Fuel Cell Mass Transport

Basic Operation

H2+1/2O2 = H2OH2 = 2H+ + 2e-

1/2O2 + 2H+ + 2e- = H2Ohttp://www.odec.ca/projects/2007/truo7j2/fuel_cell_small.JPG

Concentration Lossor Mass Transport Loss

• Reactant/product concentrations � fuel cell performance

• Reactant/product concentrations within the catalyst layer, not the fuel cell inlet, matter

• Reactant depletion/product accumulation adversely affects performance

• Can be minimized by optimization of mass transport and flow structures

• Transport in flow structure– mm ~ cm scale– convection

• Transport in fuel cell electrode structure– nm ~ µm scale– diffusion

Diffusion Layer

• H2 concentration falls from the bulk value Co

H2into at the flow

channel to a much lower value C*

H2at the catalyst layer

http://pubs.acs.org/cen/img/83/i05/8305bus2fuel.gifhttp://www.directindustry.com/prod/tech-etch/fuel-cell-plate-30189-212422.html

H2H+

flow channelanode electrolyte

diffusion layerH

2co

ncen

trat

ion

CoH2

C*H2

Convection vs. Diffusion

• Convection driven by the pressure we apply to introduce fuel or oxidant to the fuel cell

• Diffusion driven by the concentration difference which is developed by consumption of reactant species at the catalyst layer

Convection vs. Diffusion• Boundary between the convective and diffusive flow is

around where the gas channel and porous electrode meet

• Gas channel � gas stream well mixed � no concentration gradients – the velocity of the moving gas stream tends toward zero at

the electrode-channel boundary

• Thickness of diffusion layer is not well defined and dependent on flow conditions, flow channel geometry or electrode structures– Extremely high gas velocity � convective mixing may

penetrate into the electrode– Very low gas velocity � diffusion layer may stretch out into

the middle of the flow channel

Diffusive Transport

• Transport in electrode is based on diffusion

• Assumption– Electrode thickness = diffusion layer

thickness

• Electrochemical reaction drives the diffusion

Mass Transport• Electrochemical reaction

leads to reactant depletion (and product accumulation) at the catalyst layer

• C*R < Co

R and C*P > Co

P– C*

R and C*P : reactant and

product concentration at the catalyst layer

– CoR and Co

P : bulk reactant and product concentration (flow channel)

• Concentration loss (or mass transport loss)– Nernstian Losses– Reaction Losses

Concentration Loss(or mass transport loss)

• Nernstian Losses: reversible fuel cell voltage will decrease

• Reaction Losses: reaction rate (activation) losses will increase

Reactant concentration & Current density

• j: current density (a measure of the electrochemical reaction rate)

• Jdiff: diffusion flux of reactants to the catalyst layer

• nF: conversion factor from molar diffusion flux into the current density

• Deff: effective reactant diffusivity (Deff = ετD) (pore structure)

• δ: electrode (diffusion layer) thickness

• C*R: catalyst layer reactant

concentration• C0

R: bulk reactant concentrationeffRR

RReff

RReff

diff

diff

diff

nFD

jCC

ccnFDj

ccDJ

dx

dcDJ

nFJj

δ

δ

δ

−=

−−=

−−=

−=

=

0*

0*

0*

Reactant concentration in the catalyst layer is less than the bulk concentration� Low current density ( j) � low concentration loss� Thin diffusion layer (δ) � low concentration loss� High effective diffusivity (Deff) � low concentration loss

Flux

• Positive J means matter (or energy) flows towards positive z

• Matter flows from high to low concentration

ATKINS’ Physical Chemistry 8th Ed.

