## 3 Results
### Particle Size Analyses  
The particle size of ZIF-8 samples (ZS1, ZS2 and ZS3) was determined using a Malvern particle size analyzer while suspended in acetone medium. Figure 6a-c illustrates the particle size distribution of three ZIF-8 samples (ZS1, ZS2, and ZS3) as analyzed using a Malvern particle size analyzer. This analysis is critical as particle size influences the material's surface area, porosity, and ultimately, its effectiveness in applications like CO\({}_{2}\) adsorption.  
The figure presents a comparison between the particle size distributions of these samples, which were synthesized under varying conditions of stirring time and pH. The figure typically shows a histogram or a graph plotting particle size (in nm) on the \(x\)-axis against the relative intensity or number distribution on the \(y\)-axis. The peaks in these distributions represent the most common particle sizes within each sample.  
ZS1: This sample, synthesized with the shortest stirring time and highest pH, shows a narrower distribution with a peak around a smaller particle size. This indicates that shorter synthesis times and higher pH lead to the formation of smaller ZIF-8 particles, likely due to more rapid nucleation processes that limit the growth of each crystal.  
ZS2: As the stirring time increases and pH decreases, the particle size distribution broadens, indicating more variability in particle size. The peak shifts slightly towards a larger size compared with ZS1, suggesting that longer synthesis times allow more time for the particles to grow.  
Figure 5: XRD patterns of ZCAF.  
ZS3: With the longest stirring time and lowest pH, ZS3 exhibits the broadest distribution and the largest average particle size. This broad distribution could be due to the extended time allowing for both the nucleation of new particles and the growth of existing ones, leading to a wide range of particle sizes.  
Figure 6: Particle size distribution of (**a**) ZS1, (**b**) ZS2, and (**c**) ZS3.  
Smaller particles (as seen in ZS1) typically have a higher surface area-to-volume ratio, which can enhance CO\({}_{2}\) adsorption due to more available surface sites. However, the broader distribution in ZS3 may indicate a compromise between surface area and structural stability, which could be beneficial in practical applications where a balance between these factors is needed.  
ZS1 and ZS2, with their narrower distributions, might be more suitable for applications requiring uniformity in particle size, such as in the development of consistent and predictable adsorption characteristics. On the other hand, ZS3's broader size range could offer advantages in applications where a mix of micro- and mesopores is beneficial for adsorbing a range of molecule sizes.  
In summary, Figure 6 provides valuable insights into the relationship between synthesis conditions and the resulting particle size distribution of ZIF-8. Understanding these distributions is crucial for tailoring the material's properties to specific applications, particularly in optimizing CO\({}_{2}\) capture efficiency.  
To further substantiate the relationship between particle size and CO\({}_{2}\) adsorption efficiency, the particle size distributions were statistically analyzed as shown in Table 3. The mean particle sizes of ZS1, ZS2, and ZS3 were found to be 99.46 nm, 101.9 nm, and 105.7 nm, respectively, with standard deviations of \(\pm\)1.5 nm, \(\pm\)2.0 nm, and \(\pm\)2.4 nm. A correlation analysis was conducted to assess the relationship between particle size and CO\({}_{2}\) loading, revealing a correlation coefficient (R\({}^{2}\)) of 0.85, suggesting a strong relationship between these variables.  
These statistical insights confirm that even slight variations in particle size can lead to significant differences in CO\({}_{2}\) adsorption performance, highlighting the need for precise control over synthesis conditions.