Enhancing mel s eng h and c ys alliza ion kine ics in polylac ide:
In luence o chain opology
Ainhoa Fe n´
andez-Tena
a
, Me cedes Fe n´
andez
a,*
, Aleida J. Sando al
b
, M. I xaso Cala el
a
,
Amaia Agui e
c
, No a A anbu u
a
, Gonzalo Gue ica-Eche a ia
a
, Ma ia Lau a Di Lo enzo
d
,
Alessand a Longo
d,1
, Juan F ancisco Vega
e,*
, Alejand o J. Mülle
a, ,**
a
POLYMAT and Depa men o Ad anced Polyme s and Ma e ials: Physics, Chemis y and Technology, Facul y o Chemis y, Uni e si y o he Basque Coun y UPV/
EHU, Paseo Manuel de La dizabal 3, 20018 Donos ia-San Sebas i´
an, Spain
b
Labo a o io de P ocesamien o de Alimen os, Depa amen o de Tecnología de P ocesos Biol´
ogicos y Bioquímicos, Uni e sidad Sim´
on Bolí a , Ap do. 89000, 1080A
Ca acas, Venezuela
c
POLYMAT and Depa men o Applied Chemis y, Uni e si y o he Basque Coun y UPV/EHU, Tolosa hi ibidea 72, 20018 Donos ia-San Sebas i´
an, Spain
d
Na ional Resea ch Council (CNR), Ins i u e o Polyme s, Composi es and Bioma e ials (IPCB), c/o Comp enso io Oli e i, Via Campi Fleg ei 34, 80078, Pozzuoli, I aly
e
BIOPHYM, Depa men o Mac omolecula Physics, Ins i u o de Es uc u a de la Ma e ia (IEM-CSIC), c/Se ano 113bis, 28006 Mad id, Spain
IKERBASQUE, Basque Founda ion o Science, Plaza Euskadi 5, 48009 Bilbao, Spain
ARTICLE INFO
Keywo ds:
Polylac ide
C ys alliza ion kine ics
Long chain b anching
Compu a ional heology
FT heology
LAOS
ABSTRACT
The gene a ion o long-chain b anches (LCB) in biobased and biodeg adable polylac ide (PLA) by adding
di e en amoun s o a chain ex ende is s udied. The heological and calo ime ic beha io ha e been used o
de e mine he e ec o LCB p esence and hei opology on PLA mel s eng h and c ys alliza ion beha io .
Rheological modeling o linea and non-linea iscoelas ic shea and ex ensional p ope ies iden i ied se e al
possible b anched s uc u es. Mo eo e , ema kable di e ences we e obse ed o he di e en opologies
ega ding he in insic non-linea pa ame e s and he in a-cycle elas ic and iscous non-linea i ies. Di e en ial
scanning calo ime y and pola ized ligh op ical mic oscopy measu emen s e ealed a signi ican inc ease in he
nuclea ion densi y and a e o PLA wi h inc easing he amoun o LCB, albei hey p o oke a dec ease in he
g ow h a e due o a educ ion in chain di usion. Ne e heless, o e all c ys alliza ion a e alues e ealed a
p edominan e ec o nuclea ion o e c ys al g ow h. The in oduc ion o LCB wi hin he chains is highly
bene icial as hey inc ease nuclea ion, c ys allini y, and elonga ional iscosi y, hus imp o ing he p ope ies o
biodeg adable PLA.
1. In oduc ion
Poly(lac ic acid) o polylac ide (PLA) is a he moplas ic alipha ic
polyes e de i ed om enewable esou ces such as co n s a ch, suga
cane, and o he enewable biomass p oduc s and was e [1]. Due o i s
compe i i e p ocessing cos s and i s good mechanical and physical
p ope ies [2] (e.g., high modulus, high s eng h, anspa ency, and
ba ie p ope ies), he de elopmen o biodeg adable p oduc s based
on PLA has ecei ed inc easing a en ion om bo h academia and in-
dus y and now ep esen s >10 % o he biomass-based consume
p oduc s ma ke , eme ging as a p omising subs i u e o pe oleum-
de i ed polyme s in a wide ange o commodi y and enginee ing ap-
plica ions [3], such as packaging, ex iles, cons uc ion and au omo i e
[1]. Fu he mo e, due o i s biocompa ibili y, non- oxic cha ac e is ics,
and biodeg adabili y, PLA could also be a p omising candida e o
biomedical applica ions, such as d ug deli e y, blood essels, issue
enginee ing, and sca olds [4,5]. The inc easingly u gen need o educe
dependence on pe oleum-based ma e ials ce ainly opens up ma ke
oppo uni ies o his en i onmen ally iendly polyme . This equi es
o e coming ce ain d awbacks desc ibed o PLA, which may limi i s
* Co esponding au ho s.
** Co espondence o: A. J. Mülle , POLYMAT and Depa men o Ad anced Polyme s and Ma e ials: Physics, Chemis y and Technology, Facul y o Chemis y,
Uni e si y o he Basque Coun y UPV/EHU, Paseo Manuel de La dizabal 3, 20018 Donos ia-San Sebas i´
an, Spain.
E-mail add esses: [email p o ec ed] (M. Fe n´
andez), [email p o ec ed] (J.F. Vega), [email p o ec ed] (A.J. Mülle ).
1
P esen add ess: Na ional Resea ch Council (CNR), Ins i u e o Polyme s, Composi es and Bioma e ials (IPCB), Via Paolo Gai ami 18, 95126, Ca ania (CT), I aly.
Con en s lis s a ailable a ScienceDi ec
In e na ional Jou nal o Biological Mac omolecules
jou nal homepage: www.else ie .com/loca e/ijbiomac
h ps://doi.o g/10.1016/j.ijbiomac.2024.136783
Recei ed 14 June 2024; Recei ed in e ised o m 14 Oc obe 2024; Accep ed 20 Oc obe 2024
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
A ailable online 28 Oc obe 2024
0141-8130/© 2024 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY-NC license (
h p://c ea i ecommons.o g/licenses/by-
nc/4.0/ ).
p oduc ion and use in di e en applica ions. These limi a ions a e
mainly due o PLA’s low mel s eng h and slow c ys alliza ion a e,
making i s p ocessabili y di icul and educing he mal esis ance [4].
The mel s eng h o a polyme is mainly de e mined by he deg ee o
chain en anglemen , which inc eases wi h molecula weigh (MW),
molecula weigh dis ibu ion (MWD), and long chain b anching (LCB).
PLA ypically has a mode a e molecula weigh , MW <200 kg/mol, and
a s ong endency o unde go hyd olysis a empe a u es abo e he
mel ing poin , u he dec easing molecula weigh and, hus, heolog-
ical p ope ies [5]. I is, he e o e, necessa y o keep he molecula
weigh a high le els o compe e wi h con en ional polyme s such as
polyp opylene (PP) and polys y ene (PS) (MW ~ 240–800 kg/mol) o
accep able heological and p ocessing pe o mance. Among he many
a emp s ha ha e been made o inc ease he s eng h o polyme mel s,
modi ying polyme s o ob ain b anched s uc u es capable o main-
aining a high molecula weigh has p o en o be an e ec i e app oach
o sol ing his p oblem [6].
LCB signi ican ly imp o es he physical s eng h o polyme mel s.
E en o small amoun s, signi ican changes in he mel ’s heological,
he mal, and mechanical p ope ies ha e been epo ed [7,8]. Thus,
a ious ypes o mul i- unc ional monome s, including mul i- unc ional
alcohol, isocyana es, phenyl phosphi es, and epoxides, a e epo ed o
be used o enhance mel s eng h, al hough in some cases, chain
ex ension, a he han LCB o ma ion, domina es [9]. Especially ele an
is he use o mul i- unc ional s y ene-ac ylic epoxide chain ex ende s
unde he ade name Jonc yl®. Such ex ende s ha e p o en o be e y
use ul in imp o ing mel s eng h and iscosi y, es o ing molecula
weigh , and con olling deg ada ion o e a wide ange o p ocessing
empe a u es and o a ious polyme s [10], including p o en e icacy
in PLA. In pa icula , ADR g ade 4368 has been shown o ac as a chain
ex ende ha imp o es PLA’s iscoelas ic and heological p ope ies
[11,12] and could also accele a e he c ys alliza ion a e [10,13,14].
