The mochimica Ac a 703 (2021) 178994
A ailable online 11 July 2021
0040-6031/© 2021 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license
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Hea capaci y, densi y, su ace ension, and con ac angle o
polyalphaole ins and es e lub ican s
M´
onica A. Coelho de Sousa Ma ques
a
,
b
, Ma ía J.G. Guima ey
b
,
c
, Vicen e Domínguez-A ca
d
,
Al edo Amigo
a
,
*
, Jose a Fe n´
andez
b
a
Labo a o y o The mophysical and Su ace P ope ies o Liquids, Depa men o Applied Physics, Facul y o Physics, Uni e si y o San iago de Compos ela, 15782
San iago de Compos ela, Spain
b
Labo a o y o The mophysical and T ibological P ope ies, Na oma G oup, Depa men o Applied Physics, Facul y o Physics, Uni e si y o San iago de Compos ela,
15782 San iago de Compos ela, Spain
c
Depa men o Design and Enginee ing, Facul y o Science & Technology, Bou nemou h Uni e si y, Poole BH12 5BB, Do se , Uni ed Kingdom
d
Biophysics and In e aces G oup, Depa men o Applied Physics, Facul y o Physics, Uni e si y o San iago de Compos ela, 15782 San iago de Compos ela, Spain
ARTICLE INFO
Keywo ds:
Polyalphaole ins
Es e -based lub ican s
The mophysical and su ace p ope ies
We ing beha iou
ABSTRACT
The mophysical p ope ies o lub ican s a e impo an o unde s and which ones a e app op ia ed o he in-
dus ial condi ions expec ed. The mophysical p ope ies o wo di e en amilies o lub ican s we e analysed:
polyalphaole ins (PAO6, PAO20, PAO32 and PAO40) and ou es e -based lub ican s. Speci ic hea capaci y,
densi y, su ace ension, and con ac angle we e expe imen ally de e mined o e a b oad empe a u e ange
h ough me hods such as
μ
DSC, U- ube ib a ion, d op olume, and sessile d op me hod, espec i ely. A clea
di e ence be ween he wo amilies was obse ed due o hei s uc u e and composi ion, g ouping by na u e.
Es e -based lub ican s showed lowe speci ic hea capaci y bu highe su ace ension and densi y han poly-
alphaole ins. PAO6 clea ly has he lowes densi y and su ace ension and p esen s he highes speci ic hea
capaci y o all lub ican s, and oge he wi h ime hylolp opane iolea e, TMPTO, p esen s he bes we abili y.
Hea capaci y alues we e used o es he alidi y o wo p edic i e me hods.
1. In oduc ion
One o he main asks o lub ican s, besides o ming a p o ec i e ilm
ha educes ic ion and wea o he machine y mo ing pa s and p o-
ec s agains co osion, is o emo e hea . Mo e e icien hea ans e
can esul in signi ican economic and ene gy sa ings [1]. Tu bine and
au omo i e engines a e equi ed o ope a e a e e inc easing empe -
a u es. Uncooled low hea ejec ion (LHR) engines do no ha e oil coole
and adia o , being he engine oil he only hea ans e luid [2,3]. The
p esence o he lub ican ci cula ing wi h he ope a ing luid in e e se
Rankine cycle machines o e ige a ion sys ems a ec s he he mohy-
d aulic p ocesses in he hea exchange s, condense and e apo a o [4].
Lub ican p ope ies, such as hea capaci y, su ace ension, con ac
angle and densi y a e impo an in de e mining hea - ans e a es o
o he applica ions as je engines, elec ic d i e ains... [5–7].
The e ec o ic ion and he e o e he wea o he pieces a e
ampli ied by he inc ease o empe a u e [8]. Hea capaci y alues a e
needed o know how much he mal ene gy he lub ican can emo e
om he ic ion zone. Lub ican s wi h a la ge hea capaci y, C
p
, su e a
smalle empe a u e inc ease o he same amoun o hea ene gy ab-
so p ion [2]. In addi ion, o imp o ing he load-ca ying capaci y o he
hyd odynamic bea ings o analyze he gea losses, olume ic hea ca-
paci y o he oils is an essen ial p ope y [9]. Thus, when he olume ic
hea capaci y o he lub ica ing oil is high, he empe a u es in he
bea ing gaps a e lowe , and consequen ly he iscosi ies highe o he
same ope a ing condi ions [10,11].
The endency o he lub ican s o sp ead on a solid su ace is a e y
impo an ac o a ec ing hei pe o mance. The we ing abili y can be
cha ac e ized using su ace ension and con ac angle measu emen s.
Su ace ension and con ac angle by hei e ec on sp eadabili y, may
also in luence he cooling capaci y. Poo we abili y o su ace educes
he hea ans e when phase changes a e in ol ed. These p ope ies
con ol he o ma ion and g ow h o bubbles, and hus play an impo an
ole in sys ems in ol ing boiling and condensa ion [12]. Besides su ace
ension is an impo an pa ame e in he beha iou o seals, oil
sp eading a es, oam s abili y, mis lub ica ion, we abili y o
low-ene gy solids, and lub ican s a a ion [13–15].
* Co esponding au ho .
E-mail add ess: [email p o ec ed] (A. Amigo).
Con en s lis s a ailable a ScienceDi ec
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jou nal homepage: www.else ie .com/loca e/ ca
h ps://doi.o g/10.1016/j. ca.2021.178994
Recei ed 19 No embe 2020; Recei ed in e ised o m 29 June 2021; Accep ed 5 July 2021
The mochimica Ac a 703 (2021) 178994
2
Oil densi y,
ρ
, plays an impo an ole in p ocesses in ol ing hea
ans e exchanges. I in o ms o he basic beha iou o he lub ican ,
de ec s he pu i y o he luid, and is needed o ob ain he olume ic
hea capaci y. Sanchez [16] p oposed an equa ion ela ing he su ace
ension, densi y and iso he mal comp essibili y based on gene alized
squa e-g adien app oxima ion o he ee ene gy densi y o a
wo-phase luid. This equa ion was e i ied o 50 pola and non-pola
o ganic liquids. Recen ly, Pinhei o e al. [17] based on he Sanchez
equa ion ound ha he loga i hm o he su ace ension co ela ed e y
well wi h he loga i hm o he densi y o nine was e lub ican s.
In his wo k, su ace ension, densi y and con ac angle o empe -
a u es om 283.15 K o 323.15 K and speci ic hea capaci ies in he
empe a u e ange (283.15–353.15 K), o ou polyalphaole ins o
di e en molecula weigh , PAO6, PAO20, PAO32, PAO40, and ou
es e -based lub ican s we e measu ed. These es e s a e ime hylolp o-
pane iolea e, TMPTO, iiso idecyl imelli a e, TTM, a biodeg adable
polyme ic es e , BIOE, and is(2-e hylhexyl) imelli a e, TOTM. This
las compound is a high- empe a u e, high-p essu e, high- iscosi y
s anda d [18]. PAOs a e one o he mos used lub ican s and
es e -based lub ican s a e looking up o subs i u e hem, so o ind an
es e ha could ma ch hei cha ac e is ics would be ideal. PAO lub i-
can bases a e usually syn hesized by mul i-s ep p ocess: e hylene is
polyme ized o 1-decene and hen oligome ized o ob ain bigge s uc-
u es; in he inal s ep, hese oligome s a e hyd ogena ed o p oduce a
ully sa u a ed, e y s able hyd oca bon mix u e. In compa ison wi h
mine al lub ican s, PAOs ha e e y high oxida ion and hyd oly ic s a-
bili ies, high iscosi y index, low pou poin , good inhe en lub ici y.
