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Wulff-Based Approach to Modeling the Plasmonic Response of Single Crystal,Twinned, and Core–Shell Nanoparticles

Christina Boukouvala†,Emilie Ringe†,‡,*
†Department of Materials Science and Metallurgy,University of Cambridge, 27 Charles Babbage Road, CambridgeCB3 0FS, U.K.
‡Department of Earth Sciences, Universityof Cambridge, Downing Street, Cambridge CB2 3EQ,U.K.
*

E-mail:er407@cam.ac.uk.

Received 2019 Aug 8; Revised 2019 Sep 16; Issue date 2019 Oct 17.

Copyright © 2019 American Chemical Society

This is an open access article published under a Creative Commons Attribution (CC-BY)License, which permits unrestricted use, distribution and reproduction inany medium, provided the author and source are cited.

PMCID: PMC6822593  PMID:31681455

Abstract

graphic file with name jp9b07584_0005.jpg

The growing interest in plasmonic nanoparticles and their increasingly diverseapplications is fuelled by the ability to tune properties via shape control, promotingintense experimental and theoretical research. Such shapes are dominated by geometriesthat can be described by the kinetic Wulff construction such as octahedra, thintriangular platelets, bipyramids, and decahedra, to name a few. Shape is critical indictating the optical properties of these nanoparticles, in particular their localizedsurface plasmon resonance behavior, which can be modeled numerically. One challenge ofthe various available computational techniques is the representation of the nanoparticleshape. Specifically, in the discrete dipole approximation, a particle is represented bydiscretizing space via an array of uniformly distributed points-dipoles; this can bedifficult to construct for complex shapes including those with multiple crystallographicfacets, twins, and core–shell particles. Here, we describe a standaloneuser-friendly graphical user interface (GUI) that uses both kinetic and thermodynamicWulff constructions to generate a dipole array for complex shapes, as well as thenecessary input files for DDSCAT-based numerical approaches. Examples of the use of thisGUI are described through three case studies spanning different shapes, compositions,and shell thicknesses. Key advances offered by this approach, in addition to simplicity,are the ability to create crystallographically correct structures and the addition of aconformal shell on complex shapes.

Introduction

Plasmonic nanoparticles (NPs) have gained much attention in the scientific community owingto their optical properties that can be exploited for a variety of applications, rangingfrom sensing1 and photocatalysis,2 tobiomedicine3 and optical circuits.4 NPs of freeelectron metals confine light via collective electron cloud oscillations triggered by anincident oscillating electromagnetic field, giving rise to resonances known as localizedsurface plasmon resonances (LSPRs). LSPRs enhance light scattering and absorption whilstamplifying local electric fields at the NP’s surface. Commonly, plasmonic NPs aresynthesized from Au and Ag5 but novel plasmonic structures ofearth-abundant materials such as Al, Cu, and Mg have recently been demonstratedtheoretically and experimentally.6−11 Other metals, such as Ga and In also present significantLSPR tunability12,13while Pd and Pt sustain rather weak and broad LSPRs.14,15

The energy and peak width of a LSPR can be tuned by controlling the composition,environment, size, and shape of the NPs, to name a few.5,16,17 Shape is particularlyappealing, as it easily and predictably controls the near-field distribution around aparticle, creating for instance localization around either the corners or faces in acube18 or tip and shaft in a rod,19 depending on theresonance frequency. Shape tuning can be supplemented by composition tuning by incorporatinglayers of different materials, either as a simple core–shell structure or complexmultishell, egg-yolk, or other shapes.20 Such core–shellstructures are of particular interest not only because they introduce new parameters thataffect LSPRs, such as shell composition and thickness,21 but also becausethey can combine plasmonic and nonplasmonic materials,22 thus providingfurther means to design functional NPs. Core–shell structures may also be used toprevent the oxidation of a core,23 or occur spontaneously uponself-limiting oxidation of a metal.7,9

The shape of NPs, so critical for their optical properties, is dictated by the crystalstructure and growth environment. At thermodynamic equilibrium (e.g., in vacuum or anotherscarcely interacting environment), NP shape can be predicted analytically from the(thermodynamic) surface free energy according to the Wulff construction.24 Briefly, the distance normal to an (hkl) facet,hhkl, is related to its surface energyγhklas

graphic file with name jp9b07584_m001.jpg1

whereΛ is a constant accounting for volume. While this is only valid for a free-floatingparticle during growth, extensions to the model including interaction with one or twointerfaces with a substrate have been developed, named the Winterbottom and the Summertopconstructions, respectively.25,26 Similarly, the addition of internal rather than external boundaries toaccount for twinning leads to the modified Wulff construction.27Realizing that the thermodynamic shapes were rarely present in reaction products, thekinetic Wulff construction28 was developed, where a growth velocityvhkl is used instead of the thermodynamicsurface free energy γhkl. The kinetic approach to thegrowth of twinned structures was then, recently, developed,29 where twinboundaries, disclinations, and re-entrant surface kinetic effects help explain mostexperimentally obtained shapes for face-centered cubic (fcc) materials, which include mostplasmonic metals (Cu, Ag, Au, Al).

Here, this kinetic version of the regular (single crystal) and modified (twinned) Wulffconstruction29 is used as the basis of a shape modeling code integratedin a user-friendly, standalone graphical user interface (GUI). Briefly, to derive aNP’s shape from the inputs ofvhkl andoptional enhancements at re-entrant surfaces, twin boundaries, and disclinations, space isdiscretized in a cubic three-dimensional grid and growth velocities(vg) are calculated at each point of the grid, described as avectorp⃗ with respect to the center of the shape. This ismathematically implemented by calculating the following expression on each grid pointp⃗

graphic file with name jp9b07584_m002.jpg2

whereb is a smoothing factor andn⃗ =Fvhkln̂, wheren̂ is the unit vector of the corresponding crystallographic facet,andF is the enhancement factor givenby

graphic file with name jp9b07584_m003.jpg3

The Wulff shape is then defined as an isosurface of growth velocities, because this isdirectly proportional to the distance from the geometric center of the particle to the facet(eq1). In the case of twinned NPs the createdshape is mirrored along the twin plane for NPs with a single twin plane or rotated aroundthe five-fold symmetry axis for NPs with five nonparallel twin planes.30

Modeling shape effects is the key to understand how geometry affects LSPRs (both far andnear-field) and can support and inspire the design and synthesis of NPs for tailoredlight–matter interactions. To do this, one must solve Maxwell’s equations,which describe the electromagnetic interactions at play. Because analytical solutions toMaxwell’s equations are limited to a small number of simple geometries, such asspheres with the Mie solution31 or ellipsoids with the Mie–Ganssolution,32 various numerical techniques have been developed to modelarbitrary shapes. Prevailing approaches include the finite difference time domain (FDTD)method,33 the discrete-dipole approximation (DDA),34the finite-element method (FEM)35 and the boundary element method(BEM).36 The first three approaches (FDTD, DDA, FEM) requirediscretization over the NP volume while for BEM the discretization is applied only to the NPsurface.