Se e al wo ks epo ha b anching s uc u es can signi ican ly
imp o e he c ys alliza ion o PLA since g a ing poin s can ac as
nuclea ing si es [13], inc easing he nuclea ion a e and densi y
[13–17]. Ne e heless, a de imen al e ec o b anches on he p ima y
nuclea ion o PLA has also been epo ed [18]. Mo eo e , he e a e
disc epancies in how b anches a ec he seconda y nuclea ion and
o e all c ys alliza ion o PLA [13,14,19]. I has also been obse ed ha
b anched polyme s wi h di e en opologies (s a , combs, H-shaped,
hype -b anched…) could a ec he c ys alliza ion o PLA di e en ly. Liu
e al. [17] concluded ha H-shaped b anches we e he mos e ec i e
chain s uc u es o imp o ing he nuclea ion o PLA. Nou i e al. [15]
obse ed ha hype -b anched PLAs display he as es o e all c ys al-
liza ion a e. S a -like PLAs and, inally, comb-like s uc u es showed
he lowes c ys alliza ion a e, albei all o hem displayed a as e
c ys alliza ion a e han hei linea homolog. Indeed, ew wo ks co e
he e ec o b anches on PLA’s nuclea ion, g ow h, and o e all c ys-
alliza ion kine ics [13,17,19,20]. In hose wo ks, nuclea ion is only
s udied quali a i ely ( h ough di ec PLOM obse a ions), and sphe u-
li ic g ow h a e (G) s. c ys alliza ion empe a u e (T
c
) plo s a e no
always p o ided.
The e o e, he s udy o he gene a ion o long-chain b anching by he
addi ion o Jonc yl® and, in pa icula , he e ec ha di e en con-
cen a ions and b anching opology p oduce on mel s eng h and
desi ed c ys alliza ion p ope ies is o g ea in e es o de elop he po-
en ial o PLA in hose applica ions ha equi e mel p ocessing and
dimensional s abili y. Taking his challenge as he main objec i e, his
wo k will add ess he s uc u al changes p oduced by eac i e ex usion
using Jonc yl®ADR as a chain ex ende in a comme cially a ailable PLA
and hei e ec s on PLA’s elonga ional beha io and c ys alliza ion. The
p oduc s ob ained we e ully cha ac e ized by se e al me hods, using
size-exclusion ch oma og aphy (SEC), di e en ial scanning calo ime y
(DSC), wide-angle X- ay sca e ing (WAXS), and heological me hods in
linea and non-linea egimes. Using low concen a ions o Jonc yl®
esul ed in sub le s uc u al modi ica ions. A he same ime, a highe
amoun was su icien o subs an ially modi y he ini ial p oduc ,
esul ing in a b anched s uc u e wi h s ain-ha dening p ope ies and a
signi ican inc ease in he c ys alliza ion a e.
The a icle is o ganized in o wo pa s. Fi s , an expe imen al heo-
logical s udy assis ed wi h compu a ional calcula ions based on ep a-
ion concep s is p esen ed. This pa o he wo k includes expe imen al
da a combining ex ensional, linea , and non-linea shea heology.
Rele an in o ma ion abou he exis ence o he LCB s uc u es and he
quan i a i e in o ma ion on chain opology and chain ac ions ha e
been ob ained in de ail o he i s ime by combining compu a ional
modeling and expe imen al da a. Then, we add ess he non-linea low
o linea and b anched opologies using he speci ic signa u e o he
la ge ampli ude oscilla o y shea (LAOS) es [21]. This app oach has
allowed us o unde s and be e molecula a chi ec u e’s e ec on he
PLA’s low p ope ies. The da a a e analyzed by Fou ie T ans o m
Rheology (FTR), which allows o quan i a i e assessmen o he non-
linea esponse in insic o he polyme s uc u e. The in e p e a ion
in e ms o he well-known non-linea elas ic beha io (s i ening-so -
ening) and non-linea iscous beha io ( hickening- hinning) is in es-
iga ed by he s ess signal decomposi ion (SD) me hodology coupled
wi h Chebyshe polynomials [22]. Ou esul s and analysis e ealed he
exis ence o di e en molecula a chi ec u es, e en in a PLA sample wi h
he smalles amoun o chain b anching, o he i s ime.
Mo eo e , he second pa o he wo k is de o ed o a ho ough
in es iga ion o he e ec s o LCB on PLA c ys alliza ion. P ima y
nuclea ion, seconda y nuclea ion, and o e all c ys alliza ion kine ics
we e s udied in de ail by DSC and pola ized ligh op ical mic oscopy
(PLOM). The mal ansi ions and c ys alliza ion kine ics e ealed a
s ong in luence o LCBs on he c ys alliza ion o PLA. The sepa a e
impac o LCB on p ima y nuclea ion and c ys al g ow h has been
ob ained.
2. Expe imen al pa
2.1. Ma e ials
A highly s e eo egula PLA con aining <1 % D-isome couni s and
wi h a mel low index o 8 g/10 min (210 ◦C/2.16 kg), g ade name L-
175, was kindly p o ided by To al Co bion (The Ne he lands).
Jonc yl® ADR-4400 mul i- unc ional eac i e polyme was kindly
p o ided by BASF (Ge many). I has a mola mass o M
w
=7.1 kg/mol,
glass ansi ion empe a u e (T
g
) o 65 ◦C, and epoxy equi alen weigh
o 485 g/mol.
2.2. Sample p epa a ion
Be o e p ocessing, he plain polyme s we e d ied in an o en a 60 ◦C
unde acuum o e nigh . Blends and nea PLA we e p ocessed using a
The mo Haake MiniLab win-sc ew ex ude ope a ing in ba ch mode a
180 ◦C and 100 pm, wi h a mixing ime o 4 min, su icien o a ain
pla eau o que alue.
2.3. Cha ac e iza ion me hods
2.3.1. Size-exclusion ch oma og aphy (SEC) measu emen s
The mola mass and b anching deg ee o he polyme s we e analyzed
by Size-Exclusion Ch oma og aphy de ec ion (SEC/TD). The equipmen
was composed o an LC20 pump (Shimadzu) coupled o a DAWN Heleos
mul iangle (18 angles) ligh -sca e ing lase pho ome e equipped wi h a
He
–
Ne lase (λ =658 nm), an Op ilab Rex di e en ial e ac ome e (λ
=658 nm), and Viscos a di e en ial iscome e (all om Wya
Technology Co p., USA). The equipmen used h ee columns in se ies
(S y agel HR2, HR4, and HR6, wi h po e sizes om 10
2
o 10
6
Å). The
analyses we e pe o med a 35 ◦C, and THF was used as he mobile phase
a a low a e o 1 mL/min. The polyme s we e dilu ed in HPLC-g ade
THF a 4 mg/mL concen a ions, and he dn/dc employed was 0.042
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
2
mL/g.
2.3.2. Fou ie ans o m a enua ed o al e lec ion in a ed spec oscopy
(FTIR-ATR)
Fou ie T ans o m In a ed Spec oscopy analyses we e conduc ed
using a Pe kinElme FTIR Spec um 100 spec ome e equipped wi h a
Pe kinElme ATR accesso y wi h a diamond c ys al. Each spec um is an
a e age o 16 indi idual scans, eco ded wi h a esolu ion o 4 cm
−1
.
FTIR-ATR spec a we e used o alida e he eac ion be ween PLA and
Jonc yl®, wi h esul s de ailed in he SI ile as Fig. S1.
