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![(Color online) Mechanical properties of the polyethylene chain. (a). The density of strain energy versuses strain. The Young's modulus Y = 374.5 Gpa is obtained by fitting strain energy density to E = 0.5Y ǫ 2 in small strain region ǫ ∈ [−0.01, 0.01]. A big jump in the curve reveals the ultimate strain to be ǫc = 32.85% ± 0.05%. Inset shows two neighboring ethylene moleculars after the phase transition of the polyethylene chain at ǫ = ǫc. (b). Stress-strain relation.](profile/Timon-Rabczuk/publication/221703294/figure/fig6/AS:647550575071232@1531399496743/Color-online-Mechanical-properties-of-the-polyethylene-chain-a-The-density-of.png)
(Color online) Mechanical properties of the polyethylene chain. (a). The density of strain energy versuses strain. The Young's modulus Y = 374.5 Gpa is obtained by fitting strain energy density to E = 0.5Y ǫ 2 in small strain region ǫ ∈ [−0.01, 0.01]. A big jump in the curve reveals the ultimate strain to be ǫc = 32.85% ± 0.05%. Inset shows two neighboring ethylene moleculars after the phase transition of the polyethylene chain at ǫ = ǫc. (b). Stress-strain relation.
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The upper limit of the thermal conductivity and the mechanical strength are
predicted for the polyethylene chain, by performing the {\it ab initio}
calculation and applying the quantum mechanical non-equilibrium Green's
function approach. Specially, there are two main findings from our calculation:
(1). the thermal conductivity can reach a high val...
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Citations
... Such a counterintuitive prediction has attracted increasing attention over the past decades and has been studied extensively from a theoretical perspective. 220 In particular, simulations have been performed based on various methods such as molecular dynamics, 184 Green-Kubo, 218 and nonequilibrium Green function (NEGF), 221 and some calculations have reported the value of b = 0.4 as a general characteristic of 1D chains. Addressing the FPU divergence question necessitates a non-perturbative approach rooted in many-body physics. ...
... For a realistic polymer system, the extended chain length introduces mechanical constraints like bending, torsion, nonbonding, and convection. 229 Jiang et al. 221 studied a PE chain of 100 nm in length and calculated a denitive upper limit for thermal conductivity (k = 310 W m −1 K −1 ) and Young's modulus (E = 374.5 GPa). Further computational studies on materials other than PE have found diverging thermal conductivity in single-chain forms. ...
Designing polymers with desirable thermal or thermoelectric properties has been a great goal in the field of organic functional materials. This is widely considered challenging because polymers manifest complicated transport...
... The first-principles anharmonic lattice dynamics calculation is a method based on the computation of the interatomic force constants extracted from DFT. First-principles-based lattice dynamics predicted that the thermal conductivity of an individual PE chain can be as high as 1400 W/mK, 40 while that of a 100 nm crystalline PE fiber can reach 310 W/mK. 41 ...
In this article, we review thermal transport in polymers with different morphologies from aligned fibers to bulk amorphous states. We survey early and recent efforts in engineering polymers with high thermal conductivity by fabricating polymers with large-scale molecular alignments. The experimentally realized extremely high thermal conductivity of polymer nanofibers are highlighted, and understanding of thermal transport physics from molecular simulations are discussed. We then transition to the discussion of bulk amorphous polymers with an emphasize on the physics of thermal transport and its relation with the conformation of molecular chains in polymers. We also discuss the current understanding of how the chemistry of polymers would influence thermal transport in amorphous polymers and some limited, but important chemistry-structural-property relationships. Lastly, challenges, perspectives and outlook of this field are presented. We hope this review will inspire more fundamental and applied research in the polymer thermal transport field to advance scientific understanding and engineering applications.
... Aa discussed in previous sections, numerous experimental studies revealed that very high Ä can be achieved by aligning the PE chains. On the other hand, number of theoretical studies have accurately predicted the upper limit of Ä of fully aligned PE chains, although it is almost impossible to exactly mimic the complex experimental conditions in a theoretical framework [64]. Using simulation tools, the theoretical value of Ä for aligned PE chains can be as high as 300 W/m.K [65]. ...
... Using simulation tools, the theoretical value of Ä for aligned PE chains can be as high as 300 W/m.K [65]. Using ab initio calculations, Jiang et al. [64] predicted Ä = 310 W/m.K for 100-nm long PE chain at RT and Ä increases with the chain length. Wang et al. [66] predicted Ä as high as 237 W/m.K for bulk PE crystal along the axial direction using the firstprinciples-based harmonic lattice dynamic. ...
The low thermal conductivity of polymers hinders their use in applications requiring high thermal conductivity such as electronic packaging, heat exchangers, and thermal management devices. Polyethylene and polypropylene (polyolefins) account for ∼55% of the global thermoplastic production. Improving the thermal conductivity of this class of thermoplastics is important for many applications. This comprehensive review analyzes the advances on enhancing the thermal conductivity of pristine polyolefins. First, the mechanism of thermal transport in polymers and the key parameters that govern conductive heat transfer through polymers are discussed. Moreover, the progress in modeling and simulation of thermal conductivity of polyolefins are analyzed. Furthermore, the different approaches to enhance the thermal conductivity of polyolefins through controlling their microstructure, crystallinity and chain orientation are presented. Finally, the key challenges and prospective directions for developing thermally enhanced pristine polyolefins are outlined.
