The models were then equilibrated by a series of energy minimization and molecular dynamics runs. The crystal structures for the semicrystalline polymers were generated by using Crystal Cell.
The quality of the resulting structure for both amorphous and cystalline structures were tested by comparing the X-ray scattering patterns determined from the molecular models with experimental data. The simulated bulk structures were then subjected to three different methods for evaluating their mechanical behaviour: the static method, developed by Theodorou and Suter; the fluctuation method of Parinello and Rahman; and the dynamic method, originally introduced by Berendsen et al.
In the static method, each structure was subjected to a number of successive deformations followed by a reminimization in order to map out the energy hypersurface and subsequently determine the elastic modulus.
The dynamic method involves using constant stress molecular dynamics to measure the stress-strain behavior of a material subjected to an applied load. For the dynamic method a force field united atoms and a software developed in the group of Professor J. Clark from Manchester University was used.
The fluctuation method makes use of the fact that the elastic constants appear in the fluctuation formulae applied to statistical ensembles obtained by simulation.
Liquid Crystalline Polymers
For the static method, the procedure is illustrated in Fig. The methods were tested on several amorpous and semicystalline polymers polysulfone, polyethersulfone, polypropylene. Investigations for other polymers are in progress PEEK, polyethylene. As pointed out above, the mother lamellae were detected in parallel in the SAXS measurement. All of these data suggest that, in the time region II , the mother lamellae consisted mainly of the hexagonal phase with the conformationally disordered chain segments. The WAXD data should show the peak of the hexagonal phase clearly in order to confirm this conclusion [ 18 ].
However, as shown in Figure 10 a, the diffraction angle region predicted for the hexagonal peak was covered with a strong amorphous halo, making it difficult to judge the existence of the hexagonal phase peak. Then, the integrated intensity of the whole broad peak was evaluated, the intensity of which was found to change at the two stages. The broad peak intensity started to decrease in the time region II and plateaued for a while. Then it decreased steeply Figure 10 b ; at this moment the orthorhombic peaks started to appear. This behavior strongly suggests the presence of the intermediate hexagonal phase before the appearance of the orthorhombic phase.
With the passage of time, the intensity of the disordered trans IR band decreased gradually, but it was detected even in the time region III. Time dependence of a WAXD profile and b the intensity of the amorphous halo and reflection obtained in the isothermal crystallization of high-density polyethylene. In this way, the hexagonal phase transforms to the structurally regular orthorhombic phase.
The daughter lamellae started to appear in the amorphous region and coexisted with the mother lamellae. Even after the several tens of minutes, where the orthorhombic phase increased appreciably, the signal of the intermediate state was detected, as known from the observation of the disordered-trans IR band. Besides, the WAXD and peaks increased the intensity gradually, not sharply.
As shown in Figure 11 , one model satisfying these observations may be illustrated in such a way that the disordered lamellae grew still in the time region III , and they were regularized to the orthorhombic phase. Strobl et al. However, it is still ambiguous whether the intermediate phase generates only at the front face or it remains inside the regular lamellar plate and coexists with the orthorhombic phase Figure 11 b. The same question might be invoked also for the daughter lamellae.
There are four possibilities regarding the daughter lamellae: they are generated in the amorphous region among the mother lamellae as the intermediate phase and transforms to the orthorhombic phase in a later stage Figure 11 c,d , or they exist totally as the intermediate phase Figure 11 e,f. Aliphatic nylon consists of the alternate arrangement of methylene segments and amide groups along the chain axis.
In the crystal lattice, the sheets, which are constructed by the parallel packing of zigzag chains linked by the intermolecular hydrogen bonds, are stacked together by the weaker van der Waals interactions, as illustrated in Figure 12 [ 38 ]. For the study of the structural evolution process from the melt, we need to know the conformational regularization of the chains, the arrangement of the methylene segmental parts, and the formation of hydrogen bonds among the amide groups in addition to the generation of the lamellar sacking structure.
In order to trace the conformational regularization, the nylon sample with relatively long methylene segments is better because of the easier detection of a series of the so-called progression bands [ 39 , 40 , 41 ].
At the same time, the melting point is lower for such an aliphatic nylon with longer methylene segments and the thermal degradation is depressed more effectively. Besides, it is better to distinguish the behavior of the two methylene segments of the monomeric unit. As shown in Figure 12 b, the IR CH 2 bands shifted before and after the partial deuteration, making it easier to trace the behaviors of these two different types of the methylene segments. For example, this figure shows the temperature dependence of the IR spectra in the heating process, where the methylene bands of the NH side disappeared at a lower temperature than those of the CO side.
The thermal mobility of the NH-side methylene segments seems more active than that of the CO-side methylene part [ 39 , 40 , 41 ]. The band position was seen to shift toward the lower frequency side by the deuteration. Figure 13 shows the various experimental data collected for this partially deuterated nylon sample in the isothermal crystallization from the melt.