They a e used in engine c ankcase, comp esso , u bine o gea oils, and
as hyd aulic, dielec ic, b ake, me alwo king o au oma ic ansmission
luids as well as hea ans e media, gels o coa ing op ical ibe s,
o -sho e d illing, shock abso be s, and space applica ions [19,20]. The
usual p ope ies o es e oil bases a e high iscosi y index, biodeg ad-
abili y, excellen lub ici y and low oxici y [21]. The alues o densi y
and su ace ension ob ained in his wo k we e used o es he Pinhei o
e al. [17] equa ion. In addi ion, hea capaci y expe imen al alues we e
used o es he p edic ion capabili y o he g oup-con ibu ion me hods
o Rùzicka and Domalski and Ce iani e al. [22,23]. We selec ed hese
models as hey a e simple and p o ide es ima es wi hin he limi s o
accu acy equi ed in indus ial applica ions.
2. Expe imen al sec ion
2.1. Ma e ials
Table 1 shows he sou ce, main cha ac e is ics and he analy ical
me hods used o cha ac e ize he di e en lub ican s. Samples o ou
polyalphaole ins o di e en molecula weigh (PAO6, PAO20, PAO32,
and PAO40) ha e been p o ided by REPSOL (PAO20 and PAO32 a e
mix u es o PAO40 wi h small amoun s o PAO6). Cha ac e iza ion o
he PAO6 sample (NMR, FTIR spec um and MALDI-TOF mass spec-
oscopy) we e epo ed by Guima ey e al. [24]. In he case o PAO40
sample, Li˜
nei a del Río e al. [25] epo ed he FTIR spec um. PAO32
sample is a mix u e o PAO40 (89 w %) and PAO6 (11 w %), i s FTIR
and Raman spec a we e ecen ly epo ed by Nasse e al. [26]. PAO20
Nomencla u e
PAOs polyalphaole ins
TMPTO ime hylolp opane iolea e
TTM iiso idecyl imelli a e
BIOE biodeg adable polyme ic es e
TOTM is(2-e hylhexyl) imelli a e
C
p
hea capaci y, J g
−1
K
−1
ρ
densi y, g cm
−3
θ con ac angle, ◦
σ
su ace ension, mN m
−1
T empe a u e, K
AAD a e age absolu e de ia ion, %
C linea co ela ion pa ame e , -
λ linea co ela ion pa ame e , -
σ
SM
su ace ension be ween he su ace and he
su ounding medium, mN m
−1
σ
SL
su ace ension be ween he su ace and he liquid, mN
m
−1
σ
LM
su ace ension be ween he liquid and he su ounding
medium, mN m
−1
S sp eading pa ame e , mN m
−1
W
A
wo k o adhesion (solid-liquid in e ace), mN m
−1
W
C
wo k o cohesion (liquid), mN m
−1
Table 1
Sou ce, weigh a e age molecula weigh , M
w
, molecula mass, polydispe si y
index, pu i y and analy ical me hods used o cha ac e ize he lub ican s.
Chemical
name
Sou ce M
w
/g
mol
−1
Polydispe si y
index
Analy ical me hod
PAO6
a
Repsol 604.29 1.043 NMR [24]
FTIR spec um [24]
MALDI-TOF mass
spec oscopy [24]
PAO20
a
Repsol 627.34 1.031 MALDI-TOF mass
spec oscopy, SM
PAO32
a
Repsol 667.79 1.075 MALDI-TOF mass
spec oscopy, SM
FTIR
spec um [26]
Raman spec um [26]
PAO40
a
Repsol 699.21 1.020 MALDI-TOF mass
spec oscopy, SM
FTIR
spec um [25]
Chemical
name
Sou ce Molecula
mass/g mol
−1
Pu i y (mole
ac ion)
Analy ical me hod
TMPTO
b
C oda 926.79 0.683
g
HPLC–ESI-Q-TOF-
MS analysis [28]
FTIR spec um [25,
28]
TTM
c
Ve kol 746.64 0.454
h
UHPLC–APCI-TOF-
MS analysis, SM
FTIR spec um [27]
TOTM
d
Sigma-
Ald ich
546.79 0.99
i
BIOE
e
Ve kol 337.75 0.95 HPLC–ESI-Q-TOF-
MS analysis, SM
FTIR spec um [27]
Chemical
name
Sou ce Molecula mass/
g mol
−1
Pu i y (mole
ac ion)
Analy ical
me hod
Squalane Sigma-
Ald ich
422.81 0.99
i
–
n-Decane Sigma-
Ald ich
142.28 0.99
i
–
n-Hep ane Sigma-
Ald ich
100.20 0.99
i
–
a
PAOs =polyalphaole ins.
b
TMPTO = ime hylolp opane iolea e.
c
TTM = iiso idecyl imelli a e.
d
TOTM = is(2-e hylhexyl) imelli a e.
e
BIOE =biodeg adable polyme ic es e .
SM =Supplemen a y ma e ial. Figs S1-S10
g
68.3% o TMPTO, 27.6% o a compound wi h a C=C bond mo e han
TMPTO, and a 4.1% o a compound wi h wo C=C bonds mo e han TMPTO [28]
(% composi ion in mole ac ion).
h
45.4% o TTM, 35.2% o a compound wi h a me hylene g oup (CH
2
) less
han TTM, and a 19.4% o a compound wi h wo me hylene g oups (CH
2
) less
han TTM (composi ion gi en in w %).
i
De e mined by he supplie .
M.A. Coelho de Sousa Ma ques e al.
The mochimica Ac a 703 (2021) 178994
3
is a mix u e o PAO40 (65 w %) and PAO6 (35 w %).
Ve kol Lub ican es p o ided he syn he ic es e s ( iiso idecyl i-
melli a e, TTM, and he biodeg adable polyme ic es e , BIOE) whe eas
he base oil ime hylolp opane iolea e (TMPTO, CAS: 57675-44-2,
molecula mass 926.79 g mol
−1
) was kindly p o ided by C oda. An
aliquo o he TTM (CAS: 2583122-54–5; molecula mass 746.64 g
mol
−1
) sample was cha ac e ized p e iously [27] h ough FTIR and
mass spec um. TTM cha ac e iza ion was comple ed by an Ul a-High
Pe o mance Liquid Ch oma og aphy, UHPLC, coupled wi h an
APCI-TOF mass spec ome e (Fig. S8). An aliquo o he TMPTO sample
was cha ac e ized by Li˜
nei a del Río e al. [28] using FTIR spec um, and
HPLC–ESI-Q-TOF-MS analysis. Guima ey e al. [27] p o ided a FTIR
spec a o BIOE (molecula mass o 337.75 g mol
−1
). The sample o is
(2-e hylhexyl) imelli a e es e (TOTM, CAS 3319-31-1) s udied in his
wo k was supplied by Sigma-Ald ich. I has a mole ac ion pu i y highe
han 0.99 and a molecula weigh o 546.79 g mol
−1
, and has been
cha ac e ised by Li˜
nei a del Río e al. [29].
