J Therm Anal Calorim DOI 10.1007/s10973-015-4689-7
Solidification and thermal degradation of printable, stretchable electrical conductor from waterborne polyurethane and silver flakes Hui-Wang Cui1 • Jin-Ting Jiu1 • Tohru Sugahara1 • Shijo Nagao1 Katsuaki Suganuma1 • Hiroshi Uchida2 • Katsunori Kihara3
•
Received: 1 June 2014 / Accepted: 2 April 2015 Akade´miai Kiado´, Budapest, Hungary 2015
Abstract In this study, we prepared high-performance printable, stretchable electrical conductor from waterborne polyurethane and micro-silver flakes. The solidification and thermal degradation were investigated using differential scanning calorimetry and thermogravimetric analysis methods. The electrical conductor achieved solidification by volatilizing and removing the free water. The thermal degradation mainly happened in the range of 250–450 C caused by the pyrolysis of the polymeric matrix of polyurethane. The pyrolysis kinetic equations were obtained using the kinetic methods, e.g., da/dt = e22.16(1 - a)0.78 a0.13e(-149.14/RT) for the polyurethane, da/dt = e22.76(1 - a)0.84 a0.11e(-150.69/RT), da/dt = e21.43(1 - a)0.77a0.06e(-143.77/RT), and da/dt = e19.06(1 - a)0.75a0.12e(-130.53/RT) for the electrical conductor containing 80, 85, and 90 % mass percentage of micro-silver flakes, where a was the fractional extent conversion at a given time t (or a given temperature T). Their overall order of reaction was 0.91, 0.95, 0.83, and 0.87, respectively, less than 1, demonstrating the thermal degradation was a single, simple reaction. Keywords Electrical conductor Solidification Thermal degradation Kinetics
& Hui-Wang Cui
[email protected] 1
Institute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567, Japan
2
Institute for Polymers and Chemicals Business Development Center, Showa Denko K. K., 5-1 Yawata Kaigan Dori, Ichihara, Chiba 290-0067, Japan
3
Innovation Center Japan, Sumika Bayer Urethane Co., Ltd. 3-13-26, Kukuchi, Amagasaki, Hyogo 661-0977, Japan
Introduction The stretchable electronics can be used in paper-like displays, highly flexible solar cells, wearable health care devices, implantable medical devices, sensors for artificial skins, actuators for artificial muscles, and loudspeakers [1–3]. Their electrical components must be robust to stretching and folding that the conventional rigid devices cannot tolerate. Recently, there have been a lot of approaches (e.g., thin metal films [4–6], electrically conductive polymers [7–9], nanoparticles [10–12], etc.) have been used to realize the stretchable conductors as passive components, but they also have displayed low stretchability, poor chemical stability, low charge carrier mobility, disordered structures, and low mechanical strength. Moreover, their fabrication processes are rather complicated. In view of this, we prepared high-performance printable, stretchable electrical conductor (SEC) using waterborne polyurethane (PU) and micro-silver flakes; the SEC presented low initial electrical resistance, e.g., 0.0016 X, before the tensile test (unpublished). During the dynamic stretching, the SEC that contained more than 80 % mass percentage of micro-silver flakes showed good electrically conductive stability and high electrically conductive durability, e.g., the normalized resistance defined as the stretching electrical resistance divided by the initial electrical resistance less than 2.5 in the range of 0–43.89 % strain at 1 load cycle and the electrically conductive probability at about 18 % after continuous 5 load cycles. The SEC also showed excellent electrically conductive stability (e.g., the normalized resistance less than 2.5 in the range of 0–100 % strain) during the static stretching contributed by the electrical resistance relaxation (unpublished). However, as electronic materials, the electrical conductors should also involve the thermal management, such as high temperature
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stability, curing, solidification, and thermal degradation. These items definitely influence the durability and life of electronic devices. Therefore, in this study, we investigated the solidification and thermal degradation of the obtained SEC using Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and thermogravimetric (TG) analysis methods. In addition, we also used kinetic methods [13, 14] to determine the kinetic equation, reaction mechanism, activation energy (E), and preexponential factor (A) for the thermal degradation of SEC, in hope of providing helpful guidance for the related application.
