolyte by –

i=njzjF..................................................................................................................................(1)

where denotes the current, is the molar transfer rate of ion, i.e. the number of moles of ionstransported across the electrolyte per unit time, is Faraday’s constant (96,500 C/mol) and is thecharge number of the ion. In case of a proton exchange membrane fuel cell (PEMFC) the H+ ion istransported across the solid polymer electrolyte (generally the Nafion membrane)and therefore,zj= +1. On the other hand, O2- ion moves through the electrolyte (typically yttria stabilizedzirconia) in a solid oxide fuel cell (SOFC), and therefore, we have zj= -2.

The ions can be transported by three mechanisms namely, the convection, diffusion and migration.The details of these mechanisms are discussed below –

1) Convective Transport – In this case, the mass transfer of ions occur as a result of net motionof the electrolyte (e.g., stirred liquid solutions). Convective transport can itself be classified intoforced and natural convection based on the cause of transport. Forced convection results from anexternally controlled fluid motion while natural convection is a result of buoyant forces resultingfrom a density gradient. For example, the fluid flow under a pressure drop can be regarded as aforced convection, while the upward movement of less dense water, in the case of boiling water, isan example of natural convection.

Forced convection can be represented mathematically by the following equation –

nj,i=Cjvj.................................................................................................................................(2)

where is the molar flux rate of species j in the ith direction , is the molarconcentration of the jth species, is the velocity field vector of the fluid. In general, the velocityfield vector of the fluid is represented by –

where vx,vy and represent the components of velocity along the X, Y and Z axis respectively.

The convective transport of jth species can be represented by the following set of equations –

a) Along X – axis: nj,x=Cjvx

b) Along Y – axis: nj,y=Cjvy strain

c) Along Z – axis: nj,z=Cjvz

In natural convection, the transport depends on the density difference which arises throughseveral reasons, e.g. temperature difference, etc. The analysis for natural convection is therefore,much more complex.

2) Diffusive Transport – In this case, the mass transfer of ions take place due to concentrationgradient across the electrolyte.

Mathematically, the diffusive transport can be quantified by the following equation

...............................................................................................................(3)

where ni,jis the molar flux rate of species j in the ith direction , is the diffusivity of jth species along

the ith direction , is the molar concentration of the jth species, is the positionfield vector. In general, we have –

xi=xi+yj+zk................................................................................................................(4)

The negative sign on the right-hand-side (RHS) of the equation 3 signifies that the direction oftransport is opposite to the increase in concentration. In other words, mass transfer of species j,occurs in the direction of decreasing concentration of species j.

As discussed for the case of convective transport, equations 3 and 4, yield three scalar equationsin the three axes, X, Y and Z. Therefore, we have –

a) Along X – axis:

b) Along Y – axis:

c) Along Z – axis:

3) Migration – Here, the mass transport of charged species is driven by an external electric field.In addition to convection and diffusion, the ions can be transported across the electrolyte by anapplying an external electric field. The transport equation for migration is given by –

..........................................................................................(5)

where nj,i is the molar flux rate of species j in the ith direction ,zj is the charge numberof the ion,Dj,i is the diffusivity of jth species along the ith direction,Cj is the molar concentration ofthe jth species, F is Faraday’s constant (96,500 C/mol), is the universal gas constant (8.314 JK-1mol-1), is the absolute temperature (in Kelvin), xi is the position field vector, and, φ is theelectric potential. The negative sign signifies that the transport of positively charged jth species isin the direction of decrease in the potential field. On the other hand, the transport of a negativelycharged species would be in the direction of increase in the potential field.

On similar basis, as discussed for the case of convective and diffusive transport, we have the

following equations along the three axes, X, Y and Z –

a) Along X – axis:

b) Along Y – axis:

c) Along Z – axis:

Therefore, the net transport of the species j across the electrolyte can be represented by thesummation of contributions from the convection, diffusion and the migration. This leads us to thefollowing equation –

.....................................................................................(6)

This equation can be expanded to the following equations in the X, Y and Z directions.

a) Along X – axis:

b) Along Y – axis:

c) Along Z – axis:

Using Equations 1 and 6, we get the following expression for the total current –

Where, , is known as the mobility of the jth species in the electrolyte.

Thus, the ion mobility of a particular species is related to its diffusion coefficient, and this equationis popularly known as Nernst – Einstein relation. Additionally, the mobility also depends on theionic charge, operating temperature and pressure, ionic concentration and size.

.....................................................................................(7)

This is the general equation to calculate the total current in any electrochemical system. It shouldbe noted that at open circuit voltage (OCV), there is no net current drawn from the system andtherefore, at OCV the above equation reduces to –

Hence at OCV, the convective transport of the species in the electrolyte is balanced by diffusionand migration. Further, in case of static electrolyte, there is no velocity field, i.e. the velocity fieldvector is zero. Therefore, in case of static electrolyte the left-hand-side (LHS) of the aboveequation reduces to zero and we have –

Therefore, the diffusion and migration transport balance each other and there is zero current.Themobility of an ion can be related to its conductivity by the following equation –

where the symbol have their usual meanings as defined already; and is the absolute valueof zj. This expression helps us to understand the ion conduction process in an electrolyte –

a) As the charge number zj. is increased, the total current carried per ion increases proportionally,increasing the effective conductivity.

b) As the mobility of the charge carriers increases, the conductivity increases.

c) As the concentration of charge carriers (participants in the ion exchange) increases, the ionicconductivity increases, although this trend does not hold for highly concentrated solutions.

It should be noted that in electrochemical systems, the term overpotentials and/or polarization areoften used to indicate inefficiency. In other words, this overpotential results in loss of the voltage

that the system can achieve at a particular current density. In case of a SOFC, a ceramicelectrolyte is used, while a solid polymer electrolyte is employed for a PEMFC. The details of ohmiclosses in both the cases are discussed here.

Ceramic Electrolytes in SOFCs

In a SOFC, O2- ions move from the cathode to anode through a ceramic electrolyte, typically yttria(Y2O3) stabilized zirconia (ZrO2), termed YSZ. Ceramics are generally inorganic nonmetallicmaterials synthesized by action of heat and subsequent cooling. Besides yttria, several other oxidematerials have been used to dope YSZ, such as Yb2O3, Nd2O2, and Sc2O3. Doped YSZ conductsnegative O2- ions, which are transported through oxygen vacancies in the zirconia structure. Yttriais typically added around 10 mol % to stabilize ZrO2as pure YSZ in not a good ion conductor.

High electrolyte temperature is required for sufficient oxygen ion conductivity in the solid-stateceramic electrolyte, since oxygen ion mobility is almost negligible till 650oC. This is the why theSOFCs are operated at very high temperatures, i.e. between 600 – 1000oC. Therefore, there lies achallenge in finding new materials which can be used as electrolytes in SOFC. Presently,researchers have been successful in improving the ion conductivity by doping YSZ with severaloxide materials, as discussed above.

The YSZ exhibits mixed (electrical and ionic) conductivity; however, the electrical conductivity ispretty low for typical operating conditions in the SOFC. The ionic and electrical conductivity of 8%mole fraction yttria YSZ, (ZrO2)0.92(Y2O3)0.08, has been reported in literature –

.....................................................................................(8)

.....................................................................................(9)

where KB is the Boltzmann constant (8.61 × 10-5 eV/K = 1.38 × 10-23 J/K), T is the absolutetemperature, and PO2 is the partial pressure of oxygen; kBT should only be in eV to use the aboveequations. A plot of the ionic conductivity of (ZrO2)0.92(Y2O3)0.08, as a function of temperature isshown in Figure 1.

As it is clearly evident from Equations 8 and 9, the ionic and electrical conductivity of the ceramicelectrolyte increases with increase in temperature, however, increasing the partial pressure ofoxygen would decrease the electrical conductivity. The conductivity can be related to the voltagedrop by ohm’s law –

ΔV=IR

The total current through the circuit can be calculated by multiplying the current density, i with thegeometric surface area of the electrode, and hence we have –

.........................................................................................(10)

Where,l is the electrolyte thickness, generally around 50 microns. As it can be seen clearly, alower electrolyte thickness and a higher ionic conductivity would decrease the ohmic drop. In orderto increase the power output from the fuel cell, we need to reduce the ohmic loss as much as

possible. However, thin film electrolytes (electrolyte thickness, l< 25 µm), are not very stableduring operation.

Fig. 1. Ionic Conductivity of (ZrO2)0.92(Y2O3)0.08 vs. temperature

Solid Polymer Electrolytes in PEMFCs

In a solid polymer electrolyte, ion mobility is a result of an electrolyte solution integrated into aninert polymer matrix. Generally, the solid electrolytes are perflourinated ionomers with a fixed sidechain of sulfonic acid bonded covalently to the inert, but chemically stable, polymerpolytetrafluoroethylene (PTFE) structure. As a result, the membrane consists of two very differentsub-structures –

a) hydrophilic and ionically conductive phase related to the bonded sulfonic acid groups thatabsorbs water

b) hydrophobic and relatively inert polymer matrix that is not ionically conductive but provideschemical stability and durability.

The most widely studied perflourinated ionomers for fuel cells is Nafion, developed by DuPont, aU.S. based company. When Nafion is hydrated, H3O+-SO3- groups enable motion of H+ ions. Dryperflourinated ionomers act as insulators, therefore PEMFCs typically operate with hydrated Nafionmembranes to facilitate ion transport and reduce ohmic losses. People have tried to understandthe fundamental nature of proton transport through the Nafion membrane and reported twomechanisms, depending upon the water content in the membrane –

a) When the water content is low, the ionically conductive hydrated portion of the membranesbehaves as nearly isolated clusters, and proton transport is dominated by diffusion.

b) When the proton content is high, a proton hopping mechanism is verified, where protons hopfrom one H3O+ to another along a connected pathway in the ionomer structure.

The molecular weight of Nafion can’t be determined accurately due to differences in processingand solution morphology. Instead, the equivalent weight (EW) and material thickness are used todescribe most commercially available membranes. The EW is calculated by the following equation

–

.........................................................................................................(11)

where k is the number of tetrafluoroethylene groups per chain. Generally, Nafion, 11×, electrolyteis used for fuel cell operations, where 11 represents an EW of 1100, while the last digit indicatesthe thickness of dry membrane in thousandths of an inch. For example, Nafion 112 represents a0.002 inch (or 51 µm) thick membrane with 1100 EW. However, it should be noted that thicknessof the membrane depends on the water content of the membrane. In other words, the thicknesschanges when exposed to different relative humidity environments.

The ionic conductivity through Nafion is a function of its water content. Therefore, one first needsto quantify the water content of the membrane. In general the water uptake, ?, is defined in termsof water molecules per sulfonic acid site, i.e. –

.........................................................................................................(12)

In literature, the water uptake of Nafion 1100 EW membrane at 30° C is reported as –

.........................................................................................................(13)

where a (0 < a = 1) is the relative humidity (RH), which is a function of temperature.

Figure 2 below shows the graphical representation of water uptake, ?, as a function of relativehumidity. It can be seen clearly, for 0 < a = 1, i.e. between zero and 100 percent RH, the wateruptake of the membrane increases with increase in RH. It should be noted that the water uptakeof the Nafion membrane is much higher, when equilibrated with liquid water and therefore, theabove relation can only be used when the membrane is equilibrated with water vapor.

Fig. 2. Water uptake, λ, vs. relative humidity at 30° C

Although, the water uptake of the Nafion 1100 EW membrane depends on temperature, theequation can be still be used to good effect to quantify the water content of the Nafion membraneat higher temperatures. However, it should be noted that water uptake of the membranedecreases with increase in temperature.

The water uptake of the Nafion membrane can further be related to its ionic conductivity as follows–

.....................................................................................................(14)

where T is absolute temperature (in Kelvin) and ? is the water uptake as defined above and can bequantified using equation 13.

The Nafion membrane, though has negligible electrical conductivity unlike ceramic electrolytes andhence, we have –

..................................................................................................................(15)

Fig. 3. Ionic conductivity vs. temperature at different RH values

Fig. 4. Ionic conductivity vs. RH at different temperature values

Figures 3 and 4 depict the variation in ionic conductivity with temperature and various RH values.The increase in temperature clearly increases the ionic conductivity. Moreover, the increase in RHconsiderably increases the ionic conductivity. This can be attributed to the transition from diffusionto hopping transport mechanism because of increasing water content in the membrane.

Since we now know the ionic conductivity through the Nafion membrane, the voltage drop can becalculated using ohm’s law as discussed in the case of a SOFC. Therefore, we have –

Where, l is the wet membrane thickness and is the current density. It should be noted thatthickness of a membrane depends on its water content. Generally, the dry membrane thickness isonly known to us and thus needs to be determined based on the RH environment, beforecalculating the ohmic overpotential.

