Multiwalled carbon nanotubes (MWCNTs)/epoxy thin film nanocomposites were prepared using spin coating technique. The effects of process parameters such as sonication duration (5–35 min) and filler loadings (12 vol%) were studied using the design of experiment (DOE). Full factorial design was used to create the design matrix for the two factors with threelevel experimentation, resulting in a total of 9 runs (
In the past 20 years, carbon nanotubes (CNTs) are the most exciting new materials that have been discovered. Their remarkable properties have attracted huge interest from the scientific community and industry [
However, there are various types of parameters and variables involved which may affect the thin film produced, such as sonication time and filler contents, and the list goes on. From our previous works [
Design of experiment (DOE) is one widely used experimental study method on many processes in engineering. It is a statistical approach in which a mathematical model is developed through experimental runs. Besides, it provides the researchers or users with the opportunity to optimize and predict possible output based on the parameters setting [
Therefore the aim of this work is to verify the factors which have significant effects on the properties of the MWCNTs/epoxy thin film by using DOE. The optimization process was performed using RSM coupled with desirability function which is the useful method to optimize multiple responses. The functional relationships between the independent variables such as sonication duration and filler loadings were studied while the interactions between the input variables were clarified.
Epoxy type DER
Filler loading varies from 1 to 2 vol% with respect to epoxy resin. Mixing of epoxy resin and fillers was done using ultrasonic agitation method. This method is more efficient at dispersing particles into viscous systems compared with other techniques, such as conventional stirring [
Experimental range and level of the respective independent variables.
Variable  Notation  Unit  Level  

−1  0  1  
Sonication duration 

min  5  20  35 
Filler loadings 

vol%  1  1.5  2 
The tensile properties (tensile strength, elastic modulus, and elongation at break) of the composite systems were determined using Instron 3366 according to ASTM D88202 with the crosshead of 1 mm/min. In order to minimize the error, five specimens were averaged to collect the results. Thermal conductivity of epoxy thin film composites was determined using a hot disk thermal constant analyzer (TPS 2500S Thermal Conductivity System) according to ISO 220072:2008. The testing time for each sample was varied from 40 s to 70 s and operating power from 1 W to 2 W. Electrical resistances of thin film samples were measured using AdvanTest R8340 Ultra High Resistance Meter. Voltage of 10 V was used.
The Minitab software, version 16.2.1 based on full factorial design, was used to perform the design matrices for the experiment. The Minitab software based on RSM was used to perform the statistical analysis and generate the regression model. The variables in this study included two numerical factors of sonication duration (
Table
Table
The experimental design and actual responses of MWCNTs/epoxy thin film composites.
Run number  Variables in decoded levels  Actual responses  

Sonication duration (min) 
Filler 
Tensile strength (MPa) 
Elastic modulus (MPa) 
Elongation at break (%) 
Thermal conductivity (W/mK) 
Electrical conductivity (ohm^{−1} m^{−1}) 

1  35  1.0  48.31  2140.80  2.91  0.05995  2.75 × 10^{−10} 
2  35  1.5  53.42  2221.40  2.90  0.06345  3.94 × 10^{−10} 
3  5  1.0  22.74  1217.66  2.41  0.05518  2.15 × 10^{−8} 
4  20  1.0  40.65  1779.00  2.88  0.05669  7.62 × 10^{−6} 
5  5  2.0  20.36  1163.40  2.19  0.09750  4.71 × 10^{−8} 
6  35  2.0  35.79  2240.00  2.45  0.07189  8.26 × 10^{−10} 
7  5  1.5  36.71  1800.00  2.42  0.08550  2.96 × 10^{−8} 
8  20  1.5  52.24  2202.40  2.83  0.08732  6.35 × 10^{−6} 
9  20  2.0  50.96  2493.40  2.79  0.10050  1.11 × 10^{−5} 
The quality of developed models was determined by the coefficients of determination (
The ANOVA for the quadratic model for tensile strength (
ANOVA for tensile strength (
Source  Sum of squares  DF  Mean square 



Model  1100.88  5  220.18  5.06  0.106 

555.07  1  555.07  12.74  0.038 

3.51  1  3.51  0.08  0.795 

275.11  1  275.11  6.32  0.087 

241.49  1  241.49  5.54  0.099 

25.70  1  25.70  0.59  0.498 
Residual  130.66  3  43.55  
Cor total  1231.54  8 
ANOVA for elastic modulus (
Source  Sum of squares  DF  Mean square 