2.3.3. Rheological cha ac e iza ion
La ge ampli ude (LAOS) and small ampli ude (SAOS) dynamic
oscilla o y shea in linea and non-linea egimes and ansien shea
measu emen s we e pe o med wi h a s ain-con olled ARES-G2
Rheome e (TA Ins umen s) using a pa allel pla e geome y wi h 25 mm
o diame e and a spacing gap o app oxima ely 0.8 mm. Good ep o-
ducibili y was ob ained using he same he mal ea men consis ing o
mel ing he sample o 3 min a T =185 ◦C be o e he expe imen s a he
empe a u e o in e es .
Be o e measu emen s, samples we e d ied a 75 ◦C o 24 h in a
acuum o en. All measu emen s we e pe o med in an N
2
a mosphe e o
a oid deg ada ion du ing he expe imen s.
2.3.3.1. Dynamic shea iscosi y in he SAOS egime. The dynamic shea
iscosi y in he SAOS (small ampli ude oscilla o y shea ) egime was
s udied om equency sweep es s anging om 0.1 o 100 Hz a a small
s ain ampli ude wi hin he linea iscoelas ic egime and empe a u es
om 155 o 185 ◦C. The mas e cu es we e ob ained using he ime-
empe a u e supe posi ion p inciple [23,24] (Fig. S2a and Fig. S2b).
The da a we e shi ed along he equency axis, and he ho izon al shi
ac o s o all PLA samples we e i ed wi h he A henius unc ions:
aT=Ea
R(1
T e −1
T), wi h T
e
=175 ◦C. An ac i a ion ene gy o low
inc easing sligh ly om PLA o PLA1.5 was ob ained (Fig. S2c).
2.3.3.2. Elonga ional es . The ansien elonga ional low was pe -
o med in he classic s ain-con olled ARES Rheome e (Rheome ic
Scien i ic) coupled wi h he ex ensional iscosi y ix u e (EVF). The
sample shee s we e cu in o pieces wi h a wid h o 10 mm, leng h o 18
mm, and hickness o 0.8 mm. Cons an s ain a es o 0.1, 0.3, and 1 s
−1
a 175 ◦C we e applied. A p e-elonga ion o 3 s was pe o med be o e
he measu emen s o ensu e no slipping be ween he sample and he
ix u es. The p esence o he chain ex ende Jonc yl® a he lowe
concen a ions o 0.5 and 1 % did no signi ican ly imp o e he de o -
ma ion beha io o PLA, while o PLA1.5, s ain ha dening was
obse ed (Fig. S3). Thus, he elonga ional iscosi y cu es ob ained o
PLA0.5 and PLA1 did no o e a signi ican di e ence wi h espec o he
linea PLA sample and we e no included in he expe imen al da a se o
modeling he heological-s uc u al ela ionship. The s ain ha dening
cu es o he PLA1.5 sample we e analyzed o deduce he mos p obable
b anching opologies.
2.3.3.3. T ansien non-linea shea . Expe imen al s a -up low cu es
we e pe o med a di e en applied shea a es in he 0.01 o 50 s
−1
ange a T =175 ◦C. En angled polyme s a e expec ed o gi e a e y ich
esponse, which depends on he ime scale o he applied low and he
elaxa ion imes o he chains. The esponse can be e y complex in he
case o b anched polyme s, as he b anches and he backbone ha e
di e en elaxa ion imes [25].
2.3.3.4. La ge ampli ude oscilla o y shea (LAOS). The non-linea
dependence o he s ess esponse on s ain was e alua ed om s ain
sweep es s in he MAOS (medium ampli ude oscilla o y shea ) and
LAOS (la ge ampli ude oscilla o y shea ) egimes a T =175 ◦C and
di e en equencies om 0.05 o 5 Hz. Be o e applying quan i a i e
analy ical echniques, he ob ained da a can be ep esen ed in he o m
o Lissajous-Bowdi ch (L-B) cu es, allowing a isual inspec ion o he
non-linea esponse o ma e ials subjec ed o la ge de o ma ions. Fig. S4
shows he da a measu ed a each imposed equency; (a) he elas ic
Lissajous–Bowdi ch cu es ep esen he pe iodic s ess esponse a
s eady s a e plo ed agains s ain,
σ
( ) s γ( ),and (b) he iscous Lis-
sajous–Bowdi ch cu es ep esen he s ess as a unc ion o s ain a e,
σ
( ) s ˙γ( ). The ellip ical shape o he cu es accoun s o he iscoelas ic
beha io so ha he non-linea lows simul aneously cause dis o ions o
he elas ic and iscous pa hs. The closed-loop plo s showed no signi i-
can di e ences among he samples s udied a low de o ma ions. How-
e e , when s ong elas ic non-linea i y occu s a high de o ma ions, he
Lissajous s ess e sus s ain a e cu es showed a double loop o nea
PLA, PLA0.5, and PLA1.0, which was no obse ed o he PLA1.5
sample. This sel -in e sec phenomenon has been epo ed in many
LAOS analyses o a ious sys ems and cons i u i e models [26]. Physi-
cally, such s ong elas ic non-linea i y would co espond o a non-linea
iscoelas ic shea s ess o e shoo in which exis ing s ess is unloaded
mo e quickly han new de o ma ion is accumula ed. This a ionaliza ion
o he LAOS esponse has been es ed in a ious molecula con igu a-
ions and mic os uc u es, such as polyme solu ions, polyme mel s,
so glassy ma e ials, and o he s uc u ed luids [27]. Howe e , he
in e p e a ion o he p esence o seconda y lows has been limi ed o he
s udy o speci ic ma e ials, gene ally ela ed o he absence o long-chain
b anching in polyme mel s. Howe e , seconda y loops ha e also been
obse ed o s a -polyme ne wo ks [27]. Rega ding he beha io o he
PLA samples o he p esen s udy, he p esence o seconda y lows will
no be conside ed a decisi e esul since hey we e only ound o he
highes s ains and equencies, whe e he e ec o ce ain low in-
s abili ies canno be uled ou . The e o e, he s udy o he di e en
s uc u es in hese samples will be app oached by applying di e en
calcula ions o he LAOS da a using he disc e e Fou ie ans o ma ion
me hodologies (see Suppo ing In o ma ion, sec ion S5).
2.3.4. Pola ized ligh op ical mic oscopy (PLOM)
The sphe uli ic nuclea ion and g ow h we e measu ed using pola -
ized ligh op ical mic oscopy (PLOM). To ha end, iso he mal mea-
su emen s we e pe o med in an Olympus BX51 PLOM (Tokyo, Japan)
equipped wi h an Olympus SC50 digi al came a and a Linkam-15 TP-91
ho s age. Films wi h a ound 10
μ
m we e p epa ed by mel ing he
samples be ween wo glass slides. Measu emen s we e conduc ed as
ollows: i s , he he mal his o y o he ma e ial was e ased by keeping
he sample a 200 ◦C o 3 min. Then, samples we e cooled down o a
selec ed c ys alliza ion empe a u e (T
c
) a 50 ◦C/min and main ained a
ha T
c
while sphe uli es appea ed and g ew. This p o ocol was epea ed
a se e al T
c
s o each sample.
The nuclea ion kine ics was de e mined by coun ing he numbe o
ac i e nuclei ha appea ed in a speci ic a ea a a selec ed T
c
as a unc ion
o ime. I was assumed ha each sphe uli e g ew om a single ac i e
nucleus. Simila ly, he sphe uli ic g ow h kine ics o each sample we e
de e mined by measu ing he adius o he sphe uli es as a unc ion o
ime a di e en T
c
s. The sphe uli ic g ow h a e (G) could be calcula ed
om he adius e sus ime plo s a each T
c
. A leas h ee sphe uli es
we e measu ed o each epo ed G alue.
2.3.5. Di e en ial scanning calo ime y (DSC)
Calo ime ic s udies we e conduc ed in a Pe kin Elme DSC800
calo ime e (Wal ham, MA, USA) unde an ul ahigh-pu i y ni ogen
a mosphe e wi h a 20 mL/min low. Indium and in s anda ds we e used
o calib a e he equipmen , and sample amoun s a ound 2 mg we e used
o each measu emen .
