Supporting Information
Nucleation, crystallization and thermal fractionation of poly(‒caprolactone)‒grafted‒lignin:
Effect of the grafted chains length and lignin content.
Ricardo A. Pérez–Camargo1-2, Guery Saenz2, Stéphanie Laurichesse3, María Teresa Casas4, Jordi Puiggalí4,
Luc Avérous3 and Alejandro J. Müller1,2,5
(a)
15
PCL2
PCL3
PCL
63.3
127
PCL
0
44
Heat flow endo up (W/g)
PCL
(b)
PCL
15
PCL2
PCL3
PCL
44
63.3
127
149
10
20
30
40
Temperature (°C)
50
4.0 W/g
5.0 W/g
Heat flow endo up (W/g)
Standard DSC Scans
PCL
149
10 20 30 40 50 60 70 80
Temperature (°C)
(c)
25
PCL10
16.7
PCL17
20
PCL18
13.7
Heat flow endo up (W/g)
Heat flow endo up (W/g)
24.4
PCL6
11.9
PCL37
0
10
20
30
40
PCL6
50
Temperature (°C)
24.4
25
PCL10
16.7
PCL17
20
PCL18
PCL29
10 W/g
10 W/g
PCL29
(d)
13.7
11.9
PCL37
10 20 30 40 50 60 70 80
Temperature (°C)
Figure S1. DSC cooling and subsequent heating scans at 20°C/min for (a), (b) neat PCLs and PCL–g–lignin
copolymers with 2 and 3 wt% of lignin content respectively and (c), (d) PCL–g–lignin copolymers with
lignin contents higher than 3 wt%. The plots are normalized by PCL weight fraction. The red curves are
for neat PCLs and the blue curves for PCL–g–lignin copolymers.
Avrami Fit
The Avrami Fit was performed using an Origin® software application called Polymer Crystallization
Plugin. This Origin® plugin was developed by Lorenzo et al.1, and can be used not only to perform Avrami
Fits but also to perform Lauritzen‒Hoffman Crystallization Fits. The Plugin is offered free upon request to
Prof. A.J. Müller.
The data obtained by isothermal Differential Scanning Calorimetry (DSC) tests were used to perform the
Avrami Fits and the graphical comparisons between the experimental data and the predictions of the
theory. Firstly, it allows the baseline to be established and later calculate the integral of the calorimetric
isothermal curve. Secondly, the linear fit according to the Avrami equation and fitting errors can be
performed. Vc (relative volume fraction crystallinity) is calculated according to Ec. 1, whereas 𝑉𝑐 range is
selected from 0.03 to 0.20 in order to obtain the best fit within the primary crystallization range.
𝑉𝑐 =
𝑊𝑐
𝜌𝑐
𝑊𝑐 + 𝜌 (1 − 𝑊𝑐 )
𝑎
(1)
𝜌𝑐 and 𝜌𝑎 are the fully crystalline and fully amorphous polymer densities, respectively. For all
calculations, 𝜌𝑐 = 1.200 and 𝜌𝑐 = 1.090 g/cm3 were used for PCL. The relative crystalline mass fraction
𝑊𝑐 is calculated as:
𝑊𝑐 =
∆𝐻(𝑡)
∆𝐻𝑡𝑜𝑡𝑎𝑙
(2)
where ∆𝐻(𝑡) and ∆𝐻𝑡𝑜𝑡𝑎𝑙 are the enthalpy as a function of crystallization time and the maximum
enthalpy after completion of the crystallization process.
(Hf)theoretical
(Hf)experimental
(H.Flow)theoretical
(H.Flow)experimental
Heat Flow Endo Up (mW)
(a)
(b)
1.0
Hm(norm)
0.8
0.6
0.4
0.2
50%
0
1
2
3
50%
0.0
4
t-t0 (min)
5
6
0
1
2
3
4
5
Time (min)
6
7
(1-Vc)theoretical
(1-Vc)experimental
1
(c)
1.0
Log(-ln(1-Vc))
0.8
1-Vc
0.6
(d)
0
-1
0.4
0.2
-2
50%
0.0
-1
0
-3
1
-0.5
0.0
0.5
Log(t-to)
Log (t-to)
Figure S2. Avrami plots obtained by the Origin® plugin developed by Lorenzo et al. (a) Experimental DSC
crystallization isotherm of PCL15 at 31ºC and its fitting with the Avrami equation. The experimental
crystallization half–time is indicated. (b) Relative enthalpy of crystallization (Ec. 2) as a function of time.
(c) Evolution of the normalized volumetric fraction of the amorphous phase as a function of
crystallization time. (d) Linear fitting of the Avrami equation in the primary crystallization range, where
the slope indicates the Avrami index and the intercept the overall crystallization rate constant.
