Optimization of Carbon Nanotube Dispersions in Water Using Response Surface Methodology.

The aim of this work was to demonstrate an optimization methodology to reliably obtain stable macrodispersions (i.e., for ≥24 h) of carbon nanotubes in water using sonication. Response surface methodology (RSM) was utilized to assess and optimize the sonication parameters for the process. The studied input parameters were (i) sonication time (duration), (ii) amplitude (of vibration), and (iii) pulse-on/off (duration) of the sonicator. The analyzed responses were mean diameter and size distribution of multiwalled carbon nanotube (MWNT) aggregates in water, which were measured by the dynamic light scattering technique. A semiempirical model was developed and statistically tested to estimate the magnitude of sonicator parameters required to obtain specified MWNT macrodispersions (i.e., aggregates' mean diameter and distribution) in water. The results showed that MWNT aggregates of 2 ± 0.5 μm can be obtained by optimizing sonicator parameters to a sonication time of 89 s, amplitude of 144 μm, and pulse-on/off cycle of 44/30 s. These process settings for 100 mg/L MWNTs in a 30 mL aliquot of deionized water would consume 863 J/mL of sonication energy. Contrary to the popular belief, "sonication time" and/or "sonication energy input" were not found to be proportional to the degree of dispersion of MWNTs in water. This might be the reason for the frequent disparity and nonreproducibility of sonication results reported in scientific literature, especially for dispersing nanomaterials in a number of different systems. The amplitude of vibration was noted to be the most sensitive parameter affecting MWNT aggregates' diameter and distribution in water. The characterization of MWNTs was performed using electron microscopy, surface area analyzer, thermogravimetric analyzer, and zeta potential analyzer. This study can be helpful in evaluating sonication dispersion of particulate matter in other incompressible fluids such as graphene dispersion in organic solvents.

Introduction

Carbon nanotubes form suspensions in water but their dispersion state changes over time making it difficult to quantify their degree of dispersion.[1] To address this problem, NIST and NASA defined the terms “macrodispersion” and “nanodispersion” for carbon nanotube suspensions.[2] Macrodispersion represents dispersed aggregates of carbon nanotubes, while nanodispersion refers to ones consisting of individual carbon nanotubes.[3] Both types of dispersions have their own significance and applications; however, this work is focused on macrodispersions of carbon nanotubes.

Carbon nanotubes are known to remarkably improve the electrical, mechanical, and photocatalytic properties of composites.[4−6] These exceptional benefits of carbon nanotubes can be harnessed only if they are reasonably dispersed (in the medium) during the synthesis of composites.[6−9] However, strong interaction forces between carbon nanotubes cause their agglomeration into aggregates, thereby limiting their dispersion in most solvents.[6,10] On average, 500–950 eV binding energy per micrometer of carbon nanotube length holds them together in an aggregate.[11−15] To disperse them, an appropriate amount of external energy is required to overcome this high amount of binding energy. Continual efforts have been underway to obtain stable dispersions of carbon nanotubes since their discovery. The methods used to disperse carbon nanotubes can be broadly categorized into either chemical or mechanical methods. For chemical methods, researchers have approached the problem by mostly varying (i) solvents,[16] (ii) solvent compositions,[14,17] and (iii) solvent additives such as surfactants and macromolecules.[6,9,10,12,18,19] Mechanical methods such as shear mixing, ball milling, and melt blending are sometimes used;[20] however, ultrasonication (aka sonication) remains the most popular mechanical method to disperse carbon nanotubes.[6,9,12,21,22]

Unless otherwise required, water is a natural choice for solvent owing to its universal availability, low cost, inherent nontoxicity, and ease of handling and because it facilitates high solubility for a variety of solutes. Carbon nanotubes tend to aggregate in water owing to nonspecific hydrophobic forces against the solvent and substantial van der Waals attractions between the CNTs.[1] The magnitude of the van der Waal’s attractions was calculated to be up to 950 eV/μm (carbon nanotube length) by Girifalco et al.[15] A molecular dynamics study performed by Walther and Jaffe[23] calculated a 28.66 kJ/mole increase in free energy when carbon nanotubes are moved from air to water. This positive change in free energy, thought to be contributed by the carbon–carbon and water–water (cost of cavity) interactions, makes the dispersion of carbon nanotubes in water thermodynamically unfavorable.[23] This hinders the ability of water to disperse carbon nanotubes without the provision of an external energy source. This external energy source can be mechanical tools like rotor–stator mixers, colloid mills, ball mills, shear mixers, and sonicators.