2.2. The mophysical and su ace cha ac e iza ion echniques
Densi y a a mosphe ic p essu e o he samples was measu ed om
(283.15 o 323.15) K by using a ib a ing ube densime e (An on Paa
DSA 5000, Aus ia). Calib a ion was pe o med using mechanically
degassed ul apu e wa e (Elix 3 pu i ica ion sys em, Millipo e Co p.)
and d y ai as densi y s anda ds. The uppe limi o he s anda d un-
ce ain y o densi y measu emen s (samples wi h iscosi y highe han
100 mPa s) is 0.0002 g cm
−3
. Fo samples wi h a iscosi y lowe han 30
mPa s, a s anda d unce ain y o 0.00004 g cm
−3
is ob ained [24, 30].
Equilib ium su ace ensions we e measu ed wi h a Lauda d op
olume ensiome e (TVT 2 model, Ge many) using he s anda d mode.
A sy inge o 2.5 ml a ached o a s eel capilla y wi h an inne adius o
1.345 mm, u nished be ween 50 and 60 d ops o each sample. Cali-
b a ion was pe o med using ul apu e wa e (Elix 3 pu i ica ion sys em,
Millipo e Co p.). Bo h he equipmen and he p ocedu e we e desc ibed
in de ail in he pas [31–33]. Depending on he wo king empe a u e
(283.15 o 323.15) K, he su ace ension was de e mined wi h a com-
bined expanded unce ain y anging om 0.2 o 0.4 mN m
−1
a he 95%
con idence le el. The empe a u e o he ex e nal ba h o which he
measu emen cell is connec ed was con olled wi hin ±0.01 K.
The we ing beha iou o he eigh base oils was e alua ed using a
con ac angle analyse , Phoenix MT(A), a di e en empe a u es ( om
293.15 o 323.15 K). Me hod alida ion was pe o med using a ce i ied
d op calib a ion e e ence ool made o glass, which includes h ee im-
ages o sessile d ops wi h nominal con ac angles o 30◦, 60◦and 120◦.
Be o e he s a ic con ac angle measu emen s, he su ace was insed
wi h e hanol and d ied in a s eam o ho ai . The su ace ma e ial
selec ed o de e mine he we abili y beha iou o he base oils was AISI
420 s ainless s eel, which is equen ly used o ibological es s. One
d op o lub ican sample was d opped on he s eel su ace using a sy-
inge. To ob ain he alue o he a e age s eady-s a e con ac angle, a
pe iod o 5 s was wai ed o s abilize he d ople and a leas h ee
measu emen s we e eplica ed o each base oil. Fo he de e mina ion
o he s a ic con ac angle, he expanded unce ain y is 1◦(le el o
con idence o 95%). In addi ion, sp eading pa ame e was calcula ed
using su ace ension and con ac angle measu emen s.
Speci ic hea capaci ies we e ob ained using he iso he mal s ep
me hod wi h a Mic o DSCIII di e en ial scanning calo ime e om
Se a am, F ance. Calib a ion was pe o med using a Joule e ec cali-
b a ion essel (Se a am) and checked using n-decane and squalane
(Sigma-Ald ich ≥99%) as hea capaci y s anda ds, hei C
p
alues being
aken om he li e a u e [34,35]. Backg ound noise o he Mic o DSCIII
was less han 3 µW. The expe imen al echnique has p e iously been
desc ibed [30], and he s anda d unce ain y in C
p
expe imen al alues
is es ima ed o be 0.002 J g
−1
K
−1
. Fig. S11 shows he compa ison be-
ween he measu ed hea capaci y o n-decane and squalane and li e -
a u e da a and Table S1 (Supplemen a y ma e ial) shows he C
p
alues
ob ained o n-decane and squalane in he empe a u e ange
(283.15–353.15) K. Table S2 includes he calcula ion o he di e en
con ibu ions o he unce ain y associa ed wi h he de e mina ion o
he speci ic hea capaci y. Fo his calcula ion, squalane was used as he
calib a ion subs ance, n-hep ane as he sample and he chose empe a-
u e was T =298.15 K.
3. Resul s and discussion
Densi ies and su ace ensions o he eigh base-oils in he ange o
empe a u es om 283.15 o 323.15 K a e epo ed in Table 2. Bo h
p ope ies dec ease linea ly wi h empe a u e. Densi ies o se e al o he
s udied base- luid lub ican s ha e been p e iously published. Guima ey
e al. [27] ( om he same p o ide ) and O e o e al. [36] published
densi y alues o BIOE and TTM wi h an a e age absolu e de ia ion
(AAD%) o 0.2% and 0.03% om 283.15 o 333.15 K, and o 0.3% and
0.004% a 20 ◦C, espec i ely. Li˜
nei a del Río e al. [37] epo ed he
densi y o TTM om he same p o ide ob aining a de ia ion o 0.03%.
Densi y o TMPTO published by O e o e al. [36] de ia es by 0.09%. Mia
e al. [38] measu ed PAO32 densi y a 15 ◦C ob aining a de ia ion o
2.2% wi h ou esul s. Besides, Nasse e al. [26] measu ed densi y o
PAO32 wi h a de ia ion o 0.06%. Li˜
nei a del Río e al. [25] ob ained he
densi y alue o PAO40 a 313.15 K o 0.8346 g cm
−3
. Table S3 shows
he AAD% be ween he expe imen al densi ies and p e iously published
alues measu ed by ou expe imen al g oup. The only base oil ha
p esen s a di e ence g ea e han 0.06% is BIOE. The di e ence (0.24%)
wi h he esul s o e e ence [28] may be due o he use o di e en lo s
o his compound. Fig. 1 shows he de ia ions be ween he expe imen al
densi y alues o Table 2 o he e e ence luid TOTM and li e a u e
da a [29,39–43].
As can be seen in Fig. 2, he e is a clea di e ence be ween he
beha iou o polyalphaole ins and ha o es e based lub ican s. PAO6 is
he one wi h lowe molecula mass among he PAOs, p esen ing he
lowes densi y and su ace ension o all samples. PAO40 is he one wi h
highe densi y and su ace ension, while PAO20 and PAO32 show e y
simila p ope ies once hey a e blends o PAO40 wi h small amoun s o
PAO6 o ob ain in e media e iscosi ies.
Syn he ic es e s a e in e es ing due o hei high pola i y and
biodeg adabili y; hei p ope ies depend on he ami ica ion o he
alcohol and he size o he acid ha composes hem, which allows
ailo ing p ope ies by molecula design. Alkyla ed a oma ic es e lu-
b ican s’ p ope ies a e de ined mainly by he a oma ic componen [44],
he e o e TOTM and TTM, bo h imelli a es, a e homologous and
possible o compa e. TOTM wi h lowe molecula weigh p esen s
highe densi y and su ace ension as expec ed. TMPTO shows he
highes su ace ension o all samples, a esul o i s highe pola i y.
