Ci a ion: Baˇca, P.; Vanýsek, P.; Lange ,
M.; Zimáko á, J.; Chladil, L. Hea
E ec s du ing he Ope a ion o
Lead-Acid Ba e ies. Ba e ies 2024,10,
148. h ps://doi.o g/10.3390/
ba e ies10050148
Academic Edi o s: Ad ian Calbo ean
and Ca los Ziebe
Recei ed: 24 Janua y 2024
Re ised: 23 Ap il 2024
Accep ed: 26 Ap il 2024
Published: 27 Ap il 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
ba e ies
A icle
Hea E ec s du ing he Ope a ion o Lead-Acid Ba e ies
Pe Baˇca * , Pe Vanýsek , Ma in Lange , Jana Zimáko áand Ladisla Chladil
Depa men o Elec o echnology, Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o
Technology, Technická10, 616 00 B no, Czech Republic; [email p o ec ed] (P.V.); [email p o ec ed] (M.L.);
[email p o ec ed] (J.Z.); [email p o ec ed] (L.C.)
*Co espondence: [email p o ec ed]
Abs ac : The mal e en s in lead-acid ba e ies du ing hei ope a ion play an impo an ole; hey
a ec no only he eac ion a e o ongoing elec ochemical eac ions, bu also he a e o discha ge
and sel -discha ge, leng h o se ice li e and, in c i ical cases, can e en cause a a al ailu e o he
ba e y, known as “ he mal unaway.” This con ibu ion discusses he pa ame e s a ec ing he
he mal s a e o he lead-acid ba e y. I was ound by calcula ions and measu emen s ha he e is a
cooling componen in he lead-acid ba e y sys em which is caused by he endo he mic discha ge
eac ions and elec olysis o wa e du ing cha ging, ela ed o en opy change con ibu ion. Thus,
unde ce ain ci cums ances, i is possible o lowe he empe a u e o he lead-acid ba e y du ing
i s discha ging. The Joule hea gene a ed on he in e nal esis ance o he cell due o cu en low,
he exo he mic cha ging eac ion, and abo e all, he g adual inc ease in pola iza ion as he cell
ol age inc eases du ing cha ging all con ibu e o he hea ing o he cell, o e aking he cooling
e ec . O hese h ee sou ces o he mal ene gy, Joule hea ing in pola iza ion esis ance con ibu es
he mos o he empe a u e ise in he lead-acid ba e y. Thus, he maximum ol age eached
de e mines he slope o he empe a u e ise in he lead-acid ba e y cell, and by a sui ably chosen
limi ing ol age, i is possible o limi he dange o he “ he mal unaway” e ec . The o e all
he mal condi ions o he expe imen al cell a e signi ican ly a ec ed by he ambien empe a u e
o he ex e nal en i onmen and he a e o hea ans e h ough he walls o he calo ime e . A
se ies o expe imen s wi h di ec empe a u e measu emen o indi idual loca ions wi hin a lead-acid
ba e y uses a calo ime e made o expanded polys y ene o minimize ex e nal in luences. A hi he o
unpublished phenomenon is discussed whe eby he empe a u e o he posi i e elec ode was lowe
han ha o he nega i e elec ode h oughou he discha ge, while du ing cha ging, he o de was
e e sed and he empe a u e o he posi i e elec ode was highe han ha o he nega i e elec ode
h oughou he cha ge. The au ho s ela e his phenomenon o he highe eac ion en opy change o
he ac i e mass o he posi i e elec ode han ha o he nega i e elec ode.
Keywo ds: lead-acid accumula o ; hea e ec ; he mal beha io ; endo he mic eac ions; exo he mic
eac ions; Joule hea ; cooling e ec
1. In oduc ion
The aim o his s udy is o look a a less app ecia ed ac ha du ing lead-acid ba -
e y discha ge, an en opy-based phenomenon leads o a cooling e ec , which may no
be in ui i ely appa en as i is o en nega ed by Joule hea ing due o la ge cu en low.
Unde s anding he he mal balance o a lead-acid ba e y is impo an o con inuous use ul
applica ion o his ime-p o en elec ochemical echnology. Ene gy s o age esea ch is
p esen ly a highly ega ded and also highly compe i i e en i onmen , a ying in di e en
applica ion solu ions om au omobile SLI (s a ing, ligh s, igni ion) o small powe appli-
ca ions o daily use o la ge powe applica ions ensu ing ene gy s abili y and powe g id
quali y [
1
–
6
]. Lead-acid ba e ies (LAB) s ill play an impo an pa on he ba e y ma ke ,
and a e inancially he bes comp omise in powe , longe i y and abili y o be ecycled in
he ci cula i y managemen [
7
–
12
]. In 2019, LAB domina ed he ma ke sha e, accoun ing
Ba e ies 2024,10, 148. h ps://doi.o g/10.3390/ba e ies10050148 h ps://www.mdpi.com/jou nal/ba e ies
Ba e ies 2024,10, 148 2 o 18
o an es ima ed 32.29% o he o al ba e y ma ke wi h a u he o ecas g ow h o 5.2%
by 2030. The abo e ad an ages will con inue o lead o he applica ion o LAB in majo
au omo i e sec o s and in low-cos o -g id ene gy s o age sys ems [13,14].
In he LAB pe o mance issues, i is impo an o unde s and in de ail he he mal
p ocesses ha play a majo ole in he li e ime and o he impo an pa ame e s o LAB.
