*2.1. Materials*

EVOH containing 32 mol% ethylene content, i.e., EVOH32, was supplied by Nippon Gohsei (Osaka, Japan) as Soarnol™ DC3212B. The copolymer has a density of 1.19 g/m<sup>3</sup> (23 ◦C) and a melt flow rate (MFR) of 12 g/10 min (210 ◦C, 2160 g). Graphite powder, G282863 grade, was purchased from Sigma-Aldrich S.A. (Madrid, Spain). Sodium nitrate (NaNO3), hydrogen peroxide solution (H2O2) at 30 wt.-%, hydrazine hydrate (N2H4) at 50–60 wt.-%, ammonia solution (NH4OH) at 25 wt.-%, potassium permanganate (KMnO4) of 97% purity, and isopropyl alcohol (IPA) with purity ≥99% were also purchased from by Sigma-Aldrich S.A. Sulfuric acid (H2SO4) of 96% purity was provided by Panreac S.A. (Barcelona, Spain).

#### *2.2. Oxidation of Graphite*

In a first stage, graphite oxide (GO) was prepared by oxidizing graphite powder based on the modification of the so-called Hummer's method described by Hirata et al. [19]. Briefly, 10 g of graphite powder and 7.5 g of NaNO3 were placed into a 2000 mL round-bottom glass flask. Then, 621 g of H2SO4 was added and the mixture was stirred while being cooled in an ice water bath. Thus, 45 g of KMnO4 was gradually added for about 1 h. Cooling was completed after 2 h and the mixture was allowed to stand for five days at about 20 ◦C with gentle stirring to obtain a highly viscous liquid. After this, 1000 cm<sup>3</sup> of 5 wt.-% H2SO4 aqueous solution was gradually added to the resultant solution for 1 h under continuous and gentle stirring. The resultant mixture was further stirred for 2 h. Then, 30 g of the H2O2 aqueous solution was added to the above liquid and the mixture was stirred for another 2 h. In order to remove the ions of oxidant origin, especially manganese ions, the resultant liquid was purified by repeating the following procedure cycle 15 times: Centrifugation, removal of the supernatant liquid, addition of a mixed aqueous solution of 3 wt.-% H2SO4/0.5 wt.-% H2O2, and shaking to re-disperse. The mixed solution amounted, in total, to about 13 g. The purification procedure was similarly repeated a further three times, except that the liquid to be added was replaced with water. The resultant mixture was allowed to stand for at least 24 h to precipitate thick particles, which were filtered and removed. The remaining dispersion was purified several times with water. Finally, a brown-black viscous flurry containing GO particles was obtained. The GO content was ca. 1 wt.-%, as determined from weight difference of the dispersion before and after drying at 150 ◦C for 1 h in an oven.

#### *2.3. Reduction of Graphite Oxide*

In a second stage, the resultant GO particles were reduced to graphene using NH4OH based on previous methodology [20]. For this, 0.1 g of the above-obtained GO particles was mixed with 100 mL of deionized water in a 250 mL round-bottom glass flask, yielding an inhomogeneous yellow-brown dispersion. This dispersion was bath ultrasonicated using a Fisher Scientific FS60 Ultrasonic Cleaner (150 W) from Thermo Fisher Scientific (Waltham, MA, USA) until it became clear, i.e., with no visible particulate matter. Then, 10 mL of N2H4 and 10 mL of NH4OH were added and the resultant solution was heated overnight in an oil bath at 90 ◦C under a water-cooled condenser, in which the reduced GO gradually precipitated out as a black solid. The final suspension was isolated by filtration and then vacuum-dried at 60 ◦C until the solids reached a concentration of ca. 0.1 wt.-%.

#### *2.4. Preparation of Electrospun Fiber Mats*

The polymer solution for electrospinning was prepared by fully dissolving 7 wt.-% EVOH in 4/1 (vol./vol.) IPA/water. The obtained EVOH solution was then added to the above-described water-based solution containing graphene, pre-heated at 50 ◦C, to reach the following weight contents of GNPs in EVOH: 0.1, 0.5, 1, and 2 wt.-%. The resultant GNPs dispersions in EVOH were then ultrasonicated for 15 min and transferred immediately to a 5 mL plastic syringe. A control solution of EVOH without GNPs was prepared in identical conditions.

The electrospinning process was performed using a Fluidnatek® LE-50 benchtop line from Bioinicia S.L. (Valencia, Spain) with a dual polarizer yielding a variable high-voltage ranging from 0–60 kV and with temperature and humidity control. The EVOH solutions containing the GNPs were pumped through a stainless-steel needle injector and collected on a grounded metallic flat plate. The applied voltage, flow-rate, and tip-to-collector distance were set at 15 kV, 0.5 mL/h, and 15 cm, respectively. All samples were electrospun in a controlled environmental chamber at 29 ◦C and 30% relative humidity (RH). The electrospun fiber mat thickness was ca. 200 microns. All the characterization work was carried out in the electrospun fibers mats.

Additionally, the obtained electrospun fibers mats were proven to be conformable into continuous films by annealing in a hydraulic press 4122-model from Carver, Inc. (Wabash, IN, USA). This step was optimally performed at 158 ◦C, without pressure, for 10 s. The resultant films were air cooled at room temperature.