The linea dependence be ween ln (
σ
) and ln (
ρ
) was analysed
h ough he co ela ion p oposed by Pinhei o e al. [17]:
ln(
σ
/mN⋅m−1)=C+λln(
ρ
/kg⋅m−3)(1)
whe e C and λ a e pa ame e s o he linea eg ession, s a ed in Table 3.
In Fig. 2, he linea beha iou is pe cei ed o all lub ican s. The e is an
ob ious sepa a ion in wo classes: alkanes and es e s, wo di e en na-
u es o lub ican s wi h di e en chemical composi ion and physical
beha iou .
As ega ds o we abili y, he con ac angle, θ, is de ined as he angle
ha he su ace o a liquid o ms when i comes in o con ac wi h a solid
su ace. The alue o he con ac angle depends mainly on he ela-
ionship be ween he adhesi e o ces o he liquid and he solid and he
cohesi e o ces o he liquid i sel .
Fig. 3 shows he con ac angles measu ed o all lub ican s in he
ange o empe a u es om 293.15 o 323.15 K. Se e al a emp s o
de e mine he con ac angle o he base oils we e made a 283.15 K, bu
he esul s ob ained we e disca ded due o wa e condensa ion on he
s eel su ace in e e ing wi h he con ac angle alue. Fo he
M.A. Coelho de Sousa Ma ques e al.
The mochimica Ac a 703 (2021) 178994
4
Table 2
Densi y,
ρ
a
, and su ace ension,
σ
b
, o he analysed lub ican s in he ange o empe a u es, T
c
, om 283.15 K o 323.15 K, and a p essu e p =0.0991 MPa
d
.
T/K
ρ
/g cm
−3
σ
/mN m
−1
ρ
/g cm
−3
σ
/mN m
−1
ρ
/g cm
−3
σ
/mN m
−1
ρ
/g cm
−3
σ
/mN m
−1
PAO6 PAO20 PAO32 PAO40
283.15 0.83016 30.24 0.84424 30.63 0.84851 30.94 0.85268 31.38
288.15 0.82702 29.84 0.84118 30.35 0.84560 30.55 0.84949 30.89
293.15 0.82389 29.46 0.83811 29.92 0.84269 30.13 0.84628 30.42
298.15 0.82075 29.08 0.83504 29.51 0.83979 29.80 0.84328 30.00
303.15 0.81763 28.70 0.83199 29.10 0.83690 29.38 0.84028 29.57
308.15 0.81450 28.27 0.82899 28.71 0.83401 28.98 0.83729 29.17
313.15 0.81137 27.91 0.82598 28.32 0.83111 28.59 0.83430 28.78
318.15 0.80824 27.54 0.82297 27.96 0.82817 28.18 0.83131 28.40
323.15 0.80512 27.17 0.81996 27.61 0.82524 27.82 0.82833 28.00
TMPTO BIOE TOTM TTM
283.15 0.92352 33.44 0.95253 32.74 0.99562 31.61 0.96144 31.40
288.15 0.92023 33.04 0.94906 32.30 0.99194 31.21 0.95796 30.90
293.15 0.91692 32.70 0.94554 31.88 0.98825 30.80 0.95437 30.40
298.15 0.91360 32.36 0.94202 31.49 0.98454 30.42 0.95090 30.03
303.15 0.91030 31.97 0.93873 31.10 0.98096 30.03 0.94761 29.63
308.15 0.90699 31.64 0.93544 30.72 0.97735 29.67 0.94432 29.28
313.15 0.90368 31.28 0.93217 30.38 0.97366 29.34 0.94101 28.84
318.15 0.90038 30.92 0.92890 30.04 0.97011 28.99 0.93769 28.57
323.15 0.89709 30.57 0.92563 29.69 0.96648 28.63 0.93443 28.17
a
Combined expanded densi y unce ain y is U
c
(
ρ
) =4 ×10
−4
g cm
−3
.
b
Combined expanded su ace ension unce ain y is U
c
(
σ
) =0.4 mN m
−1
c
Expanded empe a u e unce ain y is U(T) =0.02 K.
d
Expanded p essu e unce ain y is U(p) =0.0005 MPa (0.95 le el o con idence).
Fig. 1. De ia ions be ween densi y li e a u e da a a a mosphe ic p essu e and TOTM expe imen al da a o Table 2.
Fig. 2. Linea co ela ion be ween ln (
σ
) and ln (
ρ
) o he base- luids.
M.A. Coelho de Sousa Ma ques e al.
The mochimica Ac a 703 (2021) 178994
5
empe a u es es ed, high we abili y was e ealed o all base oils
ob aining small con ac angles (<< 90◦). The be e we abili y beha -
iou was ob ained o PAO6 and TMPTO base oils wi h con ac angle
alues o 6.8◦and 11.3◦a 323.15 K, espec i ely. An inc ease can be
obse ed in he con ac angle as he deg ee o polyme isa ion o he
PAOs inc eases. This can be explained by hei su ace ension. The
con ac angle is ela ed by Young´s equa ion wi h he su ace ensions a
he di e en in e aces as ollows [45]:
cos(θ) =
σ
SM −
σ
SL
σ
LM
(2)
whe e
σ
SM
is he su ace ension be ween he su ace and he su -
ounding medium (ai ),
σ
SL
is he su ace ension be ween he su ace
and he liquid and
σ
LM
is he su ace ension be ween he liquid and he
su ounding medium. The e o e, as he
σ
LM
inc eases, he cosine o he
con ac angle dec eases, in o he wo ds, he con ac angle o ha liquid
inc eases. Thus, he esul s ob ained o bo h su ace ension and con ac
angle o polyalphaole ins a e consis en . Howe e , his is no he case
wi h es e -based lub ican s. The e is no di ec ela ionship be ween he
su ace ension o hese lub ican s and he con ac angles hey o m on
he s ainless s eel su ace. This may be due o he di e en composi ion
o hese lub ican s, which a ec s he adhesi e o ce o he liquid and he
su ace (
σ
SL
). The we ing beha iou o mos base oils wi h ega d o
empe a u e a ia ion was as expec ed. I should be no ed ha no
a ia ion wi h he empe a u e was obse ed o he BIOE oil, he di -
e ences a e wi hin he limi s o e o o he measu emen s. Fo all o he
base oils, he con ac angle dec eases as he empe a u e ises, his end
is he same as o he su ace ension. The a ia ions o con ac angles
ange om 1.2◦ o 16.3◦ o BIOE and TTM, espec i ely, in a empe -
a u e ange o 30 K.
