Mixing polymer cocktails: Diffusion and relaxation distributions of mixed and polydisperse poly (ethylene oxide) melts

Author: Lindt, Kevin; Mattea, Carlos; Stapf, Siegfried; Mailhiot, Sarah

Publisher: Zenodo

DOI: 10.5281/zenodo.17376125

Source: https://zenodo.org/records/17376125/files/ANZMAG2025_Poster_pub.pdf

Mixing polyme cock ails: Di usion and elaxa ion dis ibu ions o
mixed and polydispe se poly (e hylene oxide) mel s
Ke in Lind a, Ca los Ma eaa, Sieg ied S ap a, Sa ah Mailhio b
a
Dep . o Technical Physics II, Technische Uni e si ä Ilmenau, D-98684 Ilmenau, Ge many
b
B uke BioSpin GmbH & Co. KG, D-76275 E lingen, Ge many
Mo i a ion, Samples & Me hods
Polyme s in he mel ollow cha ac e is ic scaling
dependences o hei dynamics: di usion and NMR
elaxa ion [1-4]
Sel -di usion is de e mined di ec ly ia PFG/CFG and
indi ec ly om elaxa ion
Relaxa ion possesses bo h weigh and equency
dependence
All heo e ical and expe imen al wo k elies on well-
de ined polyme s wi h na ow weigh dis ibu ion, i.e.
PDI = Mw/Mn< 1.1
is he assump ion o a de ined weigh jus i ied?
a e di usion and elaxa ion single-componen ?
how o de e mine and quan i y dis ibu ion unc ions?
Wha de ines he dynamics in bina y mix u es?
T2decays o bulk and mix u esDi usion o bulk polyme s
Relaxome y o bulk and mix u es
Conclusions & Ou look
Re e ences
[1] de Gennes, P. G, J. Chem. Phys. 1971, 55, 572.
[2] Doi, M.; Edwa ds, S. F. The Theo y o Polyme Dynamics; Cla endon: Ox o d, 1986.
[3] Fa kullin, N.; Kimmich, R., Ad . Polym. Sci. 2004, 170, 1−113.
[4] Fa kullin, N.; S ap , S.; Ho mann, M.; Meie , R.; Rossle , E. A., J. Non-C ys . Solids 2015, 407, 309.
Di usion o mix u es
Dis ibu ion o di usion coe icien s and T2 a e non- anishing e en o
comme cial PEO wi h na ow dis ibu ion
Enhanced dis ibu ion wid h o mix u es o di e en weigh s
E ec o ma ix (ligh , hea y) on o polyme di usion and elaxa ion
de ec ed
P o ac ed ansi ion Rouse  ep a ion dynamics also e ealed by T1
dispe sion
Da a analysis and heo y equi es aking in o accoun molecula weigh
dis ibu ion e en o appa en ly well-de ined polyme mel s and blends
bulk T2depends s ongly on Mw, up o 10 imes longe in deu e a ed ma ix
Decays a e non-exponen ial e en o na ow mola mass dis ibu ions
Di usion measu emen s ca ied ou a B uke 11.7 T
spec ome e wi h Di BB g adien a 17 T/m and 29 T/m
Relaxa ion measu emen s ca ied ou a B uke 7.0 T
spec ome e wi h mul ipulse echo sequences
Relaxome y measu emen s ca ied ou wi h S ela
SpinMas e elaxome e be ween 0.05 mT and 0.5 T
10-3 10-2 10-1 100101102103
10-2
10-1
100
PEO Bulk, T = 358 K
3 kg/mol
6 kg/mol
11 kg/mol
30 kg/mol
95 kg/mol
220 kg/mol
1000 kg/mol
T1 (s)
n (MHz)
~n0.28
~n0.39
10-3 10-2 10-1 100101102103
10-2
10-1
100
PEO Blend, T = 358 K
90% 2H 10 kg/mol
10% 1H
11 kg/mol
30 kg/mol
95 kg/mol
220 kg/mol
T1 (s)
n (MHz)
~n0.24
~n0.32
le :
