By building physically sound interatomic force constants, we offer evidence of the universal presence of a quadratic phonon branch in all unstrained 2D materials, thus contradicting much of the existing literature. Through a reformulation of the interatomic force constants (IFCs) in terms of internal coordinates, we find that a delicate balance between the IFCs is responsible for this quadraticity. We use this approach to predict the thermal conductivity of Pmmn borophene, which is comparable to that of MoS 2 , and displays a remarkable in-plane anisotropy. These qualities may enable the efficient heat management of borophene devices in potential nanoelectronic applications. IMPACT STATEMENTThe newly found universality of quadratic dispersion will change the way 2D-material phonons are calculated. Predicted results for borophene shall become a fundamental reference for future research on this material. ARTICLE HISTORY

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Structural and dynamical properties of room-temperature ionic liquids containing the cation 1-butyl-3-methylimidazolium ([BMIM](+)) and three different anions (hexafluorophosphate, [PF6](-), tetrafluoroborate, [BF4](-), and bis(trifluoromethylsulfonyl)imide, [NTf2](-)) doped with several molar fractions of lithium salts with a common anion at 298.15 K and 1 atm were investigated by means of molecular dynamics simulations. The effect of the size of the salt cation was also analyzed by comparing these results with those for mixtures of [BMIM][PF6] with NaPF6. Lithium/sodium solvation and ionic mobilities were analyzed via the study of radial distribution functions, coordination numbers, cage autocorrelation functions, mean-square displacements (including the analysis of both ballistic and diffusive regimes), self-diffusion coefficients of all the ionic species, velocity and current autocorrelation functions, and ionic conductivity in all the ionic liquid/salt systems. We found that lithium and sodium cations are strongly coordinated in two different positions with the anion present in the mixture. Moreover, [Li](+) and [Na](+) cations were found to form bonded-like, long-lived aggregates with the anions in their first solvation shell, which act as very stable kinetic entities within which a marked rattling motion of salt ions takes place. With very long MD simulation runs, this phenomenon is proved to be on the basis of the decrease of self-diffusion coefficients and ionic conductivities previously reported in experimental and computational results.

We have performed extensive molecular dynamic simulations to analyze the influence of cation and anion natures, and of water concentration, on the structure and dynamics of water-1-alkyl-3-methylimidazolium ionic liquid mixtures. The dependence on water concentration of the radial distribution functions, coordination numbers, and hydrogen bonding degree between the different species has been systematically analyzed for different lengths of the cation alkyl chain (alkyl = ethyl, butyl, hexyl, and octyl) and several counterions. These include two halogens of different sizes and positions in Hoffmeister series, Cl(-) and Br(-), and the highly hydrophobic inorganic anion PF(6)(-) throughout its whole solubility regime. The formation of water clusters in the mixture has been verified, and the influences of both anion hydrophobicity and cation chain length on the structure and size of these clusters have been analyzed. The water cluster size is shown to be relatively independent of the cation chain length, but strongly dependent on the hydrophobicity of the anion, which also determines critically the network formation of water and therefore the miscibility of the ionic liquid. The greater influence of the anion relative to the cation one is seen to be reflected in all the analyzed physical properties. Finally, single-particle dynamics in IL-water mixtures is considered, obtaining the self-diffusion coefficients and the velocity autocorrelation functions of water molecules in the mixture, and analyzing the effect of cation, anion, and water concentration on the duration of the ballistic regime and on the time of transition to the diffusive regime. Complex non-Markovian behavior was detected at intermediate times within an interval progressively shorter as water concentration increases.

The structure of solutions of lithium nitrate in a protic ionic liquid with a common anion, ethylammonium nitrate, at room temperature is investigated by means of molecular dynamics simulations. Several structural properties, such as density, radial distribution functions, hydrogen bonds, spatial distribution functions, and coordination numbers, are analyzed in order to get a picture of the solvation of lithium cations in this hydrogen-bonded, amphiphilically nanostructured environment. The results reveal that the ionic liquid mainly retains its structure upon salt addition, the interaction between the ammonium group of the cation and the nitrate anion being only slightly perturbed by the addition of the salt. Lithium cations are solvated by embedding them in the polar nanodomains of the solution formed by the anions, where they coordinate with the latter in a solid-like fashion reminiscent of a pseudolattice structure. Furthermore, it is shown that the average coordination number of [Li](+) with the anions is 4, nitrate coordinating [Li](+) in both monodentate and bidentate ways, and that in the second coordination layer both ethylammonium cations and other lithiums are also found. Additionally, the rattling motion of lithium ions inside the cages formed by their neighboring anions, indicative of the so-called caging effect, is confirmed by the analysis of the [Li](+) velocity autocorrelation functions. The overall picture indicates that the solvation of [Li](+) cations in this amphiphilically nanostructured environment takes place by means of a sort of inhomogeneous nanostructural solvation, which we could refer to as nanostructured solvation, and which could be a universal solvation mechanism in ionic liquids.