Molecular Analysis of the Relationship between Water Clusters and Proton Diffusion Properties inside a Polymer Electrolyte Membrane in PEFC under Subzero Conditions

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A1110
Molecula Analysis o he Rela ionship be ween Wa e
Clus e s and P o on Di usion P ope ies inside a
Polyme Elec oly e Memb ane in PEFC unde Subze o
Condi ions
Hi oki Nishizawa* (1,2), Takuya Mabuchi (1), Takashi Tokumasu (1)
(1) Ins i u e o Fluid Science, Tohoku Uni e si y, Sendai/Miyagi/Japan;
(2) G adua e School o Enginee ing, Tohoku Uni e si y, Sendai/Miyagi/Japan;
*Con ac co esponding au ho s: www.EFCF.com/Con ac Reques
Abs ac
Polyme Elec oly e Fuel Cells (PEFCs) play a c ucial ole in achie ing ca bon neu ali y and
he Sus ainable De elopmen Goals (SDGs). PEFCs ace se e al challenges, including
di usion pola iza ion, ma e ial anspo e iciency, and du abili y. Ou esea ch ocuses
pa icula ly on he ope a ion o PEFCs unde he ha sh condi ions o subze o empe a u es.
Many egions wo ldwide expe ience cold clima es, making he esolu ion o hese issues
i al o he u he popula iza ion o PEFCs. In such en i onmen s, he anspo e iciency
o ma e ials wi hin he polyme elec oly e memb ane (PEM), including p o ons c ucial o
uel cell ope a ion, dec eases due o he po en ial eezing o wa e molecules and a
signi ican educ ion in kine ic ene gy. Ne e heless, p e ious esea ch[1] elucida ed ha
p o on hopping con ibu es p o on di usion in ice. The e o e, his phenomenon is c i ical o
he con ex o his esea ch.
In his s udy, we conduc ed a de ailed analysis o he ela ionship be ween changes in wa e
clus e s and p o on di usion p ope ies wi hin PEM. We pe o med ReaxFF[2] MD
simula ions, which can ea p o on hopping. The pa ame e se , which comp ehensi ely
de ines he empi ical coe icien s, was modi ied om he one de eloped by D. Fan auzzi e
al.[3] This modi ica ion includes adjus ing he ioniza ion deg ee o heo e ical alue and
p e en ing he abno mal bond which occu ed in Na ion chains.
Based on he anspo analysis, bo h wa e and hyd onium ions educed di usion
coe icien s unde subze o condi ions, wi h he dec ease in wa e , which is mo e p onounced
a highe wa e con en s. In con as , he di usion coe icien o hyd onium ions dec eased
less signi ican ly. To in es iga e his disc epancy, p o on anspo by p o on hopping was
analyzed, e ealing ha p o on hopping inc eased unde subze o condi ions. This inc ease
likely mi iga ed he educ ion in hyd onium ion di usi i y compa ed o wa e . S uc u al
analysis u he indica ed ha he hyd ogen-bonding ne wo k among wa e molecules
becomes mo e enhanced unde subze o condi ions, leading o he o ma ion o la ge wa e
clus e s a ound sul onic acid g oups. This s uc u al change is p esumed o ha e acili a ed
addi ional p o on hopping pa hways, he eby enhancing p o on anspo .
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In oduc ion
Fuel cells a e being inc easingly deployed as pa o ini ia i es aimed a achie ing ca bon
neu ali y and he sus ainable de elopmen goals (SDGs). Among a ious ypes, polyme
elec oly e uel cells (PEFCs) ha e a ac ed signi ican a en ion owing o hei capabili y o
oom empe a u e s a -up and hei po en ial o minia u iza ion and ligh weigh design.
These cha ac e is ics ha e acili a ed hei applica ion in esiden ial s a iona y powe
sys ems and uel cell ehicles. PEFCs ace pe sis en challenges, including he
enhancemen o mass anspo e iciency[4], [5], [6], educ ion o p ecious me al loading[7],
[8], and s able ope a ion unde ha sh en i onmen al condi ions[9], [10], [11].