... It is noteworthy that the level of the disentanglement stress σ de under uniaxial tension is significantly high (Fig. 4 (b-i)), especially in the cases of large M n . For M n = 65 kg/mol, stress reaches ≈10 GPa at ε ≈ 5, which is comparable to the theoretical strength of chemical bonds (e.g., the ideal strength of polyethylene is theoretically evaluated using quantum calculation to be 19 GPa by Boudreaux [20], 66 GPa by Crist et al. [21] and ≈40 GPa by Jiang et al. [22]). Thus, bond breaking may play an important role in actual fracture processes of PC, while we did not consider that effect for simplicity. ...
Polycarbonate is a promising candidate material for applications as structural element owing to its prominent properties including lightness, strength and toughness. To sustain complex mechanical loadings and resist fracture, it is essential to obtain reliable constitutive relations of deformation. Such constitutive laws that are used for the design and optimization of polymer-based engineering products can be directly obtained from computer simulations. In this study we performed coarse-grained molecular dynamics (CGMD) simulations of polycarbonate to gain a better understanding of the deformation and fracture mechanisms at the molecular level and to clarify its dependency on the molecular structure. In particular, we investigated how the state of entanglement influences the deformation behavior for simulation models with various molar masses. We found a significant effect of the molar mass on the stress-strain curves; i.e. the larger the molar mass is, the larger stress can be reached after yielding, suggesting that molar mass plays a major role in the brittle-ductile transition of polycarbonate.
... where N inter is the average number of interchain heat transfers, R intrin = ξ Sκ 0 (K/W), ξ is the mean distance between two adjacent points, and κ 0 and S are the intrinsic TCs and cross sections of polymer chains, respectively. Taking polyethylene (PE) as an example, S is approximately 18 Å 2 [7] and the simulated κ 0 is 10-100 W m −1 K −1 [7][8][9][10]. Then the general form of TC of an isotropic d-dimensional polymer system ...
... , which means the intrinsic TC of molecular chains is dominant and R inter is negligible. We then take κ 0 ≈ χ T near room temperature according to MD simulations [9] where χ is a constant. Then Eq. (9) can be simplified as κ = (r 1 + r 2 T /T 0 ) −1 with two fitting parameters r 1 and r 2 . ...
The thermal conductivities (TCs) of the vast majority of amorphous polymers are in a very narrow range, 0.1–0.5 W m−1K−1, although single polymer chains possess TCs of orders of magnitude higher. The chemical structure of polymer chains plays an important role in determining the TC of bulk polymers. We propose a thermal resistance network (TRN) model for the TC in amorphous polymers taking into account the chemical structure of molecular chains. Our model elucidates the physical origin of the low TC universally observed in amorphous polymers with various chemical structures. The empirical formulas of the pressure and temperature dependence of TC can be successfully reproduced not only in solid polymers but also in polymer melts. We further quantitatively explain the anisotropic TC in oriented polymers.
... For PE, there are a number of reference κ-values available from both experiments 4,22,37−43 and ab initio calculations. 10,44 Here, we benchmark the PE system to validate our framework, considering both the crystal and one-dimensional chain shown in Figure 2. The former models an extreme case of bulk polymers, whereas the latter models thin fibers. The experimental references include those of both "crystals" and "fibers" (with apostrophes supplied for the following reasons). ...
We investigated the lattice thermal conductivity (LTC) of a subset of polymer crystals from the Polymer Genome Library to explore high LTC polymer systems. We employed a first-principles approach to evaluate the phonon lifetime within third-order perturbation theory combined with density functional theory, and then solved the linearized Boltzmann transport equation with a single-mode relaxation time approximated by the computed lifetime. Typical high LTC polymer systems, namely, polyethylene (PE) crystal and fiber, were benchmarked to validate our approach. In addition to PE, we evaluated the LTC of polyphenylene sulfide (PPS) and polyethylene terephthalate (PET), because, although their experimental LTC values are not obtained from their ``perfect'' crystals, they are mostly available. Our simulations reproduced an experimentally observed LTC ordering (PE >> PPS > PET). Applying our scheme to a number of polymer crystals for the first time, we discovered that the β phase of a poly(vinylidenesurely fluoride) (PVDF-β) crystal at low temperatures has the highest LTC among all the cases considered. We also found the LTC correlating to the curvature of an energy-volume plot. This curvature can be used as one of descriptors of constructing modern machine learning models to further explore high LTC polymer crystals by means of a data-driven approach beyond a human-based one.
... The "metal-metal" and "metal-nitrogen" bonds in this category of nitrogen compounds causes the materials to have better chemical stability and interesting ceramic properties [10,11]. These compounds possess special physical and chemical features which make them desirable for many practical applications. ...
... In order to investigate the structure's behavior under large strains, PK2 strain curves are calculated using Eq. S (11). True stress is computed using the QUANTUM ESPRESSO package under DFT framework. ...
