The proposed synthesis of the PdNPs represents an environmentally pleasant different to traditional strategies, notably when mixed with a industrial multi-synthesis machine for working a number of reactions in parallel and a multivariate optimization, decreasing reagent consumption and experimental waste. The optimization of those parameters is very vital to advertise an analytically accessible and standardized PdNPs synthesis process, minimizing the uncontrolled broadening of the dimensions distribution. A quick overview of the synthesis and characterization of the thiol-capped PdNPs is demonstrated within the workflow in Fig. 1.

Workflow of the synthesis of PdNP-MPA, and PdNP-Cys, purification for unbounded ligand elimination, multi-analytical strategy for characterization and ligand density evaluation.
The synthesized PdNPs have been completely purified to take away unbound ligands, previous to characterizing their dimension, dimension distribution, form, PNC, and composition, by means of a complementary analytical method. The entire Pd and S concentrations have been decided by ICP-MS. The concentrations decided have been utilized for the thiol ligand density dedication on PdNPs floor.
Nanoparticles synthesis utilizing multivariate optimization
Multivariate optimization for NPs synthesis was carried out first by fractionated factorial design 25−1, for screening of the numerous parameters for NPs synthesis (p < 0.05) in addition to the potential interaction of parameters within the evaluated vary, adopted by response floor methodology (Doehlert design). The utilized 2⁵⁻¹ design matrix and its corresponding responses (1–PDI) are introduced in Desk 1. As noticed, for the analysis experimental uncertainty and reproducibility of experiments the central level carried out in triplicate, minimizing the overall variety of experiments and preserving the statistical robustness of the mannequin.
Contemplating a confidence stage of 95%, the impact of the chosen parameters and their interactions was assessed by evaluation of variance (ANOVA) and the Pareto´s chart (Determine S1). The ANOVA desk, displaying vital results and the dedication coefficient (R²) for the evaluated parameters of the two5−1 factorial design, is introduced in Desk S1. The response time, temperature and the concentrations of Pd, ligand and reductant agent in addition to most of their interplay didn’t considerably have an effect on the dimensions, dimension distribution, and form of the obtained PdNPs. Moreover, the curvature and the interaction between temperature and Pd focus confirmed a constructive and vital (p < 0.05) impact over the PDI of the synthesized PdNPs, suggesting that the optimum synthesis situation could also be included within the evaluated vary. Thus, because the interplay between temperature and Pd focus confirmed a big impact, a response floor methodology (Doehlert design) was utilized to find out the optimum circumstances for the PdNPs synthesis. The utilized Doehler design matrix and the corresponding responses primarily based in 1–PDI are introduced in Desk 2.
For the Doehlert design optimization, the impact of temperature and Pd focus over the PDI of the synthetized PdNP-MPA and PdNP-Cys have been evaluated. The obtained contour floor for (A) PdNP-MPA and (B) PdNP-Cys utilizing a Doehlert design optimization and the respective TEM pictures for the chosen synthesis circumstances of experiments 1 and 5 are proven in Fig. 2.

Contour surfaces and TEM pictures of nanoparticles obtained beneath the circumstances of experiments 1 and 5 for (A) PdNP-MPA and (B) PdNP-Cys synthesis utilizing Doehlert design optimization. The numbers on the floor correspond to the experimental runs of the Doehlert design. The colour scale ranges from inexperienced (larger PDI) to crimson (decrease PDI).
