Response Surface Methodology Based Desirability Function

Article pubs.acs.org/IECR

Response Surface Methodology Based Desirability Function Approach To Investigate Optimal Mixture Ratio of Silver Nanoparticles Synthesis Process Ö znur Karhan,† Ö zge Bildi Ceran,*,† Osman Nuri Şara,‡ and Barış Şimşek† †

Department of Chemical Engineering, Faculty of Engineering, Ç ankırı Karatekin University, 18120 Ç ankırı, Turkey Department of Chemical Engineering, Faculty of Natural Sciences Architecture and Engineering, Bursa Technical University, 16310 Bursa, Turkey

‡

ABSTRACT: Silver nanoparticles are known especially because their antimicrobial properties can be used as conductive ink or adhesives for different electronics in compliance with their unique electronic and optical properties. As they are well-known, these practices require smaller nanoparticle formation. A response surface methodology based desirability function approach has been first applied to achieve the desired size of silver nanoparticles with the green synthesis methods. It is notable that the improvement rates at 7.9% by the mean of particle size distribution in AgNPs manufacturing process have been obtained with the utilization of utilizing the proposed methodology. When these results are evaluated, it can be seen that an 89.3% lower standard deviation has been obtained in comparison with the studies in literature. The results also show that the minimization of the nanosilver production variance should be performed to obtain the high quality and large scale manufacturing process.

1. INTRODUCTION The supreme thermal, electrical, and chemical properties of the silver nanoparticles (AgNPs) unlike the other metal nanomaterials have made them an attractive material in the fields of optics,1,2 electronic,3,4 catalysis,5,6 and nanomedicine.7−10 Sodium borohydride, hydrazine, or citrate is generally used as reducer in the chemical reduction methods, which are preferred much more than a chemical precipitation method, sol−gel method, and lithography methods.7 However, there is a general view regarding that these reducers are the carcinogenic and toxic ones.11,12 Thus, the studies have focused on the silver nanoparticles’ green synthesis.12−14 Microorganisms,15,16 polysaccharides,17,18 and plant extracts10,19−23 have been involved in the reducers, which are used often to obtain a silver nanoparticle with an eco-friendly and low-cost green synthesis. The greatest disadvantage of these reducers is that any products cannot be obtained in the large scales with these reducers, and they have uncontrolled silver nanoparticle sizes.12,24 The optimization techniques can be used for silver nanoparticle synthesis with much higher amounts that have a smaller particle size by the green synthesis methods. It is expected that the green nanoparticles have a high surface area so that they can be used as catalysis, and they have a low particle size so that they can have got the high antibacterial effect.2,25−27 One of the most important criteria in the practices of spray composite is the size of particle, and it requires being minimized.28 Some of the researchers have used a design of experiment (DoE) based optimization methodology to obtain the stable, uniform, and smaller silver nanoparticles and to understand the synthesis mechanism. Ortega-Arrayo et al.29 synthesized the silver nanoparticles with the use of a starch as the capping agent with the use of response surface methodology. The optimum AgNP size that is at the range of 2−24 nm has been © 2017 American Chemical Society

determined by transmission electron microscopy (TEM). Ondari Nyakundi et al.30 used the response surface methodology to obtain the highly stable, uniform silver nanoparticles. They have used a particle size analyzer and obtained such a particle size, which has been at the range of 40.6−139 nm with the use of reducing agent as a Tridax procumbens leaf extract. They have found the optimum parameters with the use of graphical optimization through the response surfaces. Mohamedin et al.31 synthesized the silver nanoparticles by Stertomyces viridodiastaticus and optimized the mixture parameters with the use of response surface methodology. They have used TEM and obtained such a particle size, which has been at the range of 15− 45 nm. Biswas and Mulaba-Bafubiandi32 used the reducing agent as Aspergillus wentii maximized the value of absorbance at 455 nm with the use of response service methodology (RSM). They achieved the optimum silver nanoparticles at the size range of 15−45 nm by analyzing with the TEM device. Chowdhury et al.33 are also used the RSM to improve the AgNPs’ synthesis process yield. The average particle size of synthesized AgNPs at the optimum condition has been found as nearly 10−20 nm by the TEM analyzer. Pourmortazavi et al.34 used Taguchi orthogonal arrays to minimize the mean of AgNPs’ particle size, and they reduced the AgNPs’ particle size to 21 nm by the extract of Eucalyptus oleosa reducing agent. As it is seen from these studies, the determination of particle size with the use of scanning electron microscopy (SEM),23 TEM, or the particle size analyzer or the different reducer type,35,36 which is chosen as the effects on the optimum AgNPs Received: Revised: Accepted: Published: 8180

