Fabrication, characterization, and optical properties of gold nanoparticle/porous alumina composites: The nonscattering Maxwell-Garnett limit

Article abstract of DOI:10.1021/jp962685o

We have been exploring the optical properties of nanoscopic gold particles prepared by electrochemically depositing Au within the pores of nanoporous alumina membranes. Maxwell-Garnet (MG) effective medium theory has been used as a guide for modeling the optical properties of these Au nanoparticle/alumina membrane composites. MG theory is, however, rigorously applicable only in the limit of metal nanoparticles with infinitesimally small diameters. As a result, the position of the plasmon resonance absorption predicted theoretically using MG theory was always blue-shifted relative to the position of the experimental absorption band. The smallest diameter particles investigated in this prior work had diameters of 60 nm. Au nanoparticles with smaller diameters (52 nm down to 16 nm) were prepared, and the optical properties of composites containing these nanoparticles are described here. The λ_max values for the smallest diameter particles are essentially identical with the values predicted by MG theory. Hence, we have succeeded in preparing Au nanoparticles that experimentally achieve the MG-predicted plasmon resonance absorption limit.

Full text of DOI:10.1021/jp962685o

1548
J. Phys. Chem. B 1997, 101, 1548-1555
Fabrication, Characterization, and Optical Properties of Gold Nanoparticle/Porous Alumina
Composites: The Nonscattering Maxwell-Garnett Limit
Gabor L. Hornyak, Charles J. Patrissi, and Charles R. Martin*
Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523-1872
X
ReceiVed: August 30, 1996; In Final Form: December 12, 1996
We have been exploring the optical properties of nanoscopic gold particles prepared by electrochemically
depositing Au within the pores of nanoporous alumina membranes. Maxwell-Garnet (MG) effective medium
theory has been used as a guide for modeling the optical properties of these Au nanoparticle/alumina membrane
composites. MG theory is, however, rigorously applicable only in the limit of metal nanoparticles with
infinitesimally small diameters. As a result, the position of the plasmon resonance absorption predicted
theoretically using MG theory was always blue-shifted relative to the position of the experimental absorption
band. The smallest diameter particles investigated in this prior work had diameters of 60 nm. Au nanoparticles
with smaller diameters (52 nm down to 16 nm) were prepared, and the optical properties of composites
containing these nanoparticles are described here. The λmax values for the smallest diameter particles are
essentially identical with the values predicted by MG theory. Hence, we have succeeded in preparing Au
nanoparticles that experimentally achieve the MG-predicted plasmon resonance absorption limit.
Introduction
diameters (52 nm down to 16 nm). We have found, again, that
as the Au nanoparticle diameter decreases, the experimental λmax
approaches the MG-predicted value. Furthermore, the λmax
values for the smallest diameter particles (16 nm) are essentially
identical with the values predicted by MG theory. Hence, we
have succeeded in preparing Au nanoparticles which experi-
mentally achieve the MG-predicted plasmon resonance absorp-
tion limit. The results of these investigations are described here.
We1,2 and others have been investigating the properties of
nanomaterials prepared within the pores of nanoporous alumina
membranes. These membranes are prepared electrochemically
from aluminum metal and contain monodisperse, cylindrical
3
1
-4
pores that are packed into a regular hexagonal array.
The
diameter of the pores in these membranes can be varied by
controlling the potential used during the electrochemical
preparation. In addition, these membranes are highly optically
transparent, which makes them ideal for visible spectroscopic
characterization of nanoparticles deposited within the pores of
these membranes.2
Experimental Section
Preparation of the Nanoporous Alumina Template Mem-
branes. The template membranes were prepared by anodizing
high-purity (>99.999%) aluminum (Reynolds). Prior to anod-
ization, the Al was rerolled by PV&D Research Materials Inc.
to a thickness of 1 mm. Anodes of dimensions 8 × 10 cm
were cut from this Al sheet. The anodes were degreased in a
We have been exploring the optical properties of nanoscopic
gold particles prepared by electrochemically depositing Au
1,2
within the pores of such alumina membranes. In particular,
we are interested in investigating the effect of Au nanoparticle
diameter (determined by the pore diameter of the alumina
membrane) and length (determined by the quantity of Au
deposited within the pores) on the position of the plasmon
resonance adsorption of the nanoparticle.2 We have used
Maxwell-Garnet (MG) effective medium theory as a guide for
modeling the optical properties of these Au nanoparticle/alumina
1
:2:1 (by volume) ethanol-dichloromethane-acetone solution
and then rinsed with acetone and distilled water. The anodes
were then etched in 0.05 M NaOH for 10 min, rinsed in purified
water, 50% (w/w) nitric acid, and then water again. The purified
water was obtained by passing house-distilled water through a
Milli-Q (Millipore) water-purification system. This water was
used for all aqueous solutions.
