We present ensembles of surface-ordered nanoparticle arrangements, which are formed by template-assisted self-assembly of monodisperse, protein-coated gold nanoparticles in wrinkle templates. Centimeter-squared areas of highly regular, linear assemblies with tunable line width are fabricated and their extinction cross sections can be characterized by conventional UV/vis/NIR spectroscopy. Modeling based on electrodynamic simulations shows a clear signature of strong plasmonic coupling with an interparticle spacing of 1-2 nm. We find evidence for well-defined plasmonic modes of quasi-infinite chains, such as resonance splitting and multiple radiant modes. Beyond elementary simulations on the individual chain level, we introduce an advanced model, which considers the chain length distribution as well as disorder. The step toward macroscopic sample areas not only opens perspectives for a range of applications in sensing, plasmonic light harvesting, surface enhanced spectroscopy, and information technology but also eases the investigation of hybridization and metamaterial effects fundamentally.
We present ensembles of surface-ordered nanoparticle arrangements, which are formed by template-assisted self-assembly of monodisperse, protein-coated gold nanoparticles in wrinkle templates. Centimeter-squared areas of highly regular, linear assemblies with tunable line width are fabricated and their extinction cross sections can be characterized by conventional UV/vis/NIR spectroscopy. Modeling based on electrodynamic simulations shows a clear signature of strong plasmonic coupling with an interparticle spacing of 1-2 nm. We find evidence for well-defined plasmonic modes of quasi-infinite chains, such as resonance splitting and multiple radiant modes. Beyond elementary simulations on the individual chain level, we introduce an advanced model, which considers the chain length distribution as well as disorder. The step toward macroscopic sample areas not only opens perspectives for a range of applications in sensing, plasmonic light harvesting, surface enhanced spectroscopy, and information technology but also eases the investigation of hybridization and metamaterial effects fundamentally.
Entities:
Keywords:
electromagnetic simulations; gold nanoparticle chains; protein coating; strong plasmon coupling; superradiant and subradiant modes
Though the
investigation of plasmonic resonances is a classic topic of optics,
the modern renaissance of plasmonic systems as tools for nanophotonics
is intimately related to the study of strongly coupled plasmonic nanostructures.
Strong coupling of localized plasmon resonances opens opportunities
for tailoring near-fields and inducing drastic field enhancement,
allows distance dependent tuning of absorption and scattering characteristics,
and even enables the transition from localized resonances to guided
plasmon polaritons.[1] Consequently, a large
range of applications, including surface-enhanced Raman spectroscopy
(SERS),[2−8] the fabrication of optical metamaterials,[9−11] ultracompact
optoelectronic circuitry,[12−15] or plasmon-based light harvesting systems,[16,17] has been targeted.In all these applications and fundamental
studies, the limited scalability with which strongly coupled plasmonic
nanostructures can be fabricated is recognized as a bottleneck; many
prospective applications such as plasmonic light harvesting require
scaling to macroscopic areas at low costs. Similarly, experimental
investigations of strongly coupling nanostructures are hampered by
the fact that they have to be carried out on microscopic areas, which
dramatically increases the instrumental efforts.Compared to
lithographically prepared structures, arrangements of nanoparticles
produced by wet-chemical approaches are advantageous as these building
blocks offer high crystallinity and can be synthesized in bulk processes
that are scalable.[18,19] Independent of the preparation
method, strong coupling between plasmonic components is possible only
for nanometer-sized gaps.[20,21] Successful assembly
of nanoparticles into such close-packed arrangements has been facilitated
mainly by two techniques: chemical linking using either bifunctional
molecules or specifically tailored DNA strands and convective assembly
on lithographically structured templates.[22−28] An advantage of these approaches is that the limited resolution
of lithographic techniques, which ultimately determines the minimal
gap size, can be overcome. Indeed, studies on close-packed assemblies
combining single particle spectroscopy with high-resolution electron
microscopy have contributed remarkably to a fundamental understanding
of the optical properties of plasmonic nanoparticles and their arrangements.[29−31] Besides small clusters,[32,33] special attention has
been dedicated to the investigation of linear nanoparticle chains,[34,35] which show great potential for applications that require waveguiding
below the diffraction limit.[36] An important
feature of these complex particle assemblies is their anisotropic
optical response, in particular, a polarization dependency of the
extinction cross section.The fabrication of surface-supported
particle assemblies with well-defined orientation is so far severely
limited with regards to scalability. Chemical linking generally suffers
from low yields and requires subsequent fractionation, whereas convective
particle assembly demands template fabrication with nanoscale precision.