Waltham, MA, USA); 32 scans were collected at a spectral resolution of 1 cm-1. The thermal degradations of the samples were measured using a NETZSCH 2000SE/H/24/1 TGA analyzer (NETZSCH, Selb, Germany) operated under a pure N2 atmosphere. The sample (ca. 10 mg) was placed in a Pt cell and heated at a rate of 5, 10, 15, and 20 C min-1, respectively, from 30 to 900 C under a N2 flow rate of 60 mL min-1.
Results and discussion Solidification
The SEC consisted of a matrix resin and electrically conductive fillers. The matrix resin was a milky white Dispercoll U 42 waterborne PU from Bayer MaterialScience, Leverkusen, Germany. The nonvolatile content was 48–52 %, viscosity 150–800 mPas, pH 6.0–9.0, density approx. 1.1 g cm-3, and minimum film-forming temperature approx. 5 C. Electrically conductive fillers were AgC-239 micro-silver flakes from Fukuda Metal Foil & Powder Co., Ltd., Kyoto, Japan. The size was 2–15 lm and the thickness approx. 0.5 lm. The mass ratio between PU and micro-silver flakes were 40:80, 30:85, and 20:90. After the solidification, the water had been volatilized and the SEC became into solid films, in which the mass percentage of micro-silver flakes was about 80, 85, and 90 %. The corresponding SEC was named as SEC-80, SEC-85, and SEC-90. To fabricate these SEC, micro-silver flakes were incorporated into PU using a THINKY ARV-310 planetary vacuum mixer (THINKY Corporation, Laguna Hills, CA, USA.) under 2000 rpm for 20 min, and then the mixture was printed on glass substrates. After solidified at room temperature for 2 days, the SEC samples (30 mm 9 5 mm 9 200 lm) were obtained. The mass percentages of micro-silver flakes were 80, 85, and 90 % in the solidified SEC-80, SEC-85, and SEC-90, respectively. Characterization The solidifying of the samples was studied using a NETZSCH 204 F1 DSC (NETZSCH, Selb, Germany) operated under an atmosphere of pure Ar atmosphere. The sample (ca. 5 mg) was placed in a sealed Al pan. The curing scans were conducted from 30 to 300 C at a rate of 20 C min-1 under an Ar flow rate of 25 mL min-1. The structures of the samples were recorded using a PerkinElmer Frontier TN FTIR spectrophotometer (PerkinElmer,
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PU
Exo.
Samples
Figure 1 shows the solidifying curves of PU, SEC-80, SEC-85, and SEC-90. All presented an endothermic peak in the range of 100–130 C caused by volatilizing and removing the free water from them. It was a physical procedure without any chemical reaction happening in the solidifying. We also investigated this solidification using FTIR. The unsolidified PU, SEC-80, SEC-85, and SEC-90 all presented a strong, wide, sharp absorption peak near 3380 cm-1 (Fig. 2a). It covered the stretching vibrations of O–H in free water, free N–H, hydrogen bonding of water, and hydrogen-bonded N–H with C=O and C–O–C. The unsolidified samples contained so much free water that these stretching vibrations concluded together and formed such an absorption peak. Conversely, the solidified samples, including solidified PU, SEC-80, SEC-85, and SEC90, just presented a wide, weak absorption peak near the same wavenumber because most free water was removed (Fig. 2b). The stretching vibrations of free and hydrogenbonded C=O often feature an absorption peak at 1730 and 1700 cm-1, respectively. As Fig. 2 shows, the unsolidified
SEC-80
Heat flow/μV
Experimental
SEC-85
SEC-90
50
100
150
200
250
300
Temperature/°C Fig. 1 DSC solidifying curves of PU, SEC-80, SEC-85, and SEC-90 at the heating rate of 20 C min-1
Solidification and thermal degradation of printable, stretchable electrical conductor from…
(a)
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Unsolidified PU Unsolidified SEC-80 Unsolidified SEC-85
Unsolidified SEC-90 4000
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were enhanced (Fig. 2b) compared to those in Fig. 2a, showing the formation of carbamate groups. In a word, the FTIR spectra coincided well with the solidifying curves that the prepared SEC achieved solidification and formed thermoplastic electrical conductor by volatilizing and removing the free water. It also can be seen that the PU, SEC-80, SEC-85, and SEC-90 presented different endothermic peak temperatures around 110, 108, 108, and 106 C, respectively (Fig. 1). The temperatures displayed a slight decreasing trend. PU was the polymeric matrix of SEC. It is an insulator that cannot conduct electricity or heat. During the solidification of PU, the heat passed through the molecular chains and molecular segments, and heated the free water, which was then volatilized and removed. Relatively, the heat transferring was a little faster in the solidification of SEC than that in the solidification of PU. Micro-silver flakes are good conductors. They accelerated the heat transferring and the free water volatizing in SEC. The more the micro-silver flakes, the greater the acceleration. Because of the incorporated micro-silver flakes, the endothermic peak temperatures shifted to low values as aforementioned.