Model  1.45 × 10^{6}  5  2.90 × 10^{5}  2.90  0.205 

9.77 × 10^{5}  1  9.77 × 10^{5}  9.78  0.052 

9.61 × 10^{4}  1  9.61 × 10^{4}  0.96  0.399 

2.61 × 10^{5}  1  2.61 × 10^{5}  2.61  0.205 

1.11 × 10^{5}  1  1.11 × 10^{5}  1.11  0.369 

5.89 × 10^{3}  1  5.89 × 10^{3}  0.06  0.824 
Residual  3.00 × 10^{5}  3  9.99 × 10^{4}  
Cor total  1.75 × 10^{6}  8 
ANOVA for elongation at break (
Source  Sum of squares  DF  Mean square 



Model  0.56  5  0.11  8.87  0.051 

0.26  1  0.26  20.35  0.020 

0.099  1  0.099  7.85  0.068 

0.16  1  0.16  13.05  0.036 

0.025  1  0.025  1.98  0.254 

0.014  1  0.014  1.14  0.363 
Residual  0.038  3  0.013  
Cor total  0.60  8 
ANOVA for thermal conductivity (
Source  Sum of squares  DF  Mean square 



Model  2.37 × 10^{−3}  5  4.73 × 10^{−4}  9.41  0.047 

3.07 × 10^{−4}  1  3.07 × 10^{−4}  6.10  0.090 

1.60 × 10^{−3}  1  1.60 × 10^{−3}  31.91  0.011 

1.71 × 10^{−4}  1  1.71 × 10^{−4}  3.41  0.162 

5.28 × 10^{−5}  1  5.28 × 10^{−5}  1.05  0.381 

2.31 × 10^{−4}  1  2.31 × 10^{−4}  4.59  0.122 
Residual  1.51 × 10^{−4}  3  5.02 × 10^{−5}  
Cor total  2.52 × 10^{−3}  8 
ANOVA for electrical conductivity (
Source  Sum of squares  DF  Mean square 



Model  1.43 × 10^{−10}  5  2.86 × 10^{−11}  10.70  0.040 

1.56 × 10^{−15}  1  1.56 × 10^{−15}  0.00  0.982 

2.05 × 10^{−12}  1  2.05 × 10^{−12}  0.77  0.446 

1.39 × 10^{−10}  1  1.39 × 10^{−10}  51.99  0.005 

2.02 × 10^{−12}  1  2.02 × 10^{−12}  0.75  0.449 

1.57 × 10^{−16}  1  1.57 × 10^{−16}  0.00  0.994 
Residual  8.03 × 10^{−12}  3  2.68 × 10^{−12}  
Cor total  1.51 × 10^{−10}  8 
Table
According to Tables
Meanwhile, it can be observed that “Model
Response surface regression is used to examine the relationship between a response and a set of quantitative experimental variables or factors. The regression analysis for each response was done using coded units and summarized in Tables
Response surface regression for tensile strength (
Term  Coef.  SE Coef. 



Const.  55.2756  4.919  11.237  0.002 

9.6183  2.694  3.570  0.038 

−0.7650  2.694  −0.284  0.795 

−11.7283  4.667  −2.513  0.087 

−10.9883  4.667  −2.355  0.100 

−2.5350  3.300  −0.768  0.498 


 

Response surface regression for elastic modulus (
Term  Coef.  SE Coef. 



Const.  2315.30  235.6  9.826  0.002 

403.52  129.1  3.127  0.052 

126.56  129.1  0.981  0.399 

−361.06  223.5  −1.615  0.205 

−235.56  223.5  −1.054  0.369 

38.36  158.1  0.243  0.824 


 

Response surface regression for elongation at break (
Term  Coef.  SE Coef. 



Const.  2.90778  0.08364  34.765  0.000 

0.20667  0.04581  4.511  0.020 

−0.12833  0.04581  −2.801  0.068 

−0.28667  0.07935  −3.613  0.036 

−0.11167  0.07935  −1.407  0.254 

−0.06000  0.05611  −1.069  0.363 


 

Response surface regression for thermal conductivity (
Term  Coef.  SE Coef. 



Const.  0.08493  0.005283  16.077  0.001 

−0.00715  0.002893  −2.471  0.090 

0.01635  0.002893  5.649  0.011 

−0.00926  0.00501  −1.847  0.162 

−0.00514  0.00501  −1.025  0.381 

−0.00756  0.003544  −2.143  0.121 





Response surface regression for electrical conductivity (
Term  Coef.  SE Coef. 