The ANOVA for each PdNPs (Tables S2 and S3) exhibits no vital impact of the evaluated parameters within the vary thought of. These outcomes suggest that any of the evaluated circumstances employed within the Doehlert design experiments could possibly be utilized to PdNPs synthesis. Nonetheless, evaluating TEM pictures of PdNPs synthetized at average temperature and a low Pd focus (60 °C, 10 µmol ‒ experiment 1) with these obtained at excessive temperature and Pd focus (80 °C, 25 µmol ‒ experiment 5), beneath the latter circumstances there’s a larger aggregation, with small nanoparticles hooked up to the floor of bigger ones. However, beneath the circumstances utilized in experiment 1, the focus of smaller particles is barely minimized resulting in extra uniform particles. Accordingly, since optimum circumstances couldn’t be clearly outlined, the next compromise experimental circumstances have been chosen for the synthesis of PdNPs: 10 µmol of Pd, 0.15 mmol of ascorbic acid as decreasing agent, 0.08 mmol of ligand (MPA or Cys), temperature of response of 60 ± 3 °C for 90 min. Afterwards, PdNPs obtained beneath the compromise circumstances underwent a purification step to take away the unbound ligands, carried out by means of washing cycles, monitoring the focus of S within the ultrafiltrate options (Determine S2). From the sixth to the eighth washing cycle the focus of S within the washing supernatant didn’t change considerably (Anova, 95% of confidence stage). Thus, six washing cycles have been carried out to take away the unbound ligands. That is in good settlement with the findings of Elzey et al. for unbound ligand elimination from thiol-capped gold NPs31.
Total, multivariate optimization mixed with the applying of a multi-synthesis setup enabled to effectively outline the compromise circumstances for the PdNPs synthesis and to evaluate the parameters’ interaction with a decreased variety of experiments. Beneath these synthesis circumstances, the uncontrolled broadening of the NP dimension distribution is minimized, resulting in a standardized process for PdNP synthesis. Moreover, in comparison with typical procedures utilizing univariate optimization and single batch response methods, the multivariate optimization and multi-synthesis strategy markedly scale back the variety of experiments required to determine the synthesis circumstances. Consequently, this strategy decreases the consumption of reagents, vitality, and the era of waste, traits which might be aligned with the ideas of inexperienced chemistry.
Construction and composition
The morphological and composition characterization of the synthetized PdNPs capped with MPA and Cys was carried out by TEM/EDS evaluation. The obtained TEM pictures and elemental mapping for Pd and S within the synthetized PdNPs are proven in Fig. 3.

TEM pictures and EDS mapping of Pd and S for PdNPs capped with MPA and Cys.
As noticed within the TEM pictures, each PdNP-MPA and PdNP-Cys samples comprise NPs various in dimension and form. The measured imply dimension for PdNP-MPA and PdNP-Cys have been 96 ± 33 nm and 71 ± 30 nm, respectively. The form of each synthetized PdNPs is difficult to outline since combined shapes (e.g., cuboctahedron, truncated octahedrons, quasi-spherical, and many others.), and a few multi-pod particles have been noticed. Contemplating the proposed water-based synthesis and L-ascorbic acid as a decreasing agent, the quick discount of Pd ions might promote the formation of thermodynamically favorable species akin to truncated octahedrons and multiple-twinned particles32. Due to this fact, beneath the utilized synthesis circumstances, the TEM pictures recommend a non-uniform nanoparticle progress.
Mapping of Pd and S reveals the distribution of those parts in PdNP-MPA and PdNP-Cys particles. No vital quantity of S and/or Pd was detected in areas outdoors of the nanoparticles, indicating that no related quantity of Pd ions or unbound ligand is current. As anticipated, the basic mapping for each varieties of synthesized PdNPs exhibits that Pd is evenly distributed in every particle. The distribution of S for each PdNP-MPA and PdNP-Cys, which completely overlaps with the nanoparticle areas, suggests efficient and uniform floor protection by the thiol-based ligands. Utilizing EDS evaluation, the focus of S on the PdNPs floor was additionally estimated. The evaluation was carried out over two to a few nanoparticle areas, and the discovered S focus in each PdNPs was comparable: PdNP-MPA (0.21 ± 0.11% (w/w)) and PdNP-Cys (0.14 ± 0.11% (w/w)). Though these outcomes might have a excessive uncertainty, they verify the presence of S on the particles´ floor. As well as, these outcomes are in good settlement with these obtained after bulk ICP-MS evaluation, the place the overall S focus onto particles´ floor was decided to judge ligand density31, these outcomes shall be mentioned within the part Ligand density evaluation.
Measurement, dimension distribution and suspension stability
The floor cost of the PdNP-MPA and PdNP-Cys which correlates with colloidal stability21 was evaluated by zeta potential evaluation. The zeta potential of the analyzed samples ranged from -29.6 mV to -35.0 mV indicating the nice stability of the PdNPs suspension. Subsequent, hydrodynamic sizes and polydispersity index (PDI) for PdNP-MPA and PdNP-Cys have been decided by DLS and NTA. The outcomes are summarized in Desk 3.