2
membrane composites. MG theory is, however, rigorously
applicable only in the limit of metal nanoparticles with
infinitesimally small diameters. As a result, the position of the
plasmon resonance absorption predicted theoretically using MG
The Al anodes were then electropolished in a 2:3 (v/v)
phosphoric/sulfuric acid solution that was 1% in glycerol. An
2
electropolishing current density of ca. 75 mA/cm was used,
theory was always blue-shifted relative to the position of the
and the cell was maintained at a temperature of 70-80 °C.5
Convection was provided by nitrogen gas bubbling and by
mechanical stirring. Polishing was done for approximately 10
min until a mirror finish was obtained. The electropolished Al
was rinsed immediately in distilled water (often requiring a
strong stream to remove the tenacious gelatinous oxide layer),
immersed in concentrated nitric acid for 10 min, rinsed, and
left to dry in air.
experimental absorption band.2
a,b
We have developed a modi-
fied form of MG theory, called the dynamic MG (DMG) theory,
to model the optical properties of such Au nanoparticles.
2
b
In our previous studies we found that as the diameter of the
Au nanoparticle decreased, the position of the experimental
plasmon resonance band (as defined by the wavelength of
maximum absorption intensity, λmax) approached the λmax
predicted by MG theory.
investigated in our previous study had diameters of 60 nm.
We have since prepared Au nanoparticles with even smaller
2b
The smallest diameter particles
2
b
The pretreated Al was then anodized at constant potential
which converts the surface into the desired nanoporous alumina
template membrane. The method and cell have been described
2b,c
previously.
The diameter of the pores obtained in the alumina
*
Corresponding author: crmartin@lamar.colostate.edu.
Abstract published in AdVance ACS Abstracts, February 1, 1997.
X
membrane depends on the anodization potential. The potentials
S1089-5647(96)02685-5 CCC: $14.00 © 1997 American Chemical Society

Gold Nanoparticle/Porous Alumina Composites
J. Phys. Chem. B, Vol. 101, No. 9, 1997 1549
TABLE 1: Conditions Used for Electrochemical Preparation of the Nanoporous Alumina Membranes and Characteristics of
the Resulting Membranes
applied dc potential (V)
anodization time (h)
electrolyte and concn (% w/w)
detaching acid and concn(% w/w)
pore diam (nm)
3
2
1
1
0
0
5
0
12
4
6
oxalic acid (4%)
phosphoric acid (25%)
sulfuric acid (25%)
sulfuric acid (25%)
sulfuric acid (25%)
52
32
22
16
sulfuric acid (10%)
sulfuric acid (10%)
sulfuric acid (15%)
10
TABLE 2: Conditions Used to Electrodeposit the Au
Nanoparticles and Characteristics of the Resulting
Nanoparticles
plating
membrane pore coulombs Au particle Au particle aspect
a
diam (nm)
used
diam (nm) length (nm) ratio
κ
5
2
0.10
52 ( 6
32 ( 4
68 ( 14
142 ( 20
406 ( 110
32 ( 4
48 ( 10
80 ( 30
138 ( 56
208 ( 90
370 ( 70
26 ( 2
1.3 1.71
2.7 1.27
7.8 1.06
1.0 1.99
1.5 1.60
2.5 1.32
4.3 1.15
6.5 1.08
0
0
.20
.40
3
2
0.05
0.10
0.20
0.30
0.50
0.56
12
1.04
1.2 1.81
2.5 1.31
3.1 1.22
5.0 1.11
2
2
6
0.05
22 ( 2
16 ( 2
0.40
0.50
1.00
1.50
54 ( 14
68 ( 12
110 ( 40
316 ( 60
36 ( 10
96 ( 38
14
1.02
2.3 1.34
6.0 1.08
1
0.13
0
0
.54
.42
300 ( 130 19
1.01
a
Area of membrane exposed to solution ) 3.14 cm2.
and electrolytes used to produce the membranes studied here
are shown in Table 1. To avoid a large current surge, the
potential was ramped over a period of 2 min to the final values
indicated in Table 1. The cell was maintained at ca. 5 °C during
anodization. The thicknesses of the membranes obtained varied
from 20 to 40 µm.