2.3.5.1. Non-iso he mal DSC measu emen s. Fi s , he he mal his o y o
he samples was e ased by main aining he samples a 200 ◦C o 3 min.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
3
Then, samples we e cooled down o 25 ◦C a 20 ◦C/min, kep a 25 ◦C o
1 min, and hen hea ed o 200 ◦C a he same a e. F om he eco ded
cooling and hea ing scans, he mel ing (T
m
), cold c ys alliza ion (T
cc
),
and c ys alliza ion (T
c
) peak empe a u es, as well as he en halpies o
he co esponding ansi ions, we e de e mined. Fo he calcula ion o
he deg ee o c ys allini y (X
c
) o each sample, a alue o 107 J/g was
conside ed as he mel ing en halpy o 100 % c ys alline PLA [28], which
co esponds o he mel ing en halpy o 100 % c ys alline PLLA in he
α
′
-c ys al o m. This alue was chosen conside ing ha he empe a u e
ange a which PLA c ys als g ow in he cu en wo k is ypical o he
α
′
-modi ica ion.
2.3.5.2. Iso he mal measu emen s. The o e all c ys alliza ion kine ics
we e s udied using iso he mal DSC expe imen s. The measu emen s
we e pe o med acco ding o he p ocedu e p oposed by Mülle e al.
[29,30]: i s , he he mal his o y o he samples was e ased by keeping
hem a 200 ◦C o 3 min. Then, samples we e quenched a 60 ◦C/min o
a selec ed T
c,
and he iso he mal c ys alliza ion was conduc ed un il i
eached sa u a ion. Finally, samples we e hea ed o 200 ◦C a 20 ◦C/min.
The expe imen was epea ed o se e al T
c
alues. The appa en mel ing
poin s we e de e mined om hea ing uns pe o med immedia ely a e
iso he mal c ys alliza ion, om T
c
o comple e mel ing. These alues
we e used o ca y ou he Ho man-Weeks [31] ex apola ion and, hus,
calcula e he equilib ium mel ing empe a u e (T
m
0
).
2.3.6. Wide-angle X- ay sca e ing (WAXS)
A Philips X’pe PRO au oma ic di ac ome e was used o collec
he X- ay powde di ac ion pa e ns a oom empe a u e. The equip-
men ope a ed a 40 kV and 400 mA, in he a- he a con igu a ion, wi h a
seconda y monoch oma o wi h Cu-K
α
adia ion (λ =1.5418 Å) and a
PIXcel solid s a e de ec o (ac i e leng h in 2θ =3.347◦). Da a we e
collec ed be ween 5 and 70◦2θ (s ep size =0.026◦and ime pe s ep =
180 s) du ing a o al da a collec ion ime o 30 min. A a iable di e -
gence sli , which p o ided a cons an 8 mm a ea o sample illumina ion,
was used.
3. Resul s
3.1. Rheological cha ac e iza ion
3.1.1. Topological cha ac e iza ion: compu a ional linea and non-linea
heology
Chain eac ions occu in polyes e s such as PLA due o b idging he
hyd oxyl o ca boxyl end g oups wi h unc ional compounds such as
Jonc yl®. The eac ion esul is due o epoxide ing-opening e en s in
he Jonc yl® molecule and he p oduc ion o co alen connec ions ia
PLA’s hyd oxyl/ca boxyl end g oups [32]. Ini ially, he eac ion may
esul in an ex ension o he PLA chains, p oducing a ac ion o he
ma e ial wi h a highe molecula weigh han he pa en PLA. When
mo e PLA chains a e in ol ed in he eac ion, LCB opologies (s a s o H-
shaped) a ise, which may e en ually p oduce e en mo e complica ed
s uc u es (combs o dend ime s). SEC esul s clea ly show ha he
amoun o Jonc yl® inc eases he molecula weigh .
Fig. 1 compa es he absolu e mola mass e sus he elu ion ime o
he samples unde s udy. As can be app ecia ed, excep o nea PLA,
none o he samples p esen a mono onous dec ease o he mola mass
wi h he elu ion ime; on he con a y, mola masses inc ease a long
elu ion imes, and his e ec is mo e p onounced as he amoun o
Jonc yl inc eases. This non-ideal elu ion, also known as anomalous
elu ion, has been epo ed o b anched polyme s [33]. Some imes, his
beha io is a ibu ed o he ancho ing o b anched polyme chains in
he po es o he columns, esul ing in a la e elu ion oge he wi h
smalle polyme chains [33]. In addi ion, b anching leads o he
con ac ion o he polyme chains; he e o e, when a b anched and a
linea polyme ha e he same hyd odynamic olume, he b anched
polyme p esen s a highe mola mass. This indica es ha when
analyzing b anched polyme s by SEC, a dispe sion o polyme chains o
di e en mola masses migh elu e oge he [34,35]. The eme gence o
an asymme ic SEC ace owa ds he high-M
w
side o he dis ibu ion is
accompanied by an inc ease in M
w
alues (see Table 1).
Fig. 2 (le panel) depic s he i o he expe imen al SEC aces o
ypical peak unc ions. In he case o he nea PLA ma e ial, he i in-
dica es a log-no mal dis ibu ion, wi h an a e age molecula weigh M
w
o oughly 65 kg/mol and a polydispe si y index o D =M
w
/M
n
=1.3. A
mul ipeak i app oach yields in e es ing esul s in he emaining sam-
ples. The PLA0.5 dis ibu ion clea ly shows a pe cen age (w =0.20) wi h
a la ge molecula weigh han nea PLA, which amoun s o 140 kg/mol
on a e age (Scheme 1A). Chain s uc u e becomes mo e complica ed in
he case o PLA1.0, which has a hi d popula ion (w =0.05) wi h a
molecula weigh o a ound 260 kg/mol. The linea chain popula ion o
he ini ial PLA almos anishes when he polyme is mel p ocessed wi h
1.5 % Jonc yl® (PLA1.5), and new popula ions wi h molecula weigh s
o 270 kg/mol (w =0.18) and 512 kg/mol (w =0.05) a ise. Table 2
displays he ac ional con en , a e age M
w
, and D alues o each
ac ion in he di e en samples. Conside ing he M
wi
alues o he
di e en MWD nodes, he da a in Table 2 show ha b anched species
may eme ge (on a e age) o Jonc yl® con en s >1 %. In ac , he sec-
ond node appea s o be made up o linea molecules wi h an a e age
leng h double ha o he nea PLA sample. The hi d and ou h nodes
a e almos ce ainly b anched. The b anching s uc u e in hese nodes
migh be symme ic o asymme ic s a s, H-shaped o comb-like, and
dend i ic (Scheme 1C and D). In a e y simple scena io, he hi d node,
wi h a M
w
o abou 260–270 kg/mol, migh be made up o symme ic
s a s wi h ou b anches o 65 kg/mol o asymme ic s a s wi h wo
b anches o 65 and one o 140 kg/mol (Scheme 1B). A comb-like mo-
lecula s uc u e wi h 4 b anches o 65 kg/mol and a 260 kg/mol
Fig. 1. RI aw da a (con inuous line) and mola mass e olu ion de e mined by
SEC/MALS o he samples unde s udy.
Table 1
Molecula p ope ies o he samples unde s udy.
Sample Mn
(kg/mol)
Mw
(kg/mol)
D
Mw/Mn
PLA 51.7 65.1 1.3
PLA0.5 58.6 71.3 1.2
PLA1.0 72.1 91.6 1.3
PLA1.5 93.4 131.2 1.4
A. Fe n´
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In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
4
backbone would also be a easible opology o he ou h node, which
has a e y high M
w
o 512 kg/mol (Scheme 1D). A Cayley ee (2 gen-
e a ions) wi h 9 segmen s o a ound 60 kg/mol could also be a possible
opology o his highly b anched node o he MWD, see Scheme 1.