Sonication is the most extensively used mechanical dispersion technique, primarily due to its simplicity of application.[6,9,12,21,22] It reduces the size of carbon nanotube aggregates, shortens their length, opens their ends, and creates functional groups at their sidewalls and on their terminal ends.[6,7] This alteration in the morphology and functionality of carbon nanotubes increases their hydrophilicity and enables them to better disperse in water. However, a great risk of damage to carbon nanotube integrity is also associated with improper sonication because of the occurrence of complex physical and chemical phenomena during the process.[24−26] If not accounted for properly, these phenomena can lead to adverse alterations to the characteristics of carbon nanotubes in dispersion.[8] Unfortunately, little attention is paid to the simple process of sonication, resulting in the frequent occurrence of either “under-sonication” or “over-sonication” of carbon nanotube dispersions. Inadequate dispersion and inadvertent breakage of carbon nanotubes during sonication are some such examples.[10]

In this study, a process is reported for optimizing sonication parameters to obtain multiwalled carbon nanotube (MWNT) dispersions of required aggregate size (mean diameter and standard deviation). MWNTs were dispersed in water with the aid of a probe sonicator under different sonicator operational settings (parameters/variables/factors) of sonication time, vibration amplitude, and pulse (on/off) mode to observe their effects on mean diameter and distribution (i.e., standard deviation) of MWNT aggregates. Using response surface methodology (RSM), a model was developed, analyzed, and validated to predict the dispersion of MWNTs for different sonicator parameters. Finally, a desired range of sonicator parameters was identified for the set criteria of minimizing size and variability (in the sizes) of carbon nanotubes aggregates at minimal sonication energy cost.

Materials and Methods

Materials

MWNTs with average diameter and length of 10 and 1500 nm, respectively, were purchased from Sigma-Aldrich (St. Louis, MO, USA). The MWNTs were over 95% pure and had been prepared by the catalytic carbon vapor deposition method. Sodium hydroxide (98.8%) was provided by Poch Basic (Gliwice, Poland). Reagent-grade hydrochloric acid, dibasic potassium phosphate, and sodium chloride were acquired from Sigma-Aldrich. Vacuum filtration was carried out using GF/F glass microfiber filter disks (Millipore Corp., Billerica, MA, USA). Fresh deionized water, with an average resistivity of 18.2 MΩ·cm, was used in all experiments.

Cleaning Procedure for MWNTs

The as-received MWNTs were treated with hydrochloric acid, using previously established protocol[27] summarized in Figure S1. Briefly, 1 g of MWNTs was added to 500 mL of Pyrex glass container followed by the addition of 200 mL of 10 M hydrochloric acid. The suspension was stirred for 6 h using a magnetic stirrer. Three hundred milliliters of deionized water were added, and the suspension was filtered through binder-free glass microfiber filter, Whatman GF/F (GE Healthcare Life Sciences, UK), using a vacuum filtration apparatus. At least seven washes of the MWNT cake, hence obtained, were performed (using deionized water) to remove residual hydrochloric acid. Finally, the MWNT cake was dried to constant mass in the oven at 70 °C to remove moisture and vaporize away the hydrochloric acid, if any. The cake was ground to powder using a glass rod in the prewashed borosilicate beaker and stored in an air tight container until further use.

Characterization of MWNTs and MWNT Dispersions

The structure of MWNTs was examined by scanning electron microscopy (SEM) using an FEI Quanta FEG 250 SEM from FEI Co. (Hillsboro, OR, USA). The equipment was operated at ∼20 keV. Prior to imaging, the sample surface was coated with <50 nm layer of gold and palladium using a GATAN model 682 precision etching coating system. Thermal analysis of MWNTs was carried out using a PerkinElmer Thermogravimetric Analyzer (Waltham, MA, USA) using nitrogen as a carrier gas. The temperature was gradually increased from 30 to 800 °C using approximately 10 mg of sample. The difference in weight over the temperature gradient provided the information about the sample. The charge on MWNTs was measured, using a ZetaPALS analyzer (Brookhaven, NY, USA), through electrophoretic mobilities of MWNTs at variable pH of the background solution.