1500
1000
Wavenumber/cm–1 Fig. 2 FTIR spectra of a unsolidified and b solidified PU, SEC-80, SEC-85, and SEC-90
and solidified samples both presented a strong, sharp absorption peak at 1717 cm-1, indicating the C=O was partially hydrogen-bonded. Similarly, the wavenumber representing the stretching vibration of C–O in O=C–O shifted to 1120 cm-1 (hydrogen-bonded state) from 1250 cm-1 (free state), as that of C–O in C–O–C did to 1071 cm-1 (hydrogen-bonded state) from 1125 cm-1 (free state). Besides, the unsolidified and solidified samples all featured sharp, weak absorption peaks at 2935 and 2860 cm-1 for the stretching vibration of C–H in CH2 and CH3, a sharp, strong absorption peak at 1270 cm-1 for the stretching vibration of C–N, and a sharp, weak absorption peak at 742 cm-1 for the out-plane bending vibration of C– H in phenyl group. Moreover, the disappearance of isocyanate groups and formation of carbamate groups were also observed. The unsolidified PU, SEC-80, SEC-85, and SEC-90 all presented a small, weak absorption peak around 2210 cm-1 (Fig. 2a), indicating the stretching vibration of N–C=O, while this peak was not found in the solidified samples (Fig. 2b), showing the disappearance of isocyanate groups. And the absorption peaks near 1717 cm-1 representing C=O and 1550 cm-1 representing H–N–C=O both
Figure 3 shows the TG traces of PU, SEC-80, SEC-85, and SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1. It can be seen that there was only one sharp mass loss in the range of 250–450 C for all of them. This agreed well with the results of FTIR and DSC that the PU and SEC achieved solidification through volatilizing the free water and almost all of the free water was removed from the solidified samples. Therefore, no mass loss (Fig. 3), no heat flow peak (Fig. 4), and no mass loss rate (Fig. 5) were found at the temperatures below 250 C. The pyrolysis of the polymeric matrix of PU caused the mass loss at 250–450 C. The char yield was about 0 % for PU (Fig. 3a), 80 % for SEC-80 (Fig. 3b), 83 % for SEC-85 (Fig. 3c), and 88 % for SEC-90 (Fig. 3d). They roughly equaled to the mass percentages of micro-silver flakes in SEC, indicating the polymeric matrix of PU had been pyrolysized completely. During the thermal degradation, the fast heating often pushes the pyrolysis to high temperature zones and then lags the reaction, while the slow heating often allows more accurate pyrolysis and then advances the reaction. As Fig. 3 shows, the TG traces all shifted to high temperature zones as the heating rate increased from 5 to 10, 15, and 20 C min-1. We obtained the initial temperature (Ti), peak temperature (Tp), and final temperature (Tf) of the mass loss from Figs. 3, 4, and 5, and listed them in Table 1. Apparently, they also shifted to high temperature zones. For example, SEC-90 presented Ti values at 281.50,
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(b)
(a) 100
5 °C min–1
100
5 °C min–1
10 °C min–1
80 60 40
85 80
0
75 400
600
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90
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Mass/ %
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–1
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Temperature/°C
90
94 92 90
85
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86 200
