5 Stress-Induced Crystallization
5.3 Structure development within oriented precursor
5.3.2 The RDF, average size, and tosional angle of precursors
In this section, the results of the maximum size of the precursor in each condition are analyzed using the same method as described in section 4.3. Figures 5.33, 5.35, and 5.37 show the time evolution of RDF intensity at 4.11Å, and the average size of precursor at 200K, 300K, and 400K, respectively, with a draw speed of 1x109s-1; Figures 5.39, 5.41, and 5.43 show the results for draw speed 1x1010s-1; Figures 5.45, 5.47, and 5.49 for draw speed 1x1011s-1. On the other hand, Figures 5.34, 5.36, and 5.38 show the results of the fractions of backbone torsions in the oriented precursors at 200K, 300K, and 400K, respectively, with a draw speed 1x109s-1; Figures 5.40, 5.42, and 5.44 show the results for draw speed 1x1010s-1; Figures 5.46, 5.48, and 5.50 for draw speed 1x1011s-1. Moreover, the temperature dependence of the growth rate of precursor size (Figure 5.51) and that of transition rate of torsional angles (Figure 5.52) are analyzed by averaging all of oriented precursors at each temperature.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0
Figure 5.33 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 200 K with draw speed 1x109s-1.
Figure 5.34 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 200K with draw speed 1x109s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0
Figure 5.35 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 300 K with draw speed 1x109s-1.
Figure 5.36 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 300K with draw speed 1x109s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0
Figure 5.37 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 400 K with draw speed 1x109s-1.
Figure 5.38 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 400K with draw speed 1x109s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0 1 2 Size 3
RDF
Figure 5.39 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 200 K with draw speed 1x1010s-1.
Figure 5.40 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 200K with draw speed 1x1010s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0 1 2 Size 3
RDF
Figure 5.41 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 300 K with draw speed 1x1010s-1.
Figure 5.42 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 300K with draw speed 1x1010s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0 1 2 Size 3
RDF
Figure 5.43 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 400 K with draw speed 1x1010s-1.
Figure 5.44 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 400K with draw speed 1x1010s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0
Figure 5.45 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 200 K with draw speed 1x1011s-1.
Figure 5.46 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 200K with draw speed 1x1011s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0
Figure 5.47 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 300 K with draw speed 1x1011s-1.
Figure 5.48 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 300K with draw speed 1x1011s-1.
The intensity of the RDF
The average size of precursor
0
The average size of precursor
0 1 2 Size 3
RDF
Figure 5.49 The time evolution of RDF intensity (4.11Å) (diamond) and the time averaged number of parallel segments contained in a representative precursor (triangle) at 400 K with draw speed 1x1011s-1.
Figure 5.50 The backbone torsions <φ1> in trans (triangles) and <φ2> in gauche (circles) for segments in a precursor at 400K with draw speed 1x1011s-1.
0
150 200 250 300 350 400 450 500
temperature (K)
Growth rate (number of segment/DR)
1x1011s-1
150 200 250 300 350 400 450 500
temperature (K)
Growth rate (number of segment/DR)
1x1011s-1 1x1010s-1 1x109s-1
Figure 5.51 The temperature dependence of the growth rate of precursor size with different draw speeds.
-0.10
150 200 250 300 350 400 450 500
draw ratio
Torsionalangle transition rate of <φ1>
-0.10
150 200 250 300 350 400 450 500
draw ratio
Torsionalangle transition rate of <φ1>
Figure 5.52 The temperature dependence of transition rate of torsional angle φ1 with different draw speeds.
-0.10
150 200 250 300 350 400 450 500
draw ratio
Torsionalangle transition rate of <φ2>
-0.10
150 200 250 300 350 400 450 500
draw ratio
Torsionalangle transition rate of <φ2>
Figure 5.53 The temperature dependence of transition rate of torsional angle φ2 with different draw speeds.
5.3.3 Discussion
In Table 5.9 it is found that the number of precursors for system under stress is slightly higher than that in the case of isothermal crystallization. In addition, the stress-induced crystallization could create larger precursor in size than isothermal crystallization. Both factors lead to the much higher fraction of precursors in the stress-induced crystallization. The results of the average size of precursor agree with intensity of RDF at 4.11Å in each precursor. Most precursors grow with increasing DR until DR≒3.5 and their intensities of RDF show a similar behavior as DR. This indicates the highly oriented precursors are developing in stress-induced crystallization.
Besides, these results suggest that the definition of precursor is adequate for identifying any local structure developed in the polymer systems. From Figure 5.51, the maximum
of the growth rate of oriented precursor occurs below the glass transition temperature, suggesting that that local motion of polymer segments would be induced by uni-axis stresses. The maximum growth rate appears at draw speed 1x1010s-1 and temperature region between 250K and 350K, implying the better condition of stress-induced crystallization are not the faster.
The states of backbone torsional angles in precursors evolve with DR differently in different processing conditions. The fraction of φ1 in trans increases with DR, but the fraction of φ2 in gauche decreases with DR in most precursors. The stress and thermal effects are different in these two torsional angles. Slower draw speed and lower temperature would improve the change of φ1 to the trans state; on the other hand, the faster draw speed and medium temperatures would improve the change of φ2 to the gauche state. Furthermore, the fraction of φ1 in trans is very high (~70%) in each precursor, but the fraction of φ2 in gauche only 20~30%. That indicates that the stress-induced transition in φ2 is faster than that in φ1. In addition, the faction of φ2 in gauche fluctuates in some cases, indicating the torsional angle φ2 would favorably move to the gauche after forcing to the trans state by the external stress.