The e ec o we abili y on lub ica ion is ypically cha ac e ized
using he sp eading pa ame e , S, which can be de ined as [46]:
S=
σ
SM − (
σ
SL +
σ
LM)(3)
Combining Eqs. (2) and (3) he sp eading pa ame e can be desc ibed
as he di e ence be ween he adhesion wo k be ween he liquid and he
su ace (W
A
) and he cohesion wo k be ween liquid molecules (W
C
)
[47]:
S=
σ
LMcosθ−
σ
LM =
σ
LM(cosθ−1)(4)
The e o e, adhesi e and cohesi e o ces can be es ima ed as:
WA≈
σ
LM(cosθ+1)(5)
WC=2
σ
LM (6)
Thus, sp eading pa ame e can be exp essed app oxima ely as:
S=WA−WC≈
σ
LM(cosθ+1) − 2
σ
LM (7)
When S>0, WC<WA, he liquid sp eads comple ely o e he su ace
in o de o dec ease i s su ace ene gy. When S<0, WC>WA, he liquid
o ms a d op on he su ace due o cohesi e o ces be ween oil molecules
which a e a ac ed mo e s ongly o each o he .
The sp eading pa ame e alues de e mined by Eq. (7) om expe -
imen al su ace ension and con ac angle o he eigh base oils we e
ga he ed in Table 4. I can be obse ed ha S is nega i e o all cases
s udied; his means ha he cohesi e o ces o base oils a e highe han
he adhesi e o ces in he solid-liquid in e ace. As men ioned abo e, as
he empe a u e inc eases, he con ac angle and su ace ension o he
liquid dec eases. This is because he cohesion wo k, W
C
, ha akes place
be ween he molecules o he liquid becomes weake wi h an inc ease o
molecula he mal ac i i y and he e o e, S inc eases owa ds ze o.
Finally, he speci ic hea capaci y o he base oils in he empe a u e
ange (283.15 – 353.15 K) a e epo ed in Table 5. As Fig. 4a shows,
he e is a clea di e ence be ween polyalphaole ins and he es o he
base-oils. PAO40, PAO32, and PAO20 show e y simila speci ic hea
capaci y (no e ha PAO32 and PAO20 a e mix u es o PAO40 wi h small
amoun s o PAO6). PAO6 and PAO40 hea capaci y has been epo ed
om 273.15 o 323.15 K by Rudnick [19] wi h an AAD o 6.8% and
1.3%, espec i ely. Likely, his a e age de ia ion is due o he di e en
sample (PAO6 a e oligome s o dime s, ime s and e ame s). Fo he
es e -based lub ican s, he wo a oma ic es e s (TTM and TOTM) ha e
he lowes hea capaci y as he ing bonds con ibu e less o he hea
Table 3
Linea co ela ion pa ame e s o Eq. (1) o he di e en lub ican s.
C λ R
2
PAO6 −20.184 3.5102 0.9998
PAO20 −21.170 3.6498 0.9990
PAO32 −22.459 3.8395 0.9996
PAO40 −22.965 3.9135 0.9997
TMPTO −17.486 3.0748 0.9998
BIOE −19.854 3.4030 0.9996
TOTM −19.507 3.3258 0.9995
TTM −22.066 3.7141 0.997
Fig. 3. Con ac angles o he eigh base oils wi h a s eel su ace o a pla e a
empe a u es om 293.15 o 323.15 K.
Table 4
Expe imen al da a o he con ac angle, θ
a
, and sp eading pa ame e , S, a
di e en empe a u es, T
b
, and a p essu e p =0.0991 MPa
c
.
T / K θ/◦S ±u
(S)
d
/mN
m
−1
θ/◦S ±u
(S)
/mN
m
−1
θ/◦S ±u
(S)
/mN
m
−1
θ/◦S ±u
(S)
/mN
m
−1
PAO6 PAO20 PAO32 PAO40
293.15 20.7 −1.9
±0.2
22.5 −2.3
±0.2
26.5 −3.2
±0.2
31.4 −4.5
±0.3
303.15 16.4 −1.2
±0.1
19.6 −1.7
±0.2
25.3 −2.8
±0.2
30.0 −3.9
±0.3
313.15 10.9 −0.5
±0.1
17.2 −1.3
±0.1
20.2 −1.8
±0.2
22.7 −2.2
±0.2
323.15 6.8 −0.2
±0.1
12.6 −0.7
±0.1
18.1 −1.4
±0.2
20.1 −1.7
±0.2
TMPTO TOTM TTM BIOE
293.15 26.2 −3.4
±0.3
21.9 −2.2
±0.2
32.0 −4.6
±0.3
34.4 −5.6
±0.3
303.15 24.4 −2.9
±0.2
18.0 −1.5
±0.2
24.7 −2.7
±0.2
32.5 −4.9
±0.3
313.15 19.4 −1.8
±0.2
16.2 −1.2
±0.1
20.5 −1.8
±0.2
34.1 −5.2
±0.3
323.15 11.3 −0.6
±0.1
12.6 −0.7
±0.1
15.7 −1.0
±0.1
33.2 −4.9
±0.3
a
Expanded con ac angle unce ain y is U(θ) =1◦.
b
Expanded empe a u e unce ain y is U(T) =0.2 K.
c
Expanded p essu e unce ain y is U(p) =0.0005 MPa. (0.95 le el o
con idence).
d
S anda d unce ain y o sp eading pa ame e .
M.A. Coelho de Sousa Ma ques e al.
The mochimica Ac a 703 (2021) 178994
6
s o age [23]. TTM wi h highe molecula mass han TOTM p esen s
highe hea capaci y. Es e s show lowe speci ic hea capaci y, due o
ca bon double bonds and a oma ic ings ewe possibili ies o hea
s o age [48]. The ca boxylic g oup is mo e complex, acco ding o
Rùzicka and Domalski [23, 49], C=O bonds ha e a e y good con i-
bu ion in s o age bu he –O– con ibu es nega i ely due o he lack o
ib a ion modes o his bond. E en hough TMPTO as a ies e was
expec ed o ha e a much highe C
p
han BIOE, he p esence o ca bon
double bonds lowe ed i s hea capaci y nea BIOE’s alues as a dies e .
TOTM hea capaci y has been epo ed om 297.91 o 368.80 K by
Bazile e al. [39] wi h an AAD o 2.8%.
In Fig. 4b he expe imen al C
p
alues o he analyzed liquids wi h
known s uc u es (PAO6, TMPTO, TTM, TOTM) we e compa ed wi h he
da a ob ained wi h he g oup con ibu ion me hod p oposed by Rùzicka
and Domalski [23,49] in all he empe a u e ange. The me hod p o-
posed by Ce iani e al. [22] was only applied o PAO6 and TMPTO
because he g oup pa ame e s o a oma ic bonds we e no epo ed.
The bes p edic ions we e ob ained o TMPTO wi h AAD% o 0.72% o
he i s g oup con ibu ion me hod and 1.89% o he second. Fo he
o he compounds, he de ia ions ange om 4% (PAO6 wi h Ce iani
e al.) o 10% (TOTM wi h Rùzicka and Domalski).
4. Conclusion
In his wo k, he he mophysical and su ace p ope ies o se e al
base oils ha e been de e mined expe imen ally o check i es e -based
oils could eplace polyalphaole ins in hei indus ial applica ions. The
ollowing poin s could be concluded:
Double bonds and a oma ic ings aise densi y because hey compac
he molecule, so, as expec ed, es e -based lub ican s p esen highe
densi y han polyalphaole ins. Among es e s, imelli a es showed
highe densi y.