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Fig. 3 TG traces of a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
284.90, 291.90, and 295.00 C, Tp values at 403.50, 412.10, 428.90, and 441.70 C, and Tf values at 362.87, 380.44, 391.74, and 398.31 C, for the heating rate of 5, 10, 15, and 20 C min-1, respectively. The heating rate also influenced the heat flow peaks and mass loss rates. As the heating rate increased from 5 to 10, 15, and 20 C min-1, the heat flow peaks in the range of 250–450 C became sharper and their areas became larger (Fig. 4). For example, the heat flow peak of SEC-90 was the weakest and its area was the smallest at the heating rate of 5 C min-1, then were those at the heating rate of 10 and 15 C min-1 successively; the heat flow peak at the heating rate of 20 C min-1 was the sharpest with the largest area. Similarly, the mass loss rates increased in the range of 250–450 C with increasing heating rates (Fig. 5). The mass loss rates at Tp (vp) are listed in Table 1. SEC-90, for example, presented the vp values at 1854, 4191, 5840, and 8069 ng s-1 for the heating rate of 5, 10, 15, and 20 C min-1, respectively. The micro-silver flakes also influenced the mass loss, heat flow peak, and mass loss rate. As mentioned above, the chair yields of SEC-80, SEC-85, and SEC-90 were
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almost as the same as the mass percentages of micro-silver flakes in them; they increased with the increasing microsilver flakes (Fig. 3). The heat flow peaks in the range of 250–450 C got weaker and their areas got smaller for PU, SEC-80, SEC-85, and SEC-90 at the same heating rate (Fig. 4). For example, the heat flow peak of PU was the sharpest and its area was the largest at the heating rate of 20 C min-1, those of SEC-80 and SEC-85 followed at the same heating rate; SEC-90 presented the weakest heat flow peak with the smallest area compared to PU, SEC-80, and SEC-85 at the heating rate of 20 C min-1. The mass loss was caused by the pyrolysis of the polymeric matrix of PU. The incorporated micro-silver flakes increased while the polymeric matrix of PU deceased in SEC-80, SEC-85, and SEC-90, so the mass loss decreased accordingly (Fig. 3). The decreasing mass loss coincided well with increasing char yields. Moreover, the mass loss rate also reflected the decreasing mass loss. As Fig. 5 and Table 1 show, the mass loss rate decreased successively for PU, SEC-80, SEC-85, and SEC-90. Taking the vp for an example, the values at the heating rate of 20 C min-1 were 80,270, 15,381, 11,772, and 8069 ng s-1, respectively, for PU,
Solidification and thermal degradation of printable, stretchable electrical conductor from…
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Fig. 4 Heat flow of a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
SEC-80, SEC-85, and SEC-90. As did in the solidifying detected by DSC, the micro-silver flakes also accelerated the heat transferring in the thermal degradation that advanced the pyrolysis temperatures of SEC. As Figs. 3–5, and Table 1 show, the Ti, Tf, and Tp all decreased from PU to SEC-80, SEC-85, and SEC-90. Taking the Tp for an example, the values were 408.74, 399.23, 398.57, and 398.31 C, respectively, for PU, SEC-80, SEC-85, and SEC-90.