Brunauer, Emmett, and Teller (BET) surface area and porosity of MWNTs was measured by NOVA 2200e automated gas sorption system (Quantachrome, FL., USA) using nitrogen gas at 77 K. The data were analyzed by Quantachrome NOVAWIN data acquisition and reduction software version 11.02 provided by the manufacturer. The adsorption/desorption isotherms of N2 were measured at a relative pressure (P/Po), ranging from 0.0001 to 0.99. The BET equation was utilized to determine the specific surface area.

MWNT Dispersions in Water

MWNT dispersions were prepared by adding 3 mg MWNTs to 30 mL of deionized water (to obtain 100 mg/L concentration). The sonications were performed at different settings of the pre-calibrated probe sonicator (Q125) that had a 3 mm diameter probe (Qsonica LLC, Newton, CT, USA). The resulting suspensions were allowed to stabilize for a period of 24 h. After 24 h, the sample was drawn for dispersion analysis from the middle of the 30 mL cylindrical vial using 0.5 mL pipette.

MWNTs are rod-like particles with a high aspect ratio. Therefore, ideally, they should be described as such in aqueous systems. However, it is difficult to find an analytical expression to describe rod-like particles following Derjaguin–Landau–Verwey–Overbeek theory.[28] Therefore, MWNT aggregates were approximated to spherical particles and their effective diameter was calculated using Stokes–Einstein relationship.[1,3,19,28] MWNT aggregate size and particle distribution was determined using ZetaPALS analyzer (Brookhaven, NY, USA), which was also used for zeta potential measurements. Dynamic light scattering (DLS) technique was used to measure aggregate size and distribution of MWNTs after sonication. The data were analyzed using Particle Solutions software from the manufacturer. The effective diameter of MWNTs was calculated using the Stokes–Einstein relationship as shown in eq where dh is the hydrodynamic diameter (m) of an equivalent sphere of MWNT aggregates, kB is the Boltzmann constant (1.3807 × 10–23 J K–1), T is the absolute temperature (K), and η is the dynamic viscosity of water (0.009 kg m–1 s–1) under the experimental conditions. The standard deviation of MWNT aggregates, representing the distribution of MWNTs, was calculated using MS Excel software. To obtain the standard deviation, at least 10 runs of five cycles each were performed on each sample.

Experimental Design

RSM was applied to identify the effect of various sonicator parameters on MWNT dispersion. RSM is a collection of statistical and mathematical techniques helpful for developing, improving, and optimizing processes.[29,30] The use of RSM in dispersing MWNTs reduces the process variability and requires fewer resources. Central composite design (CCD), a form of RSM, was used with four variables at five levels. To understand the relationship between the sonicator’s operating parameters and the dispersion of MWNTs in water, four independent variables (sonication time, the amplitude of vibration, pulse-on duration, and pulse-off duration) were selected. The effects of these variables on two responses, namely, MWNT aggregate size and aggregate distribution, were examined. The details of actual variables and their corresponding dimensionless factors, at studied levels, can be found in Table . Alpha (α) is the coded level of the axial point and “1” is for a factorial point from the center “0”. The coding was performed to normalize the effects of factors on responses, and the coded levels were obtained by subtracting the actual values of the variables from their value at the central point and dividing by the step chance value. Full factorial design requires 54 = 625 experiments, however (as shown in Table ), RSM reduced the required experiments to 30 only: 8 at axial, 16 at factorial, and 6 at center points of deign. Table provides the detailed description of actual experimental conditions recommended by RSM and their position in the design space. It should be noted that (in Table ) the values of sonicator’s input variable [A: time (s)] and its corresponding total sonication energy (J) are based on unit volume (1 mL) of dispersions. In practice, 30 mL aliquots were processed. Therefore, the sonication time [A: time (s)] (and water volume) should be multiplied by the factor of 30 to mimic actual experimental conditions of this study.

Table 1

Variables and Levels of Chosen Factors for Central Composite Design

			coded levels
factor	variable	units	–α	–1	0	1	α
A	time	s	2	31	60	89	118
B	amplitude	μm	36	72	108	144	180
C	pulse-on	s	2	16	30	44	58
D	pulse-off	s	0	15	30	45	60