The DLS outcomes present that PdNP-MPA has a barely larger hydrodynamic diameter and PDI values in comparison with PdNP-Cys indicating that PdNP-MPA is extra polydisperse. Although, in line with a paired t-test at 95% confidence, there isn’t any vital distinction (p-value > 0.05) between the imply dimension obtained from DLS and NTA for PdNP-MPA and PdNP-Cys (Desk S4). Furthermore, in comparison with the number-based dimension distribution given by DLS (Determine S3), the NTA analyses enable for a greater analysis of the dimensions distribution of the PdNP-MPA and PdNP-Cys as demonstrated in Determine S4. The imply dimension decided by NTA was comparable (PdNP-Cys) or barely decrease than these obtained utilizing DLS, as noticed for PdNP-MPA. Moreover, the NTA outcomes verify the presence of a number of sizes of NPs in PdNP-MPA and a extra uniform distribution for PdNP-Cys. Total, the PdNP-Cys present a narrower dimension distribution and a decrease PDI, whereas in PdNP-MPA the particles comprise larger polydispersity.
The imply dimension and dimension distribution for each PdNP-MPA and PdNP-Cys was additionally assessed by high-resolution pictures of TEM evaluation and element-specific dedication utilizing sp-ICP-MS. The imply sizes and obtained histograms are proven in Fig. 4.

Imply dimension and dimension frequency distribution histograms obtained through TEM (A – PdNP MPA, B – PdNP Cys), and sp-ICP-MS (C – PdNP-MPA, D – PdNP-Cys).
The broad dimension distribution revealed by TEM and sp-ICP-MS have been, normally, comparable and in line with the outcomes obtained by DLS, and NTA. Nonetheless, evaluating the imply sizes obtained by TEM for PdNP-MPA (96 ± 33 nm) and PdNP-Cys (71 ± 30 nm), the sizes have been barely decrease than these obtained by sp-ICP-MS (PdNP-MPA 111 ± 43 nm and PdNP-Cys 96 ± 43 nm). However, contemplating the constraints of 2D pictures for figuring out NPs dimension, some smaller or no uniform particles could also be excessively represented in TEM evaluation33,34. Moreover, sp-ICP-MS takes 1000’s of PdNPs into consideration, whereas TEM is restricted to some hundred particles.
The scale distribution obtained by sp-ICP-MS exhibits that full dimension distribution for each PdNP-MPA and PdNP-Cys weren’t acquired, and a bimodal dimension distribution was obtained. This reality, mixed with the broad dimension distribution of the synthesized NPs, means that particles smaller than 30 nm (sp-ICP-MS LODdimension) won’t have been thought of within the calculation of the imply dimension and complete particle quantity. In addition to the size-dependent LODs, this reality might also be associated to the restricted linear vary, and bodily points throughout pattern introduction through nebulization. Furthermore, bigger or aggregated particles is probably not sufficiently ionized within the plasma, resulting in a decreased sensitivity (and therefore, incorrect dimension allocation), and restoration charges35. Consequently, these details can have an effect on the dedication of the overall particle quantity and the common dimension as mentioned by Gimenez-Ingalaturre et al. (2023)36.
Particle quantity focus by sp-ICP-MS
To evaluate the accuracy sp-ICP-MS measurements for PNC and for dimension dedication, the evaluation of a platinum nanoparticles (PtNPs) reference materials was carried out (Determine S5-A). The outcomes obtained by sp-ICP-MS for dimension (49 ± 1 nm) and PNC (3.5 × 1013 ± 2.5 × 1012 particles/L) confirmed a great settlement with these discovered within the PtNP certificates (51 nm and 4.0 × 1013 particles/L). The standard of the dimensions distribution and particle counting carried out by sp-ICP-MS depends upon the right pattern dilution. In line with Gimenez-Ingalaturre et al. 2023, performing the evaluation with completely different dilutions permits the choice of applicable pattern dilution to make sure high quality management for dimension, dimension distribution and PNC36. Thus, the accuracy PdNP-MPA and PdNP-Cys evaluation carried out by sp-ICP-MS was assessed beneath completely different dilutions (Determine S6). As may be seen, contemplating the evaluated dilutions (100 × 103 to 1000 × 103 instances), the particle dimension decided for each PdNP-MPA and PdNP-Cys didn’t change expressively. Nonetheless, it was observed that the outcomes for particle counting have been affected for each PdNPs when dilutions larger than 200 × 103 instances have been utilized. Taking this into consideration and preserving acquisition time (180 s) fixed, the noticed variation in PNC could also be related to statistical points because of the low variety of detected particles36. Thus, a dilution as much as 200 × 103 instances is relevant for the dedication of dimension, dimension distribution and particle quantity focus of the proposed PdNP-MPA and PdNP-Cys.
