Light-Driven Autocatalytic Nucleation

Building on prior knowledge of NP interactions²⁰ and crystallization behavior^{12, 21} we investigated silver NPs with citrate ions as surface ligands for a possibility of autocatalytic nucleation (Figure 1A). Citrate surface ligands address the challenges highlighted above by being small and labile. They also provide a minimal redox barrier while still sufficiently preventing rapid NP_m growth. Citric acid and citrate ions are known to be involved in Szent-Györgyi-Krebs metabolic cycle in bacteria as a substrate for enzyme aconitase catalysing stereo-specific isomerization of citrate to isocitrate via cis-aconitate in a non-redox-active process.²² Note that aconitase is a large protein with a molecular weight of 80,000 - 85,000 Da depending on the organism and specific isoform whose catalytic activity is dependent on the [Fe₄S₄] cluster.²³ The chemical functionality of citrate molecules in the NP-based system is conceptually different from their known biological functions. Concomitantly, the NPs are chemically much simpler than aconitase or any other enzyme known to convert citrate into other biomolecules.

Excitation of plasmonic states of metal NPs leads to electromagnetic hot spots, enabling electron photo-ejection into the surrounding medium.^{24, 25} The electrons in aqueous media become solvated forming electrostatic complexes with water molecules with a size of 2.5–2.8 Å and a lifetime exceeding 250 ps.^{26, 27} The solvated electrons reduce Ag⁺ to Ag⁰, which results in nucleation and growth of NP_d near the NP_m (Figure 1, and Supplementary Text 1). Simultaneously the remaining holes in parent NP oxidized the molecules of citrate (Figure 1A). The oxidation products of citrate may be multiple and may temporarily remain attached to the NP surface; the repeated electron transfer from these products to the NP will ultimately lead to formation of CO₂.

In practice, a solution of 0.1 mM silver nitrate (AgNO₃) and 3 mM sodium citrate dihydrate at pH 10.3 was illuminated with 365 nm ultraviolet (UV) light at an intensity of 1.3 mW/cm² (Figure S2 and Supplementary Text 2). The optical extinction peak between 400 and 420 nm displayed nearly ideal S-shaped kinetics (Figure 1C, Figure S2), expected for self-replicating and autocatalytic systems.^28-30 The initial lag seen in Figure 1C corresponds to the slow emergence of a few NP_m, followed by explosive growth in the middle of the S-curve as the local Ag⁺ concentration remains high. The final S-curve plateau is reached as Ag⁺ depletes.³¹ This system is robust across a wide range of physical conditions, including illumination with photons and electrons of varying energies. The photoinduced reduction pathway Ag⁺+e⁻→Ag⁰→NP allows for realization under 1D, 2D, and 3D diffusion conditions, enabling spatial modulation of autocatalytic nucleation.

Transmission electron microscopy (TEM), leveraging the high contrast of NPs in electron beams, was used to determine the structural and temporal patterns of NP product(s) (Figures 1,2). Under conditions that yielded the S-shaped accumulation kinetics, the irregularly shaped NPs grew gradually during the illumination (Figure S3). The peak wavelength shifted slightly from 417 nm (Figure S1A and Supplementary Text 3) to 402 nm due to increased charge density around the NPs (Figure S4).³² Cryo-TEM images indicated that clusters of 1.1–1.5 nm critical nuclei formed near the NP_m surface, with an average diameter d ~8 nm (Figure 1D, 60 min), confirming the mechanism of photoinduced autocatalytic nucleation, depicted in Figure 1A. These clusters produced NP_d (Figures 1 and 2, Figure S7B) via interparticle exchange of Ag⁰ and catalytic reduction of Ag⁺.

The high optical contrast of NPs in light beams also allowed us to investigate their dynamics and localization using nanoscale tracking analysis (NTA), enabling direct particle counting in the media. NTA data revealed S-shaped kinetics (Figure 1C), characterized by an initial incubation period, followed by a rapid increase in NP count, and concluding with a plateau as expected for the autocatalytic nucleation process with limited availability of the starting reactant, i.e. Ag⁺.