Commonly employed techniques for template structuring, such as e-beam
lithography or focused ion beam milling, run into the same scalability
issues as direct lithographic fabrication of plasmonic nanostructures.
Recently, we reported on the wrinkle-assisted assembly of nanoparticles
as a lithography-free alternative for template-assisted self-assembly.[37,38] This method circumvents typical scalability restrictions of conventional
nanofabrication techniques and is capable of producing regular, close-packed
assemblies as demonstrated for a variety of particle systems.[39,40] However, the essential goal of creating assemblies of plasmonic
nanoparticles that are both strongly coupling and at the same time
homogeneous in their optical properties on macroscopic areas has not
been achieved so far. In the present study, we demonstrate this crucial
step toward the precise assembly of macroscopic scale arrays for the
case of spherical gold nanoparticles that are coated with a nanoscopic
protein shell. Utilizing a purely bottom-up, template-assisted approach,
highly ordered, linear arrangements of closely spaced plasmonic nanoparticles,
thus, can be fabricated with unprecedented uniformity over centimeter-squared
areas. Strong plasmonic coupling between the gold nanoparticles gives
rise to both dipolar and extremely separation-sensitive quadrupolar
coupling modes. The well-defined plasmonic mode structure of the assembled
nanoparticle chains is maintained on centimeter-squared areas, as
we show by comparison of spectroscopic measurements and electrodynamic
simulations. In particular, we find that effective interparticle distances
(IPDs) of 1–2 nm can be homogeneously achieved over these areas
and that consequently, collective resonances can be shifted up to
a wavelength of 1500 nm, using particulate building blocks with an
isolated plasmon resonance around 500 nm.
Colloidal Building Blocks
Spherical gold nanoparticles with an average diameter of 78 ±
4 nm were synthesized via a two-step seeded growth process.[41] Template-assisted organization imposes several
requirements on the colloidal interactions of the employed particles;
long-range electrostatic attraction between the template and the particles
has to be avoided and at the same time, the particles should maintain
colloidal stability at elevated concentrations and possess hydrophilic
surfaces.[42] As prepared, the particles
are coated by a layer of cetyltrimethylammonium bromide (CTAB), of
which a large excess present in solution is necessary in order to
ensure colloidal stability. During template-assisted assembly, this
surfactant strongly adsorbs onto the surface of the used silica substrate,
changing the wettability in an unfavorable fashion. Thus, the removal
of CTAB is desirable for successful particle assembly.If strongly
coupled particle assemblies are targeted, a second aspect of the ligand
coating becomes vital: the ligand layer ultimately limits the minimal
interparticle distance. Indeed, earlier studies using CTAB-coated
particles showed that only interparticle distances of 8 nm could be
attained,[39] which is comparable to twice
the thickness of a CTAB layer.[43] A suitable
surface modification is achieved by ligand exchange with bovine serum
albumin (BSA), which yields stable particles with a sufficiently thin
shell and at the same time allows the complete removal of CTAB from
the solution.[44,45] For pH values above the isoelectric
point of BSA, these particles have a negative zeta potential around
−45 mV and can be used for the assembly process. Details on
the employed gold nanoparticles can be found in the Supporting Information, including optical spectra in suspension
before and after surface modification as well as pH dependent zeta
potential measurements and a TEM characterization of the protein-coated
particles (see Supporting Information,
Figures S1 and S2). Whereas the dried protein shell itself is only
few nanometers thick, interparticle distances even smaller than the
resolution limit of our TEM can occur as the shell is soft and deformable.
Thus, in close-packed assemblies very strong plasmonic coupling between
the particles becomes feasible.