Figure 1. Transmission electron micrograph of a planar section of a
typical nanoporous alumina membrane.
The alumina membrane was removed from the substrate Al
anode using the voltage reduction technique.6 This entails
stepwise reduction of the potential to obtain an interfacial oxide
layer that has a network of much smaller pores. After formation
of this highly porous layer, the electrode was immersed into an
acidic detachment solution (Table 1) which results in rapid
dissolution of the interfacial oxide. The acid then has access
to the substrate Al, and H2 gas is evolved at the interface
between the Al and the alumina membrane. The evolving H2
gas bubbles can be seen through the transparent alumina
membrane. When these bubbles coalesce, detachment is
complete. The Al electrode (with the detached alumina
membrane still clinging to the surface) was removed from the
detaching solution, rinsed by immersion into three portions of
water and dried in air. The membrane was collected by sliding
an index card between the alumina and the substrate Al. The
Al electrode can then be used to prepare another alumina
membrane.
The two faces of the detached alumina membrane are not
equivalent. The face that was detached from the substrate Al
surface contains remnants of the interfacial oxide layer. This
was removed by floating the membrane onto the surface of a
Figure 2. Variation of pore diameter in the nanoporous alumina
membranes with voltage used during anodization.
0.2 M KOH solution in ethylene glycol. This makes both faces
of the membrane essentially equivalent. The membranes were
checked visually for optical clarity. Defects on the Al metal
surface such as pits and scratches produce defects in the oxide
membrane which scatter light. Such defective membranes were
discarded.
of the alumina membranes. The procedure used has been
2
c
described previously. Briefly, a thin (ca. 100 nm) layer of
Ag was first evaporated onto the KOH/glycol-etched face of
the membrane. The Ag film was used to electrodeposit Ag
“nanopedestals” into the pores of the membrane. The Au
nanoparticles were then deposited onto these Ag pedestals. This
Gold Particle Electrodeposition. The nanoscopic Au par-
ticles were obtained by electrodepositing gold within the pores

1550 J. Phys. Chem. B, Vol. 101, No. 9, 1997
Hornyak et al.
the lengths and diameters of the Au nanoparticles were measured
2
using transmission electron microscopy (Table 2).
Spectrophotometric Investigations. UV/visible absorption
data were obtained using a transmission-mode experiment on
the Au nanoparticle/alumina membrane composite. The method
2
b
used has been described previously.
Optical data on the
alumina membrane, before deposition of the Au nanoparticles,
were used to obtain the refractive index (n0) and the absorption
coefficient (k0) for the membrane. The method used is reviewed
in the Theory section. After deposition of the Au nanoparticles,
the membranes show a strong absorption in the visible region
called the plasmon resonance band. This absorption is the focus
of this paper.
Transmission Electron Microscopy (TEM). TEM images
were obtained using a JEOL 2000 electron microscope. An
ultramicrotome equipped with a diamond knife was used to cut
thin transverse and planar sections through the Al/alumina
composite membrane. The transverse sections show the length
and diameter of the Au nanoparticles. These data are collected
in Table 2. The planar sections show the particle diameter. In
addition, planar sections of the membrane, prior to deposition
of Au, were used to evaluate the porosity of these membranes.
Details of the TEM procedures can be found in ref 7.
0
Figure 3. Plot of the wavelength-dependent k for the alumina
membranes vs wavelength. Upper curve is for membranes prepared in
oxalic acid; lower curve is for membranes prepared in sulfuric acid
(Table 1).
Computer Simulations. The energy of the plasmon reso-
nance band (as defined by the wavelength of maximum
absorption, λmax) is determined by both the diameter and length
of the Au nanoparticles deposited within the template mem-
approach was used because it puts the Au nanoparticles into
the bulk of the alumina membrane where the pore diameter is
more uniform. The Ag was then dissolved by immersion of
the membrane into concentrated nitric acid.