Table 2

Experimental Design Matrix Based on a Central Composite Design Using Full Factorial

	sonicator input variables (factors)						dispersion of MWNTs (responses)
run	space type	A: time (s)	B: amplitude (μm)	C: pulse-on (s)	D: pulse-off (s)	total sonication energy (J)	MWNTs mean diameter (nm)	standard deviation of MWNTs aggregates [nm]
1	axial	60	108	30	60	341	2864	672
2	center	60	108	30	30	348	3773	1188
3	center	60	108	30	30	341	1999	655
4	axial	118	108	30	30	668	3132	1074
5	factorial	89	72	44	15	259	10 411
6	center	60	108	30	30	345	2143	509
7	factorial	89	144	44	45	872	2427	754
8	factorial	31	144	44	15	304	3431	2679
9	axial	60	108	2	30	236	2974	1944
10	axial	60	180	30	30	858	1879	634
11	factorial	31	72	16	15	85	4937	3443
12	factorial	89	72	16	45	244	2830	930
13	factorial	31	72	16	45	86	1674	697
14	factorial	89	144	44	15	872	2203	906
15	factorial	31	144	44	45	304	3108	1573
16	factorial	31	72	44	45	88	3978	2821
17	axial	60	36	30	30	35	6022
18	axial	2	108	30	30	11	1318
19	axial	60	108	58	30	349	4638	2667
20	center	60	108	30	30	344	2489	474
21	factorial	89	72	44	45	259	3023	2317
22	center	60	108	30	30	340	3958	2520
23	factorial	89	144	16	45	861	2000	561
24	factorial	31	144	16	45	300	4151	3658
25	factorial	89	72	16	15	248	5464
26	center	60	108	30	30	341	4090	2934
27	axial	60	108	30	0	342	4402	2955
28	factorial	31	144	16	15	300	4163	1793
29	factorial	31	72	44	15	87	5831	4569
30	factorial	89	144	16	15	861	2639	502

Results and Discussion

Characterization

Figure a presents the SEM images of MWNTs revealing their morphology, structure, and intertubular cohesion. The outer diameter of MWNTs was approximately 10 nm, which was comparable to the reported value from the manufacturer. No obvious amorphous carbon particles and other impurities were spotted at all magnifications, possibly a result of the acid treatment performed to dissolve away impurities.[27]

Figure 1

Characterization of MWNTs used in this study: (a) scanning electron micrograph, (b) TGA, (c) zeta potential, (d) adsorption/desorption of nitrogen gas, and (e) pore size distribution.

Thermal stability and purity of materials can be evaluated by thermogravimetric analysis (TGA). In TGA, the oxidation temperature represents the thermal stability of a material and can be identified as a peak in the derivative of the weight loss as a function of temperature.[31] The decomposition profile of MWNTs is exhibited in a weight loss curve as represented in Figure b. The mass loss of materials can be divided into four distinct regions: (i) 0–100 °C represents the loss of moisture; (ii) 100–300 °C represents the decomposition of carboxylate, anhydride, and lactone functional groups; (iii) 300–500 °C is indicative of more stable phenol and carbonyl functionalizations; and finally, (iv) >500 °C exhibits the decomposition of amorphous carbon.[32] Therefore, it can be seen that the MWNTs carry adsorbed water (0.6% mass loss until 100 °C), contain some functionalities (3.5% mass loss until 500 °C), and oxidize at 600 °C. The 3.5% mass loss (until 500 °C) cannot be wholly attributed to functional groups, because some might be due to amorphous carbon. Lehman et al.[33] reported the oxidation temperature of single-walled carbon nanotubes at 350 °C. MWNTs, in this study, were prepared by catalytic vapor deposition, where metal catalyst acts as a precursor for the growth of carbon nanotubes. In this process, the probability of single-walled carbon nanotube formation cannot be completely ignored. In the case of our material, however, there was only a 0.5% loss in mass from 350 to 500 °C, indicating very few single-walled carbon nanotubes, if any.

Figure c displays the change in zeta potential of MWNTs with the change in surrounding aqueous pH. Zeta potential measurements are indicative of ionically stabilized colloid systems, that is, the stability of colloidal system increases with the increase of zeta potential of suspended particles above ±25 mV.[34] Zeta potential can also be explained in terms of two layers of liquid surrounding the particle: (i) the stern layer and (ii) the diffuse layer. The stern layer exists as an inner layer where the ions are strongly bound to the particle, whereas the diffuse layer is the outer layer where ions are less firmly bound to the particles. The potential at this outer boundary is measured through electrophoretic mobility using the Smoluchowski equation to estimate zeta potential.[22] The point of zero charge of MWNTs was calculated, by interpolating the measured zeta potential values at pH 3, 4.5, 6, 7.5, 9, and 10.5, to be at pH 6.6.

