*3.1. Optimization of Electrosteric NCC*

A summary of the input variables used to optimize the manufacture of NCC identified using the CCD are summarized in Table 3.



Shaded cells reflect results that have met the critical quality attributes (CQA) [25]. PS, particle size; PDI, polydispersity index; ZP, Zeta potential.

### 3.1.1. Response Surface Quadratic Model for PS (Y1)

The ANOVA results for the response surface quadratic model for PS are listed in Table 4. The model F value was 26.82 indicating that the model was significant. The model F-value is used to ascertain the utility of a model that the data has been fitted to and determine whether the data is best fitted by the model. The F-value is explained and unexplained variability and the larger the F-value, the more useful the model [42]. The particle size was influenced by SDS and TPGS 1000 concentration and an increase in % w/v content of each resulted in a reduction in particle size.


**Table 4.** ANOVA data for response surface quadratic model for PS.

Significant factors are reported in red.

The mean PS of the NCC fell between 304.1 and 859.4 nm. The impact of SDS on the size of NCC resulted in a large F-value of 83.23, indicating that this parameter had a significant impact on the size of NCC produced when compared to the other variable investigated. However, the TPGS 1000 content and the quadratic effect of the SDS concentration produced F-values of 29.29 and 36.65, respectively, indicating that these parameters had an intermediate, ye<sup>t</sup> significant, impact on the resultant size of the NCC produced.

The three-dimensional (3D) response surface plot in which the impact of SDS and TPGS 1000 concentration on particle size is depicted in Figure 1. These data reveal that a synergistic relationship exists between the SDS and TPGS 1000 concentration on particle size. The surface plots reveal that relatively small NCC are produced when the amount of SDS used is high and TPGS 1000 content is constant. The same effect is observed when the SDS concentration is constant and TGPS 1000

concentration is increased. However, this effect is minimal when SDS concentrations are at a maximum of 1% w/v. These results are consistent with previous findings that reported a decrease in mean PS with increasing content of an electrostatic or steric surfactant [20,43–45]. The desired mean particle size can be produced by a manipulation of the combined effects of SDS and TPGS 1000 when producing NCC using this method.

**Figure 1.** 3D response surface plot depicting the impact of SDS and TPGS 1000 concentration on particle size of the NCC.

### 3.1.2. Response Surface Model for PDI (Y2)

The ANOVA results for the response surface linear model for PDI are listed in Table 5. The model F value was 6.37, indicating that the model was significant. Increasing the amount of SDS used increases the PDI.


**Table 5.** ANOVA data for response surface linear model for PDI.

Significant factors are reported in red.

The 3D response surface plot in Figure 2 depicts the impact of SDS concentration on PDI and that a linear correlation exists. A reduction of TPGS 1000 concentration appears to increase the PDI for the NCC when the SDS concentration is kept constant, but only marginally.

**Figure 2.** 3D response surface plot depicting the impact of SDS and TPGS 1000 concentration on the PDI of the NCC.

### 3.1.3. Response Surface Model for ZP (Y3)

The ANOVA results for the response surface quadratic model for ZP are listed in Table 6. The model F value was 17.56, indicating that the model was significant. Increasing the amount of SDS used results in a decrease in ZP.


**Table 6.** ANOVA data for response surface linear model for ZP.

Significant factors are reported in red.

The 3D response surface plot in Figure 3 depicts the impact of SDS concentration on the ZP and that a linear correlation exists between SDS content and ZP. The concentration of TPGS 1000 appears to have an insignificant impact on the ZP of the NCC. The effect of SDS on ZP is consistent with that previously reported for SDS-stabilized nanosuspensions [46–50].

**Figure 3.** 3D response surface plot depicting the impact of SDS and TPGS 1000 concentration on ZP of the NCC.