2
brane. The objective of the computer simulations was to
Because of the cylindrical pore geometry, rod-shaped Au
nanoparticles were obtained. The diameter of these rod-shaped
particles is determined by the pore diameter. The aspect ratio
calculate the absorption spectra for the various Au nanoparticle/
alumina membrane composites. These calculated spectra were
then compared to the experimental spectra. We are particularly
interested in the extent of agreement between the calculated
and experimental λmax values. Alumina optical constants were
obtained experimentally and those for Au were taken from the
(length divided by diameter) is determined by the quantity of
Au deposited (Table 2). It is important to point out, however,
that not all of the electroplated Au is deposited within the pores.
For example, an O-ring is used to hold the membrane in place
in the electrochemical cell, and the portion of the membrane
directly under this O-ring is typically completely covered with
a visible layer of Au. This is due to the pressure exerted from
the O-ring, which creates cracks in the membrane. Hence, the
current efficiency for plating of the Au within the pores was
always less than unity. This is not, however, a problem because
8
literature. The computational methods are described in the
Theory section. Simulations were done using MatLab version
4.2c.1 (Mathworks, Inc.) software running on a Power Mac
7200/90 personal computer (Macintosh). Kaleidagraph (Abel-
beck Software) was used to convert both the simulated and
experimental absorption data to the spectral format presented
in this paper.
Figure 4. Transmission electron micrographs of transverse sections of Au nanoparticle/alumina membrane composites. The membranes had a pore
diameter of 52 nm. The magnification and the length of the scale bar on the image are given in parentheses below. (A) Aspect ratio ) 1.3 nanoparticles
(×75K, 100 nm). (B) Aspect ratio ) 2.7 nanoparticles (×60K, 100 nm). (C) Aspect ratio ) 7.8 nanoparticles (×20K, 200 nm).

Gold Nanoparticle/Porous Alumina Composites
J. Phys. Chem. B, Vol. 101, No. 9, 1997 1551
Figure 5. Experimental (A) and DMG-simulated (B) absorption spectra for membranes containing 52 nm diameter Au nanoparticles. Particles
with three different aspect ratios (Table 2) are shown. The uppermost curve is for the highest aspect ratio nanoparticle, and the lowermost curve
is for the lowest aspect ratio nanoparticle.
functions of the alumina ( ꢀ˜ 0) and the Au ( ꢀ˜ µ) via
ꢀ
˜ - ꢀ˜
ꢀ˜ m - ꢀ˜ 0
ꢀ˜ m + κ ꢀ˜ 0
c
0
)
fm
(1)
(
)
ꢀ˜ c + κ ꢀ˜ 0
where fm is the volume fraction of the Au in the composite,
and κ is the shape-dependent screening parameter.
9
-12
For eq
1
to be valid, fm must be significantly less than the alumina
1
3
volume fraction, f0.
The magnitude of the radius of the Au nanoparticle does not
enter into eq 1 because, as noted above, MG theory assumes
that the radius is infinitesimally small. However, the shape and
orientation of the particle determine the value of the screening
parameter, κ. For example, κ has a value of 2 for a spherical
particle and a value of unity for an infinitely long, needlelike
1
2b
particle oriented perpendicular to the electric field.
κ values
were calculated, as described in ref 2b, from the known diameter
and length of the nanoparticles (Table 2). Equation 1 can then
be used to calculate the complex dielectric function of the
composite at any λ, and this, in turn, can be used to calculate
the absorption at any wavelength. The methods used have been
2
b,c
Figure 6. Plot of λmax for experimental and simulated absorption spectra
vs natural logarithm of the aspect ratio of the Au nanoparticle. The
aspect ratio is defined as a/b, where a is the length and b is the diameter
of the nanoparticle. These data are for 52 nm diameter nanoparticles.
The experimental data are in bold (with data points). The DMG-
simulated results are the dotted curve. The MG-simulated results are
the dashed curve.
described previously.
2a,b
In our prior work, we could not achieve this quasi-static
regime because the diameters of the Au nanoparticles were not
infinitesimally small relative to the wavelengths of visible light.