Adsorption, dispersion, catalytic activity, functionalization, and toxicity are some of the characteristics that are directly dependent upon the surface architecture of a material. Many uncommon properties of MWNTs are attributed to their unique three-dimensional surface structure.[33,35] Therefore, understanding the surface area helps in elucidating MWNT interaction with other materials. In an individual MWNT, the spaces between concentric cylinders of graphene are 0.34 nm[36] which are too narrow to accommodate nitrogen gas molecule whose kinetic diameter is approximately 0.36 nm.[37] However, MWNTs tend to aggregate, in water and air, at ordinary conditions. The typical MWNT aggregate carries four distinct sites for nitrogen adsorption: (i) external surface area; (ii) groove area; (iii) interstitial area; and (iv) inner pores.[35,38,39] The overall magnitude of these multiple nitrogen adsorption sites depends upon a number of factors such as synthesis procedure, purification methods, and chemical and physical modifications.[40] These factors can be held responsible for large differences (up to 75×) in reported specific surface areas of MWNTs from 22.4 to 1670 m2/g.[41,42] The curves of the nitrogen adsorption/desorption isotherms of MWNTs (Figure d) are convex and comparable to the reversible type III isotherm under IUPAC classification, which exhibit weak attractive adsorbate–adsorbent interactions.[43] The type III isotherm is characterized by heats of adsorption less than the adsorbate heat of liquefaction, whereby adsorption proceeds with the adsorbate’s interaction with an adsorbed layer (i.e., adsorbate–adsorbate interaction) that is greater than that of the adsorbent’s surface (adsorbate–adsorbent interaction).[43−46] This kind of isotherm is reported for nitrogen adsorption on the basal plane of graphite.[45] Therefore, from the structure of MWNT aggregate, it can be assumed that most of the nitrogen adsorption took place on the external surface area of MWNTs. The desorption of nitrogen was employed to calculate BET surface area at low-pressure ranges.[46,47] The recommended range of P/Po from 0.35 to 0.05 was utilized to calculate BET surface area.[47] MWNTs, in this study, carried a specific surface area of 440.7 m2/g.

Pore size distribution was investigated using density functional theory (DFT). Classical macroscopic theories such as the BJH method, DR approach, and SF semiempirical treatment all fail to provide a realistic description of the filling of micropores and narrow mesopores, leading to an underestimation of pore sizes. To achieve a reasonable description of pore size distribution, DFT was applied to understand the sorption and phase behavior of fluids in narrow pores at a molecular level.[48]Figure e shows the pore size distribution of MWNTs. It can be seen that the majority of the pores in MWNTs are mesopores having a diameter between 6 and 20 nm.

MWNTs Dispersion in Water

Macrodispersions of MWNTs were prepared using sonication energy. Table describes the details of experimental runs (from column 1 to 9): (i) number of experiments, (ii) position of each experiment in the CCD space, (ii) time duration of sonication, (iv) amplitude of vibration, (v) duration of pulse-on, (vi) duration of pulse-off, (vii) resulting sonication energy from time, amplitude, and pulse-on/off, (viii) average diameter of MWNT aggregates, and (ix) size distribution of MWNT aggregates in dispersion. The values of input variables A–D were suggested by RSM and outputs were calculated by (i) calibrating the sonicator (sonication energy)[22,49] and (ii) analyzing the MWNT dispersions by DLS (the responses average aggregate size and distribution). Figure a presents the photographic images of MWNTs, sonicated at the different conditions specified in Table . These images can be visually evaluated in comparison to the factors and responses (Table ). Therefore, before proceeding further, the data were tested for their smoothness (precision) by correlating distribution of MWNT aggregates with their mean sizes at different sonication energies. Figure b, hence obtained, gives a reasonable correlation (R2 = 0.84) between the diameter and standard deviation of MWNT aggregates. Also, the high sonication energy dispersions (red dots, see key within Figure b) cluster in the region where MWNTs diameter is small and distribution is narrow. This improves confidence in the validity of the dataset. From Figure a,b, one can pick up the visually desirable dispersion state of MWNTs and estimate its aggregate size corresponding to the required sonication energy. A general conclusion drawn from Figure a,b was that the average aggregate size of ∼2–6 ± 0.5 μm can be achieved by sonicating MWNTs in water at energies below 1 kJ per mL water, provided that the working volume is 30 mL and concentration of MWNTs is 100 mg/L. Figure b (along with Figure S2 in the Supporting Information) can be helpful for a rough estimation of MWNT macrodispersions. The average diameter and standard deviation (distribution around mean diameter) were measured to estimate the aggregation state of MWNTs in water. The diameter and distribution data of MWNT aggregates in Figures b and S2 can be plotted against input variables (variables A–D in Table ) to find their mutual relationship, if any. Therefore, the effect of each factor on MWNT dispersion was studied by plotting the MWNT aggregates’ mean diameter and size distribution against sonication time, amplitude, pulse-on duration, and pulse-off duration (Figures S3–S6). The objective, there, was to find out whether any correlation exists between the sonicator’s operating parameters and dispersion of MWNTs in water. Figure S3 shows the absolute absence of correlation between time of sonication and MWNT aggregates’ diameter as well as its distribution. This raises a serious concern for researchers reporting carbon nanotubes dispersion in water in terms of sonication time. Similarly, amplitude also failed to explain MWNT dispersion (Figure S4), as did the pulse-on (Figure S5) and pulse-off (Figure S6) durations. Pulse-off duration was studied owing to its indirect effect on dispersion by impacting the temperature of the system being sonicated. This effect will become more prominent in subsequent sections (Pareto analysis). Because the individual sonicator’s parameters could not explain the macrodispersion of MWNTs, their combined effect was plotted. Figure S7 shows the plot of sonication energy versus dispersion of MWNTs. The increase in the quantity of sonication energy was expected to enhance the dispersion of MWNTs; however, no significant correlation between sonication energy and MWNTs dispersion in water was observed. Therefore, contrary to the popular belief, it was hypothesized that “the sonication energy is not proportional to the quality of MWNTs aqueous dispersions”.[50]