Limiting Current Density• When the reactant concentration in the catalyst layer is zero �

limit maximum current density

• Mass transport design strategies– High C0

R (by designing good flow structures that evenly distribute reactants)

– Deff is large and δ is small (by carefully optimizing fuel cell operating conditions, electrode structure, and diffusion layer thickness)

• Typically– δ = 100 ~ 300 µm– Deff = 10-2 cm2/s– jL = 1 ~ 10 A/cm2

• Fuel cell will never be able to produce a higher current density than that determined by its limiting current density

δ

δ

Reff

L

effRR

CnFDj

nFD

jCC

0

0* 0

=

=−=

Nernstian Loss

– ηconc: voltage loss due to reactant depletion in the catalyst layer– E0

Nernst: Nernst voltage using c0 values– E*

Nernst: Nernst voltage using c* values– C0

R: bulk reactant concentration– C*

R: catalyst layer reactant concentration

– (product accumulation is neglected)

R

R

RR

NernstNernstconc

R

P

C

C

nF

RT

CnF

RTE

CnF

RTE

EE

C

C

nF

RTEE

*

0

*

0

0

0

*0

0

ln

)1

ln()1

ln(

ln

=

−−−=

−=

−=

η

Nernstian Loss

• This expression is valid only for j < jL

• For j << jL– concentration loss

will be minor

• For j � jL– concentration loss

will increase sharply

jj

j

nF

RT

C

C

nF

RT

jj

j

nFDjnFDj

nFDj

C

C

nFD

j

nFD

j

nFD

jCC

nFD

jC

CnFDj

L

Lconc

R

Rconc

L

L

effeff

L

eff

L

R

R

effeff

L

effRR

eff

LR

Reff

L

−=

=

−=

−=

−=

−=

=

=

ln

ln

//

/

*

0

*

0

0*

0

0

η

η

δδ

δ

δδ

δ

δ

δ

Reaction Loss

• J00 is measured at the reference reactant and product concentration values C0*R

and C0*P

• J00 is exchange current density at “standard concentration”• C*

R and C*P are arbitrary concentrations

)eC

C- e

C

C( j = j

e j - e j = j

/RT)nF-(1-

*0

P

*

P /RTnF

*0

R

*

R0

0

/RT)nF--(1

0

/RTnF

0

actact

actact

ηαηα

ηαηα

*0

0

*0

ln

)

R

Ract

/RT nF

*0

R

*

R0

0

Cj

jC

nF

RT

eC

C( j =j act

αη

ηα

=

Butler-Volmer equation

• High current density region, the 2nd term in the Butler-Volmer equation drops out

Reaction Loss

• η0act activation loss using c0

• η*act activation loss using c*

jj

j

jj

j

C

C

C

C

Cj

jC

Cj

jC

L

Lonc

L

L

R

R

R

R

R

R

R

R

actactonc

−=

−=

=

−=

−=

lnnF

RT

lnnF

RT

)lnnF

RT()ln

nF

RT(

c

*

*0

*

0

00

0

*0

*0

0

*0

0*

c

αη

α

αα

ηηη

Concentration Loss

• Total concentration loss = Nernstian Loss + Reaction Loss

jj

jc

jj

j

nF

RT

jj

j

nF

RT

jj

j

nF

RT

L

Lconc

L

L

L

L

L

Lconc

−=

−+=

−+

−=

ln

ln)1

1)((

lnln

η

α

αη

Summary

ηact = (aA + bB lnj) + (aA + bB lnj): activation losses from both the anode (A) and the cathode (C)

ηohmic = j ASR

ηconc = c ln[ jL/( jL – j)]

6 7 8

9

Application of a small signal voltage perturbation confines the impedance measurement to

a pseudolinear portion of a fuel cell’s i-V curve

Nyquist plot (Fuel Cell)

• Example Nyquist plot from a hypothetical fuel cell

• Relative size of the three regions ~ relative magnitude of the three losses

Merging

In many fuel cells, cathode impedance is significantly larger than the

anode impedance

� RC loops for the cathode overwhelms the RC loop for the anode

Equivalent Circuit

EIS at Different Points

(a) low current density: activation kinetics dominate and R is large

(b) intermediate current, activation loops decrease since R decreases with increasing ηact

(c) high current density, activation loops may continue to decrease, but the mass transport effects begin to

intercede.