When c i ical alues a e exceeded, an e ec called he he mal unaway (TRA) can occu ,
which ul ima ely leads o he des uc ion o he LAB. The mal unaway in LAB is ela ed
o bo h exo- and endo he mal elec ochemical eac ions du ing cha ging and discha ging
and o he low o elec ic cu en h ough he in e nal s uc u es o he LAB wi h a non-
ze o elec ical esis ance. I is also impo an o pay a en ion o he hea capaci y o he
indi idual pa s o he LAB and he hea exchange o he LAB wi h he en i onmen .
A lead-acid elec ochemical cell wi h a gi en hea capaci y can be di ided in o h ee
basic pa s— he aqueous sul u ic acid solu ion wi h he highes he mal capaci y and low
he mal conduc i i y, he plas ic ba e y pack wi h bo h low he mal capaci y and low
he mal conduc i i y, and he elec odes, whe e he ac ual elec ochemical eac ions ake
place a he ac i e mass/elec oly e in e ace. The elec odes made o lead and i s oxides
and sul a es a e ela i ely hea y and ha e good he mal conduc i i y. Thei hea capaci y
is e y low and, he e o e, pa icula ly in AGM ba e ies wi h a lowe amoun o sul u ic
acid solu ion ela i e o hese elec odes, hea ing o c i ical empe a u e can occu much
mo e apidly wi hin a sho ime.
Hea issues, in pa icula , he empe a u e inc ease in a lead-acid ba e y du ing
i s cha ging has been undoub edly a conce n e e since his echnology became used in
p ac ice, in pa icula in he au omobile indus y. Howe e , i came o g ea e o e on
when many ba e ies we e g ouped in a s ack oge he o he pu pose o ene gy s o age and
sole p opulsion in elec omobili y [
15
]. A la ge olume o closely packed ba e ies has led o
mo e di icul hea ans e o he su ounding en i onmen and o e hea ing and he mal
unaway [
16
,
17
], causing se e e issues in longe i y, eliabili y and sa e y [
18
]. In e es ingly,
hea issues in lead-acid ba e ies became a subjec o ma hema ical simula ions, pe haps
because o he complica ed physical access o empe a u e p obes in o la ge s acks and he
hos ile chemical en i onmen [19,20].
In 1995, Newman and Tiedemann [
21
] p esen ed wha is now a classical app oach,
a s udy showing he empe a u e inc ease inside a ba e y wi h cons an hea gene a ion.
Cai and Whi e [
22
,
23
] published an e icien elec ochemical- he mal model o ba e y
simula ion. The model was speci ically o a li hium-ion ba e y, al hough i can gene ally
be used o o he ba e y sys ems as well. Howe e , in lead-acid ba e y he e is one speci ic
ha needs ca e ul ea men , which is he sul u ic acid elec oly e, which exis s in he
ba e y in a iable quan i ies and di ec ly en e s he s oichiome y o he elec ochemical
eac ion. This has been pe o med ho oughly ia ma hema ical modeling [
24
–
26
], which
also included compa isons wi h o he s udies. B oda and Inzel in es iga ed in e nal
esis ance inc ease and empe a u e change o bo h he nega i e and he posi i e elec ode
in a lead-acid ba e y [
27
]. Kˇ i ík dedica ed his e o o he mal e en s in lead s o age
ba e ies [
28
–
31
]. Fo he calcula ions, he used he modynamic alues o a 100% sul u ic
acid. Wi h hose alues, he discha ge eac ion came ou e oneously as exo he mic. La e
in his pape , we demons a e ha he mo e ealis ic concen a ion o 30%mass will lead
o an endo he mic alue. The wo k also lacked he alida ion o heo e ically de e mined
da a by p ac ical expe imen s.
The aim o his con ibu ion, whe e lies i s no el y, is a deepe insigh in o he complex
le el o he mal p ocesses o lead-acid ba e ies wi h he de ini ion o he le el o indi idual
in luences a ec ing he esul ing empe a u e o he LAB elec odes. He e, we poin ou
some e o s o o he au ho s [
28
–
32
], especially in ela ion o he heo e ical calcula ions o
he he modynamic alues assuming 100% sul u ic acid. I u ns ou ha hose alues o
a ealis ic acid concen a ion (30%mass) yield di e en alues ha signi ican ly a ec he
o e all he mal pe o mance o he lead-acid ba e y sys em. In con as o he indings
in [
28
–
31
], we con i m he accu acy o he heo e ical calcula ions by good ag eemen wi h
Ba e ies 2024,10, 148 3 o 18
ac ual measu emen s on a eal LAB. As a i s s ep, based on he p esen ed heo e ical
calcula ions and p ac ical measu emen s, we w i e ha by adjus ing he cha ge/discha ge
mode, he magni ude o he he mal p ocesses aking place in he LAB can be in luenced
o a ce ain ex en , and hus he empe a u e o he LAB can be in luenced o minimize
he TRA haza d. The goal o his wo k is o p opose egime measu es ha can a ec he
in e nal empe a u e o he LAB du ing ope a ion.