In DDA,34 particles are represented by an array of small cubic elementsconsidered dipoles interacting with each other and with the incident electric field. Theseinteractions result in a system of Maxwell’s equations that can be solved to obtainthe polarization of each dipole and subsequently to calculate the absorption and scatteringproperties of the particle, as well as near-field effects such as field enhancement mappingand local charge distribution around nanostructures. The latter can give importantinformation about LSPR modes such as their localization on the edges and corners oftriangular plates.37 In FDTD33 the space and timederivatives that appear in Maxwell’s equations are replaced by finite differences,therefore requiring a discretization over both time and space, the latter achieved by a gridof cuboid elements; the problem is then solved iteratively until a steady-state solution isachieved, where the error is better defined than in DDA.38,39 In the case of FEM, space discretization isachieved using elements, usually tetrahedral, for which the Helmholtz equation is satisfiedalong with appropriate conditions to ensure continuity and a consistent solution.35

The DDA is a hugely successful and popular method because in general, it requirescomparatively low computational power, depending of course on the dipole number andinterdipole distance.39,40 Unlike other techniques, it uses a simple and straightforwardlyphysically meaningful discretization of space in dipoles. One downside to this simplicity isthat equally sized cubic elements do not allow for a denser, better fitting grid for curvedsurfaces, making it difficult to model high aspect ratio structures for instance.41 When modeling NP shapes, for DDA and for the aforementioned computationaltechniques, the appropriate geometry input must be created, which can prove difficult,especially for shapes with complex features or with many facets and angles such as a Marksdecahedron. Here we present an approach to solve this struggle and facilitate simulation ofthe plasmonic properties of various NP shapes.

Acknowledging the advantages of the DDA technique and the already validated Wulffconstruction theory, we incorporate the modified kinetic Wulff construction code29 in a GUI that creates a crystallographically correct NP shape and all theappropriate inputs for DDSCAT,34 an open source code that uses the DDAmethod to calculate the optical properties of nanostructures. We show the modeling of singlecrystal and twinned fcc NPs with and without a shell for both concave and convex geometries,in both the kinetic and thermodynamic regime. Below we first describe the GUI, and thendemonstrate its capabilities by modeling and calculating the absorption and scatteringproperties of Au, Ag, and Al NPs of various shapes as well as core–shell structuresincluding Au@SiO2 decahedra, Ag@SiO2 cubes, andAl@Al2O3 bipyramids with various shell thicknesses.

Computational Details

Au and Ag refractive indices (RI) were obtained from Johnson and Christy,42 those of Al and Al2O3 from Palik,43and that of SiO2 from Rodríguez-de Marcos et al.44 ForAl, RI from Palik was available only up to 190 nm and the DDA extrapolation was used for150–190 nm. The ambient RI was set to 1 (vacuum), and electron surface scatteringcorrections on the RI were not deemed necessary because all NPs are sufficiently small, thatis, they have an effective diameter greater than 30 nm.45 Scattering(Csca) and absorption (Cabs) crosssections were calculated by multiplying the corresponding DDSCAT output efficiencies withthe effective area (πaeff2). The shapes weremodeled with an interdipole distance range of 0.3–2.6 nm depending on the total size,shape, and material of the NP (Tables S1 and S2), with no fewer than 105 dipoles, except forcubes, to ensure accuracy.39 The convergence of the results with thenumber of dipoles was investigated only for the smallest NPs (Figures S2–S5) as larger NPs are expected to require fewer dipoles toget results with the same accuracy.39 In all cases, the incident light ismodeled having two orthogonal polarizations, an approach commonly used to mimic unpolarizedlight, and propagates along the highest symmetry axis of the particle, that is,perpendicular to a face for the cube, along the direction of the 4-fold axis for theoctahedron, along the direction of the 5-fold axis for the sharp and Marks decahedron, andperpendicular to the twin plane for the bipyramid and triangle. The contribution of the twopolarization components was also investigated for Au and Ag decahedra and was found tomainly influence the LSPR intensities with little effect on the LSPR energy. These results(Figure S6) along with the GUI input parameters used for the shape modeling(Table S3) and further computational details can be found in theSupporting Information.

Results

User Interface

Figure1 shows the process of calculating asharp decahedron and generating the dipole array with the aid of the Wulff constructionGUI, and the subsequent calculation of the absorption and scattering spectra, as well aselectric field distribution with the DDA. The Matlab-based GUI, deployed as a standaloneapplication, features a main window (Figure1a)with input panels and action buttons that guide the user through the steps from modelingthe NP’s shape to creating the shape file (shape.dat) and then the parameter file(ddscat.par) which are inputs for the DDSCAT simulation. Additionally, a RI file is to beprovided by the user (RI files of Au, Ag, Al, SiO2, andAl2O3 available in theSupporting Information).

Figure 1.

Figure 1

Wulff construction tool. (a) Main Wulff construction GUI window, (b) resulting dipolerepresentation, (c) scattering spectrum, and (d) near field(E⃗2) distribution at theNP’s mid-height obtained from the DDA calculation for a sharp Audecahedron.

Specifically, the surface growth velocities(vhkl) of the {100}, {110}, and {111}planes as well as the kinetic growth re-entrant surface (φre-entrant),twin (φtwin), and disclination (φdisclination)enhancements are specified in the basic parameters panel. Thermodynamic surface energiescan be used instead of growth velocities, with no enhancement, for thermodynamic shapes.The user can select no twin plane (single crystal), one {111} twin plane (monotwin), ascommon in fcc structures, or five nonparallel {111} twin planes (pentatwin). NPs with ashell can be calculated, providing information about the thickness of the shell (shellpercentage) and the curvature of the shape (concave or convex) is supplied. The shellgenerated is conformal, that is, it has the same geometry as the Wulff NP without ashell.

