Modelling and optimization of Candida rugosa nanobioconjugates catalysed synthesis of methyl oleate by response surface methodology

Figures & data

Table 1. The actual and coded independent variables in the Box–Behnken design for the CRL-MWCNTs catalysed synthesis of methyl oleate.

		Levels
Variables	Symbols	−1	0	+1
Reaction time (h)	A	6	10	14
Reaction temperature (°C)	B	40	50	60
Molar ratio of oleic acid to methanol	C	1:2	1:3	1:4

Figure 1. FTIR absorption spectra of as-synthesized MWCNTs (a), F-MWCNTs (b) and CRL-MWCNTs (c).

Figure 2. Thermogram of as-synthesized MWCNTs (a), F-MWCNTs (b) and CRL-MWCNTs (c).

Figure 3. TEM images of as-synthesized MWCNTs (a), F-MWCNTs (b) and CRL-MWCNTs (c).

Figure 4. Results of the GC analysis for the production of methyl oleate catalysed by the CRL-MWCNTs nanobioconjugates sampled at 0 h (a) and 11 h (b).

Figure 5. Esterification reaction of oleic acid and methanol catalysed by the CRL-MWCNTs.

Table 2. Experimental design and results of the response surface design.

Run no.	A: Reaction time (h)	B: Reaction temperature (°C)	C: Molar ratio (Oleic acid: Methanol)	Actual yield (%)	Predicted yield (%)
1	14	50	1:2	75.5	74.98
2	6	50	1:4	66.4	66.91
3	10	60	1:4	74.8	73.11
4	10	50	1:3	79.3	78.42
5	14	60	1:3	84.2	84.45
6	6	40	1:3	69.1	68.85
7	10	40	1:4	65.9	65.64
8	10	50	1:3	80.8	78.42
9	10	50	1:3	78.1	78.42
10	14	50	1:4	89.9	91.34
11	6	50	1:2	73.7	72.26
12	14	40	1:3	74.7	73.53
13	10	40	1:2	63.9	65.58
14	10	50	1:3	76.5	78.42
15	6	60	1:3	60.8	61.97
16	10	60	1:2	61.9	62.16
17	10	50	1:3	77.4	78.42

Figure 6. Comparison between the predicted and actual values for the percentage conversion in the CRL-MWCNTs catalysed synthesis of methyl oleate.

Table 3. Analysis of variance and coefficients of the model.

Source	Sum of squares	Degrees of freedom	Mean square	F-value	p-value
Model	1013.13	9	112.57	31.97	<0.0001
A: time (h)	368.56	1	368.56	104.69	<0.0001
B: temperature (°C)	8.20	1	8.20	2.33	0.1708^ns
C: molar ratio	60.50	1	60.50	17.18	0.0043
AB	79.21	1	79.21	22.50	0.0021
AC	117.72	1	117.72	33.44	0.0007
BC	29.70	1	29.70	8.44	0.0228 ^ns
A^2	13.12	1	13.12	3.72	0.0949 ^ns
B^2	268.46	1	268.46	76.25	<0.0001
C^2	61.12	1	61.12	17.36	0.0042
Residual	24.64	7	3.52
Lack of fit	13.38	3	4.46	1.58	0.3258 ^ns
Pure error	11.27	4	2.82
Corr. Total	1037.78	16
R^2	0.9763
Adjusted R^2	0.9457

Note: Not significant (^ns).

Figure 7. Deviation of the reference point for the percentage conversion of methyl oleate for the effect of time (A), temperature (B) and molar ratio (C).

Figure 8. Graphs depicting the response surface plot (a) and contour plot (b) showing the effect of time (A) and temperature (B), and their mutual interaction in the enzymatic synthesis of methyl oleate at a constant molar ratio of 1:3 (oleic acid:methanol).

Figure 9. Graphs depicting the response surface plot (a) and contour plot (b) showing the effect of time (A) and molar ratio (C), and their mutual interaction in the enzymatic synthesis of methyl oleate at a constant temperature (50 °C).

Figure 10. Graphs depicting the response surface plot (a) and contour plot (b) showing the effect of temperature (B) and molar ratio (C), and their mutual interaction in the enzymatic synthesis of methyl oleate at constant time (10 h).

Table 4. The attained optimum conditions for the CRL-MWCNTs catalysed synthesis of methyl oleate.

Experiment	Reaction time (h)	Reaction temperature (°C)	Molar ratio (Oleic acid : Methanol)	Predicted yield (%)	Actual yield (%)	Deviation (%)
1*	13.87	51.00	1:3.80	91.26	90.90	0.39
2*	6.00	47.07	1:2.54	74.51	72.80	2.29

Note: Selection for the highest percent conversion with all variables in the model range (1*); Selection for the highest percent conversion at the shortest reaction time (2*).