Self-Assembly of Photogenerated Nanoparticles

TEM images (Figure 1F, Figure S7, S8), zeta-potential distribution (Figure S5), NTA dark field microscopy videos, and snapshots (Figure S6, Movie S1) revealed that autocatalytic nucleation is accompanied by the self-assembly of NPs into particle chains (Supplementary Texts 4, 5) when a bigger NP formed earlier produces an offspring nucleating in the vicinity of its surface (Figure 2A). Subsequently the ‘daughter’ NPs do the same which substantiates the use of this terminology that follows the prior practice of using these terms in respect to bacteria.^{33, 34}

The average quasi-steady-state NP size depends on the illumination conditions and can range from d equal to 6.6 nm ±2.7 nm, 16.1 nm ±2.2 nm, and 18.2 nm±2.1 after 30, 60, and 180 min of 365 nm illumination, respectively (Figure S3). Illumination by a 130 e⁻/Å⋅s electron beam produces chains with an average d =13.6±3.5 nm. These NP chains form through spatially restricted attachment resulting from propagating linear anisotropy, leading to organized chains rather than disordered agglomerates. Starting from NP pairs, the energy barrier to assembly is higher at the chain's midpoint than at the apexes aligning the NPs into chains than can also be assisted by the dipolar interactions due to their asymmetry.¹²

Demonstrating the robustness of the process, conformal self-assembly of continuously generated NPs was also observed on surfaces, for example, on polyelectrolyte-functionalized³⁵ TEM grids floating on the growth solution surface (Figure 1E, Figure S8, and Supplementary Text 6). The distances between NPs ranged from 0.5 to 0.9 nm (Figure S9), which is consistent with the ejection of hot electrons that reduce Ag⁺ ions in solution around the NP_m,^{25, 36} as illustrated schematically in Figure 1A.

Nanoscale videography using liquid-phase TEM (LPTEM) demonstrated the rapid growth of intersecting NP chains following autocatalytic nucleation (Movie S2, Figure 2, Supplementary Text 7). Movie S3 also shows that NPs can nucleate outside the focus area, then diffuse and attach to a pre-formed chain from a different NP_m. Chain length is reduced in NP systems when NP_m growth is too slow (Figure S10, Movie S4, and Supplementary Text 8), resulting primarily in the generation of individual NPs.

Kinetics and Thermodynamics of the Autocatalytic Nucleation of Nanoparticles

To quantitatively describe the S-shaped kinetics (Figure 1C, Figure S2) of our NP system, we focused on experimentally accessible parameters. The standard Finke-Watzky model, commonly used to describe NP growth,³⁷ fit poorly to our temporal trajectories (Figure S11C, S12, S14, Supplementary Text 9). Therefore, we modified the model to account for the chemical reactions described by Eq. S7–S9, incorporating two populations of exchangeable and non-exchangeable silver atoms on NP surfaces and cores. The validity of Eqs. S4–S6 and Eqs. S7–S9 for photoreduction of silver ions was confirmed by N. T. K. Thanh et al. and Völkle et al.^{37, 38} Additional validation is demonstrated by nearly perfect fit of experimental and theoretical curves in Figure 3A, B, C. Our modified kinetic model achieved high-confidence fits to the S-shape experimental curves under various illumination conditions (Figure 3A, B, C) and predicted S-shape curves for other chemical species, (i.e., Ag⁺ and Ag⁰, Figure S13).

A kinetic model with a set of three kinetic constants–k₁, k₂, and k₃– cumulatively describe light-driven redox reactions initiated by photo-ejected electrons interacting with Ag⁺ and NPs (Supplementary Text 10, Figure S1A). Futhermore, our kinetic model predicted trends for temporal derivatives of NP concentration, that is, d[NP]/dt, d²[NP]/dt², and d³[NP]/dt³ (Figure S14). Using experimental data from three light intensities (i.e., 1.3, 8, and 17.2 mW/cm²) and validation points from TEM images (Figure S15 and Figure S16), we estimated these parameters (Figure 3, C-F and Figure S13, C-F). The calculated k₁, k₂, and k₃ values (Table S1) closely matched known rate constants for diffusion-controlled nucleation, growth, and agglomeration of transition-metal nanoclusters.^{39, 40} As predicted from Eq. S1–S6, k₁, k₂, and k₃, increased linearly with light intensity (Table S1, Figure S17), consistent with photoinduced reaction behavior.