Transport of Electricity: Ohmic Polarization

The ohmic polarization arises due to electrical resistance in the cell components, including

Resistance to the flow of ions in the electrolyte (ionic resistance) Resistance to the flow of electrons and ions in the catalyst layer (ionic and electronic

resistance) Resistance to the flow of electrons through the electrode-backing layer, or gas- diffusion

layer (electronic resistance), and Resistance to the flow of electrons through the interface contact and the terminal

connections (electronic resistance)

Ohmic polarization can be determined by Ohm’s law,

ηohm=IR

where R is the sum of electronic, ionic, and contact resistance.

For practical fuel cells, ohmic polarization is mainly caused by ionic resistance in the electrolyte.

In fuel cell literature, the use of electrical resistance of the cell components, including electrolytes,is often avoided and reciprocal resistance or conductance is commonly used. The conductance issimply the inverse of resistance,

Conductance: γ=1/R

The resistance R depends on the material property as well as the geometry of the conductor asfollows,

R=Ρ L/A

Ρ=The specific resistance (resistivity) is a material property, representing the capability of thematerial in the transport of electricity.

L = Where L is the length of the conducting path, A is the cross-sectional area of the conductornormal to the conducting path and the electrical field has been assumed uniform in arriving theabove equation.

Area specific resistance = A R

Specific conductance (or conductivity) = 1/Ρ(S/cm)

Inverse of sp. resistance

Details of Mass and Electricity Transport in Electrolyte

As discussed earlier that the ohmic polarization is contributed by many components. However, infuel cell the ohmic polarization is largely contributed by the electrolyte. The electrolyte transportsthe ions, that means the mass as well as the charge (or electricity) are transported by theelectrolyte. Therefore, the transport processes in the electrolyte will be discussed in theelectrolyte.

The Mass transfer in the electrolyte is very similar to reactant transfer to the electrode asdescribed earlier. However, only exception is that the mass transfer arises in the electrolyte is bythe motion of mobile ionic species in the electric field set up between the anode and cathode. Themotion of charged species in the electric field is known as migration of the ions.

Thus in order to understand the complex behaviour of transport in the electrolyte, the discussion isdivided into 3 situation to make it simplified.

In the first situation, it will be considered that the mass transfer of the ionic species in theelectrolyte is purely due to the diffusion and there is no electric field between the anode andcathode. In the second situation, it will be considered that the mass transport of the ionic speciesin the electrolyte is due to migration only. That is the transporting species is having charge andelectric field is set up between the anode and cathode. In the third situation, the transport ofcharged species will be considered due to simultaneous diffusion and migration.

Based on the previous discussion, the three situations are written below,

1. Mass transfer by diffusion2. Mass transfer by migration3. Mass transfer by simultaneous diffusion and migration of ions

All above three situations are described in the following discussion one by one.

Mass transfer in Electrolyte by Diffusion of Ionic Species

Consider the situation of a mobile ionic species, i, that is being discharged at an electrode surface.

The transfer process for the ionic species is thus created by the concentration difference (diffusionmechanism). A representative concentration profile is shown in the adjacent figure.

The rate of diffusion towards the electrode surface for the ionic species i is, in terms of molar flux(Fick’s law)

Di is the diffusion coefficient of the ionic species, i, with respect to the electrolyte solution and ismainly a function of nature & molecular size of the species, temperature, and electrolyte viscosity.

Thus current density corresponding to the rate of ion transport is,

Where, δi is the thickness of the diffusion layer adjacent to the electrode surface. The typical valueof the diffusion layer is in the rage ~300 micrometer).

The limiting current density can be obtained at Ci,s = 0

where δL,i is the diffusion layer thickness at limiting current density.

If the diffusion layer thickness could be assumed almost invariant (which may not be necessarilytrue), then δi = δL,i

Assuming all other processes at the electrode are reversible, the voltage loss due to lowering ofthe ion concentration at the electrode surface can be estimated from the Nernst equation,

Mass transfer in Electrolyte by Diffusion of Ionic Species

In the earlier discussion, the charge on the species did not matter. However, while discussingmigration the charge on the species matters. The electrolyte may have positively and negativelycharged species along with the neutral species. Thus,

Electrolyte

Positive ion Negative ion Neutral species (eg. water) for electrolyte

Ions are constantly in random thermal motion. However, they start to accelerate in the direction ofthe electric field once an external field is set-up across the electrolyte layer.

Acceleration is retarded by: viscous and electrical forces (mainly from ionic interactions).

Terminal velocity: (Driving forces = Retarding forces)

Electrical field is represented by the gradient of the electrical potential in the x-direction

ui is the mobility (ionic velocity/potential gradient) of the ion (m2.mol/J.s).

The negative sign reflect that positively charge ion (ni > 0) moves in the direction of decreasingpotential.

The molar flux due to terminal velocity,

Thus the current density arises,

Where, conductivity of the ion i is the transport property of the ion in the electrolyte is defined as

Then,

Which is simply an expression of Ohm’s law

The eq. is valid when Ci is uniform throughout

At this moment, the question comes that if all the charged species are involved then how to knowthe effect of individual species. In this concern, the total current density J resulting from themigration of all the ions in the electrolyte is equal to the sum of the contribution made by thetransport of each of the ionic species or,

On comparing this equation with the previous one, we can find out that the conductivity of theelectrolyte may be written as,

The migration of each ionic species in the electrolyte contributes to the total current densitycarried by the electrolyte. In order to quantify the relative contributions, the transference numberof the ionic species, i, is defined as the fraction of the total current density that is carried by thegiven ionic species, i, or

Substituting J and Ji,

Since k is transport property, t is also a transport property of the electrolyte

If we integrate the equation, across the electrolyte layer thickness, we obtain the ohmicoverpotential due to the electrolyte,

On integration,

The relationship is valid only if the concentration is uniform in the electrolyte.

Mass Transfer by Simultaneous Diffusion and Migration of Ions

Total molar flux for the ion i under the combined effect of diffusion and ion migration,

Total molar flux for the ion i under the combined effect of diffusion and ion migration,

Corresponding current density,

When a fuel cell reach a steady state, all the current is carried by the transport of ions thatparticipate in the electrode reactions

For all other ions present in the electrolyte, their flux due to the electric field effect (migration) iscounterbalanced by the flux due to the concentration gradient (diffusion) and no net transport ofelectricity arises from the motion of these ions.

At this point we may emphasize that both the diffusion coefficient Di and the ion mobility ui arethe transport property of the ionic species i through the electrolyte solution and they may berelated to each other.

Consider a situation where there is no net current flow (J=0) through the electrolyte, that is, thecurrent arising from the ion diffusion due to the concentration gradient and from the ion migrationin an applied electric field reaches the same magnitude, but in the opposite direction.

Thus thermodynamic equilibrium is attained and the conc. of the ion i is given by thethermodynamic Boltzmann distribution.

Where Ci, , is the concentration of the ionic species i corresponding to zero (0) local potential ( Φ).

On the other hand, at J=0 and integrating the below written equation, from Ci, , at φ=0 to Ci at

&phie,

we obtain,

On comparing with the equation written in the previous slide,

ui=Di/RT

The relation is known as the Nernst-Einstein relation. It relates the transport processes of ionicspecies by diffusion and migration in an electrolyte and provides an important link between massdiffusion and electrical conductance.

It should be pointed out that the Nernst-Einstein relation is valid even when the total currentthrough the electrolyte does not reduce to zero value, although it was derived when J=0. This isbecause both ui and Di are the (transport) properties of the ion i in the electrolyte.

Considering equations

On rearranging

On integrating from the surface where x=0, φ =φ1 and Ci = Ci,s and in the bulk electrolytesufficiently away from the electrode surface where φ = φ2 and C =Ci, ∞ ,

It may be noted that the above equation is the basis of current interruption method, that we willdiscuss in characterization techniques.

At this point we may think if diffusion and migration is considered then why not the convectionprocess. Of course, we will discuss that also. The mass transfer, that is, the movement of materialfrom one location in solution to another, arises from atleast by one of them,

1. Migration2. Diffusion3. Convection

The mass transfer to an electrode is governed by the Nernst-Planck equation, written for 1-D masstransfer along the x-axis as,

The above equation is known as Nernst-Planck Equation

Modelling of fuel cell: current-voltage predictions

Need Of modeling

A virtual prototypes of fuel cell, which helps in fabrication Insight into the electrochemistry of the fuel cell & processes that takes place in the heart of the fuel cell Optimize the design parameters of fuel cell system

A combination of modeling and experimentation can reduce the cost and accelerate the pace of building and understanding prototype systems[1]. Thiswill further help in commercialization of fuel cell.

development process [2]

Figure 1: Flow chart of fuel cell development process

Characteristics of a good model [2]

A good model should balances,

Robustness: model should able to predict fuel cell performance under a large range of operating conditions and physical parameters. Accuracy: it can be developed by using the correct assumptions, correct physical quantities and input parameters, correct governing equations,

and validation with experimental data. Computational efforts: time required for calculation should be less, but sometimes for accuracy, computational efficiency is compromised.

A basic fuel cell model[3]

The real output voltage (V) of fuel cell can be calculated subtracting all the overvoltage losses from the thermo-dynamically predicted voltage

............................................................................................(1)

where,

Ethermo =thermodynamically predicted voltage of fuel cellηact =activation losses due to reaction kineticsηohmic =ohmic losses from the ionic and electronic resistanceηconc =concentration losses due to mass transport

Using the expression for ηconc , ηact , ηohmic from the previous chapter, the net j - v behaviour can br given as,

................................................(2) Here we use the Tafel equation for the fuel cell kinetics, therefore Eq.(2) means this model is only valid for j>>jo.For modelling at low current

density region, full form of Butler - Volmer equation should be used. In this model there are seven fitting parameters: μA, μC,βA, βC,γ,A,Rohmicand jL, where the values of μ,β,γ are related to α and j0

Graphical representation of the factors that contributes to fuel cell performance

Figure 2: Graphical representation of all the losses

A 1D FUEL CELL MODEL (ANALYTICAL)

This model is more sophisticated than the basic model. It is based on the flux balance concept. Flux balance allows us to keep tracks of all the species flowing in, out and through the fuel cell. The model is well suited for polymer electrolyte fuel cell (PEMFC) and solid oxide fuel cell (SOFC). In the present models, we only concentrated on fuel cell species transport and determine the species concentration profiles, electrochemical

losses and j-V curve.

Flux Balance in Fuel Cells

PEMFC

Figure 3shows the flux details needed in 1D model. Individual fluxes are represented by the numbers. Infuel cells, all species transport flux are related to the single charcter flux-the current density or charge flux of the fuel cell.From the figure 2

one can write as,

flux-flux5=flux1 - flux4 = flux8 - flux 13 ....................................................................(3)

mathematically,

...........................................................(4)

where, j is the cell current density (A/cm2), F is Faraday's constant (96,484 C/mol), N is the molar flux (mol/s.cm2) , r is the generation term due toelectrochemical reaction

Figure 4: Flux detail diagram of SOFC

is the net hydrogen flux (in - out) in the anode, i.e., the amount consumer in the oxidation reaction. Similarly, is the net flux of

oxygen at cathode is the water generation rate due to oxygen reduction reaction at cathode. water flux balance in the PEMFC is given as,

................................................(5)

water flux through the membrane is given by the balance between electro-osmotic drag and back diffusion water fluxes.Flux 5 represent the

flux due to water generation. Mathematically above equation can be written as,

...................................................(6)

where, is the net flux into the anode catalyst layer, across the membrane layer, and into the cathode catalyst layerrespectively and j/2F term represent the water generation rate.

Let ς (unknown) is the ratio between the water flux across membrane and charge flux across the membrane is hiven as,

..............................................................................................(7)

Putting Eq. (7) in Eq. (6) one can gets,

.............................................................................................(8)

On combining eq. (5) - (8), all the flux in the fuel given as,

............................................(9)

SOFC flux balance

Figure 4 shows the flux detailed diagram of SOFC. Similar to PEMFC model, the flux balance equation for SOFC is given as,

.............................................(10)

Overall flux balance in SOFC is simpler compared to PEMFC because water produced at the anode and does not transport through themembrane, hence no need of water balance . The water flux at the anode equal to the charge flux. The species transport through membrane isonly of oxygen ions (O2-). Water flux at the cathode is zero. The water generates at the anode is in vapor form because of high temperature.

In PEMFC model, water present in liquid form and transport through the membrane. So, water balance across the membrane is necessary.

Figure 4: Flux detail diagram of SOFC

Model Assumptions

To simplify the model, some assumptions are made which are as follows:

1. convective transport is ignored. Although, convection is dominant phenomena in fuel cells.Bur here, for iD model convection is not cosideredalong x-axis .