(The prior work involved Au particles with diameters ranging
from 60 to 120 nm.) As a result, the λmax values in the
experimental absorption spectra were always greater than those
calculated using MG theory. A modified version of MG theory,
that takes into account the finite diameter of the Au nanoparticle,
Theory
Maxwell-Garnett Theory. We have previously shown that
Maxwell-Garnett (MG) effective medium theory can be used
to qualitatively describe the absorption spectra of Au/alumina
composite membranes of the type described here.2 MG theory
2
b
was developed. In this dynamic Maxwell-Garnett (DMG)
model, the static κ of eq 1 is replaced by a complex and
wavelength-dependent keff, which accounts for extinction due
2
b,14
assumes that the radius of the Au nanoparticle is infinitesimally
to scattering by the larger particles.
theory can be found in ref 2b.
Details of the DMG
small relative to the wavelength of light.9
-11
This is called the
“
quasistatic” regime, and Kreibig and Vollmer specify that this
Alumina Optical Constants. There are no data tables
available in the literature listing the wavelength-dependent
optical constants for alumina of the type used here. (These
membranes consist of hydrated amorphous alumina into which
some anodization electrolyte has been incorporated4 ). To
11
regime is characterized by r/λ e 0.01, where r is the radius
of the metal nanoparticle and λ is the wavelength of light
employed. According to MG theory, the complex dielectric
function of the composite ( ꢀ˜ ø), at any λ, is related to the dielectric
a,f

1552 J. Phys. Chem. B, Vol. 101, No. 9, 1997
Hornyak et al.
Figure 7. Experimental (A) and DMG-simulated (B) absorption spectra for membranes containing 32 nm diameter Au nanoparticles. Particles
with six different aspect ratios (Table 2) are shown. The uppermost curve is for the highest aspect ratio nanoparticle, and the lowermost curve is
for the lowest aspect ratio nanoparticle.
and applying the following equation at each wavelength:
2
2
c(i,j)
(
nc(i,j) - 1) + k
4πkc(i,j)di
ln Tc(i,j) ) 2 ln 1 -
-
(2)
2
2
[
]
λj
(
nc(i,j) + 1) + k
c(i,j)
where Tc(i,j) is the transmittance of an alumina/air composite of
some thickness (di in microns) at some wavelength (λi in
microns). According to eq 2, a plot of ln Tc(i,j) versus membrane
thickness is linear; kc is obtained from the slope and nc from
the intercept.
The alumina optical constants were obtained from these
experimental nc and kc values using the Bruggeman approxima-
1
5
tion, another type of effective medium theory, which for this
specific case, takes the form
ꢀ
˜ - ꢀ˜
1 - ꢀ˜ c
1 + ꢀ˜ c
0
c
0
) f0
+ P
(3)
(
)
(
)
ꢀ
˜ + ꢀ˜
0
c
where ꢀ˜ 0 and ꢀ˜ ø are the complex dielectric functions of the
alumina and the air/alumina composite membrane, respectively,
f0 is the volume fraction of the alumina, and P is the porosity
Figure 8. Plot of λmax for experimental and simulated absorption spectra
vs natural logarithm of the aspect ratio of the Au nanoparticle. The
aspect ratio is defined as a/b, where a is the length and b is the diameter
of the nanoparticle. These data are for 32 nm diameter nanoparticles.
The experimental data are in bold (with data points). The DMG-
simulated results are the dotted curve. The MG-simulated results are
the dashed curve.
(
1 - f0). This expression is solved for ꢀ˜ 0 for each desired λ,
2b,c
and ꢀ˜ 0 is then converted into the optical constants n0 and k0.
Results and Discussion
Membranes. A TEM image of a planar-section of a typical
nanoporous alumina membrane is shown in Figure 1. These
membranes have monodisperse pore diameters, and the pores
are hexagonally packed. The pore diameter is proportional to
the dc potential used to prepare the membrane (Figure 2).16 The
pore diameters for the membranes investigated here are shown
in Table 1. The porosity of the membrane (P) was also
determined from TEMs such as that shown in Figure 1. The
porosity was found to be P ) 0.27 + 0.03, independent of pore
diameter.
As discussed in the Experimental and Theory sections, optical
constants n0 and k0 were measured for the alumina component
of the membranes used here. Figure 3 shows the variation in
k0 with wavelength, over the wavelength region of interest for
these studies. The k0 values for all membranes are quite low,
obtain accurate optical data for use in spectral modeling of the
composites, we needed to determine n0 and k0 for these alumina
membranes. This is not as simple as it seems because the
membrane, itself, is a composite of alumina and the air-filled
pores. Hence, two sets of optical constants can be defined for
the membrane, n0 and k0, which are the optical constants of the
alumina portion of the membrane, and nc and kc, which are the
optical constants of the alumina/air composite. The alumina/
air composite constants are obtained experimentally, and the
alumina constants can then be extracted from these experimental
data.