Nanoparticle Assembly
For templating we employed wrinkled elastomer stamps, which can
be fabricated with the desired geometry by simple plasma oxidation
of macroscopically strained PDMS stripes (see Figure 1A). Particle assembly into close-packed, linear chains is
facilitated by spin coating. The subsequent transfer onto flat substrates
can be accomplished effectively by wet contact printing (Figure 1A). Whereas a variety of parameters (pH, particle
concentration, rotational acceleration and speed) influences the assembly
structure formed during spin coating, we found adjustment of the wrinkle
geometry to be the most reliable method for tuning the width of the
particle chains. By varying the wrinkle periodicity in the range between
360 and 1060 nm, while maintaining adequate amplitudes for confinement,
we were able to assemble the gold nanoparticles into close-packed
single particle, dimer, and even tetramer lines. AFM images of the
particle-filled PDMS stamps are included in Figure S3 in the Supporting Information.
Figure 1
Assembly of nanoparticle chains: structured templates
were fabricated by plasma oxidation of stretched PDMS stripes and
subsequent relaxation (A). After spin coating the nanoparticle assemblies
were transferred onto flat substrates by wet contact printing. Depending
on the geometry of the employed wrinkles, single particle chains (B),
dimer chains (C), or tetramer chains (D) were obtained with homogeneous
surface coverage over centimeter-squared-scale areas. In reflection,
the nanoparticle gratings diffract light (photographs).
Figure 1B–D display the morphology of the colloidal
arrangements after transfer onto flat quartz substrates covering all
length scales from nanoscopic (SEM), via microscopic (AFM) up to macroscopic
(photography) dimensions. A quantitative transfer was achieved for
all samples, yielding highly regular 1- and 2-dimensional nanoparticle
chains in parallel orientation. The inset photographs in Figure 1B–D recorded under sideways illumination
show strong iridescence due to diffraction by the periodic arrangement
of the parallel chains. Clearly, the presented method enables the
fabrication of nanoparticle chains with structural quality comparable
to colloidal arrangements produced by intricate assembly techniques
such as DNA strand linking or advanced lithographic templating.[19,22,23,27,28] In contrast to those works, we achieved
regular structure formation over centimeter-squared-scale areas, which
for the first time allowed a correlation of extinction spectra, obtained
by standard UV/vis/NIR spectroscopy, with simulated spectra of ideal
particle chains.Assembly of nanoparticle chains: structured templates
were fabricated by plasma oxidation of stretched PDMS stripes and
subsequent relaxation (A). After spin coating the nanoparticle assemblies
were transferred onto flat substrates by wet contact printing. Depending
on the geometry of the employed wrinkles, single particle chains (B),
dimer chains (C), or tetramer chains (D) were obtained with homogeneous
surface coverage over centimeter-squared-scale areas. In reflection,
the nanoparticle gratings diffract light (photographs).
Optical Characterization
For optical
characterization of the particle assemblies, we utilized a commercial
dual beam spectrometer configured in transmission geometry. For the
entire spectral range probed, a halogen lamp was employed as the light
source. Between the monochromator and the sample a rotatable polarizer
was mounted. Light passing through the aligned samples was recorded
by a detector array consisting of a photomultiplier tube covering
the spectrum from 400 to 900 nm and a PbS detector for the near-infrared
(NIR) regime between 900 and 2500 nm. Note that in the employed setup,
the sample is irradiated under normal incidence, where grating effects
that are responsible for the iridescent colors shown in Figure 1 are of minor importance. Indeed, under this illumination
angle (Figure 2) the samples exhibit a grayish
appearance, and despite the surface coverage not exceeding 25% of
a dense particle monolayer on any substrate, the extinction caused
by the assemblies is significant.
Figure 2
Optical
characterization of nanoparticle chain assemblies: the polarization-dependent
extinction spectra of single particle chains (A), dimer chains (B),
and tetramer chains (C) display strong optical anisotropy with regard
to the relative orientation between polarizer and assembled lines.
Inset photographs illustrate the significant extinction caused by
the nanoparticle films. The extinction at the absolute maxima follows
a cos2 dependency as a function of the polarization angle
θ (bottom).