This s udy ocuses on he ope a ion o PEFCs unde subze o condi ions. Unde such
en i onmen s, se e al c i ical issues eme ge: anspo impedimen s due o wa e eezing
wi hin he ca alys laye (CL)[9], ma ked de e io a ion o mass anspo wi hin he polyme
elec oly e memb ane (PEM), and mechanical delamina ion be ween he PEM and CL[9]
a ising om olume ic expansion o ozen wa e du ing shu down phases[9]. Fu he mo e,
e en unde condi ions o ully hyd a ed s a e, pa ial eezing o wa e wi hin he PEM has
been epo ed[11]. Con e sely, p o on di usion media ed by he G o huss mechanism[12],
[13] may be enhanced. These phenomena ha e p ima ily been in es iga ed h ough
expe imen al app oaches, while he speci ic mechanisms and nanoscale s uc u al changes
in ol ed emain la gely unexplo ed. Based on hese conside a ions, his s udy speci ically
a ge s he in es iga ion o mass anspo p ope ies and he in e nal s a e o he PEM unde
subze o condi ions.
P o on anspo in he PEM is gene ally go e ned by wo p incipal mechanisms: Vehicle
mechanism and G o huss mechanism[12], [13]. In Vehicle mechanism, hyd onium ions
di use by physical mig a ion. In con as , he G o huss mechanism in ol es he
eo ganiza ion o hyd ogen bonds and co alen bonds be ween wa e molecules and
hyd onium ions, acili a ing p o on hopping. Unde subze o condi ions, a p onounced
dec ease in kine ic ene gy is expec ed o signi ican ly hinde p o on anspo ia Vehicle
mechanism. Meanwhile, U i ski e al.[14] epo ed ha p o on di usion in ice inc ease by
G o huss mechanism. Thus, conside ing he con ibu ion o G o huss mechanism is
necessa y when analyzing p o on anspo beha io unde subze o condi ions. Wa e
clus e s, agg ega es o wa e molecules o med a ound he hyd ophilic unc ional g oups o
he PEM, play an essen ial ole in acili a ing G o huss mechanism. Because hyd onium
ions end o localize wi hin hese clus e s[15], [16], la ge clus e s p o ide mo e ex ensi e
hyd ogen-bond ne wo ks, he eby p omo ing p o on hopping. Acco dingly, bo h he
p esence and size o wa e clus e s a e c i ical ac o s in luencing p o on anspo wi hin he
PEM.
The inal objec i e o his esea ch is o p o ide undamen al insigh s ha may guide he
de elopmen o PEM ma e ials wi h imp o ed esis ance o pe o mance deg ada ion unde
subze o condi ions, h ough a de ailed in es iga ion o p o on anspo p ope ies and
in e nal s uc u al s a es. In pa icula , his s udy ocuses on elucida ing he ela ionship
be ween he cha ac e is ics o wa e clus e s wi hin he PEM and p o on di usion beha io ,
which a e deemed c i ical ac o s go e ning PEM pe o mance.
P o on anspo p ope ies wi hin PEM and in e nal s uc u e o PEM ha e been ex ensi ely
in es iga ed no only by expe imen al me hodologies bu also ia nume ical simula ions.
P e ious s udies ha e employed classical molecula dynamics (MD) simula ions[4], [17],
[18], densi y unc ional heo y (DFT) calcula ions[19], [20], and ab ini io calcula ions[21]. As
p e iously no ed, conside a ion o G o huss mechanism is indispensable o an accu a e
unde s anding o p o on anspo unde subze o condi ions. While DFT and ab ini io MD
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simula ions can cap u e G o huss mechanism, hei applica ion is cons ained by he limi ed
abili y o add ess dynamics p ocesses o e ex ended ime scales. Acco dingly, in his s udy,
nume ical simula ions u ilizing eac i e o ce ield molecula dynamics (ReaxFF MD)[2] we e
conduc ed, a me hod capable o simul aneously accoun ing o bo h chemical eac ions and
dynamics beha io .