2. Ma e ials and Me hods
2.1. Theo e ical Founda ion
A good place o s a when conside ing elec ici y and hea in a echa geable ba e y is
wi h he modynamics. To be ue, laws o classical he modynamics apply o he s a e o
equilib ium, hus hey can be used only as guidance du ing cha ging and discha ging o a
ba e y, which is no an equilib ium p ocess. I is use ul o use he modynamic pa ame e s
called he s a e unc ions which do no depend on he eac ion pa h. They depend only
on he di e ence in he alues o he p oduc s and o he eac an s, he inal and ini ial
componen s in he p ocess. In ou conside a ion, he s a e unc ions a e he eac ion
en halpy,
∆
H, which desc ibes he amoun o ene gy eleased du ing he p ocess; he Gibbs
ee ene gy,
∆
G, which desc ibes he maximum amoun o chemical ene gy ha can be
con e ed in o use ul wo k (in ba e ies, in o elec ical ene gy), o wo k, ha can be used
o gene a e chemical compounds; and he en opy o he eac ion,
∆
S, which desc ibes
e e sible gain o loss o ene gy associa ed wi h ongoing chemical (o elec ochemical)
eac ion. The s a e unc ions om he p ac ical poin o iew desc ibe he uppe limi s
o pe o mance. As he eac ions p oceed (in he case o a ba e y as he cu en lows),
kine ic pa ame e s educe hese uppe limi s [
32
]. The o he pa ame e , which will in e es
us in his delibe a ion, is hea , Q, associa ed wi h elec ochemical p ocesses. Hea is no a
s a e unc ion, hus hea eleased o gene a ed will depend on he manne wi h which he
ba e y is cha ged o discha ged.
The basic ela ionship be ween he h ee men ioned s a e unc ions is
∆G=∆H−T∆S(1)
whe e Tis he empe a u e in kel ins. This is a use ul ela ionship in elec ochemis y, as i
ela es o he cell po en ial U0
∆G=−nFU0(2)
whe e nis he numbe o exchanged elec ons in he uni y eac ion and Fis he Fa aday
cons an , a cha ge o one mole o elec ons.
Se e al basic he mal p ocesses occu ha a ec he esul ing ba e y empe a u e
du ing ope a ion. These p ocesses include hea exchange wi h he en i onmen ,
QZ
, Joule
hea gene a ion a he in e nal esis ance o he cells,
QJ
, and he change in hea om he
he mochemical eac ions a he elec odes hemsel es, QR.
Q=QZ+QJ+QR(3)
The exchange o he mal ene gy be ween he lead-acid ba e y and he su ounding
en i onmen QZis desc ibed by New on’s law o cooling:
QZ=kZ(Tai −Tba ) (4)
whe e k
z
is a hea ans e coe icien , a cons an cha ac e izing a pa icula ba e y (is a
unc ion o hea ans e esis ance o he whole sys em) and T
ai −
T
ba
is he di e ence in
empe a u es be ween he ba e y and he en i onmen and is he ime du ing which he
hea exchange be ween he ba e y and he su oundings akes place.
The Joule hea , o he he mal ene gy gene a ed a he indi idual in e nal esis ances,
QJ, is gi en by:
QJ=RI2 (5)
Ba e ies 2024,10, 148 4 o 18
whe e Ris he in e nal esis ance o he lead-acid ba e y, Iis he magni ude o he cu en
and is he discha ge ime. Because o he g adual inc ease in in e nal esis ance du ing
discha ge, his hea will be mos p onounced owa ds he end o he discha ge.
In he la e case, i is he he mochemical hea gene a ed (o consumed) by he
elec ochemical eac ion a he elec odes du ing discha ge, i.e., he con e sion o lead and
lead oxide o lead(II) sul a e. The discha ge eac ion is desc ibed as:
Pb +PbO2+2 H2SO4→2 PbSO4+2 H2O (6)
The eac ion en opy o ba e y discha ge
∆
S
dis
can be calcula ed as he di e ence o he
sum o en opies o all he p oduc s, minus he sum o en opies o all eac an s [
33
,
34
] wi h
he en opy alues ob ained om [
34
]. In u he calcula ions, we will use o Equa ion (6)
∆
S
dis
=
−
10.4 J
·
mol
−1·
K
−1
. The p oduc wi h absolu e empe a u e T
∆
Sco esponds o
ene gy bound in o he sys em and e lec s he change o he s uc u e o he a omic bonds
o he compounds [
35
]. The co esponding en opic ol age o po en ial o he eac ion a
oom empe a u e [36] is calcula ed om he eac ion en opy:
UR=T∆Sdis
nF =−0.016 V (7)
whe e Tis he empe a u e, n= 2 is he numbe o exchanged elec ons and F= 96,485 C
·
mol
−1
is he Fa aday cons an . The ela ionship (8) comes di ec ly om he e e enced wo k [
28
] a
ela ionship which was sou ced om a seldom quo ed wo k by Be nd [
37
,
38
]. The idea is
ha he U
R
is de ined as a new a iable, he en opic po en ial, i.e., po en ial con ibu ion
due o en opy, hus independen o en halpy changes. The he mochemical hea is hen
calcula ed om he en opic po en ial o he eac ion [28]:
QR=−T∆Sdis
nF I =−URI (8)
The alue o he he mochemical hea is posi i e, so hea is eleased du ing he
elec ochemical eac ion. In o he wo ds, i he en opy di e ence
∆
Sis nega i e, he
ba e y will hea up du ing discha ge [29].
The abo e alue om Equa ion (7) is, howe e , calcula ed o 100% sul u ic acid. I
we conside o he calcula ions he ac ual concen a ion o sul u ic acid used in lead-acid
ba e ies, he esul ing alues will di e . Sul u ic acid in lead-acid ba e ies is usually
a 30% aqueous solu ion in he ully cha ged s a e, so i s en opy will be di e en . The
en opy alue o his dilu ed sul u ic acid is 128.1 J
·
K
−1·
mol
−1
[
34
] and i will signi ican ly
a ec he conclusions abou cell hea balance [
39
]. The esul ing
∆
S
dis
o he discha ge in
app op ia ely concen a ed sul u ic acid is
∆
S
dis
= 47.2 J
·
mol
−1·
K
−1
, and he co esponding
en opic po en ial o he eac ion he e o e will be UR= 0.0726 V.