After all the parameters are defined the shape isosurface is calculated and displayed; atthis stage the shape is dimensionless. In the DDSCAT the size of the studied target isintroduced in the parameter file as the effectiveradius

graphic file with name jp9b07584_m004.jpg4

whereV is the volume of the target. TocalculateV and the effective radius (calculate effective radius), theuser selects two arbitrary points on the shape and inputs the distance between them(Figure S1b). Conveniently, the two points can be on the same or differentfacets, or on the shell or core of the particle, allowing, for example, defining the sizeof the particle based on the plasmon length.

When performing the DDSCAT calculations the choice of number of dipoles or equivalentlythe interdipole distance is important for the accuracy of the obtained result. In DDSCATthe interdipole distance is defined by the total number of dipoles and the total volume ofthe studied structure. In the GUI, the user can specify the interdipole distance (defineinterdipole distance) through a dialog box (Figure S1c); the code then readjusts the number of dipoles to fit both thevolume and interdipole distance requirements. To achieve a good accuracy the interdipoledistance must be small compared to both any structural length of the target and thewavelength of the incoming radiation.34 The convergence of the resultscan be checked by manipulating the interdipole length for a given shape.

The first DDSCAT input file generated is the shape file (create shape file), whichcontains the array of dipoles that represent the NP as well as information about itsorientation and composition. The second DDSCAT input file is the parameter file (createddscat file), which includes details about the computational setup of the calculations,the material and effective radius of the target, the incident field, and the output files.A detailed description of the shape and parameter files and their variables can be foundin the DDSCAT manual,46 and a typical parameter file along with anextended description of the GUI can be found in theSupporting Information.

Case Study 1: NP Shape and Composition

Au and Ag NPs are dominant among plasmonic metals as they exhibit strong, tunable LSPRsthroughout the visible and infrared region.5 Unlike Ag, Au NPs arestable toward oxidation and biocompatible, enabling biomedical applications.3 Alternatives to the rather expensive Ag and Au are becoming commonplace, Albeing an example that is earth abundant and sustains LSPRs in the visible and ultraviolet(UV) region, providing opportunities for UV plasmonics6 All threemetals have well-established synthetic techniques7,47,48 leading to a variety ofsingle-crystal and twinned NPs49 whose shape-dependent plasmonicproperties can be predicted or confirmed via numerical simulations. Here, Au and Ag cubes,{100}-capped bipyramids, and decahedra are chosen as examples of single crystal, monotwinand pentatwin noble metal shapes, respectively, while cubes, octahedra, and {100}-cappedbipyramids are chosen as representative Al shapes. The different structures studied, allgenerated with the Wulff construction tool (Table S3), are shown inFigure2a.The effective radius of the NPs is 31 nm, corresponding to a cube with an edge length of50 nm.

Figure 2.

Figure 2

Wulff construction shapes where the black line shows the edge length (a) and thecorresponding simulated scattering and absorption cross sections for (b) Au, (c) Ag,and (d) Al. Green, blue, and red solid lines correspond to cube, decahedron, andbipyramid, respectively; green and blue dotted lines correspond to the octahedron andMarks decahedron, respectively. The effective radius is 31 nm for all NPs.

The scattering and absorption cross sections of Au NPs as a function of wavelength areshown inFigure2b. As expected, these rathersmall Au cubes and decahedra exhibit one, dipolar, LSPR peak in the region of500–550 nm50,51while, given its higher anisotropy, the bipyramid features a red-shifted main peak and asecond peak as a high energy shoulder.52 The dominant peak for allshapes shifts toward higher wavelengths in the order: Marks decahedra, cubes, sharpdecahedra, and bipyramids, a trend that reflects the combined effects of increasingplasmon length and anisotropy of the shapes. More specifically, given that the NPs havethe same volume, the plasmon length, defined as the length over which the dipoleoscillations take place,17 increases in the order: cube, decahedron,and bipyramid. As the plasmon length increases, resonance occurs at higher wavelengths,that is, causing the noted red-shifts. This also explains the smaller peak wavelength ofMarks decahedron compared to the sharp one. On the other hand, higher symmetry causes ablue-shift. The thicker Marks decahedron is more similar to a sphere further explainingits blue-shifted LSPR compared to the sharp decahedron and the cube. The peak intensitiesfollow an increasing trend from marks decahedron, to cube, bipyramid, and sharpdecahedron. Peak intensity increases with the plasmon length unless high anisotropy causesthe appearance of a new peak or shoulder, consequently decreasing the highest peakintensity as observed in the case of the Au bipyramids. The near-field response for a Ausharp decahedron is also reported inFigure1d.

The absorption and scattering cross sections for the Ag NPs are presented inFigure2c. The six characteristic main LSPR modes ofAg cubes, well-identified in the literature,53,54 span roughly 330–420 nm. The LSPR peaks arebroader for the decahedra and the bipyramids as their symmetry leads to less modedegeneracy than the cube.53,55 A red-shift trend in the peak wavelength follows the Au NPspattern.

Finally, the LSPRs of Al NPs (Figure2d) appearat lower wavelengths than Ag and Au of the same size, in the range of 150–250 nm.This is consistent with previous calculations for Al nanorods and spheres of comparablesize.56 Other calculations for Al octahedra have shown the presenceof two peaks in the octahedron spectrum,57 one of which in the200–400 nm range shown here. Note that for Al the scattering and absorptionprofiles look different because the scattering and absorption peak intensity ratio changeswith wavelength. This feature depends on the dielectric constant of the material and isless prominent as we move to Ag and Au. The ratio also depends on the shape and size ofthe NP.

Case Study 2: Core–Shell NPs

Silica (SiO2) shells are commonplace in nanoscience because silica is an inertmaterial that helps increase the stability of the NPs while its thickness can be used tocontrol the LSPR characteristics of the core material.48 The opticalproperties of Al NPs which develop self-limiting alumina (Al2O3)shells are also attractive as the oxide can passivate and protect theNP.7,58 Here wedemonstrate the capabilities of our approach by calculating the scattering and absorptionproperties of Au@SiO2 sharp and Marks decahedra, Ag@SiO2 cubes, andAl@Al2O3 bipyramids for varying oxide thickness t. The coregeometry has an edge length of 50 nm for cubes, sharp decahedra, and bipyramids and 20 nmfor Marks decahedra and is as illustrated for all shapes inFigure2a.