Rouse unc ion (M<Mc i ) s.
powe -law unc ion (M>Mc i ) in bulk
acco ding o ep a ion heo y [1,2]
igh :
longe T1and educed powe -law
exponen in 90% deu . ma ix due o
(a) no in e molecula con ibu ion
(b) highe mobili y in 10 kDa ma ix
010 20 30 40
10-3
10-2
10-1
100PEO Bulk, T = 358 K
S/A T2 (ms)
3 kg/mol 409(9)
6 kg/mol 234(6)
11 kg/mol 203(6)
30 kg/mol 35(2)
95 kg/mol 10.7(5)
220 kg/mol 11.8(5)
1000 kg/mol 9.3(4)
S/A = e- /T2
S/A
/T2
010 20 30 40
10-3
10-2
10-1
100PEO Blend, T = 358 K
90% 2H 10 kg/mol & 10% 1H
S/A T2 (ms)
11 kg/mol 378(10)
30 kg/mol 185(6)
95 kg/mol 112(4)
220 kg/mol 88(3)
S/A = e- /T2
S/A
/T2
in bulk and deu e a ed ma ix simila non-exponen iali y o la ge Mw
02x1012 4x1012 6x1012 8x1012 1x1013
10-4
10-3
10-2
10-1
100
d = 3 ms, D = 200 ms
da a exp. i
3 kg/mol
6 kg/mol
11 kg/mol
30 kg/mol
d = 5 ms, D = 500 ms
95 kg/mol
S/Smax
g2d2g2(D-d/3) [s/m²]
bulk
linea poly (e hylene oxide) PEO-hLxxx
and mix u es o
10% linea poly (e hylene oxide) PEO-hLxxx in
90% deu e a ed linea poly (e hylene oxide) PEO-dLxxx
Mola mass dis ibu ion (GPC)
102103104105106
0
1
2
3
4
P(log M)
Mola Mass [g/mol]
1H PEO
3 kg/mol
30 kg/mol
95 kg/mol
P ojec numbe 238391017
name
iso ope
Mw(g/mol
)
Mn(g/mol) PDI
PEO
-hL3b 1
H
3060
2980
1.03
PEO
-hL6a 1
H
6000
5850
1.03
PEO
-hL11 1
H
11200
10800
1.04
PEO
-hL30 1
H
29100
26400
1.10
PEO
-hL95 1
H
94600
81900
1.16
PEO
-hL220 1
H
220000
197000
1.12
PEO
-dL10 2
H
11000
10100
1.09
PEO
-dL300 2
H
310000
242000
1.28
0500 1000 1500 2000 2500
10-3
10-2
10-1
100PEO Blend, T = 358 K
90% 2H 10 kg/mol & 10% 1H
A1e- / 1
11 kg/mol
30 kg/mol
95 kg/mol
220 kg/mol
in eg al/max [a b. uni ]
ime [ms]
We s udy linea poly (e hylene oxide) in bulk
(1H) and in mix u es (10% 1H in 90% 2H)
0500 1000 1500 2000 2500
10-3
10-2
10-1
100PEO Bulk, T = 358 K
A1e- / 1
3 kg/mol
6 kg/mol
11 kg/mol
30 kg/mol
95 kg/mol
220 kg/mol
1000 kg/mol
in eg al/max [a b. uni ]
ime [ms]
10.5281/zenodo.17376125
Mix u e I: 6 kDa wi h di e en PDI
102103104105
0.00
0.01
0.02
0.03
0.04
PDF(logM)
M [g/mol]
PEO-hL6b
PDI = 1.06 / 1.09 (PSS/calc.)
Mw (g/mol) = 6650 / 6448
Mn (g/mol) = 6170 / 5938
PEO-hL6a
PDI = 1.03 (PSS)
Mw (g/mol) = 6000 g/mol
Mn (g/mol) = 5850 g/mol
Mc
w
Mc
n
102103104105
0.000
0.005
0.010
0.015
PDF(logM)
M [g/mol]
0.44 * PEO-hL3b
0.18 * PEO-hL5
0.38 * PEO-hL10
hL6mix (sum)
PDI = 1.52 (calc.)
Mw (g/mol) = 6003
Mn (g/mol) = 3948
Mc
w
Mc
n
Pu chased na ow 6 kDa
s. mix u e o h ee
di e en mola masses
wi h he same mass
a e age bu la ge PDI
1091010 1011 1012 1013 1014
10−5
10−4
10−3
10−2
10−1
100
Mw = 6 kg/mol
T = 358 K, d = 3 ms, D = 200 ms
PDI = 1.03 (hL6aa)
PDI = 1.52 (hL6mixb)
a 100% 1H 6 kg/mol
b 44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol
Smax
no m
g2d2g2(D-d/3) [s/m²]
343 358 373
10-12
10-11
Mw = 6 kg/mol
d = 3 ms, D = 200 ms
PDI = 1.03 (hL6aa)
PDI = 1.52 (hL6mixb)
a 100% 1H 6 kg/mol
