Using the Box–Benkhen design (BBD) to minimize the diameter of electrospun titanium dioxide nanofibers

Abstract

A response surface model (RSM) for predicting the diameter of electrospun titanium dioxide (TiO₂) nanofibers was developed using the Box–Benkhen experimental design (BBD) technique. The three electrospinning factors in preliminary studies using the BBD design included the potential difference (kV), the infusion rate (ml h⁻¹) and the separation distance between electrodes (cm). Verification of the model was accomplished through the analysis of residuals. The model was subsequently used to locate the optimal experimental values (electrospinning variables) which yielded the minimum TiO₂ nanofiber diameter. A minimum diameter of 43.3 nm was predicted by the model when the potential difference was set at 40 kV, the electrodes were separated by 32.5 cm apart and the infusion rate was set at 0.6 ml h⁻¹. The average experimental observed fiber diameter (47.8 ± 8.7 nm) was 9.5% greater than the predicted value (43.3 nm) under identical electrospinning settings. The nanofibers diameter was affected by the percent titanium (Ti) (by weight) in the electrospinning solution. Hence, in the final analysis, the model was refined to include a term representing the proportion of Ti in the electrospinning solution. A smaller nanofibers diameter of 39.0 ± 6.6 nm with a specific surface area (SSA) of 259 ± 23 m² g⁻¹ was produced using a solution containing 1.3% Ti. The SSA value was comparable with that for commercially available 5 nm TiO₂ nanoparticles. The diameter of the immobilized TiO₂ nanofibers was significantly less than the values reported in the literature. The model could serve as a tool for researchers.

Introduction

Traditional methods of catalyst development and nanoparticle manufacture are based on rational approaches such as literature data and experimental design. However, variable optimization can be accomplished by full or fractional factorial designs [1], [2]. Statistical experimental design methods are routinely used to evaluate the impact of variables on chemical processes and particularly in processes where the variables influence each other [3], [4], [5]. An experimental design based method is a compilation of mathematical and statistical tools for designing experiments, constructing numerical models, evaluating the effects of variables and searching for the optimum combinations of variables [6], [7], [8]. Experimental design techniques such as response surface methodology (RSM) follow a sequential approach wherein the first step is to screen the independent variables (factors) and their levels. The second step is to build the response surface model using an appropriate experimental design method [6], [7], [9], [10]. The third step involves estimating the coefficients of the mathematical model and in the final step, the accuracy of the response is assessed using experimental data.

Among the different experimental design methods, a Full-Factorial design (FFD) is often considered impractical due to its requirement of a large number of experiments. Based upon the desirable feature of accurate prediction throughout the factor space Central-Composite design (CCD) and Box–Benkhen design (BBD) are commonly selected experimental design procedures [6], [9], [10]. However, for a quadratic response surface model with three or more factors, the BBD procedure is much more advantageous when compared to the CCD [6], [7], [11]. In the case of TiO₂ nanoparticle preparation, factors controlling the particle size include surfactant, reaction temperature, calcination time and calcination temperature [12]. Establishing optimum process conditions for preparing TiO₂ nanoparticles have been accomplished using factorial design [12], [13]. Hence, a similar approach can be adopted for the manufacture of TiO₂ nanofibers.

In comparison to other treatment technologies, TiO₂ photocatalysis is a low cost method for converting recalcitrant organic pollutants into CO₂ plus water [12], [13]. The reaction is mediated by the simultaneous action of TiO₂ nano-photocatalyst plus ultraviolet (UV) light. The efficiency of heterogeneous catalysts such as a photocatalyst is dependent upon the number of active sites per unit mass of catalyst interacting with the substrate molecules [14], [15]. A catalyst with a large number of catalytic active site per unit mass is highly efficient in its ability to mediate chemical reactions [14], [15], [16], [17]. In supported metal catalysts, the number of active sites per unit mass is correlated with the specific surface area (SSA) (m² g⁻¹) [14], [15], [16], [17]. Consequently, a major task is to manufacture high surface area TiO₂ nanofiber catalysts by assessing the effect of process variables on SSA.

According to several reports, nanometer-size TiO₂ formulations, primarily in form of slurry, have been manufactured and tested for their photocatalytic potential [18], [19], [20], [21], [22]. However, using nanoparticles in form of a slurry is associated with many practical constraints. These problems include solid/liquid separation for catalyst removal and recycling and implementing measures to minimize human health hazards associated with fugitive emissions during slurry preparation [22], [23], [24]. Immobilizing TiO₂ nanoparticles onto a solid support can potentially eliminate many problems associated with the use of nanoparticles in the form of slurries [15], [23].

Dispersing nanometer-sized particles on a high surface area support is a popular method of producing a high surface area supported catalyst system [23]. However, a major bottleneck of this method relates to the loss of surface area due to sintering or aggregation of the nanoparticles during thermal treatment [23]. Particle sintering results in a supported catalyst with a surface area less than that of discrete nanoparticles by a few orders of magnitude [15]. Hence, another key research task is to develop an immobilized TiO₂ nanocatalyst system with surface area comparable to that of discrete nanoparticles.

Fabricating ultra thin nanofibers catalysts from a broad range of polymers and polymer blends has been accomplished using the electrospinning technique [25], [26]. Recently, electrospinning coupled with the sol–gel synthesis technique has been used to fabricate TiO₂ nanofibers [27], [28], [29]. According to many reports, the diameter, surface morphology and crystal structure of electrospun TiO₂ nanofibers are affected by the characteristics of the spinning solution, electrospinning process variables and thermal treatment conditions [27], [30], [31], [32].

Several studies have described methods for preparing and characterizing TiO₂ nanofibers and nanoparticles [33], [34]. Elecrospinning of nanofibers is a well established process which is influenced by the potential difference, the separation distance between electrodes and viscosity [27], [35], [36], [37]. According to Watthanaarun et al. [30], the formation of small diameter nanofibers can be accomplished using high potential differences (voltages). The viscosity of the electrospinning solution beyond a specific range can also affect the formation of nanofibers [35]. However, if the viscosity is maintained within the range of 130–160 centipoise (cps), fiber formation is unaffected [38]. Evidence describing the effects of separation distance between the electrodes (nozzle to collector) as well as the impact of solution flow rate on nanofiber formation has been provided by Thompson et al. [36] and Evcin and Kaya [37]. Evcin and Kaya [37] reported decreasing nanofiber diameter with decreasing flow rates while according to Thompson et al. [36], decreasing diameters were correlated with increasing separation distances between the nozzle to collector. The main driving force for producing high SSA anatase TiO₂ catalyts for enhanced photocatalytic performance [31], [32], [39], [40] is related to the improved performance of these nanosize supported systems.

The objectives of this study are as follows: (1) evaluate the effects of Ti content, potential difference, infusion rate and separation distance of electrodes on nanofiber diameters diameters and (2) develop a BBD based response surface model to predict and optimize the diameter of TiO₂ nanofibers.