The scattering and absorption of Au@SiO2 sharp decahedra are shown inFigure3a. As the oxide shell increases the plasmonpeak red-shifts gradually by 50 nm att = 10 nm because of the higher RIof SiO2 compared to that of vacuum. This value fits between the ∼20 nmredshifts reported for silica-coated Au spheres of various sizes59 andlarger ∼100 nm shifts for silica-coated Au triangles.60 Thistrend is consistent with the observation that higher wavelength LSPRs, found in moreanisotropic shapes, exhibit higher RI sensitivity.16 The scattering andabsorption for silica-coated Marks decahedra (Figure3b) follow a similar pattern.

Figure 3.

Figure 3

Simulated scattering and absorption cross sections for core–shellAu@SiO2 sharp decahedra (a), Au@SiO2 Marks decahedra (b),Ag@SiO2 cubes (c), and Al@Al2O3 bipyramids (d) withvarying oxide thickness. Spectra offset for clarity.

Silica-coated Ag cubes (Figure3c) demonstrate aslightly higher red-shift than Au for the high wavelength peaks and a smaller red-shiftfor lower wavelength peaks. The high wavelength LSPR shifts more than what has beenreported for SiO2-coated Ag spheres owing to the larger RI sensitivity ofcubes.61

Figure3d shows the scattering and absorption ofAl@Al2O3 core–shell bipyramids with differentAl2O3 shell thickness. The significant decrease in intensity foran oxide layer as small ast = 10 nm is consistent with reports ofsimilar LSPR suppression for other shapes.56,58 We also note that Al2O3 causes anotable red-shift of the LSPR positions, following the trend of computational findings forcylinders which, similarly to bipyramids, are highly anisotropic shapes.56

Case Study 3: Triangular Plates

Thin nanoplates, including triangles,62−64disks,65 and hexagons,66 are another interestinggroup of plasmonic NPs. Triangular plates are quite attractive as their high RIsensitivity, stemming from their sharp corners, makes them suitable for sensingapplications64 while their high anisotropy creates strong localfields.37 In this last case study, we demonstrate the applicabilityof our approach by modeling Au and Ag triangular plates and calculating their scattering,absorption, and near-field properties. The modeled NPs (Figure4a) have an edge length of 75 nm and thickness of 10 nm.

Figure 4.

Figure 4

Wulff modeled triangular plate (a) and calculated (b)E⃗2 field distribution at the NPmid-height and scattering and absorption cross sections for (c) Au and (d) Ag of edgelength 75 nm and thickness 10 nm.

Figure4b shows theE⃗2 field distribution for a Autriangular plate, calculated at a peak wavelength of 656 nm and shown at the NPmid-height. Here, light is polarized vertically, that is, along the height of the triangleincluding the top corner. The plasmon-enhanced field is localized at the three sharpcorners of the plate, with a higher intensity around the top corner owing to thepolarization.37 Additional, weaker enhancement is present along theNP’s edges.Figure4c,d shows thescattering and absorption cross sections for the Au and Ag triangular plates,respectively. Au has a dominant peak at 656 nm with a shoulder at 740 nm, while Agfeatures at least six distinct peaks ranging from 460 to 630 nm. As expected, for bothcompositions peaks are red-shifted with respect to the previous studied shapes followingthe anisotropy trend discussed in the first case study.

Discussion

The results above have shown the applicability of the code to a variety of NPs, somewell-studied and some novel; all being crystallographically correct. To our knowledge,current shape-generating tools, used to provide the geometry for various electromagneticsimulation open source codes or commercial packages do not take into accountcrystallographic directions. For example, built-in 3D drawing platforms are used to generatearbitrary geometry inputs for FEM calculations performed with the COMSOL package and forFDTD packages such as CST Microwave or Lumerical. Some crystallographically correct shapescan be imported as 3D CAD structures created with the open-source FORTRAN code SOWOS67 which performs Wulff construction modeling, although without includingkinetic enhancements or twin planes. Other FDTD software like the open source MEEP68 use manually created geometries defined through a variety of optionsincluding vectors or equations. For the DDA it is possible to find tools, such as DDSCATConvert,69 that create the dipole array from a file containingthree-dimensional information about the geometry, but again crystallographic orientation isignored.

Unlike these approaches, with the Wulff construction GUI we provide a facile way to createintrinsically correct NP shapes with correct angles between the NP facets and a consistentarea for the facets of the same type. This is encoded in the crystallographic directionsthat are considered for the Wulff construction, that is, the facet angles are the anglesformed between the well-defined crystallographic planes. Currently only the three moststable fcc facets, {111}, {110}, and {100}70 are considered but theaddition of more facets, when required, is trivial. Note that other Wulff shape modellingtools67,71 are eitherrestricted to shape visualization or the output data needs to be processed in a nontrivialway before used in any electromagnetic simulation software. They also do not offer therequired control over the critical parameters for DDA such as the interdipole distance.Conveniently for convergence studies, our tool can be used to systematically alter theinterdipole distance, by controlling its value through the appropriate action button, or tomaintain the same number of dipoles for varying shape sizes, by fixing the step size value,the latter being applicable only for particles with the same shape.

Further, with the second case study we have specifically demonstrated the use of the Wulffconstruction tool to calculate the properties of coated NPs. This is a useful feature wheninvestigating optical trends for deliberate or spontaneously formed conformal shells. Ittherefore, applies very conveniently to most oxide layers, which are of increasing interestgiven the increasing importance of non-Au plasmonics.

It is important to note that the Wulff construction tool tends to create slightly roundedshapes because of the adopted discretization process; this conveniently happens to mirrorthe typical experimental shapes. Yet this is not perfect, and one must be careful torecognize that small shape changes can influence the plasmonic behavior and thus care shouldbe taken to choose an appropriate step size for each shape in order to eliminate theso-called staircase effect. As the number of dipoles decreases, deviations from the user-setdimension and interdipole distance are more apparent because the numerical volumecalculation becomes inevitably less accurate. The shell is conformal, as appropriate forrelatively thin shell layers on shapes of varying complexity.72 The GUIdoes not currently support core and shell of different shapes73 or allowfor thickness variations at the NP edges and tips.60 Another limitationis the minimum thickness that can be modeled: as the code (and DDSCAT) uses the same dipoledensity for the core and shell, creating a very thin (<4 nm) shell requires a dense arraythat leads to long computational time.