Density functional theory-based calculations in combination with the continuum approach are used to study the mechanical properties of vanadium nitride (VN) and the method of Debye-Grüneisen is used to investigate its thermodynamic characteristics. Elastic constants of the structure C 11 = 580.97, C 12 = 205.02 and C 44 = 108.92 GPa are obtained. Ductility ratio between 2.35 and 2.52 is calculated which predicts the VN compound to be malleable and structurally stable and it is categorized among tough coating materials. Also, thermodynamic behavior, bulk modulus, specific heat capacity in constant pressure and temperature expansion coefficient of VN are rigorously investigated. Results indicate that as the temperature increases, the bulk modulus decreases. At room temperature the bulk modulus reaches 294.53 GPa, at 400 K it is 284.24 GPa and finally reduces to 221.25 GPa at 1000 K. Hence, compared to the ground state calculations the bulk modulus obtained here is fairly consistent with the experimental data.
... The theoretical strength and modulus of a perfect crystalline PE (strength >11 GPa and modulus >370 GPa) 36,56 are still much larger than the ones measured here for the PE/TrGO composite films, since the mechanical behaviors of our films are still limited by the intermolecular vdW interactions (i.e., aligned chains can still slide relative to one another when subject to strain). In this scenario, for the TrGO filler to enhance the already high mechanical property of PE films, it is important that the interactions between PE molecules and graphene are stronger than those among the PE molecules themselves. ...
Polymers with superior mechanical properties are desirable in many applications. In this work, polyethylene (PE) films reinforced with exfoliated thermally reduced graphene oxide (TrGO) fabricated using a
roll-to-roll hot-drawing process are shown to have outstanding mechanical properties. The specific ultimate tensile strength and Young’s modulus of PE/TrGO films increased monotonically with the drawing ratio and TrGO filler fraction, reaching up to 3.2 ± 0.5 and 109.3 ± 12.7
GPa, respectively, with a drawing ratio of 60× and a very low TrGO weight fraction of 1%. These values represent by far the highest reported to date for a polymer/graphene composite. Experimental characterizations indicate that as the polymer films are drawn, TrGO fillers are exfoliated, which is further confirmed by molecular dynamics (MD) simulations. Exfoliation increases the specific area of the TrGO fillers in contact with the PE matrix molecules. Molecular dynamics simulations show that the PE−TrGO interaction is stronger than the PE−PE intermolecular van der Waals interaction, which enhances load transfer from PE to TrGO and leverages the ultrahigh mechanical properties of TrGO.
... For PE, there are a lot of reference values of κ available from both experiments [4,19,[34][35][36][37][38][39][40][41] and ab initio calculations. [10,42] Thus, we will check the reliability of our FIG. 1. ...
Lattice thermal conductivities (LTC) for a subset of polymer crystals from the Polymer Genome Library were investigated to explore high LTC polymer systems. We employed a first-principles approach to evaluating phonon lifetimes within the third-order perturbation theory combined with density functional theory, and then solved the linearized Boltzmann transport equation with single-mode relaxation time approximated by the computed lifetime. Typical high LTC polymer systems, polyethylene (PE) crystal and fiber, were benchmarked, which is reasonably consistent with previous references, validating our approach. We then applied it to not only typical polymer crystals, but also some selected ones having structural similarities to PE. Among the latter crystals, we discovered that beta phase of Poly(vinylidenesurely fluoride) (PVF-$\beta$) crystal has higher LTC than PE at low temperature. Our detailed mode analysis revealed that the phonon lifetime of PVF-$\beta$ is more locally distributed around lower frequency modes and four-times larger than that of PE. It was also found from a simple data analysis that the LTC relatively correlates with curvature of energy-volume plot. The curvature would be used as a descriptor for further exploration of high LTC polymer crystals by means of a data-driven approach beyond human-based one.
... To predict the thermal conductivity r ph , within the mean free path of the phonon, r ph is proportional to the length of the scattering region (L); therefore, r ph ¼ K ph L=A, 37 where A is the cross-sectional area (CSA). Also, we assume that there are no phonon scattering factors caused by rough edges and vacancy defects in pure 12 C carbyne. ...
The isotope effect on the quantum thermal transport of carbyne is studied by combining the central insertion scheme and the non-equilibrium Green's function method based on density function theory. This combined method avoids the disadvantage of the cascading scattering model and scaling theory method, which in principle only can process the phonon with low-concentration (≤10%) isotope impurity scattering. Also, the molecular dynamics method greatly overestimates the carbyne thermal transport property. By using our combined method, the calculated thermal conductivity of 100% ¹²C carbyne with the phonon mean free path of 775 nm at room temperature is 4.44 × 10³ W m−1 K⁻¹. When a ¹²C carbyne consisting of 400 carbon atoms is randomly mixed with ¹³C or ¹⁴C atoms at 300 K, the largest isotope effect of thermal conductance locates at the mixing ratio of 50% ¹³C/¹⁴C. Compared to the pure ¹²C carbyne, the average thermal conductance is reduced by 30% and 49% for the ¹³C and ¹⁴C, respectively.