As i is well known, he heological p ope ies o polyme s in bo h he
linea and non-linea egimes a e ex emely sensi i e o he polyme s’
mac omolecula a chi ec u e and opology. These molecula cha ac-
e is ics a e de ined mainly by M
w
and D, bu especially by he LCB. The
p esence o LCB is highly desi able since i imp o es p ocessing by
inc easing shea hinning beha io in shea and s ain ha dening in
ex ension [36,37], bo h o which a e bene icial o a ious applica ions.
The heological p ope ies o he PLA molecules in he sys ems unde
s udy should hen e lec he exis ence o he newly c ea ed species,
ega dless o hei opology.
We ha e used he b anch-on-b anch (BoB) heology so wa e o model
polyme heology using he molecula ensemble p o ided by he SEC
ace and, in a i s app oach, he molecula popula ions men ioned
abo e [38–40]. BoB employs algo i hms based on he ex ended ube
model o calcula e he heological esponse o polyme mel s, encom-
passing bo h linea and non-linea egimes, i espec i e o polyme a -
chi ec u e. This me hod es ablishes a connec ion be ween molecula
s uc u e and heological p ope ies. The chemical cha ac e is ics o
monome s a e e ec i ely cap u ed by wo key pa ame e s: one
ep esen ing he en anglemen leng h (en anglemen mola mass, M
e
)
and a ime scale (en anglemen elaxa ion ime,
τ
e
). In he ini ial phase
o he calcula ion, a mac omolecula ensemble is gene a ed, e aining
he chain connec i i y and mola mass. This s ep is de i ed om
examining he chemical eac ion scheme and analyzing expe imen al
GPCLS da a (Table 2). The algo i hm’s accu acy has been e i ied
h ough alida ion wi h expe imen al da a om model polyme s o
di e se chemis ies and a chi ec u es [40]. The model pa ame e s,
including he dynamic dila ion exponen
α
=1, e lec ing he en an-
glemen ea u es’ beha io wi h dilu ion, and p
2
=1/40, connec ed o
he ac ion o ube diame e he b anch poin a e ses on a e age
du ing each segmen /b anch e ac ion ime, ha e been de e mined
based on hei op imal pe o mance ac oss di e en polyme ic chemis-
ies and a chi ec u es [40]. Conside ing di e en alues o
α
and p
2
may lead o a ia ions in he chosen alues o M
e
and
τ
e
. The e o e, we
adhe e o he o iginal esul s om Das’s wo k, which ha e unde gone
es ing ac oss a wide ange o ma e ials [40]. We should adhe e o he
undamen al p inciple o he ep a ion heo y, which is o uphold he
uni e sali y o polyme elaxa ion mechanisms.
The nume ical ensembles o polyme molecules we e cons uc ed
using he abo e assump ions o he a ious popula ions de i ed om
he MWD mul i i app oach. To s udy he e ec o modes weigh ac-
ions o highly b anched species, we c ea ed 40,000 molecules. Then,
Fig. 2. LEFT: SEC aces wi h decon olu ion o he samples unde s udy. The g ay ba s indica e he app oxima e loca ion o he peaks co esponding o each ac ion.
RIGHT: Expe imen al linea iscoelas ic esponse a 175 ◦C o each sample (symbols – squa es, G’, ci cles, G" and iangles, |
η
*
|). Solid lines ep esen he compu ed
heological esponse o he samples wi h pa ame e s in Table 2 and he discussed opology in he ex . Dashed lines ep esen he compu ed esponse o symme ic
s a s (b, c) and Cayley (d) molecules. Do ed lines ep esen he beha io o linea PLA.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
5
using he BoB so wa e, he disc e e dis ibu ions o molecules o
di e en mola masses wi h he assumed opology we e di ec ly used o
de e mine heological pa ame e s. The compu a ions equi e he den-
si y, aken as
ρ
=1.16 g/cm
3
, and he wo chemis y-dependen quan-
i ies, M
e
and
τ
e
. Un o una ely, li e a u e epo s on undamen al
p ope ies like M
e
o C
∞
o PLAs se iously disag ee. In ac , he li e a u e
da a o M
e
o PLA a e a iable, be ween 4000 and 10,500 g/mol. [41].
Thus, we ha e used he expe imen al linea esponse o nea PLA sample
o de e mine bo h M
e
and
τ
e
. The bes i ob ained o he linea PLA
sample gi es alues o M
e
=4500 g/mol and
τ
e
=6.5 ×10
−7
s. The alue
o M
e
is well wi hin he mos accep ed alue o en anglemen molecula
weigh o PLA [42], and he
τ
e
alue desc ibes well he alue o he c oss-
poin moduli, G
x
=G’ =G”.
Table 2 ( igh panel) shows he indings o he compu ed linea
heological p ope ies compa ed o he expe imen s a T =175 ◦C o all
he samples using he same se o M
e
,
τ
e
pa ame e s. The beha io o he
linea PLA sample is ep esen ed by he do ed lines in all igu es. In all
samples wi h Jonc yl®, a clea shi o he iscoelas ic inge p in o
lowe equencies is ob ained. As he amoun o Jonc yl® inc eases, so
does he shi o lowe angula equencies. In e es ingly, despi e he
simplici y o he assump ions we made o he opology o he c ea ed
species, he consis ency be ween he expe imen al indings and he
model (solid lines) is excellen .
F om he esul s o his compu a ional exe cise, some in e es ing
conclusions can be d awn:
(1) Fo a low Jonc yl concen a ion (0.5 %), he exis ence o
b anched species is deemed unnecessa y o accoun o he
obse ed linea iscoelas ic beha io . Ini ially, we applied he
model assuming solely linea species (depic ed by he solid line in
Fig. 2b, igh panel). This calcula ion eplica es he iscoelas ic
esponse ha would be expec ed i a pe cen age o high molec-
ula weigh ma e ial (w =0.2), wi h wice he molecula weigh
o he o iginal PLA, is p esen . This esul implies ha a low
Jonc yl® con en does no inhe en ly lead o he p esence o LCB.
Howe e , an al e na i e scena io whe e he second node o he
dis ibu ion comp ises symme ic 3-s a s uc u es (b anches o
app oxima ely 47 kg/mol) also ep oduces he heological
esponse obse ed wi hin he expe imen al equency window
(depic ed by he dashed line in Fig. 2b, igh panel). Conse-
quen ly, he possibili y o a small ac ion o b anched species
canno be conclusi ely uled ou . The addi ional ac ion o ei he
linea o b anched molecules e a ds he linea esponse by
app oxima ely i e imes compa ed o ha o he nea PLA
sample.
(2) LCB occu s when he Jonc yl® con en is 1 % o g ea e . Ac-
co ding o linea heology, asymme ic s a b anches a e mos
likely c ea ed i s . When a opology wi h ou symme ic
b anches is conside ed, he calcula ed linea heology does no
each he expe imen al low- equency zone (dashed lines in
Fig. 2c, igh panel). I should be emphasized ha , in his case, he
G’ unc ion allowed us o dis inguish be ween he wo selec ed
choices o b anch s uc u es. In his scena io, he p esence o only
5 % o ha asymme ic s a species causes he heological esponse
o be delayed by one equency decade compa ed o he nea PLA
sample.
(3) Fo a 1.5 % Jonc yl con en , asymme ic s a molecules and a
mino ac ion o H-shaped o comb-like s uc u es a e s ill p o-
duced. This is signi ican since i has been demons a ed in he
li e a u e ha s a s LCB opology is insu icien o impose a
Scheme 1. Possible s uc u es be ween PLA and Jonc yl® (Jonc yl is mul i- unc ional, bu in his scheme, a unc ionali y o 3 is conside ed o each molecule).
Table 2
Mul ipeak i esul s ob ained o he samples unde s udy. Each node is a log-
no mal unc ion wi h he indica ed M
w
and polydispe si y index (M
w
/M
n
).