2. Diffusion transport in flow channel is ignored.Convection is dominant phenomena in flow channel, since convection is ignored (assumption 1))in flow channel , diffusion can also be ignored.

3. Ohmic losses only due to electrolyte membrane.4. For H2 - O2 fuel cells, anode activation losses is much smaller than cathode activation losses. Hence, anode reaction kinectics is ignored.5. Catalyst layer are assumed as extremely thin like 'interface'(no thickness).Hence convection, diffusion and conduction processes in catalyst

layer are ignored.6. Water assumed to be exists as water vapor.For SOFC, this assumption is valid because SOFC operates at high temperature. In PEMFC, water

exist in water vapor and in liquid form.

Governing Equations

Equations that deal specificially with phenomena in a fuel cell are- Deacy's equation for fluid flow in conduits and porous media, Fick's law of diffusion, Stefan-Maxwell equation for multispecies diffusion, Fourier's Law for heat conduction, Faraday's Law for relationship between electrical current and consumption of reactants in an electrochemical reaction, Butler-Volumer equation for relationship between electrical current and Potential Ohm's Law of electrical current conduction.

For the present model, simplified version of equations are used by choosing appropriate assumptions.By solving these equations we can determineconcentration profiles, activation overpotential (ηact), ohmic overpotential (ηact), and concentration overpotential (ηact).

For the present model, simplified version of equations are used by choosing appropiate assumptions.By solving these equation we can determinecocentration profiles, activation overpotential(ηact), ohmic overpotential (ηohmic), and concentration overpotential(ηconc) .

Electrode layer

Species transport (H2,O2,N2,H2O) in this layer is given by simlified Fick's Law of diffusion,

......................................................................(11)

In case of gaseous reactants, above equation can be written as,

.....................................................................(12)

where, Ni is the molar flux (mol/s-cm2) of the species i, Ci is the concentration (mol/cm3) of the species i,pi=pxi is the partial pressure (Pa) of the

species i,p is the total pressure of the gas,xi is the mole fraction of the species i, is the effective binary diffusivity (cm2/s) between species i and j,it can be determine using the nominal binary diffusity, Dij and void fraction, ε by Bruggeman's correction,

.......................................................................................(13)

Electrolyte layer

Governing equations for species transport in the electrolyte.From Eq.(10)

oxygen ion flux can be given as,

.......................................................................................................(14)

From assumption 3, ohmic overpotential is given by,

..............................................................................(15)

where, LM is the electrolyte thickness, KM is the electrolyte conductivity (S/cm) which is given as,

...............................................................................(16)

where, A (K/ohm) and activation energy, ΔGact(J/mol) are usually determine experimently.

For PEMFC, water and proton (H+) both transport through the membrane electrolyte.Proton flux is given by Eq.(4) nd water flux through themembrane can be describe as combined effect of back diffusion and electroosomotic drag,

..................................................................(17)

...................................................................(18)

...................................................................(19)

Where, ndrag is the electroosmotic drag coefficient, Ρdry is the density (g/am3) of dry membrane, Mm is the molecular weight, Dmis the diffusivity(cm2/s)of water inmembrane, λ is the water content membrane.

Sustitute Eqs. (18) and (19) in Eq. (17), one gets,

..........................................................................(20)

Ohmic overpotential is determined as,

..............................................................................................(21)

Resistance of the membrance, Rm is given by,

..............................................................................................(22)

Membrance conductivity, KM for Nafion membrane is expressed as [3],

................................................................(23)where, λ can be determine using Eq.(20)

Catalyst layer

Cathode side kinetics is represented by modified form of Butler-Vilmer equation,

.........................................................................(24)

For an ideal gas(p=CRT), the above equation becomes,

................................................................(25)

where, p0=1atm

Modeling Examples

1d SOFC Model

Figure 5 shows the 1D schematic of SOFC. Anode: H2,H2O transport is given by Eq. (12)

...............................................................(26)

................................................(27)

Figure 5: Schematic of SOFC

Using Eq. (10), H2, H2O flux are related with cell current density.

Integrating Eq.(26) and (27), gives linear profile of H2,H2O concentration at anode,

.....................................................................(28)

......................................................................(29)

At interface 'a', values of xH2,xH2O are known. Solving Eqs. (28) and (29) at interface 'b' yields,

....................................................................(30)

...........................................................(31)

where, tA is the thickness of the anode

Cathode

Siimilarly, one can obtained oxygen profile at cathode,

....................................................(32)

At interface 'c', Eq. (32) yields,

......................................................(33)

Combine Eqs. (25) and (33), cathode overpotential is given as,

.....................................(34)

Electrolyte

From Eqs. (15) and (16), ohmic loss is given by,

.................................(35))

Finally, a real SOFC voltage is written as,

.............................(36)

............................(37)

PEMC Model

Figure 6 shows the 1D schematic of PEMFC

Reactants (H2, H2O, O2, N2) transport in flow channel is by convection and in electrodes by diffusion. Electrons transport is through the external circuit, whereas ions transport through membrane electrolyte.

In membrane, water transport is by electroosmotic drag and back diffusion

Anode

Figure 6: Schematic of PEMFC

Similar to SOFC model, H2, H2O fluxes described as,

........................................................................................(38)

...........................................................................................(39)

Using Eq. (9), the solution of the above equations,

..........................................................................................(40)

.......................................................................................(41)

here, ς is unknown.

At interface 'b', Eq. (40) and (41) yields,

....................................................................................(42)

...............................................................................(43)

Cathode

Oxygen concentration profile at cathode interface 'c' is expressed as

...............................................................................(44)

water concentration profile at cathode interface 'c' is given as,

...........................................................................(45)

where, tc is the thickness of the cathode.

Similar to SOFC model, cathodic overpotential is determine using Eqn (34)

Membrance electrolyte:

To calculate ohmic overpotential, water profile in membrane is required. Substitute Eq. (7) in Eq. (20) and integrate, Eq.(20) becomes,

........................................................(45)

At interface 'b' .......................................................................(46)

At interface 'c'.......................................................................(47)

Nation watrer content can be relate with the water activity as,

......................................................................(48)

......................................................................(49)

......................................................................(50)

Combining Eqs.(43) and (48) and Eqs. (45) and (49) gives,

.....................................................................(51)

........................................(52)

From Eqs. (46),(47),(51) and (52), two unknowns, ζ and B in Eq.(45),the conductivity, KM profile in membrance can calculated by Eqs.(23)and (45).

Resistance in membrane is calculated by Eq. (22), hence ohmic overpotential is determine as,

..................................................................(53)

Finally, fuel voltage is given as,

.............................................................(54)

Direct Methanol Fuel Cell Modeling (DMFC) [4]

Figure 7 shows the schematic diagram of DMFC. Complete oxidation of methanol (fuel at anode) takes place and product obtained is CO2 via 6 e- release. Model consider the mass transport in the anode compartment. Kinetics and ohmic effect considered in the catalyst layer. Influence of different parameters on anode performance is investigated.

Figure 7: Schematic diagram of the anode bonded PEM DMFC

Mathematical Model

A membrane region of solid polymer electrolyte (PEM), protons produced at the catalyst layer are transported via migration through it. Active catalyst region(catalyst layer) on which oxidation of glucose takes place, it formed as a thin film of proton conductive ionomer (e.g.

Nafion) and carbon supported catalyst (e.g. Pt-Ru/C) uniformly dispersed in the ionomer. A diffusion region (diffusion layer) composed of highly porous and electronically material (collect the electrons generated at the catalyst layer

into the current collector).

Figure 8 : Schematic illustration of catalyst layer [5]

Model Assumptions

Steady state, isothermal conditions were considered . Anode and cathode compartment have the same pressure . Anode and cathode compartment assumed as mixed reactor . Two phase flow in anode channel is neglected .

The electro-osmotic drag coefficient of the water for PEM is taken as fully hydrated, therefore it depend only on temperature . Concentration of oxygen taken high, so assumed constant concentration at cathode compartment so no need of mass balance .

Electrochemical Cell Reactions

Governing Equations

Methanol transport in flow channel

.....................................................................................(55)

Mass transport in diffusion layer

water flux balance equation is given as,

.....................................................................................(56)

Methanol flux equation is expressed as,

.....................................................................(57)

.................................................................(58)

..............................................................(59)

Integrating Eq. (59) gives,

...............................................................(60)

Combining Eqs. (55) and (66)

................................................................(67)

where, is the mass transfer coefficient,

is the superficial velocity of water

Mass transport in catalyst layer

Electrochemical reaction rate described by Tafel type Butler-Volumer Equation,

..........................................................................(68)

Methanol flux equation given as,

..........................................................................(69)

Flux balance of water is expressed as,

...........................................................................................(70)

Methonal, flux in catalyst layer decrease along z-axis due to its oxidation at the catalytic site, therefore material balance of methonol,

.............................................................................................(71)

Anodic over potential at any location within the catayst layer is written as,

.............................................................................................(72)

Ohm's law for solid phase,

.............................................................................................(73)

Ohm's law for ionomer phase,

.............................................................................................(74)

Variation of the over potential within in the catalyst layer given by,

.............................................................................................(75)

Mass transport in PEM

Water transport through the PEM results from both the electro-osmotic drag and diffusion, i.e.

Water flux caused by elctro-osmotic drag, at constant cell temperature is given by,

...................................................................................................(76)

Water flux caused by water concentration gradient in the PEM,

....................................................................................................(77)

At higher current density enhanced water accumulation at cathode reaction raise its concentration on the cathodic side into fully hydrated state, alsoanode is in fully hydrated condition, so we can neglect Ndrag

Final water flux equation is expressed as,

............................................................................................(78)

Similarly as anode diffusion layer, methanol flux in membrane given as,

........................................................................................(79)

Solution Procedure

................................(80)

...........................................(81)

These equations can br transferred into first order equation as,

.......................................................................................(82)

.......................................................................................(83)

..............................................(84)

..............(85)

Dependent variables:

Boundary Conditions

Diffusion layer is ionically insulated, so that the protonic current density must be zero at the diffusion layer/catalyst layer interface(z-0),

................................................................................(86)

Material balance of methonal at diffusion layer/catalyst layer interface(z=0)

................................(87)

In shooting technique appropriate initial guess is given to the variable and iterate it until the final value due to initial guess will match with the actualfinal value.

At catalyst layer/PEM interface(z=lc), the protonic current density must be equal to the cell current density l

.......................................................................................(88)

The flux through the catalyst layer is partly consumed in electrochemical reaction and remaining pass through the membrane sa menthonol crossover,therefore,

Intial value of i is known , others variables values are unknown so for solve these equations, proper shooting technique is used.

Base - case parameterrs values

Results [4]

Anode overpotential of DMFC:Catalyst –Pt-Ru, Methanol concentration in feed- 2 M

Methanol concentration variation with in the diffusion layer and catalyst layer at various current density

Variation of methanol crossover with current density at various feed concentrations

Effect of current density on anodic overpotential at various current density

Variation of reaction rate within the catalyst layer at different values of and at cell current density of 0.3 A/cm2

Vriation of anodic overpotential with effective protonic conductivity at different current density

References

1. Modeling of fuel cell, http://www.aip.org/tip/INPHFA/vol-7/iss-4/p14.pdf2. Frano Barbir, PEM Fuel Cells: Theory and Practice, 2005, Elsevier Inc.3. Ryan O'Hayre, Suk-Won Cha, Whitney Colella, Fritz B. Prinz, Fuel Cell Fundamentals, 2nd Edition, 2008, Wiley.4. K.T. Jeng, C.W. Chen, Modeling and simulation of a direct methanol fuel cell, Journal of Power Sources 112 (2002) 376-375.5. Lixin You, Hongtan Liu, A parametric study of the cathode catalyst layer of PEM fuel cells using a pseudo-homogeneous model, International

Journal of Hydrogen Energy 26 (2001) 991–999

Fuel Cell Components

In this particular section, we will discuss about the fuel cell components. We would consider thecomponents of polymer electrolyte membrane fuel cells as it is the most widely used fuel cell andhave a potential to use in wide variety of applications as discussed at the beginning.

Moreover, the PEMFC components are more or less same for the other type of low temperaturefuel cells. The major components of the fuel cell are,

1. Polymer electrolyte membrane (membrane)2. Bipolar plate3. Gas diffusion layer (electrode)4. Catalyst

The following figure shows a representative cost break up of the major components in the PEMFC.We have already discussed time to time about all the components. However, as it can be seen thatbipolar plate is the most costly among others, we will discuss a few more information on bipolarplate little later.

We also know that at present the Nafion (a trademark of DuPont) is the most suitable membranefor the PEMFC and in order to make the PEMFC commercially viable there should be some othercompetitive membrane in the market. Therefore, some more information on the membrane is alsoprovided in this section apart from bipolar plate.