Figure 2

(a) Photographic images of MWNT macrodispersions after sonication and one-day settling time. The number corresponds to experimental runs listed in Table . (b) Correlation between mean diameter and size distribution of MWNT aggregates as a function of sonication energy supplied. Correlation between the experimental and predicted values of MWNT aggregates’ (c) mean diameter and (d) size distribution in water.

Model Fitting and Analysis

Because the individual sonicator operational parameters failed to describe the dispersion of MWNTs in water, experimental results were utilized to develop semiempirical expressions capable of expressing MWNT dispersions in water. Equations and 3 represent the relationship between sonicator’s parameters and mean diameter of MWNT aggregates in coded and actual terms of studied factors, respectively. Similarly, eqs and 5 were developed for MWNT aggregates’ size distribution in water, in terms of standard deviation from the mean aggregate diameter. The coded equations (eqs and 4) are useful for comparing the relative impact of factors while equations with actual factors (eqs and 5) are suitable for predicting responses. Equations and 5 cannot be used to compare the relative impact of sonicator’s variables on dispersion within each equation because the terms in these relationships are corrected to accommodate for units.

Tables S1 and S2 display the results obtained from analysis of variance (ANOVA) of the quadratic models developed for estimation of MWNT aggregates’ mean diameter and size distribution, respectively. The F-value of 8.32 and 12.7 imply that the models are significant.[51] There is only a 0.01% chance that an F-value this large could occur because of noise. Values of probability > F and less than 0.05 indicate that model terms are significant. In the case of MWNT aggregates’ mean diameter, there are five significant model terms (B, D, AB, BC, and BD), whereas in the case of MWNT aggregates’ size distribution six significant model terms were identified (B, D, AB, AD, BD, and B2). The amplitude (B), pulse-off (D), sonication time × amplitude (AB), and amplitude × pulse-off (BD) are common significant model terms in the two models. In addition to these four terms, amplitude × pulse-on duration (BC) term is significant for MWNT aggregates’ mean diameter only. However, sonication time × pulse-off (AD) and amplitude2 (B2) terms are significant for the MWNT aggregates’ size distribution only. This implies that along with amplitude of vibration, the sonicator’s pulse-on duration is influential to the mean aggregate diameter while the size distribution is sensitive towards pulse-off duration. This difference might be due to the system temperature regulation for MWNT dispersion, which is often recommended in the literature.[8,50,52] This might also be the reason for the failure of sonication energy to describe dispersions (Figure S7) because sonication energy is unable to account for the “duration” of pulse-off. The “lack of fit values” for the two models were not found to be significant, hence providing further evidence for their validity. There were 42 and 18.9% chances for the occurrence of lack of fit due to noise for MWNT aggregate mean diameter and its size distribution, respectively. When it came to regression of the models, a reasonable agreement (0.185 < 0.2) between predicted and adjusted R2 was observed for MWNT diameter but a little less than desired (0.27) for MWNTs distribution. This can be attributed to the block effect and/or outliers. The predictability of the model could be slightly improved (5–10%) by transforming the response to square root function but the significant variables as well as the shape of response surface will be minimally altered. Therefore, the response was not transformed. However, “adequate precision” value (i.e., signal-to-noise ratio) for both models was at least three times higher than the required value of 4, allowing these models to navigate throughout the design space. To conclude, ANOVA results supported the model.