The optical constants nc and kc were obtained by measuring
the transmittance of membranes of at least three thicknesses

Gold Nanoparticle/Porous Alumina Composites
J. Phys. Chem. B, Vol. 101, No. 9, 1997 1553
Figure 9. Experimental (A) and DMG-simulated (B) absorption spectra for membranes containing 22 nm diameter Au nanoparticles. Particles
with five different aspect ratios (Table 2) are shown. The uppermost curve is for the highest aspect ratio nanoparticle, and the lowermost curve is
for the lowest aspect ratio nanoparticle.
parameters2b for all of the Au nanoparticles studied here are
shown in Table 2.
Experimental and Simulated Absorption Spectra. Ex-
perimental optical absorption spectra for the composite mem-
branes containing the 52 nm diameter Au nanoparticles are
shown in Figure 5A. The uppermost spectrum is for the highest
aspect ratio particles (Table 2), and the lowermost spectrum is
for the lowest aspect ratio particles. As would be expected,2
the intensity of the plasmon resonance band increases, and λmax
decreases, with increasing aspect ratio (a/b, where a is the length
and b is the diameter of the Au nanoparticle). As a result of
this shift in λmax, the color of these composites change with
aspect ratio. When illuminated from behind with a tungsten
source, the aspect ratio (a/b) ) 1.3 composite (bottom curve in
Figure 5A) displayed a blue-purplish hue (λmax ) 540 nm). The
membranes containing the highest aspect ratio particles appeared
red (λmax ) 518 nm).
a,b
DMG-simulated absorption spectra for composites containing
Au nanocylinders of these dimensions are shown in Figure 5B.
The only adjustable parameter in these simulations is the
2b,c
thickness of the optical layer, and this parameter affects only
the absolute absorption intensity. That is, λmax and the general
shape of the band are not influenced by the magnitude of this
adjustable parameter. Rather, these characteristics of the
absorption spectrum are determined by the nonadjustable input
parameters, which are the length and diameter of the nanopar-
ticle and the optical constants of the metal and the alumina.
The agreement between the experimental and simulated
spectra is, qualitatively, good. The shape of the band is
faithfully reproduced; however, the widths of the experimental
bands are greater than the simulated bands. The broadening in
the experimental spectra is due to the finite distribution in both
the length and diameter of the particles (Table 2). Kreibig and
Vollmer have suggested approaches for modeling this inhomo-
Figure 10. Plot of λmax for experimental and simulated absorption
spectra vs natural logarithm of the aspect ratio of the Au nanoparticle.
The aspect ratio is defined as a/b, where a is the length and b is the
diameter of the nanoparticle. These data are for 22 nm diameter
nanoparticles. The experimental data are in bold (with data points).
The DMG-simulated results are the dotted curve. The MG-simulated
results are the dashed curve.
as would be expected from the high optical transparency of these
membranes. The k0 values for the sulfuric-acid-prepared
membranes are lower and are independent of wavelength. The
k0 values for the oxalic-acid-prepared membranes are higher
and decrease with increasing wavelength. The n0 values for
both types of membranes were found to be independent of
wavelength. The average n0 value for the oxalic-acid-prepared
films over the wavelength range of interest here was 1.50. The
average n0 value for sulfuric-acid-prepared films was 1.54.
TEMs of the Gold Nanoparticles. Figure 4 shows TEM
images of Au nanoparticles with three different aspect ratios
that were prepared in the membrane with 52 nm diameter pores.
The lengths, diameters, aspect ratios, and static screening
11
geneous broadening. Most importantly, in agreement with the
experimental spectra, the simulated spectra show a blue-shift
in λmax with increasing aspect ratio.
We are especially interested in the extent of agreement
between the experimental and simulated λmax values. This
interest stems from our previous work on Au nanoparticles that
2a,b
had larger diameters than those investigated here.
We found

1554 J. Phys. Chem. B, Vol. 101, No. 9, 1997
Hornyak et al.
Figure 11. Experimental (A) and DMG-simulated (B) absorption spectra for membranes containing 16 nm diameter Au nanoparticles. Particles
with three different aspect ratios (Table 2) are shown. The uppermost curve is for the highest aspect ratio nanoparticle, and the lowermost curve
is for the lowest aspect ratio nanoparticle.
