Deformation of a solid usually leads to an increase in the internal potential energy U in of the solid. In inelastic and plastic deformation, the increase in U in is due to the formation of excited structural defects in the solid under the action of the external force (e.g., in crystals, dislocations form). The storage of U in has been studied experimentally in detail for crystalline metals [1, 2], rubbers [3], and glassy organic polymers [4]. However, experimental measurements on polymer systems cannot determine the contributions of inter actions of various types to the increase in U in . Today, computer simulation can identify such contributions [4,5] and can suggest what types of interactions con trol the energy storage and influence the mechanical behavior of material [6]. In this work, we performed molecular dynamic simulation of uniaxial compres sive and tensile deformation of a full atom model of amorphous glassy polymethylene and analyzed the contributions of interactions of various types to the increase in its potential energy. NUMERICAL SIMULATION PROCEDUREThe simulation was performed by molecular dynamics in a computational cell under periodic boundary conditions. The initial system comprised 3072 molecules of butadiene С 4 Н 8 (a total of 36 864 atoms) in the trans configuration with terminal СН 2 groups. At 800 K for 182 ps, the volume of the system continuously decreased under the action of hydrostatic compression, and the density increased from 0.07 to 0.8 g/cm 3 . Then, simultaneously with cooling to 300 K, there was "polymerization": new "chemical bonds" formed between the terminal car bons that approached each other to a distance of 3.5 Å without branching of chains. Thereafter, the forming polymer system relaxed at 300 K and cooled at a rate of 1 K/ps to 50 K.Thereby, 32 specimens of polymer glass were obtained, which had an average degree of polymeriza tion of 211 ± 16 (dispersity index 2.03 ± 0.22), a glass transition temperature of 171 ± 6 K, and a density at 50 K of ρ = 0.865 ± 0.001 g/cm 3 . A visual analysis of the obtained specimens showed neither microcrystal line regions, nor noticeable density fluctuations. A detailed study of the orientation ordering of chains also demonstrated the absence of marked anisotropy in their arrangement.The equations of motion were numerically inte grated by the Verlet velocity algorithm [7]. The pres sure was maintained by a Berendsen barostat [7]. The temperature in the system was maintained by a collisional thermostat [8]. The step of integration was 0.5 fs. Figure 1 presents the calculated σ t -ε t stress-strain curves for stretching and compression, where σ t = F/S c is the true stress, F is the acting force, S c is the current cross sectional area of the specimen, ε t = ln(l/l 0 ) is the true strain, l is the current specimen length, and l 0 is the initial specimen length. The shape of the calculated curves agrees well with the experi mental data, and so do the calculated values ε у ≈ 12-14% [9]. The excess of the compressive stress over the tensile ...
Using molecular dynamics, a comparative study was performed of two pairs of glassy polymers, low permeability polyetherimides (PEIs) and highly permeable Si-containing polytricyclononenes. All calculations were made with 32 independent models for each polymer. In both cases, the accessible free volume (AFV) increases with decreasing probe size. However, for a zero-size probe, the curves for both types of polymers cross the ordinate in the vicinity of 40%. The size distribution of free volume in PEI and highly permeable polymers differ significantly. In the former case, they are represented by relatively narrow peaks, with the maxima in the range of 0.5–1.0 Å for all the probes from H2 to Xe. In the case of highly permeable Si-containing polymers, much broader peaks are observed to extend up to 7–8 Å for all the gaseous probes. The obtained size distributions of free volume and accessible volume explain the differences in the selectivity of the studied polymers. The surface area of AFV is found for PEIs using Delaunay tessellation. Its analysis and the chemical nature of the groups that form the surface of free volume elements are presented and discussed.
In this Letter we describe analytically and simulate numerically the softening of flexural surface acoustic waves, localized in the plane of few-layer graphene embedded in soft matrix of low-density polyethylene. The softening of surface acoustic wave is triggered by the compressive strain in the matrix, which results in compressive surface stress in the few-layer graphene. Softening of the flexural surface acoustic wave leads to spatially periodic static bending deformation (modulation) of the embedded nanolayer with the definite wave number. Few-layer graphene with different numbers of graphene monolayers is considered. We describe the different models of interlayer bonding of graphene monolayers in a few-layer graphene, which correspond to the weak and strong interlayer bonding. The considered models give substantially different scaling of the wave number of periodic bending deformation and of the threshold compressive strain in the matrix as functions of the number of graphene monolayers in the few-layer graphene. Both the wave number of periodic bending deformation and the values of the threshold compressive surface stress in the few-layer graphene and of the compressive strain in the matrix are very well confirmed by the numerical simulations. Bending instability of few-layer graphene can be used for the study of bending stiffness and two-dimensional Young modulus of the graphene nanolayers, embedded in a soft matrix.
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