Electronic Supplementary Information

Removal of methylene blue by silver nanoparticles loaded on activated carbon by ultrasound assisted device: optimization by experimental design methodology

M. Ghaedia,*, M. Roostaa, A. M. Ghaedib, A. Ostovana, I. TyagiC, S. Agarwalc,d, Vinod Kumar Guptac,d,e**

a Chemistry Department, Yasouj University, Yasouj 75918-74831, Iran

bDepartment of Chemistry, Gachsaran Branch, Islamic Azad University, P.O. Box 75818-63876, Gachsaran, Iran

cDepartment of Chemistry, Indian Institute of Technology Roorkee, Roorkee 247667, India

dDepartment of Applied Chemistry, University of Johannesburg, Johannesburg, South Africa

eCenter for Environment and Water, The Research Institute, King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia

* Author to whom correspondence should be addressed. Tel & fax: (0098)-741-2223048,

E-mail: ; (V. K. Gupta**)

Characterization of Ag-NP-AC

From the full-width at half-maximum of diffraction peaks, it was calculated that the average size of the Ag nanoparticles based on the Debye–Scherrer equation [1] was around 40-60 nm. The sharp and smooth XRD pattern has its high purity and crystallinity. Two well-known situations such as nucleation and crystal growth strongly compete during precipitation reaction, while at higher time, agglomeration and adhesion of particles lead to crystal growth. According to super saturation ratio, at larger initial concentration, the nucleation was the major contribution process and led to formation of lower size particles. Drop wise addition and vigorous stirring of diluted reagents (increasing volume) also are associated with lower size nanoparticles. It was found that the absence of any surfactant (stabilizing agent) leads to higher size material and subsequent decrease in removal percentage. Surfactant addition to the mixture at a level above critical micelle concentration leads to formation of internal cores as suitable places for trapping the produced Ag-NP and hinder their subsequent growth, while further concentrations do not significantly influence the size and properties of Ag-NP. Lower concentration due to non-sufficiency of trapping media leads to increase in their size and subsequent decrease in removal percentages.

Fig.S1.Temporal evolution of UV-visible absorption spectra after addition of AgNO3 solution into soluble starch solution at 50 C

Fig.S2.X-ray diffraction pattern of the (a) AC and (b)starch-stabilized Ag nanoparticles

Fig.S3.FESEM image of the (a) AC; (b) Ag nanoparticles loaded onto activated carbon.

Table S1Different conditions of Ag-NP preparation

Sample / Average size (nm) / Ag NO3
(M) / Starch
(% w/w) / Surfactant (g) / T 0C / pH / Removal (%)
1 / >105 / 0.2 / 0.10 / - / - / 75 / 9 / 76
2 / >90 / 0.1 / 0.10 / - / - / 10 / 86
3 / >150 / 0.2 / 0.15 / - / - / 50 / 63
4 / >80 / 0.1 / 0.12 / CTAB / 0.03 / 50 / 97
5 / ≈ 55 / 0.08 / 0.08 / CTAB / 0.03 / 50 / 98
6 / ≈ 80 / 0.1 / 0.10 / CTAB / 0.02 / 50 / 90
7 / ≈ 120 / 0.2 / 0.15 / CTAB / 0.03 / 75 / 10 / 90
8 / > 90 / 0.1 / 6 / SDS / 0.04 / 50 / 11 / 87
9 / >95 / 0.1 / 6 / SDS / 0.04 / 75 / 8 / 92
10 / >110 / 0.08 / 6 / Triton / 80 μL / 20 / 9 / 89

The pore size of these adsorbents (lower than 20 nm) makes possible their external and internal surfaces of the analytes transfer to sorbents.

Table S2 BET analysis of Ag-NP

Ag-NP / Summary Report
Surface Area
1410.7 m²/g / BET Surface Area:
1751.9 m²/g / Langmuir Surface Area:
154.312 m²/g / between 17.000 Å and 3000.000 Å width:
BJH Desorption cumulative surface area of pores
175.70 m²/g / between 17.000 Å and 3000.000 Å width:
Pore Volume
0.154 cm³/g / BJH Adsorption cumulative volume of pores
between 17.000 Å and 3000.000 Å width:
0.156 cm³/g / BJH Desorption cumulative volume of pores
between 17.000 Å and 3000.000 Å width:
Pore Size
21.18 Å / Adsorption average pore width (4V/A by BET):
32.67 Å / BJH Adsorption average pore width (4V/A):
33.63 Å / BJH Desorption average pore width (4V/A):

Desirability function

The individual desirability scores for the predicted values were combined into overall DF, computing their geometric mean of different dfi values.