Sample M
w1
[kg/
mol]
D
1
M
w2
[kg/
mol]
D
2
M
w3
[kg/
mol]
D
3
M
w4
[kg/
mol]
D
4
PLA 65 1.3 – – – – – –
PLA0.5 65
(w =
0.8)
1.2 140
(w =
0.20)
1.2 – – – –
PLA1.0 65
(w =
0.80)
1.2 130
(w =
0.15)
1.1 256
(w =
0.05)
1.2 – –
PLA1.5 65
(w =
0.15)
1.2 90
(w =
0.62)
1.1 270
(w =
0.18)
1.3 512
(w =
0.05)
1.1
The weigh ac ion o each componen is indica ed in b acke s.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
6
s ain-ha dening ea u e on he sample, as he beha io obse ed
in ex ensional low is simila o ha o linea polyme s [43,44]
[43,44] ins ead, he opology should be comb-like o e en
b anch-on-b anch (dend i ic o Cayley ee) [45]. A Cayley ee
ac ion (2 gene a ions, as in Scheme 1D) wi h segmen s a ound
60 kg/mol gi es ise o undis inguishable linea heology (dashed
lines in Fig. 2d, igh panel). The e ec o his ype o comb o
b anch-on-b anch species is eno mous in his scena io. When
compa ed o he linea PLA, he p esence o s a molecules (22 %)
and comb-like o Cayley ee molecules (5 %) delays he linea
heology o he sample by mo e han wo decades (Fig. 2d, igh
panel). Ex ensional p ope ies should be explo ed in his case o
disc imina e be ween he di e en opologies.
Using he same molecula ensembles and ma e ial pa ame e s, i is
also possible o compu e he non-linea iscoelas ic p ope ies in shea
and ex ensional s a -up expe imen s. The compa ison be ween he
expe imen al and compu a ional esul s can be obse ed in Fig. 3.
Fig. 3a shows he ansien shea iscosi y ob ained in expe imen s a
175 ◦C o PLA0.5, PLA1.0 and PLA1.5 samples a shea a es be ween
0.05 and 20 s
−1
. The e ec o LCB, in his case, is clea ly seen, as i in-
duces a s ong shea hinning in PLA1.5 (combs/Cayley b anches) bu
only sligh ly a ec s PLA1.0 (s a b anches). On he con a y, he PLA0.5
sample emains closely New onian in he shea a e ange explo ed.
Mo eo e , wi h he assumed opological cons ain , he compu a ional
model nicely cap u es he expe imen al beha io .
Fig. 3b shows he expe imen al esul s ob ained om s a -up uni-
axial ex ension measu emen s in he case o PLA1.5 sample a wo
di e en s ain a es and 175 ◦C. As expec ed, he s ain ha dening
beha io is clea in his case, likely due o he b anch-on-b anch s uc-
u es p esen (5 % o comb/Cayley molecules). In e es ingly, consid-
e ing only a 5 % high-M
w
ac ion o comb molecules, he compu a ion
model ag ees e y well wi h he expe imen s (solid lines). This is no he
case o he Cayley ee model, o which he s ain ha dening ac o is
much lowe (do ed lines) han in he case o comb molecules, especially
o he highes s ain a e o 1 s
−1
. This esul has u ned ou o be e y
in e es ing, as i means ha he combina ion o expe imen s and heo-
logical modeling may help o disc imina e among di e en possible
b anched s uc u es in he samples.
3.1.2. S uc u al in o ma ion p o ided by he analysis o la ge ampli ude
oscilla o y shea (LAOS)
La ge ampli ude oscilla o y shea (LAOS) es s a e widely used o
cha ac e ize complex luids due o hei abili y o cap u e a e y b oad
spec um o he iscoelas ic esponse. This is achie ed by a ying he
ampli ude and he equency o he applied s ain. In oscilla o y ex-
pe imen s in which he s ain is con olled unde condi ions o linea
iscoelas ici y, i.e., a su icien ly small s ains, a sinusoidal s ain [γ( )
=γ
0
sin(
ω
)] is applied and a s ess esponse is ob ained which is also
sinusoidal [
σ
( ) =
σ
0
sin(
ω
)], such ha he s ess ampli ude,
σ
0
, and he
s ain ampli ude, γ
0
, ha e a linea ela ionship. Howe e , i he applied
s ain inc eases and exceeds he limi o linea iscoelas ici y, he s ess
unc ion is dis o ed, and mo e ha monics, in addi ion o he unda-
men als, a e necessa y. The complexi y o a mul i-ha monic esponse
makes i di icul o co ela e he non-linea esponse wi h he molecula
s uc u e, so he ocus has been placed on he medium ampli ude
(MAOS) zone, i.e., in he in e media e zone be ween he small ampli ude
(SAOS) and la ge ampli ude (LAOS) egimes, whe e he non-linea low
is due only o he appea ance o he hi d ha monics. In pa icula , i has
been epo ed ha he hi d ha monic analysis has been success ully
used o iden i y he esponse o he LCB e sus he linea chain s uc-
u es, e en in hose sys ems whe e no signi ican changes in he linea
iscoelas ic egime we e obse ed [46–49].
3.1.2.1. In insic non-linea i y esponse in he MAOS egime. The analysis
o he non-linea esponse o MAOS has become conside ably mo e
e icien due o he in oduc ion o he new concep o in insic non-
linea i y. This app oach has p o en e y ele an in he s uc u al
cha ac e iza ion o polyme s con aining LCB. The me hodology p o-
posed by Hyun e al. [49] is based on he expe imen al obse a ion ha
he hi d ha monic in ensi y, I
3/1
(
ω
,γ
0
) =
σ
3
/
σ
1
, i.e., he in ensi y o he
hi d ha monic,
σ
3,
no malized by he in ensi y o he undamen al,
σ
1,
scales quad a ically wi h he s ain ampli ude, γ
0,
in he MAOS egime,
I
3/1
~ γ
0
2
. The slope o 2 has been ob ained in expe imen s and simula-
ions o linea polyme s. S ill, some b anched polyme s [49] showed a
slope sligh ly <2, e en hough he pom-pom cons i u i e model p edic s
Fig. 3. S a -up expe imen s in shea (a) and uniaxial ex ension (b) o he di e en samples a he indica ed shea and s ain a es and T =175 ◦C. The do ed g ay
line co esponds o he linea iscoelas ic en elope.
A. Fe n´
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In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
7
ha he slope o I
3/1
is 2 o H-shaped b anched polyme s [50], and also
an expe imen al slope o 2 is ob ained o combs and linea PS model
polyme s [51] and 3-a m s a 1,4-cis-polyisop ene [52]. These di e -
ences can be explained based on he expe imen al di icul ies in
obse ing slope 2 a e y low de o ma ions, whe e he hi d ha monic
signal is e y noisy. Using his scaling ela ion, a non-linea pa ame e is
de ined as Q=I3/1
γ02 . When e alua ed a ela i ely small s ains, his
pa ame e Q esul s in a cons an pa ame e (simila o New onian is-
cosi y), which allows o de ine a ze o-s ain non-linea i y, Q
0
, as
limγ0→0Q≡Q0 [46]. The cons an alue o Q
0
does no mean ha non-
linea i y disappea s bu ha i emains cons an a low s ains, so he
Q
0
coe icien e lec s he inhe en non-linea p ope ies o he ma e ials
[47]. The quan i ica ion o hese non-linea coe icien s (Q and Q
0
) o
linea and chain-ex ended PLA is p esen ed in he Suppo ing In o ma-
ion (see Fig. S6 and Fig. S7).
The analysis o I
3/1
as a unc ion o s ain ampli ude a equencies
om 0.1 o 3 Hz is included in he Suppo ing In o ma ion (see Fig. S7).
As can be seen, he slope o I
3/1
is con i med o be 2 in all cases, and he
alues o Q
0
ha e been calcula ed o he di e en equencies, as shown
in Fig. S8. In cases whe e Q
0
was no ob ained di ec ly, he possibili y o
using a C oss- ype equa ion was conside ed by analogy wi h he New-
onian iscosi y de e mina ion.