Ul ima ely, he alue o he he mochemical hea (see Equa ion (8)) will be nega-
i e, i.e., he hea is consumed by he elec ochemical eac ion. Thus, du ing discha ge,
he gene a ed Joule hea hea s up he ba e y, while he elec ochemical con e sion o
lead-based ac i e ma e ials wi h sul u ic acid o lead sul a e and wa e is accompanied
by an endo he mic eac ion ha canno be neglec ed in e ms o he mal managemen
o he ba e y.
Du ing cha ging, in addi ion o he abo e-men ioned discha ge eac ions (now wo k-
ing in he opposi e di ec ion), o he pa allel eac ions occu acco ding o he eached
cha ging ol age. When he second cha ging s age ( his is he second ol age cha ging
pla eau a e o e coming he in lec ion poin o app oxima ely 2.45 V) is eached, elec oly-
sis begins o occu o a signi ican ex en and he decomposi ion o wa e in o hyd ogen
and oxygen akes place. In he case o VRLA ba e y designs, an in e nal oxygen cycle
begins o occu , wi h oxygen ecombining back o wa e a he nega i e elec ode o o m
wa e and gene a e hea . When cha ging, he alue o he pola iza ion esis ance u he
inc eases and he e o e addi ional pola iza ion losses by Joule hea occu [29].
Ba e ies 2024,10, 148 5 o 18
A he beginning o cha ging, Joule hea ing losses again occu due o he in e nal
esis ances o he ba e y and he elec ochemical cha ging eac ions gene a e hea o he
same magni ude as he hea o discha ge, bu o he opposi e sign. The ba e y will be
hea ed by bo h o hese sou ces du ing cha ging.
In he case o cha ging, he hea consumed o elec olysis (wa e decomposi ion)
mus also be aken in o accoun , which is pa icula ly applicable a e a ‘gassing’ ol age
o app oxima ely 2.4 V (o when app oxima ely 70% o he su ende ed cha ge om he
p e ious discha ge has been ecei ed) has been eached pe cell. The chemical eac ion
desc ibing his p ocess is:
H2O→1
2O2+H2(9)
∆Sdec =163.4 J·mol−1·K−1(10)
QRP =−T∆Sdec
nF I (11)
This hea alue will be ecei ed by he sys em o accompany he elec olysis o he
wa e ( he ba e y will be cooled).
When cha ging wi h inc easing ol age, he pola iza ion esis ance inc eases. I we
conside a b eakdown ol age o 2.4 V pe cell, we calcula e he pola iza ion esis ance as:
Rpol =U−UEMF −U0
I=2.4 −2.035 −0.25
I(12)
whe e U
EMF
[
40
] is he elec omo i e o ce o he cell and U
0
is he en opic po en ial o
decomposi ion o wa e [29].
As he cell ol age inc eases, he pola iza ion esis ance will inc ease, and hus he
o al pola iza ion he mal ene gy will also inc ease. Fo pola iza ion esis ance, a cell
po en ial o 2.40 V, he he mal ene gy eleased QJpol will be in he o m o Joule hea :
QJpol =Rpol I2 =0.115 I· (13)
Fo ba e ies whe e he oxygen cycle is no enabled ( looded ypes), we ob ain he o al
hea o cha ge wi hou conside ing he losses o he en i onmen :
Q=QJ+QR+QRP +QJpol (14)
Fo ba e ies wi h an in e nal oxygen cycle (VRLA, GEL ba e ies), we mus also
conside he hea gene a ed by he ecombina ion o oxygen on he nega i e elec ode back
o wa e and he Joule hea , which is also gene a ed by he enabled oxygen cycle [
41
]. The
hea gene a ed in he ecombina ion o oxygen ( he in e nal oxygen cycle) can be ound
om he basic equa ion o he eac ion:
Pb +H2SO4+1
2O2→PbSO4+H2O (15)
The change in s anda d mola en opy o eac ion (15) is
∆Soc =−77.05 J·mol−1·K−1(16)
Wi h co esponding en opic hea gene a ed du ing he oxygen cycle (OC):
QROC =−T∆Soc
nF I (17)
The measu ed sys em consis ing o he elec ochemical cell wi hin he insula ing
box can be iewed as hea -accumula ing elemen s. I we assume o simplici y ha he
empe a u es o he elec oly e, bo h elec odes and he cell con aine a e he same, hen

Ba e ies 2024,10, 148 6 o 18
om he known masses and hea capaci ies o he ac i e masses, elec oly e and cell
packaging, we can calcula e he o al alue o he mal ene gy abso bed by he cell:
Qcell =Qelec oly e +QABS +QPb =melec oly e·celec oly e +mABS·cABS +mPb·cPb·∆T(18)
whe e Q
elec oly e
is he o al hea ecei ed by he elec oly e o he ba e y, Q
ABS
is he hea
s o ed by he used cell pack and space s, Q
Pb
is he hea ecei ed by he elec odes, and
∆
T
is he empe a u e change wi hin he s udied ime span.
The o he hea -accumula ing elemen s a e he ai in he insula ing box space and he
polys y ene oam box i sel . Simila o he i s case, assuming equal ai empe a u es inside
he insula ing box and he walls o he insula ing box, we calcula e accumula ed hea o he
insula ing box as:
Qcal =Qai +Qbox =(mai ·cai +mbox·cbox)·∆T(19)
whe e Q
ai
is he o al hea ecei ed by he ai in he insula ing box, Q
box
is he hea s o ed
by he walls o he insula ing box, and
∆
Tis he empe a u e change wi hin he s udied
ime span.