The evaluation of PtNP reference materials was additionally carried out by NTA (Determine S5-B). Opposite to the noticed by sp-ICP-MS, the dimensions (76 ± 33 nm) and PNC (5.6 × 1014 ± 1.7 × 1013 particles/L) obtained by NTA confirmed a considerable distinction in comparison with the reference values. The noticed distinction most likely happens because of the basic detection bias of NTA in direction of bigger NPs or agglomerates37. Thus, the upper PNC measured by NTA could also be because of the inclusion of non-target or particles that don’t contribute to the element-specific sign in sp-ICP-MS. Nonetheless, PNC decided in PdNP-MPA and PdNP-Cys by NTA and sp-ICP-MS (Fig. 5). The PNC obtained by NTA and sp-ICP-MS strategies are statistically equal, giving the paired t-test, at a 95% confidence stage (p-value > 0.05) (Desk S5).

Particle quantity focus in PdNP-MPA and PdNP-Cys decided by NTA and sp-ICP-MS.
Research have in contrast the outcomes obtained by NTA with these utilizing sp-ICP-MS and noticed that NTA might have overestimated the dimensions and complete particle quantity. Hellmann et al., 2024 carried out the characterization of NPs reference supplies (AuNPs, SiO₂, and Fe₃O₄) in ethanolic suspension utilizing sp-ICP-MS and in contrast the outcomes with these obtained by NTA38. In line with the authors, the dimensions distribution decided by NTA was, normally, bigger than that obtained utilizing sp-ICP-MS and confirmed an inclination to overestimation for small particles (< 51 nm). Usually, the sizes for SiO₂, Fe₃O₄ NPs confirmed a great settlement with these obtained by NTA. Nonetheless, for SiO₂, Fe₃O₄ NPs, the PNC decided by sp-ICP-MS have been barely nearer to the licensed values. This depends on the truth that, for heterogeneous NPs, NTA might not deal with all of the NPs equally, resulting in an overestimation of the PNC38.
Ligand density evaluation
The thiol ligand density of PdNP-MPA and PdNP-Cys have been calculated contemplating a monolayer of the thiol-based ligands MPA and Cys covalently certain to NPs assumed as being of spheric form utilizing the imply particle sizes and PNC obtained by sp-ICP-MS and the overall focus of S and Pd measured by ICP-MS. Additionally, contemplating that nanoparticles have been subjected to a number of washing cycles to take away unbound ligand, the S focus in PdNPs was attributed to surface-bound ligands. Thereby, completely different approaches have been used: (A) a technique proposed by Elzey et al.31, which is predicated on the sulfur-to-metal ratio for figuring out ligand density in metallic nanoparticles, and (B) primarily based on the stoichiometric relation of ligand and S focus, and PNC. Within the PdNPs suspensions, the overall focus of Pd was 343.80 ± 13.25 mg L− 1 (PdNP-MPA) and 310.33 ± 5.91 mg L− 1 (PdNP-Cys), respectively; the focus of S was 0.39 ± 0.09 mg L− 1 (0.11 ± 0.03% (w/w), and 0.35 ± 0.08 mg L− 1 (0.11 ± 0.02% (w/w)), respectively, for PdNP-MPA and PdNP-Cys. These outcomes have been obtained through bulk ICP-MS evaluation and are in good settlement with these obtained through TEM/EDS (PdNP-MPA (0.21 ± 0.11% (w/w)) and PdNP-Cys (0.14 ± 0.11% (w/w)), as talked about above in part Construction and composition.