Const.  0.000008  0.000001  6.305  0.008 

−0.00000  0.000001  −0.024  0.982 

0.000001  0.000001  0.875  0.446 

−0.000008  0.000001  −7.211  0.005 

0.000001  0.000001  0.869  0.449 

−0.00000  0.000001  −0.008  0.994 


 

Table
Meanwhile,
Also, from the response surface regression analysis the final empirical model in terms of coded factors can be obtained. For each case, the models are as listed:
A good estimated regression model will explain the variation of the dependent variable in the sample. Normal plots have the residuals being plotted versus their expected values when the distribution is normal. Residuals are the difference between the observed and the fitted response value. The residuals from the analysis should be normally distributed. In practice, for balanced or nearly balanced designs or for data with a large number of observations, moderate departures from normality do not seriously affect the results.
The normal plot of residuals of the two variables (sonication duration and filler loadings) for tensile strength is plotted in Figure
Normal probability plot for tensile strength (
Normal probability plot for elastic modulus (
Normal probability plot for elongation at break (
Normal probability plot for thermal conductivity (
Normal probability plot for electrical conductivity (
Numerical optimization was provided by the DOE method using Minitab software to find out the optimum combinations of parameters to fulfill the desired requirements. The ultimate goal of this optimization was to obtain the maximum responses that simultaneously satisfied all the variables properties.
In order to simultaneously optimize several responses, each of the transformed responses, called
Using the product of the desirability functions assures that if any single desirability is 0 (undesirable), the overall desirability is 0. Therefore, the simultaneous optimization of several responses has been reduced to optimizing a single response: the overall desirability,
Overlaid contour plot for responses.
Overlaid contour plot is a plot that places the contours of each response on top of each other in a single graph. Each set of contours defines the boundaries of acceptable response values. The solid contour line is the lower bound and the dotted contour is the upper bound. The contours of each response are displayed in a different color. The white region in the overlaid contour plot is the feasible region. It is an area such that the acceptable values for each response are between their respective contours. The possible combination of parameter settings can be obtained within the feasible region.
In order to produce MWCNTs/epoxy thin film composites acquired with acceptable properties which are also known as responses, the ranges of the responses are needed to be determined. In this study, two gradient lines, namely, Gradient 1 and Gradient 2, were drawn on the feasible region. However, the gradient lines have to be carefully drawn so that they do not touch the color region. The gradient line which connects points 1 and 2 is Gradient 1 while for points 3 and 4 the line is Gradient 2. Table
Values of the four points on Gradients 1 and 2.
Factors  Gradient 1  Gradient 2  

Point 1  Point 2  Point 3  Point 4  
Sonication duration  6.167  15.136  6.570  27.734 
Filler loadings  1.800  1.108  1.599  1.874 

33.409  44.140  37.131  49.406 

1605.9  1912.7  1673.6  2404.9 

2.389  2.827  2.474  2.756 

0.0958  0.0684  0.0883  0.0852 

1.33 × 10^{−6}  6.97 × 10^{−6}  1.17 × 10^{−6}  6.46 × 10^{−6} 
Optimization plot of multiple responses for Gradient 1.
Optimization plot of multiple responses for Gradient 2.
From Figures
For the factor of sonication duration, increasing the sonication duration increases the responses of
Among the two possible combinations of operating condition, global solution of Gradient 2 is chosen as it produces composite with higher predicted responses than that of Gradient 1. Besides that, Gradient 2 has lower filler loadings than Gradient 1 and just a slight difference in the sonication duration. Lower filler loadings will eventually reduce the cost of composite produced. Hence, the global solution of 12.88 min sonication duration and 1.67 vol% filler loadings is chosen as higher sonication duration and lower loadings provide better dispersion of MWCNTs into the epoxy matrix.
After optimization using the proposed method in the above work, the properties of the MWCNTs/epoxy thin film nanocomposites increased 17% for tensile strength (MPa), 7% for elastic modulus (MPa), 2.1% for elongation at break (%), 22.8% for thermal conductivity (W/mK), and no changes in electrical conductivity (ohm^{−1} m^{−1}).
This study showed the use of statistical design to optimize the multiple properties of the MWCNTs/epoxy thin film composites. The optimization was carried out to investigate the effects of parameters (sonication duration and filler loadings) on the thin film composites properties. Based on the optimization through the desirability optimization approach, the optimal parameter setting was achieved with reinforcing 1.67 vol% MWCNTs by ultrasonication for 12.88 min to disperse MWCNTs in epoxy matrix. A global solution of 12.88 min sonication and 1.67 vol% filler loadings was obtained to have maximum desired responses with composite desirability of 1. The significant amount of improvement has been made in the results of MWCNTs/epoxy thin film nanocomposites where 17% for tensile strength (MPa), 7% for elastic modulus (MPa), 2.1% for elongation at break (%), and 22.8% for thermal conductivity (W/mK) are as tangible increment in each response except in electrical conductivity (ohm^{−1} m^{−1}) without any changes.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study was supported by Research University Grant (814055) from the Universiti Sains Malaysia and the Ministry of Science, Technology, and Innovation (MOSTI).