Gauche-trans transitions in amorphous polymers under annealing:
Lattice model and polarized light scattering
Masaru Matsuo,
1,
*
Yanling Luo,
1
and Andrzej Galeski
2
1
Department of Apparel and Clothing Science, Faculty of Human Life and Environment, Nara Women’s University,
Nara 630-8506, Japan
2
Centre of Molecular and Macromolecular Studies, Polish Academy of Science, Lodz, Poland
Received 8 October 2008; published 10 April 2009
The driving force of density fluctuation of amorphous polymer films under annealing processes was evalu-
ated synthetically in terms of thermodynamics on the basis of the logarithmic light intensity as a function of
annealing time. The time dependence of nI of polyethylene terephthalatePET as an example for char-
acterizing an amorphous state was classified into three stages: the first stage stage I, where nI showed
insignificant changes with time; the second stage stage II, where nI 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 orien-
tation 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 orien-
tation 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 fluctua-
tion 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.
DOI: 10.1103/PhysRevE.79.041801 PACS numbers: 36.20.-r, 61.41.+e, 81.10.-h
I. INTRODUCTION
There are a number of papers describing the kinetics of
crystallization of polymers in terms of crystal growth and the
initiation of crystallization relating to the nucleation step.
This concept is due to experimental evidence that polymer
crystallization may be assisted by the formation of an inter-
mediate metastable state, and the long-range structure due to
some structure relaxations is formed during the annealing
processes. Among crystalline polymers, polyethylene tereph-
thalate PET can form amorphous films. As such, PET pro-
vides the opportunity to study crystallization kinetics during
the induction period, which is defined as the time required
for the formation of high-density regions exceeding the criti-
cal size directly from the homogeneous amorphous state
1–10.
Apart from the observation of crystal growth processes,
crystallization of PET has been studied primarily by depolar-
ized light scattering under the induction period in terms of
density fluctuation of the amorphous phase 1,8,9. The re-
sults show that the period is associated with spinodal decom-
position SD caused by orientational fluctuation of chain
segments on the basis of the concept concerning the trans-
formation from the isotropic-to-nematic phase proposed by
Doi et al. 11.
The detailed observation of light scattered intensity
against annealing time was classified into three regions 8,9,
based on the annealing experiment when the amorphous PET
film was put into a hot oven fixed at a desired temperature
and an incident beam of He-Ne gas laser was directed at the
film. In the first stage stage I, the scattered intensity
showed insignificant changes. In the second stage stage II,
the logarithm of scattered intensity increased linearly. Such
behavior has been analyzed within the framework of the lin-
ear theory of SD, determining that the amorphous chains at
elevated temperatures were thermodynamically unstable and
tended to incur a density fluctuation. In the third stage stage
III, x-ray diffraction and density measurements revealed the
initiation of crystallization. The stage I period shortened with
increasing annealing temperature; however, any changes
could not be confirmed by density, x-ray diffraction, and po-
larized light scattering measurements.
This paper focuses on conformational changes of amor-
phous PET chains using a combined experimental and theo-
retical approach to probe whether the conversion from
gauche-to trans-conformation in stage I aids SD at stage II.
The amorphous PET film with a thickness of 75 m was
used as a test specimen to obtain a clear Fourier transform
infrared FTIR absorption peak. The analysis was performed
synthetically by using depolarized light scattering, small-
*
Author to whom correspondence should be addressed: Tel and
Fax: 81-742-20-3462; m-matsuo@cc.nara-wu.ac.jp
PHYSICAL REVIEW E 79, 041801 2009
1539-3755/2009/794/04180115 ©2009 The American Physical Society 041801-1