Modeling caffeine adsorption by multi-walled carbon nanotubes using multiple polynomial regression with interaction effects

Caffeine (CFN) with chemical formula C₈H₁₀N₄O₂ is an alkaloid appertaining to the methylxanthine group naturally available in foods including tea, coffee, kola nuts and cacao beans. In humans, caffeine acts not only as a central nervous system provocative but also as a natural pesticide for the plant (Pavel et al. 2003). Caffeine is liberated in the aquatic environment and has been found in surface water, ground water and also in wastewater effluents in large concentration (∼10 g L⁻¹) (Glassmeyer et al. 2005). Because caffeine is difficult to metabolize and is commonly found in ground water and surface water, it has been proposed as a chemical indicator of environmental pollution. For instance, zebra fish embryos could not survive when the dose of caffeine in water was greater than 300 mg L⁻¹ (Chen et al. 2008). Literature also indicated that this substance is toxic to most of the aquatic environment (Pollack et al. 2009). Caffeine can damage soil fertility, cause barriers to seed germination and lowers growth of seedlings (Pollack et al. 2009). Thus, elimination of excess caffeine from different water sources is necessary.

Different chemical and physical technologies have been employed for the elimination of this substance in water including coagulation/flocculation, ion exchange, oxidation/reduction, membrane separation, biological treatment and adsorption (Ma et al. 2012). Traditional procedures applied for caffeine elimination are either expensive or involve the utilization of toxic organic materials. However, as traditional wastewater treatment do not degrade caffeine, it is important to look for alternatives (Álvarez-Torrellas et al. 2016). Adsorption procedure is one of the best wastewater treatments due to the simplicity, ease of operation, high efficiency and can be utilized in small scale household units; thus, adsorption techniques are commonly applied. Adsorbents must have suitable characteristics including high adsorption capacity, surface area, selectivity, lifetime and capacity for regeneration (Arshadi et al. 2014).

Nowadays, a great deal of interest is being concentrated on the use of nano-structured materials such as carbon nanotubes (CNTs) as adsorbents to eliminate harmful and toxic organic pollutant from aqueous media. CNTs which were described by Iijima (1991), are one of the most commonly investigated carbon nano-materials and can act as good adsorbents for the removal of toxic pollutants due to their layered and hollow structure, and also large surface area (Tan et al. 2012). CNTs materials can be divided into three groups: functionalized CNTs, single-wall CNTs and multi-wall CNTs (MWCNTs) (Yu et al. 2014). MWCNTs are successfully applied in the removal of many pollutants such as methyl red (Ghaedi & Kokhdan 2012), methyl orange (Hosseini et al. 2011), Eriodirome Cyanine R (Ghaedi et al. 2011), pharmaceuticals and personal care products (Wang et al. 2016) from wastewater. However, examples of the utilization of MWCNTs for caffeine removal are rather scarce in the literature.

The main factors affecting the adsorption reaction including pH, reaction time (t), adsorbent mass (M), temperature (T) and initial pollutant concentration (C) were investigated and analyzed, using the equations governing the adsorption process such as adsorption isotherm or/and adsorption kinetic models. In these equations only one factor is variable and the others are held constant. It is better to use an equation that encompasses all factors affecting the adsorption process. In other words, it is better to investigate the effects of all factors simultaneously. Several researchers have employed artificial intelligence models to predict adsorption efficiency of pollutant from aqueous media. These models include artificial neural networks (Yetilmezsoy & Demirel 2008; Gamze Turan et al. 2011a, 2011b; Amiri et al. 2013a), adaptive neural-based fuzzy inference systems (Amiri et al. 2013b), wavelet neural networks and support vector regression (Mousavi et al. 2012). However, many cases of prediction, such as adsorption process polynomial regression, did at least as well if not better than the artificial intelligence models. The main purpose of this research was data modeling of caffeine removal from aqueous media using MWCNTs by multiple polynomial regression with interaction effects.

Caffeine (i.e 1,3,7-trimethylpurine-2,6-dione) was purchased from Sigma–Aldrich Co. (Germany), in analytical purity and applied in the experiments directly without any further purification. Suitable concentrations of caffeine solutions were provided by diluting a stock solution with deionized water. MWCNTs were prepared by Nanocyl Co. (Belgium) and used as adsorbent. All other chemicals were purchased from Merck (Germany). Some of the physical characteristics of MWCNTs are seen in Table 1.

The pH of solution was modified using 0.1 M HCl/NaOH using a pH meter (Metrohm, 827 pH Lab). Zero point charge (pH_ZPC) of MWCNTs was measured with the solid addition method (Balistrieri & Murray 1981). Nitrogen (99.999%) adsorption tests were carried out at −196 °C using volumetric apparatus (Quantachrome NOVA automated gas sorption analyzer). The concentrations of caffeine solutions were obtained by using a UNICO-2100 UV-Vis spectrophotometer at a wavelength corresponding to the maximum absorbance, λ_max = 275 nm. The functional groups existing in MWCNTs was investigated using the Fourier transform infrared (FTIR spectroscopy) technique. FTIR spectra were recorded using a Jasco FT/IR-680 plus spectrophotometer as KBr pellets. The size and surface morphology of MWCNTs were determined using a scanning electron microscope (SEM) (MIRA3TESCAN-XMU).