1. Me hods
1.1 Simula ion de ails
ReaxFF MD simula ions we e pe o med o e alua e he ela ionship be ween wa e clus e s
and p o on di usi i y in PEM unde subze o condi ions. The pa ame e se used in ReaxFF
MD de ines a comp ehensi e collec ion o empi ical coe icien s ha go e n in e a omic
in e ac ions. The pa ame e se is de ined o speci ic molecules and a oms, so cons uc ing
an app op ia e one is c ucial o pe o ming accu a e simula ions. In his s udy, a pa ame e
se o iginally de eloped by D. Fan auzzi e al.[3] was employed, wi h modi ica ions o
add ess issues ela ed o ioniza ion deg ee and he o ma ion o anomalous bonds wi hin
he PEM.
Na ion wi h EW=1100, a ma e ial widely used in p e ious s udies o polyme memb anes,
was selec ed as he ma e ial o PEM. All simula ions we e pe o med wi h la ge-scale
a omic/molecula massi ely pa allel simula o (LAMMPS)[22]. The sys em con igu a ion
included 10 Na ion chains, 100 hyd onium ions, and 200, 600 o 900 wa e molecules,
co esponding o wa e con en s o 3, 7, 10, espec i ely. A ime s ep o 0.25 s and a
sampling in e al o 250 s we e adop ed, wi h h ee-dimensional pe iodic bounda y
condi ions.
Fo he annealing p ocess, classical MD simula ions we e i s conduc ed using he
DREIDING o ce ield[23]. As in p io s udies, s uc u al elaxa ion was achie ed h ough
epea ed applica ion o NVT and NPT ensembles[23]. Following his, he o ce ield was
ansi ioned om DREIDING o ce ield o ReaxFF, accompanied by addi ional sho
elaxa ion s eps using NVT and NPT ensembles. Sampling calcula ions we e conduc ed o
10 ns, and he esul ing da a we e used o analysis. Six simula ion condi ions we e
in es iga ed in o al, combining wo empe a u es (300 K and 200 K) wi h h ee wa e
con en s (3,7 and 10).
1.2 Analysis de ails
The sel -di usion coe icien is a widely used me ic in nume ical simula ions ha
quan i a i ely e alua es he ease wi h which molecules di use. In his s udy, sel -di usion
coe icien s we e calcula ed om he slope o he linea egion o he mean squa e
displacemen (MSD) cu e. Equa ion (1) was used o he calcula ion, whe e 𝐷 is he
di usion coe icien , 𝑡 is he sampling ime, and 𝑅𝑖(𝑡) deno es he posi ion ec o o each
a om a ime 𝑡. In his equa ion, he ime a e age is calcula ed by a ying he ini ial ime 𝑡0,
which helps elimina e sample dependence a ising om he ini ial condi ions.
𝐷= lim
𝑡→∞ 1
6𝑡〈|𝑅(𝑡+𝑡0)−𝑅(𝑡0)|2〉 (1)
The adial dis ibu ion unc ion (RDF) is a me hod ha allows he e alua ion o he local
s uc u e o med by molecules in he sys em. In his s udy, RDF was compu ed using
equa ion (2), which desc ibes he p obabili y o inding a pa icle B a a dis ance 𝑟 om
pa icle A. He e, 𝑛𝐵 is he numbe o pa icles B wi hin a sphe ical shell o hickness Δ𝑟 a
dis ance 𝑟 om pa icle A, 𝑁𝐵 is he o al numbe o pa icles B in he sys em, and 𝑉 deno es
he olume o he simula ion cell.
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𝑔𝐴−𝐵(𝑟)=(𝑛𝐵
4𝜋𝑟2Δ𝑟)
(𝑁𝐵
𝑉) (2)
The coo dina ion numbe is also analyzed by equa ion (3). In his analysis, he coo dina ion
numbe was calcula ed by in eg a ing he RDF esul s. 𝑐(𝑟) deno es he coo dina ion
numbe .
𝑐(𝑟)=∫ 𝑔𝐴−𝐵(𝑟)𝑑𝑟
𝑟
0(3)
To analyze di usion ia G o huss mechanism, bo h he numbe o p o on hopping e en s
and a ling[24] beha io we e examined. The numbe o hopping e en s was coun ed using
he scheme illus a ed in Fig. 1(a), enabling a consis en coun ega dless o sampling
du a ion. Ra ling, as shown in Fig. 1(b), e e s o epea ed p o on hopping be ween he
same hyd onium ions and wa e molecule, a p ocess ha does no con ibu e o p o on
di usion. The e o e, he p opo ion o non- a ling e en s was calcula ed o assess he
e ec i e con ibu ion o p o on hopping o di usion. The non- a ling a e was e alua ed
using equa ion (4).