2.2. Equipmen and Ma e ials Used
The cell o he lead-acid ba e y was cons uc ed om wo comme cially a ailable
elec odes o he 60
·
130
·
1 mm dimensions and placed in an ABS cell con aine (Figu e 1).
The elec odes we e sepa a ed by an AGM sepa a o Recoma F2140XP, manu ac u ed by
Be na d Dumas. ABS space s we e used o ensu e comp ession o he cell. The capaci y o
he cell was 6.7 Ah. The P 100 empe a u e mic osenso s wi h special ea men agains
e ec o sul u ic acid we e placed on he su ace o bo h he posi i e and nega i e elec odes
a 1/3 o he elec ode heigh . The inished cell was placed in o a comme cially a ailable
he mally insula ed box made o expanded polys y ene wi h dimensions o 280
·
230
·
280
mm, wi h a wall hickness o 35 mm, was used as a calo ime e (Figu e 1). Addi ional
empe a u e senso s we e placed in he same posi ion as he empe a u e senso s o he
posi i e and nega i e elec ode on he inside and ou side o he he mally isola ing box.
The po en ial di e ence measu emen was made agains he me cu y-me cu ous sul a e
e e ence elec ode MRSE (615 mV s. NHE).
Ba e ies 2024, 10, x FOR PEER REVIEW 6 o 18
pe a u es o he elec oly e, bo h elec odes and he cell con aine a e he same, hen om
he known masses and hea capaci ies o he ac i e masses, elec oly e and cell packaging,
we can calcula e he o al alue o he mal ene gy abso bed by he cell:
𝑄 =𝑄
 +𝑄
 +𝑄
 =𝑚
 ∙𝑐
 +𝑚
 ∙𝑐
 +𝑚
 ∙𝑐
∙∆𝑇 (18)
whe e Qelec oly e is he o al hea ecei ed by he elec oly e o he ba e y, QABS is he hea
s o ed by he used cell pack and space s, QPb is he hea ecei ed by he elec odes, and
ΔT is he empe a u e change wi hin he s udied ime span.
The o he hea -accumula ing elemen s a e he ai in he insula ing box space and he
polys y ene oam box i sel . Simila o he i s case, assuming equal ai empe a u es in-
side he insula ing box and he walls o he insula ing box, we calcula e accumula ed hea
o he insula ing box as:
𝑄 =𝑄
 +𝑄
 =󰇛𝑚 ∙𝑐
 +𝑚
 ∙𝑐
󰇜∙∆𝑇 (19)
whe e Qai is he o al hea ecei ed by he ai in he insula ing box, Qbox is he hea s o ed
by he walls o he insula ing box, and ΔT is he empe a u e change wi hin he s udied
ime span.
2.2. Equipmen and Ma e ials Used
The cell o he lead-acid ba e y was cons uc ed om wo comme cially a ailable
elec odes o he 60·130·1 mm dimensions and placed in an ABS cell con aine (Figu e 1).
The elec odes we e sepa a ed by an AGM sepa a o Recoma F2140XP, manu ac u ed by
Be na d Dumas. ABS space s we e used o ensu e comp ession o he cell. The capaci y o
he cell was 6.7 Ah. The P 100 empe a u e mic osenso s wi h special ea men agains
effec o sul u ic acid we e placed on he su ace o bo h he posi i e and nega i e elec-
odes a 1/3 o he elec ode heigh . The inished cell was placed in o a comme cially
a ailable he mally insula ed box made o expanded polys y ene wi h dimensions o
280·230·280 mm, wi h a wall hickness o 35 mm, was used as a calo ime e (Figu e 1).
Addi ional empe a u e senso s we e placed in he same posi ion as he empe a u e
senso s o he posi i e and nega i e elec ode on he inside and ou side o he he mally
isola ing box. The po en ial diffe ence measu emen was made agains he me cu-
y-me cu ous sul a e e e ence elec ode MRSE (615 mV s. NHE).
Figu e 1. Concep ual diag am o he expe imen design.
The measu ing wo ks a ion consis ed o an Agilen 34980A mul i unc ion swi ch,
Agilen N6700B powe supplies (all Agilen ins umen s ob ained om Agilen , San a
Cla a, Cali o nia, USA) and a con ol PC. I allowed moni o ing ol age and cu en , po-
Figu e 1. Concep ual diag am o he expe imen design.
The measu ing wo ks a ion consis ed o an Agilen 34980A mul i unc ion swi ch,
Agilen N6700B powe supplies (all Agilen ins umen s ob ained om Agilen , San a
Cla a, CA, USA) and a con ol PC. I allowed moni o ing ol age and cu en , po en ials o
Ba e ies 2024,10, 148 7 o 18
bo h elec odes, and empe a u e o he senso embedded in he cell a he se modes o
ope a ion. The esolu ion o he da a acquisi ion sys em is 6.5 digi s (22 bi s). The loca ion
and minia u iza ion o he empe a u e senso allows he no mal unc ion o he lead cell
wi hou a ec ing i s esponse.
Measu emen o he in e nal esis ance o he in si u cell was ca ied ou wi h a labo a-
o y ins umen o domes ic p o enance, which supe imposes he sinusoidal componen o
he cu en a a equency o 1 kHz on he DC discha ge/cha ge cu en and he in e nal
esis ance is calcula ed om he a io o he AC ol age esponse o he cu en . The
magni ude o he AC pe u bing ol age is se o 10 mV. Measu ing o he AC componen s
o ol age and cu en was ca ied ou simul aneously wi h collec ing o he pa ame e s,
using he Agilen wo k s a ion.
