**1. Introduction**

Multiwall inorganic nanotubes of WS2 (INT-WS2) were discovered in 1992 [1], and the route for their scaled-up synthesis was developed in 2009 [2]. Together with BN [3] and MoS2 [4,5], they probably constitute the most investigated kind of inorganic nanotubes from layered compounds. The crystalline and electronic structure of INT has been studied in great detail [6–8]. In particular, calculations have shown that multiwall WS2 (MoS2) nanotubes become more stable than the respective nanosheets at a threshold outer diameter of about 15 to 20 nm and being made up of at least 5–10 layers [9]. Indeed, many of the high-temperature (above 700 °C) synthetic strategies ended up in multiwall nanotubes exhibiting a high-crystalline order, which agree quite well with the predicted sizes [2,10,11].

Nonetheless, these conditions are not sufficiently exergonic to drive the reaction into windows of (meta-) stability far enough from equilibrium, where 1–3-layer nanotubes could be formed. It was shown in the past that reactions carried out under highly exergonic conditions, like laser ablation [12], for example, can yield closed-cage MoS2 nanoparticles having a small size and number of layers. Calculations based on density functional tight-binding theory (DFTB) [9] (see Figure 1) present the energy-per-atom of nanotubes as a function of the number of atoms in the unit length (unit cell), Ntot, and for different number of layers (*k* = 1–4). They are compared with nanostripes (nanoribbons) of the same number of atoms. For the sake of simplicity, the calculations were carried out for MoS2, which is structurally analogous to WS2. It is noticed that the energy-per-atom increases with a decreasing number of atoms for both the nanostripes and the nanotubes, but for different reasons. The energy-per-atom for the nanostripes increases, due to edge effects, *i.e.*, the abundance of rim atoms with dangling bonds. On the other hand, the nanotubes become less stable at a smaller radius of curvature, due to the increasing elastic energy of folding. In addition, the folding energy increases more steeply for the nanotubes than the energy of the nanoribbons as the number of atoms shrinks. Consequently, smaller diameter nanotubes become less stable than the straight nanostripes to the left of the cross-over point (stability threshold) of the two curves. While the cross-over point itself moves to the left as the number of layers decreases, the corresponding threshold energy-per-atom rapidly increases (becomes less negative), particularly for nanotubes with three layers and below. It is therefore clear that the generation of nanotubes of a small size and number of layers (*k* < 4) requires highly exergonic conditions, which is the subject of the present work.

**Figure 1.** The calculated energy-per-atom for MoS2 nanotubes and nanostripes with 1–4 walls as a function of the number of atoms in the tube unit cell, *N*tot.

Interestingly, in the range of ~390 < *N*tot < 670, which corresponds to nanotubes with outer diameters of 5.1 nm < *D*3 < 8.0 nm, the triple layer nanotubes are more stable than nanotubes with *k* = 2 and *k* = 4 (see Figure 1). The diameter (*Dk*) represents here the outer diameters of the nanotubes with *k* shells. This theoretical prediction is in agreement with experimental results presented in this work: the majority of the daughter nanotubes were triple-walled. Note that nanotubes with the same (outer) diameters, but different number of shells, have consequently a different (total) number of atoms. Thus, a single-wall tube with a larger diameter may have less atoms than triple-walled tubes of a smaller diameter.

A similar situation has been encountered with the stability window of MoS2 nanotetrahedra and nanooctahedra consisting of 2–4 layers. These nanostructures were proposed first in [13,14] and realized in [15,16]. Indeed, MoS2 nanooctahedra/nanotetrahedra were obtained by rapid quenching of laser- [15–18] or solar- [19] ablated MoS2 soot or by an arc-discharge process [20]. It can, therefore, be concluded that highly exergonic reaction conditions and rapid quenching of the nanoclusters can access (meta-) stability windows, which favor new nanotubes that are not reachable by the conventional thermally-driven synthesis at <1000 °C.

#### **2. Results and Discussion**

In the present work, 1–3-layer WS2 nanotubes with a diameter of 3–7 nm and a length of 20–100 nm were produced by applying inductively coupled radio-frequency plasma irradiation on multiwall INT-WS2.