March 20, 2017 May 29, 2017 June 21, 2017 June 21, 2017 DOI: 10.1021/acs.iecr.7b01150 Ind. Eng. Chem. Res. 2017, 56, 8180−8189

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Industrial & Engineering Chemistry Research

the quality criteria of AgNPs synthesis process. Glucose/ AgNO3mole ratios, reaction temperature, and pH of the mixture, which have been adjusted with sodium hydroxide solution, have been defined as the factors effect on AgNPs properties. The optimal mixture levels of AgNPs have been determined by the response surface design based desirability function approach. The statistical analysis has been carried out with the use of analysis of variance, main effect, and surface plots. Lastly, to determine whether the optimum mixture ratio is found, three validation experiments have been carried out.

particle that is obtained. In some of the studies, the optimum size of AgNPs is 40−120 nm;33 it has decreased to 10 nm in the other studies.32 However, it can be said on the basis of these studies that RSM is effective in the determination of AgNPs’ optimum synthesis parameters and in the recovery of process. However, all of these studies have focused on one property of AgNPs just as an average particle size or a product yield. Moreover, it has been focused on minimizing the average of particle size distribution, and it has not been not studied to minimize the standard deviation or variance of particle size distribution in the studies, which have been done. However, it is very crucial to evaluate the mean and standard deviation of particle size distribution belonging to AgNPs simultaneously to utilize the real world practices. When the environmental sustainability and AgNPs’ production with the high quality at the high amounts are considered, they should be aimed with the low standard deviation and the small particle size. In the nanomanufacturing industry, a product’s property such as the particle size distribution is evaluated by the concepts of mean and standard deviation concepts. To get the desired AgNPs particle sizequalities, a RSM based desirability function approach has been proposed in this study. The main innovation for the study is that the mean and standard deviation of particle size distribution belonging to AgNPs have been analyzed and optimized as simultaneously via RSM and the desirability function approach. Thus, it is aimed to expose the effect on the mean and standard deviation of AgNPs particle size distribution of synthesis variables such as glucose/AgNO3 mole ratios, reaction temperature, and pH of the mixture. It will be possible to produce these materials in the great amounts with the production of AgNPs, which have a small particle size with the low variance.

3. IDENTIFYING PERFORMANCE OPTIMIZATION PROPERTIES OF AGNPS 3.1. Optimization Objectives of AgNPs Synthesis Process. A goal of this study is to analyze the properties such as the mean of particle size distribution and the standard deviation of particle size distribution of synthesized AgNPs. It is aimed to determine whether the factors, as glucose/AgNO3 mole ratios, reaction temperature, and pH of the mixture, are effective on particle size distribution. The multiresponse optimization methodology has been used to decrease the variability of synthesis process, which means to improve the quality. On the other hand, this study aims also aimed to show how to optimize of the process, which includes AgNPs synthesis. The methodology, which has been used in this study, has an adaptable quality to the other nanosilver particle synthesis methods such as a chemical vapor precipitation and sol−gel methods. 3.2. AgNPs’ Performance Criteria. The mean of particle size distribution of synthesized AgNPs, which has been selected as the first criterion, is required to be smaller for antibacterial activity.25,30,32 Therefore, this response has been tried to be minimized in this study. The second criterion has been selected as the standard deviation of particle size distribution of synthesized AgNPs, which provides information about the synthesis product quality. DoE is implemented as a crucial methodology to reduce the variability in the manufacturing processes, and it is known as a powerful collection of graphical and statistical tools to achieve the process stability and to improve the capability through the reduction of variability.37 Consequently, this criterion is demanded to be minimized for the sustainable manufacturing process. All performance criteria and their demanded properties have been presented in Table 1.

