A theoretical methodology
based on quantum chemistry to calculate
mechanical properties of polymer crystals has been developed and applied
to representative polymers. By density functional theory calculations
including a dispersion force correction under three-dimensional periodic
boundary conditions, crystal structures of poly(methylene oxide) (PMO),
polyethylene (PE), poly(ethylene terephthalate) (PET), poly(trimethylene
terephthalate) (PTT), and poly(butylene terephthalate) (PBT) were
optimized and their mechanical properties, such as crystalline moduli
and linear and volume compressibilities, were calculated. The optimized
crystal structures were proved to be fully consistent with those determined
by X-ray and neutron diffraction. The crystalline moduli (
E
∥
) parallel to the chain axis were calculated
to be 114 GPa (PMO), 333 GPa (PE), 182 GPa (PET), 7.1 GPa (PTT), and
20.8 GPa (PBT) and compared with those determined from X-ray diffraction,
Raman spectroscopy, and neutron inelastic scattering experiments.
Herein, the
E
∥
values thus determined
are interpreted in terms of conformational characteristics of the
polymeric chains and the validity of the homogeneous stress hypothesis
adopted in the X-ray diffraction method is also discussed.
This
study is an attempt to develop a theoretical methodology to
elucidate or predict the structural characteristics and the physical
properties of an isolated polymeric chain and its crystalline state
precisely and quantitatively. To be more specific, conformational
characteristics of a biobased and biodegradable polyamide, nylon 4,
in the free state have been revealed by not only ab initio molecular
orbital calculations on its model compound but also nuclear magnetic
resonance experiments for the model and nylon 4. Furthermore, the
crystal structure and solid-state properties of nylon 4 have been
elucidated by density functional theory calculations with a dispersion
force correction under periodic boundary conditions. In the free state,
the nylon 4 chain forms intramolecular N–H···O=C
hydrogen bonds, which force the polymeric chain into distorted conformations
including a number of gauche bonds, whereas nylon 4 crystallizes in
the fully extended all-trans structure (α form) that is stabilized
by intermolecular N–H···O=C hydrogen
bonds. The intermolecular interaction energy (Δ
E
CP
) in the crystal was accurately calculated via a counterpoise
(CP) method contrived here to correct the basis set superposition
error, and the ultimate crystalline modulus (
E
b
) in the chain axis (
b
axis)
direction at 0 K was also evaluated theoretically. The results were
compared with those obtained from the α and γ crystalline
forms of nylon 6, and, consequently, the superiority of nylon 4 to
nylon 6 in thermal stability and mechanical properties was indicated:
the Δ
E
CP
and
E
b
values are, respectively, −214 cal
g
–1
and 334 GPa (nylon 4), −191 cal g
–1
and 316 GPa (α form of nylon 6), and −184
cal g
–1
and 120 GPa (γ form of nylon 6). In
conclusion, nylon 4 is expected to be put to practical use as a tough
environmentally friendly polyamide.
Aromatic polythioesters and polydithioesters with different numbers of methylene units have been synthesized and characterized in terms of solubility, crystallinity, glass transition, melting, thermal decomposition, molecular motion, and thermal transition.
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