(5)

wheredfi displays the desirability of the response Ui (i = 1, 2, 3,..., n), and vi represents the significance of responses. The desirability profiles determine which levels of the predictor factors create the most desirable responses on the dependent factors.

Random forest model

The random forest algorithm requires the tuning parameters: ntree, the number of regression trees grown based on a bootstrap sample of the original data set (the default value is 500 trees); mtry, the number of various predictors to be examined at each node (the default value is one third of the total number of the variables); the node size, the minimum size of terminal nodes. Larger value of node size leads to smaller trees (the default values are 1 and 5 for classification and regression, respectively). The RF regression model accomplishes as follows (for more details see [2]): The first step of the tool is the random selection, generally, about two thirds of the initial data are selected in a bootstrap sample (called in-bag samples), and one third the initial number of data are left out (called out-of-bag (OOB) samples). Bootstrap is a statistical terminology for sampling with replacement. In this work 80% and 20% of initial data were selected for OOB and in-bag samples, respectively. The second step consists of mtry selection. It is recommended that the value of defaults, half of them and twice be utilized, and then obtain the best value among them. For the random forest approach, selecting the small tuning parameter mtry, over-fitting may be avoided. The third step includes choices of the ntree and the constructing of a tree based on the in-bag and the mtryvariables selected. To achieve the optimum of the ntree, trees must be constructed until the error no longer decreases. The tree partitioning algorithm is constructed using, recursively, partitioning the larger space into two smaller spaces. The selection of split point is an optimization problem based on the squared error loss. An alternative way to think about the splitting process is that the algorithm begins with the root node. The algorithm splits are ceased when some stopping criterion is obtained. The most common cessation criterion is to keep the number of samples that fall in each region Rm (disjoint subspaces of the input space). For the random forest tool, over-fitting may occur if the regression trees grown at each generation are too complex. For example, if mtry is large, it is possible that at each generation, the regression tree output may be grown too large.

Table S3Analysis of variance (ANOVA) for CCD

SVa / SSb / DFc / MSd / F- value / P- value
X1 / 10.648 / 1 / 10.648 / 3.5579 / 0.117926
X12 / 9.990 / 1 / 9.990 / 3.3380 / 0.127255
X2 / 290.411 / 1 / 290.411 / 97.0379 / 0.000184
X22 / 0.555 / 1 / 0.555 / 0.1854 / 0.684724
X3 / 48.885 / 1 / 48.885 / 16.3345 / 0.009907
X32 / 9.900 / 1 / 9.900 / 3.3079 / 0.128612
X4 / 673.558 / 1 / 673.558 / 225.0630 / 0.000024
X42 / 65.004 / 1 / 65.004 / 21.7205 / 0.005529
X5 / 1831.532 / 1 / 1831.532 / 611.9887 / 0.000002
X52 / 294.986 / 1 / 294.986 / 98.5666 / 0.000177
X1X2 / 0.680 / 1 / 0.680 / 0.2273 / 0.653673
X1X3 / 105.123 / 1 / 105.123 / 35.1258 / 0.001950
X1X4 / 12.820 / 1 / 12.820 / 4.2835 / 0.093279
X1X5 / 36.227 / 1 / 36.227 / 12.1049 / 0.017674
X2X3 / 21.150 / 1 / 21.150 / 7.0670 / 0.044971
X2X4 / 168.859 / 1 / 168.859 / 56.4226 / 0.000662
X2X5 / 153.178 / 1 / 153.178 / 51.1828 / 0.000829
X3X4 / 11.109 / 1 / 11.109 / 3.7120 / 0.111970
X3X5 / 8.692 / 1 / 8.692 / 2.9044 / 0.149062
X4X5 / 30.438 / 1 / 30.438 / 10.1705 / 0.024289
Lack of Fit / 41.619 / 6 / 6.937 / 2.3178 / 0.187232
Pure Error / 14.964 / 5 / 2.993
Total SS / 3852.734 / 31

a)Source of variation; b) Sum of square; c) Degree of freedom; d) Mean square

Thermodynamic study

The sticking probability (S*) is a function of the adsorbate/adsorbent system under investigation. The parameter S* displays the amount of the potential of an adsorbate to remain on the adsorbent indefinite. The values of S* presented in Table S4 were found to be 3.9×10– 5 that lies in the range of 0 <S*< 1 and is dependent on the temperature of the system. The surface coverage (θ) can be calculated from the following equation:

(14)

The activation energy and sticking probability were estimated from a plot of ln (1−θ) vs. 1/T (Table S4).

