**2.3. Preparation of cassava starch-zinc nanocomposite film and thickness determination**

The starch composite was prepared by adding analytical grade glycerol (45–55%, w/w) and zinc nanoparticles (0–2%, w/w) to 24 g of the prepared cassava starch. The mixtures were homogenised using a locally fabricated screw extruder to form the nanocomposites. The resulting nanocomposites were dispersed into 600 mL of distilled water to form suspensions and heated for 30 minutes until viscous thermoplastic liquid were formed. The thickness of the film was determined by casting the thermoplastic solution in plastic mould of 8, 10 and 12 mm depths. In the design of the plastic mould, the surface area was first determined by wrapping 50 g of biomaterials (50 mm major and 10 mm minor axial dimensions) using aluminium foil and the layout was traced on the graph paper. The size of the plastic mould was computed from the empirical relationship expressed in Eq. (1).

$$TSA = Na + e\tag{1}$$

where *N* is the number of equivalent biomaterials (50 g), *a* = is the surface area of the mould mm2 , *e* is the allowance (assumed 600 mm2 ) and *TSA* is the total surface area of the mould (mm2 ).

Based on the expression in Eq. (1), the total surface area of the mould measured was 350 × 180 mm and this was used to cast the thermoplastic solutions into films. The thickness of the dried film, whose moisture content was 4% (db), was determined at the four edges of the films and the average taken. The plastic mould with 8 mm depth gave an average dried thickness of 15.14 ± 0.22 µm, whereas those with 10 and 12 mm depths were 16.21 ± 0.36 and 17.38 ± 0.13 µm, respectively. Twenty-seven samples of the cassava starch-zinc nanocomposite film, obtained from the 33 full factorial experiments (three levels from each of the zinc nanoparticles, glycerol and thickness), were prepared and stored in separate polyethylene bags to avoid subsequent hydration.

#### **2.4. Determination of rheological properties of the film**

The nanoindenter was used to determine the rheological properties of the nanocomposite films. A typical profile of the load-displacement curve of the film, obtained from the nanoindenter, is shown in **Figure 1**. The profile shows loading, unloading and holding stages from which other rheological behaviours such as the hardness, Young's modulus and creep were computed (Eqs. 2 and 3). Also, the strain rate sensitivity, which corresponds to creep response of the films, was determined at the holding stage of the profile (stage 2). The elastic and plastic works correspond to the areas under the loading and the unloading stages of the hysteresis loop [7, 11]:

$$H = \frac{P\_{\text{max}}}{A\_{\text{c}}h\_{\text{c}}} \tag{2}$$

where *P*max is the maximum load, *Ac* is the contact area (nm2 ), *hc* is the contact depth (nm) and *H* is the hardness of the nanocomposite film.

$$\frac{1}{E\_r} = \frac{1-\nu^2}{E} + \frac{1-\nu\_i^2}{E\_i} \tag{3}$$

where *Er* is the reduced modulus (MPa), is the Poison's ratio of the nanocomposite film, which was obtained by assuming that the material is isotropic in nature with the elastic modulus evenly distributed in all crystallographic directions = 0.5, is the Poison's ratio of the diamond indenter = 0.25, is the elastic modulus of the diamond indenter = 1140 GPa and is the elastic modulus of the nanocomposite film [6, 7].

**Figure 1.** Load-displacement profile of a typical nanocomposite film (1, loading stage; 2, holding stage; 3, unloading stage).