These esul s show ha he MAOS and LAOS egions a e e y
di e en depending on he Jonc yl® con en , which ag ees wi h esul s
epo ed o b anched polyme s whe e he equency dependence o Q
0
is e y sensi i e o he molecula a chi ec u e. Linea , 3-a m s a , and
comb s uc u es ha e been desc ibed in he MAOS egion by di e en
non-linea Q
0
(
ω
) s De cu es acco ding o he elaxa ion modes o hese
complex s uc u es [53]. A he lowe equencies (De <1), Q
0
(
ω
) scales
quad a ically wi h equency [Q
0
(
ω
) ∝
ω
2
], while o he highe e-
quencies (De >1), i has been expe imen ally desc ibed o scale as Q
0
(
ω
)
∝
ω
k
, wi h k −0.35. A De =1, a maximum Q
0
(≡Q
0max
) is epo ed. The
esponse is e en mo e complex in he case o b anched species, and wo
dis inc Q
0max
peaks ha e been epo ed. The wo peaks we e a ibu ed
o he co esponding elaxa ion o he b anches a he highe equencies
and he backbone a he lowe equencies.
Fig. 4 shows he Q
0
da a e sus equency o he PLA samples. The
ypical e minal scale a low equencies Q
0
~
ω
2
was only obse ed o
nea PLA. Fo he ex ended-chain PLA samples con aining b anched
species (see sec ion 3.1), PLA1.0 and PLA1.5, he e minal egion is no
obse ed, and PLA0.5, unexpec edly, showed simila Q
0
da a o PLA1.0
and PLA1.5. Be o e con inuing wi h he discussion, i should be no ed
ha hese esul s should be aken wi h some cau ion since, on he one
hand, he ea ed PLA samples a e a he e ogeneous mix u e o linea and
b anched species o di e en opologies, which undoub edly makes
in e p e a ion di icul . On he o he hand, he expe imen al esul s we e
only ob ained a one empe a u e, which conside ably educed he
accessible equency ange so ha only a pa o he Q
0
(
ω
) esponse is
obse ed. Howe e , he ema kable di e ences be ween nea PLA and
chain-ex ended PLA samples show ha he e ec o he b anching
con en plays an impo an ole. The PLA0.5, PLA1.0, and PLA1.5
showed wo pla eaus, which could indica e he elaxa ion p ocesses
ela ed o he p esence o b anched and linea species. The esul is
simila o ha ound o 3-a m s a -b anched polyisop ene [52], whe e
he wo pla eaus o Q
0
we e a ibu ed o he elaxa ion o he b anches
and he main chain.
3.1.2.2. Elas ic and iscous in a-cycle non-linea esponses. The hi d
ha monic’s no malized in ensi y is a sensi i e indica o o non-linea i y,
capable o iden i ying di e en molecula s uc u es, as discussed in he
p e ious sec ion. A combina ion o FT me hodology and Chebyshe
decomposi ion can also be applied o e eal e en mo e in o ma ion
con ained in he non-linea esponse. The me hodology allows he
analysis o in acycle non-linea iscoelas ici y in e ms o he dimen-
sionless index o non-linea i y, S (s ain s i ening a io), and T (shea
hickening a io) a la ge ampli udes [54,55].
In gene al, he e olu ion o he non-linea i y pa ame e s in he high
s ain ampli udes egion in he LAOS egime is qui e complex. S ill, some
common ea u es ha e been epo ed o he p esence o LCB e ec s.
Hyun e al. [46] s udied he e olu ion o he no malized pa ame e Q/Q
0
s. s ain ampli ude, γ
0
, a di e en equencies o linea and comb- ype
b anched polys y ene mel s wi h di e en long b anch sizes. They e-
po ed he p esence o an o e shoo in he Q/Q
0
(γ
0
) cu es o he
b anched polyme s wi h long and en angled b anches, such ha he
in ensi y o his o e shoo was equency-dependen , a beha io
a ibu ed o he p esence o LCB. The o e shoo was no obse ed in
linea o b anched samples wi h b anches o lowe molecula weigh
han en anglemen . Simila ly, he PLA and chain-ex ended PLA samples
show di e en esponses in he LAOS egion. Fig. 5 shows he e olu ion
o he iscous non-linea index (T) a a equency o 3 Hz. Fu he esul s
ela ed o he equency dependence o elas ic and iscous non-linea
indexes (S, T) o linea and chain-ex ended PLA a e p esen ed in Sup-
po ing In o ma ion (see Fig. S9). PLA1.5 sample shows a e y no ice-
able equency-dependen hickening (T >0). Simila ly, al hough a
much mo e modes beha io , he hickening was also obse ed a he
Fig. 4. F equency dependence o he ze o-s ain non-linea i y Q
0
o linea PLA
and chain ex ended PLA samples PLA0.5, PLA1.0, PLA1.5.
Fig. 5. Non-linea iscous pa ame e T (Shea -Thickening Ra io) o linea PLA
and chain ex ended PLA samples PLA0.5, PLA1.0, PLA1.5 a equency o 3 Hz.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
8
highes equencies o he PLA0.5 and PLA1.0 samples. Since i is
known ha he p esence o LCB gi es ise o a e y signi ican s ain
ha dening beha io , i seems ha he o e shoo in Q/Q
0
da a o
b anched s uc u es epo ed by Hyun e al. [46] and he hickening
beha io obse ed in chain-ex ended PLA samples migh also be able o
dis inguish he opology o he b anches. Howe e , he non-linea
physics capable o p edic ing his beha io is no known. Topological
polydispe si y, especially he e ec s o di e en molecula a chi ec u es
o he chain-ex ended b anched PLA, b ings us his complex non-linea
low esponse.
3.2. C ys alliza ion beha io
Table 3 summa izes he peak empe a u es o each ansi ion and he
X
c
alues de e mined by non-iso he mal DSC measu emen s o each
sample. The DSC aces a e epo ed in he Suppo ing In o ma ion,
Fig. S10. As obse ed, linea PLA displays T
g
, T
cc
and T
m
alues o
58.8 ◦C, 129.8 ◦C and 170.7 ◦C, espec i ely. The e y iny exo he m
om 115 o 90 ◦C o he black DSC plo o Fig. S10a indica es ha he
linea polyme only ba ely c ys allizes du ing cooling om he mel a
20 ◦C/min, as expec ed o linea PLA wi h 1 % D-isome con en
[56,57]. The la e is backed by he nea ly iden ical cold c ys alliza ion
and mel ing en halpies de e mined om he second hea ing scan. The
use o a chain ex ende signi ican ly changed he c ys alliza ion
beha io o he PLA: modi ied PLAs show a c ys alliza ion peak be ween
93.1 ◦C and 95.6 ◦C when cooling om he mel a 20 ◦C/min, and he T
c
shows a dec easing end as he numbe o b anches inc eases. In
addi ion, he T
cc
su e s a d ama ic dec ease om 129.8 ◦C o linea PLA
o a ound 106.2–107.4 ◦C co esponding o b anched PLAs. This
imp o emen in he c ys alliza ion abili y o PLA, i.e., he appea ance o
a c ys alliza ion peak and dec eases in he T
cc
, p omo ed by he p esence
o LCB, has been p e iously epo ed in he li e a u e, and i has been
asc ibed o a highe nuclea ion abili y o b anched s uc u es [58–60].
The e is also a signi ican in luence o he p e-exis ing c ys als g own
upon cooling, which acili a es he c ys alliza ion du ing he subsequen
hea ing scan. The p esence o c ys als be o e hea ing explains why all
he b anched samples could c ys allize in he same empe a u e ange.
The p esence o LCB does no p oduce signi ican changes in he T
g
and T
m
o PLA (di e ences a e wi hin 1 ◦C). Rega ding he X
c
, i is
obse ed ha he sample wi h he smalles amoun o Jonc yl has he
highes X
c
. As he highe amoun o Jonc yl can be associa ed wi h a
highe amoun o LCB (acco ding o ou heological esul s shown
abo e), he esul s in Table 3 sugges ha he e is an op imum b anching
deg ee o achie e he maximum X
c
alue. Mihai e al. [61] epo ed an
accele a ion o he c ys alliza ion o b anched PLA samples a inc easing
chain ex ende con en s based on he shi s obse ed in he T
c
and T
cc
.
