Photocarrier Recombination Dynamics in Highly Scattering Cu2O Nanocatalyst Clusters

Inversion analysis of transient absorption data to capture the photoexcited charge carrier population rate dynamics is a powerful technique for extracting realistic lifetimes and identifying recombination pathways. However, for highly scattering samples such as Cu2O nanoparticles (NPs) with associated dielectric Mie scattering, the scattering leads to an inaccurate measure of the excited photocarrier. This work studies methods to correct for the scattering to generalize the use of inversion analysis and provide secondary information about the nature of the scattering NPs. Scattering profiles of semitransparent disks containing Cu2O NPs with different shapes and sizes are measured to demonstrate that the inclusion of scattering in analysis reduces the photoexcited carrier density by 1 order of magnitude. It is found that the photocarrier density response is affected by shape rather than size. A Fourier transform of the scattering profiles produces a distribution of length scales within the sample characteristic of the mean separation of scatterers. This analysis reveals that NPs are forming clusters. Links are made between the scattering and carrier dynamics.

The synthesis of larger Cu 2 O nanospheres, with a diameter of approximately ~145 nm, was achieved through the utilization of the chemical reduction method at a synthesis temperature of 55°C.Initially, a 100 mL round bottom flask was employed to prepare a 10 mM CuCl 2 aqueous solution, consisting of 50 mL.The mixture was subjected to stirring at a rate of 900 revolutions per minute (rpm) while maintaining a temperature of 55°C.Subsequently, a 2 M NaOH solution of 5 mL was introduced into the mixture.This combined mixture continued to stir under consistent heating at 55°C for a duration of 30 minutes.Following this, an additional 5 mL of a 0.6 M ascorbic acid aqueous solution, serving as the reducing agent, was added to the mixture.The synthesis mixture underwent stirring for a period of 5 hours.The resultant nanoparticles were separated from the synthesis mixture through a thorough washing process.This entailed washing the nanoparticles three times in both deionized (DI) water and ethanol.The aim of this washing was to meticulously remove any residues associated with the synthesis mixture.

Cu 2 O Nanocubes:
Using a chemical reduction method at room temperature (around 20°C), we successfully synthesized larger Cu 2 O nanocubes with average edge lengths ranging from 280 to 300 nm.The synthesis process involved several key steps.Prepare a copper source through the combination of 30 mL of a 0.0032 M aqueous CuCl 2 solution.This solution was carefully introduced into a three-neck round bottom flask placed within an inert nitrogen environment.At room temperature, we added 1 mL of a 0.35 M aqueous NaOH solution to the CuCl 2 mixture, promptly leading to the creation of distinct, blue-colored Cu(OH) 2 colloids.Through gradual and incremental additions of sodium ascorbate (the reducing agent), the solution underwent a visible transformation to an orangish-yellow shade, signifying the formation of cubic Cu 2 O particles.This synthesis phase extended for a period of one hour.Following synthesis, the Cu 2 O nanocubes underwent a thorough washing process involving ethanol, with three cycles of washing that incorporated both sonication and subsequent centrifugation.
Small Cu 2 O nanocubes with an edge length of approximately ~33 nm was synthesized through a chemical reduction method conducted at room temperature (around 20°C).In this process, a 120 mL aqueous solution of CuCl 2 with a concentration of 0.0032 M was introduced into a 250 mL three-neck round bottom flask.The flask was then placed within an environment saturated with inert nitrogen gas for a duration of 45 minutes.Following this, 4 mL of a 0.35 M aqueous NaOH solution was added, and subsequently, a solution containing 0.1 M of sodium ascorbate (acting as the reducing agent) was introduced with a volume of 4 mL.The resulting solution underwent a noticeable transformation to a vibrant yellow hue, indicating the formation of Cu 2 O nanoparticles.These nanoparticles took the form of nanocubes with an edge length of 33 ± 6 nm.After the course of 45 minutes, the Cu 2 O nanocubes were subjected to the same washing procedure as previously mentioned.The Cu 2 O nanocubes underwent a thorough washing process involving ethanol, which was repeated three times.During each washing step, the nanocubes were subjected to sonication and subsequent centrifugation to ensure effective cleansing.