The IR spectral change tells us about the formation of hydrogen bonds among the amide groups. Therefore, it may be said that, even in the molten state, a number of hydrogen bonds were formed in addition to the free amide groups. This observation suggests the existence of the domains composed of the nylon chain segments connected by the weak hydrogen bonds, though the methylene parts were totally disordered. Correspondingly, the SAXS data shows the central scattering from the early stage of the temperature jump, which was interpreted using the Debye—Buche equation Equation 4 under the assumption of the existence of domains in the time region A, as indicated by the IR spectral data.
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Time dependence of the various data measured for the partially-deuterated nylon sample in the isothermal crystallization from the melt [ 13 ]. The IR data tell us about the conformational regularization of the methylene segmental parts. In the time region C, the slight increase in the hydrogen bonds was detected and, at this moment, the vibrational bands intrinsic to the zigzag methylene segments of CO side, —CO CD 2 8 CO—, started to appear. This indicates that the nylon chains started to extend and form the parallel array in the crystal lattice, where only the CO-side methylene segments were regularized, but the NH-side methylene parts were still in the disordered state.
As illustrated in Figure 14 , nylon shows the unique structural evolution in such a way that the hydrogen bonds were already formed in the molten state, and the correlation among the domains constructed by the hydrogen-bonded chain segments became stronger with the increasing number of hydrogen-bonded amide groups time regions A and B.
Following this, the regularization of the methylene segmental parts started to occur in parallel to the formation of the crystal lattice as well as the creation of the stacked lamellar structure time region C. It should be noted that the methylene segments of CO-side and NH-side behave in a different way in the regularization process. Schematic illustration of the structural evolution of nylon in the isothermal crystallization process from the melt. This copolymer shows the solid-state phase transition between the ferroelectric phase the low-temperature phase, LT and the paraelectric phase the high-temperature phase, HT at a Curie transition temperature see Figure 15 [ 43 ].
In the cooling process from the melt, the HT phase crystallizes first and then transforms to the LT phase. If the sample is cooled from the molten state to the temperature region of the LT phase, the LT phase should appear directly from the melt. But we did not know whether this prediction was correct or not, and then the temperature jump experiment was performed [ 44 ]. After that, the LT phase peak started to increase the intensity instead of the HT phase peak.
In this way, the HT phase always appeared at first even when the isothermal crystallization was performed in the LT phase region. The appearance of the thermodynamically unstable HT phase was due to the kinetic factor; the HT phase is kinetically more preferable than the LT phase.
The HT phase takes the loose packing structure of the conformationally disordered chains and so this phase appears more easily than the LT phase of the regular zigzag conformation. This situation is similar to the case of the crystallization of the orthorhombic PE, where the hexagonal phase, corresponding to the HT phase, appears at first and transforms to the orthorhombic phase gradually since the latter is always thermodynamically more stable than the former as long as the crystallization is performed under atmospheric pressure. At high pressure, the hexagonal phase is existent as a stable state.
In this way, the crystalline phase existent in the lamellae is controlled by a combination of kinetic and thermodynamic factors. It is dangerous to simply expect that only the thermodynamically stable phase LT phase appears when the crystallization experiment is performed in the low temperature region.
Crystal structure and chain conformation of the VDF—TrFE copolymer: a low-temperature phase and b high-temperature phase. Depending on the number m of the methylene units, the chain conformation in the crystal lattice changes systematically. In the cases of short m value, the chain conformation is remarkably different between the members of odd and even m values. PET 2GT takes a trans-zigzag conformation [ 45 ], while 3GT takes a helical conformation contracted from the extended form by the introduction of gauche CC bonds [ 46 ].
As the number m is longer, the methylene segmental part tends to take a fully extended all-trans conformation irrespective of the m value [ 47 , 48 ]. The regularization of the long methylene units can be traced clearly by measuring the time dependent IR spectral data, since the assignment of a series of methylene progression bands was made already.
The wavelength of an incident X-ray beam was 0. In this figure, the total number of spherulites generated in the isothermal crystallization process was also plotted, which was estimated by the polarized optical microscopic observation under the same temperature jump condition.
Developments in Crystalline Polymers—2 | David C. Bassett | Springer
In the polarized optical microscopic observation, a few numbers of tiny spherulites started to appear. In the time region III , the number of spherulites increased further. The X-ray peak, intrinsic to the chain conformation, started to increase the intensity in this region, although not very strongly.
The hk 0 reflections were not detected. In this way, in the time region III , the stacked lamellae were formed, but the molecular chains were still in the conformationally disordered state. It is noted that the spherulites were already produced even in such a structurally disordered inner state.
Developments in Crystalline Polymers-1
In other words, the spherulite was in a liquid—crystalline state. It is important to note again that the spherulites were formed in the relatively early stage of crystallization, but the inner structure was in the disordered state, and, then, the inner structure was regularized gradually without a drastic increase in the spherulites themselves [ 49 ]. In this way, we observed the structural evolution in the isothermal crystallization process from the melt for the various kinds of crystalline polymers on the basis of the time-resolved measurements of WAXD, SAXS, and FTIR data.