We also sought to determine the chemical basis for the consistent switch from NP_m to NP_d growth, which correlates with a rapid drop in the chemical potential, μ, as particle volume increases. (Supplementary Text 11). Thermodynamic estimates, based the Gibbs−Thomson relation, surface tension (γ), and the dependence of μ on particle size,^{31, 36} predict a NP diameter of d=6.4 nm for the transition from rapid to slow NP_m growth, marking the onset of the rapid NP_d growth. This estimate aligns closely with the experimental diameter of d=6.6 nm ±2.7 nm observed for the self-replicated NPs after 30 minutes of illumination (Figure 1C, Figure S3). A similar NP size of ~6 nm was observed in mother-daughter pairs when the post-formation growth rate decreased (Figure S10). Additionally, cryo-TEM data for NP_m indicated a characteristic diameter of ~8 nm (Figure 1E). The continued growth of NPs within chains is attributed to the finite probability of plasmon localization on any NP in the chain and the gradual oxidation of citrate, which increases γ and, consequently, the particle size.

Self-assembly into Hierarchically Organized Particles

Nucleation events at interfaces facilitate NP formation and confine growth, allowing for detailed structural examination. Additionally, solid–liquid interfaces stabilize NP assemblies against fluidic distortions and capillary forces during drying.

We investigated the formation and organization of NP assemblies produced by autocatalytic nucleation in the presence of “hedgehog” particles (HPs) and flat glass substrates. The electromagnetic field localized between the HP spikes restricts the location and growth direction of NP chains but without impeding Ag⁺ diffusion, creating opportunities for spatial organization of newly formed NPs (Figure 3 and Figure S18). HPs with zinc oxide (ZnO) spikes⁴¹ produce hotspot singularities at their apexes (Figure 3D-F) and 365 nm light illumination further induces high-field zones that bridge the spikes (Figure 3F, upper inset). Consequently, NPs preferentially nucleate, grow, and self-assemble on the apexes, forming a second generation of Ag spikes and, in some cases, NP bridges between the ZnO spikes.

Using analysis of structural complexity based on graph theory (GT), as described in a previous study,⁴² we calculated the complexity index (CI) from GT models of the self-assembled nanostructures. Assuming a uniform distribution of silver nanospikes self-assembled on the apexes of the ZnO mesoscale spikes, the particle in Figure 3D is represented by a graph model in Figure 3G. Similarly, particles with mesoscale ZnO spikes interconnected by self-assembled nanoscale bridges from silver NPs, as shown in Figure 3E, can be represented by a graph model in Figure 3H. Although these models are idealizations of the fully decorated HP subsets, they yield maximum CIs for these colloidal particles that are equal to 19.5 and 37.0, respectively (see calculations in SI). Interestingly, the CI for double-spike HPs shows a linear dependence on the number of silver nanospikes, S_Ag, as CI=(45/8) • S_Ag + (81/4). The values of CIs for the hierarchical double-spike and spike-bridged particles, which combine both nanoscale and microscale structural elements, are comparable to the inorganic skeleton of the phytoplankton Emiliania huxleyi⁴³ (Figure 3I). Its graph model aligns with that in Figure 3H, with the same CI value of 37 indicating that the complexity of self-assembled nanostructures can be similar to those observed in nature.

Self-organization into NP Networks

Networks are a nearly universal higher-order structural motif in biology. Illuminating glass slides floating on the growth solution and surface-functionalized with (PSS/PDDA)₃PDDA bilayers leads to the formation of nanostructured “colonies” comprising hundreds of interconnected NPs localized in microscale patches. These NP colonies produce neurite-like networks that radiate from a central nucleation site (Figure 4D). Self-organization into networked architectures results from strong attractive vdW forces (Figure 1A), combined with spatial restrictions on NP attachment imposed by the electrostatic repulsion, plasmonic properties of the chains and the solid–liquid interface. Continuous conduction through NP networks conformally grown on solid surfaces can be obtained via electroless metal deposition catalysed by the NPs (Figure S19, and Supplementary Text 12).