The ligand density obtained contemplating the 2 said approaches and assuming spherical formed particles are proven in Fig. 6. The ligand density primarily based on the S/Pd ratio was barely decrease than the ligand density obtained by the ligand stoichiometric relation and PNC. Nonetheless, in line with ANOVA, at a 95% confidence stage (Desk S6), there isn’t any vital distinction (p-value > 0.05) among the many values of ligand density obtained by the completely different calculation approaches. Utilizing the S/Pd ratio for ligand density estimation is especially fascinating as a result of the variety of particles doesn’t have an effect on the calculation, and any potential NPs loss throughout ligand elimination might haven’t any affect on the outcomes31.

Ligand density assuming spherical formed PdNPs and calculation by (A) S/Pd ratio and (B) the stoichiometric relation of ligand, S focus and complete particle quantity.
Nonetheless, it is very important spotlight that particle morphology and polydispersity have an vital affect on the calculation of the ligand density. Contemplating spherical, cubic, isooctahedral, and dodecahedral formed particles and assuming particles with the identical quantity, the spherical ones have the bottom surface-to-volume ratio and have a tendency to point out the best common ligand density. Consequently, particles with the identical quantity, the non-spheric PdNP-MPA and PdNP-Cys will most likely present a barely decrease ligand density than these noticed for spherical particles.
Conclusion and outlook
Total, our research demonstrated the (i) potential of multivariate approaches to determine and optimize the elements influencing NP formation, all through the synthesis of PdNP-MPA and PdNP-Cys NPs taking sustainability into consideration, (ii) benefits of a multi-analytical strategy to a complete characterization of NPs, offering outcomes of top quality and good reproducibility, (iii) and the applicability of ICP-MS primarily based strategies for NPs complete size-, surface-characterization and number-based quantification. The PdNP-MPA and PdNP-Cys, used as proof-of-concept confirmed to be fascinating mannequin methods for actual world NP samples encountered, e.g., in environmental evaluation, which reveal a broad dimension and form distribution. Thus, to supply conceptual help and promote coherent choice of uni/multivariate approaches for NPs synthesis optimization, and complementary multi-technique characterization methods for non-ideal NP methods, a decision-tree framework is usually recommended under (Fig. 7).

Determination-tree framework for the optimization of the NPs synthesis and characterization utilizing a multi-technique strategy. Yellow warning image signifies vital determination level related to incomplete or biased outcomes for non-ideal NPs utilizing solely NTA or DLS evaluation.
The institution of NPs synthesis circumstances is a crucial step that can drive the structural and compositional traits of the particles. For well-known synthesis the univariate strategy can be a helpful, quick, and environment friendly means for particle synthesis. Nonetheless, if the synthesis course of shouldn’t be totally understood or for tailor-made NPs, a multivariate strategy for NPs synthesis optimization permits the simultaneous analysis of essentially the most vital parameters in a time environment friendly means. For characterization of superb methods containing spherical and monodisperse methods, the introduced strategies shall be completely well-suited. Nonetheless, for non-ideal methods one ought to pay attention to some potential bias attributable to dimension and form variation. The DLS and NTA evaluation demonstrated passable efficiency for the estimation of hydrodynamic diameter of PdNP-MPA and PdNP-Cys NPs. However, in polydisperse methods DLS measurements could also be biased in direction of bigger particles. sp-ICP-MS is a robust device for the characterization of polydisperse and non-defined form particles permitting for the dedication of the dimensions and dimension distribution; outcomes are comparable with these obtained by complementary analytical strategies. In addition to bodily characterization bulk ICP-MS demonstrated to be helpful for floor characterization by means of the ligand density dedication of thiol-capped nanoparticles.
In abstract, we current a NPs synthesis route in aqueous medium in addition to a subsequent complementary multi-technique analytical strategy for full NPs characterization. As an authors´ prediction – we consider in future work, each “sides” will carefully hyperlink collectively: automated NPs synthesis comprising a closed suggestions loop underpinned with complementary multi-technique evaluation.