Finally, the Avrami equation is rearranged as follows:
log[− ln[1 − 𝑉𝑐 (𝑡 − 𝑡0 )]] = log(𝐾) + 𝑛 log(𝑡 − 𝑡0 )
(3)
where n is the Avrami index and K is the overall crystallization rate constant.
The experimental and predicted half‒crystallization time 𝜏50% can be also determined by this Origin®
plugin. According to the Avrami equation, 𝜏50% is:
1⁄
𝑛
𝜏50%
ln[1 − 𝑉𝑐 ]
= [−
]
𝐾
(4)
Then, depending on the goodness of the fit (up to 50% conversion) there may be a difference between
the experimental and predicted values of 𝜏50%. The parameters obtained by Avrami Fits are collected in
Table S1 (samples of neat PCLs), Table S2 (samples with low lignin content), Table S3 (samples with
intermediate lignin content) and Table S4 (samples with high lignin content).
44
PCL3
PCL10
25
PCL17
PCL29
13.7
PCL2
15
127
PCL
PCL
149
PCL
63.3
PCL37
16.7
24.4
PCL6
PCL18
20
11.9
(a)
(b)
2
10
-1
n
n
10
-1
K (min )
-1
K (min )
10
-8
25
30
35
40
Tc (ºC)
45
50
10
-11
20
30
40
50
Tc (ºC)
Figure S3. Kn values as a function of Tc for (a) neat PCLs and (b) PCL–g–Lignin.
Figure S3 shows the Kn values obtained at different Tc for (a) neat PCLs and (b) PCL‒g‒lignin. The trends
exhibited in Figure S3 are in line (as expected) with the trends exhibited by 1/50% versus Tc, since both Kn
and 1/50% represent a measurement of the overall crystallization rates.
127
PCL
16.7
PCL3
63.3
PCL18
PCL6
20
24.4
PCL29
PCL10
13.7
25
PCL37
4
(a)
3
11.9
(b)
3
2
1
0
20
44
PCL17
Avrami Index (n)
Avrami Index (n)
4
PCL2
149
PCL
15
PCL
25
30
35
40
Tc (°C)
45
50
2
1
0
20
25
30
35
40
45
50
Tc (°C)
Figure S4. Avrami index values for: (a) neat PCLs and (b) PCL–g–lignin samples.
Figure S4 shows the Avrami Indexes for neat PCLs (see Fig. S4(a)) and PCL–g–lignin samples (see Fig. S4
(b)) as a function of the crystallization temperature.
Table S1. Parameters obtained by fitting the Avrami theory to neat PCLs
PCL127
Tc
(°C)
n
26
27
28
29
30
31
32
33
37
38
39
40
41
42
43
44
----------------1.9
2.0
2.1
2.1
2.2
2.1
2.3
2.3
K×103
min–n
----------------242.4
151.0
88.3
47.7
27.0
15.9
5.9
2.5
τ1/2t
min
----------------1.75
2.17
2.72
3.49
4.49
5.80
8.25
11.1
PCL15
τ1/2e
min
----------------1.60
2.02
2.58
3.38
4.40
5.72
8.23
11.1
R2
n
----------------0.9993
0.9995
0.9998
0.9999
1.0000
1.0000
1.0000
1.0000
2.3
2.3
2.3
2.3
2.5
2.8
3.1
3.0
-----------------
K×103
min–n
77530
37317
1801
5365
978.2
160.7
32.5
10.8
-----------------
τ1/2t
min
0.13
0.18
0.25
0.42
0.87
1.67
2.71
4.1
-----------------
PCL149
τ1/2e
min
0.15
0.20
0.25
0.42
0.87
1.67
2.75
4.1
-----------------
R2
n
1.0000
1.0000
0.9999
0.9999
0.9997
0.9998
0.9999
1.0000
-----------------
----------------1.9
2.0
2.2
2.3
2.3
2.3
2.3
2.3
K×103
min–n
----------------815.4
570.7
331.8
179.3
92.7
45.0
19.8
9.8
τ1/2t
min
----------------0.92
1.10
1.41
1.81
2.38
3.28
4.62
6.4
τ1/2e
min
----------------1.02
1.22
1.57
2.02
2.60
3.53
4.83
6.6
R2
----------------0.9997
0.9998
0.9997
0.9996
0.9998
0.9998
1.0000
1.0000
Table S2. Parameters obtained by fitting the Avrami theory to low PCL-g-lignin samples.