The highes su ace ensions a e obse ed o es e -based lub ican s,
his is due o hei highe pola i y esul ing in highe cohesi e o ces and
highe con ac angle, which means less we abili y. As expec ed TMPTO
has he highes su ace ension due o i s high pola i y.
All base oils s udied on he s ainless s eel su ace showed nega i e
alues o sp eading pa ame e , bu hei we abili y beha iou imp o ed
wi h inc easing empe a u e. The inc ease o con ac angle o poly-
alphaole ins was linea wi h he inc ease o su ace ension and o mo-
lecula weigh . On he o he hand, es e -based lub ican s had mo e
con o e sial con ac angle esul s wi h no ela ion o he su ace en-
sions p obably due o he oxygen a om and he double bonds in hei
s uc u e. Compa ing be ween he wo imelli a e molecules, TTM is
he la ges and p esen s lowe su ace ension and highe con ac angle,
esul ing in lowe we abili y han TOTM.
PAOs show highe speci ic hea capaci y, due o he la ge sa u a ed
hyd oca bon s uc u es, han es e -based lub ican s. As expec ed, he
imelli a e es e s ha e he lowes speci ic hea capaci y due o hei
a oma ic ings.
PAO6 clea ly has he lowes densi y and su ace ension and p esen s
he highes speci ic hea capaci y o all lub ican s.
Decla a ion o Compe ing In e es
The au ho s epo no con lic o in e es .
Acknowledgmen s
Au ho s acknowledge Repsol and Ve kol o p o iding us he PAOs
and es e samples espec i ely. This wo k was suppo ed by MINECO
and he ERDF p og am h ough ENE2017-86425-C2-2-R p ojec , and by
Xun a de Galicia (ED431E 2018/08, and GRC ED431C 2020/10). M.A.C.
S.M. acknowledges he E asmus p og am o unding he esea che s ay
a he San iago de Compos ela Uni e si y. M.J.G.G. hanks Xun a de
Galicia (Spain) he suppo h ough a Pos doc o al Fellowship (ED481B-
2019-015).
Supplemen a y ma e ials
Supplemen a y ma e ial associa ed wi h his a icle can be ound, in
he online e sion, a doi:10.1016/j. ca.2021.178994.
Table 5
Speci ic hea capaci y, C
pa,
o he base- luids a di e en empe a u es, T
b
, and a
p essu e p =0.0991 MPa
c
.
T / K C
p
/J g
−1
K
−1
PAO6 PAO20 PAO32 PAO40
283.15 2.236 2.128 2.124 2.121
293.15 2.275 2.157 2.152 2.143
303.15 2.301 2.187 2.185 2.186
313.15 2.328 2.218 2.215 2.217
323.15 2.362 2.251 2.246 2.246
333.15 2.396 2.280 2.278 2.281
343.15 2.420 2.314 2.314 2.312
353.15 2.479 2.350 2.348 2.351
TOTM TTM TMPTO BIOE
283.15 1.831 1.879 1.965 1.972
293.15 1.862 1.908 1.986 1.995
303.15 1.881 1.939 2.014 2.023
313.15 1.910 1.966 2.032 2.045
323.15 1.931 1.996 2.057 2.070
333.15 1.956 2.026 2.084 2.095
343.15 1.983 2.049 2.113 2.122
353.15 2.005 2.092 2.138 2.151
a
Expanded speci ic hea capaci y unce ain y is U(C
p
) =0.004 J g
−1
K
−1
.
b
Expanded empe a u e unce ain y is U(T) =0.2 K.
c
Expanded p essu e unce ain y is U(p) =0.0005 MPa (0.95 le el o
con idence).
Fig. 4. Speci ic hea capaci y o he base oils: (a) Expe imen al alues, (b)
Compa ison wi h he p edic ions o he g oup con ibu ion me hods o Rùzicka
& Domalski [23,49] and Ce iani e al. [22]. The dashed line in Fig. 4a is a guide
o he eye.
M.A. Coelho de Sousa Ma ques e al.
The mochimica Ac a 703 (2021) 178994
7
Re e ences
[1] D.P. Ba ai, B.A. Bhan ase, S.H. Sonawane, A e iew on g aphene de i a i es-based
nano luids: in es iga ion on p ope ies and hea ans e cha ac e is ics, Ind. Eng.
Chem. Res. 59 (2020) 10231–10277, h ps://doi.o g/10.1021/acs.iec .0c00865.
[2] S. W enick, P. Su o , H. Pangilinan, E.E. Schwa z, Hea T ans e P ope ies o
Engine Oils, Wo ld T ibology Cong ess III, 2005, pp. 595–596, in:.
[3] L. Yang, W. Jiang, W. Ji, O. Mahian, S. Baz i, R. Sad i, I.A. Bad uddin,
S. Wongwises, A e iew o hea ing/cooling p ocesses using nanoma e ials
suspended in e ige an s and lub ican s, In . J. Hea Mass T ans . 153 (2020),
119611, h ps://doi.o g/10.1016/j.ijhea mass ans e .2020.119611.
[4] M.R. Conde, Es ima ion o he mophysical p ope ies o lub ica ing oils and hei
solu ions wi h e ige an s: an app aisal o exis ing me hods, Appl. The m. Eng. 16
(1996) 51–61, h ps://doi.o g/10.1016/1359-4311(95)00011-2.
[5] T.J. B uno, T.J. Fo in, M.L. Hube , A. Laesecke, E.W. Lemmon, E. Mans ield, M.
O. McLinden, S.L. Ou cal , R.A. Pe kins, K.N. U ness, The mophysical P ope ies o
Polyol Es e Lub ican s, U.S. Depa men o Comme ce, Na ional Ins i u e o
S anda ds and Technology, 2019.
[6] T.J. Fo in, Densi y, speed o sound, and hea capaci y measu emen s o polyol
es e lub ican s, J. Chem. Eng. Da a 63 (2018) 4325–4338, h ps://doi.o g/
10.1021/acs.jced.8b00358.
[7] Y. Kwak, C. Cle eland, A. Adh a yu, X. Fang, S. Hu ley, T. Adachi, Unde s anding
Base Oils and Lub ican s o Elec ic D i e ain Applica ions, SAE In e na ional,
2019 in.
[8] S.T. Pham, A.K. Tieu, S. Wan, J. Hao, H. Zhu, H.H. Nguyen, D.R.G. Mi chell,
Oxida i e and ic ional beha io o a bina y sodium bo a e–silica e composi e in
high- empe a u e lub ican applica ions, Ind. Eng. Chem. Res. 59 (2020)
2921–2933, h ps://doi.o g/10.1021/acs.iec .9b05767.
[9] A. Ziegl um, T. Lohne , K. S ahl, TEHL simula ion on he in luence o lub ican s on
load-dependen gea losses, T ibol. In . 113 (2017) 252–261, h ps://doi.o g/
10.1016/j. iboin .2016.12.018.