Electrolytes

The use of polymeric membranes as electrolytes in fuel cells has received a tremendous impetus inthe recent past. The PEM fuel cell gained prominence after an ion exchange resin was incorporatedas an electrolyte for space application by General Electric (GE), in 1959 with the testing of phenolicmembranes, prepared by polymerization of phenol–sulfonic acid with formaldehyde. Thesemembranes had low mechanical strength and a short lifetime of a few hundred hours and powerdensity of a few hundred kW.m-2.

During 1962–1965, GE attempted to improve the power density by developing partially sulfonatedpolystyrene sulfonic acid membranes (prepared by dissolving polystyrene sulfonic acid in ethanolstabilized chloroform followed by sulfonation at room temperature). This membrane exhibited abetter water uptake and an improved power density of 0.4–0.6 kWm-2 that enabled its applicationin NASA’s Gemini flights. However, this membrane exhibited brittleness in the dry state.

In the late sixties, cross-linked polystyrene-divinylbenzene sulfonic acid membrane/polymer wasprepared in an inert matrix by GE. The life of the membrane ranged from 1000 to 10,000 h andthe power density attained was 0.75–0.8kWm-2 [Costamagna, 2001].

In 1970s, DuPont developed a perfluorosulfonic acid called “Nafion®” that not only showed a two-fold increase in the specific conductivity of the membrane but also extended the lifetime by fourorders of magnitude. The Dow Chemical Company and Asahi Chemical Company synthesizedadvanced perfluorosulfonic acid membranes with shorter side chains and a higher ratio of SO3H toCF2 groups [Guarau, 2000].

P. Costamagna, S. Srinivasan, J. Power Sources 102 (2001) 242–252. V. Guarau, F. Barbir, H. Liu, J. Electrochem. Soc. 147 (7) (2000) 2468.

Currently PEMFC finds a wide range of applications due to its perceived simplicity of design andweight advantages, combined with optimum compatibility [Neburchilov, 2007].

Membrane materials used till date for PEM fuel cells can be classified as,

fluorinated polymer membranes, hydrocarbon membranes, acid–base blends.

V. Neburchilov, J. Martin, H. Wang, J. Power Sources 169 (2007) 221–238

A brief description on each type of membrane system is given below.

Fluorinated polymer membranes

The perfluorinated sulfonic acid (PFSA) membranes have been the subject of intense research andare the key polymers used currently in portable fuel cell applications [Motupally, 2000].

Nafion® by DuPont is a perfluorinated polymer and used most extensively in fuel cells. Similarpolymers are Flemion® produced by Asahi Glass and Aciplex-S® produced by Asahi Chemical.

S. Motupally, A.J. Becker, J.W. Weidner, J. Electrochem. Soc. 147 (9) (2000) 3171–3177.

Among the three major types, the DuPont product is considered to be superior because of its highproton conductivity, good chemical stability and mechanical strength [Neburchilov, 2007].

However, Nafion® and related polymers are still being intensely researched upon for improvingthe proton conductivity and chemical stability along with longevity of 60,000 h at 800C.

The PFSA membranes are associated with some major limitations such as high cost of membrane,requirement of supporting system and temperature related issues.

V. Neburchilov, J. Martin, H. Wang, J. Power Sources 169 (2007) 221–238

Requirements of supporting equipment for uses with PFSA membranes, such as the hydrationsystem add considerable cost and complexity to the vehicle power train [Neburchilov, 2007].

Membrane dehydration, reduction of ionic conductivity, decreased affinity for water, loss ofmechanical strength due to softening of polymer backbone and increased parasitic losses throughhigh fuel permeation are some of the other serious issues associated with these membranes[Neburchilov, 2007].

V. Neburchilov, J. Martin, H. Wang, J. Power Sources 169 (2007) 221–238

With regard to the application in direct methanol fuel cells (DMFC), Nafion® exhibits a highmethanol permeability, which drastically reduces the DMFC performance and renders it unsuitablefor DMFCs [Sakari, 1985]. Efforts are directed to eliminate the disadvantages such as methanolcrossover problems and loss of hydration above 1000C.

The influence of addition of different additives, such as silica, titanium dioxide, in Nafion®, wasstudied to improve the retention of water in the membrane and to enable the operation of the fuelcell at higher temperature.

T. Sakari, H. Takenaka, N. Wakabayashi, Y. Kawami, K. Tori, J. Electrochem. Soc. 132 (1985)1328.

Perfluro-sulphonic Acid Membrane

Polymer Electrolyte Membrane for PEMFC

Polymer electrolyte membrane (PEM) is a solid electrolyte and thus has various advantagescompared to liquid electrolyte.

allows simple and compact cell structure and operation no free corrosive liquid; minimum corrosion of cell components can be made very thin thus ohmic losses can be minimized able to withstand large pressure differentials and thus control is easy as well as expensive

, precision sensors and control units can be avoided) insensitive to orientation and therefore ideal for mobile application no CO2 poisoning issue acid concentration of the electrolyte is fixed during membrane

fabrication quick start-up thus ideally suitable for transportation no need of electrolyte maintenance to refurbish or regenerate the electrolyte

However, the PEMs have certain disadvantages also, which are given below,

Low temp. operation results in low quality of waste heat Noble metal catalysts are required CO poisoning is an issue

Qualitatively the PEM should have the following main properties related to the lowtemperature fuel cell:

ionic (protonic or hydroxyl) conductivity should be as high as possible, chemical stability should be high , thermal stability should high to sustain in the operating temperature , mechanical properties (strength, and flexibility ) should be high enough to have good

processability and can bear the fuel cell assembly condition , low fuel permeability is required, Moderate water drag is required, fast kinetics for electrode reactions should be supported, and The cost must be low and the raw materials must be ready availability.

Some information on Nafion

Nafion is a trademark of DuPont, USA, and work as an excellent proton exchangemembrane for PEMFC.

It is a sulfonated tetra fluoro-ethylene copolymer. Tetra fluoro-ethylene is the backbone of the Nafion and therefore it has very good

chemical resistance and mechanical strength The sulphonic acid groups provide the proton conductivity to Nafion. The Nafion can hold or absorb large quantity of water in it. Once they absorb the water,

the H+ (proton) of sulphonic group becomes hydrated and the hydrated proton can movequite freely with in the material.

The water is essential for the protonic conductivity of the Nafion. Therefore, the fuel cellmade up of Nafion can not work at higher temperatures. Thus the general operatingtemperature of the PEMFC is around 80oC.

Nafion solution as well as membrane are available in the market.

Nafion115 and Nafion117 are widely used as fuel cell membranes. The various importantnomenclature of the Nafion is given below,

Eg., Nafion115

The first two digits multiplied by 100 gives the equivalent weight of the polymer. In this case it willbe 11x100=1100.

The last digit gives us the thickness of the membrane in mil. One mill is 1000 part of an inch.Thus, in this case, the thickness of the Nafion115 membrane would be 5/1000 inch (or aorund112micrometer).

Basics of equivalent weight

Equivalent weight = Atomic (formula) wt./valence (gm/mol)

Valence is number of electrons that the species can donate or accept . Thus the equivalent weightof hydrogen or oxygen will be,

H=1/1; O=16/2=8

The sulfonic group (SO3H+) in nafion has a valence of 1 since only one proton can beaccepted

Equivalent weight of nafion is equal to the average weight of the polymer chain structurethat can accept one proton.

Hydrocarbon polymer membranes

Despite its shortcomings, Nafion® is still the polymer of choice for most PEFC and DMFCapplications. However, it has been suggested that in order to produce materials that are lessexpensive than Nafion, some sacrifice in material lifetime and mechanical properties may beacceptable, provided the cost factors are commercially realistic [Neburchilov, 2007].

Hence the use of hydrocarbon polymers, even though they had been previously abandoned due tolow thermal and chemical stability, has attracted renewed interest.

V. Neburchilov, J. Martin, H. Wang, J. Power Sources 169 (2007) 221–238

Hydrocarbon membranes provide some definite advantages over PFSA membranes and have thepotential to compete with Nafion® membranes. They are less expensive, commercially availableand their structure permits the introduction of polar sites as pendant groups in order to increasethe water uptake [Kreuer, 2001].

Poly(vinyl alcohol) (PVA) membranes are known to be good methanol barriers. Based on thisobservation, a method of crosslinking PVA was suggested so that the extent of swelling in watercould be controlled. Presence of aromatic hydrocarbon in the backbone of hydrocarbon polymerenhances its performance at high temperature [Smitha, 2005].

K.D. Kreuer, J. Membr. Sci. 185 (2001) 13. B. Smitha, S. Sridhar, A.A. Khan, J. Membr. Sci. 259 (2005) 10–26.

Aromatic hydrocarbons can be:

(a) incorporated directly into the backbone of a hydrocarbon polymer, or(b) polymers modified with bulky groups in the backbone.

Polyarylenes are high temperature rigid polymers with glass transition temperature, Tg, >2000Cowing to the presence of inflexible and bulky aromatic groups. The aromatic rings offer thepossibility of electrophilic as well as nucleophilic substitution. Polyethersulfones (PESF), polyetherketones (PEK) with varying number of ether and ketone functionalities (such as PEEK, PEKK,PEKEKK, etc.), poly(arylene ethers), polyesters and polyimides (PI) are some of the relevantexamples of main chain polyarylenes [Gowariker, 1999].

V.R. Gowariker, N.V. Vishwanathan, J. Sridhar, Polymer Science, New Age International, NewDelhi, 1999.

Acid-base polymer membranes

Acid–base complexes have been considered as one of the alternative for high temperature fuel celloperations. In general, an acid component is incorporated into an alkaline polymer to promoteproton conduction.

Poly(2,21-(m-phenylene)-5,51-bibenzimidazole)/phosphoric acid (PBI/H3PO4) complex is bothintriguing and promising at the same time.

It has shown a great deal of potential for medium temperature fuel cell applications and hencemany attempts were made to understand and optimize this particular system.

Fuel Cell Catalysts

The electro-catalysts have a central part in the fuel cell and impact the efficiency, durability, andcost of the cell to a large extent. Carbon supported platinum or platinum alloys are commonly usedas catalyst on both the anode and the cathode of PEMFC. The oxygen reduction reaction (ORR)taking place on the cathode has sluggish kinetics, which give a major contribution to the efficiencyloss of the fuel cell. High amount of catalyst is required on the cathode to reach sufficient activitycompared to the fast hydrogen oxidation reaction on the anode.

Platinum is used as an active catalyst for not only hydrogen electrooxidation at anode but alsoused for oxygen electroreduction at cathode of PEMFC. However, the use of bulk platinum (e.g. Pt-sheet or foil) neither yields good performance of the PEMFC nor it is economical due to low surfacearea per unit weight of platinum. In order to increase the surface area per unit weight, thenanoscale Pt particles are dispersed on supporting materials.

The researchers are using the Pt based bimetallic, ternary catalyst, and other non-presious metalto decrease the use of Pt and improving the support material. The regular transition elements aregood candidates as electrocatalysts, like, palladium, rhodiam, ruthenium, iridium, and osmium areused by various reaserchers to decrease the use of Pt.

The platinum poisons by trace amounts of carbon monooxide and sulphur compounds, thereforelosing its efectiveness as an electrocatalyst. Non -noble metal catalysts are more tolerant to theseimpurities. In general, the high temperature operation of the fuel cell reduces the effect of catalystpoisoning. However, the cell operation may be limited due to various other reasons.

High electrocatalytic activity of a catalyst is generally achieved by a high surface area per unitmass of the catalyst. It is possible if we reduce the size of the catalyst particle. However, it maynot be beneficial by reducing the size of the particles only but also there is a need to provide theactive sites open to the reantant gases. It may be done by providing more porosity to the catalystbed. The porosity may be developed without much hamperring the active sites of the catalyst, ifthe catalyst patricles are loaded on support material.

It is well known that the electrocatalytic activity in the PEMFC were improved using the supportedmetal catalyst as compared to the unsupported bulk metal catalyst

The carbon (Vulcan XC-72) is used commercially as a support material for the platinum in PEMFCapplication. Generally, the requirements for catalyst support material are high surface area, highelectrical conductivity, high electrochemical stability and good interaction with catalyst under fuelcell operating conditions. Even a small increase in the eletrical conductivity of the supportmaterials may improve the PEMFC performance significantly.

The above figure shows a catalyst for PEMFC, consist of platinum dispersed on carbon particle. Aswe are aware that the triple phase boundary is necessary for the transport of the species due tothe reaction at electrode. The reactant reaches at the electrode and involves in the electrochemicalreaction. The products thus formed have to be transported away from the catalyst site in order tokeep the site free for further reaction. The reactant and product of the electrochemical reactioninvolves reactant, electron, ionic species, and any by product.