Figure 12. Plot of λmax for experimental and simulated absorption
spectra vs natural logarithm of the aspect ratio of the Au nanoparticle.
The aspect ratio is defined as a/b, where a is the length and b is the
diameter of the nanoparticle. These data are for 16 nm diameter
nanoparticles. The experimental data are in bold (with data points).
The DMG-simulated results are the dotted curve. The MG-simulated
results are the dashed curve.
Figure 13. Plot of λmax for DMG-simulated spectra vs the natural
logarithm of the radius of the nanoparticle in the composite. The upper
curve assumes spherical nanoparticles. The lower curve assumes long,
needlelike particles (aspect ratio ) 100).
large-diameter particles,2b the λmax values predicted by conven-
tional quasi-static MG theory, bottom curve, are significantly
smaller than the experimental λmax values. The DMG theory
does a much better job of predicting the experimental λmax
values. Experimental optical absorption spectra for the Au/
alumina composite membranes containing the 32 nm diameter
Au nanoparticles are shown in Figure 7A. Spectra for nano-
cylinders having six different aspect ratios are shown. Again,
we see the characteristic increase in absorption intensity and a
decrease in λmax, with increasing aspect ratio. The color of these
membranes proceeded from bluish-purple (a/b ) 1.0, λmax )
539 nm) through various red hues and finally to orange-red (a/b
) 12, λmax ) 508 nm).
that λmax values blue-shifted with decreasing nanoparticle
diameter but that λmax values for all of the particles investigated
were significantly larger than values predicted by the conven-
tional (i.e., quasi-static) MG theory. Hence, the quasi-static MG
theory can be viewed as a limiting case in the optical properties
of nanometals. One of the objectives of the current study was
to see if nanoparticles with small enough diameters to achieve
this limiting case could be prepared.
Figure 6 shows both the experimental and simulated (MG
and DMG) variation in λmax with aspect ratio for the 52 nm
diameter Au nanoparticles. As would be expected for such

Gold Nanoparticle/Porous Alumina Composites
J. Phys. Chem. B, Vol. 101, No. 9, 1997 1555
Simulated (DMG) absorption spectra for composites contain-
ing Au nanoparticles of these dimensions are shown in Figure
decreasing particle radius. However, at sufficiently small radius,
λmax reaches a lower limit and shows no further change with
radius. This lower limit is the quasi-static limit. In agreement
with the experimental data obtained here, these calculations
show that this quasi-static limit is achieved for particles with
radii of ca. 7.5 nm or smaller.
7B. The agreement between the experimental and simulated
spectra is, again, qualitatively, quite good. Figure 8 shows both
the experimental and simulated variation in λmax with nanopar-
ticle aspect ratio for the membranes containing the 32 nm
diameter Au particles. In this case, the agreement between the
experimental and DMG-simulated λmax values is better than for
the larger diameter particles discussed above (Figure 6).
Furthermore, a comparison with the curve obtained from the
quasi-static MG simulation, the lowest curve in Figure 8, clearly
shows that these smaller diameter particles are approaching the
quasi-static regime.
Acknowledgment. This work was supported by the Office
of Naval Research. We also acknowledge the Colorado State
University Electron Microscopy Center.
References and Notes
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Experimental optical absorption spectra for the Au/alumina
composite membranes containing the 22 nm diameter Au
nanoparticles are shown in Figure 9A. Again, we see the
characteristic changes in intensity and position of the spectra
with aspect ratio. The colors of these membranes proceeded
from bright ruby-pink (a/b ) 1.2, λmax ) 522 nm) to various
reddish hues and finally to orange-red (a/b ) 14, λmax ) 508
nm). The corresponding DMG-smulated spectra are shown in
Figure 9B. Figure 10 shows both the experimental and
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nm) is sufficiently small that the quasi-static limit is being
approached. The experimental λmax values are essentially
identical with the values produced by the DMG simulation.
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nm) diameter Au nanocylinders are shown in Figure 11. The
agreement between the experimental and simulated spectra is
reasonably good. However, the experimental peaks are not as
well-defined as in the spectra for the larger diameter particles.
This is due to the lower absolute absorption intensity for these
very small diameter particles. Finally, Figure 12 shows both
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