Determining the composition of gold nanoparticles: a compilation of shapes, sizes, and calculations using geometric considerations

Gold nanoparticles are everywhere! Aside from the curious and beautiful historic uses as colloidal additives to stain Roman glass in the fourth century and the discovery of the wondrous and different properties of colloidal gold by Michael Faraday in the mid nineteenth century (Tweney et al. 2004), gold nanoparticles and nanoclusters have penetrated almost every facet of science. Each year there are numerous educational and critical reviews on the use and study of gold nanoparticles for topics including in vitro diagnostics (Aillon et al. 2009; Almeida et al. 2011; Azzazy et al. 2006; Johnston et al. 2010; Khlebtsov and Dykman 2011; Mulder et al. 2009; Rosi and Mirkin 2005; Wolinsky and Grinstaff 2008), cancer diagnostics and therapy (Bhattacharyya et al. 2011; Chikkaveeraiah et al. 2012; Dreaden et al. 2011; Gindy and Prud’homme 2009; Jain et al. 2012; Kennedy et al. 2011; Lal et al. 2008; Perfezou et al. 2012; Wang and Thanou 2010; Yong et al. 2009; Zhang et al. 2013), biological and chemical sensors (Askim et al. 2013; Howes et al. 2014; Kim et al. 2012; Perfezou et al. 2012; Pingarron et al. 2008; Sepulveda et al. 2009; Stewart et al. 2008), catalysis (Crooks et al. 2001; Hou and Cronin 2013; Panigrahi et al. 2007; Sarina et al. 2013), gold meta-atoms for metamaterials (Ross et al. 2016), self-assembly (Bishop et al. 2009; Boeker et al. 2007; Grzelczak et al. 2010; Lin et al. 2006; Ofir et al. 2008), intrinsic chirality (Ben-Moshe et al. 2013; Gautier and Bürgi 2009; Guerrero-Martínez et al. 2011; Wang et al. 2013; Xia et al. 2011), and this list could go on. Mind you, 20 years after the beautiful and simple Brust-Schiffrin synthesis methods (Brust et al. 1994, 1995) were published we are finding it increasingly difficult to summarize the contents of review articles, not even individual papers, on gold nanoparticles. Our group, working on understanding interactions between functionalized gold nanoparticles and soft condensed matter, even added a few to this list of reviews, summarizing studies on these magnificent nanomaterials as versatile additives in liquid crystal phases (Hegmann et al. 2007; Qi and Hegmann 2008; Shivakumar et al. 2011; Stamatoiu et al. 2012). The search for “gold nanoparticle” in Thomson Reuters Web of Science shows an ever-increasing number of papers (several thousand), and just looking at the last couple of years, a Google search leads to a mind-boggling number of over 1.8 million hits. Numerous established chemical suppliers as well as smaller startup companies now sell gold nanoparticles, but the majority of laboratories it seems still enjoy synthesizing their own, partially perhaps for educational reasons, mainly most likely for their need of specific surface functionalization toward specific application- or research-driven size or shape requirements. We are not going to summarize these synthetic efforts here, largely because, as you can easily imagine, multiple review articles heretofore did exactly that already (Alexandridis 2011; Crooks et al. 2001; Ganguli et al. 2010; Gopidas et al. 2003; Grzelczak et al. 2008; Lohse and Murphy 2013; Lu et al. 2009; Mourdikoudis and Liz-Marzan 2013; Shan and Tenhu 2007; Walther and Mueller 2013; Zhao et al. 2013; Zhou et al. 2009).

The goal of this compendium of gold nanoparticle tables, which list and compare models to more precisely calculate size and composition, is to be there for the experimentalist once the synthesis is done, and when the characterization of the just prepared precious gold nanoparticles begins. Several groups have recently shown that precise nanoclusters (magic-numbered or not) can be made exclusively, or isolated from batches with initially wider size and shape distribution, with great reproducibility (vide infra). These synthesis pathways become more and more refined, as indicated by the increasing number of articles describing new clusters. Aided by high-resolution X-ray diffraction, mass spectrometry, single-particle (a combination of low dose and aberration-corrected) transmission electron microscopy (TEM) (Azubel et al. 2014), electrophoretic mobility calculations and electromigration (Pyell 2010), thermogravimetric analysis (TGA), elemental analysis, NMR, small-angle X-ray scattering, as well as an array of surface characterization techniques (Auger, AFM, XPS, etc.) (Baer et al. 2010), these gold nanoclusters can now be fully characterized and their composition unambiguously determined. However, most laboratories and research endeavors do not require the rigor and use of well-defined gold nanoclusters. In these cases, average size and well-defined surface chemistries are more critical as is the determination of the overall, yet average composition for a gold nanoparticle sample with a given size and likely shape distribution. The functions these nanoparticles need to perform, for example as plasmonic additives, in drug delivery, in biosensing, as surface-enhanced Raman probes, among many others, do nevertheless require a precise knowledge of the nanoparticle composition. Reproducibility is a great concern for biological and medical applications as well as various other uses in device technologies, affecting performance, reliability, and last but not least intellectual property (IP). To assist in this process and create a practical go-to guide to more precisely determine the core and, in part, ligand shell composition of synthesized nanoparticles, we collected and calculated compositions and best approximations and assembled these datasets based on the overall nanocluster shape. With more and more refined and higher-resolution transmission electron microscopy (TEM) instrumentation available on the market, experimentalists should be in a position to more accurately determine their nanoparticle core composition using the nanoparticle shape revealed by TEM and using the datasets and calculations collected in the tables to come.