The figure on the left side shows a typical electrode system for hydrogen electro-oxidation in arepresentative way. Whereas, the figure at the right side shows the detailed transport of thevarious species from the triple phase boundary, infact the triple phase point is shown.

A good interaction between catalyst and support materials improves the catalyst eficiency anddecreases the loss of catalyst with time during operation of the fuel cell. The support material mayaffact the formation of platinum particales size during the preparation of metal catalyst. It isknown that the electrochemical surface area (ESA) of electrocatalyst depends upon the supportmaterial as well as Pt particles size. Higher the ESA, better the PEMFC performance. The supportmaterial affect the Pt particles distribution during the synthesis of electrocatalyst. Therefore, theselection of catalyst support material is most important towards determining the ESA, stability,durability, and overall performance of the PEMFC.

As discussed earlier, the carbon (Vulcan XC-72) is generally used commercially as a supportmaterial for the platinum in PEMFC application. However, during dynamic operation of the cell,there is a deterioration of the fuel cell performance, partly caused by the loss of electrochemicallyactive surface area. The mechanism for the loss of platinum surface area has been widelyinvestigated and can basically be described by the dissolution or detachment of Pt from carbonsubstrate and further re-deposition onto existing Pt particles or diffusing into the membrane orother inactive parts of the membrane electrode assembly.

The detachment and mobility of the platinum is affected by the corrosion of the carbon support,which has been shown to be very severe not only on the cathode but also at the anode. Moreover,carbon cannot be used as the support in catalysts for PEM-water electrolysis and regenerative fuelcells because its corrosion occurs easily at the high oxygen-evolution potential.

Moreover, low surface area (around 250 m2·g-1) carbon material may not sufficient toaccomodate Pt nanoparticles. Moreover, due to corrosion of carbon, Pt nanoparticle on the carbonsupport agglomerates and looses the suport material (carbon).

Therefore, the electrochemical active sites reduce and as a result the performance of the PEMFCalso reduce with the fuel cell operation time. Moreover, the researchers focus has shifted towardscarbonaecous nanomaterials support for PEMFC catalyst due to their faster electron ransfer andhigh electrocatalyctic activity. e

The carbon nanotube, carbon nanofiber, and graphene have been wiedly used as a carbonnanomaterial for catalyst support in PEMFC. These carbon nanostructures are basically allotrops ofcarbon atoms with high specific surface area, high electrical conductivity, and relatively goodstability towards electrochemical environment.

Due to the changes in the hybridization structure of source bulk materials, the electronical,mechanical, and physical properties of the nanomaterials are quite different and improved.

In the recent efforts, it has been found that carbonless multifunctional active catalyst supports for

the PEMFC and electrolyser electro-catalysts may enhance the activity, utilization as well as thestability of the electro-catalyst.

Bipolar Plate for PEMFC

Why bipolar plate is required?

The main functions of the bipolar plates in a PEMFC system are

to support the membrane electrode assembly (MEA) robustly, to distribute reactant gases uniformly over the active areas, to conduct current between adjacent cells, to remove heat from adjacent cells, and to prevent leakage of reactant gases.

What are the materials available for bipolar plate?

The following table summarizes the different material available for the bipolar plate as well as theiradvantages and disadvantages.

Material Advantages Disadvantages

Metal1. High electrical conductivity2. High mechanical strength

1. Corrosive2. High contact resistance3. High density

Coated metal1. High electrical conductivity2. High mechanical strength

1. Uneven expansion2. High density

Graphite bipolar plate1. High electrical conductivity2. Good corrosion resistance

1. Low mechanical strength2. High H2 permeability3. Machining of flow field

Carbon-carboncomposite

1. Moderate electricalconductivity

2. Good corrosion resistance

1. Long processing time2. High production

temperature3. Cost ineffective4. High porosity

Carbon-polymercomposite

1. Moderate electricalconductivity

2. Good corrosion resistance3. Good mechanical strength

1. Long processing time

If we have to develop a bipolar plate for the PEMFC then we should have a fair idea of therequirement of the bipolar plate. Thus to have a feel the following table shows that if one have towork on carbon/resin composite bipolar plate then the developed bipolar plate should haveachieved properties. How to measure these properties are discussed in the proceeding sectionswith a focus on a few of the properties.

Required properties Target Values

Low weight < 0.4 kg·kW-1

Density < 2.0 g·cm-3

High flexural strength > 50 MPa *

Highly flexible 3–5 % deflection at mid-span

High electrical conductivity > 100 S·cm-1

High thermal conductivity > 10 W·m-1·K-1

Low gas permeability < 2×10-6 cm3·sec-1·cm-2 at 80°C and 3atm

High corrosion resistance < 1 µA·cm-2

High shore hardness > 40*

O’Hayre et al., Fuel Cell Fundamentals, John Wiley 2009

Fuel cell characterization

Why to characterize fuel cell?

This topic is one of the most important topics of the fuel cell technology. The fuel cellcharacterization is of particular importance to the fuel cell developers, scientists andresearchers.

Once the fuel cell is prepared, it is required to access whether a fuel cell is good or badfrom the pool of the developed cells. It is required to know whether the fuel cell iscomparatively inferior or superior to the competitive cell either prepared by others or theimprovement from the previous cells.

In order to distinguish between inferior or superior fuel cell, the characterizationtechniques are very straight forward by using i-v characteristics of the fuel cell.

If a fuel cell performance is not upto the expectation or if you want to make it moreeffective, you must understand and to be able to quantify the different losses occurringin the fuel cell.

The fuel cell characterization can be divided into two broad categories,

1. In-situ characterization

In–situ characterization means the fuel cell is fabricated and now you would like toperformance of the fuel cell. You may also be interested to know how much losses areoccurring in the fuel cell, quantity of the losses, location of the losses etc. Thus we haveto characterize the fuel cell in the ready form.

On careful analysis, we may understand that the in-situ characterization can use theelectrochemical variables of V, I, and time to characterize the performance of fuel cellunder operating conditions.

A few major in-situ characterization techniques are ,

1. Current voltage measurements2. Current interruption technique3. Cyclic voltammetry4. Electrochemical impedance spectroscopy

2. Ex-situ characterization

Once we know that the performance of the fuel cell is not upto the desired standard thenwe have to find out the route cause. We need to identify the problematic component(s)as well as the reasons of ill-performance. Thus we need to characterize the componentfor its properties. Moreover, before using and developing a component for the fuel cell, itis to be characterize fully in order to know the desired properties.

Some of the properties in which we are be interested are kinetic properties (?out, jo, aetc.), ohmic properties (Rohmic, electrolytic R etc.), mass transport properties (JL,Deff, ?P etc.), parasitic losses (jleak, side reactions, crossover), electrode structure (?,

tortuosity, etc.), catalyst structure (TPB, conductivity, AE, etc), flow structure (pressuredrop, gas distribution, conductivity, etc.), heat generation/ heat management, watermanagement, life time issues (degradation, cycling, startup/shut-down, corrosion, etc.),and many more.

Various characterization techniques may be followed depending upon the individualcomponents of the fuel cell. A some of them are shown below,

Electrolyte : Proton conductivity; cross-over etc.

Bipolar plate : Mechanical and chemical strength; flow field design; electricalconductivity etc.

Catalyst : Surface area; selectivity etc.

Gas diffusion layer : Porosity; hydropholicity; hydrophilicity; strength etc.

However, we will focus on just a few of the most widely used characterization techniquesin the forthcoming slides.

In-situ characterization

1. Current – Voltage measurement

Current-voltage measurement or polarization curve provides overall quantitative evaluation of fuelcells performance. It is very useful technique and provides an information of various losses likeactivation polarization, ohmic polarization, and mass transfer limitations or concentrationpolarization. With the help of polarization curve we can understand various processes happening inthe fuel cell. For example, if at zero current the difference in the corresponding voltages of twosimilar direct methanol fuel cells indicate that the difference in the voltage may be because of theanode side fuel (methanol) crossover through the electrolyte to cathode side. Similarly, differentconcentration polarization may indicate about the slow transfer of the reactant to the electrode.

For details, please refer to the earlier discussion on the polarization curve.

2.Current Interruption Technique

The method separates the contribution of ohmic and non-ohmic processes of the fuel cell. Thistechnique is very simple as compared to the other techniques like cyclic voltammetry, andelectrochemial impedance spectrometry, etc.

In the next slide an illustration is provided for the better understanding. Consider a current A1 isflowing through a fuel cell is abruptly interrupted as shown in figure (a). The resulting voltage-timeresponse is shown in the figure (b). The interruption of the current causes an immediate reboundin the voltage, followed by an additional, time-dependent rebound in the voltage.

Illustration of current interruption technique

The immediate voltage rebound from V1 to V2 is associated with the ohmic resistance of the fuelcell. The time-dependent rebound is associated with capacitive nature of the much slower reactionand mass transport processes. The recovery time for this process is slow and thus it takes time tocome to the open circuit voltage (V3) corresponding to A1.

If we recall the following equation discussed before to understand it.

For zero current the ohmic part contribution gets zero. However, the reactant molecules and ionicspecies takes some time to get re-oriented due to the removal of electric field..

3. Cyclic Voltammetry (CV)

The cyclic voltammetry has become a very popular technique for initial electrochemical studies ofnew systems and has proven a very useful in in obtaining information about fairly complexelectrode reactions.

In the technique, the potential of an electrochemical system swept back and forth between twovoltage limits and the response of the current is measured against the voltage. In general thevoltage is changes linearly with a predefined rate (V/s).

Illustration of the CV: The voltage is scanned from V1 to V2 and then back to V1

For a reversible electrochemical reaction the CV recorded has certain well defined characteristics.

(i) The voltage separation between the current peaks is

(ii)The ratio of the peak currents is equal to one

(iii)The positions of peak voltage do not alter as a function of voltage scan rate

(iv)The peak currents are proportional to the square root of the scan rate

Note: Subscript p denotes the peak, superscripts a and c denote the anodic and cathodiccomponents , and v denote the voltage scan rate

4. Electrochemical Impedance Spectroscopy (EIS)

Electrochemical Impedance Spectroscopy is also called AC Impedance or just ImpedanceSpectroscopy. It is a method of characterization of the electrochemical system. It utilizes themodeling of the electrochemical system into the electrical circuit of resistances, capacitances, or

other electrical components. EIS is a recent tool in corrosion and solid state laboratories and itsusefulness lies in the ability to distinguish the dielectric and electric properties of individualcontributions of components under investigation.

The polarization curve provides general quantification of fuel cell performance. However, the EIScan be used for accurate quantification. It is a very common method to distinguish the differentlosses in the fuel cell.

Basics of the EIS

We know that like resistance, the impedance is a measure of the ability of a system to impede theflow of electrical current (electron or ions). However, impendance can deal with time or frequencydependent phenomena unlike resistance.

The resistance is the ratio of voltage to current, similarly the impedance is also the ratio of timedependant voltage to time dependant current.

In EIS technique, we provide a sinusoidal voltage perturbation to the fuel cell and the response ismeasured. As the EIS is modelled using electrical components, we would first learn the basics ofthe electrical components generally used for the fuel cell under sinusoidal perturbation.

At first we will refresh the complex theory,

If V(t) is the potential at time t, V0 is the amplitude of the signal, and ? is the radial frequency.The relationship between radial frequency ? (expressed in radians/second) and frequency f(expressed in Hertz (1/sec)).ω = 2πf

Thus the impedance becomes,

As there is a phase shift between the voltage and current for a sinusoidal input, we generallyrepresent the same in a complex plane shown in the next slide.

Some of the equations related to complex numbers are as follows:

Electrical Components and their Impedance

Registor, R V=IR

Let V = V0sin(ωt), then I = V0sin(ωt)/R

So, current and voltage are in the same plane to each other and hence the impedance of a registoris R only.

2.Capacitor, C q = CV

Let V = V0sin(ωt)I = CωV0cos(ωt) = ωCV0 sin (ωt + 900)So, current leads voltage by 90o and hence impedance of a capacitor = 1/jωC

Inductor, L V= L.dl/dt

Similarly, - V0cos(ωt) =ωLI = V0sin(ωt - 90o) So, current lags voltage by 900 and henceImpedance of an Inductor = j?L

4. Warburg Element, W

It represents the diffusion part of an electrochemical cell, associated with a double layercapacitance.

Impedance, ZW = Aw/√ω+Aw/j√ω

Series and parallal combination of electrical components

Very few electrochemical cells can be modeled using a single equivalent circuit element. Instead,EIS models usually consist of a number of elements in a network. Both serial and parallelcombinations of elements occur.