As a newly developed tool, the Wulff construction GUI has a generous range of futuredevelopments including for instance further crystal structures, addition of asubstrate,74 and the ability to model NPs with multiple shells.20 While the current output is tailored to the DDSCAT, the isosurface caneasily be used to generate a CAD shape and in principle provide a crystallographicallyaccurate geometry input for the FDTD and FEM techniques, or for 3D printing.

Conclusions

We described a MATLAB-based standalone GUI that models the shape of fcc NPs, based on themodified kinetic Wulff construction theory, and creates the required input files for theDDSCAT simulations. The range of accessible shapes includes, but is not limited to, cubes,octahedra, bipyramids, stars, plates, pentagonal rods, and multiple decahedra-relatedstructures. All structures modeled have crystallographically correct angles. To demonstratethe capabilities of the GUI we modeled the plasmonic properties of Au, Ag, and Al NPs ofvarious shapes. Next, the effects of oxide shells, including SiO2 and the nativeAl2O3 on Al, on the optical response of NPs was used to display thecapability of the GUI to add a conformal shell on a complex NP. Finally, the near-field andfar-field optical properties of triangular plates were also calculated. The results,consistent with the literature when available, show the simplicity and power of the coupleduse of the GUI and DDSCAT to predict the plasmonic response of metallic nanomaterials. ThisGUI is therefore, expected to be an advantageous tool for facilitating the studies ofnanoplasmonics, with interesting future extensions.

Acknowledgments

Support for this project was provided by the EU Framework Programme for Research andInnovation Horizon 2020 (Starting Grant SPECs 804523 to E.R.) and the Engineering andPhysical Sciences Research Council (Standard Research Studentship (DTP) EP/R513180/1 toC.B.).

Supporting Information Available

The Supporting Information is available free of charge on theACS Publications website at DOI:10.1021/acs.jpcc.9b07584.

  • Detailed description of the GUI; convergence plots with the number ofdipoles for different shapes and materials; comparison of scattering and absorptionprofiles for different polarization states; GUI input parameters; details of numericalsimulations (PDF)

  • DDSCAT files, WulffDDSCAT installationand use guide, and WulffDDSCAT code (ZIP)

The authors declare no competing financial interest.

