5 Stress-Induced Crystallization
5.2 Structure development of the PTT upon drawing
5.2.3 Torsional angle transition
From section 1.5, we know that the mechanism of torsional angle transition during stress-induced crystallization is questionable. Table 5.7~ Table 5.9 shows the fraction of trans and gauche state, and also shows the trans-to-gauche ratio in φ1 and the gauche-to-trans ratio in φ2 in different conditions. We show the percentage of trans state (in Figure 5.21, Figure 5.22, and Figure 5.23), percentage of gauche state (in Figure 5.24, Figure 5.25, and Figure 5.26), the trans-to-gauche ratio in φ1(in Figure 5.27, Figure 5.28, and Figure 5.29), and the gauche-to-trans ratio in φ2 (in Figure 5.30, Figure 5.31, and Figure 5.32) depends on temperature at DR=2, 3, and 4 with draw speed 1x109 s-1, 1x1010 s-1,and 1x1011 s-1, respectively.
2 4 6 8 10
Figure 5.17 The DR variation of RDF at (a) 400K, (b) 300K, and (c) 200K with draw speed 1x109 s-1.
Figure 5.18 The DR variation of RDF at (a) 400K, (b) 300K, and (c) 200K with draw speed 1x1010 s-1.
r (Å)
Figure 5.19 The DR variation of RDF at (a) 400K, (b) 300K, and (c) 200K with draw speed 1x1011 s-1.
Figure 5.20 The results of orientation factor at various temperatures and DR.
30 32 34 36 38 40 42
150 200 250 300 350 400 450 500
temperature (K)
Trans (%)
DR=4 relax DR=4 DR=3 relax DR=3 DR=2 relax DR=2 DR=1
Figure 5.21 The percentage of trans state depends on temperature at DR=2, 3, and 4 with draw speed 1x109 s-1.
30 32 34 36 38 40 42 44
150 200 250 300 350 400 450 500
temperature (K)
Trans (%)
DR=4.0 relax DR=4.0 DR=3.0 relax DR=3.0 DR=2.0 relax DR=2.0 DR=1.0
Figure 5.22 The percentage of trans state depends on temperature at DR=2, 3, and 4 with draw speed 1x1010 s-1.
27 29 31 33 35 37 39
150 200 250 300 350 400 450 500
temperature (K)
Trans (%)
DR=4.0 relax DR=4.0 DR=3.0 relax DR=3.0 DR=2.0 relax DR=2.0 DR=1.0
Figure 5.23 The percentage of trans state depends on temperature at DR=2, 3, and 4 with draw speed 1x1011 s-1.
15 17 19 21 23 25 27 29
150 200 250 300 350 400 450 500
temperature (K)
Gauche (%)
DR=4 relax DR=4DR=3 relax DR=3DR=2 relax DR=2 DR=1
Figure 5.24 The percentage of gauche state depends on temperature at DR=2, 3, and 4
15 17 19 21 23 25 27 29
150 200 250 300 350 400 450 500
temperature (K)
Gauche (%)
DR=4.0 relax DR=4.0 DR=3.0 relax DR=3.0 DR=2.0 relax DR=2.0 DR=1.0
Figure 5.25 The percentage of gauche state depends on temperature at DR=2, 3, and 4 with draw speed 1x1010 s-1.
15 17 19 21 23 25 27 29
150 200 250 300 350 400 450 500
temperature (K)
Gauche (%)
DR=4.0 relax DR=4.0 DR=3.0 relax DR=3.0 DR=2.0 relax DR=2.0 DR=1.0
Figure 5.26 The percentage of gauche state depends on temperature at DR=2, 3, and 4 with draw speed 1x1011 s-1.
0
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.27 The trans-to-gauche ratio in φ1 depends on temperature at DR=2, 3, and 4 with draw speed 1x109 s-1.
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.28 The trans-to-gauche ratio in φ1 depends on temperature at DR=2, 3, and 4
0
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.29 The trans-to-gauche ratio in φ1 depends on temperature at DR=2, 3, and 4 with draw speed 1x1011 s-1.
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.30 The gauche-to-trans ratio in φ2 depends on temperature at DR=2, 3, and 4 with draw speed 1x109 s-1.
0.4
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.31 The gauche-to-trans ratio in φ2 depends on temperature at DR=2, 3, and 4 with draw speed 1x1010 s-1.
150 200 250 300 350 400 450 500
temperature (K)
150 200 250 300 350 400 450 500
temperature (K)
Figure 5.32 The gauche-to-trans ratio in φ2 depends on temperature at DR=2, 3, and 4
Table 5.4 The index of torsional angle with draw speed at 1x109s-1.