Far-field UV/vis/NIR spectra
recorded in air are displayed in Figure 2.
For each morphology, 11 polarization angles between 0° and 90°
relative orientation to the chain axis were probed. In contrast to
isolated particles, which display a polarization-independent, single
plasmon resonance peak at 520 nm (see Supporting
Information, Figure S4) the microscopic organization of nanoparticles
in parallel chains gives rise to a pronounced macroscopic optical
anisotropy. Generally, for polarization perpendicular to the chains,
extinction is limited mostly to the visible spectrum, whereas rotation
of the polarization angle toward parallel orientation leads to increasing
extinction in the near-infrared range. As shown in the lower section
of Figure 2, the extinction efficiency of the
pronounced NIR bands exhibit a clear cos2 dependence on
the polarizer angle, which is typical for dipolar plasmonic modes.Optical
characterization of nanoparticle chain assemblies: the polarization-dependent
extinction spectra of single particle chains (A), dimer chains (B),
and tetramer chains (C) display strong optical anisotropy with regard
to the relative orientation between polarizer and assembled lines.
Inset photographs illustrate the significant extinction caused by
the nanoparticle films. The extinction at the absolute maxima follows
a cos2 dependency as a function of the polarization angle
θ (bottom).
Individual Chain Approximation
For an in-depth analysis of the measured spectra it is crucial
to consider the probed surface area. In all measurements, the size
of the illuminated spot was kept constant at approximately 1 ×
10 mm2 corresponding to 28 000 single particle lines,
13 000 dimer lines, and 9 000 tetramer lines probed.
Intriguingly, even with these huge ensembles we observe a distinct
set of peaks for each chain morphology. We start the discussion of
these features by considering individual chains and subsequently expand
the model to assess the influence of defects (chain length distribution
and interparticle distance fluctuations) as well as grating effects.As the optical response of aligned nanoparticle chains is fully
described by their extinction cross sections for parallel and perpendicularly
polarized excitation, that is, their longitudinal and transversal
modes, we will focus on the analysis of these two polarization states.
In Figure 3, experimentally determined extinction
spectra of single particle, dimer, and tetramer chain ensembles are
compared to simulation data modeled for ideal chains via the generalized
multisphere Mie theory (GMMT).[46,47] The optical response
of the investigated chain ensembles is largely determined by plasmonic
coupling between adjacent nanoparticles, which allows a description
via theoretical modeling of individual chains (see Figure 3).
Figure 3
Experimental
and modeled extinction cross sections of single particle (A), dimer
(B), and tetramer chains (C): the spectra in the lower frames were
modeled via GMMT for corresponding chain types consisting of 10 repeat
units each. Blue curves in the experimental spectra illustrate the
nongrating case for transversal polarization. FDTD modeled surface
charge images of a single particle chain (D): the upper plot (1) features
the dipolar transversal mode D (electric polarization
vector E perpendicular to particle line, wave vector k perpendicular to particle line). The lower plot highlights
the longitudinal subradiant and superradiant modes (2, 3). Black lines
indicate the surface charge density integrated along the particle
chain and perpendicular to it, respectively. Modeled surface charge
images of a dimer chain (E): the left graph shows
the transversal modes, namely, a dipolar D (5) and
a quadrupolar QT coupling mode (4). The
right graph displays the longitudinal quadrupolar coupling mode QL (6) and the radiant longitudinal modes (7,
8). The surface charge intensities were adjusted for better clarity.