Supplementary Material

References

  1. Mayer K. M.; Hafner J. H.Localized Surface Plasmon Resonance Sensors. Chem. Rev.2011, 111, 3828–3857. 10.1021/cr100313v. [DOI] [PubMed] [Google Scholar]
  2. Baffou G.; Quidant R.Nanoplasmonics for Chemistry. Chem. Soc. Rev.2014, 43, 3898–3907. 10.1039/c3cs60364d. [DOI] [PubMed] [Google Scholar]
  3. Lim W. Q.; Gao Z.Plasmonic Nanoparticles in Biomedicine. Nano Today2016, 11, 168–188. 10.1016/j.nantod.2016.02.002. [DOI] [Google Scholar]
  4. Davis T. J.; Gómez D. E.; Roberts A.Plasmonic Circuits for Manipulating Optical Information. Nanophotonics2017, 6, 543–559. 10.1515/nanoph-2016-0131. [DOI] [Google Scholar]
  5. Kelly K. L.; Coronado E.; Zhao L. L.; Schatz G. C.The Optical Properties of Metal Nanoparticles: The Influence of Size,Shape, and Dielectric Environment. J. Phys. Chem. B2003, 107, 668–677. 10.1021/jp026731y. [DOI] [Google Scholar]
  6. Gutierrez Y.; Ortiz D.; Sanz J. M.; Saiz J. M.; Gonzalez F.; Everitt H. O.; Moreno F.How an Oxide Shell Affects the Ultraviolet Plasmonic Behavior of Ga, Mg,and Al Nanostructures. Opt. Express2016, 24, 20621. 10.1364/oe.24.020621. [DOI] [PubMed] [Google Scholar]
  7. McClain M. J.; Schlather A. E.; Ringe E.; King N. S.; Liu L.; Manjavacas A.; Knight M. W.; Kumar I.; Whitmire K. H.; Everitt H. O.; et al. Aluminum Nanocrystals. Nano Lett.2015, 15, 2751–2755. 10.1021/acs.nanolett.5b00614. [DOI] [PubMed] [Google Scholar]
  8. Chan G. H.; Zhao J.; Hicks E. M.; Schatz G. C.; Van Duyne R. P.Plasmonic Properties of Copper Nanoparticles Fabricated by NanosphereLithography. Nano Lett.2007, 7, 1947–1952. 10.1021/nl070648a. [DOI] [PubMed] [Google Scholar]
  9. Biggins J. S.; Yazdi S.; Ringe E.Magnesium Nanoparticle Plasmonics. Nano Lett.2018, 18, 3752–3758. 10.1021/acs.nanolett.8b00955. [DOI] [PubMed] [Google Scholar]
  10. Chan G. H.; Zhao J.; Schatz G. C.; Van Duyne R. P.Localized Surface Plasmon Resonance Spectroscopy of Triangular AluminumNanoparticles. J. Phys. Chem. C2008, 112, 13958–13963. 10.1021/jp804088z. [DOI] [Google Scholar]
  11. Duan X.; Liu N.Magnesium for Dynamic Nanoplasmonics. Acc. Chem. Res.2019, 52, 1979–1989. 10.1021/acs.accounts.9b00157. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Knight M. W.; Coenen T.; Yang Y.; Brenny B. J. M.; Losurdo M.; Brown A. S.; Everitt H. O.; Polman A.Gallium Plasmonics: Deep Subwavelength Spectroscopic Imaging of Single andInteracting Gallium Nanoparticles. ACS Nano2015, 9, 2049–2060. 10.1021/nn5072254. [DOI] [PubMed] [Google Scholar]
  13. Magnan F.; Gagnon J.; Fontaine F.-G.; Boudreau D.Indium@Silica Core-Shell Nanoparticles as Plasmonic Enhancers of MolecularLuminescence in the UV Region. Chem. Commun.2013, 49, 9299–9301. 10.1039/c3cc45276j. [DOI] [PubMed] [Google Scholar]
  14. Sugawa K.; Tahara H.; Yamashita A.; Otsuki J.; Sagara T.; Harumoto T.; Yanagida S.Refractive Index Susceptibility of the Plasmonic Palladium Nanoparticle:Potential as the Third Plasmonic Sensing Material. ACS Nano2015, 9, 1895–1904. 10.1021/nn506800a. [DOI] [PubMed] [Google Scholar]
  15. Zhang N.; Han C.; Xu Y.-J.; Foley IV J. J.; Zhang D.; Codrington J.; Gray S. K.; Sun Y.Near-Field Dielectric Scattering Promotes Optical Absorption by PlatinumNanoparticles. Nat. Photonics2016, 10, 473–482. 10.1038/nphoton.2016.76. [DOI] [Google Scholar]
  16. Miller M. M.; Lazarides A. A.Sensitivity of Metal Nanoparticle Surface Plasmon Resonance to theDielectric Environment. J. Phys. Chem. B2005, 109, 21556–21565. 10.1021/jp054227y. [DOI] [PubMed] [Google Scholar]
  17. Ringe E.; Langille M. R.; Sohn K.; Zhang J.; Huang J.; Mirkin C. A.; Van Duyne R. P.; Marks L. D.Plasmon Length: A Universal Parameter to Describe Size Effects in GoldNanoparticles. J. Phys. Chem. Lett.2012, 3, 1479–1483. 10.1021/jz300426p. [DOI] [PubMed] [Google Scholar]
  18. Nicoletti O.; de la Peña F.; Leary R. K.; Holland D. J.; Ducati C.; Midgley P. A.Three-Dimensional Imaging of Localized Surface Plasmon Resonances of MetalNanoparticles. Nature2013, 502, 80–84. 10.1038/nature12469. [DOI] [PubMed] [Google Scholar]
  19. Guiton B. S.; Iberi V.; Li S.; Leonard D. N.; Parish C. M.; Kotula P. G.; Varela M.; Schatz G. C.; Pennycook S. J.; Camden J. P.Correlated Optical Measurements and Plasmon Mapping of SilverNanorods. Nano Lett.2011, 11, 3482–3488. 10.1021/nl202027h. [DOI] [PubMed] [Google Scholar]
  20. Ghosh Chaudhuri R.; Paria S.Core/Shell Nanoparticles: Classes, Properties, Synthesis Mechanisms,Characterization, and Applications. Chem. Rev.2012, 112, 2373–2433. 10.1021/cr100449n. [DOI] [PubMed] [Google Scholar]
  21. Chen Y.; Wu H.; Li Z.; Wang P.; Yang L.; Fang Y.The Study of Surface Plasmon in Au/Ag Core/Shell CompoundNanoparticles. Plasmonics2012, 7, 509–513. 10.1007/s11468-012-9336-6. [DOI] [Google Scholar]
  22. Xu Z.; Hou Y.; Sun S.Magnetic Core/Shell Fe3O4/Au andFe3O4/Au/Ag Nanoparticles with Tunable PlasmonicProperties. J. Am. Chem. Soc.2007, 129, 8698–8699. 10.1021/ja073057v. [DOI] [PubMed] [Google Scholar]
  23. Li C.-Y.; Meng M.; Huang S.-C.; Li L.; Huang S.-R.; Chen S.; Meng L.-Y.; Panneerselvam R.; Zhang S.-J.; Ren B.; et al. “Smart” Ag Nanostructures for Plasmon-EnhancedSpectroscopies. J. Am. Chem. Soc.2015, 137, 13784–13787. 10.1021/jacs.5b09682. [DOI] [PubMed] [Google Scholar]
  24. Wulff G.On the Question of Speed of Growth and Dissolution of CrystalSurfaces. Z. Kristallogr. - Cryst. Mater.1901, 34, 449. 10.1524/zkri.1901.34.1.449. [DOI] [Google Scholar]