2.3. Measu emen Me hodology and Expe imen al Condi ions
The expe imen al cell was placed in he insula ing box and kep in a closed hood a
oom empe a u e. Fo cycling he expe imen al cell, 100% dep h o discha ge (100% DOD)
mode cons an cu en /cons an ol age (CC/CV) was used. The cu en o discha ging
and cha ging he cell was se o C5 (1.2 A), he end o discha ging was a a se poin
when he ol age o he cell d opped below 1.6 V. Cha ging cu en s a ed o limi when
he limi ing alue o 2.45 V was eached. Du ing he expe imen , he o al ol age, he
po en ials o bo h elec odes, he cu en lowing h ough he cell, he empe a u es o bo h
elec odes, and he empe a u e o he inne and ou e su ace o he insula ing box, as well
as he in e nal esis ance o he cell, we e eco ded. All moni o ed alues we e eco ded
e e y 30 s. The se pe iod was one cycle pe day.
3. Resul s
3.1. Cycling o he Cell CC/CV
Figu e 2shows he ou pu s o all he moni o ed pa ame e s o he expe imen al cell. The
discha ge/cha ge cycle was pe o med en i ely unde ai ly cons an ex e nal condi ions.
Ba e ies 2024, 10, x FOR PEER REVIEW 7 o 18
en ials o bo h elec odes, and empe a u e o he senso embedded in he cell a he se
modes o ope a ion. The esolu ion o he da a acquisi ion sys em is 6.5 digi s (22 bi s).
The loca ion and minia u iza ion o he empe a u e senso allows he no mal unc ion o
he lead cell wi hou affec ing i s esponse.
Measu emen o he in e nal esis ance o he in si u cell was ca ied ou wi h a la-
bo a o y ins umen o domes ic p o enance, which supe imposes he sinusoidal com-
ponen o he cu en a a equency o 1 kHz on he DC discha ge/cha ge cu en and he
in e nal esis ance is calcula ed om he a io o he AC ol age esponse o he cu en .
The magni ude o he AC pe u bing ol age is se o 10 mV. Measu ing o he AC com-
ponen s o ol age and cu en was ca ied ou simul aneously wi h collec ing o he pa-
ame e s, using he Agilen wo k s a ion.
2.3. Measu emen Me hodology and Expe imen al Condi ions
The expe imen al cell was placed in he insula ing box and kep in a closed hood a
oom empe a u e. Fo cycling he expe imen al cell, 100% dep h o discha ge (100%
DOD) mode cons an cu en /cons an ol age (CC/CV) was used. The cu en o dis-
cha ging and cha ging he cell was se o C5 (1.2 A), he end o discha ging was a a se
poin when he ol age o he cell d opped below 1.6 V. Cha ging cu en s a ed o limi
when he limi ing alue o 2.45 V was eached. Du ing he expe imen , he o al ol age,
he po en ials o bo h elec odes, he cu en lowing h ough he cell, he empe a u es o
bo h elec odes, and he empe a u e o he inne and ou e su ace o he insula ing box,
as well as he in e nal esis ance o he cell, we e eco ded. All moni o ed alues we e
eco ded e e y 30 s. The se pe iod was one cycle pe day.
3. Resul s
3.1. Cycling o he Cell CC/CV
Figu e 2 shows he ou pu s o all he moni o ed pa ame e s o he expe imen al cell.
The discha ge/cha ge cycle was pe o med en i ely unde ai ly cons an ex e nal condi-
ions.
Figu e 2. Reading o empe a u e esponses o he lead-acid cell du ing he second cycle o he
expe imen ( op) and he co esponding ol age and cu en (bo om) as a unc ion o ime.
Figu e 2. Reading o empe a u e esponses o he lead-acid cell du ing he second cycle o he
expe imen ( op) and he co esponding ol age and cu en (bo om) as a unc ion o ime.
The empe a u e cha ac e is ics gi e us in o ma ion abou he empe a u e cou se on
he posi i e and nega i e elec ode and on he inne and ou e wall o he insula ing box.
A he end o he p e ious cha ging ( i s cycle) we obse e cooling a di e en a es o he
indi idual componen s and he equaliza ion o all empe a u es a he beginning o he
discha ge. As he cell discha ges, he e is a linea inc ease in he empe a u e o bo h he
Ba e ies 2024,10, 148 8 o 18
posi i e and nega i e elec odes un il app oxima ely 70–80% o discha ge, when he em-
pe a u e inc ease becomes exponen ial, wi h he posi i e elec ode inc easing signi ican ly
as e han he nega i e. We a ibu e his phenomenon o he o de o magni ude highe
inc ease in in e nal esis ance o he posi i e elec ode han he nega i e elec ode a he
end o he discha ge [
42
,
43
], when lead sul a e accumula es on he su ace o he ac i e
ma e ials and blocks he ac i e su ace o he po ous s uc u e o he ma e ials.
The di e ence in elec ical esis ance ( esp. conduc i i y) o posi i e and nega i e
elec odes was discussed by Calábek and Micka [
44
], who, al hough in his wo k hey did
no ye dis inguish be ween he esis ance o he ac i e ma e and he con ac esis ance
o he collec o /ac i e ma e ansi ion, hey ne e heless concluded ha o he posi i e
elec ode he conduc i i y was in he single digi s o siemens, while o he nega i e
elec ode o he same concep he conduc i i y was in he hund eds o siemens. Simila ly,
in a ollow-up pape wi h an ad anced expe imen al elec ode concep by Calábek and
Micka [
42
,
45
] ha e al eady been able o expe imen ally dis inguish be ween he ac i e
mass esis ance and he ansien esis ance o he wo elec odes and ha e shown ha bo h
esis ances a e one o wo o de s o magni ude highe o he posi i e elec ode han o
he nega i e elec ode.
