## 3 Results and Discussion
### Diffusion of Blowing Agent in the VDC-MMA-AN Copolymer Thermally Expandable Microspheres  
VDC-MMA-AN copolymer microspheres were selected as the research objects, and the various loss of weight measurements of the polymer microspheres were recorded in a certain time at 50 \({}^{\circ}\)C. As shown in Figure 9a, the loss weight of blowing agent was less than 0.5 wt% at the first 30 h in the VDC-MMA-AN copolymer microspheres, and the feeding mass ratios of VDC-MMA-AN were 50/40/10, 50/30/20, and 60/20/20, respectively. It satisfied the formula of \(M_{t}/M_{0}=kt^{n}\) and the fitting parameters are shown in Table 6. It can be seen that it fitted Fick diffusion when \(n=0.5\), which belongs to the general diffusion behavior. The results show that the copolymer microspheres at such feeding mass ratio possessed excellent barrier properties and retention to pentane blowing agent. However, when the feeding mass ratios of VDC-MMA-AN were 70/20/10 and 70/10/20, the loss of weight of blowing agent in copolymer microspheres was nearly 1.0 wt% at the first 30 h, and then the loss rate slowly decreased, as shown in Figure 9b. By fitting the experimental data, it belonged to non-Fick diffusion when \(\frac{1}{2}<n<1\), and the fitting parameters \(k\) and \(n\) values are shown in Table 6[33; 34].  
When the feeding mass ratios of VDC-MMA-AN were 50/40/10, 50/30/20, and 60/20/20, the \(T_{\text{g}}\) of shell copolymer of copolymer microspheres were 63.8 \({}^{\circ}\)C, 63.4 \({}^{\circ}\)C, and 61.5 \({}^{\circ}\)C, respectively, which were all higher than the experimental temperature (50 \({}^{\circ}\)C). Therefore, under the 50 \({}^{\circ}\)C test conditions, the shell copolymers were in a glass state resulting in the low activity of the molecular chain of shell copolymer, the solubility and diffusion velocity of blowing agent in shell polymer were low, in which the diffusion process approached to the Fick diffusion. However, the \(T_{\text{g}}\) of shell copolymer of VDC-MMA-AN copolymer microspheres with the feeding mass ratios of 70/20/10 and 70/10/20 were 51.4 \({}^{\circ}\)C and 42.4 \({}^{\circ}\)C, respectively, which were close or below to the experimental temperature (50 \({}^{\circ}\)C). Therefore, the shell copolymer in such test condition was in the glass transition zone or the high elastic zone, resulting in an increase in the molecular chain activity of shell copolymer. The solubility  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**VDC-MMA-AN**} & \multicolumn{2}{c}{\(t\)} & \multicolumn{2}{c}{\(n\)} & \multirow{2}{*}{**Adj. R-Square**} \\ \cline{2-2} \cline{4-5}  & **Value** & **Standard Error** & **Value** & **Standard Error** \\ \hline
50/40/10 & \(6.76\times 10^{-4}\) & \(1.87\times 10^{-5}\) & 0.50 & \(2.51\times 10^{-7}\) & 0.93 \\
50/30/20 & \(1.01\times 10^{-3}\) & \(3.93\times 10^{-5}\) & 0.50 & \(2.10\times 10^{-7}\) & 0.88 \\
60/20/20 & \(1.02\times 10^{-3}\) & \(5.75\times 10^{-5}\) & 0.50 & \(2.37\times 10^{-7}\) & 0.83 \\
70/10/20 & 0.041 & 0.0032 & 0.25 & 0.018 & 0.96 \\
70/20/10 & 0.049 & 0.0022 & 0.26 & 0.011 & 0.99 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Diffusion mechanism of pentane in VDC-MMA-AN copolymer microspheres.  
Figure 9: Diffusion behavior of pentane in VDC-MMA-AN copolymer microspheres with different compositions at 50 \({}^{\circ}\)C.  
and diffusion velocity of blowing agent in shell polymer increased. In order to ensure a favorable expansion effect of low-temperature thermally expandable microspheres in the future application process, it should be preserved at a lower temperature.