Elastic properties of mono‐ and polydisperse two‐dimensional crystals of hard‐core repulsive Yukawa particles

Abstract

Monte Carlo simulations of mono‐ and polydisperse two‐dimensional crystals are reported. The particles in the studied system, interacting through hard‐core repulsive Yukawa potential, form a solid phase of hexagonal lattice. The elastic properties of crystalline Yukawa systems are determined in the NpT ensemble with variable shape of the periodic box. Effects of the Debye screening length (κ−1), contact value of the potential (ε), and the size polydispersity of particles on elastic properties of the system are studied. The simulations show that the polydispersity of particles strongly influences the elastic properties of the studied system, especially on the shear modulus. It is also found that the elastic moduli increase with density and their growth rate depends on the screening length. Shorter screening length leads to faster increase of elastic moduli with density and decrease of the Poisson's ratio. In contrast to its three‐dimensional version, the studied system is non‐auxetic, i.e., shows positive Poisson's ratio.

Auxeticity enhancement due to size polydispersity in fcc crystals of hard-core repulsive Yukawa particles

“…52 Studies of two-dimensional Yukawa crystals revealed that this system is not auxetic. 53 However, as mentioned before, the three-dimensional Yukawa crystals exhibit negative Poisson's ratio in the [110][1% 10]-direction and are partial auxetics, supposedly with a similar mechanism of partial auxeticity as discussed for fcc crystals by Milstein and Huang 54 and as found in the hard sphere model near melting 55 and near close packing 56 and as reported by Baughman et al for some fcc metals. 49 Moreover, the value of Poisson's ratio can be modified by changing the screening length -an increase of the screening length causes Poisson's ratio to decrease.…”

Auxetic properties of a tangram-inspired metamaterial

“…Indeed, it has earlier been shown that purely auxetic and partially auxetic systems can be constructed from rigid particles, i.e. by means of purely geometrical interactions [72][73][74][75].…”

Behavior of Extreme Auxetic and Incompressible Elastic Materials

“…[1][2][3][4][5][6] Yet the majority of auxetic materials are artificially made with the microstructure engineered to exhibit negative Poisson's ratio(s) at macroscopic level. These include re-entrant honeycomb structures, [7][8][9] tethered-nodule networks, [10][11][12] chiral systems, [13][14][15][16][17] rotating rigid and semi-rigid units, [18][19][20][21][22] interlocking units, [23,24] some granular materials, [24][25][26] molecular systems, [8,[27][28][29][30][31][32][33] foldable structures, [34] foams with missing ribs, [35] perforated sheets, [36][37][38][39][40] auxetic lattices, [41,42] beam and pivots networks, [43] multiphase composites with re-entrant microstructure, [44,45] multilayered composite...…”

“…Yet the majority of auxetic materials are artificially made with the microstructure engineered to exhibit negative Poisson's ratio(s) at macroscopic level. These include re‐entrant honeycomb structures, tethered‐nodule networks, chiral systems, rotating rigid and semi‐rigid units, interlocking units, some granular materials, molecular systems, foldable structures, foams with missing ribs, perforated sheets, auxetic lattices, beam and pivots networks, multiphase composites with re‐entrant microstructure, multilayered composites and hollow sphere stacks . Also conventional (positive Poisson's ratio) foam can be converted into the auxetic one using heat treatment, thermo‐forming, and compaction .…”