Optimization

Thus far, the effect of three studied factors on the specified response was investigated.

The results confirmed that one factor could influence the response in a positive way,

while others could have an effect in a negative way. Although the output models provided

some insights into the significance of the studied factors, as well as into the interactions

between them, the optimal operational condition was still not obvious. Hence, an

optimization of statistical results was needed. A graphical optimization method was used

to obtain the optimal formulation. This method involved overlaying all model responses

in the form of contour plots with specified constrains on inputs and desired goals. The

target ranges based on typical requirements were set for each input, and the optimization

was performed. In order to show the concept of optimization, the following optimization

problem was chosen:

(4)

Figure 6-9 depicts the plot with the area in which the desired output can be obtained.

The corresponding values of three studied factors are shown as well. The results were

validated by performing three experiments using the formulation obtained from the

statistical optimization and the optimal PCE obtained was 7.42%, which is within 95%

Figure 6-9: Optimization results (Time=2h)

6.6 Conclusions

In summary, we prepared N2 doped, highly smooth and ordered TiO2 NTs by

two-step process and then annealed under N2 atmosphere. The photoelectrochemical

water splitting efficiencies (PCE) of the N2 doped TiO2 nanotubes under visible light

were measured and used as the response for DOE optimization. The changing parameters

are annealing temperatures, heating rates and annealing time respectively. The optima of

these factors were determined based on the polynomial equations generated by response

modelling and the optimal PCE was 7.26%. The optimal result was validated by

performing real experiments using the formulation obtained from the statistical

optimization and the average optimal PCE obtained was 7.42%, which is within 95%

confidence interval of the model. The visible light active N- doped TiO2 nanotubes has

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