*3.1. Response Surface Methodology*

The design of experiment data (ref: Table 1) was used as independent variables inputs. The best outputs of photoluminescent quantum yield (*PLQY*) of carbon dots, the predicted and actual experimental values of photoluminescent quantum yield, is reported in Table 2 below.

It shows a positive model with an R<sup>2</sup> value of 0.956 as revealed on the fits statistics (Table 6), a high experimental value of PLQY of 27.75%, and a predicted value of 27.38% with a residual value of 0.37%. The experimental data was then used to calculate the coe fficient of polynomial equation for the response yield with the inputs data of temperature, time, dosage, and solvent ratio; by adopting Equation (1).

The results of design of experiment was computed by central composite design (CCD) as stated earlier. Photoluminescent quantum yield of the predicted and experimental yield was given by a model equation as in Equation (1) and represented by the expression below.

A = temperature, B = dosages, C = time, D = solvent (H2O/C3H6O/NaOH) Now, let;

A = X1, B = X2, C = X3, D = X4 (refer to RSM Table 2)

i Final equation in terms of coded (predicted) factors (full model): Also see Table 3 below for R<sup>2</sup> values and lack of fit for the polynomial regression equation.

Photoluminescent quantum yield (Response) = 23.63 − 0.1732 X1 + 0.03498 X2 + 0.1905 X3 − 0.0802 X4 − 2.38 X1 X2 + 1.61 X1 X3 − 2.68 X1 X4 + 0.1894 X2 X3 − 1.30 X2 X4 − 0.9353 X3 X4 + 0.2905 X<sup>2</sup> 1 + 1.07 X<sup>2</sup> 2 − 1.38 X<sup>2</sup> 3 − 3.36 X<sup>2</sup> 4.

ii Final equation in terms of actual factors (full model): Also see Table 4 below for R<sup>2</sup> values and lack of fit for the polynomial regression equation.

> Photoluminescent quantum yield (Response) = −3.3822 + 0.03866 X1 + 22.7576 X2 + 0.1385 X3 + 1.3133 X4 − 0.2379 X1 X2 + 0.0010 X1 X3 − 0.0033 X1 X4 + 0.0315 X2 X3 − 0.4069 X2 X4 − 0.0019 X3 X4 + 0.0001 X<sup>2</sup> 1 + 26.8733 X<sup>2</sup> 2 − 0.0015 X<sup>2</sup> 3 − 0.0131 X<sup>2</sup> 4.





Analysis of Variance and Model Statistical Report

The data set for the response surface methodology as generated by the software made the model to fit in to quadratic significance, and the analysis of variance (ANOVA) for statistical significance of the quadratic model is computed on Table 5 below;


**Table 5.** ANOVA for quadratic model.

*F*-value of 23.45 implies the model is significant and the subsequent values for the parameters show their degree of e ffects on the response of photoluminescent quantum yield for fluorescent carbon dots. Herewith, in Table 5, the most e ffective single–multiple parameter is the solvent ratio (D2) with an *F*-value of 77.89. While, interactive most e ffective parameters are temperature and solvent ratio (AD) with *F*-value 74.93. The least e ffective single parameter is temperature (A2) with an *F*-value of 0.5735 and the least e ffective interactive parameters are dosage and time (BC) with an *F*-value of 0.3875 [16,17].

Model *p*-values less than 0.0500 indicate the model terms are significant [18]. In this case AB, AC, AD, BD, CD, B2, C2, D<sup>2</sup> are significant model terms. Values greater than 0.1000 indicate the model terms are not significant, hence, individual lone factors are independent and are non-e ffective. Favorable interactive e ffects were observed between temperature and dosage (AB), temperature and time (AC), temperature and solvent (AD), dosage and solvent ratio (BD), and time and solvent ratio (CD), while the individual factor e ffects were observed with dosage (D2), time (C2), and solvent ratio (D2). Non favorable interactive e ffects were observed with dosage and time (BC), and the multiple factor of non-e ffect is temperature (A2). If there are many insignificant model terms (not counting those required to support hierarchy), model reduction may be considered to improve the model, however, in this study the non-e ffects are few and infinitesimal. The lack of fit *F*-value of 2.44 implies the lack of fit is not significant relative to the pure error. Non-significant lack of fit is an excellent requirement, since it is needed for the model to fit [19].

The experimental R<sup>2</sup> of 0.9563 in Table 6, shows a significant response [20]. The predicted R<sup>2</sup> of 0.7689 is in reasonable agreemen<sup>t</sup> with the adjusted R<sup>2</sup> of 0.9155; i.e., the di fference is less than 0.2 [21]. Adequate precision, measures the signal to noise ratio, thus, ratio greater than 4 is desirable. Ratio of 17.519 indicates an adequate signal.


**Table 6.** Fit statistics summary.

This model is significant to navigate the design space. It is necessary for a model to comply with the following;


Furthermore, from Figure 4 below, the three dimensional (3D) plots have shown interactive responses to the favorable yield of photoluminescent quantum yield at 27.75% and the intercept value of 23.63 on the 2nd order polynomial equation of actual values is suitable.

In Figure 4A the interactive behavior of temperature (A) at 170 ◦C and dosage (B) at 0.1 g has an effective interaction with an *F*-value of 61.18 and a *p*-value less than 0.0001 with a value of −0.2379 in the 2nd order polynomial equation of actual factors. Figure 4B is an interactive effect of temperature (A) and time (C) at 1 h 40 min. It records a linear effect on the response value of photoluminescent quantum yield with a favorable *p*-value that is less than 0.001 and a coefficient value of 1.6143 on the polynomial equation. The interactive effect of temperature (A) and solvent ratio W/Ace/NaOH (D) at 12 mL have the best effect on the response yield of photoluminescent quantum yield with an *f*-value of 74.93 and a *p*-value less than 0.0001, coefficient of −2.68 as seen in the 2nd order polynomial equation with a linear response as shown in Figure 4C.

Figure 4D shows a non-effective interaction between dosage (B) and time (C) on the response of photoluminescent quantum yield. *p*-value at 0.5430 and *f*-value of 0.3875 all fall short of the requirement of a *p*-value <0.100 and an *f*-value that is extremely low. The interactive effect of dosage (B) and solvent ratio W/Ace/NaOH (D) at *p*-value 0.0008 as shown in the 3D plot on Figure 4A,C,E,F is the most important factor in the sustainability of environmental resources. Environmental resources managemen<sup>t</sup> is an essential factor to be considered in the synthesis of products, with high emphasis on minimal resource requirement [18].
