Gauche-trans transitions in amorphous polymers under annealing: Lattice model and polarized light scattering

Abstract

The driving force of density fluctuation of amorphous polymer films under annealing processes was evaluated synthetically in terms of thermodynamics on the basis of the logarithmic light intensity as a function of annealing time. The time dependence of ln(I) of polyethylene (terephthalate) (PET) as an example for characterizing an amorphous state was classified into three stages: the first stage (stage I), where ln(I) showed insignificant changes with time; the second stage (stage II), where ln(I) increased linearly; and the third stage (stage III), where the intensity deviated from the linear relationship and tended to level off. The density fluctuation by chain diffusion, termed quasi-spinodal decomposition, in stage II was analyzed in terms of an increase of trans-conformation of an amorphous chain in stage I. To provide conclusive evidence, the orientation function of chain segments was calculated by using a lattice model that accounts for entropic and energetic characters. The former character is associated with segmental orientation due to the effect of chain stiffness of Kuhn segments characterized by a rod with a relatively large length-to-width ratio x , whereas the latter is associated with thermotropic systems with anisotropic polarizabilities. By using the theoretical orientation function, Hv light scattering patterns were calculated by a statistical approach in which the optical axis of a PET chain segment was chosen along the direction perpendicular to the benzene ring. This selection was justified by comparison of the three principal refractive indexes of a PET chain. The calculated patterns provided a clear X-type lobe, when the correlation between optical elements concerning the rotational fluctuation became stronger. The calculated patterns were in good agreement with the patterns observed in stage III. The series of experimental and theoretical results indicated that the conversion from gauche- to trans-conformation plays an important role to derive the density fluctuation of amorphous polymer chains associated with the initiation of crystallization.

Characteristics of several kinds of polyethylene gel estimated by small‐angle light scattering under cross polarization

“…On the basis of the theoretical calculation of eq 4, the optically anisotropic rod can be constructed by coagulation of anisotropic scattering elements associated with loose folding structures as shown in Figure 6(c). Such a phenomenon is thought to be similar to the initial crystallization of amorphous poly(ethylene terephthalate) films 32…”

Understandable Unified Description about Diffraction and Scattering of X‐Ray and Visible Light Beams from Soft Matters in Terms of Educational Aspects

“…The four lobes taking an X‐type become sharper with increasing b/a, indicating that the pattern is strongly affected by azimuthal angle dependence for the correlation distance. The pattern is in good agreement with the pattern observed at initial stage of the formation of polymer rich phases by concentration fluctuation in the crystalline polymer solutions and initial crystallization process of polyethylene (terephthalate) …”

“…The statistical approach has been adopted for scattering from gels [21,22] and amorphous films. [23,24] When there exist many small assemblies with ordered chain arrangement as a function of distance between their chains in polymer film or gel, each assembly can be considered as optical elements, In such a case, H v scattering pattern becomes very weak and the pattern could not be observed on the photo screen of frosted glass (as shown in Figure 21(a)), since the very weak light scattered from the gels could not pass through the analyzer. [20] The pattern was observed on the sample surface by the reflection from the analyzer, and then photographs were taken using a commercial camera, as shown in Figure 21(b).…”

“…The pattern is in good agreement with the pattern observed at initial stage of the formation of polymer rich phases by concentration fluctuation in the crystalline polymer solutions [20][21][22] and initial crystallization process of polyethylene (terephthalate). [23,24] Of course, the concept shown in Figure 24 was applied to the systems concerning spherulite and rod. [25] The theoretical patterns were in good agreement with the observed patterns.…”

“…Another treatment for SALS is statistical approach model and this is useful for the system where the morphology observed by polarized microscopy provides unclear and dark structure. The statistical approach has been adopted for scattering from gels and amorphous films . When there exist many small assemblies with ordered chain arrangement as a function of distance between their chains in polymer film or gel, each assembly can be considered as optical elements, In such a case, H v scattering pattern becomes very weak and the pattern could not be observed on the photo screen of frosted glass (as shown in Figure (a)), since the very weak light scattered from the gels could not pass through the analyzer.…”