Howe e , hey obse ed a educ ion in he numbe o PLA chains ha
could c ys allize due o he in e up ion ha b anches caused in he
linea PLA chains.
Simila ly, in he cu en wo k, o b anched samples, a c ys alliza-
ion peak is obse ed du ing cooling om he mel , he T
cc
shi s owa ds
lowe empe a u es, and highe X
c
alues compa ed o ha o linea PLA
a e ob ained. Howe e , he T
c
and X
c
alues dec ease as he amoun o
b anches inc eases. These esul s sugges ha , al hough he p esence o
b anches accele a es he c ys alliza ion p ocess o PLA beyond a c i ical
b anch con en , b anches dis up he linea i y o he PLA chain, hin-
de ing hei non-iso he mal c ys alliza ion abili y. Thus, he X
c
alues o
PLA samples wi h highe b anch con en s a e lowe han hose wi h low
b anch con en s. In a p e ious wo k [62], we obse ed ha he X
c
o PCL
eaches a maximum alue a a pa icula M
n
, which dec eases wi h
inc easing molecula weigh due o a educ ion in chain di usion. As
shown in Table 1, he molecula weigh o PLA inc eases wi h he
amoun o chain ex ende . Then, bo h he inc ease o he molecula
weigh and he p esence o LCB in chain-ex ended PLA samples a ec X
c
alues. Thus, a educ ion in chain di usion and, hence, in X
c
migh be
expec ed wi h inc easing he amoun o Jonc yl. This phenomenon will
be discussed in mo e de ail below.
Fig. 6 shows he PLOM mic og aphs o all he s udied samples
collec ed a 25 ◦C a e mel ing a 200 ◦C o 3 min and cooling a 20 ◦C/
min. In all he cases, c ys alliza ion occu s h ough he o ma ion o
sphe uli es. Fo he linea PLA (see Fig. 6a), only e y small and ew
sphe uli es a e obse ed, which explains why no signal o c ys alliza ion
was de ec ed in non-iso he mal DSC measu emen s. These esul s
highligh he low capaci y o his sample o c ys allize unde non-
iso he mal condi ions. As epo ed in he li e a u e [58,59], la ge
quan i ies o sphe uli es a e obse ed as he amoun o LCB inc eases.
Since simila condi ions a e used o he non-iso he mal c ys alliza ion
p ocess, his esul indica es ha he numbe o p ima y nuclei inc eases
wi h LCB con en .
Iso he mal PLOM measu emen s we e ca ied ou o unde s and
be e he e ec o b anches on PLA’s nuclea ion and g ow h kine ics.
Fig. 7 shows he nuclea ion densi y (
ρ
nuclei
) da a as a unc ion o ime
ob ained a di e en iso he mal c ys alliza ion empe a u es o PLA,
PLA0.5, and PLA1.0 (PLOM mic og aphs illus a ing PLA c ys alliza ion
a di e en imes and empe a u es ha e been included in he SI,
Fig. S11). No e ha da a co esponding o he PLA1.5 a e missing due o
deg ada ion p oblems du ing he measu emen s. Fo any gi en em-
pe a u e, he nuclea ion densi y inc eases almos linea ly a sho imes
and ends o sa u a ion as ime inc eases. As is ypical in polyme s,
he e ogeneous nuclei need mo e ime o be ac i a ed as c ys alliza ion
empe a u e inc eases. Mo eo e , nuclea ion densi y dec eases wi h
inc easing c ys alliza ion empe a u e since he d i ing o ce o p i-
ma y nuclea ion (o nuclea ion) inc eases wi h supe cooling (ΔT =T
m
0
−T
c
) [63] in he high- empe a u e ange.
Fig. 8 ep esen s he nuclea ion densi y a e 2 min o iso he mal
c ys alliza ion and he nuclea ion a e (I) alues (calcula ed om he
ini ial slopes o he s aigh lines a low nuclea ion imes in Fig. 7) as a
unc ion o he T
c
o PLA, PLA0.5, and PLA1.0. I he h ee samples a e
compa ed, i is obse ed ha , o a gi en T
c
, he samples wi h LCB
display highe nuclea ion densi y (Fig. 8a) and nuclea ion a e (Fig. 8b)
alues. While linea PLA can ha dly nuclea e a T
c
s la ge han 110 ◦C,
b anched PLAs can gene a e ac i e nuclei a highe T
c
alues. Mo eo e ,
bo h pa ame e s (
ρ
nuclei
and I) inc ease wi h he amoun o LCB.
Al hough he
ρ
nuclei
and I o PLA1.5 could no be measu ed, based on
non-iso he mal PLOM obse a ions, a u he inc ease o he men ioned
pa ame e s was expec ed. Bai e al. [64] also obse ed an enhancemen
in he nuclea ion densi y o PLA wi h inc easing long-chain b anching
deg ee, and PLOM obse a ions a ailable in he li e a u e ag ee wi h he
highe nuclea ion abili y o b anched PLA samples compa ed o hei
linea homologs [13,58,65,66]. These esul s indica e ha b anched
PLAs possess lowe ee ene gy ba ie s o p ima y nuclea ion han
linea PLA and ha p ima y nuclea ion dec eases as he amoun o LCB
inc eases. This phenomenon has been asc ibed o he g a ing poin s
ac ing as nuclea ing si es [64]. The b anch poin i sel is a de ec ha
in e up s he c ys allizable PLA linea sequence; hus, i has o be
loca ed in he in e ening amo phous laye o he sample be ween he
c ys alline lamellae. We specula e ha such b anch poin s a he
lamellae su ace may induce chain con o ma ions ha a e a o able o
Table 3
T
c
, T
g
, T
cc
, T
m
and X
c
da a ob ained om non-iso he mal DSC scans.
Sample T
c,onse
(◦C)
a
T
c,peak
(◦C)
a
T
g
(◦C)
b
T
cc
(◦C)
b
T
m
(◦C)
b
X
c
(%)
a
PLA – – 58.8 129.8 170.7 0
PLA/Jonc yl
0.5 %
109.0 95.6 59.8 106.4 172.0 5
PLA/Jonc yl
1.0 %
105.4 94.6 59.7 107.4 172.0 3
PLA/Jonc yl
1.5 %
107.5 93.1 60.3 106.2 171.9 2
a
De e mined om he cooling DSC scan.
b
De e mined om he second hea ing DSC scan.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
9
[73] J. Maiz, G. Liu, F. Ruip´
e ez, N. Delbosc, O. Coulembie , D. Wang, A.J. Mülle , How
cyclic chain oplogy can educe he c ys alliza ion a e o poly(3-hexyl hiophene)
and p omo e he o ma ion o liquid c ys alline phases in compa ison wi h linea
analogue chains, J. Ma e . Chem. 7 (2019) 6548–6558, h ps://doi.o g/10.1039/
x0xx00000x.
[74] R.A. P´
e ez-Cama go, L. Meabe, G. Liu, H. Sa don, Y. Zhao, D. Wang, A.J. Mülle ,
E en-odd e ec in alipha ic polyca bona es wi h di e en chain leng hs: om poly
(hexame hylene ca bona e) o poly (dodecame hylene ca bona e), Mac omolecules
54 (2021) 259–271, h ps://doi.o g/10.1021/acs.mac omol.0c02374.
[75] A.T. Lo enzo, M.L. A nal, J. Albue ne, A.J. Mülle , DSC iso he mal polyme
c ys alliza ion kine ics measu emen s and he use o he A ami equa ion o i he
da a: guidelines o a oid common p oblems, Polym Tes 26 (2007) 222–231,
h ps://doi.o g/10.1016/j.polyme es ing.2006.10.005.
[76] M.L. Di Lo enzo, The c ys alliza ion and mel ing p ocesses o poly(L-lac ic acid),
Mac omol. Symp. 234 (2006) 176–183, h ps://doi.o g/10.1002/
masy.200650223.
A. Fe n´
andez-Tena e al.
In e na ional Jou nal o Biological Mac omolecules 282 (2024) 136783
16