DR=1 DR=1.5 DR=2 DR=2.5 DR=3 DR=3.5 DR=4 T (K) index
draw relax draw relax draw relax draw relax draw relax draw relax draw relax 200 trans (%) -- 35 33 -- 34 34 35 -- 36 37 33 -- 41 37
gauche (%) -- 28 26 -- 25 26 24 -- 23 23 22 -- 21 22
<φ1> t/g -- 2.57 3.28 -- 3.34 3.03 3.19 -- 3.69 3.31 3.86 -- 5.25 3.90
<φ2> g/t -- 1.47 1.66 -- 1.46 1.42 1.25 -- 1.17 1.13 0.99 -- 1.02 1.17 250 trans (%) -- 35 32 -- 33 -- 35 -- 36 -- 32 -- 36 --
gauche (%) -- 26 25 -- 23 -- 22 -- 21 -- 21 -- 21 --
<φ1> t/g -- 3.07 2.90 -- 3.29 -- 3.73 -- 4.07 -- 3.69 -- 4.11 --
<φ2> g/t -- 1.39 1.54 -- 1.38 -- 1.25 -- 1.17 -- 1.01 -- 1.18 -- 300 trans (%) -- 33 33 -- 34 36 35 -- 36 38 38 -- 39 40
gauche (%) -- 26 24 -- 23 22 22 -- 21 21 22 -- 20 20
<φ1> t/g -- 3.16 3.61 -- 3.67 4.18 3.94 -- 4.58 5.54 5.21 -- 5.32 6.01
<φ2> g/t -- 1.61 1.51 -- 1.35 1.19 1.25 -- 1.20 1.14 1.12 -- 1.03 1.03 350 trans (%) -- 34 32 -- 33 -- 35 -- 36 -- 36 -- 38 --
gauche (%) -- 24 24 -- 23 -- 21 -- 21 -- 21 -- 20 --
<φ1> t/g -- 3.53 2.98 -- 3.27 -- 4.15 -- 4.95 -- 5.14 -- 5.43 --
<φ2> g/t -- 1.37 1.41 -- 1.32 -- 1.23 -- 1.20 -- 1.15 -- 1.05 -- 400 trans (%) -- 33 31 -- 32 37 34 -- 34 35 36 -- 37 36
gauche (%) -- 24 24 -- 22 20 21 -- 21 21 21 -- 19 19
<φ1> t/g -- 3.46 3.02 -- 3.54 5.34 3.75 -- 4.00 4.19 4.38 -- 4.73 5.37
<φ2> g/t -- 1.47 1.43 -- 1.32 1.14 1.24 -- 1.16 1.10 1.06 -- 0.98 1.09 450 trans (%) -- 32 32 -- 33 -- 34 -- 35 -- 35 -- 35 --
gauche (%) -- 23 22 -- 21 -- 20 -- 20 -- 20 -- 19 --
<φ1> t/g -- 3.06 3.27 -- 3.88 -- 4.19 -- 4.22 -- 4.54 -- 4.54 --
<φ2> g/t -- 1.33 1.30 -- 1.18 -- 1.07 -- 1.04 -- 1.08 -- 1.03 --
Table 5.5 The index of torsional angle with draw speed at 1x1010s-1
DR=1 DR=1.5 DR=2 DR=2.5 DR=3 DR=3.5 DR=4 T (K) index
draw relax draw relax draw relax draw relax draw relax draw relax draw relax 200 trans (%) -- 35 33 -- 33 32 34 -- 35 38 36 -- 37 42
gauche (%) -- 28 25 -- 23 23 23 -- 23 21 23 -- 22 23
<φ1> t/g -- 2.57 3.23 -- 3.31 3.16 3.55 -- 3.61 3.88 3.58 -- 3.69 4.41
<φ2> g/t -- 1.47 1.52 -- 1.37 1.32 1.31 -- 1.24 1.02 1.15 -- 1.09 1.04 250 trans (%) -- 35 32 -- 32 -- 34 -- 35 -- 36 -- 37 --
gauche (%) -- 26 25 -- 24 -- 23 -- 22 -- 22 -- 21 --
<φ1> t/g -- 3.07 3.28 -- 3.41 -- 3.50 -- 3.74 -- 3.91 -- 4.18 --
<φ2> g/t -- 1.39 1.67 -- 1.55 -- 1.31 -- 1.19 -- 1.12 -- 1.01 -- 300 trans (%) -- 33 33 -- 33 36 34 -- 36 39 36 -- 36 38
gauche (%) -- 26 23 -- 22 22 21 -- 21 21 21 -- 21 22
<φ1> t/g -- 3.16 3.31 -- 3.21 3.39 3.37 -- 3.67 3.96 3.98 -- 4.08 3.93
<φ2> g/t -- 1.61 1.37 -- 1.24 1.07 1.11 -- 1.06 0.91 1.10 -- 1.12 1.15 350 trans (%) -- 34 31 -- 32 -- 32 -- 34 -- 35 -- 36 --
gauche (%) -- 24 24 -- 23 -- 22 -- 21 -- 21 -- 20 --