[10] R. Nicole i, The impo ance o he hea capaci y o lub ican s wi h nanopa icles in
he s a ic beha io o jou nal bea ings, J. T ibol. 136 (2014) 1–5, h ps://doi.o g/
10.1115/1.4027861.
[11] J. Salgado, T. Teijei a, J.J. Pa aj´
o, J. Fe n´
andez, J. T oncoso, Isoba ic hea capaci y
o nanos uc u ed liquids wi h po en ial use as lub ican s, J. Chem. The modyn.
123 (2018) 107–116, h ps://doi.o g/10.1016/j.jc .2018.03.031.
[12] P. Es ell´
e, D. Cabalei o, G. ˙
Zyła, L. Lugo, S.M.S. Mu shed, Cu en ends in su ace
ension and we ing beha io o nano luids, Renew. Sus ain. Ene gy Re . 94 (2018)
931–944, h ps://doi.o g/10.1016/j. se .2018.07.006.
[13] D. Blanco, M. Ba olom´
e, B. Ramajo, J.L. Viesca, R. Gonz´
alez, A. He n´
andez Ba ez,
We ing p ope ies o se en phosphonium ca ion-based ionic liquids, Ind. Eng.
Chem. Res. 55 (2016) 9594–9602, h ps://doi.o g/10.1021/acs.iec .6b00821.
[14] D. Blanco, N. Ri e a, P. Oulego, M. Díaz, R. Gonz´
alez, A.H. Ba ez, No el a y acid
anion-based ionic liquids: con ac angle, su ace ension, pola i y ac ion and
sp eading pa ame e , J. Mol. Liq. 288 (2019), 110995, h ps://doi.o g/10.1016/j.
molliq.2019.110995.
[15] J.W.R. Jones, L.D. Wede en, Su ace Tension Measu emen s in Ai o Liquid
Lub ican s o 200 ◦C By he Di e en ial Maximum Bubble P essu e Technique,
1971, p. 18. h ps://n s.nasa.go /ci a ions/19710024039.
[16] I.C. Sanchez, Liquids: su ace ension, comp essibili y, and in a ian s, J. Chem.
Phys. 79 (1983) 405–415, h ps://doi.o g/10.1063/1.445536.
[17] C.T. Pinhei o, R.F. Pais, A.G.M. Fe ei a, M.J. Quina, L.M. Gando-Fe ei a,
Measu emen and co ela ion o he mophysical p ope ies o was e lub ican oil,
J. Chem. The modyn. 116 (2018) 137–146, h ps://doi.o g/10.1016/j.
jc .2017.08.039.
[18] J. Fe nandez, M.J. Assael, R.M. Enick, J.P.M. T usle , In e na ional S anda d o
iscosi y a empe a u es up o 473 K and p essu es below 200 MPa (IUPAC
Technical Repo ), Pu e Appl. Chem. 91 (2019) 161–172, h ps://doi.o g/
10.1515/pac-2018-0202.
[19] L.R. Rudnick, Polyalphaole ins, in: L.R. Rudnick (Ed.), Syn he ics, Mine al Oils,
and Bio-Based Lub ican s: Chemis y and Technology, CRC P ess, 2013, pp. 4–38.
[20] S. Boyde, S.J. Randles, Es e s, in: L.R. Rudnick (Ed.), Syn he ics, Mine al Oils, and
Bio-Based Lub ican s: Chemis y and Technology, CRC P ess, 2013, pp. 51–80.
[21] Y. Wu, W. Li, M. Zhang, X. Wang, Imp o emen o oxida i e s abili y o
ime hylolp opane iolea e lub ican , The mochim. Ac a 569 (2013) 112–118,
h ps://doi.o g/10.1016/j. ca.2013.05.033.
[22] R. Ce iani, R. Gani, A.J.A. Mei elles, P edic ion o hea capaci ies and hea s o
apo iza ion o o ganic liquids by g oup con ibu ion, Fluid Phase Equilib. 283
(2009) 49–55, h ps://doi.o g/10.1016/j. luid.2009.05.016.
[23] V. Rùzicka, E.S. Domalski, Es ima ion o he hea capaci ies o o ganic liquids as a
unc ion o empe a u e using g oup addi i i y. II. Compounds o ca bon,
hyd ogen, halogens, ni ogen, oxygen, and sul u , J. Phys. Chem. Re . Da a 22
(1993) 619–657, h ps://doi.o g/10.1063/1.555924.
[24] M.J.G. Guima ey, M.J.P. Comu˜
nas, E.R. L´
opez, A. Amigo, J. Fe n´
andez,
The mophysical p ope ies o polyalphaole in oil modi ied wi h nanoaddi i es,
J. Chem. The modyn. 131 (2019) 192–205, h ps://doi.o g/10.1016/j.
jc .2018.10.035.
[25] J.M. Li˜
nei a del Río, E.R. L´
opez, J. Fe n´
andez, F. Ga cía, T ibological p ope ies o
dispe sions based on educed g aphene oxide shee s and ime hylolp opane
iolea e o PAO 40 oils, J. Mol. Liq. 274 (2019) 568–576, h ps://doi.o g/
10.1016/j.molliq.2018.10.107.
[26] K.I. Nasse , J.M. Li˜
nei a del Río, E.R. L´
opez, J. Fe n´
andez, Syne gis ic e ec s o
hexagonal bo on ni ide nanopa icles and phosphonium ionic liquids as hyb id
lub ican addi i es, J. Mol. Liq. 311 (2020), 113343, h ps://doi.o g/10.1016/j.
molliq.2020.113343.
[27] M.J.G. Guima ey, M.R. Salgado, M.J.P. Comu˜
nas, E.R. L´
opez, A. Amigo,
D. Cabalei o, L. Lugo, J. Fe n´
andez, E ec o Z O
2
nanopa icles on he mophysical
and heological p ope ies o h ee syn he ic oils, J. Mol. Liq. 262 (2018) 126–138,
h ps://doi.o g/10.1016/j.molliq.2018.04.027.
[28] J.M. Li˜
nei a del Río, M.J.G. Guima ey, M.J.P. Comu˜
nas, E.R. L´
opez, A. Amigo,
J. Fe n´
andez, The mophysical and ibological p ope ies o dispe sions o
g aphene in a ime hylolp opane iolea e based oil, J. Mol. Liq. 268 (2018)
854–866, h ps://doi.o g/10.1016/j.molliq.2018.07.107.
[29] J.M. Li˜
nei a del Río, M.J.G. Guima ey, M.J.P. Comu˜
nas, J. Fe n´
andez, High
p essu e iscosi y beha iou o is(2-e hylhexyl) imelli a e up o 150 MPa,
J. Chem. The modyn. 138 (2019) 159–166, h ps://doi.o g/10.1016/j.
jc .2019.06.016.
[30] T.J. Fo in, A. Laesecke, M. F eund, S.L. Ou cal , Ad anced calib a ion, adjus men ,
and ope a ion o a densi y and sound speed analyze , J. Chem. The modyn. 57
(2013) 276, h ps://doi.o g/10.1016/j.jc .2012.09.009.