This empe a u e ise pe sis s e en a he momen o swi ching o he cha ging phase
(app oxima ely he i s 5% o cha ge supplied du ing cha ging), which we a ibu e o he
dissolu ion o he su ace blocking sul a e s uc u e and he o ma ion o a supe sa u a ed
laye o sul a e ions in he immedia e icini y o he ac i e su ace o he masses. Con inued
cha ging leads o a educ ion in he s eepness o he empe a u e ise (5–70% supplied
cha ge du ing cha ging), ye his empe a u e ise is highe han du ing he discha ge phase
(despi e he ac ha he e is now mo e hea dissipa ion o he su oundings). A e eaching
a ol age alue o app oxima ely 2.35 V, he empe a u e o he elec odes g adually
inc eases s eeply. This ise in elec ode empe a u e eached a maximum a e he limi ing
ol age o 2.45 V was eached and he cha ging cu en s a ed o be limi ed. Subsequen ly,
a g adual almos linea dec ease in cell empe a u e occu s o e a pe iod o 12 h, ollowed
by ano he discha ge/cha ge cycle.
In Figu e 3we can see he ol age, cu en , po en ials o bo h elec odes and he
in e nal esis ance o he cell. F om he elec ode po en ial esponse i can be seen ha
he e is a uni o m u iliza ion o bo h elec odes. I can be seen ha he dec ease in he o al
cell ol age du ing discha ge is gi en by he summa ion o he po en ial d ops o bo h
elec odes owa ds ze o alue (i.e., owa ds he po en ial o he e e ence elec ode).
Ba e ies 2024, 10, x FOR PEER REVIEW 9 o 18
Figu e 3. Time change o po en ial, cu en , empe a u e and esis ance in he cou se o he second
cycle.
The in e nal esis ance o he cell du ing discha ge shows an inc ease in i s magni-
ude by app oxima ely 250%, while in he las 1/3 o he discha ge, he s eepness o he
inc ease in cell esis ance inc eases wi h he p og essi e ans o ma ion o he cha ged
o m o he ac i e ma e ials in o non-conduc i e lead sul a e. Du ing cha ging, he alue
o he in e nal esis ance e u ns o i s o iginal alue, bu he dec ease in cell esis ance a
he beginning o cha ging is signi ican ly s eepe han du ing discha ging, which is
a ibu ed o he dissolu ion o he su ace blocking sul a e s uc u e, ide sup a.
3.2. Discha ging
Figu e 4 shows in de ail he changes o all ou moni o ed empe a u es (posi i e
and nega i e elec ode, inne and ou e wall o he insula ing box), along wi h he in e -
nal esis ance du ing he discha ge. The cu es show ha du ing he i s 2/3 o he dis-
cha ge he e is a g adual linea inc ease in he empe a u es o bo h elec odes and he
inne wall o he insula ing box. The appa en ini ial sligh d op in he empe a u e o he
posi i e elec ode is due o i s highe empe a u e eached du ing he p e ious cha ging.
The empe a u e change in he ou e wall o he insula ing box is independen o he
empe a u e ise inside he insula ing box and is due o he empe a u e luc ua ion in he
ex e nal en i onmen . The magni ude o he in e nal esis ance shows a sligh linea in-
c ease o e his in e al o he i s app oxima ely 2/3 o he discha ge. Du ing ap-
p oxima ely he las hi d o he discha ge, he e is a signi ican empe a u e inc ease
wi h a pa ially exponen ial pa e n o bo h elec odes and he inne wall o he insula -
ing box. The posi i e elec ode shows he s eepes empe a u e ise, ollowed by he
nega i e elec ode. In his discha ge in e al, he in e nal esis ance shows a sha p in-
c ease wi h an exponen ial pa e n, wi h he inal alue o he in e nal esis ance showing
an inc ease o app oxima ely 250% o he ini ial alue.
Figu e 3. Time change o po en ial, cu en , empe a u e and esis ance in he cou se o he second cycle.
Ba e ies 2024,10, 148 9 o 18
The in e nal esis ance o he cell du ing discha ge shows an inc ease in i s magni ude
by app oxima ely 250%, while in he las 1/3 o he discha ge, he s eepness o he inc ease
in cell esis ance inc eases wi h he p og essi e ans o ma ion o he cha ged o m o he
ac i e ma e ials in o non-conduc i e lead sul a e. Du ing cha ging, he alue o he in e nal
esis ance e u ns o i s o iginal alue, bu he dec ease in cell esis ance a he beginning
o cha ging is signi ican ly s eepe han du ing discha ging, which is a ibu ed o he
dissolu ion o he su ace blocking sul a e s uc u e, ide sup a.
3.2. Discha ging
Figu e 4shows in de ail he changes o all ou moni o ed empe a u es (posi i e and
nega i e elec ode, inne and ou e wall o he insula ing box), along wi h he in e nal
esis ance du ing he discha ge. The cu es show ha du ing he i s 2/3 o he discha ge
he e is a g adual linea inc ease in he empe a u es o bo h elec odes and he inne wall
o he insula ing box. The appa en ini ial sligh d op in he empe a u e o he posi i e
elec ode is due o i s highe empe a u e eached du ing he p e ious cha ging. The
empe a u e change in he ou e wall o he insula ing box is independen o he empe a u e
ise inside he insula ing box and is due o he empe a u e luc ua ion in he ex e nal
en i onmen . The magni ude o he in e nal esis ance shows a sligh linea inc ease o e
his in e al o he i s app oxima ely 2/3 o he discha ge. Du ing app oxima ely he las
hi d o he discha ge, he e is a signi ican empe a u e inc ease wi h a pa ially exponen ial
pa e n o bo h elec odes and he inne wall o he insula ing box. The posi i e elec ode
shows he s eepes empe a u e ise, ollowed by he nega i e elec ode. In his discha ge
in e al, he in e nal esis ance shows a sha p inc ease wi h an exponen ial pa e n, wi h
he inal alue o he in e nal esis ance showing an inc ease o app oxima ely 250% o he
ini ial alue.