All empirical models require confirmation runs even after statistical approval.[53]Figure c,d correlate the experimental and predicted (by model) values for MWNT aggregates’ mean diameter (Figure c) and size distribution (Figure d). The plots help to assess the distribution of actual experimental observations in comparison to those predicted by the models. The experimental data were found to be in good correlation with the predicted values. The correlations were statistically significant; however, regression value for MWNT aggregates’ diameter (Figure c) was lower than that for size distribution (Figure d). It should be noted that R2 is not the most reliable test for goodness-of-fit for multiple linear regression analysis because it can be affected (improved) by adding the statistically insignificant terms.[51,53] Therefore, adjusted R2 is often recommended. From Tables S1 and S2, the adjusted R2 values of 0.64 and 0.78 can be evidenced, which approve the two models to be statistically significant.

Effects of Sonication Variables on MWNTs Dispersion in Water

After statistical analysis and experimental validation, the terms in the models were assessed for their role in producing the responses. Pareto analysis is a useful tool to quantify the relative contribution of terms in a model toward the overall response. Figure presents the results obtained from Pareto analysis. The magnitude of the terms, in the model developed for MWNT aggregates’ mean diameter, can be arranged in order of decreasing importance as follows: amplitude > amplitude × pulse-off > pulse-off > time × amplitude > amplitude × pulse-on > pulse-on > time. The share of sonication parameters in MWNT aggregates’ size distribution from highest to lowest importance was amplitude > amplitude × pulse-off > amplitude2 > time × amplitude > pulse-off > time × pulse-off > pulse-on > time × pulse-on > time. The most obvious observation made from these charts was the highest impact of sonication amplitude on both responses (MWNT aggregates’ diameter and size distribution). It also revealed the significance of “pulse-off”, which is often an ignored parameter in the literature for sonication. Interestingly, total sonication time, which is the most reported parameter to describe sonication, carries the minimum weightage in both models. Its contribution reaches above one percent only when it interacts with other parameters, such as amplitude and pulse mode.

Figure 3

Pareto graphic analysis for the contribution of sonicator’s operational parameters influencing (a) mean diameter and (b) distribution of MWNT aggregates.

Analysis of Contours and Response Surface Plots

The perturbation plot presented in Figure a shows the impact of individual factors on the response. The plot is generated by keeping all variables constant except for one, resulting in an estimation of an uninterrupted impact of variables. The slope of the line, hence generated, is proportional to the quantity of impact on the response. A positive slope corresponds to an increase in the value of the response and vice versa. Figure a depicts an increase in diameter of the MWNT aggregates upon increasing the time of sonication and pulse-on duration and, conversely, a decrease in aggregate diameter upon increasing amplitude and pulse-off duration. Hence, when it comes to the effect posed by individual operational parameters of the sonicator, amplitude of vibration causes the highest desired impact (i.e., steepest negative slope) on the mean diameter of MWNT aggregates. To note, the negative slope means a reduction in MWNT aggregate mean diameter with an increase in amplitude. A similar trend of sonicator’s operational parameters is observed for MWNT aggregates’ size distribution (Figure e), except that the effect of amplitude is higher when compared with that of MWNT aggregate’s mean diameter. In the absence of interaction of factors, perturbation plots reveal that MWNT aggregates were reduced in diameter and limited to a narrower size distribution by an increase in amplitude, increase in pulse-off duration, decrease in total time of sonication, and decrease in pulse-on duration.

Figure 4

(a) Perturbation plot for the impact of variables on mean diameter of MWNT aggregates in water. The contours for the combined effect of (b) sonication time and amplitude, (c) amplitude and pulse-off duration, and (d) amplitude and pulse-on duration, on the mean diameter of MWNT aggregates in water. (e) Perturbation plot for the impact of variables on the size distribution of MWNT aggregates in water. The contour plots for the combined effect of (f) sonication time and amplitude, (g) amplitude and pulse-off duration, (h) sonication time and pulse-on duration, and (i) sonication time and pulse-off duration on the size distribution of MWNT aggregates in water.