Due to the limited resolution of SEM on
nonconducting surfaces, a direct determination of the interparticle
distance is not possible. We therefore took advantage of the well-known
plasmon ruler concept, which allows estimating interparticle distances
from the characteristic position of the energetically lowest resonance
(superradiant mode).[48] The spectral position
of the superradiant mode is practically independent of the chain length
above a threshold value of 10 repeat units, known as the “infinite
chain limit”.[34,49,50] Thus, we performed simulations for 10 repeat units and varied the
interparticle distance. The best agreement was found for a gap size
of 1.5 nm (see Figure 3). Further details on
the selection of the parameters can be found in the Supporting Information in Figure S5 and S6. Despite the simplicity
of this first approximation, we found a good agreement with the experimental
data of the single particle and dimer chains (Figure 3). This elementary model also provides information beyond
an estimation of the interparticle distance. The simulations predict
the appearance of quadrupolar coupling modes for dimer and tetramer
chains at approximately 530 nm, which are indeed visible in the experimental
spectra. These modes will be discussed in detail later. In the case
of the tetramer chains, the measured optical response is generally
consistent with the simulations. However, the Fano-like resonances
present in the modeled spectra at around 800 nm could not be observed
experimentally. Fano resonances are very sensitive toward geometrical
variations[51] and most likely not resolved
in the measured spectra due to averaging effects. Also, the experimental
tetramer chain spectrum displays a stronger red shift of the superradiant
mode than predicted by the simulations. For further discussion, we
will therefore focus on the single particle and dimer chains, whose
spectra exhibit remarkable agreement with the optical response of
ideal colloidal assemblies modeled on the individual chain level.The physical meaning of different plasmonic modes can be seen from
the surface charge distributions at the specific resonance frequencies
(Figure 3D/E). In the case of the single particle
chain exposed to a polarization perpendicular to the chain axis (transversal
excitation), we observe one plasmonic mode (peak 1) only. As expected,
this transversal mode is located close to the single particle resonance
in air (520 nm). The surface charge distribution pattern identifies
this resonance D as a nonradiant dipolar mode, which
is characterized by its stronger absorption than scattering cross
section. For a better understanding of the complex charge distributions
we integrated the surface charge density along the polarization axis
(black lines in Figure 3D and E). An exposure
to a polarization parallel to the chain axis (longitudinal excitation)
reveals several radiant modes (peaks 2 and 3), for which scattering
is predominant over absorption. These so-called chain plasmon resonances,
termed as super- and subradiant modes, feature charge density distributions
along the main chain axis that can be described by standing wave patterns.[20] Whereas the most prominent feature, the energetically
lowest mode, is defined by the presence of two nodal points at the
chain ends, the less pronounced subradiant modes possess additional
nodes in the charge density distribution. For longitudinal excitation
at the corresponding wavelengths, the chain exhibits a net dipole
moment allowing the experimental detection of these resonances as
bright modes.Densely packed dimer chains display similar mode
characteristics as single particle chains. The surface charge distributions
modeled for a hexagonal arrangement are presented in Figure 3E. Hereby, an interparticle spacing of 1.5 nm was
assumed. For transversal excitation, the additional particle line
gives rise to a new spectral feature. Due to the close packing of
the nanoparticles, the transversal resonance peak splits into two
distinct modes: a dipolar coupling mode D near 600
nm (peak 5) and an energetically higher, quadrupolar coupling mode QT (peak 4). Compared to the dipolar mode the
quadrupolar mode displays one more polarity change as depicted by
the integrated surface charge density (black line). Further investigations
of isolated dimers are included in the Supporting
Information and prove that the spectral position of the quadrupolar
mode is extremely distance-sensitive (visible only for interparticle
distances below 3 nm) but nearly independent of the relative orientation
(Supporting Information Figures S7, S8,
and S9). In fact, the surface charge distribution of the longitudinal,
quadrupolar coupling mode QL displays
a close resemblance to the transversal mode QT and can be excited with the same energy (peak 6). Our experimental
spectra clearly show the presence of the quadrupolar mode as a left
shoulder near 530 nm for both transversal and longitudinal polarization.