2. MATERIALS AND METHODS 2.1. Materials. Silver nitrate (AgNO3, > 99.8%) and extra pure starch soluble that are used in the experiments are supplied from Merck Millipore. Sodium hydroxide pellets (NaOH,>99%) have been purchased from Merck Millipore for pH adjustment. D-(+)-Glucose anhydrous, which has been selected as the reducing agent, has been also procured from Merck Millipore. 2.2. Methodology. There are six flow steps in the determination of the optimal mix proportions of the AgNPs synthesis process (Figure 1). First, the mean of particle size distribution and the standard deviation of particle size distribution of synthesized AgNPs have been determined as

Table 1. Quality Criteria for AgNPs Synthesis quality criteria

exemplar

1

Mps

2

Sps

definition mean of particle size distribution of synthesized AgNPs standard deviation of particle size distribution of synthesized AgNPs

desired properties minimize minimize

3.3. Synthesis of AgNPs and Factors’ Levels. Of the starch solution, 0.2% has been dissolved as a capping agent at the minimum 65 °C for 15 min in 40 mL ultrasonic bath. Ten milliliters from 0.001 M AgNO3 solution has been added to the mixture and it has been mixed for 10 min. The glucose has been added to the mixture at an amount, which has been determined from 0.1 M glucose solution on the base of glucose/AgNO3 ratio. Then the mixture’s pH is regulated as the necessary amount from 0.1 M NaOH solution has been added. Reducing agents glucose reduced the silver ions (Ag+) to metallic silver (Ag0) in sodium hydroxide alkaline solutions. This reduction mechanism can be

Figure 1. Offered performance optimization framework of AgNPs synthesis. 8181

DOI: 10.1021/acs.iecr.7b01150 Ind. Eng. Chem. Res. 2017, 56, 8180−8189

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been confirmed in the presence of the silver nanoparticles for all experimental runs32 (Figure 2).

seen in the following eq 1. In this way, it has been provided that the mixture has been mixed at a certain temperature for 1 h and the occurrence of a yellow color can be seen up to the end of this period:

4. RSM BASED DESIRABILITY FUNCTION APPROACH A response surface methodology based on the central composite design has been chosen to implement the experiments in this study. In Table 3, columns 2−4 represent the three control factors and their uncodified levels. Columns 5−7 show the uncoded factor levels for all experiments. In Table 3, the experimental results are illustrated in columns 9−10. The mean and standard deviations of particle size distribution of synthesized AgNPs have been measured with the use of MALVERN Nano ZS90. The MALVERN device draws a graph, which is referred to as the particle size distribution by what percentage of the volume of the sample that is measured has what particle size. With the help of this particle size distribution graph, the standard particle size and standard deviation can be determined. 4.1. Nonlinear Regression Meta-Models. Quadratic meta-models have been obtained with the use of Minitab version 17 and transferred in Table 4. The coefficient of determination (R2), which defines the meta-model accuracy, has been used to designate the useful models for an optimization stage. As the pvalues are smaller than 0.05 (% 95 confidence interval), which is given in Table 4 (and the regression coefficients, R2 is larger than 85.0 in Table 4), it can be said that all of the meta-models have been useful for the optimization stage.38 4.2. Validation of Nonlinear Meta-Models. The experimental data of responses versus the predicted responses are plotted in Figure 3 as the real and estimated values, respectively. The correlation between the real and estimated data has been analyzed with the use of these graphics. It is said to be a good fit between the real and estimated values (R2 values have been found as 0.851 and 0.920 by means of particle size distribution and the standard deviance of particle size distribution of synthesized AgNPs, respectively). 4.3. Multiresponse Optimization of AgNPs’ Synthesis Process Properties. The changing in response on the base of

2Ag +NO3− + C6H12O6 + 2NaOH = 2Ag 0 + C6H12O7 + 2NaNO3 + H 2O

(1)