Perturbation plots are good tools for exploiting variables individually, however, they cannot describe the interaction between factors and their effect on responses.[53] There is also a significant contribution from interactions of factors as revealed by Pareto analysis. Figure b shows the combined impact of sonication time and amplitude on the mean diameter of MWNT aggregates. It displays the region where the combined impact of [sonication time + amplitude] produces conditions to generate MWNT aggregates of a narrowly defined diameter range. This plot can be helpful for estimating the required amount of sonication time and amplitude to obtain the desired range of MWNT aggregates provided that pulse-on/off is kept constant at 30/30 s. Similarly, Figure c represents the combined effects of [amplitude + pulse-off], and Figure d shows combined impacts of [amplitude + pulse-on] on MWNT aggregates. Figure f–i evaluates combined effects of factors on MWNT aggregates’ size distribution.

Optimization of Sonication Energy

The ultimate objective of this study was to obtain well-dispersed MWNTs in an aqueous system. The detailed criteria set to achieve this goal can be seen in Table . Briefly, the entire range of sonicator’s parameters was scanned to obtain conditions at which a small MWNT mean aggregate size with a narrow size distribution could be achieved. Figure S8 shows these ramps of defined desirability. The flat ramps represent uniform desirability, whereas the negative slope of the ramps represent the minimization of numerical value (MWNT aggregate diameter and MWNT distribution) defined in the optimization criteria. The factors and responses are represented by blue and red dots, respectively. As shown in Figure S8, 96.7% of the set criteria can be achieved by sonicating MWNTs for 89 s, keeping the amplitude at 144 μm, and pulse-on/off cycle of 44/30 s. Also, on the basis of these settings, 863 J sonication energy will be consumed (per mL water) during this process. The two-dimensional contour plot in Figure a displays the “Flag” where maximum desirability can be achieved with respect to the optimal sonicator settings listed in Table . Figure b–d represents the corresponding sonication energies, MWNT aggregates’ mean diameter, and MWNT aggregates’ size distribution, respectively, for the optimal settings (Table and Figure a).

Table 3

Criteria for Optimization of Sonicator’s Parameters to Obtain Desirable Dispersion of MWNTs in Water

constraint	units	lower limit	upper limit	goal
time	s	31	89	entire range
amplitude	μm	72	144	entire range
pulse-on	s	16	44	entire range
pulse-off	s	15	45	entire range
sonication energy	J	11.3	871.8	entire range
MWNTs mean dia	nm	1318	10 411	minimize
MWNTs distribution	nm	474	13 106	minimize

Figure 5

(a) Desirability, (b) its corresponding sonication energy, (c) MWNT aggregates’ mean diameter, and (d) size distribution, obtained at optimized parameters of sonicator’s operation. Optimization criteria are described in Table .

Conclusions

The following conclusions were derived from this study:

Sonication is a useful tool to disperse MWNTs in water, provided that it is used with appropriate understanding.

Dispersion of MWNTs in water depends on amplitude, sonication time, and the pulse mode of the sonicator.

RSM can be utilized to understand and optimize the MWNT macrodispersions in water.

MWNT dispersion in water by sonication is not the function of individual sonication parameter whether it be sonication time, amplitude, or pulse mode.

MWNT dispersion in water is not proportional to the magnitude of sonication energy provided to the system.

Total time of sonication, which corresponds to magnitude of sonication energy, cannot alone describe the dispersion of MWNTs in water.

The amplitude of sonicator’s vibration collectively (alone and in combination with other parameters) contributes over 75% toward dispersing MWNTs as portended by Pareto analysis.

“Pulse-off” duration of sonicator plays an important role in the dispersion of MWNTs in water.

In our [MWNT–water-sonication] system, the desired diameter (2 ± 0.5 μm) and distribution of MWNT aggregates were obtained by optimizing sonicator’s parameters to sonication time of 89 s, amplitude of 144 μm, and pulse-on/off cycle of 44/30 s. During this process, 863 J/mL sonication energy was expended to disperse 100 mg/L MWNTs in a 30 mL aliquot of deionized water.

This optimization process can be adopted (with modification) for other [particle-solvent/aqueous-sonication] systems where appropriate dispersions are required such as synthesis of graphene from graphite-diethyl ether-sonication.[54]