To the best of our knowledge, this is the first report of such a highly
sensitive plasmonic coupling effect being observed experimentally
by a macroscopic ensemble measurement. For longitudinal excitation,
the dimer chain further exhibits bright radiant modes that display
wave-like surface charge distributions similar to that of the single
particle line. In direct comparison, the longitudinal modes are more
red shifted for the dimer line, which can be attributed to stronger
retardation.[35] Though the charge distribution
assigned to the superradiant mode (peak 8) of the dimer chains shows
strong similarity to the single particle chain, the subradiant mode
(peak 7) exhibits two knots of the surface charge distribution concentrated
near the center of the assembly.So far, we have dedicated our
attention to individual particle chains with a fixed number of repeat
units, fixed interparticle distance, and without interaction to neighboring
chains. This simple approach is a good first approximation but cannot
fully describe the macroscopic optical response of the fabricated
chain ensembles. SEM investigations show that structural defects can
be avoided only to a certain degree. During assembly processes based
on controlled drying, attractive capillary interaction between adjacent
particles, jumping menisci, and shrinking of the originally hydrated
shell can induce distance variations along the chains. In the case
of plasmonic particles these variations can have a pronounced influence
on the optical properties of the assembled structures. We find two
characteristic types of defects: first, occasionally particles in
the chain are missing; second, within the chains the gap size is not
constant. In the following, we thus extend our initial approach from
individual chain simulations to modeling of larger ensembles consisting
of chains with different lengths and variable interparticle distance.Experimental
and modeled extinction cross sections of single particle (A), dimer
(B), and tetramer chains (C): the spectra in the lower frames were
modeled via GMMT for corresponding chain types consisting of 10 repeat
units each. Blue curves in the experimental spectra illustrate the
nongrating case for transversal polarization. FDTD modeled surface
charge images of a single particle chain (D): the upper plot (1) features
the dipolar transversal mode D (electric polarization
vector E perpendicular to particle line, wave vector k perpendicular to particle line). The lower plot highlights
the longitudinal subradiant and superradiant modes (2, 3). Black lines
indicate the surface charge density integrated along the particle
chain and perpendicular to it, respectively. Modeled surface charge
images of a dimer chain (E): the left graph shows
the transversal modes, namely, a dipolar D (5) and
a quadrupolar QT coupling mode (4). The
right graph displays the longitudinal quadrupolar coupling mode QL (6) and the radiant longitudinal modes (7,
8). The surface charge intensities were adjusted for better clarity.
Variation of the Chain
Length
We therefore conducted simulations of chains containing
up to 120 particles arranged in single particle and dimer lines. The
results are displayed in Figure 4. For both
chain morphologies, the position of the superradiant mode converges
to a fixed value at around 10 repeat units. However, raising the chain
length further does have a pronounced influence on the number and
the spectral positions of the subradiant modes. With increasing chain
length, the subradiant modes converge toward the energy level of the
superradiant mode, which is accompanied by considerable spectral broadening.
In consequence, for both morphologies the longitudinal spectra of
very long chains (repeat units ≫10) are dominated by a single,
broad peak. In this regime, the subradiant modes are observed as a
wavy left shoulder of the respective superradiant mode. Thus, the
common approximation of long particle chains by a simplified model
with 10 repeat units can be considered valid only for certain resonances
(here: D, QT, QL, and the superradiant mode), whereas the appearance
of the subradiant modes changes with the number of repeat units even
for much longer chains.
Figure 4
GMMT simulations of the longitudinal modes calculated
with a constant interparticle distance of 1.5 nm and varying chain
lengths: extinction spectra of single particle (A) and dimer (B) lines
are shown for chain lengths up to 60 repeat units. The normalized
extinction is mapped for all chain lengths in the image plots below
the graphs. For both chain types, the energy of the superradiant mode
converges toward a fixed value around 10 repeat units. Additional
subradiant modes that occur with increasing chain length converge
to the spectral position of the superradiant mode.
GMMT simulations of the longitudinal modes calculated
with a constant interparticle distance of 1.5 nm and varying chain
lengths: extinction spectra of single particle (A) and dimer (B) lines
are shown for chain lengths up to 60 repeat units. The normalized
extinction is mapped for all chain lengths in the image plots below
the graphs. For both chain types, the energy of the superradiant mode
converges toward a fixed value around 10 repeat units. Additional
subradiant modes that occur with increasing chain length converge
to the spectral position of the superradiant mode.To assess the amount of defects in our assemblies,
we studied the single particle and dimer lines via SEM and evaluated
their chain length distributions. Though plasmonic coupling has been
demonstrated for interparticle distances as large as 5× the particle
radius for gold particles, the observed spectral shift decays almost
exponentially with increasing gap size.[52,53] Significant
chain coupling is only feasible for distances below one particle radius
(see Supporting Information, Figure S10).