PCL624.4
Tc
(°C)
n
34
35
36
37
38
39
40
41
42
43
44
45
46
2.6
2.8
3.1
3.2
3.5
3.5
3.1
3.2
-----------
K×103
min–n
4643
2627
1143
454
143
31
22
4.5
-----------
τ1/2t
min
0.48
0.62
0.85
1.14
1.58
2.45
3.04
4.81
-----------
PCL244
τ1/2e
min
0.47
0.60
0.85
1.13
1.58
2.43
3.02
4.78
-----------
R2
n
0.9995
0.9995
0.9997
0.9998
0.9999
0.9999
0.9998
0.9999
-----------
----------2.5
2.7
2.9
2.9
2.9
2.8
2.7
2.5
K×103
min–n
----------1809
790
260
120
40
14
5
3
τ1/2t
min
----------0.7
1.0
1.4
1.8
2.7
4.0
6.2
9.3
PCL363.3
τ1/2e
min
----------0.7
0.9
1.4
1.8
2.6
3.9
6.0
9.0
R2
n
----------0.99954
0.99955
0.99966
0.9998
0.99978
0.9998
0.99977
0.99977
----------2.4
2.7
3.0
2.6
3.3
2.7
2.7
2.8
K×103
min–n
----------1606
679
216
127
12
10
1.6
0.21
τ1/2t
min
----------0.71
1.01
1.48
1.92
3.41
5.01
9.32
18.1
τ1/2e
min
----------0.70
1.00
1.50
1.90
3.50
4.98
9.22
17.8
R2
----------0.9999
1.0000
1.0000
1.0000
0.9999
1.0000
1.0000
1.0000
Table S3. Parameters obtained by fitting the Avrami theory to intermediate PCL-g-lignin samples.
PCL1820
Tc
(°C)
n
28
29
30
31
32
33
34
35
36
37
38
39
40
41
--2.2
2.3
2.6
3.1
3.2
3.2
3.1
3.0
3.1
2.7
-------
K×103
min–n
--7491.0
3044.5
780.7
127.9
45.9
18.8
9.1
3.3
0.69
0.93
-------
τ1/2t
min
--0.34
0.52
0.95
1.74
2.32
3.09
4.13
6.0
9.4
12.0
-------
PCL1716.7
τ1/2e
min
--0.37
0.53
0.97
1.75
2.33
3.10
4.12
5.9
9.3
12.1
-------
R2
n
--1.0000
0.9999
0.9999
0.9999
0.9999
0.9999
0.9998
0.9999
1.000
1.000
-------
2.4
2.5
2.6
2.9
2.9
2.9
2.9
2.7
-------------
K×103
min–n
8552
3202
1065
259
86
39
16
8
-------------
τ1/2t
min
0.35
0.54
0.85
1.40
2.06
2.72
3.72
5.20
-------------
PCL1025
τ1/2e
min
0.38
0.58
0.87
1.42
2.03
2.67
3.65
5.08
-------------
R2
n
0.99999
0.99999
0.99989
0.99988
0.99981
0.99984
0.99984
0.99983
-------------
------------3.3
3.4
3.5
3.4
3.5
3.1
2.7
2.4
K×103
min–n
------------604
230
74
22
4.2
1.9
1.5
0.72
τ1/2t
min
------------1.04
1.38
1.91
2.73
4.28
6.54
9.97
17.47
τ1/2e
min
------------1.00
1.33
1.83
2.62
4.10
6.15
9.13
15.92
R2
------------0.9990
0.9992
0.9992
0.9991
0.9991
0.9990
0.9992
0.9995
Table S4. Parameters obtained by fitting the Avrami theory to high PCL-g-lignin samples.
PCL3711.9
Tc
(°C)
n
21
22
23
24
25
26
27
28
29
30
31
32
2.1
2.2
2.1
2.2
2.2
2.1
2.3
-----------
K×103
min–n
621
454
329
155
73
43
10
-----------
τ1/2t
min
1.05
1.21
1.42
1.99
2.74
3.82
6.46
-----------
PCL2913.7
τ1/2e
min
1.15
1.32
1.50
2.15
2.95
4.17
6.85
-----------
R2
n
0.99994
0.99993
0.99998
0.99993
0.99988
0.99995
0.99996
-----------
--------2.7
2.8
2.7
2.5
3.5
3.2
3.3
2.9
K×103
min–n
--------9999
2581
942
323
30
17
3
4
τ1/2t
min
--------0.37
0.63
0.89
1.36
2.46
3.21
5.00
5.88
τ1/2e
min
--------0.40
0.70
0.92
1.35
2.52
3.28
4.98
5.80
R2
--------0.99997
0.99993
1.0000
0.99987
0.99999
1.0000
0.99949
0.99997
References
1. A. T. Lorenzo, M. L. Arnal, J. Albuerne, A. J. Müller, Polymer Testing 2007, 26, 222–231.