Recent experiments (Wang et al., 2010) have found evidence of phase transitions of gases adsorbed on a single carbon nanotube. In order to understand the observations, we have carried out classical grand canonical Monte Carlo simulations of this system, for the cases of Ar and Kr on zigzag and armchair nanotubes with radius R > 0.7 nm. The calculated behavior resembles the experimental results in the case of Ar. However, the prominent, ordered phase found for Kr in both simulations and (classical) energy minimization calculations differs from that deduced from the experimental data. A tentative explanation of the apparent discrepancy is that the experiments involve a nanotube of rather large radius (>1.5 nm).

Recent advancements in computing technologies coupled with the need to make sense of large amounts of raw data have renewed much interest in data-driven materials design and discovery. Traditional materials science research relies heavily on experimental data to gauge the properties of materials. However, this paradigm is purely based on trial and error and ongoing research can take decades to discover new materials. Data-driven modeling tools such as machine learning and its proven libraries can help speed up the materials’ discovery process through the implementation of powerful algorithms on readily available material datasets mined from the ever-increasing private- and government-funded material databases. In this Perspective, we applied various machine learning models on tens of hundreds of thermoelectric compounds obtained from density functional theory calculation results. In our preliminary analysis, we made use of pymatgen and the powerful materials science library matminer to add and explore key material features that have the propensity to accurately predict our achievable target output. We evaluated the accuracy and performance of our models with the coefficient of determination (R2), the root mean square error, and K-fold cross-validation metrics and identified the most important descriptors for our materials. Finally, we reviewed the current state-of-the-art in data-driven thermoelectric materials’ design and discovery, its current challenges, and prospects.

Three problems involving quasi-one-dimensional (1D) ideal gases are discussed. The simplest problem involves quantum particles localized within the 'groove', a quasi-1D region created by two adjacent, identical and parallel nanotubes. At low temperature (T), the transverse motion of the adsorbed gas, in the plane perpendicular to the axes of the tubes, is frozen out. Then, the low T heat capacity C(T) of N particles is that of a 1D classical gas: C(*)(T) = C(T)/(Nk(B)) --> 1/2. The dimensionless heat capacity C(*) increases when T ≥ 0.1T(x, y) (transverse excitation temperatures), asymptoting at C(*) = 2.5. The second problem involves a gas localized between two nearly parallel, co-planar nanotubes, with small divergence half-angle γ. In this case, too, the transverse motion does not contribute to C(T) at low T, leaving a problem of a gas of particles in a 1D harmonic potential (along the z axis, midway between the tubes). Setting ω(z) as the angular frequency of this motion, for T ≥ τ(z) ≡ ω(z)ħ/k(B), the behavior approaches that of a 2D classical gas, C(*) = 1; one might have expected instead C(*) = 1/2, as in the groove problem, since the limit γ ≡ 0 is 1D. For T << τ(z), the thermal behavior is exponentially activated, C(*) ∼ (τ(z)/T)(2)e(-τ(z)/T). At higher T (T ≈ ε(y)/k(B) ≡ τ(y) >> τ(z)), motion is excited in the y direction, perpendicular to the plane of nanotubes, resulting in thermal behavior (C(*) = 7/4) corresponding to a gas in 7/2 dimensions, while at very high T (T > ħω(x)/k(B) ≡ τ(x) >> τ(y)), the behavior becomes that of a D = 11/2 system. The third problem is that of a gas of particles, e.g. (4)He, confined in the interstitial region between four square parallel pores. The low T behavior found in this case is again surprising--that of a 5D gas.

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