Consequently, we have chosen a maximum interparticle distance of 40
nm as the cutoff criterion for the statistical analysis. The determined
chain length distributions are displayed in Figure 5. Clearly, the vast majority of the nanoparticles is located
inside chain fragments containing more than 10 repeat units (84% in
case of single particle lines and 96% for dimer lines). It must be
noted that the maximum chain length measurable in the highly magnified
SEM micrographs is limited to about 6 μm, for which the content
of long chains may even be underestimated. Especially for the dimer
chains, the limiting effect of finite image sizes is reflected in
the statistical analysis by an accumulation of counts around 60 dimers
(Figure 5B). However, due to the discussed
convergence of the radiant modes, the impact of even higher chain
lengths on the optical properties is minimal.
Figure 5
Statistical chain length distributions of single particle
(A) and dimer lines (B) obtained from SEM images: the inset plots
compare measured and modeled spectra. Besides GMMT simulations of
individual long chains (120 particles, blue), averaged extinction
spectra (green) calculated from the experimentally determined chain
length distributions are shown.
Utilizing the
previously established library of simulated spectra (Figure 4), we calculated ensemble extinction spectra of
single particle and dimer lines by averaging based on the experimentally
determined chain length distributions. The results are displayed in
the insets of Figure 5 and compared to the
measured optical responses as well as the simulated extinction spectra
of extremely long, individual chains containing 120 particles. For
the single particle lines, the averaged spectrum nearly matches the
spectrum of an individual, long chain displaying little spectral broadening
and only a minor blue shift. Further, this averaged ensemble spectrum
provides an adequate description of the spectral position and form
of the dominant longitudinal peak observed for the macroscopic ensemble.
The averaging results cannot reproduce the left shoulder of the superradiant
mode visible in the measured spectrum. Similar observations arise
for the dimer lines. Again, the measured and modeled spectra are in
excellent agreement regarding the position of the superradiant mode.
However, the measurements clearly display a spectral modulation in
the form of an additional peak near 700 nm not predicted by the averaged
simulations as well as an unexpectedly sharp decay of the energetically
lowest mode in the NIR region.Possible reasons for these features
are collective phenomena, dark mode excitation, or disorder. As the
position of the spectral notch at 800 nm and the fast decay around
1200 nm both correspond to the periodicity of the line ensemble (d = 770 nm, see Figure 3B), grating
effects are the most likely cause of these features. Grating effects
due to the periodic arrangement of the nanoparticle lines manifest
themselves in the transversal modes as deviations from the exponential
decay. The expected spectral response in the absence of grating effects
is illustrated for the transversal modes by the blue curves in Figure 3. Qualitatively similar effects are expected for
the peak shapes in the longitudinal modes. This could explain the
sharp decay of the superradiant mode. Further discussion is included
in the Supporting Information (Figure S11).
Another possible explanation could be the excitation of dark modes,
which results in a similar signature with a spectral notch.[54,55] These interesting additional features will be subject to future
investigations.Statistical chain length distributions of single particle
(A) and dimer lines (B) obtained from SEM images: the inset plots
compare measured and modeled spectra. Besides GMMT simulations of
individual long chains (120 particles, blue), averaged extinction
spectra (green) calculated from the experimentally determined chain
length distributions are shown.
Impact of Gap Size Variations within the Particle Chains
In the final section, we investigate the influence of irregular interparticle
distances on the optical properties of individual chains of coupling
nanoparticles and the respective chain ensembles. For this purpose,
the spectral responses of linear assemblies containing 10 repeat units
were modeled for an array of configurations with varying interparticle
distances randomly distributed along the chains. The resulting longitudinal
extinction spectra are illustrated for a selection of single particle
and dimer chain ensembles with different interparticle distance variability
in Figure 6A and B next to the corresponding
gap size distributions. As references the spectra of chains modeled
with a constant gap size of 1.5 nm (in green color) are included as
well as the measured spectra (in orange color). A red shift compared
to the reference could be observed only when allowing gap sizes smaller
than 1.5 nm. Larger interparticle distances lead to an overall blue
shift accompanied by spectral broadening. Thus, the spectra of individual
chains react sensitively to variations of the gap sizes.
