Crystalline Moduli of Polymers, Evaluated from Density Functional Theory Calculations under Periodic Boundary Conditions

Kurita, Taiga; Fukuda, Yuichiro; Takahashi, Morihiro; Sasanuma, Yuji

doi:10.1021/acsomega.8b00506

Cited by 32 publications

(47 citation statements)

References 88 publications

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“…In general, polymer crystals exhibit the largest modulus in the chain axis direction. For many polyesters, theoretical values of this limiting elastic modulus are of the order 10–10 2 GPa (Matsuo et al, 1993; Tashiro, 1993; Wasanasuk and Tashiro, 2012; Kurita et al, 2018; Lee et al, 2018). Due to the strong mechanical anisotropy of polymer crystals, the theoretical crystalline modulus along the chain axis is 1–2 order of magnitude higher than those in different directions (Tashiro and Kobayashi, 1996).…”

Section: Resultsmentioning

confidence: 99%

Constrained Amorphous Interphase and Mechanical Properties of Poly(3-Hydroxybutyrate-co-3-Hydroxyvalerate)

et al. 2019

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In the present study, for the first time the evolution of tensile mechanical properties of different poly(3-hydroxybutyrate-co-3-hydroxyvalerate) copolymers (PHBV8 and PHBV12, with 8 mol% and 12 mol% of HV co-units, respectively) as a function of the storage time at room temperature has been investigated in parallel with the quantification of the crystalline, mobile amorphous, and rigid amorphous fractions. A comparison with the evolution of the crystalline and amorphous fractions in the homopolymer poly(3-hydroxybutyrate) (PHB) was also performed. For all the samples, the crystallinity was found to slightly increase during storage. In parallel, the mobile amorphous fraction (MAF) decreased markedly, with the result that a relevant increase in the rigid amorphous fraction (RAF) was detected. The RAF content in the copolymers was lower than that of PHB. For all the samples, the RAF formation during aging was ascribed to the growth of secondary crystals in geometrically restricted areas. It was demonstrated that the storage at Troom leads in PHB, PHBV8, and PHBV12 to a progressive increase in the total solid fraction (crystal phase + rigid amorphous fraction) and to a simultaneous physical aging of the rigid amorphous fraction. The two different processes cannot be separated and distinguished, so that only the resulting effect on the mechanical properties was considered. The experimental elastic modulus of both PHBV8 and PHBV12 was found to increase regularly with the total solid fraction, as well as the tensile strength. Conversely, the elongation at break turned out to be an increasing function of the mobile amorphous fraction. The elastic moduli of the crystalline, mobile amorphous, and rigid amorphous fractions of PHBV8 and PHBV12 were estimated by means of a three-phase modified Takayanagi's model, to take into account also the contribution of the rigid amorphous fraction. The calculated values were found in agreement with theoretical expectations.

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Section: Resultsmentioning

confidence: 99%

Constrained Amorphous Interphase and Mechanical Properties of Poly(3-Hydroxybutyrate-co-3-Hydroxyvalerate)

et al. 2019

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“…Inasmuch as semicrystalline polymers comprise crystalline and amorphous regions, the crystalline modulus in the chain axis direction at 0 K is, in principle, the largest modulus that the polymer can exhibit. 43 Shown in Appendix A (Supporting Information) are the stiffness and compliance tensors calculated for the α form of nylon 4 and the α and γ forms of nylon 6. The compliance tensor yields Young’s moduli ( E a , E b , and E c , respectively) in the a , b (chain axis), and c axis directions of the crystal.…”

Section: Results and Discussionmentioning

confidence: 99%

Computational Characterization of Nylon 4, a Biobased and Biodegradable Polyamide Superior to Nylon 6

Fukuda

Sasanuma

2018

ACS Omega

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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.

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“…The material parameters at the nanoscale were determined by means of the available literature sources [ 31 , 32 , 33 ] for the parameters given in Table 1 .…”

Section: Predicting the Materials Behavior Under Consideration Of The Micro- And Nanoscalementioning

confidence: 99%

“…The material parameters at the nanoscale were determined by means of the available literature sources [31][32][33] for the parameters given in Table 1. Thus, the mechanical properties at the nanoscale can be determined.…”

Section: Predicting the Materials Behavior Under Consideration Of The Micro-and Nanoscalementioning

confidence: 99%

Multiscale Simulation of Semi-Crystalline Polymers to Predict Mechanical Properties

et al. 2021

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A multiscale simulation method for the determination of mechanical properties of semi-crystalline polymers is presented. First, a four-phase model of crystallization of semi-crystalline polymers is introduced, which is based on the crystallization model of Strobl. From this, a simulation on the nanoscale is derived, which models the formation of lamellae and spherulites during the cooling of the polymer by using a cellular automaton. In the solidified state, mechanical properties are assigned to the formed phases and thus the mechanical behavior of the nanoscale is determined by a finite element (FE) simulation. At this scale, simulations can only be performed up to a simulation range of a few square micrometers. Therefore, the dependence of the mechanical properties on the degree of crystallization is determined by means of homogenization. At the microscale, the cooling of the polymer is simulated by a cellular automaton according to evolution equations. In combination with the mechanical properties determined by homogenization, the mechanical behavior of a macroscopic component can be predicted.

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Crystalline Moduli of Polymers, Evaluated from Density Functional Theory Calculations under Periodic Boundary Conditions

Cited by 32 publications

References 88 publications

Constrained Amorphous Interphase and Mechanical Properties of Poly(3-Hydroxybutyrate-co-3-Hydroxyvalerate)

Constrained Amorphous Interphase and Mechanical Properties of Poly(3-Hydroxybutyrate-co-3-Hydroxyvalerate)

Computational Characterization of Nylon 4, a Biobased and Biodegradable Polyamide Superior to Nylon 6

Multiscale Simulation of Semi-Crystalline Polymers to Predict Mechanical Properties

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