**1. Introduction**

Design of experiments (DOE) [1,2] is a widely used discipline applied in a variety of areas, including engineering [3–5], social sciences [6] and natural sciences [7–9]. Design of experiments is a powerful statistical methodology in its own right, with a number of software applications readily available to aid researchers in both designing and globally optimizing multi-parametric experiments to achieve the best results through analysis and interpretation. In this context, combining software-based applications with a researcher's experience and scientific intuition is a powerfully growing trend that typically results in significant savings in time and materials. The design of experiments methodology includes formal, planned experimentation with the goal of optimizing a set of reaction parameters that may disclose synergism between reaction parameters. The optimization typically comprises six main steps: (1) selection of variables and defining their range of variation; (2) selection of responses; (3) experimental design selection; (4) performing the designed experiments in random order; (5) determination of coefficients in a mathematical model; and (6) predicting the response and evaluating the model relevance. In this context, we designed a series of experiments to optimize globally the reaction conditions for maximizing the yield of covalently functionalized tungsten disulfide inorganic fullerene-like nanotubes (WS2 INTs). This specific functionalization reaction comprises a polycarboxylation technique [10,11], developed recently in our laboratories, that uses a modified highly electrophilic Vilsmeier–Haack reagent [12].

It is well known that classical Vilsmeier–Haack reactions use DMF (secondary *N*-formyl amine) and POCl3/SOCl2 to effect the formylation of a wide range of electrophilic substrates via intermediate electrophilic iminium salts of Type A (Scheme 1a). Such Vilsmeier–Haack reactions have been studied extensively and found to be quite versatile, leading to a number of oxygen and nitrogen heterocycles [13–18], as well. For example, a modified Vilsmeier–Haack reagent that uses ethyl chloroformate in place of POCl3 was found useful when reacted with active methylene compounds [19]. Analogously, we have discovered that by using a mixture containing DMF (a 2nd *N*-CHO amine) and O-alkylating 2-bromoacetic acid with catalysis by Ag(I)OAc, WS2 nanotubes may be polycarboxylated readily and quite effectively according to the mechanism described in Scheme 1c. Indeed, DMF removal or replacement with other polar, non-protic materials/solvents (e.g*.*, 1,4-dioxane, DME, *etc.*) leads to unsuccessful polycarboxylation. This strict requirement of DMF (2nd *N*-CHO amine) as an essential component of the reaction mixture led us to propose and detail a corresponding Vilsmeier–Haack-like reaction mechanism, displayed in Scheme 1c.

Interestingly, silver acetate (Ag(I)OAc) was also included as an essential reaction factor due to its well-known ability to chemically trap halogens and, thereby, assist in halogen (Br) abstraction. Depicted in Scheme 1b is the reaction of Ag(I)OAc with the Br atom of bromoacetic acid, leading to the formation of the Vilsmeier–Haack complex of Type B1 with subsequent precipitation of Ag(I)Br.

Because several reaction factors are involved in the polycarboxylation reaction mentioned above, we selected a DOE methodology as the most economical means of optimizing the reaction factors to produce the highest yields of polycarboxylation. In this context, the level of polycarboxylation was determined indirectly by reacting the functionalized INTs with an excess of 1,3-diaminopropane, resulting in a terminal primary amine that was quantified by the Kaiser test [20]. Due to a one-to-one reaction between the diamine and carboxylic acid, the amount of terminal amine is equal to the amount of carboxylic acid.

In addition to the Kaiser test; further confirmation of the successful functionalization of the WS2 INTs was obtained by a combination of FT-IR; TGA and zeta potential analyses (see the Supplementary Information).

Thus far, we have investigated this unique functionalization method only for the polycarboxylation of WS2 nanotubes. However, we strongly believe it may prove applicable for similar polycarboxylation of other layered dichalcogenide nanomaterials (*M*S(Se)2, *M* = Mo, Sn).

**Scheme 1.** (**a**) Generalized Vilsmeier–Haack generation of electrophilic iminium salts; (**b**) Vilsmeier–Haack generation of DMF-based electrophilic iminium salt complex with bromophilic Ag(I) assistance in halide abstraction; (**c**) sulfur-mediated nucleophilic addition of the iminium salt complex to the outermost sulfur atoms of WS2 INTs, producing the corresponding polycarboxylated INTs.
