Understanding the Morphology and Mass Transport Resistance of Mesoporous Carbon-Supported PEMFC Based on Modeling Analysis

Abstract

Mesoporous carbon supports mitigate Pt sulfonic poisoning through nanopore-confined Pt deposition, yet their morphological impacts on oxygen transport remain unclear. This study integrates carbon support morphology simulation with an enhanced agglomerate model to establish a mathematical framework elucidating pore evolution, Pt utilization, and oxygen transport in catalyst layers. Results demonstrate dominant local mass transport resistance governed by three factors: (1) active site density dictating oxygen flux; (2) ionomer film thickness defining shortest transport path; (3) ionomer-to-Pt surface area ratio modulating practical pathway length. At low ionomer-to-carbon (I/C) ratios, limited active sites elevate resistance (Factor 1 dominant). Higher I/C ratios improve the ionomer coverage but eventually thicken ionomer films, degrading transport (Factors 2-3 dominant). The results indicate that larger carbon particles result in a net increase in local transport resistance by reducing external surface area and increasing ionomer thickness. As the proportion of Pt situated in nanopores or the Pt mass fraction increases, elevated Pt density inside the nanopores exacerbates pore blockage. This leads to the increased transport resistance by reducing active sites and increasing ionomer thickness and surface area. Lower Pt loading linearly intensifies oxygen flux resistance. The model underscores the necessity to optimize support morphology, Pt distribution, and ionomer content to prevent pore blockage while balancing catalytic activity and transport efficiency. These insights provide a systematic approach for designing high-performance mesoporous carbon catalysts.

Keywords

mesoporous carbon support / electrochemical active surface area / Pt coverage / oxygen transport resistance / pore volume distribution

List of symbols

A_{\text{CCL}}: Active area (m²)

A_{\text{ion,in}}^{\text{total}}: Total geometric area of ionomer inside nanopores (m²)

A_{\text{ion,out}}^{\text{total}}: Total geometric area of ionomer on the support surface (m²)

A_{\text{Pt,in}}: Total area of Pt particles inside nanopores (m²)

A_{\text{Pt,out}}: Total area of Pt particles on the support surface (m²)

A_{\text{Pt,in,covered}}: Total area of Pt covered by ionomer inside nanopores (m²)

A_{\text{Pt,out,covered}}: Total area of Pt covered by ionomer on the support surface (m²)

A_{\text{C,in}}^{\text{'}}: Specific surface area of carbon inside nanopores per unit mass of carbon ( {\text{m}}^2\cdot {\text{ g}}_{\text{C}}^{-1})

A_{\text{C,out}}^{\text{'}}: Specific surface area of carbon on the support surface per unit mass of carbon ( {\text{m}}^2\cdot {\text{ g}}_{\text{C}}^{-1})

C_{{\text{O}}_2\text{,g}}: Oxygen concentration in the gas phase (mol·m^-3)

C_{{\text{O}}_2\text{,Pt}}: Oxygen concentration on the Pt surface (mol·m^-3)

D_{{\text{O}}_2\text{,ion}}: Oxygen diffusivity in ionomer (m²·s^-1)

d_{\text{C}}: Diameter of Carbon support particle (m)

d_{\text{CCL}}: CCL thickness (m)

d_{\text{p}}: Nanopore diameter (m)

d_{\text{p,depth}}: Nanopore depth (m)

d_{\text{p,sec}}: Diameter of secondary pore (m)

d_{\text{p,threshold}}: Threshold pore diameter of ionomer immersed into pores (m)

d_{\text{Pt}}: Pt diameter (m)

d_{\text{Pt,in}}: Pt diameter inside nanopores (m)

d_{\text{Pt,out}}: Pt diameter on the support surface (m)

I: Output current density (A·m^-2)

k_1: Interfacial resistance coefficient

k_2: Interfacial resistance coefficient

l_{\text{p,blocked}}: Length from pore entrance (m)

L_{\text{Pt}}: Pt loading (kg·m^-2)

m_{\text{C}}^{\text{total}}: Total carbon mass of CCL (kg)

m_{\text{ion}}^{\text{total}}: Total ionomer mass of CCL (kg)

M_{{\text{N}}_2}: Molar mass of nitrogen (g·mol^-1)

M_{{\text{O}}_2}: Molar mass of oxygen (g·mol^-1)

m_{\text{Pt}}^{\text{total}}: Total Pt mass of CCL (kg)

N_{\text{C}}: Total number of carbon support particles

N_{{\text{O}}_2}^{\text{'}}: Oxygen flux around a catalyst particle (mol·m^-2·s^-1)

n_{\text{in}}: Total number of Pt diameter class inside nanopores

n_{\text{out}}: Total number of Pt diameter class on the support surface

n_{\text{p}}: Total number of pore size class

n_{\text{Pt,in}}: Number distribution of Pt inside nanopores

n_{\text{Pt,in,p}}: Number distribution of Pt inside nanopores of a certain pore size

n_{\text{Pt,out}}: Number distribution of Pt on the support surface

n_{\text{p,C}}^{\text{'}}: Pore number distribution of carbon normalized to CCL ( {\text{g}}_{\text{C}}^{-1})

n_{\text{p,Pt/C}}^{\text{'}}: Pore number distribution of carbon after Pt loading ( {\text{g}}_{\text{C}}^{-1})

P: Total gas pressure (atm)