Statistical procedures such as multiple polynomial regression are the best tools for studying any relationship between low example sizes of response and independent variables (Razi & Athappilly 2005). Statistical analysis that justifies the combinations of factor levels was used through multiple polynomial regression analysis using Minitab 17 software. Multiple polynomial regression is a procedure applied to model the relationship between one or more independent parameters and a response variable. To create this regression model, it was necessary to determine critical parameters, given that the best model must have the least number of necessary parameters and maximum accuracy. In this research, q was the response variable. Also t, C, M, pH and T were continuous predictors. To implement the multiple polynomial regression, the measured data set included 114 caffeine samples which were divided into two parts: the first group (86 observations, 75% of the data) was randomly selected for building the model, and the second group (28 observations, 25% of the data) was applied for testing the model.

Several works have been performed in order to elucidate the mechanism of adsorption of many molecules on different adsorbents. Those publications reveal that adsorption of organic molecules from dilute aqueous solutions on carbon materials is a complex interplay between electrostatic and non-electrostatic interactions and that both interactions depend on the characteristics of the adsorbent and adsorbate, as well as the solution chemical properties (Moreno-Castilla 2004). As a similar substance, MWCNTs can be considered effective in removing organic contaminants.

As can be seen in Equation (5), this model contains linear effects (t, C, M, pH, T), quadratic effects (⁠⁠), cubic effects (⁠⁠), and interaction effects (t* C, t* M, t* pH, t* T, C* M, C* pH, C* T, M* pH, M* T, pH* T). However, not all these effects are significant and step-by-step the non-effective parameters were removed. The final model has parsimonious parameters and maximum accuracy. Following on from this, we used Note 1 and 2 to determine the final model:

• Note 1 – In polynomial regression when a cubic effect is significant, we must assume linear and quadratic effects in the model (significant or not significant). Also when a quadratic effect is significant, we must assume linear effect in model (significant or not significant).

• Note 2 – In regression with interaction effects, when an interaction effect is significant, we must assume both linear effects in model (significant or not significant).

Results of the test data set show that Equation (6) slightly overestimated (MRE was positive). The R² and NRMSE of Equation (6) were calculated to be 0.9961 and 0.0916, respectively, showing the excellent performance of multiple polynomial regression in predicting q_p. As mentioned in the above section, the pH and T were removed in final model, therefore, the pH and temperature have no significant effect on adsorption capacity of caffeine in a batch mode experiment, and so the number of experiments could be reduced based on the results of the models. In this respect, for three independent variables (t, C and M), three structures were built. The statistical indices and performance of the three structures as compared with the best model (Equation (6)) are presented in Table 7.

For all linear regressions observed in Table 7, the distances from the origin are not significant at the 5% level and are considered zero. Based on Table 7, q_p values of Equation (6), Structure1, Structure2 and Structure3 were higher than the measured adsorption capacity of caffeine, where the ratios of q_Eq(6)/q_m, q_Structure1/q_m, q_Structure2/q_m and q_Structure3/q_m were 1.05, 1.07, 1.09 and 1.25, respectively. Structure1 indicated good performance, with value of NRMSE equal to 0.1544. Performance of Structure2 was fair, with NRMSE equal to 0.2171, but when Structure3 was applied, results indicated that this equation gives poor prediction of the adsorption capacity of caffeine. To determine the sensitivity of the model to each independent variable, the variation of NRMSE was investigated as compared with the best model by eliminating each operating variable from the model. As shown in Table 7, greatest increase in NRMSE was due to C, followed by M, and then t. The most efficient variable is the initial concentration of caffeine, the NRMSE amount was markedly raised (0.0916 to 0.4731) when this parameter was removed from Equation (6). Similar outcomes have been demonstrated in prior studies (Jain et al. 2009; Mousavi et al. 2012). In fact, the greater removal efficiency of caffeine was observed at the lower concentration of caffeine due to the accessibility of more unoccupied active sites. However, the removal efficiency of caffeine decreased on raising initial caffeine concentration due to saturation of exchangeable sites of the MWCNTs. Therefore, the removal of caffeine by MWCNTs is more dependent on C.

The second most efficient parameter is mass of adsorbent, where the NRMSE amount raised from 0.0916 to 0.1544. Similarity, the third most efficient parameter is contact time, where the NRMSE amount raised from 0.0916 to 0.2171. This can be attributed to the short time of equilibrium and caused less effective caffeine adsorption by MWCNTs. In fact, equilibrium is reached after 5 min for caffeine (data not presented). The removal efficiency increases with time in the first 5 min and then the adsorption curve reached equilibrium after this time. However, pH and temperature were not significant variables and were dropped from the final model which confirmed the applicability of MWCNTs for treatment of surface and ground water in the broad range of these parameters. This study demonstrated that the multiple polynomial regression could be accurate and a faster alternative to the available difficult and time-consuming models for q prediction.

In this research, the adsorption capacity of caffeine by MWCNTs is studied using multiple polynomial regression. The influences of C, M, t, T and pH on q (mg g⁻¹) were studied. The MWCNTs were specified by SEM, FTIR spectroscopy and point of zero charge. The results confirmed that the MWCNTs have a high capacity to uptake caffeine from the wastewater. Results show that multiple polynomial regression could give excellent fit to the observation adsorption capacity. The increment of input variables from only ‘C + M + t’ to ‘C + M + t + pH + T’ did not show a significant effect on the removal efficiency of caffeine from aqueous media and consequently did not affect the model. The results also indicated that C was more important in q prediction, relative to M and t. The suggested technique is easy to operate, accurate, rapid and needs less computational time.