𝑅𝑛𝑜𝑛−𝑟𝑎𝑡𝑡𝑙𝑖𝑛𝑔 =1− 𝑁𝑟𝑎𝑡𝑡𝑙𝑖𝑛𝑔
𝑁𝑡𝑜𝑡𝑎𝑙 ℎ𝑜𝑝𝑝𝑖𝑛𝑔 (4)
Fo he analysis o wa e clus e s, he ocus was placed on bo h he numbe and size o
clus e s. In his s udy, wa e molecules o ming hyd ogen bonds we e de ined as belonging
o he same clus e . Since hyd ogen-bonded wa e molecules end o ga he wi hin a speci ic
ange, he end poin o he i s peak in he RDF be ween wa e molecules was adop ed as
he cu o dis ance o iden i ying wa e clus e s. The analysis o clus e size included bo h
he maximum and a e age clus e sizes. Gi en ha a single wa e clus e can occasionally
con ain a disp opo iona ely la ge numbe o wa e molecules compa ed o o he clus e s,
including he la ges clus e in he a e age is s a is ically inapp op ia e. Acco dingly, he
a e age size was calcula ed by excluding he la ges clus e om he analysis.
Fig. 1. (a) Analysis o he numbe o p o on hopping e en s. In he uppe diag am, he
numbe o p o on hopping e en s is coun ed as one; in he lowe diag am, i is coun ed
as wo. (b) Schema ic illus a ion o a ling beha iou .
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2. Resul s and discussion
2.1 Di usion p ope ies
Di usion coe icien s o wa e molecules and hyd onium ions we e e alua ed. Fig. 2
p esen s he calcula ed di usion coe icien s o wa e and hyd onium ions. The quali a i e
end o wa e and hyd onium ion di usion coe icien s wi h espec o wa e con en is
consis en wi h p e ious s udies[23], [25]. These esul s e eal ha bo h species exhibi a
signi ican dec ease in di usion coe icien s a 200 K. While he quan i a i e alues o
hyd onium ion di usion coe icien s a y depending on he wa e con en , hei quali a i e
end emains consis en ac oss condi ions. In con as , he empe a u e-dependen ends
o wa e di usion coe icien s showed bo h quan i a i e and quali a i e di e ences wi h wa e
con en . No ably, unde he wa e con en o 10, he di usion coe icien dec eased much
mo e signi ican ly han unde o he condi ions.
To in es iga e hese di e ences in di usion beha io , p o on hopping cha ac e is ics we e
analyzed. Table. 1 summa izes he numbe o p o on hopping e en s pe picosecond and
he co esponding non- a ling a e. The analysis indica es ha a 200 K, he equency o
p o on hopping inc eases, wi h a highe inc ease obse ed a g ea e wa e con en s.
Fu he mo e, he non- a ling a e was also ound o be highe a 200 K.
These indings sugges ha p o on anspo ia G o huss mechanism becomes mo e
p ominen a 200 K, especially a highe wa e con en s. Consequen ly, al hough wa e
molecule di usi i y sha ply dec eases as wa e con en s, he hyd onium ion di usi i y
emains ela i ely less a ec ed due o he enhanced con ibu ion o p o on hopping.
2.2 S uc u e analysis
To analyze he s uc u al p ope ies, he RDF be ween wa e molecules and sul onic g oups
was analyzed o each condi ion, as shown in Fig. 3. The posi ion o he i s peak o RDF is
consis en wi h p e ious s udies[26], [27], indica ing ha he cha ac e is ic in e ac ion
dis ance be ween wa e molecules and sul onic g oups is accu a ely cap u ed. The RDF
esul s indica e ha he coo dina ion numbe inc eases a 200 K, sugges ing ha wa e
molecules end o clus e mo e densely a ound sul onic g oups unde subze o condi ions.