Three factors that each of them has five mix levels with the effect on the AgNPs’ synthesis quality have been determined as the glucose/AgNO3 mole ratios (A), reaction temperature (B), and pH of the mixture (C) via preliminary experiments. In the literature, these selected parameters, which are the controllable factors, have been commonly used to obtain the optimum AgNPs30,32 (Table 2). In all experiments, the percentage of the Table 2. Factors and Their Levels Effect on Mps and Sps of Synthesized AgNPs bounds factors

definition

A

glucose/AgNO3 mole ratios reaction temperature, (°C) pH of the mixture

B C

first bound

second bound

third bound

fourth bound

fifth bound

1.5

2.0

2.5

3.0

3.5

60

65

70

75

80

10.5

11.0

11.5

12.0

12.5

starch in deionized water has been fixed at 0.2% in the solution. The concentrations of the glucose, AgNO3, and NaOH solution have also been fixed at 0.001, 0.1, and 0.1 M, respectively. 3.4. Characterization of AgNPs. A PerkinElmer UV− visible spectrophotometer has been used to characterize AgNPs. The colloidal suspension of the AgNPs has been characterized by the UV−visible spectrophotometer within the range of 300−600 nm.32 The absorption peak is observed at the range of 400−500 nm in the UV−visible spectrophotometric graphs, which have

Figure 2. Characterization of AgNPs using UV−vis spectroscopy. 8182


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Industrial & Engineering Chemistry Research Table 3. Experimental Results variables in coded levels

variables in uncoded levels

exp. run

A

B

C

AG1 AG2 AG3 AG4 AG5 AG6 AG7 AG8 AG9 AG10 AG11 AG12 AG13 AG14 AG15 AG16 AG17 AG18 AG19 AG20

−1 1 1 −1 0 0 1 −1 −1 1 0 0 −2 2 0 0 0 0 0 0

−1 1 −1 1 0 0 −1 1 −1 1 0 0 0 0 −2 2 0 0 0 0

−1 −1 1 1 0 0 −1 −1 1 1 0 0 0 0 0 0 −2 2 0 0

2.0 3.0 3.0 2.0 2.5 2.5 3.0 2.0 2.0 3.0 2.5 2.5 1.5 3.5 2.5 2.5 2.5 2.5 2.5 2.5

65 75 65 75 70 70 65 75 65 75 70 70 70 70 60 80 70 70 70 70

responses day/block

Mps (nm)

Sps (nm)

1

101.91 62.606 30.880 78.714 55.762 65.448 79.312 102.91 98.433 79.411 55.931 57.205 108.71 49.283 76.154 91.397 90.935 91.224 54.874 60.964

13.594 0.1592 0.2473 1.1426 0.5592 0.6126 2.6750 1.0889 1.6587 6.4717 0.5824 0.9963 8.9791 0.4405 0.5726 0.6341 7.4559 10.375 0.6067 0.5628

11.0 11.0 12.0 12.0 11.5 11.5 11.0 11.0 12.0 12.0 11.5 11.5 11.5 11.5 11.5 11.5 10.5 12.5 11.5 11.5

2

3

Table 4. Regression Equations and p-Values for Mps and Sps of Synthesized AgNPs quality characteristics 1 2 a

proposed model type full quadratic polynomial full quadratic polynomial

R2, % adj.

p-value

a

71.86

0.004

a

84.83

0.000

R2, %

regression equations (analysis in uncoded factors) Mps = 8144 − 291*A − 67.6 B − 921 C + 21.08 A*A + 0.2585 B*B + 33.16 C*C + 2.53 A*B − 2.0 A*C + 2.23 B*C Sps = 2319 − 172.0 A − 13.88 B − 279.7 C + 3.93 A*A − 0.0017 B*B + 8.14 C*C + 0.836 A*B + 7.88 A*C + 1.036 B*C

85.19 92.03

Useful models: significant at 5% (p-value) because the p-value is smaller than 0.05.

The overall desirability D, another value at the range of 0 and 1, has been defined with the integration of individual desirability values.38,39 Then the optimal setting has been determined by maximizing D.38 The lower, upper, and target values belonging to these responses are given in Table 5. The individual desirability values (di’s) for smaller the better type response belonging to each response can be calculated with the use of eq 2. The overall desirability, D (eq 3), and the predicted value have been computed by MINITAB version 17 and shown in Table 5: ⎧ 1 yi ̂ (x) < Ti ⎪ ⎪⎡ ⎪ y ̂ (x) − Ui ⎤ ⎥ Ti ≤ yi ̂ (x) ≤ Ui di(yi ̂ ) = ⎨ ⎢ i ⎪ ⎣ Ti − Ui ⎦ ⎪ ⎪ 0 yi ̂ (x) > Ui ⎩