TableS4 Thermodynamic parameters for adsorption of MB onto 0.01 g Ag-NP-AC in 50 mL at pH 7 at initial dye concentration of 9 and 16 mg L−1

Adsorbent / C0
(mg L−1) / Parameter / Temperature (K)
283.15 / 293.15 / 303.15 / 313.15 / 323.15
Ag-NP-AC / 9 / kc / 7.84 / 11.51 / 31.22 / 53.21 / 125.75
16 / kc / 20.72 / 52.02 / 71.61 / 75.00 / 127.08
Ag-NP-AC / 9 / ΔG0
(kJ mol−1) / -4.45 / -6.50 / -8.56 / -10.61 / -12.66
16 / ΔG0
(kJ mol−1) / -7.65 / -9.009 / -10.36 / -11.71 / -13.06
C0 (mg L−1) / ΔS0 (J mol−1 K−1) / ΔH0 (kJ mol−1) / Ea (kJ mol−1) / S*
9 / 205.41 / 53.71 / 51.49 / 4.27E-11
16 / 135.22 / 30.63 / 29.98 / 1.09E-7

Table S5. The range of tuning parameters and achieved statistical data for training and testing data sets

Testing Set / Training Set / Extra-options / mtry / ntree
MSE / R2 / MSE / R2
0.0060 / 0.8646 / 0.0022 / 0.9705 / - / 1 / 500 / 1
0.0061 / 0.8281 / 0.0020 / 0.9705 / - / 1 / 100 / 2
0.0013 / 0.9783 / 0.0037 / 0.9730 / - / 2 / 100 / 3
0.0059 / 0.8673 / 0.0022 / 0.9709 / - / 1 / 500 / 14
0.0028 / 0.8685 / 0.0011 / 0.9545 / Without replacement / 4 / 100 / 25
0.0032 / 0.8702 / 0.0020 / 0.9431 / sampsize = size (X_trn,1)*2/3 / 4 / 100 / 6
0.0031 / 0.8744 / 0.0013 / 0.9588 / nodesize = 7 / 4 / 100 / 37
0.0029 / 0.8766 / 0.0010 / 0.9701 / importance = 1 / 4 / 100 / 48
0.0031 / 0.8635 / 0.0010 / 0.9700 / localImp=1 / 4 / 100 / 49
0.0031 / 0.8649 / 9.68e-04 / 0.9680 / proximity = 1 / 4 / 100 / 410
0.0029 / 0.8797 / 0.0010 / 0.9694 / proximity = 1
oob_prox = 0 / 4 / 100 / 511
0.0024 / 0.9044 / 0.0010 / 0.9712 / do_trace = 1 / 4 / 100 / 412
0.0030 / 0.8699 / 9.54e-04 / 0.9724 / In bag = 1 / 4 / 100 / 413
0.0059 / 0.8616 / 0.0022 / 0.9706 / importance=1
nPerm = 1 / 2 / 100 / 414
0.0035 / 0.9050 / 0.0013 / 0.9745 / importance=1
nPerm = 3 / 2 / 100 / 15
1 Set to defaults trees and mtry by specifying values as 0
2 Set sampling without replacement (default is with replacement)
3 Note that the default value is 5 for regression
4 Default (Don't) = 0 5 Default = 1 if proximity is enabled, Don't 0

Table S6. Comparison of MSE and R2 obtained using the MLR and RF models

Model / Training set / Testing set
MSE / R2 / MSE / R2
RF / 0.0037 / 0.9730 / 0.0013 / 0.9783
MLR / 0.0060 / 0.7533 / 0.0056 / 0.7573

Fig.S4. The experimental data versus the predicted values of normalized removal obtained with (A) MLR, and (B) RF models

Fig.S5. (A) The OOB error rate versus number of trees and (B) The importance of each parameter

References

[1]M. Ghaedi, A. Ghaedi, A. Ansari, F. Mohammadi, A. Vafaei, Spectrochimica ActaPart A: Molecular and Biomolecular Spectroscopy, 132 (2014) 639-654.

[2]L. Breiman, MLear, 45 (2001) 5-32.

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