universal gas constant and T is the absolute temperature at time t. Logarithmic Eq. (1): da E þ ln½Af ðaÞ ð2Þ ln ¼ dt RT
Pyrolysis kinetics
where mi is the mass of samples at Ti, mt is the mass of samples at time t (or temperature T) and mf is the mass of samples at Tf. Differentiating Eq. (3):
For the pyrolysis kinetics, we mainly focused on the thermal degradation processes of PU, SEC-80, SEC-85, and SEC-90 between the Ti and Tf. The rate of conversion (da/ dt) is expressed by [15–17]: da E ¼ AeRT f ðaÞ dt
ð1Þ
where A and E are kinetic parameters, the preexponential factor and the activation energy, respectively, R is the
In Eq. (2), a is the fractional extent conversion at a given time (or given temperature), expressed by: mi mt a¼ ð3Þ mi mf
dmt da dt ¼ dt mi mf
ð4Þ
where dmt =dt is the pyrolysis rate, or called the mass loss rate (Fig. 5). From Eqs. (2) and (4), a plot of ln(da/dt) versus 1/ T values at the same fractional extent of conversion a from
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(b)
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Mass loss rate/ngs –1
–15000
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376.17 –30000
392.62
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401.76
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393.64
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Fig. 5 Mass loss rate of a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
Table 1 Ti, Tf, Tp, vp, and kp for PU, SEC-80, SEC-85, and SEC-90 Items
Ti/C
Tf/C
Tp/C
vp/ng s-1
kp/min-1
PU-5
270.00
411.80
376.17
20,890
4.24 9 10-3
44,412
8.40 9 10
-3 -2
PU-10
280.40
447.00
392.62
Items
Ti/C
Tf/C
Tp/C
vp/ng s-1
kp/min-1
SEC-85-5
281.00
410.20
366.33
2968
3.64 9 10-3
SEC-85-10
284.60
419.50
380.49
5310
6.54 9 10-3
SEC-85-15
289.20
428.70
392.06
9061
1.04 9 10-2
PU-15
285.80
464.40
401.76
63,259
1.21 9 10
PU-20
289.20
477.80
408.74
80,270
1.59 9 10-2
SEC-85-20
292.20
446.90
398.57
11,772
1.33 9 10-2
3904
4.17 9 10
-3
SEC-90-5
281.50
403.50
362.87
1854
3.60 9 10-3
7.48 9 10
-3
SEC-90-10
284.90
412.10
380.44
4191
6.99 9 10-3
1.21 9 10
-2
SEC-90-15
291.90
428.90
391.74
5840
1.05 9 10-2
1.51 9 10
-2
SEC-90-20
295.00
441.70
398.31
8069
1.33 9 10-2
SEC-80-5 SEC-80-10 SEC-80-15 SEC-80-20
280.50 284.10 286.20 292.10
410.60 440.20 441.30 457.60
368.58 382.13 393.64 399.23
9710 10,183 15,381
The items with -5, -10, -15, and -20 means the heating rate at 5, 10, 15, and 20 C min-1, respectively
a series of dynamic TG experiments at different heating rates will result in a straight line with a slope of -E/R and an intercept of ln[Af(a)]. Repeating this procedure, E and ln[Af(a)] values corresponding to different a from the mass curves of different heating rates can be obtained. Thus, the relationship of E versus a and ln[Af(a)] versus a can be determined [13, 18]. Figure 6 is the plots of ln(da/ dt) versus 1/T for PU, SEC-80, SEC-85, and SEC-90 at various values of a (a = 0.05, 0.10, 0.15, 0.20, …, 0.90,
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0.95) covering the experimental range. Making fitted linear regression lines, the groups of E and ln[Af(a)] values were obtained for each value of a. Figure 7 shows the plots of E versus a and ln[Af(a)] versus a, of PU, SEC-80, SEC-85, and SEC-90. Apparently, E and ln[Af(a)] both presented stable values at a of 0.15–0.90. Therefore, it can be inferred that the PU, SEC-80, SEC-85, and SEC-90 had constant values of E and ln[Af(a)] during the thermal degradation.