Figure 3. Predicted values plotted against the actual values for Mps and Sps of synthesized AgNPs.

these factors (glucose/AgNO3 mole ratios, reaction temperature, and pH of the mixture) can be examined with the use of 3D plots. As it is shown in Figure 4, the response surface plots of all responses have given an unchanging point. Therefore, the surface plots, which have a saddle behavior, have been drawn at Figure 4. To solve the multiresponse optimization problem, the desirability function method has been used in this study. The desirability function approach has converted an estimated response (ŷi) into a scale-free value, and it has been denoted as di for ŷi (called desirability).38−40 The value of desirability has been at the range of 0 and 1 and has increased as the corresponding response value has become more desirable.38,39

(2)

where di (ŷi(x)) is the desirability function of ŷi(x), Ui is the upper bounds on the response, the desired target of the ith response has been symbolized as Ti, where Ti ≤ Ui and si is the parameters to determine the shape of di(ŷi(x)): if si = 1, the shape is linear; if si> 1, convex; and if 0 < si < 1, concave. The weighted geometric mean as a strategy to aggregate the individual di values can be calculated as follows:38 D = {d1(y1) × d 2(y2 ) × d3(y3 )......dn(yn )}1/ k

(3)

The factors that have been acquired at the saddle points of all responses (each responses have same weight) have been 8183


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Figure 4. Surface plots of mean of particle size distribution of synthesized AgNPs in uncoded values: (a) fixed C (pH of the mixture) at %11.5, (b) fixed B (Reaction temperature) at 70 °C, (c) fixed C (glucose/AgNO3 mole ratios) at 2.5. Surface plots of standard deviation of particle size distribution of synthesized AgNPs in uncoded values: (d) fixed C (pH of the mixture) at %11.5, (e) fixed B (Reaction temperature) at 70 °C, (f) fixed C (glucose/ AgNO3 mole ratios) at 2.5.

Table 5. Optimum Responses Predicted by RSM for Synthesized AgNPs levels

weight

response symbol

description

lower

target

upper

Mps

mean of particle size distribution (nm)

Sps

standard deviation of particle size distribution (nm)

27 27 27 0.16 0.16 0.16

30a 50b 80c 0.20a 0.40b 0.70c

108.7 108.7 108.7 13.6 13.6 13.6

stationary point saddle

1a

1b

1c

saddle

1a

1b

1c

composite desirability

predicted value

0.91316a 0.91336b 0.98843c 1.00000a 0.99944b 0.99977c

36.8353a 55.0860b 79.4318c 0.20a 0.4074b 0.7029c

optimal D 0.9556a 0.9554b 0.9941c

a

Optimum 1: Mean of the particle size distribution = 30 nm, standard deviation of the particle size distribution = 0.20 nm. bOptimum 2: Mean of the particle size distribution = 50 nm, standard deviation of the particle size distribution = 0.40 nm. cOptimum 3: Mean of the particle size distribution = 80 nm, standard deviation of the particle size distribution = 0.70 nm.

Figure 5. Optimizations plot for Mps and Sps of synthesized AgNPs (optimum 1).

AgNPs, which have the high quality or smaller particle size (please see Table 5). 4.4. Validation of the Optimal Levels. Three validation experiments for AgNPs have the same weight properties as they have been implemented at the predicted optimum condition.

calculated as the glucose/AgNO3 mole ratios = 3.50, the reaction temperature = 64.5871 °C, and pH of the mixture = 11.9721, which are known as an estimated condition (Figure 5). Two additional optimization studies (a different target has been set for each response) have been implemented to obtain 8184


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Industrial & Engineering Chemistry Research Table 6. t-Test Results for Verification of the Results number

responses

1

Mps (nm)

2

Sps (nm)

total

n=3

predicted values a

36.8353 55.0860b 79.4318c 0.20a 0.4074b 0.7029c

verification experiment a

37.40889 54.49546b 82.86495c 0.365a 0.21315b 0.756471c

differenced

mean, d̅

−0.57359 0.59054b −3.43315c −0.165a 0.19425b −0.053571c

−1.139 0.0081b

a

a

standard deviation a

2.071 0.184b

t-test statisticsf

t2;0.95 (tn−1,1−α)

