## 3 Results and Discussion
### Dynamic Light Scattering (DLS)  
Zeta potential, polydispersity index (PDI) and hydrodynamic size have been measured using the dynamic light scatter (DLS) analysis. The PDI and zeta potential have been used to evaluate the stability of the as-synthesized AuNPs. Nanoparticles must be stable and homogeneously dispersed in biological media for biomedical applications [56]. The zeta potential values from 0 to \(\pm\)5 mV indicate rapid agglomeration and suspension precipitation, \(\pm\)10 to \(\pm\)30 mV are incipient to instability, \(\pm\)30 to \(\pm\)40 mV denote moderate stability, while \(\pm\)40 to \(\pm\)60 mV denote good suspension stability [57; 58].  
The stability of metal particles in colloidal suspensions depends on the presence of electrical surface charges. In the case of AuNPs obtained sonochemically, the use of sodium citrate increases the stability of the colloids by acting as both a stabilizer and a reducing agent that hinders aggregation. Sodium citrate activates the reaction of Au ions with carboxylate ions (-COO\"), resulting in the reduction of the metal to Au\({}^{0}\).  
Figure 3: (a) Surface plasmon resonance (SPR) of AuNPs, which have a diameter of about 18.5 nm, (b) HAuCl\({}_{4}\) suspension and (c) AuNPs suspension.  
AuNP formation takes into account the fact that free radical species are generated by ultrasonic irradiation for water molecules (Equation (4)). The reaction is expressed below.  
\[\begin{CD}\text{Na}_{3}\text{C}_{6}\text{H}_{5}\text{O}_{7}@>{\text{ Sonic }\gg\gg}>{}>\text{Na}_{2}\text{C}_{5}\text{H}_{4}\text{O}_{5}\ +\text{CO}_{2}+\text{Na}^{+}+\text{H}^{+}+2\text{e}\\ \text{Au}^{+}+2\text{e}\ \rightarrow\ \text{Au}^{0}\end{CD} \tag{4}\]  
The stoichiometry of the reduction reaction can be described as; the high energy of the ultrasonic ray helps to break the ion bonds of sodium citrate, releasing a pair of free electrons. These charge carriers reduce the golden ions that are suspended in the aqueous solution creating more Au\({}^{0}\) atoms. Figure 4 shows that the colloidal stability of AuNPs in water and PBS was \(-42.1\) mV and \(-39.5\) mV, respectively, indicating that the colloidal suspension of nanoparticles is highly stable. The negative sign of the zeta potential is attributed to adsorbed negative ions such as hydroxide anions (OH\(-\)) derived from the aqueous medium [56]. This negative charge can be attributed to the absorption of citrate onto the surface of Au [40]. These high negative values of zeta potential for AuNPs confirmed the presence of negatively charged carboxylate groups on the surface of the nanoparticles. A repulsion force between suspended particles is caused by zeta potential, which increases with the increase in surface charge of the particles suspended in the solution [50]. The sonochemical method can be a valuable tool for the preparation of AuNPs because the high energy generated by the radiation waves prevents cluster agglomeration and results in stable dispersion [59].  
As shown in Figure 5, the PDI values of AuNPs dissolved in water and PBS are 0.368 and 0.406, with a hydrodynamic size of 22.17 nm and 23.49 nm, respectively. Although there is a smaller second peak corresponding to the agglomeration, the emphasis here is on the first peak to evaluate the size of the particles and, for this reason, the agglomeration peak will be overlooked [60]. It should be noted that the difference in particle sizes between DLS and TEM is the result of larger particles scattering more light in the DLS technique, which moves the peaks towards the larger end of the size range, while  
Figure 4: Zeta potential results of AuNPs suspension after 5 min of sonication. AuNPs dissolved in water (green solid line) and dissolved in phosphate-buffered saline (PBS) (red solid line).  
the TEM displays the true particle [61; 62]. More specifically, this outcome may be attributed to the broad distribution of the mixture of the two particles.