# Determining nanoparticles size and size distribution

In this part of the module students first visually examine Transmission Electron Microscopy (TEM) images of two different nanoparticle solutions synthesized under different conditions and qualitatively estimate differences in size and size distribution. Next, they can use the provided image files and a free software called ImageJ (http://imagej.nih.gov/ij/) to calculate the Feret’s diameter and particle size distribution for each synthetic condition. Instructions on how to use ImageJ are provided in the module.

Q10. Looking at the images on a qualitative basis, what differences do you observe? What can be said about the size of the particles and their size distribution at the two different experimental conditions?

There are distinct differences between the two high resolution transmission electron microscopy images. The gold nanoparticles synthesized at pH 5.4 with a 2:1 ratio of citrate to tetrachloroauric acid (Figure 5a) appear smaller and much more uniform than those synthesized at pH 5.4 with a 7:1 ratio (Figure 5b). The larger citrate to auric acid ratio definitely generates particles of larger size although a wide distribution of sizes is apparent.

Q11. What is the value of the Feret’s diameter you obtained from the analysis of the image showed in Figure 5a?

The average diameter of particles synthesized at pH 5.4 with a 2:1 ratio of citrate to tetrachloroauric acid is 21.73 ± 0.40 (estimated through ImageJ analysis). Note the small standard deviation indicating a homogeneous distribution of sizes.

Q12. What is the effect of changing the reagents molar ratio on particle size?

As the ratio of citrate to tetrachloroauric acid increases from 2:1 to 7:1, the average diameter of the gold nanoparticles increases from approximately 21 to 34 nm.

Q13. What is the effect of varying the pH on particle size?

Although within the range of pH values explored in this study the pH only slightly affects the particle size, overall pH plays a major role on particle size. Students will observe later that pH also has a dramatic effect on particle size distribution. The traditional conditions of gold nanoparticle synthesis happen to be in a fortuitous pH window (2.7 – 4, see reference 7) that promotes seed-mediated growth mechanism with particles of diameter around 10 nm. However, outside this window, the synthesis outcome is very different. For pH < 1.5, no particles are observed because the protonated citric acid is incapable of reducing Au3+ since the reduction mechanism requires one deprotonated carboxy group. For pH > 4, which is the pH range covered in this experiment, the initial amount of reactive [AuCl4]- is too low to trigger the fast formation of seed particles. As a consequence of the changed growth mechanism, the reduction of Au3+ can occur unselectively leading to nonuniform particles for very acidic or neutral reaction conditions.

Q14. What statistical tests could you apply to determine whether differences in particle diameter are statistically different?

Since the data presented in Table 2 are averages of independent measurements from 15 different images collected on each gold nanoparticle preparation, students could apply a t-test comparing two different means.

Q15. Summarize your findings. Is there a relationship between molar ratios of reagents and particle size?

The molar ratio of the reagents definitely affects the particle size. As the concentration of citrate increases compared to the concentration of gold, so does the particle size.

Q16. If you wanted to synthesize particles with a diameter of approximately 20 nm, which experimental conditions would you use?

A smaller citrate to tetrachloroauric acid ratio yields particles with an approximate diameter of 20 nm.

Q17. What trends emerge from your analysis? Is there a set of experimental conditions that yield a more uniform particle distribution?

If students don’t have access to their own experimental data, they can download the ‘Size-distribution-data’ Excel file (see experimental data section) which provides particles sizes determined on multiple images of the same particle solution. They can then generate a graph showing the percentage of occurrence of each particle of a given diameter.

By comparing particle size distributions for the different sets of experimental conditions, they should observe that lower pH values yield more homogeneous distributions. This can also be observed in Table 2 which shows smaller standard deviations for nanoparticles synthesized using the same citrate to tetrachloroauric acid ratio at lower pH values. As the pH increases the seed-mediated growth mechanism, which is predominant at lower pH values, is not retained and the final particles are rather polydisperse. The initial concentration of [AuCl4]- is too low to trigger the fast formation of seed particles. Seed particle formation might still occur but simultaneously uncontrolled growth of existing and formation of further particles can take place, resulting in a larger dispersion of particle sizes.

Q18. What can be said about the distribution obtained by this specific set of synthetic parameters?

The distribution is relatively uniform with 87% of all particles falling within approximately 2.5 nm from the average diameter.

Q19. If you purchased 30 nm gold nanoparticles from NIST, what particle size diameter would you get? Are all the particles of the same size?

This is a great opportunity for students to discover that gold nanoparticles synthesized as standard material are not truly monodisperse and have their own size distribution. Students can be asked to research the NIST website for RM 8012 gold nanoparticles (nominal 30 nm diameter). These particles have a diameter of 27.6 nm with a standard deviation of 2.1 nm. This deviation is comparable to particles of similar diameter synthesized as part of this experiment using a 7:1 citrate to tetrachloroauric acid ratio at pH 4.2.

Q20. Is there an effect on the particle size distribution when changing the reagents molar ratio?

No, the molar ratio only minimally affects the size distribution. The molar ratio plays a major role in the actual size of the particles.

Q21. Is there an effect on the particle size distribution when varying the pH?

Yes, pH has a dramatic effect on particle size and size distribution. The traditional conditions of gold nanoparticle synthesis happen to be in a fortuitous pH window (2.7 – 4, see reference 7) that promotes seed-mediated growth mechanism with particles of diameter around 10 nm. However, outside this window, the synthesis outcome is very different. For pH < 1.5, no particles are observed because the protonated citric acid is incapable of reducing Au3+ since the reduction mechanism requires one deprotonated carboxy group. For pH > 4, which is the pH range covered in this experiment, the initial amount of reactive [AuCl4]- is too low to trigger the fast formation of seed particles. As a consequence of the changed growth mechanism, the reduction of Au3+ can occur unselectively leading to nonuniform particles for very acidic or neutral reaction conditions.

Q22. Summarize your findings. Is molar ratio or pH the controlling factor in ensuring a yield of uniform particles?

pH is the parameter that more dramatically affects the size distribution. For each citrate to tetrachloroauric acid ratio explored, more monodisperse particles were obtained at lower pH values. This is in agreement with findings by Wuithschick et al. (see reference 7). The paper contains an excellent summary in figure 9 which shows the dependence of polydispersity on pH.