−0.95258a,e −0.07636a,e

−4.303a

a

Optimum 1: mean of the particle size distribution = 30 nm, standard deviation of the particle size distribution = 0.20 nm. bOptimum 2: mean of the particle size distribution = 50 nm, standard deviation of the particle size distribution = 0.40 nm. cOptimum 3: mean of the particle size distribution = 80 nm, standard deviation of the particle size distribution = 0.70 nm. dPredicted values − verification experiment. eNull hypothesis H0 = the Xi values are interdependent and identically distributed random variables with distribution function F. Since −0.95258, −0.07636 > −4.303, null hypothesis would not reject. ft = d̅√n/sd.

Figure 6. Characterization of the optimal AgNPs using (a) UV−visible spectrophotometer and (b) SEM-EDX.

Figure 7. Characterization of the optimal AgNPs using high contrast TEM: (a) optimum 1, (b) optimum 2, (c) optimum 3 (180 000× magnifications).

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Industrial & Engineering Chemistry Research Table 7. Factor Effects and Associated p-Values for Mps and Sps of Synthesized AgNPs responses Mps relationship main effects

linear

linear contribution

pure quadratic

cross product

a

Sps

factor

factor effect

p-value

factor effect

p-value

A B C A2 B2 C2 A×B B×C A×C

−62.16 10.96 −14.68 42.15 51.71 66.32 50.5 −3.9 44.5

0.000a 0.355 0.221 0.041 0.016a 0.004a 0.143 0.904 0.192

−6.252 −2.297 −0.540 7.87 −0.35 16.28 16.73 15.77 20.73

0.368 0.003a 0.175 0.738 0.893 0.000a 0.004a 0.005a 0.001a

Significant at 5% (p-value); (+) synergistic effect; (−) antagonistic effect.

Figure 8. Main effect plots for (a) Mps and (b) Sps of synthesized AgNPs.

antagonistic impact of quadratic terms of pH of the mixture via a p-value of 0.000. The standard deviation of particle size distribution of synthesized AgNPs has been also importantly influenced by the synergetic impact of interaction term between the glucose/AgNO3 mole ratios, the reaction temperature via a pvalue of 0.004 and glucose/AgNO3mole ratios and pH of the mixture via a p-value of 0.001, and the antagonistic impact of interaction term between glucose/AgNO3mole ratios and pH of the mixture via a p-value of 0.005. When it has been analyzed on the main effect plot for particle size of AgNPs, it has been concluded that the particle size of AgNPs has decreased as the glucose/AgNO3 mole ratios increase (Figure 8a). In addition, it can be said that the glucose/ AgNO3mole ratio is the most influential factor effect on the mean and standard deviation of particle size distribution of synthesized AgNPs (Figure 8a,b). 5.2. Effectiveness of the Multiresponse Optimization Study. Ondari-Nyukundi and Padmanabhan30 used RSM to optimize only one response, which is the particle size of AgNPs, and they obtained the high stable, monodispersed, relatively uniform AgNPs with a size range 40.6−139 nm. In this study, AgNPs with a size range of 30.88−108.71 nm have been achieved by RSM. In this study, the minimum mean of the particle size of AgNPs has been determined as 37.41 nm. A 7.9% [(3.4 nm-0.365 nm)/(3.4 nm)] improvement rate has been obtained in comparison with the Ondari-Nyukundi and Padmanabhan’s study by means of the particle size distribution. Some studies have been reported with regard to the standard deviation of AgNPs synthesis process.41 The lowest standard deviation, which has been achieved in these studies, is 3.4 nm.18,30 In this study, the standard deviation of particle size distribution of synthesized AgNPs with optimal mixture levels has been obtained as 0.365

MALVERN Nano ZS90 has been used to measure and calculate the mean and standard deviation of particle size distribution of the synthesized AgNPs. The paired t test has been utilized to the verification of optimum values (Table 6). The test statistic values indicate that there is no difference between the predicted and experimental values.38 4.5. Characterization of Optimum AgNPs. The absorption peak has been observed the range of 400−500 nm in the UV−visible spectrophotometric graphs, which are confirmed with the presence of the optimum silver nanoparticles32 (Figure 6a). The scanning electron microscopy with energy dispersive Xray (SEM-EDX) analysis of optimum AgNPs has also proved the conversion of silver (Figure 6b). The optimum AgNPs have been scanned by FEI Tecnai σ2 Spirit Biotwin model high contrast TEM to observe the shape and size of AgNPs (Figure 7).