Solidification and thermal degradation of printable, stretchable electrical conductor from…
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Fig. 6 Plots of ln(da/dt) versus 1/T for a PU, b SEC-80, c SEC-85, and d SEC-90 at a of 0.05–0.95
(a) E/kJ mol–1
180 160 140 120
PU SEC-80 SEC-85 SEC-90
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0.60
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1.00
Fig. 7 Plots of a E versus a and b ln[Af(a)] versus a for PU, SEC-80, SEC-85, and SEC-90
The pyrolysis of the polymeric matrix of PU caused the mass loss of SEC-80, SEC-85, and SEC-90. The TG traces only displayed a sharp mass loss in the range of 250–450 C for them (Fig. 3), showing the thermal degradation was a one-step reaction. It is known that E in single or one-step reaction is a constant that does not change with the variation of a. In addition, when dynamic TG is used to study the kinetics of thermal degradation, a at the endothermic peak is a constant, although the temperature at which the endothermic peak occurs depends on the heating rate [14, 19]. As Fig. 8 shows, a at the endothermic peak was nearly a constant; the experimental (Exp.) da/dt for PU, SEC-80, SEC-85, and SEC-90 all reached the maximum values at a of about 0.65 for the heating rate of 5, 10, 15, and 20 C min-1. Therefore, based on the above inference and analysis, E can be calculated using the Ozawa equation from the relationship between the heating rate (b, C min-1) and Tp [14]:
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0.0060
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0.60 α
α
0.60
0.80
1.00
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0.0000 0.00
0.20
0.40
α
0.60 α
Fig. 8 Comparisons of experimental data (Exp.) with the kinetic method results (Cal.) of a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
dðlnbÞ 1:052E ¼ dð1=Tp Þ R
Table 2 Calculated m, n, m ? n, E, and lnA for PU, SEC-80, SEC85, and SEC-90
Figure 9 shows the plot of -lnb versus 1000/Tp for PU, SEC-80, SEC-85, and SEC-90. A linear regression analysis suggested that, to a good agreement, the calculated values
–1.5
–1.8
–lnβ
–2.1
y 18.192x 30.081 r2 0.9963
y 18.871x 30.665 r2 0.9996
y 16.516x 27.572 r2 0.9991
–2.7
–3.0 1.48
1.50
1.52
1.54
1.56
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1000/T p/ k–1
Fig. 9 Plots of -lnb versus 1000/Tp for PU, SEC-80, SEC-85, and SEC-90
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m
n
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lnA
PU
0.13
0.78
0.91
149.14
22.16
SEC-80
0.11
0.84
0.95
150.69
22.76
SEC-85 SEC-90
0.06 0.12
0.77 0.75
0.83 0.87
143.77 130.53
21.43 19.06
y 19.067x 31.345 r2 0.9950
PU SEC-80 SEC-85 SEC-90
–2.4
1.46
Items
of E were 149.14, 150.69, 143.77, and 130.53 kJ mol-1 for them (Table 2). During the thermal degradation, the polymeric matrix of PU was pyrolysized into small molecular substances, which were then volatilized. For the thermal degradation of pure PU, they were volatilized easily without any impediment to escaping, as the pyrolysized PU in this study. In contrast, the micro-silver flakes blocked the volatilization in SEC. They accelerated the heat transferring to advance the thermal degradation, but did not transfer the mass. The small molecular substances had to escape and be swept away by the gas stream in a circuitous route around micro-silver flakes, so more energy was required to overcome the lengthening and delaying to finish the volatilization processes. This is why the SEC-80