[31] C. Be múdez-Salgue o, J. G acia-Fad ique, A. Amigo, Su ace ension da a o
aqueous bina y mix u es o me hyl, e hyl, p opyl, and bu yl ace a es a 298.15 K,
J. Chem. Eng. Da a 55 (2010) 2905–2908, h ps://doi.o g/10.1021/je900962 .
[32] J. He n´
andez-Pascacio, X. Banquy, S. P´
e ez-Casas, M. Cos as, A. Amigo, ´
A. Pi˜
nei o,
A small molecula size sys em gi ing unexpec ed su ace e ec s:
α
-Cyclodex in +
sodium dodecyl sul a e in wa e , J. Colloid In e ace Sci. 328 (2008) 391–395,
h ps://doi.o g/10.1016/j.jcis.2008.09.002.
[33] ´
A. Pi˜
nei o, P. B ocos, A. Amigo, M. Pin os, R. B a o, Su ace ensions and e ac i e
indices o ( e ahyd o u an +n -alkanes) a T =298.15 K, J. Chem. The modyn. 31
(1999) 931–942, h ps://doi.o g/10.1006/jch .1999.0517.
[34] L. Lugo, J.J. Sego ia, M.C. Ma ín, J. Fe n´
andez, M.A. Villama˜
n´
an, An
expe imen al se up o isoba ic hea capaci ies o iscous luids a high p essu e:
squalane, bis(2-e hylhexyl) sebaca e and bis(2-e hylhexyl) ph hala e, J. Chem.
The modyn. 49 (2012) 75–80, h ps://doi.o g/10.1016/j.jc .2012.01.011.
[35] J.A. Ga es, R.H. Wood, J.C. Cobos, C. Casano a, A.H. Roux, G. Roux-Desg anges, J.
P.E. G olie , Densi ies and hea capaci ies o 1-bu anol +n-decane om 298 K o
400 K, Fluid Phase Equilib. 27 (1986) 137–151, h ps://doi.o g/10.1016/0378-
3812(86)87046-7.
[36] I. O e o, E.R. L´
opez, M. Reichel , M. Villanue a, J. Salgado, Ionic liquis based on
phosphonium ca ions as nea lub ican s o lub ican addi i es o a s eel/s eel
con ac , ACS Appl. Ma e . In e aces 6 (2014) 13115–13128, h ps://doi.o g/
10.1021/am502980m.
[37] J.M. Li˜
nei a del Río, E.R. L´
opez, J. Fe n´
andez, Syne gy be ween bo on ni ide o
g aphene nanopla ele s and i(bu yl)e hylphosphonium die hylphospha e ionic
liquid as lub ican addi i es o iiso idecyl imelli a e oil, J. Mol. Liq. 301 (2020),
112442, h ps://doi.o g/10.1016/j.molliq.2020.112442.
[38] S. Mia, N. Ohno, Rela ion be ween low empe a u e luidi y and sound eloci y o
lub ica ing oil, T ibol. In . 43 (2010) 1043–1047, h ps://doi.o g/10.1016/j.
iboin .2009.12.027.
[39] J.P. Bazile, D. Nas i, J.L. Da idon, Speed o sound, densi y, and de i a i e
p ope ies o T is(2-e hylhexyl) T imelli a e unde high p essu e, J. Chem. Eng.
Da a 62 (2017) 1708–1715, h ps://doi.o g/10.1021/acs.jced.7b00162.
[40] L. De Lo enzi, M. Fe meglia, G. To iano, Densi y, kinema ic iscosi y, and
e ac i e index o Bis(2-e hylhexyl) Adipa e, T is(2-e hylhexyl) T imelli a e, and
diisononyl ph hala e, J. Chem. Eng. Da a 43 (1998) 183–186, h ps://doi.o g/
10.1021/je970200z.
[41] J.C.F. Diogo, H.M.N.T. A elino, F.J.P. Cae ano, J.M.N.A. Fa elei a, T is(2-
E hylhexyl) imelli a e (TOTM) a po en ial e e ence luid o high iscosi y. Pa
II: densi y measu emen s a empe a u es om (293 o 373)K and p essu es up o
68 MPa, Fluid Phase Equilib. 384 (2014) 36–42, h ps://doi.o g/10.1016/j.
luid.2014.10.003.
[42] J.C.F. Diogo, H.M.N.T. A elino, F.J.P. Cae ano, J.M.N.A. Fa elei a, W.A. Wakeham,
T is(2-e hylhexyl) imelli a e (TOTM) as a po en ial indus ial e e ence luid o
iscosi y a high empe a u es and high p essu es: new iscosi y, densi y and
su ace ension measu emen s, Fluid Phase Equilib. 418 (2016) 192–197, h ps://
doi.o g/10.1016/j. luid.2016.01.012.
[43] W.A. Wakeham, M.J. Assael, H.M.N.T. A elino, S. Bai , H.O. Baled, B.
A. Bamgbade, J.P. Bazile, F.J.P. Cae ano, M.J.P. Comu˜
nas, J.L. Da idon, J.C.
F. Diogo, R.M. Enick, J.M.N.A. Fa elei a, J. Fe n´
andez, M.C. Oli ei a, T.V.
M. San os, C.M. Tsolakidou, Pu sui o a high- empe a u e, high-p essu e, high-
iscosi y s anda d: he case o T is(2-e hylhexyl) T imelli a e, J. Chem. Eng. Da a
62 (2017) 2884–2895, h ps://doi.o g/10.1021/acs.jced.7b00170.
[44] N. Du up , A. Aoulmi, M. Bou oukba, M. Rogalski, Hea capaci ies o liquid
polycyclic a oma ic hyd oca bons, The mochim. Ac a 260 (1995) 87–94, h ps://
doi.o g/10.1016/0040-6031(95)90478-6.
[45] C.M. Ma e, T ibology On he Small Scale: A Bo om Up App oach o F ic ion,
Lub ica ion and Wea , Ox o d Uni e si y P ess, New Yo k, 2008.
[46] M.J. Sche ze , P. Iglesias, Me a-analysis compa ing we abili y pa ame e s and he
e ec o we abili y on ic ion coe icien in lub ica ion, Lub ican s 6 (2018) 70,
h ps://doi.o g/10.3390/lub ican s6030070.
[47] M. Kalin, M. Polajna , The co ela ion be ween he su ace ene gy, he con ac
angle and he sp eading pa ame e , and hei ele ance o he we ing beha iou
o DLC wi h lub ica ing oils, T ibol. In . 66 (2013) 225–233, h ps://doi.o g/
10.1016/j. iboin .2013.05.007.
[48] D.N. Rihani, L.K. Do aiswamy, Es ima ion o hea capaci y o o ganic compounds
om g oup con ibu ions, Ind. Eng. Chem. Fundamen. 4 (1965) 17–21, h ps://doi.
o g/10.1021/i160013a003.
[49] B.E. Poling, J.M. P asni z, J.P. O’Connell, The P ope ies o Gases and Liquids, 5 h
ed., McG aw-Hill, 2001.
M.A. Coelho de Sousa Ma ques e al.