<φ1> t/g -- 3.53 3.21 -- 3.26 -- 3.59 -- 3.91 -- 3.97 -- 4.01 --
<φ2> g/t -- 1.37 1.54 -- 1.37 -- 1.27 -- 1.18 -- 1.04 -- 0.96 -- 400 trans (%) -- 33 30 -- 31 34 32 -- 34 36 35 -- 36 37
gauche (%) -- 24 23 -- 22 22 21 -- 20 19 20 -- 18 18
<φ1> t/g -- 3.46 3.12 -- 3.38 4.27 3.91 -- 4.30 4.80 4.42 -- 4.64 4.83
<φ2> g/t -- 1.47 1.44 -- 1.33 1.28 1.21 -- 1.10 1.04 1.00 -- 0.91 0.92 450 trans (%) -- 32 30 -- 31 -- 32 -- 33 -- 33 -- 34 --
gauche (%) -- 23 22 -- 21 -- 20 -- 20 -- 20 -- 19 --
<φ1> t/g -- 3.06 2.85 -- 3.39 -- 3.64 -- 3.77 -- 4.17 -- 4.90 --
<φ2> g/t -- 1.33 1.33 -- 1.32 -- 1.19 -- 1.11 -- 1.13 -- 1.12 --
Table 5.6 The index of torsional angle with draw speed at 1x1011s-1
DR=1 DR=1.5 DR=2 DR=2.5 DR=3 DR=3.5 DR=4 T (K)
draw relax draw relax draw relax draw relax draw relax draw relax draw relax 200 trans (%) -- 35 33 -- 32 32 32 -- 33 36 34 -- 35 38
gauche (%) -- 28 25 -- 23 23 22 -- 21 22 21 -- 19 22
<φ1> t/g -- 2.57 2.96 -- 2.99 3.16 3.14 -- 3.33 3.79 3.67 -- 3.95 4.39
<φ2> g/t -- 1.47 1.43 -- 1.37 1.32 1.28 -- 1.13 1.13 1.02 -- 0.97 1.20 250 trans (%) -- 35 32 -- 31 -- 32 -- 33 -- 34 -- 35 --
gauche (%) -- 26 25 -- 23 -- 21 -- 21 -- 20 -- 20 --
<φ1> t/g -- 3.07 3.01 -- 3.26 -- 3.35 -- 3.50 -- 3.84 -- 4.04 --
<φ2> g/t -- 1.39 1.55 -- 1.41 -- 1.27 -- 1.16 -- 1.09 -- 1.01 -- 300 trans (%) -- 33 32 -- 31 33 31 -- 32 34 33 -- 34 36
gauche (%) -- 26 24 -- 22 24 21 -- 21 24 21 -- 19 23
<φ1> t/g -- 3.16 3.25 -- 3.39 3.17 3.48 -- 3.47 3.68 3.41 -- 3.55 3.31
<φ2> g/t -- 1.61 1.51 -- 1.39 1.44 1.31 -- 1.20 1.41 1.06 -- 0.99 1.08 350 trans (%) -- 34 32 -- 31 -- 32 -- 33 -- 34 -- 35 --
gauche (%) -- 24 23 -- 21 -- 20 -- 20 -- 20 -- 19 --
<φ1> t/g -- 3.53 3.37 -- 3.34 -- 3.24 -- 3.32 -- 3.56 -- 3.90 --
<φ2> g/t -- 1.37 1.43 -- 1.28 -- 1.14 -- 1.05 -- 1.00 -- 0.94 -- 400 trans (%) -- 33 30 -- 31 33 30 -- 32 35 33 -- 33 35
gauche (%) -- 24 23 -- 21 24 20 -- 20 21 20 -- 19 23
<φ1> t/g -- 3.46 3.13 -- 3.34 3.95 3.44 -- 3.45 4.68 3.44 -- 3.48 3.65
<φ2> g/t -- 1.47 1.45 -- 1.28 1.29 1.19 -- 1.12 1.14 1.03 -- 0.96 1.21 450 trans (%) -- 32 30 -- 29 -- 30 -- 31 -- 33 -- 34 --
gauche (%) -- 23 22 -- 20 -- 19 -- 19 -- 19 -- 17 --
<φ1> t/g -- 3.06 2.98 -- 3.16 -- 3.46 -- 3.64 -- 4.03 -- 4.63 --
<φ2> g/t -- 1.33 1.36 -- 1.25 -- 1.20 -- 1.08 -- 0.94 -- 0.99 --
5.2.4 Discussion
The changes in bulk properties are observed during stress-induced crystallization in our simulation. The increase of amount of precursor increases in the draw process is much more remarkable than that in isothermal crystallization. Furthermore, the subsequent process of relaxation (after the drawing process) would improve the fraction of oriented precursors.