Solidification and thermal degradation of printable, stretchable electrical conductor from…
(a)
(b)
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
2
2 1 y r2 y r2 y r2 y r2
0 –1 –2
–3
(c)
–2
–1
0.6312x 0.9755 0.6407x 0.9560 0.6473x 0.9504 0.6892x 0.9659
0 1 ln[(1 – α)/α]
2
2E 15 2E 15
–1 –2
2E 15 3
–3
(d)
1
–1 –2
–2
–1
0.7792x 3E 15 0.9937 0.75x 2E 15 0.9892 0.6583x 2E 15 0.9947 0.6636x 2E 15 0.9940
0 1 ln[(1 – α)/α]
2
3
Value I
y r2 y r2 y r2 y r2
0
–2
–1
0 1 ln[(1 – α)/α]
0.7663x 0.9970 0.7291x 0.9928 0.7384x 0.9932 0.7074x 0.9914
2E 15 2E 15 2E 15 2E 15
2
3
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
2
1
–3
y r2 y r2 y r2 y r2
0
2E 15
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
2
Value I
Value I
1
Value I
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
y r2 y r2 y r2 y r2
0
–1
–2 –3
–2
–1
0 1 ln[(1 – α)/α]
0.6639x 0.9960 0.6199x 0.9962 0.6018x 0.9981 0.6112x 0.9923
3E 15 2E 15 2E 15 2E 15
2
3
Fig. 10 Plots of Value I versus ln[(1 - a)/a] for a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
presented higher E value than the PU. Additionally, E mainly resulted from the pyrolysis of the polymeric matrix of PU. SEC-85 and SEC-90 contained so few of PU that they had shown lower E values than PU and SEC-80. In Eqs. (1) and (2), the expression of f(a) is [20]:
Eq. (6) - Eq. (7): E da E da0 þ ln þ ln Value I ¼ RT dt RT 0 dt ¼ ðn mÞln½ð1 aÞ=a
ð8Þ
f ðaÞ ¼ ð1 aÞn am
Eq. (6) ? Eq. (7): E da E da0 þ ln þ ln þ Value II ¼ RT dt RT 0 dt ¼ 2 ln A þ ðm þ nÞln½að1 aÞ
ð9Þ
ð5Þ
where m ? n is the overall order of reaction [21, 22]. Substituting Eq. (5) into Eq. (2), da E ln þ n ln ð1 aÞ þ m ln a ð6Þ ¼ ln A dt RT then 0 dða Þ E ln þ n lnð1 a0 Þ þ m ln a0 ¼ ln A dt RT 0 where a0 is the fractional extent conversion at a given temperature T0 ; let a0 = 1 - a, and then: 0 da dð1 aÞ ln ¼ ln dt dt E ¼ ln A þ n ln a þ m lnð1 aÞ ð7Þ RT 0
Values of n - m were obtained from the slopes of the plots of Value I versus ln[(1 - a)/a] (Fig. 10). The values of m ? n and 2lnA were obtained from the slopes and intercepts of the plots of Value II versus ln[a(1 - a)] (Fig. 11). In this study, we took the average values and listed the results of m, n, m ? n, and lnA in Table 2. The A is a constant determined by the reaction nature, and there is nothing to do with the reaction temperature and concentration in the system. E and A always present same variation trends in the kinetics. If E increases, A will increase, and vice versa. As Table 2 shows, lnA changed accordingly with the variations of E. The m ? n was 0.91,
123
H.-W Cui et al.
(b)
(a) 43.2 42.9
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
44.4 44.1
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
y r2 y r2 y r2 y r2
42.3 42.0 41.7 41.4 –3.0
–2.7
–2.4
–2.1
0.9134x 0.9552 0.8636x 0.9382 0.9431x 0.9502 0.9358x 0.9573
–1.8
44.334
Value II
Value II
43.8 42.6
43.5
44.239
43.2
44.402
42.9
44.336
42.6
y r2 y r2 y r2 y r2
–3.0
–1.5
–2.7
(c)
(d) 5 °C min–1 10 °C min–1 15 °C min–1
37.2 36.9
20 °C min–1
–1.8
45.638 45.477 45.648
–1.5
5 °C min–1 10 °C min–1 15 °C min–1 20 °C min–1
36.6
41.1
y r2 y r2 y r2 y r2
40.8 40.5 40.2 –3.0
–2.7
–2.4
–2.1
0.7078x 42.583 0.9915 0.719x 42.664 0.9617 0.8969x 43.03 0.9892 0.9837x 43.127 0.9920
–1.8
–1.5
ln[α(1 – α)]
Value II
Value II
41.4
–2.1
45.35
ln[α(1 – α)]
ln[α(1 – α)]
41.7
–2.4