Impedances in Series:

Zeq = Z1 + Z2 + Z3

Impedances in Parallal:

1/Zeq =1/ Z1 +1/ Z2 +1/ Z3

Representation of impedance spectroscopy

The impedance so obtained from the study can be plotted in two different kinds. They are,

i) Nyquist Plot:

The expression for Z(?) is composed of a real and an imaginary part. If the real part is plotted onthe X-axis and the imaginary part on the Y-axis of a chart, we get a “Nyquist plot”. Notice that inthis plot the Y-axis is negative and that each point on the Nyquist plot is the impedance Z at aparticular frequency. On the Nyquist plot the impedance can be represented as a vector of length|Z|. The angle between this vector and the X-axis is f. Nyquist plots have one major shortcoming.The frequency at any point cannot be determined from the plot.

Low frequency data are on the right side of the plot and higher frequencies are on the left. This istrue for EIS data where impedance usually falls as frequency rises (this is not true of all circuits).

The Nyquist plot shown in the next slide is for a RC circuit. The semicircle is characteristic of asingle “time constant”. Electrochemical Impedance plots often contain several time constants.Often only a portion of one or more of their semicircles is seen.

RC Circuit

1/Z =1/R +1/jω

Corresponding Nyquist Plot

ii) Bode Plot:

Another popular presentation method is the “Bode plot”. The impedance is plotted with logfrequency on the X-axis and both the absolute values of the impedance ( Z = Z0) and phase shifton the Y-axis. The Bode plot for the RC circuit is shown below. Unlike the Nyquist plot, the Bodeplot explicitly shows frequency information.

A typical representation of fuel cell

The fuel cell, which has three major parts, anode, electrolyte and cathode, can be expressed interms of resistance, capacitance and the Warburg element. Resistances develop mainly due to theresistance to the transport of ions or electrons. And hence we see the electrolyte section beingshown as a resistance model with small resistances in the anode and cathode part to account forthe resistance to the electron movement.

An electrical double layer generally exists at the interface between an electrode and itssurrounding electrolyte. This double layer is formed as ions from the solution to the electrodesurface. Charges in the electrode are separated from the charges of these ions. The separation isvery small and is in the order of nanometers. These charges separated by an insulator forms acapacitor. In order to have a feel of the capacitance value, it is known that a bare metal immersedin an electrolyte will generate around 25µF per cm2 of the metal electrode area. The value of thedouble layer capacitance depends on many variables such as electrode potential, temperature,ionic concentrations, types of ions, oxide layers, electrode roughness, impurity adsorption, etc.

A representative Nyquist plot for a fuel cell: The typical values on the plot is just a typical value.

The Warburg element accounts for the diffusion layer formed at the cathode section and henceresisting the flow of hydronium ions to the cathode.

Now, we see that there exist two semicircles in the Nyquist plot for the given model. This showsthat the system has two time constants, one for the cathode side and another for the anode side.While at the later section of the graph, it takes a linear form owing to the Warburg element cominginto play. The diameter of each of the semicircle represents the resistance of that particular part ofthe cell.

As we know that the kinetics at the anode is much faster than at the cathode so we have a largerresistance value for the cathode than for the anode, which is evident from the diameter of therespective semicircles. In fact for actual fuel cell system, the smaller semicircle is too small to bevisualized and in many cases removed to make the system simpler to analyze

Ex-situ characterization

We will discuss a few of the important ex-situ characterization of the major componentsof the fuel cell.

1. Electrolyte Characterization for proton conductivity

In this section we will see how to find out the proton conductivity of the cationic solidelectrolyte (proton exchange membrane).

Through plane conductivity of the membrane can determined in a conductivity cell shownin the next slide. The conductivity measurement can be performed in a two-electrode ACimpedance mode using a LCR mete.

Proton conductivity set-up for cationic solid polymer electrolyte

Conductivity measurements should be performed at a particular temperature afterequilibrating the membrane in de-ionized water for 24 hours. The membrane should belocated at the centre of the conductivity cell, having two chambers filled with 0.5 MH2SO4 solution. Both the compartments should have a platinum electrode (say, 0.5 cm2each). The electrical resistance of membrane (R1) can be measured using LCR meter.The electrical resistance of the 0.5 M H2SO4 solution (R2) without the membrane can bemeasured. The electrical resistance, R, of the membrane can be calculated by subtractingthe value of R2 from R1.

where L, R, and A denote the distance between the electrodes (cm), the measuredresistance (ohm), and the effective area of the membrane (cm2) perpendicular to ionflow, respectively.

Bipolar plate

i. Electrical conductivity

As discussed in the bipolar plate section, the electrical conductivity is one of the mostimportant properties of the bipolar plate. In this section, we would discuss about how tomeasure the electrical conductivity of a composite bipolar plate made up of carbonmaterials and polymer matrix.

Electrical conductivity of the bipolar plate can be measured as per the ASTM C611method using conventional four probe technique at a constant current supply. Theschematic of the electrical conductivity measurement set-up is shown in the figure on thenext slide. Electrometer may be used as the constant current source.

Bipolar plate conductivity measurement set-up

The electrical conductivity of the sample can be calculated by the following equation,

Electrical Conductivity

where, l (cm) and b (cm) are the width and thickness of the sample, respectively. Theconstant current supplied through the sample is represented by i (A) and V (V) is thevoltage drop between two points separated by a distance d (cm) along x-direction. Theset-up was used to measure the in-plane and through-plane electrical conductivity bychanging the orientation of the bipolar plate.

ii. Flexural strength

The flexural strength of the composite bipolar plates are important properties as the

bipolar plates may undergo high bending force during clamping within the fuel cellhardware.

The three-point flexural strength of the bipolar plate can be used to evaluate with thehelp of an universal testing machine.

Bipolar plate flexural strength measurement set-up

The movable anvil will start applying load to the specimen at the speci?ed crosshead rate,and the simultaneous load-de?ection data can be monitored with the help of a computer.The break load and the maximum deflection should be recorded accordingly.

The flexural strength of the composite bipolar plate can be calculated using followingequation,

whereP = load at a given point on the load deflection curve in N,L = support span distance in mm,b = width of the test sample in mm,d = depth of the test sample in mm.

iii. Shore hardness

The shore hardness is another important mechanical property of the composite bipolarplate. Shore hardness of a composite bipolar plate can be measured with the help of ascleroscopic hardness tester as per the ASTM C886.

It is a dynamic indentation type hardness test in which a diamond tipped hammer isallowed to fall vertically from a fixed height over the test specimen. The height of therebound of the diamond tipped hammer was noted down and it was equal to the shorehardness of the composite bipolar plate.

3. Catalyst

The usual methods of catalyst characterization may be used like surface area, particlesize etc. However, as the catalyst is to be used in electrochemical system, theelectrochemical activity as well as electrochemical surface area is very importantproperties of the catalyst rather electrocatalyst.

The cyclic voltammetery is very important technique to find the electrocatalyst activity aswell as electrochemical surface area. A typical example of two different catalysts areshown in the next slide, where CV was used to evaluate the electrochemical activesurface area

Cyclic voltammetry of Pt/G and Pt/C electrocatalysts

Where Pt/G and Pt/C are platinum supported on graphene and carbon, respectively. Thefigure on previous slide shows the cyclic voltammetry result for Pt/G and Pt/C.

The electrochemical surface area (ESA) can be calculated by the following equation usingcharge of the hydrogen adsorption peak in the cyclic voltammetry curve after base linefitting by least square method.

The charge constant for poly-crystalline Pt surface for hydrogen adsorption is 210 µC·cm-2. The high electrochemical surface area is favorable for fuel cell catalyst oxidation andreduction reaction. The ESA for Pt/G and Pt/C can be determined as 61.58 and 54.76m2·g-1Pt, respectively. Thus, the Pt/G has more than 10% ESA than the Pt/C catalyst.From the previous figure it can be seen that the forward peak current density of Pt at thepotential of 0.146 V is 0.04 A·cm-2, which is nearly four times compared to Pt/C

(0.01A·cm-2 at 0.066 V). Therefore, the electrochemical activity of Pt/G is also superiorthan that of Pt/C.

4. Gas diffusion layer

Gas diffusion layer (GDL) is one of the vital components of the polymer electrolytemembrane fuel cell (PEMFC). The GDL is placed in between the bipolar plate and thecatalyst layer of the fuel cell. The GDL of PEMFC is generally composed of microporoussubstrate and microporous layer (MPL) of carbon black. The MPL functions as a substratefor the catalyst layer by providing reduced ohmic resistance between the catalysts layerand the microporous substrate. The MPL works as a non-permeable support to thecatalyst particles during catalyst deposition. However, it should be porous enough to passthe gases without imparting much resistance to the gas flow. The properties of the GDLcan be altered by MPL. The most important desired properties of the MPL coated GDL arehigh electrical conductivity, high corrosion resistance, and high porosity. Therefore,pressure drop, porosity

High Temperature Fuel Cell: Solid Oxide Fuel Cell

What is Solid Oxide Fuel Cell (SOFC)? SOFC Components and Properties! Configuration of SOFC!

SOFC

Ceramic Ion Conductors: Early Work

Walther Nernst (1897) “that the conductivity of pure oxides rises very slowly with temperature andremains relatively low, whereas the mixtures possess an enormously much greater conductivity”

“Nernst mass (85% ZrO2 + 15% Y2 O3 )”

W. Nernst “Electrical GlowLight” U.S. Patent 623,811. April 25, 1899

Reference: Solid State Fuel Cells: Evolution and Trends, Presentation by S. C. Singhal

Solid Oxide Fuel Cells ( SOFCs )

A solid oxide fuel cell (SOFC) is a device that converts gaseous fuels (hydrogen, natural gas,gasified coal) via an electro-chemical process directly into electricity.

Advantages of SOFC

SOFCs are over 60% efficient (conversion of fuel to electricity) making them the mostefficient fuel cell currently being developed.

The efficiency makes them a good candidate for a distributed power source (generator orpower plant).

There are no liquids that cause safety and environmental problems. The reactions in SOFC require a high temperature. The advantage is that this creates a by-

product of heat.

Cell Reactions

Anode

H2 + O2- < ---------> H2 O + 2e-

CH4 +4 O2- < ---------> 2H2 O + CO2+8e-

Cathode

1/2O2+2e- <---------> O2-

Overall Cell Reaction

H2 +1/2 O2 + <------------>H2 O

E=E0+RT/2F [ln(PH2/PH20)] +RT/2F[ln(PO21/2]

CH4+ 2 O2 2 H2O + CO2

E=E0+RT/8F [ln(PcH4/PH20 2PCO2)] +RT/2F[ln(PO22]

SOFC Electrolyte: Yttria-Stabilized Zirconia

Y2O3 -------->2YZr+3OxO+Vo

YZr denotes Y in the Zr site with the apparent negative charge, and VO is the vacancy in theoxygen site with double positive charge. OxO is the lattice oxygen, i.e., oxygen in the oxygen sitewith net charge of zero.

Yttria is used as dopant for stabilizing the cubic phase of zirconia; a fully (cubic) stabilizedzirconia is obtained with aY2O3-content of >7 mol%

Y3+ have lower valency than zirconium ion (Zr4+), induces the generation of oxygenvacancies for charge compensation.

Substitution of Zr4+ with Y3+causes negative net charge in the lattice(for every mole ofyttria incorporated into the zirconia lattice, charge neutrality condition prevailed byforming an oxygen vacancy)

For an effective operation of a fuel cell, with the electrolyte within this range of thickness,the ionic conductivity of the electrolyte material must be higher than 0.1 S cm-1.

Different Electrolyte Material

Zirconia based Ceria based Lanthanum oxide based Bismuth oxide based

Excellent Stability inoxidizing and reducingenvironment ExcellentMechanical stability(3YSZ) well stsdiedmaterial

Goodcompatibility withcathode Materials

Good compatibility with cathodeMaterials High Conductivity High Conductivity

Lower Ionic Conductivity

Electronicconduction at lowpO2 Poormechanicalstrength

Ga evaporation atlowpO2 Formation ofstablesecondry phases In compatiblewith NiO

Thermodynamic instabilityin reducing atmosphereVolatilization of Bi2O3 Highcorrosion activity Poormechanical

Different Electrolytes

Zirconia electrolytes: (8YSZ, 3YSZ, ScSZ,CaSZ etc.)

Ceria electrolytes :(GDC, SDC, YDC, CDC etc.)