b 44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol
Tempe a u e [K]
NNLS Means
10−15 10−14 10−13 10−12 10−11 10−10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
20
40
60
80
100
NNLS Weigh s [%]
Log No mal PDF(lnD)
Di usion Coe icien s [m²/s]
Mw = 6 kg/mol (hL6a*)
T = 358 K, d = 3 ms, D = 200 ms
Log No mal Fi (1)
NNLS Fi (9)
*100% 1H 6 kg/mol
10−15 10−14 10−13 10−12 10−11 10−10
0.0
0.2
0.4
0.6
0.8
1.0
0
20
40
60
80
100
NNLS Weigh s [%]
Log No mal PDF(lnD)
Mw = 6 kg/mol, hL6mix*
T = 358 K, d = 3 ms, D = 200 ms
Log No mal Fi (2)
NNLS Fi (9)
*44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol
46.9%
53.0%
36%
64%
10−15 10−14 10−13 10−12 10−11 10−10
0.0
0.2
0.4
0.6
0.8
1.0
0
20
40
60
80
100
NNLS Weigh s [%]
Log No mal PDF(lnD)
Di usion Coe icien s [m²/s]
Mw = 6 kg/mol, hL6mix*
T = 358 K, d = 3 ms, D = 200 ms
Log No mal Fi (3)
NNLS Fi (9)
44% 1H 3 kg/mol + 18% 1H 5 kg/mol + 38% 1H 10 kg/mol
0.1%
Top: la ge a e age D in mixed sample
Righ : mul iple componen s (2 o 3) iden i ied
in bo h log-no mal and NNLS i
Mix u e II: 10% 3 kDa in 90% deu e a ed 300 kDa
01×1013 2×1013 3×1013 4×1013
10-6
10-5
10-4
10-3
10-2
10-1
100
T = 358 K, d = 3 ms, D = 200 ms
exp. i
hL3ba n = 1
hL3b-dL300b n = 3
a100% 1H 3 kg/mol
b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol
Smax
no m
g2d2g2(D-d/3) [s/m²]
343 358 373
1E-14
1E-13
1E-12
1E-11
19(6)% 34(11)%
17(2)%
74(5)% 60(11)%
78(2)%
7.16(6)% 6.22(6)% 4.48(2)%
T = 343 K, d = 3 ms, D = 200 ms
hL3ba
hL3b-dL300b
a100% 1H 3 kg/mol
b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol
D [m²/s]
Tempe a u e [K]
343 358 373
100
101
102
Mw = 3 kg/mol
d = 3 ms, D = 200 ms
hL3ba
hL3b-dL300b
a100% 1H 3 kg/mol
b 10% 1H 3 kg/mol & 90% 2H 300 kg/mol
Tempe a u e [K]
NNLS Sp ead
10−15 10−14 10−13 10−12 10−11 10−10
0.0
0.5
1.0
1.5
2.0
2.5
0
20
40
60
80
100
NNLS Weigh s [%]
Log No mal PDF(lnD)
Di usion Coe icien s [m²/s]
Mw = 3 kg/mol (hL3b*)
T = 358 K, d = 3 ms, D = 200 ms
Log No mal Fi (1)
NNLS Fi (4)
*100% 1H 3 kg/mol
10−15 10−14 10−13 10−12 10−11 10−10
0.0
0.5
1.0
1.5
0
20
40
60
80
100
NNLS Weigh s [%]
Log No mal PDF(lnD)
Di usion Coe icien s [m²/s]
Mw = 3 kg/mol (hL3b-dL300*)
T = 358 K, d = 3 ms, D = 200 ms
Log No mal Fi (2)
NNLS Fi (10)
*10% 1H 3 kg/mol & 90% 2H 300 kg/mol
93.9%
6.1%
smalle D and b oade
dis ibu ion o 3 kDa in
300 kDa ma ix
1% esidual p o ons in
he deu e a ed ma ix
a e obse able
Mix u e III: 10% in 90% deu e a ed 10 kDa
02x1012 4x1012 6x1012 8x1012 1x1013
10-4
10-3
10-2
10-1
100
in 90% 2H 10 kg/mol, T = 358 K
d = 3 ms, D = 200 ms
da a exp. i
10 kg/mol
30 kg/mol
95 kg/mol
220 kg/mol
S/Smax
g2d2g2(D-d/3) [s/m²]
103104105
10-14
10-13
10-12
10-11 T = 358 K
Bulk
wi h 90% 2H 10 kg/mol
Dh [m2/s]
(Mn+Mw)/2 [g/mol]
~M-1.96(15)
~M-1.35(5)
non-exponen ial decays
D~M-1.4 in mix u es weake
han D~M-2 in bulk [2,3]

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