The ligand shell is slightly more complicated. Thiolate-protected gold nanoparticles and nanoclusters dominate the literature by a large margin, and the presence of (RS–Au(I)–SR)⁻ and [RS(Au(I)–SR)₂]⁻ “staple” and bridge motifs (Pensa et al. 2012) (better described as Au(0)-thiyl surface bonding (Reimers et al. 2016)) largely governed by the synthesis method as well as the size and shape of the particle or cluster complicates a precise prediction or calculation of the full composition of a given thiolate-capped gold nanoparticle sample. With analytical methods such as NMR (before and after I₂ decomposition; i.e., oxidation of thiolates to disulfides), TGA, X-ray photoelectron spectroscopy (XPS) to the rescue, this hurdle can be overcome once the nanoparticle core composition is determined with some degree of precision.

First, however, we will provide an overview of the various polyhedral shapes relevant for gold nanoparticles. Most gold nanoparticles assumed to be quasi-spherical are in fact Platonic, Archimedean, or Catalan solids. Polyhedral gold nanoclusters are classified as icosahedra and face-centered cubic (fcc) polyhedra. The stable Ino’s and Marks’ decahedra are non-spherical shapes and are best described as ellipsoids. The icosahedral or Ino’s as well as Marks’ decahedral-based gold nanoclusters (with icosahedral structure considering the triangular faces and fcc structure when considering the rectangular faces) represent more molecular-like structures. The fcc-based gold nanoparticles have more bulk (plasmonic) structures.

There are five platonic solids constructed by regular polygonal faces (Fig. 1), with tetrahedron, cube, and octahedron combined known as fcc unit cell substructures. Magic-numbered gold nanoclusters have regular icosahedral shapes.

Two or three regular polygonal faces are needed to construct Archimedean solids, and truncating Platonic solids can compose them. As a result, Archimedean solids that are truncated from either tetrahedron, cube, or octahedron have fcc structures; other Archimedean solids have icosahedral structures as graphically shown in Fig. 2.

The process of obtaining these Archimedean solids by truncation is graphically shown in Fig. 3. The remaining Catalan solids are defined as dual solids of Archimedean solids. As their faces are not regular polygonal, it is expected that the cores of metal clusters could not be Catalan solid structures; however, ligand shells of Archimedean metal clusters could have Catalan solid structures (Fig. 4).

As one can appreciate, the approach pursued here, culminating in the presented nanoparticle tables, equations, and models, solely relies on geometrical considerations not precise electronic and atomic structural information, which are only accessible for well-defined clusters whose structure was solved by X-ray diffraction (Chen et al. 2015; Jadzinsky et al. 2007; Zeng et al. 2014, 2015) or high-resolution single-particle TEM (Azubel et al. 2014) (aberration-corrected TEM, vide supra). Numerous groups have made significant and important progress in applying density functional theory and other numerical as well as computational approaches to determine gold nanoparticle sizes, structures, and energetics (Barnard 2010; Barnard and Chen 2011; Barnard and Curtiss 2006; Barnard et al. 2009; McKenna 2009; Negishi et al. 2015) and focus increasingly on the very challenging task of elucidating the structure of the thiolate ligand shell (Barnard 2013; Xu et al. 2015). A closer look at these modeling and simulation data on various gold nanoparticle sizes and shapes, however, reveals that the current geometrically derived data tables and models capture these and that the implementation of both approaches endows experimental scientists with a powerful tool for the elucidation of nanoparticle composition. In addition, the geometrical models can much faster survey a greater number of nanoparticles and nanoclusters (including nanoparticles with larger diameters and many more gold atoms in the core) much faster. Practically speaking, the presented equations and tables are easily adjustable (via the radius of the metal atom) for the determination of the composition of other metal nanoparticles with fcc lattices (Pd, Pt, Ni (Lin et al. 2011) as well as coinage metals Ag, Cu); perhaps even alloy-type metal nanoparticles if elemental composition is determined upfront. The predicted sequences of preferred shapes by Guisbiers et al. should here be tremendously helpful (Guisbiers et al. 2014). Of the 130 + clusters included in the current tables and models, several have not been experimentally observed for gold nanoparticles as of yet, and specific shapes observed for other transition metals are not included (e.g., tetrahedral for Pd nanoparticles (Barnard 2012)). Expansion to other shapes is a focus of future work, and numerical and theoretical methods recently presented by Barnard et al. will be used as guide for metal nanorods (Gonzalez et al. 2013). Finally, the section on shell structures is currently limited to the most frequently used thiolates and not considering other ligand motifs such as amines or phosphines among others. Thinking about the vast number of thiolate ligands reported in the literature, steric considerations are extremely difficult to include in any model system (Burgi 2015; Hakkinen 2012), especially since more and more sophisticated functions expected from gold nanoparticles require functional ligands with, for example, luminescent properties, binding capabilities to proteins, chirality, drug delivery, and many more.

Centered specifically around geometrical considerations, this compendium of tables, models, and equations serves as an easy-to-use, straightforward guide for experimental scientists synthesizing thiol-protected gold nanoparticles in the laboratory to assist them in calculating the nanoparticle composition based on geometric information deduced from TEM imaging and image analysis. The majority of research thrusts and applications focusing on thiol-protected metal nanoparticles do not require the precision of well-defined metal clusters, although synthetic approaches to obtain such clusters are tirelessly pursued and refined. Nevertheless, predicting and analytically confirming the composition of all other metal nanoparticles as accurately as possible is critical for fundamental and applied research alike. A nanoparticle’s composition significantly affects its properties and defines its function, irrespective of its use in applications ranging from drug delivery and cancer diagnostics to metamaterials and chiral discriminators. With the anticipated transformation of these tables, models, and equations to a web-based tool (that would also permit viewing of model clusters from various perspectives), we trust that experimental scientists will be provided with an invaluable, helpful, and expandable tool for the elucidation of metal nanoparticle compositions.