Lanthanum based electrolytes :

LSGM LaXSr(1-X)GaYMg(1-Y)O3

LaALO3-based La1-xCax ALO3 ,La1-xBaxAlO3

Bismuth oxide-based: Bi2V0.9Cu0.1O5.5-δ,(Bi2O3)x(Nb2O5)1-x

Pyrochlorores - based: YZr2O7, Gd2Ti2O7

Barium brownmillerites : BaZrO3, Ba2In2O7, Ba3InxAOy (A=Ti,Zr,Ce,Hf) ,Ba3Sc2ZrO8

State-of-theart SOFC Bench mark properties for component materials

1.Cathode

Composition :LSM (La0.9Sr0.1

Porosity :40% (pore size 20-50 μm)

Condutivity :100 S/cm at 1000oC

TEC :10-12 ppm/ oC

Dimensions :ID-14mm, Wall -2mm, L-160mm

2.Electrolyte

Composition : YSZ [(ZrO2)0.92(Y2O3)0.08

Porosity :Nil, permeability should be zero

Condutivity :lonic~0.1S/cm

TEC :10.5 ppm/ oC

Dimensions :Film thickness-50 μm, L-125mm

3.Anode

Composition : Ni-YSZcermet (Ni - 60% by wt)

Porosity :40% (pore size 20 - 50 μm)

Condutivity :1000 - 1500 S/cm

TEC :10 - 12 ppm/ oC

Dimensions :OD - 18.1 mm, t~100μm, L~125 mm

4.Interconnect

Composition :LCM [La0.95Mg0.05(CrO3)]

Porosity :Nil, permeability should be zero

Condutivity :5 - 10 S/cm at 1000oC

TEC :10 - 12 ppm/ oC

Dimensions :W - 5 mm, L - 125mm , t~100μm

Requirement for the cathode

high electronic conductivity Chemically comatible with neighbouring cell component (usually the electrolyte) Should be porous Stable in an oxidizing environment

Large triple phase boundary Catalyze the dissociation of oxygen Adhesion to electrolyte surface Thermal expansion coefficient similar to other SOFC materials

Requirement for the anode

Electrically conductive High electro - catalytic activity Large triple phase boundary Stable in a reducing environment Can be made thin enough to avoid mass tranfer losses, but thick enough to provide area

and distribute current Thermal expansion coefficient similar neighbouring cell component Fine particle size Able to provide direct internal reforming (if applicable)

Requirements for the interconnect

Stable under high temperature oxidizing and reducing environment Very high electrical conductivity High density with "no open porosity" Strong and high creep resistances for planar configurations Good thermal conductivity Phase stability under temperature range Resistant to sulfur poisoning, oxidation and carburization Low materials and fabrication cost

Interconnect

Ceramic Interconnect for High temperature SOFC

(High material cost, sintering difficulties) eg: Doped Lanthanum Chormites and doped Yttriumchromites

Metallic Interconnects

(easy fabrication, high electrical and thermal conductivity)

High chrome alloys (C5rFe1Y2O3)

Ferritic stainless steel for temperature SOFC

Iron super alloys

Nickel super alloys

Critical Issues

Chromium evaporation (in Cr based interconnects)

Requirements for the sealing materials

Electrically insulating Thermal expansion compatibility with other cell components Chemically and physically stable at high temperatures Gastight Chemically compatible with other components Provide high mechanical bonding strength Low cost

Materials

Glass ceramic materials - SrO-La2O3-Al2O3-SiO2

SOFC:Designs

1. Tubular Designo Pioneered by Siemens - Westinghouse

2. Planar Designo Convectional 'electrolyte supported' concepto Cathode supported designo Newer - Anode supported concept

3. Monolithic design

Planar SOFC

Feature Value References

Power density at 800oC 1.935 W/cm2 Berkeley Lawrence Lab (2)

Stack power per volume over kW/L Allied-Signal Aerospace (3)

Stack power per mass over kW/Lkg Allied-Signal Aerospace (3)

Warm -up: to 800oC 1 minute Keele University (4)

or to operationg temperature 5 seconds Keele University (5)

Cool - down, 1000 to 800oC 31 hours Univ. of California (6)

Table 1 Recent results reported by distinguidhed SOFC laboratories

Features Projections

Operating temperature (550oC)600oC to 800oC

Start -up (ambient to operating temp.) less than 2 minutes

Stack power per volume 2 kW/L

stack power per mass 2 kW/kg

Fuel unleaded gasoline, diesel, Mwthanol

Reforming integrated internal and in situ

Cooling air. heat rejection by exhaust

Duty lifetime 5,000 hours

Table 2 Projected trends of development of SOFCs for transporatation

Planar SOFC

Preparation of Anode and Electrolyte suspension for Tape Casting

Cell Testing Unit

Experimental Setup

PGSTAT 3

Cathode LSM:YSZ

Comparison of SOFCs

Cell Type PEMFC HT - SOFC IT - SOFC LT - SOFC

Primaryapplication

Automotive andstationary power

Vehicle auxillarypower

Vehicle auxillarypower Vehicle auxillary power

Electrolyte Polymer (plasticmembrane)

Yttria stabilizedZirconium Oxide

(YSZ)

Cation dopedcerium oxide(GDC, SDC)

Two phase composite made by mixing Cationdoped cerium oxide and either salts(eg: GD C-

NaCl) or carbonates SD-M2CO3(M-Li, Na, K)

Operatingtemp 50 - 100OC 700 - 1000OC 500-700OC 300-600OC

Charge carrier H+ O2- O3 H+,OO2-

Cellcomponent Carbon based Ceramic Ceramic Salt based+ceramic Carbon based+ceramik

Catalyst Platinum Perovskites Perovskites Salt and carbon

Primary fuel H2 H2,CO H2,CO H2

Start up time second - minutes Hours Hours Minutes

Power Density(k W/m) 3.8 -6.5 0.1 - 1.5 3 - 4 3 - 8

Fuel cellefficency 50-60% 55-65% 55-65% 55-65%

Hydrogen Generation

Hydrogen is the fuel for low temperature fuel cell. However, for high temperature fuel cells hydrocarbon may be fed to fuel cell instead ofhydrogen. Hydrocarbon may be reformed in-situ in the fuel cell from the hydrocarbon.

It can be understood that the generation of hydrogen is one of the important processes for the fuel cell application. We may generatehydrogen from any hydrogen atom containing species (eg., hydrocarbon and water) using various techniques. A few of the importanttechniques are listed in the next slide.

Hydrogen production techniques

Hydrogen from hydrocarbon

Since hydrogen doesn't exist on earth in free form, we must separate it from other chemical species. We can separate hydrogen atoms from biomass, or natural gas molecules. Hydrogen can be produced from natural gas with approximately 80% efficiency, or from other hydrocarbons to a varying degree

of efficiency.

Hydrogen from water

Water is the another greatest source of hydrogen. High purity (ideally 100%) hydrogen can be produced from water.

We will briefly discuss about the reforming of hydrocarbon and electrolysis. The details of the processes may be read from some othersource.

Reforming of hydrocarbon

The aim of the reforming is to generate hydrogen rich gas by hydrocarbons. The reforming may be done with or without catalyst. Threetypes of major reforming process are,

Steam reforming (SR) Partial oxidation reforming (POR) Auto thermal reforming (ATR)

Steam reforming (SR)

Steam is used to reform the hydrocarbon (say natural gas) using a catalyst.

CH4+H2O -------------> 3H2+CO ; Δh=(+)

The above reaction is strongly endothermic. In subsequent reaction the CO can further be converted to CO2 and the process is known as water-gas-shift reaction,

The above reaction is mildly exothermic. The above process do not need air, thus the product is not diluted with nitrogen.

CO+H2O -------------> H2+CO2 ; Δh=(-)

Partial Oxidation Reforming (POR)

Partial reforming is the another technique for generation of hydrogen by hydrocarbon for fuel cell. As the name indicates, less oxygen (stochiometry) is required to carryout POR. POR does not require catalyst if it is carried out at high temperature. Catalyst is required for the partial oxidation at low temperature, the process is then known as catalytic partial oxidation reforming

(CPOR). A typical POR is shown below,

CH4+1/2O2----------------->CO+2H2 ; Δh=(-)

Autothermal Reforming (ATR)

It is another technique for hydrogen generation. The name suggests that the temperature is not required externally. However, the thermal energy requirement is met by the system itself. The idea is that if the endothermic steam reforming reaction and the exothermic POR occur together, there should not be any

need of heat addition or removal to/from the system.

Hydrogen Generation Through Electrolysis

Generation of hydrogen using electrolysis is one of the oldest technique. In fact the concept of fuel cell came during the electrolysis of water by Sir William Grove in 1839. In electrolysis, the energy (or electrical current) is required to dissociate water molecules into hydrogen and water.

The hydrogen formed in electrolysis is the purest form of hydrogen. Electrolytic cell is used for the electrolysis of water.

Electrolysis reactions in cationic electrolyte

Cathode Reaction:

4 H+ + 4e- <--------> 2H2

Anode Reaction:

2H2O <--------> O2 + 4 H+ + 4 e-

Overall Cell Reaction:

2 H2 O <----------> 2H2 + O2

Electrolyte (cationic or anionic) is placed between anode and cathode of the cell and the electrical current is given by the DCpower source.

Hydrogen is generated at cathode, whereas oxygen is generated at anode of the electrolytic cell.

Electrolytic Cell

Hydrogen Storage

Hydrogen may be a prospective source or energy carrier for the future because it is clean andsustainable. Hydrogen can be produced from a variety of feedstock. These include fossil resources,such as natural gas and coal, as well as renewable resources, such as biomass and water, whenwe use the energy input from renewable energy sources (e.g. solar, wind, hydro-power, etc.).Many process technologies like chemical, biological, electrolytic, photolytic, and thermo-chemicalmay be used for the hydrogen production. Each technology is in a different stage of development,and each offers unique opportunities, benefits and challenges.

Local availability of feedstock, the maturity of the technology, market applications and demand,policy issues, and costs may influence the choice and timing of the various options for hydrogenproduction. Several technologies are already available commercially for the industrial production ofhydrogen.

However, major problem with hydrogen is its efficient storage system. The most common methodto store hydrogen in gaseous form is in steel tanks, although lightweight composite tanks designedto endure higher pressures are also becoming popular. Gaseous hydrogen cooled to near cryogenictemperatures is another alternative that can be used to increase the volumetric energy density ofgaseous hydrogen.

In this course, we will discuss about a few of the techniques in which the hydrogen can be stored.The major techniques are shown below,

1. Composite tanks2. Cryogenic liquid hydrogen (LH2)3. Chemical hydrides4. Carbon based materials5. Metal hydrides

Composite tanks

There are several advantages with composite tanks. Their low weight meets key targets and thetanks are already commercially available, well-engineered and safety-tested, since extensiveprototyping experience exists. Standard size tanks are available worldwide with specific code forpressures in the range of 350-700 bar. Composite tanks does not require internal heat exchangerand may be used for cryogas with extra fittings. Their main disadvantages are the large physicalvolume required, the fact that the ideal cylindrical shape makes it difficult to conform storage toavailable space, their high cost (500-600 USD/kg H2), and the energy penalties associated withcompressing the gas to very high pressures. Figure in the next slide show a representative sketchof a composite tank.

There are also some safety issues that still have not been resolved, such as the problem of rapidloss of H2 in an accident. The long-term effect of hydrogen on the materials under cyclic or coldconditions is also not fully understood. Hence, there is still need for more research anddevelopment specifically:

Research on material embrittlement, using new ad hoc fracture mechanics techniques. Development of stronger and lower-cost construction materials, especially carbon fibers. Development of an efficient and clean (i.e. without oils) 1000-bar compressor. The consideration of hydride-type compressors utilizing waste heat or solar energy. Development of techniques that recover the compression energy during vehicle operation.

Cryogenic liquid hydrogen (LH2)

Cryogenic hydrogen, usually simply referred to as liquid hydrogen (LH2), has a density of 70.8kg/m3 at normal boiling point (–253°C). (Critical pressure is 13 bar and critical temperature is –240°C.) The theoretical gravimetric density of liquid H2 is 100%, but only 20 wt.% H2 can beachieved in practical hydrogen systems as of today. On a volumetric basis, the respective valuesare 80 kg/m3 and 30 kg/m3. This means that liquid hydrogen has a much better energy densitythan the pressurized gas solutions mentioned above.

However, it is important to recall that about 30-40% of the energy is lost when liquid H2 isproduced. The other main disadvantage with liquid H2 is the boil-off loss during dormancy, plus thefact that super-insulated cryogenic containers are needed. The main advantage with liquid H2 isthe high storage density that can be reached at relatively low pressures. Liquid hydrogen has beendemonstrated in commercial vehicles (particularly by BMW), and in the future it could also be co-utilized as aircraft fuel, since it provides the best weight advantage of any H2 storage.

Further research needed in this area is as follows:

Efficient liquefaction processes (hydride compressors, magnetic and acoustic cooling, etc.). Developing systems that automatically capture the boil-off (e.g. via hydrides) and re-

liquefying the fuel. Minimizing costs and improving the insulated containers.