At small DR (DR=2), the fraction of precursors increases in all temperatures with slower draw speeds (1x109s-1 and 1x1010s-1), but it decreases at temperatures 350K and 400K with higher draw speed (1x1011s-1). At larger DR (DR>3), the saturation of induced precursor is observed in all temperature with the slowest draw speed (1x109s-1);
on the contrary, the development of precursor continues at the higher draw speed (1x1010s-1 and 1x1010s-1). Besides, the orientation factor increases with DR, and the curves are similar in all situations, indicating that the orientation factor may be a function of draw ratio only. This implies that the stress-induced precursor is similar at the same DR with each draw speed. The several striking lower value points in Figure 5.20, which the draw speed are all 1x109s-1, support the saturation found in 1x109s-1, earlier than other higher draw speeds.
The subsequent thermal relaxation (following the drawing process) could stabilize and facilitate in the growth of oriented precursors. The results of fraction of precursor are also a function of temperature similar with the isothermal crystallization (See Figure 4.13), but the highest amount of precursor shift to lower temperature (300K with drawing vs 400 K without drawing). The local motion of polymer segments would be induced by uni-axis stress. (Note the maximum capacity of precursor formation should
be found between the temperature allowing for short rage motion and that for entire chain motion.) Comparing the results of isothermal crystallization (Figure 4.14), the intensity of RDF at ~4 Å obviously increases in all cases.
To understand the distribution of torsional angles of the PTT backbone (O-CH2-CH2-CH2-O) in bulk phase, we analyze the percentage of the trans and gauche states during the stress-induced crystallization. Different behaviors observed at different draw speeds. The percentage of φ1 and φ2 in trans state fluctuates at small DR, and increases at larger DR with slower draw speed. At higher draw speeds, this percentage decreases at small DR and increases at larger DR. The percentage value rebounds to the original value with draw speed 1x1011s-1. On the other hand, the percentage of gauche state decreases with DR at all draw speeds. During thermal relaxation, the percentage of the trans rebounds in all draw speeds, but that of gauche rebounds only in faster draw speed. These suggest that torsional angles change to transition state (i.e., angles region outside our definition in section 2.7 Definition of the torsion angle state) in the beginning drawing process, and then become trans state at higher DR or under thermal relaxation.
Detailed analysis also are performed on the two feature torsions (φ1 and φ2) in the PTT backbone. It is found that the trans-to-gauche ratio in φ1 increases rapidly (from 3 to 6) at lower drawing speed and higher temperatures; however, the increase is less significant at high drawing speed and low temperatures. In contrast, the gauche-to-trans ratio for φ2 seems to be insensitive to processing conditions (varies from 1.6 to 0.8 regardless of drawing speeds). After thermal relaxation, the value of trans-to-gauche ratio in φ1 improves significantly in the slower draw speeds, but remain almost constant
in the fastest draw speed. On the other hand, the gauche-to-trans ratio for φ2 decreases at small DR with slower draw speeds (1x109s-1 and 1x1010s-1), but increases at larger DR with faster draw speed.
Before drawing, the fraction of trans state is ~34%, and that of gauche is ~25% in the bulk phase; the most populated conformations in φ1 is trans, and that in φ2 is gauche;
i.e., the most populated conformations in the backbone torsions are t-g-g-t (φ1-φ2-φ2-φ1).
During draw process, the t-t-t-t conformation increases. Our results are in agreement with the result of Chuch’s experimental observation[28]. The thermal relaxation would change the conformations in some of our simulations, but the changes are not obvious.