  25. Winterbottom W. L.Equilibrium Shape of a Small Particle in Contact with a ForeignSubstrate. Acta Metall.1967, 15, 303–310. 10.1016/0001-6160(67)90206-4. [DOI] [Google Scholar]
  26. Zia R. K. P.; Avron J. E.; Taylor J. E.The Summertop Construction: Crystals in a Corner. J. Stat. Phys.1988, 50, 727–736. 10.1007/bf01026498. [DOI] [Google Scholar]
  27. Marks L. D.Modified Wulff Constructions for Twinned Particles. J. Cryst. Growth1983, 61, 556–566. 10.1016/0022-0248(83)90184-7. [DOI] [Google Scholar]
  28. Frank F. C. InGrowth and Perfection of Crystals; Doremus R.H., Roberts B.W., Tumbull D., Eds.;Wiley: New York,1958. [Google Scholar]
  29. Ringe E.; Van Duyne R. P.; Marks L. D.Kinetic and Thermodynamic Modified Wulff Constructions for TwinnedNanoparticles. J. Phys. Chem. C2013, 117, 15859–15870. 10.1021/jp401566m. [DOI] [Google Scholar]
  30. Marks L. D.Modified Wulff Constructions for Twinned Particles. J. Cryst. Growth1983, 61, 556–566. 10.1016/0022-0248(83)90184-7. [DOI] [Google Scholar]
  31. Mie G.Beiträge zur Optik trüber Medien, speziell kolloidalerMetallösungen. Ann. Phys.1908, 330, 377–445. 10.1002/andp.19083300302. [DOI] [Google Scholar]
  32. Gans R.Über Die Form Ultramikroskopischer Goldteilchen. Ann. Phys.1912, 342, 881–900. 10.1002/andp.19123420503. [DOI] [Google Scholar]
  33. Yee K.Numerical solution of initial boundary value problems involvingmaxwell’s equations in isotropic media. IEEE Trans. Antennas Propag.1966, 14, 302–307. 10.1109/TAP.1966.1138693. [DOI] [Google Scholar]
  34. Draine B. T.; Flatau P. J.Discrete-Dipole Approximation For Scattering Calculations. J. Opt. Soc. Am. A1994, 11, 1491. 10.1364/josaa.11.001491. [DOI] [Google Scholar]
  35. Webb J. P.Application of the Finite-Element Method to Electromagnetic and ElectricalTopics. Rep. Prog. Phys.1995, 58, 1673–1712. 10.1088/0034-4885/58/12/002. [DOI] [Google Scholar]
  36. Myroshnychenko V.; Carbó-Argibay E.; Pastoriza-Santos I.; Pérez-Juste J.; Liz-Marzán L. M.; García de Abajo F. J.Modeling the Optical Response of Highly Faceted Metal Nanoparticles with aFully 3D Boundary Element Method. Adv. Mater.2008, 20, 4288–4293. 10.1002/adma.200703214. [DOI] [Google Scholar]
  37. Nelayah J.; Stéphan O.; Kociak M.; de Abajo F. J. G.; Henrard L.; Pastoriza-Santos I.; Liz-Marzán L. M.; Colliex C.Mapping Surface Plasmons on a Single Metallic Nanoparticle Using Sub-NmResolved EELS Spectrum-Imaging. Microsc. Microanal.2007, 13, 144–145. 10.1017/s1431927607076167. [DOI] [Google Scholar]
  38. Lesina A. C.; Vaccari A.; Berini P.; Ramunno L.On the Convergence and Accuracy of the FDTD Method forNanoplasmonics. Opt. Express2015, 23, 10481. 10.1364/oe.23.010481. [DOI] [PubMed] [Google Scholar]
  39. Pathak H.; Ji A.; Sharma R.; Sharma R. P.Optical Properties of Metal Subwavelength Structures for RealisticGeometries in a Dielectric Matrix Using DDA: An Error Analysis. Plasmonics2015, 10, 783–789. 10.1007/s11468-014-9865-2. [DOI] [Google Scholar]
  40. Yurkin M. A.; Hoekstra A. G.The Discrete Dipole Approximation: An Overview and RecentDevelopments. J. Quant. Spectrosc. Radiat. Transfer2007, 106, 558–589. 10.1016/j.jqsrt.2007.01.034. [DOI] [Google Scholar]
  41. Parsons J.; Burrows C. P.; Sambles J. R.; Barnes W. L.A Comparison of Techniques Used to Simulate the Scattering ofElectromagnetic Radiation by Metallic Nanostructures. J. Mod. Opt.2010, 57, 356–365. 10.1080/09500341003628702. [DOI] [Google Scholar]
  42. Johnson P. B.; Christy R. W.Optical Constants of Noble Metals. Phys. Rev. B: Solid State1972, 6, 4370–4379. 10.1103/physrevb.6.4370. [DOI] [Google Scholar]
  43. Palik E. D.Handbook of Optical Constants of Solids; SanDiego: Academic Press,1998. [Google Scholar]
  44. Rodríguez-de Marcos L. V.; Larruquert J. I.; Méndez J. A.; Aznárez J. A.Self-Consistent Optical Constants of SiO2 andTa2O5 Films. Opt. Mater. Express2016, 6, 3622. 10.1364/ome.6.003622. [DOI] [Google Scholar]
  45. Hartland G. V.Optical Studies of Dynamics in Noble Metal Nanostructures. Chem. Rev.2011, 111, 3858–3887. 10.1021/cr1002547. [DOI] [PubMed] [Google Scholar]
  46. Draine B. T.;Flatau P. J.. User Guide for the Discrete Dipole Approximation Code DDSCAT 6.1,2004.
  47. Lu S.; Yu H.; Gottheim S.; Gao H.; Desantis C. J.; Clark B. D.; Yang J.; Jacobson C. R.; Lu Z.; Nordlander P.; et al. Polymer-Directed Growth of Plasmonic Aluminum Nanocrystals. J. Am. Chem. Soc.2018, 140, 15412–15418. 10.1021/jacs.8b08937. [DOI] [PubMed] [Google Scholar]
  48. Kang H.; Buchman J. T.; Rodriguez R. S.; Ring H. L.; He J.; Bantz K. C.; Haynes C. L.Stabilization of Silver and Gold Nanoparticles: Preservation andImprovement of Plasmonic Functionalities. Chem. Rev.2019, 119, 664–699. 10.1021/acs.chemrev.8b00341. [DOI] [PubMed] [Google Scholar]
  49. Xia Y.; Xiong Y.; Lim B.; Skrabalak S. E.Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry MeetsComplex Physics?. Angew. Chem., Int. Ed.2009, 48, 60–103. 10.1002/anie.200802248. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Ringe E.; McMahon J. M.; Sohn K.; Cobley C.; Xia Y.; Huang J.; Schatz G. C.; Marks L. D.; Van Duyne R. P.Unraveling the Effects of Size, Composition, and Substrate on the LocalizedSurface Plasmon Resonance Frequencies of Gold and Silver Nanocubes: A SystematicSingle-Particle Approach. J. Phys. Chem. C2010, 114, 12511–12516. 10.1021/jp104366r. [DOI] [Google Scholar]
  51. Seo D.; Yoo C. I.; Chung I. S.; Park S. M.; Ryu S.; Song H.Shape Adjustment Between Multiply Twinned and Single-Crystalline PolyhedralGold Nanocrystals: Decahedra, Icosahedra, and Truncated Tetrahedra. J. Phys. Chem. C2008, 112, 2469–2475. 10.1021/jp7109498. [DOI] [Google Scholar]