Chemical hydride

Some of the chemicals may be used to store the hydrogen gas. For example, Sodium borohydride(NaBH4) can be used to store the hydrogen gas. In order to release the hydrogen, the sodiumborohydride solution can be catalytically hydrolyzed as per the reaction shown below,

NaBH4 (liq.) + 2H2O (liq.) ---------> 4H2 (gas) + NaBO2 (solid)

The theoretical maximum hydrogen energy storage density for this reaction is 10.9 wt.% H2. Themain advantage with using NaBH4 solutions is that it allows for safe and controllable onboardgeneration of H2. The main disadvantage is that the reaction product NaBO2 must be regeneratedback to NaBH4 off-board.

The use of NaBH4 solutions in vehicles may be prohibitively expensive. The required cost reductionis unlikely because of the unfavorable thermodynamics. However, NaBH4 solutions may be used inhigh-value portable and stationary applications.

Further research required as follows:

Approaching the ideal energy density (10.9 wt.% H2) by optimizing the H2O needed in thereaction and management of H2O in the fuel cell system.

NaBO2 removal, regeneration, and replacement methods.

Carbon based materials

Carbon-based materials have received a lot of attention in the research community over the lastdecade. Carbon based materials mainly include graphene, fullerenes, and carbon nano-tubes. H2 isstored on these carbon allotropes by molecular physisorption. However, it is useful only atcryogenic temperatures. Pure H-chemisorptions has been demonstrated to be stored upto 8wt.%H2 with catalyst, but the covalent-bound H is liberated only at impractically high temperatures(above 400°C with catalyst). Room temperature adsorption up to a few wt.% H2 is occasionallyreported, but has not been reproducible. This requires a new bonding mechanism with energiesbetween physisorption and strong covalent chemisorption.Hence, the potential for H2 storage in carbon-based materials is yet to be established practically;therefore further research may be emphasized on,

Theoretical modeling studies of H on carbon nanostructures and in bulk phase. New C-H bonding mechanism has to be explored and, if theoretically so, how to achieve it

in practice. Study on carbon-metal composites capable of catalysing H2 dissociation and so-called “spill

over”. Minimizing production costs for promising carbons (e.g. graphene, graphite nanofibers and

nanotubes). Measuring H2 uptake and release from carbon samples has to be standardized.

5. Metal hydride

The chemically bound hydrogen storage material is metal hydrides. Many metals and alloys willreversibly react with hydrogen to form a hydride. A generic reaction is given in the figure on nextslide. The regeneration of the metal can be accomplished either by increasing the temperature orby reducing the pressure. To understand this behavior it is helpful to consider the pressure–composition isotherm (PCI) for a metal hydride.

Reversible reaction of hydrogen with metal

The PCI figure in the next slide shows that as the pressure increases the hydrogen uptakeincreases. The PCI plot also shows that there is a plateau above which pressure the metal willhydride and in a closed system will continue to hydride until the pressure of the system decreasesdown to that of the plateau pressure. The stored hydrogen can be released by reducing thepressure of the system to a level below that of the plateau pressure. The plateau pressure is alsotemperature dependent, and increases with temperature. Thus a hydride stable under a certaintemperature and pressure will decompose when the temperature is increased to a level where theplateau pressure is now higher than the system pressure. The temperature needed for a 1 barplateau pressure, T(1 bar), is a useful characteristic of metal hydrides as this gives an indication ofthe minimum working temperature for a store based on that material.

Pressure-composition Isotherm

Some of the common metal hydrides are LiH, MgH2, as well as Gallium, indium, thallium ,andlanthanide hydrides .

Balance of plant and Power electronic ans system integration

Fuel Cell System

We are at the end of the fuel cell course and now can easily understand that not only the fuel cell is necessary but also the peripheralcomponents are necessary. The peripheral components are necessary in order to have the fuel cell work efficiently as well as the efficientand effective utilization of the electrical energy by the fuel cell for an application.

When we talk about the fuel cell system it includes many sub-systems. These sub-systems are,

1. Fuel cell stack Thermal management2. Fuel delivery/processing Power electronics

All the subsystem (peripherals) except the fuel cell stack known as balance of plant (BOP). They described below.

Balance of Plant (BOP)

Fuel Cell System:

For most practical fuel cell applications, unit cells must be combined in a modular fashion into a cell stack to achieve the voltage andpower output level required for the application. Generally, the stacking involves connecting multiple unit cells in series via electricallyconductive interconnects.

In addition to the stack, practical fuel cell systems require several other sub-systems and components; the so-called balance of plant(BoP). Together with the stack, the BoP forms the fuel cell system. The precise arrangement of the BoP depends heavily on the fuel celltype, the fuel choice, and the application. In addition, specific operating conditions and requirements of individual cell and stack designsdetermine the characteristics of the BoP. Still, most fuel cell systems contain

Fuel Preparation:

Except when pure fuels (such as pure hydrogen) are used, some fuel preparation is required, usually involving the removal of impuritiesand thermal conditioning. In addition, many fuel cells that use fuels other than pure hydrogen require some fuel processing, such asreforming, in which the fuel is reacted with some oxidant (usually steam or air) to form a hydrogen-rich anode feed mixtur

Air Supply: In most practical fuel cell systems, this includes air compressors or blowers as well as air filters.

Thermal management: All fuel cell systems require careful management of the fuel cell stack temperature.

Water management: Water is needed in some parts of the fuel cell, while overall water is a reaction product. To avoid having to feedwater in addition to fuel, and to ensure smooth operation, water management systems are required in most fuel cell systems.

Electric power conditioning equipment: Since fuel cell stacks provide a variable DC voltage output that is typically not directly usablefor the load, electric power conditioning is typically required.

Some More Facts on BOP

A single fuel cell is capable of producing very low voltage (say 1 V). Therefore, a typical fuel cell design needs many individual cells toform a stack to produce significant or useful voltage. A fuel cell stack can be configured with many group of cells in series and parallelconnections to further tailor the voltage, current, and power as per the requirement for a particular applicatio

In a typical fuel cell configuration, the number of individual cells contained within the stack is more than 50 and varies mainly with thedesign of the stack. The combination of many stack may provide the useful power for a particular application.

One can understand that as the number of cells in a stack increases the complexity also increases. The stack performance depends onthe performance of individual cells within the stack.

The extra components or peripherals (or BOP) contribute significantly to the performance, and economy of the fuel cell power system.The BOP is generally depends on the type of fuel cell as well as the fuel used. Like in case of high temperature fuel cells the thermal

management is of great concern. The waste heat can be used in combined heat and power (CHP) cycle.

We have already discussed about the humidification as well as role of heating and cooling of the feed .

If we have a fuel cell stack then what are the peripherals required to obtain a useful power for an application. We will learn aboutdifferent BOP components in brief and discuss in detail about a few of the important BOP components.

As we know that the fuel and oxidant is required to be fed through the fuel cell stack. To accomplish this we need to have pumps orblowers or compressors along with the electrical motors. The fuel can be obtained from various sources and thus may need to be cleanedfor any unwanted impurities. For example, hydrogen obtained from the steam reforming of methanol contains many impurities such asCO2 and CO. If the H2 contaminated with CO is passes to the PEMFC stack then it will poison the catalyst very fast. Therefore, cleaning ofthe fuel is important depending upon the fuel cell type and catalyst used. Similarly, air should be filtered properly if it is used as anoxidant

Moreover, before feeding the fuel, there should be proper storage of the fuel is required. It becomes more important if the fuel cellsystem is designed for a mobile application. We have already discussed earlier about the hydrogen storage.

If fuel storage is not required then the system must have the fuel processing unit, which should be capable of generating the fuel for theapplication.

The various kind of control valves will be required to control the fuel and oxidant to the fuel cell stack. Sophisticated control valves, andcontrol unit is required especially for the dynamic application. The time lag of the valves are of utmost importance. The complicationbecomes more and more as deal with the high temperature fuel cell system where start-up and shut-down is very important.

Moreover, seals and gaskets are also required to prevent leakage of fluids and to maintain the pressure in the system. Gaskets aregenerally used between two static surfaces to prevent to provide a seal and the sealing is an important issues for all the fuel cellsespecially high temperature fuel cells (SOFC and MCFC) as well as for fuel processing component

Therefore, high temperature seals are very important and the development n this area is going on considering the performance of theseal towards, temperature, load swings, cycles, rapid transient temperature and pressure, and thermal gradients.

The research and development work on corrosion resistance, hermitic, solid-state, and glass seals are advancing in a great pace.

Once the stack is ready along with the proper pipelines and flow system. The fuel processor in combination with the fuel cleaning systemwill provide the feed to the fuel cell stack. The stack will generate the output, which will be direct current (DC) output, which may rarelybe suitable for direct connection to an electrical appliance. Therefore, we have to modify or regulate the fuel cell output to the desiredelectrical power. This modification is known as “power conditioning”.

Depending upon the requirement we may need:

DC/DC convertor or voltage regulator DC/AC inverter

Power Conditioning

In BOP, we will mostly focus about the power conditioning. We will first discuss about the power regulation then power inversion ion brief.

Power Regulation

In our day-to-day life we have seen that we require electrical power at a specified voltage level that is stable over time also. However,the electrical power provided by a fuel cell is neither stable nor have desired voltage output. Because a single cell may provide hardly0.7V at operating conditions . Therefore, for a desired voltage output we have to make a fuel cell stake with series connection of thecells. Even then we may not get the desired voltage for the application. For a practical size (number of cells) of the fuel cell stack

We have already discussed that a fuel cell can provide high electrical current. Therefore, if we some how convert the electrical currentinto voltage, we may achieve the higher voltage or desired voltage. Thus the concept of energy conservation may be used for convertingsome of the electrical current into electrical voltage.

Moreover, the fuel cell voltage is highly dependant on the temperature, pressure, humidification, and flow rate, of the reactant feed tothe fuel cell as well as the dynamics of the load.

In order to increase as well as to keep the the cell voltage stable at the expense of current, DC/DC convertors are used

A DC/DC convertor use the fluctuating DC fuel cell voltage as input and converts it to a stable DC voltage output which is fixed at aspecified voltage as shown in the figure.

Based on the input voltage to the DC/DC the voltage may be stepped to the convertors specified value, of course within a certain limit.

In step-up convertor the, the fuel cell voltage is stepped up to a higher fixed output voltage, whereas in step-down convertor, the fuelcell voltage is stepped down to a lower fixed output voltage.

In any of the case the power of the fuel cell must be conserved. It can be understood from the following diagram (for step-up convertor),

Figure A in the previous slide shows that the voltage is stepped up by a factor of 2, whereas in the process the current was reduced by afactor of 2, in order to keep the power conserved. It is done by a DC/DC convertor which as the 100% efficiency to do this job.

Figure B in the same slide shows that the voltage was stepped up by a factor of two but the current was reduced by more than a factor of

2. Therefore, the power was reduced slightly. This power is consumed by the DC/DC convertor to do the job as the efficiency of theconvertor may not be 100%. So depending upon the efficiency of the DC/DC convertor the power reduces. In general, the efficiency of acarefully designed DC/DC falls in between 80-95%.

DC/AC Inverters

Most of the residential appliances and utilities require single phase AC power rather than DC power. For the utilities of the industrialapplication we may need three phase AC power. Therefore, DC output of the fuel cell should be converted to the AC power before utilizingit.

We are aware that the inverter technologies are well developed and are being utilized greatly. For example, in household battery backuppower supply the inverters are used. Their efficiencies are quite good and a careful design of the inverter may be upto 95% efficient .

The details of inverters may be found in any standard text book on power electronics.

Power Supply Management System

The power supply management system is the heart of the BOP. It is used to control and manage the electrical power of the fuel cellsystem as per the requirement of the load.

A typical example is a vehicle run by fuel cell power. It can be easily understood that the power requirement of the vehicle is dynamic innature. Once we move the vehicle from stationary condition or when vehicle on moving uphill the requirement of the power increased.Whereas at a constant speed the requirement may be very low as compared to the previous condition.

The question arises that how to get and control the requirement of the dynamic power from the fuel cell. The source of power are thereactants to the fuel cell. During high demand, the requirement of the current density increases (in turn power density). Thus to achievethe high current density the reactant supply has to be increased. The power management system senses the requirement and accordinglysend the reactants to the fuel cell system.

Not only the reactants but the power management system also controls the temperature, humidity, fuel reforming system etc. to the fuelcell. It is infact the mind of the system and very essential part of the fuel cell system..

Commercialization Aspects

1 kW Stationary System

Honda FCX Clarity Specification (for U.S.)

Car

Length mm 4,835

width mm 1,845

Height mm 1,470

Weight kg 1,625

Max Speed km/h 160

Cruising Range km 620

Stack

Type ----- PEFC

Max Power kW 100

Volume L 62

weight kg 67

MotorMax Power kW 100

Max Torque N-m 256

Fuel Tank

Type ------ H2 gas

Pressure atm 350

Outer Volume L 171

Inner etimated L 18