While the NP networks produced by autocatalytic nucleation may appear random, they follow specific hierarchical patterns.⁴⁴ Their complexity can also be assessed using GT. Unlike the hierarchical particles in Figure 3, which are analyzed based on nodes with identical graph symmetry (marked by color, see SI), self-assembled networks require a different approach. For infinite graphs where each node's neighbors and degrees (i.e., the number of connected edges), can vary stochastically, the CI becomes infinite. Nevertheless, these networks exhibit non-random structural organization. The identification of their structural patterns requires assessment and comparison of multiple GT parameters (Figure 4), which, like CI, can be extracted from microscopy data.

To highlight the biosimilarity and non-randomness of the NP networks, we compared them to bacterial and fungal networks. Specifically, we used Streptococcus spp biofilms grown on agar and R. stolonifera biofilms grown on Capsicum annuum L as models for bacterial and fungal networks, respectively. Additional fungal network data were sourced from the literature, including Aspergillus fumigatus biofilm grown on human bronchial epithelia cells,⁴⁵ Trametes versicolor biofilm grown on wheat grain,⁴⁶ Ganoderma lucidum biofilm grown on wood,⁴⁷ and Aspergillus niger 55890 biofilm grown on agar (Figure S21 and Table S1).

The GT parameters (also known as descriptors or indexes) of average nodal degree (AD), average clustering coefficient (ACC), average nodal connectivity (ANC), and assortativity coefficient (AC) enabled a quantitative, multiparameter comparison of the organizational patterns. Although none of the investigated fibrous networks do not form perfectly ordered square, triangular, or other lattices, the values and variability of ACC, ANC, and AC suggest they are far from random. For example, the absolute value of |AC| ranges from 0.25 to 0.3, in contrast to the value of 0 expected in random networks. Similarly, ACC in random networks with a similar number of nodes is typically ~10⁻³, but the ACC for NP and other networks in Figure 4 is 10 times larger exceeding 10⁻².

The analysis of connectivity patterns based on multiple GT descriptors reveals that NP networks are structurally identical to those produced by Streptococcus spp (Figure 4), yet markedly different from those networks produced by a wide spectrum of fungi. Both bacteria and NP networks result from autocatalytic nucleation followed by the attachment of NP_d to NP_m in a “replicate-and-attach” mechanism. In contrast, fungal networks are the product of individual cell growth, leading to intersections (“grow-and-intersect” mechanism), which produces distinct topological patterns.

Applying Fractal Theory (FT) provides further insights into the complexity and structural motifs of both synthetic and biological structures. The average fractal dimension, d_f, for NP networks is 1.75±0.041, which is consistent with dendritic NP assemblies reported in previous studies.⁴⁸ Bacterial and fungal networks display d_f values of 1.88±0.040 and 1.85±0.020, respectively. The similarity in fractal dimensions across these networks highlights the value of GT for more nuanced and accurate analysis. Nevertheless, combining GT and FT, we achieve a quantitative evaluation of complexity based on multifractal spectra, f(α), of their graph representations.⁴⁹ The Lipschitz-Hölder exponent, α, at the maximum of f(α) is 1.41, 1.2, and 1.45 for NP networks, Streptococcus spp, and R. stolonifera, respectively (Figure S23). These findings suggest that despite their simple components, NP networks are as complex as the those produced by bacteria and fungi.

Conclusions

In summary, silver NPs can multiply autocatalytically, producing a polydisperse population of offspring by utilizing the energy of incident photons. Newly formed NPs attach to previously formed NPs via strong van der Waals attraction, counterbalanced by electrostatic repulsion, resulting in an extensive network of interconnected chains. The coupled processes of autocatalytic nucleation, growth, and self-assembly are supported by interfaces and can occur on both dispersed particles and solid substrates. Structural analysis of these solid-stabilized NP assemblies using GT and FT reveals a complexity comparable to that of their biological analogs. The emergence of NP systems with quantifiable similarities to biological patterns may provide the missing link between inorganic and organic complex systems existing in the primordial Earth. They may also explain the formation of complex inorganic structures in meteorites and fossils misclassified as biological,⁵⁰ which could otherwise be entirely abiotic.