To u he in es iga e hese s uc u al changes, he RDF be ween wa e molecules was also
analyzed. As shown in Fig. 4, he peak in ensi y o RDF is consis en ly highe a 200 K
ac oss all wa e con en s. The i s peak o RDF is consis en wi h p e ious s udies[28]. The
i s peak in wa e -wa e RDF co esponds o hyd ogen-bonded wa e molecules[29],
indica ing ha a s onge hyd ogen-bonding ne wo k o ms a 200 K.
(a) (b)
Fig. 2. (a) Di usion coe icien s o wa e molecules. (b) Di usion coe icien s o
hyd onium ions. Bo h igu es show empe a u e-dependen ends.

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Table. 1. The numbe o p o on hopping and non- a ling a e.
𝑁hopping [/ps]
𝑅Non− a ling [%]
𝜆=3,300 K
0.213
1.42
𝜆=3,200 K
0.212
1.65
𝜆=7,300 K
0.306
3.87
𝜆=7,200 K
0.410
6.18
𝜆=10,300 K
0.355
5.11
𝜆=10,200 K
0.429
6.09
Addi ional analysis was conduc ed on he size o wa e clus e s, as p esen ed in Fig. 5. The
esul s show a gene al end o dec eased a e age clus e size a 200 K o all wa e
con en s. Mo eo e , he o al numbe o clus e s ends o dec ease a 200 K. The obse ed
ela ionship be ween he a e age clus e size and he numbe o wa e clus e s is consis en
wi h p e ious s udies[15]. The hyd ogen-bonding ne wo k becomes mo e obus a 200 K.
This enhanced ne wo k likely p omo es he o ma ion o la ge wa e clus e s while educing
hei o e all numbe .
These indings collec i ely indica e ha , he hyd ogen-bonding ne wo k among wa e
molecules wi hin he PEM becomes mo e igid, leading o he o ma ion o la ge wa e
clus e s a ound sul onic acid g oups.
The esul s o he a o emen ioned analyses indica e ha , unde subze o condi ions, he
hyd ogen-bonding ne wo k o med by wa e molecules becomes mo e s ongly de eloped,
leading o he o ma ion o la ge wa e clus e s su ounding sul onic acid g oups. This
s uc u al endency is inc easingly p onounced wi h highe wa e con en s. Such s uc u al
(a) (b)
(c)
Fig. 3. The esul s o RDF be ween sul onic acid g oups and wa e molecules. The solid
lines show he esul s o RDF and he dashed lines show he esul s o coo dina ion
numbe . The coo dina ion numbe co esponds o he igh axis. (a), (b) and (c) show he
esul s o wa e con en s o 3, 7 and 10, espec i ely.
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changes a e p esumed o enhance he a ailabili y o p o on hopping pa hways o hyd onium
ions, he eby inc easing bo h he numbe o hopping e en s and he non- a ling a e. As a
esul , p o on anspo ia G o huss mechanism is acili a ed, which is likely esponsible o
he obse ed di e gence in anspo cha ac e is ics be ween wa e molecules and
hyd onium ions.
3. Conclusion
This s udy ocused on elucida ing he anspo p ope ies and in e nal s uc u e o PEM
unde subze o condi ions h ough molecula -le el analysis using ReaxFF MD simula ions.
S uc u al analyses e ealed ha , compa ed o oom empe a u e, he hyd ogen-bonding
ne wo k o med by wa e molecules wi hin he PEM becomes mo e enhanced unde subze o
condi ions. Consequen ly, la ge wa e clus e s end o o m a ound sul onic acid g oups.
This s uc u al change is conside ed o enhance he a ailabili y o p o on anspo pa hways,
he eby inc easing anspo ia G o huss mechanism. As a esul , he di usion beha io o
wa e molecules and hyd onium ions di e ges unde hese condi ions.
(a) (b)
(c)
Fig. 4. The esul s o RDF be ween wa e molecules. (a), (b) and (c) show he esul s o
wa e con en s o 3, 7 and 10, espec i ely.
(a) (b)
Fig. 5. The esul s o wa e clus e p ope ies. (a) and (b) show he esul s o he a e age
size o wa e clus e and he numbe o wa e clus e s, espec i ely.
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Keywo ds: EFCF2025, H2, LowTemp. Fuel Cells & Elec olyse s, (subze o empe a u e,
du abili y)
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