Finite difference time-domain simulations of the extinction spectra for nanoparticles
Figure S1 shows the finite-difference time-domain (FDTD) simulation for the four nanoparticle samples investigated in this work.The detailed procedure used for FDTD simulation are provided in our previous contribution 1 .

Dispersion of Mean Separation
Figure S3 shows the range of mean separation values that can be observed for different NPC with same number of NPs in the cluster for 145 nm spheres.Statistically, in a sample disk, the number of NPs will remain the same and will have some mean separation between them if they remain in single form.Now when NPs start forming clusters, there mean separation will start to increase.
From the figure it is clear that as we increase the NPs numbers in clusters, their mean separation values start dispersing more and more.For example, if two NP forms cluster they could only be arranged such that they touch each other and thus we will have a single value of mean separation.And if we have 3 NPs, they can be arranged such that they can either form rod or a triangular prism such that we only have two values of mean separation.In the same way this value of mean separation starts dispersing more and more on increasing number of NP in cluster.This is true and can easily be imagined that if we go to more than 5 NPs in the clusters, the shape they form during cluster formation can be largely different in number.This is the reason we stopped calculating the volume of clusters after 6 number of NPs in clusters.

Fig. S3
Dispersion in the mean separation values of the clusters for increasing nanoparticles counts in nanoparticle clusters.

Spontaneous Carrier Recombination Lifetime
Now that the photocarrier density  and rate curves / have been corrected for loss of pump photons due to scattering, the spontaneous carrier recombination lifetime () = /(/) can be accurately determined and compared.Figure S5 shows () for all four samples.
As is seen in the figure, each sample exhibits a distinct low-injection photocarrier density lifetime, which decreases with increasing photocarrier density as higher-order recombination mechanisms are activated.In the low injection range, the lifetimes are  SRH ≈ 800 ps for small cubes,  SRH ≈ 600 ps for larger cubes,  SRH ≈ 2000 ps for small spheres, and  SRH ≈ 2200 ps for large spheres.In contrast, the fast recombination lifetimes tend toward a similar value for a given photocarrier density for all four samples, even if the slope and mechanism may depend on size and shape. SRH

Fig. S1
Fig. S1 Finite-difference time-domain simulations of the extinction spectra for Cu 2 O nanocubes with average edge length (a) 33 nm, (b) 118 nm and nanosphere with average diameter (c) 43 nm, (d) 145 nm.

Figure
Figure S2 (a) shows the cartoon of the nanoparticle clusters (NPCs) embedded in KBr matrix to form a semi-transparent disk of diameter ~1  and the thickness of ~0.5 .As shown in the figure, NPCs inside the sample disk may have different configuration that can be estimated from a Fourier transform of the scattering profile and matched approximately to the values obtained from the calculation of mean separation given byTable 1 in main manuscript.

Figure 2
Figure 2 (b) shows two spherical NP forming NPC that resemble a linear cylindrical rod assuming they are in contact with each other.We know that the volume of a cylindrical rod, =  2 ℎ = 1.25 × 10 −4 m 3 for 43-nm spheres, where  ≈ 21.5 nm and ℎ ≈ 2 ×  = 86 nm.In this similar manner, for different possible configurations the volume of the clusters is calculated for 43-nm and 145-nm spheres.Table S1 below gives the calculated values of volume of NPCs in different arrangements.

Fig. S2
Fig. S2 (a) Nanoparticles dispersed inside the KBr matrix forming semi-transparent disks, (b)Volume estimation for clustering of two small spheres (43 nm) forming a linear rod.

Table S1
shows a list of estimated  C for small clusters comprised of 43-nm and 145-nm nanospheres.