  52. Chen H.; Kou X.; Yang Z.; Ni W.; Wang J.Shape-and Size-Dependent Refractive Index Sensitivity of GoldNanoparticles. Langmuir2008, 24, 5233–5237. 10.1021/la800305j. [DOI] [PubMed] [Google Scholar]
  53. González A. L.; Noguez C.Influence of Morphology on the Optical Properties of MetalNanoparticles. J. Comput. Theor. Nanosci.2007, 4, 231–238. 10.1166/jctn.2007.2309. [DOI] [Google Scholar]
  54. González A. L.; Noguez C.Optical Properties of Silver Nanoparticles. Phys. Status Solidi C2007, 4, 4118–4126. 10.1002/pssc.200675903. [DOI] [Google Scholar]
  55. Zhang J.; Li S.; Wu J.; Schatz G. C.; Mirkin C. A.Plasmon-Mediated Synthesis of Silver Triangular Bipyramids. Angew. Chem., Int. Ed.2009, 48, 7787–7791. 10.1002/anie.200903380. [DOI] [PMC free article] [PubMed] [Google Scholar]
  56. Hu J.; Chen L.; Lian Z.; Cao M.; Li H.; Sun W.; Tong N.; Zeng H.Deep-Ultraviolet-Blue-Light Surface Plasmon Resonance of Al and AlCore/Al2O3 Shell in Spherical and CylindricalNanostructures. J. Phys. Chem. C2012, 116, 15584–15590. 10.1021/jp305844g. [DOI] [Google Scholar]
  57. Arinze E. S.;Nyirjesy G.;Cheng Y.;Palmquist N.;Thon S. M.. Colloidal Quantum Dot Materials for InfraredOptoelectronics. In Infrared Remote Sensing and InstrumentationXXIII (Vol. 9608), Proceedings of the SPIE Optical Engineering and Applications, SanDiego, United States, Aug 9–13, 2015; Scholl M.S., Paez G., Eds.; InternationalSociety for Optics and Photonics, 2015.
  58. Gérard D.; Gray S. K.Aluminium Plasmonics. J. Phys. D: Appl. Phys.2015, 48, 184001. 10.1088/0022-3727/48/18/184001. [DOI] [Google Scholar]
  59. Rodríguez-Fernández J.; Pastoriza-Santos I.; Pérez-Juste J.; García De Abajo F. J.; Liz-Marzán L. M.The Effect of Silica Coating on the Optical Response of Sub-Micrometer GoldSpheres. J. Phys. Chem. C2007, 111, 13361–13366. 10.1021/jp073853n. [DOI] [Google Scholar]
  60. Banholzer M. J.; Harris N.; Millstone J. E.; Schatz G. C.; Mirkin C. A.Abnormally Large Plasmonic Shifts in Silica-Protected Gold TriangularNanoprisms. J. Phys. Chem. C2010, 114, 7521–7526. 10.1021/jp911889a. [DOI] [Google Scholar]
  61. Kobayashi Y.; Katakami H.; Mine E.; Nagao D.; Konno M.; Liz-Marzán L. M.Silica Coating of Silver Nanoparticles Using a Modified StöberMethod. J. Colloid Interface Sci.2005, 283, 392–396. 10.1016/j.jcis.2004.08.184. [DOI] [PubMed] [Google Scholar]
  62. Imaeda K.; Hasegawa S.; Imura K.Imaging of Plasmonic Eigen Modes in Gold Triangular Mesoplates byNear-Field Optical Microscopy. J. Phys. Chem. C2018, 122, 7399–7409. 10.1021/acs.jpcc.8b00678. [DOI] [Google Scholar]
  63. Tsai D.-S.; Chen C.-H.; Chou C.-C.Preparation and Characterization of Gold-Coated Silver Triangular Plateletsin Nanometer Scale. Mater. Chem. Phys.2005, 90, 361–366. 10.1016/j.matchemphys.2004.10.039. [DOI] [Google Scholar]
  64. Scarabelli L.; Coronado-Puchau M.; Giner-Casares J. J.; Langer J.; Liz-Marzán L. M.Monodisperse Gold Nanotriangles: Size Control, Large-Scale Self-Assembly,and Performance in Surface-Enhanced Raman Scattering. ACS Nano2014, 8, 5833–5842. 10.1021/nn500727w. [DOI] [PubMed] [Google Scholar]
  65. Imura K.; Ueno K.; Misawa H.; Okamoto H.; McArthur D.; Hourahine B.; Papoff F.Plasmon Modes in Single Gold Nanodiscs. Opt. Express2014, 22, 12189. 10.1364/oe.22.012189. [DOI] [PubMed] [Google Scholar]
  66. Matsuura T.; Imaeda K.; Hasegawa S.; Suzuki H.; Imura K.Characterization of Overlapped Plasmon Modes in a Gold Hexagonal PlateRevealed by Three-Dimensional near-Field Optical Microscopy. J. Phys. Chem. Lett.2019, 10, 819–824. 10.1021/acs.jpclett.8b03578. [DOI] [PubMed] [Google Scholar]
  67. Scopece D.SOWOS: An Open-Source Program for the Three-Dimensional WulffConstruction. J. Appl. Crystallogr.2013, 46, 811–816. 10.1107/s0021889813005426. [DOI] [Google Scholar]
  68. Oskooi A. F.; Roundy D.; Ibanescu M.; Bermel P.; Joannopoulos J. D.; Johnson S. G.Meep: A Flexible Free-Software Package for Electromagnetic Simulations bythe FDTD Method. Comput. Phys. Commun.2010, 181, 687–702. 10.1016/j.cpc.2009.11.008. [DOI] [Google Scholar]
  69. John F.; Sobh N.A.. DDSCAT Convert: A Target Generation Tool, version 2.0b;University of Illinois at Urbana-Champaign,2019.
  70. Vitos L.; Ruban A. V.; Skriver H. L.; Kollár J.The Surface Energy of Metals. Surf. Sci.1998, 411, 186–202. 10.1016/s0039-6028(98)00363-x. [DOI] [Google Scholar]
  71. Roosen A. R.; McCormack R. P.; Carter W. C.Wulffman: A Tool for the Calculation and Display of CrystalShapes. Comput. Mater. Sci.1998, 11, 16–26. 10.1016/s0927-0256(97)00167-5. [DOI] [Google Scholar]
  72. Kołątaj K.; Krajczewski J.; Kudelski A.Silver Nanoparticles with Many Sharp Apexes and Edges as EfficientNanoresonators for Shell-Isolated Nanoparticle-Enhanced RamanSpectroscopy. J. Phys. Chem. C2017, 121, 12383–12391. 10.1021/acs.jpcc.7b02695. [DOI] [Google Scholar]
  73. Zhang A.-Q.; Qian D.-J.; Chen M.Simulated Optical Properties of Noble Metallic Nanopolyhedra with DifferentShapes and Structures. Eur. Phys. J. D2013, 67, 1–9. 10.1140/epjd/e2013-40240-1. [DOI] [Google Scholar]
  74. Ringe E.; Mcmahon J. M.; Sohn K.; Cobley C.; Xia Y.; Huang J.; Schatz G. C.; Marks L. D.; Van Duyne R. P.Unraveling the Effects of Size, Composition, and Substrate on the LocalizedSurface Plasmon Resonance Frequencies of Gold and Silver Nanocubes: A SystematicSingle-Particle Approach. J. Phys. Chem. C2010, 114, 12511–12516. 10.1021/jp104366r. [DOI] [Google Scholar]

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