## 2 Materials and Methods
### Characterization  
Determination of blowing agent encapsulated content: the thermogravimetric curve of the copolymer microspheres was recorded with a Pyris 1 thermogravimetric analyzer (TGA, PerkinElmer Co., Waltham, MA, USA). The sample was heated from 50 \({}^{\circ}\)C to 650 \({}^{\circ}\)C at a heating rate of 20 \({}^{\circ}\)C/min under an N\({}_{2}\) atmosphere. A polymer sample with no encapsulated blowing agent was used to determine the amount of residual water and monomers. Thus, the content of encapsulated blowing agent in the microspheres was calculated from the thermogravimetric analysis results after the elimination of the residual water and monomer (ca. 2.4%). The \(E_{\mathrm{r}}\) of the blowing agent was defined as the ratio between the weight of the blowing agent encapsulated in the microspheres and the weight of the microspheres [27]. Determination of the composition of shell polymer of VDC-MMA-AN copolymer microspheres: the microspheres samples were extracted with methanol for 48 h, then the blowing agent was removed and dried to constant weight in vacuum oven. The content of PVDC was calculated by measuring the content of chlorine element, which was determined by oxygen flask combustion-potentiometric titration method [29]. The content of PAN was measured by determining the content of nitrogen element, which was tested by element analyzer (EA1112, CarloErba, Cornaredo, Italy). The remaining component was the content of PMMA. The gel content of the microspheres was determined by the extraction method. The weighed microspheres were placed in filter paper bags and extracted by \(N\), \(N\)-dimethylformamide for 72 h at room temperature, and the \(N\), \(N\)-dimethylformamide was exchanged for every 12 h. Then the gel was dried to a constant weight by vacuum pumping for 24 h.  
Using methanol as a solvent, copolymer microspheres were processed by soxhlet extractor for 48 h to completely remove the blowing agent. Then the \(T_{\mathrm{g}}\) of copolymer microspheres were determined by differential scanning calorimeter (DSC, TA Q200, TA instruments Co., New Castle, DE, USA) at a heating rate of 20 \({}^{\circ}\)C/min. A precision temperature control meter workbench was used at the heating rate of 0.1 \({}^{\circ}\)C/s to heat up copolymer microspheres to expand until microspheres collapse or shrink. During this process, the microsphere expansion process was observed with a Leica optical microscope (Leica Camera AG, Solms, Germany), and the microspheres start expansion temperature (\(T_{\mathrm{st}}\)), start shrinkage temperature (\(T_{\mathrm{sh}}\)), \(T_{\mathrm{r}}\) were determined. \(T_{\mathrm{st}}\) was the temperature at which the copolymer microspheres began to expand after heating. \(T_{\mathrm{sh}}\) was the temperature at which the copolymer microspheres began to crack, shrink, or collapse after heating beyond a certain temperature. \(T_{\mathrm{r}}\) was the temperature range between \(T_{\mathrm{st}}\) and \(T_{\mathrm{sh}}\) of the copolymer microspheres, which indicated the temperature-resistant range of the expanded microspheres. The statistical software was used to calculate the microspheres size of before and after expansion larger than 200 microspheres in the microscopic images, designated as \(R_{\mathrm{b}}\) and \(R_{\mathrm{a}}\), respectively. The \(E_{\mathrm{v}}\) was obtained by the formula of \(E_{\mathrm{v}}=R_{\mathrm{a}}^{3}/R_{\mathrm{b}}^{3}\). To accurately determine the quantitative and constant volume of microspheres in a scale test tube, the formula of \(\rho=\
icefrac{{m}}{{v}}\) was used to calculate the apparent density of the microsphere before expansion. The quantitative microsphere sample was fetched in a scale test tube, and placed in an oven and kept at a certain temperature for about 2 min. Then it was taken out and cooled to room temperature and the weight and volume were measured to calculate the apparent density of the microspheres after expansion using the same formula of \(\rho=\
icefrac{{m}}{{v}}\).