# Optimization of Processing Parameters to Increase Thermal Conductivity of Rice Straw Fiber Film
## 2 Materials and Methods
### Experimental Design  
Initially, preliminary experiments were conducted following a single factorial method to identify the major processing parameters affecting the performance of the fiber film and to find out the optimal ranges. Five processing parameters including basis weight (g/m\({}^{2}\)), neutral sizing agent content (%), charcoal addition ratio (%), wet strength agent content (%), and beating degree (\({}^{\circ}\)SR) were selected based on the single factorial method.  
The central composite design approach was used to study the effects and interaction of basis weight, neutral sizing agent content, charcoal addition ratio, wet strength agent content, and beating degree on dry and wet tensile strengths and thermal conductivity of rice straw fiber films. The central composite design is a type of response surface methodology (RSM). RSM is a general linear model in which attention is focused on characteristics of the fit response function; in particular, where optimum estimate response values occur. There were five levels of basis weight (50 to 70 g/m\({}^{2}\)), neutral sizing agent content (0.5% to 0.9%), charcoal addition ratio (0% to 20%), wet strength agent content (0.8% to 1.6%), and beating degree (35 to 55 \({}^{\circ}\)SR). The ranges and levels of independent variables are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multirow{2}{*}{
\begin{tabular}{c} **Basis Weight** \\ **\(x_{1}\) (g/m\({}^{2}\))** \\ \end{tabular} } & \multicolumn{2}{c}{**Neutral Sizing Agent**} & \multicolumn{2}{c}{**Charcoal Addition**} & \multicolumn{2}{c}{**Wet Strength Agent**} & \multicolumn{2}{c}{**Beating Degree**} \\  & & **Content**\(x_{2}\) (\%) & **Ratio**\(x_{3}\) (\%) & **Content**\(x_{4}\) (\%) & **\(x_{5}\) (\({}^{\circ}\)SR)** \\ \hline \(-2\) & 50 & 0.5 & 0 & 0.8 & 35 \\ \(-1\) & 55 & 0.6 & 5 & 1.0 & 40 \\ \(0\) & 60 & 0.7 & 10 & 1.2 & 45 \\ \(1\) & 65 & 0.8 & 15 & 1.4 & 50 \\ \(2\) & 70 & 0.9 & 20 & 1.6 & 55 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Central composite design for five variables at five levels.  
Figure 1: Schematic illustration.  
Equation (1) is a fitted empirical quadratic polynomial model as shown  
\[\begin{split}& y=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3 }+\beta_{4}x_{4}+\beta_{5}x_{5}+\beta_{11}x_{1}^{2}+\beta_{22}x_{2}^{2}+\beta_{3 3}x_{3}^{2}+\beta_{44}x_{4}^{2}+\beta_{55}x_{5}^{2}+\beta_{12}x_{1}x_{2}\\ &+\beta_{13}x_{1}x_{3}+\beta_{14}x_{1}x_{4}+\beta_{15}x_{1}x_{5}+ \beta_{23}x_{2}x_{3}+\beta_{24}x_{2}x_{4}+\beta_{25}x_{2}x_{5}+\beta_{34}x_{3}x _{4}+\beta_{35}x_{3}x_{5}+\beta_{45}x_{4}x_{5}\end{split} \tag{1}\]  
where, \(y\) represents the response variable, \(\beta_{0}\) the intercept; \(\beta_{1}\), \(\beta_{2}\), \(\beta_{3}\), \(\beta_{4}\), and \(\beta_{5}\) are the coefficients of the independent variables; \(\beta_{11}\), \(\beta_{22}\), \(\beta_{33}\), \(\beta_{44}\), and \(\beta_{55}\) are the quadratic coefficients; \(\beta_{12}\), \(\beta_{13}\), \(\beta_{14}\), \(\beta_{15}\), \(\beta_{23}\), \(\beta_{24}\), \(\beta_{25}\), \(\beta_{34}\), \(\beta_{35}\), and \(\beta_{45}\) are the interaction coefficients; and \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), and \(x_{5}\) are the independent variables. Multivariate regression analysis and optimization process were performed using Design Expert software version 6.0.10.0 (Stat Ease Inc., Minneapolis, MN, USA). Analysis of variance (ANOVA) was performed and \(p\) value less than 0.05 is used as significant level. The optimum values of the independent variables were found out by conducting three-dimensional response surface analysis of the independent and dependent variables [36; 37; 38] The detailed experimental design is shown in Table 2.