0.8626x 0.9876 1.0516x 0.9941 0.8821x 0.9802 1.0171x 0.9898
y r2 y r2 y r2 y r2
36.3 36.0 35.7 35.4 –3.0
–2.7
–2.4
–2.1
–1.8
0.764x 37.731 0.9832 0.8016x 37.973 0.9924 0.9329x 38.331 0.9994 0.973x 38.434 0.9970
–1.5
ln[α(1 – α)]
Fig. 11 Plots of Value II versus ln[a(1 - a)] for a PU, b SEC-80, c SEC-85, and d SEC-90 at the heating rate of 5, 10, 15, and 20 C min-1
0.95, 0.83, and 0.87 for PU, SEC-80, SEC-85, and SEC-90, respectively. All were less than 1, indicating the thermal degradation was single and simple that was mainly caused by the pyrolysis of the polymeric matrix of PU. This also agreed well with the stabilizing E and ln[Af(a)] at a of 0.15–0.90 (Fig. 7). We also investigated the reaction rate constant (k) calculated by Arrhenius equation [23–25]: k ¼ Ae
E RT
The k is related closely to the reaction temperature, reaction medium (or solvent), catalyst, etc., even to the shape and characteristics of reactors. As Table 1 shows, the k at Tp (kp) changed correspondingly with the variations of Tp, E, and A. For example, SEC-90 presented kp values at 3.60 9 10-3, 6.99 9 10-3, 1.05 9 10-2, and 1.33 9 10-2 min-1 for the heating rate of 5, 10, 15, and 20 C min-1; kp was 1.59 9 10-2, 1.51 9 10-2, 1.33 9 10-2, and -2 -1 1.33 9 10 min for PU, SEC-80, SEC-85, and SEC-90, all at the heating rate of 20 C min-1, respectively. Based on the obtained E, m, n, and lnA, the pyrolysis kinetic equations were determined, respectively, for PU, SEC-80, SEC-85, and SEC-90 as the following:
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da 149:14 ¼ e22:16 ð1 aÞ0:78 a0:13 e RT dt da 150:69 ¼ e22:76 ð1 aÞ0:84 a0:11 e RT dt da 143:77 ¼ e21:43 ð1 aÞ0:77 a0:06 e RT dt da 130:53 ¼ e19:06 ð1 aÞ0:75 a0:12 e RT dt
ð10Þ ð11Þ ð12Þ ð13Þ
Then we compared the experimental data (Exp.) with the kinetic method results (Cal.) to verify the applicability of the analysis method used in this study. The Exp. da/dt was obtained from the mass loss rate (Fig. 5) and Eq. (4), and the Cal. da/dt was calculated using Eqs. (10)–(13), for PU, SEC-80, SEC-85, and SEC-90. Figure 8 shows their comparisons. It can be seen that the Exp. da/dt and the Cal. da/dt of PU, SEC80, SEC-85, and SEC-90 all displayed good agreements with each other at the heating rate of 5, 10, 15, and 20 C min-1 . This phenomenon indicated that the thermal degradation of PU, SEC-80, SEC-85, and SEC90 could be described well using the kinetic methods used in this study.
Solidification and thermal degradation of printable, stretchable electrical conductor from…
Conclusions In this study, the solidification and thermal degradation of high-performance printable, stretchable SEC prepared from waterborne polyurethane and micro-silver flakes were studied. The SEC achieved solidification by volatilizing and removing the free water. The thermal degradation of SEC mainly happened in the range of 250–450 C caused by the pyrolysis of the polymeric matrix of PU. The pyrolysis kinetic equations, e.g., da/dt = e22.16(1 - a)0.78 a0.13e(-149.14/RT) for the PU, da/dt = e22.76(1 - a)0.84 a0.11e(-150.69/RT) for the SEC-80, da/dt = e21.43(1 - a)0.77 a0.06e(-143.77/RT) for the SEC-85, and da/dt = e19.06(1 - a)0.75 a0.12e(-130.53/RT) for the SEC-90, were obtained using the kinetic methods. Their m ? n was 0.91, 0.95, 0.83, and 0.87, respectively, less than 1, demonstrating the thermal degradation was a single, simple reaction.
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