5. RESULTS AND DISCUSSION 5.1. Estimation of Factor Effects. The factor’s effect on the responses and for the all of the criteria’s p-value is shown in Table 7. A minus mark shows an antagonistic effect, while a surplus mark presents a synergetic effect of the factor on the responses (Table 7).38 The response particle size has been importantly influenced by the antagonistic impact of linear terms of ratio of glucose/ AgNO3 mole ratios via a p-value of 0.000. The particle sizes of AgNPs have been importantly influenced by the synergetic impact of quadratic term reaction temperature and pH of the mixture via a p-value of 0.016 and 0.004, respectively. The standard deviation of particle size distribution of synthesized AgNPs has been importantly influenced by the synergistic impact of linear terms of reaction temperature via a p-value of 0.003 and 8186


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Figure 9. Comparison of the findings obtained in this study with other studies, improvement rate for (a) Mps 7.9% and (b) Sps 89.3%.

Figure 10. High contrast TEM images of the AgNPs called AG13 and optimum 1 (180 000× magnifications).

ratios cause AgNPs production with the low variance. Therefore, it can be concluded that the glucose/AgNO3 mole ratios are the key parameter for the large scale and better quality AgNPs production. Another remarkable result is that the factors such as glucose/ AgNO3 mole ratios or pH of the mixture have a significant synergistic effect on the thermal conductivity as two or three interaction in spite of the lack of individual effect on the responses. This result indicates that an experimental design approach should be used to analyze the quality criteria, which have been in a conflict with each other. Desirability function approach has been carried with the nonlinear models, which obtain the response surface design runs. The obtained nonlinear models, which are used for the optimization study, have had a high accuracy. The validation results have been proved as the optimization work’s effectiveness. It is notable that the improvement rates on the standard deviation of particle size distribution in AgNPs manufacturing process, which has been obtained after utilizing the proposed methodology, are 89.3%, and it is a quite remarkable result. The minimization of the nanomaterial production variance should be performed to obtain the high quality and large scale manufacturing process.

nm. When these results are evaluated, it can be said that an 89.3% [(3.4 nm−0.365 nm)/ (3.4 nm)] lower standard deviation has been obtained in comparison with the studies in literature (Figure 9).18 This indicates that this RSM based desirability function approach technique has been quite effective one solving AgNPs dosage problems. Furthermore, when the optimum AgNP and AG13 are compared, it can be said that a 65.58% improvement rate in the mean of particle size distribution [(108.713 nm−37.41 nm)/ (108.713 nm)]and a 95.93% improvement rate in the standard deviation of particle size distribution [(8.9791 nm−0.365 nm)/ (8.9791 nm)] of the synthesized AgNPs have been achieved by virtue of the response surface methodology based desirability function approach. The high contrast TEM images of AG13 and the optimal AgNP prove that the AgNPs with the low standard deviation and the small particle size have been obtained (Figure 10).

6. CONCLUSIONS A RSM based desirability function approach has been used to analyze and optimize the AgNPs’ properties systematically. Both the main and interaction effects on the selected responses such as the mean and standard deviation of particle size distribution of synthesized AgNPs have been analyzed statistically via the response surface design. The desirability function approach has been used to determine on the optimal mix proportions of AgNPs’ synthesis process. The most influential factors’ effect on AgNPs’particle size distribution has been determined as the glucose/AgNO3 mole ratios. The result shows that the higher glucose/AgNO3 mole

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Ö zge Bildi Ceran: 0000-0002-3147-735X 8187


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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was elaborated with the support of the Scientific Research Project (MF060416L08), which was funded by Ç ankırı Karatekin University. The authors thank Ç ankırı Karatekin University, Scientific Research Project Management Unit (Ç AKÜ -BAP). TEM and the particle size analyses were carried out in Middle East Technical University Central Laboratory.

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Response Surface Methodology Based Desirability Function

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