Figure 6
Influence
of disorder inside single particle (A) and dimer (B) chains with 10
repeat units: extinction spectra for randomly varied gap sizes (gray),
averaged spectra (red/blue), and constant 1.5 nm gap size (green)
are plotted next to the corresponding statistical distributions of
the gap size. The position of the superradiant mode is correlated
to the amount of disorder and allows estimating the gap size inside
the fabricated single particle (C) and dimer (D) chains. All spectra
were calculated using GMMT.
The
relation of the superradiant mode λsuper to the mean
interparticle distance (IPD) is of general interest. We describe the
relationship in Figure 6C and D by the allometric
power lawThe coefficients a, b, and c are listed in the Supporting Information (Table S2). Since the peak position of the superradiant mode is
largely independent of the chain length above the “infinite
chain limit”, a comparison with the experimentally observed
lowest energy peak enables an estimation of the effective gap size.
For the single particle lines (peak located at 750 nm), our model
yields a dominant gap size close to 2 nm. The superradiant mode of
the dimer chains (peak located at 1025 nm) corresponds to an even
smaller effective gap size of approximately 1 nm. This more sophisticated
model is in excellent agreement with our first approximation assuming
a fixed interparticle distance. Including the disorder in the particle
chain calculations, we obtained a robust criterion to prove the realization
of strongly coupled plasmonic modes over centimeter scale dimensions.Influence
of disorder inside single particle (A) and dimer (B) chains with 10
repeat units: extinction spectra for randomly varied gap sizes (gray),
averaged spectra (red/blue), and constant 1.5 nm gap size (green)
are plotted next to the corresponding statistical distributions of
the gap size. The position of the superradiant mode is correlated
to the amount of disorder and allows estimating the gap size inside
the fabricated single particle (C) and dimer (D) chains. All spectra
were calculated using GMMT.
Conclusion
Our study highlights the ability of wrinkle-assisted
particle assembly for precise nanofabrication over macroscopic areas,
when combined with appropriate soft spacers. Already for the simple
case of linear arrangements, strong coupling attributable to interparticle
distances of 1–2 nm induces a remarkable shift of the main
resonance from around 500 nm up to 1500 nm. This opens exciting perspectives
for light harvesting because almost the entire range of the solar
spectrum can be covered with one simple particulate building block.[56] Likewise, we expect the assemblies to be of
great interest for applications in surface-enhanced spectroscopy.
Already with interparticle distances of 8 nm, high SERS enhancement
factors of 108 were observed for similar arrangements,[39] and SERS effects are expected to increase by
orders of magnitude upon further minimization of the gap size. Finally,
the strong coupling we have observed should impact on plasmonic waveguiding
properties, especially because the assemblies can be fabricated with
macroscopic lengths.Beyond the specific example of parallel
lines, this concept can be expanded to more complex geometries. We
have demonstrated in earlier work for polymeric model particles that
wettability structuring of substrates provides control over the transfer.[42] Hydrophobic surface modifications effectively
passivate the substrates against particle attachment. Thus, wettability
structuring on the micron scale is a convenient way for breaking symmetries
and enables the transition from infinite chains to arrangements of
finite length (plasmonic polymers), which in turn has direct consequences
on their scattering and absorption properties.[34,35,57] The transfer printing process can be applied
multiple times to the same substrate.[42] Thus, not only are fishnet architectures attainable,[38] but different particle types can also be combined
with each other in a well-defined fashion.[58,59] Concerning the particle types, this concept is indeed generic because
the protein coating governs the colloidal interactions and wetting
as well as the interparticle spacing, rather than the nature of the
core. We would like to point out that we have limited our fabrication
to centimeter-squared areas, but the procedure is readily scalable.
The concept in this article involves exclusively macroscopic processing
steps, namely, macroscopic strain and relaxation, plasma treatment,
suspension drying, and printing transfer. We therefore believe that
the approach presented here opens new avenues for both basic scientific
investigations of strong coupling effects and a range of practical
applications.
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