P_{\text{Pt,in}}: Probability distribution of Pt inside nanopores

P_{\text{Pt,out}}: Probability distribution of Pt on the support surface

R_{\text{bulk},\text{sec}}: Bulk diffusion resistance in secondary pores (S·m^-1)

R_{\text{diff},\text{ion}}: Diffusion resistance in ionomer normalized to CCL (S·m^-1)

R_{\text{diss},\text{ion}}: Dissolution resistance normalized to CCL (S·m^-1)

R_{\text{Kn,sec}}: Knudsen diffusion resistance in secondary pores (S·m^-1)

R_{\text{local}}^{\text{total}}: Total local transport resistance (S·m^-1)

R_{\text{pri}}: Knudsen diffusion resistance in primary pores (S·m^-1)

R_{\text{Pt}}: Transport resistance on the Pt surface normalized to CCL (S·m^-1)

R_{\text{sec}}: Total diffusion resistance in secondary pores (S·m^-1)

R_{\text{diff},\text{ion}}^{\text{'}}: Diffusion resistance in ionomer for a catalyst particle (S·m^-1)

R_{\text{diss},\text{ion}}^{\text{'}}: Dissolution resistance for a catalyst particle (S·m^-1)

R_{\text{Pt}}^{\text{'}}: Transport resistance on the Pt surface for a catalyst particle (S·m^-1)

T: Temperature (K)

V_{\text{apparent,C}}^{\text{total}}: Total apparent volume occupied by the carbon support particles (m³)

V_{\text{CCL}}^{\text{total}}: Total volume of CCL

V_{\text{ion}}^{\text{total}}: Total ionomer volume of CCL (m³)

V_{\text{ion,in}}^{\text{total}}: Total ionomer volume of CCL inside nanopores (m³)

V_{\text{ion,out}}^{\text{total}}: Total ionomer volume of CCL on the support surface (m³)

v_{{\text{N}}_2}: Diffusion volume of nitrogen (cm³·mol^-1)

v_{{\text{O}}_2}: Diffusion volume of oxygen (cm³·mol^-1)

V_{\text{p,C}}^{\text{total}}: Total volume of nanopores (m³)

v_{\text{p}}^{\text{'}}: Pore volume distribution of carbon without normalization ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

v_{\text{pri}}^{\text{'}}: Total volume of nanopores ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

v_{\text{sec}}^{\text{'}}: Total volume of secondary pores ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

v_{\text{p,C}}^{\text{'}}: Pore volume distribution of carbon normalized to CCL ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

v_{\text{p,Pt/C}}^{\text{'}}: Pore volume distribution of carbon after Pt loading ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

v_{\text{p,ion}}^{\text{'}}: Pore volume distribution of catalyst after ionomer loading ( {\text{m}}^3\cdot {\text{ g}}_{\text{C}}^{-1})

Greek

{\delta }_{\text{ion,in}}: Thickness of ionomer film inside nanopores (m)

{\delta }_{\text{ion,out}}: Thickness of ionomer film on the support surface (m)

{\delta }_{\text{ion,out}}^{\min }: Minimum thickness of ionomer film on the support surface (m)

{\epsilon }_{\text{C,pack}}: Packing density of carbon support particles

{\epsilon }_{\text{p,C}}: Nanopore porosity inside the carbon support

{\epsilon }_{\text{pri}}: Primary porosity normalized to CCL

{\epsilon }_{\text{sec}}: Secondary porosity normalized to CCL

{\theta }_{\text{Pt,in}}: Ionomer coverage of Pt inside nanopores

{\theta }_{\text{Pt,out}}: Ionomer coverage of Pt on the support surface

{\rho }_{\text{C}}: Carbon density (kg·m^-3)

{\rho }_{\text{ion}}: Ionomer density (kg·m^-3)

{\rho }_{\text{Pt}}: Platinum density (kg·m^-3)

{\phi }_{\text{I/C}}: Mass ratio of ionomer to carbon

{\phi }_{\text{Pt,Pt/C}}: Mass ratio of Pt in catalyst

{\phi }_{\text{Pt,in}}: Distribution ratio of Pt inside nanopores

{\phi }_{\text{Pt,in}}^{\text{covered}}: Ratio of covered Pt inside nanopores to the total covered Pt particles

{\chi }_{\text{p,Pt/C,blocked}}: Fraction of blocked pores by Pt particles

Superscripts and subscripts

apparent: Apparent

blocked: Blocked pores

bulk: Bulk diffusion

C: Carbon, carbon support particle

CCL: Cathode catalyst layer

covered: Covered by the ionomer

depth: Depth

diff: Diffusion

diss: Dissolution

g: Gas phase

in: Inside nanopores

ion: Ionomer

I/C: Ionomer to carbon

Kn: Knudsen diffusion

local: Local

min: Minimum

N₂: Nitrogen

O₂: Oxygen

out: On the support surface

p: Pore

pack: Packing

pri: Primary pore

Pt: Platinum

Pt/C: Catalyst

Sec: Secondary pore

Threshold: Threshold value

Total: Total

Acknowledgements

This research was financially supported by the Program of Ministry of Science and Technology of China (No. 2023YFB2504200). The authors are also grateful to the support of Shanghai Rising-Star Program (Grant No. 24QB2703200) and the Major Science and Technology Projects of Yunnan Province (No. 202302AH360001).

Conflicts of interest

There are no conflicts of interest to declare.

Data Availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

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