Ba e ies 2024, 10, x FOR PEER REVIEW 10 o 18
Figu e 4. Changes o he in e nal esis ance o he cell and inc ease in he de ec ed empe a u es
du ing he discha ge cycle.
To calcula e he he mal p ocesses du ing discha ge, he discha ge cu e (see Figu e
4) is di ided in o wo segmen s (shown by he o ange e ical lines). These will be line-
a ized o simpli y he calcula ions.
Analysis o bo h pa s o he discha ge is summa ized in Table 1. The o al ime o
discha ge was 338 min and he in e nal esis ance inc eased o he o iginal 99 mΩ a he
onse o he discha ge o 150 mΩ a he end o he discha ge.
Table 1. Discha ge pa ame e s.
Discha ging
in e al R QJ Q
R Q
cell Q
cal Q
z
min mΩ J J J J J
1 245 99.5 2106 −1278 474 227 128
2 93 150 1205 −485 545 129 99
In he able is he du a ion o he gi en segmen , R is he in e nal esis ance o he
cell, Q
J
is he Joule hea , Q
R
is he he mochemical hea , Q
cell
is he he mal ene gy ab-
so bed by he cell, Q
cal
is he mal ene gy abso bed by he calo ime e , and Q
z
is he hea
loss o he su oundings.
F om he analysis o he i s segmen , he hea ene gy eleased o he su oundings
due o Joule hea losses was 2106 J and he endo he mic eac ion in ol ing he con e -
sion o lead and lead oxide elec odes o lead sul a e esul ed in he abso p ion o 1278 J.
Thus, as a esul o hese wo effec s (hea ing by Joule hea and cooling by elec ochemical
con e sion), 828 J o he mal ene gy was ans e ed o ou sys em unde in es iga ion.
Hea -accumula ing elemen s o he sys em [elec ochemical cell—insula ing box] in
he i s segmen o discha ge accumula ed o al hea ene gy (Q
cell
+ Q
cal
) equal o 701 J.
Conside ing he ac ha his is no a pe ec ly insula ed sys em, i is necessa y o
ake in o accoun he losses o he su oundings. Due o he s able condi ions inside he
insula ing box wi h a slow empe a u e ise homogeneously h oughou he in e io
space, we can assume ha he diffe ence o he he mal ene gy ans e ed o he sys em
Figu e 4. Changes o he in e nal esis ance o he cell and inc ease in he de ec ed empe a u es
du ing he discha ge cycle.
To calcula e he he mal p ocesses du ing discha ge, he discha ge cu e (see Figu e 4)
is di ided in o wo segmen s (shown by he o ange e ical lines). These will be linea ized
o simpli y he calcula ions.
Analysis o bo h pa s o he discha ge is summa ized in Table 1. The o al ime o
discha ge was 338 min and he in e nal esis ance inc eased o he o iginal 99 m
Ω
a he
onse o he discha ge o 150 mΩa he end o he discha ge.
Ba e ies 2024,10, 148 16 o 18
Al hough he common pe cep ion among expe s is ha lead-acid ba e ies only elease
hea du ing chemical eac ions, his a icle explains ha his pe cep ion is no en i ely
co ec . He e, we ha e shown ha a ce ain s ages o lead-acid cell use (du ing discha ge
and du ing CV cha ging mode), endo he mic eac ions may p e ail o e exo he mic
eac ions in he cell and ha he he mal s a e o he LAB depends no only on he in e nal
s uc u e o he LAB bu also on he se ope a ing pa ame e s. In his pape , we also ou line
s a egies o moni o ing he pa ame e s and ope a ion o he LAB o a oid isky condi ions
ha may lead o he TRA e ec .
In u u e expe imen al wo k, we will look a o he modes o cha ging and hei e ec
on he o e all empe a u e p o ile. We also wan o ocus on o he ypes o ba e y design
a angemen s (VRLA AGM, GEL) and hei e ec on he signi icance o he mal p ocesses.
Au ho Con ibu ions: Concep ualiza ion, P.B. and P.V.; me hodology, P.B., P.V., L.C. and J.Z.; so -
wa e, M.L.; alida ion, P.B., P.V. and J.Z.; o mal analysis, P.B., P.V., L.C. and M.L.; in es iga ion, P.B.,
P.V., J.Z., L.C. and M.L.; esou ces, P.B. and P.V.; da a cu a ion, J.Z. and M.L.; w i ing—o iginal d a
p epa a ion, P.B., P.V., J.Z., L.C. and M.L.; w i ing— e iew and edi ing, P.B. and P.V.; isualiza ion,
M.L. and L.C.; supe ision, P.B. and P.V.; p ojec adminis a ion, P.B.; unding acquisi ion, P.B. All
au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch was unded by he speci ic g adua e esea ch o he B no Uni e si y o
Technology No. FEKT-S-23-8286.
Da a A ailabili y S a emen : The o iginal con ibu ions p esen ed in his s udy a e included in he
a icle ma e ials; u he inqui ies can be di ec ed o he co esponding au ho .
Con lic s o In e es : The au ho s decla e no con lic s o in e es . The unde s had no ole in he design
o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip ; o
in he decision o publish he esul s.
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