Shape-controlled platinum nanoparticles exhibit extremely high oxygen reduction activity. Platinum nanoparticles were synthesized by the reduction of a platinum complex in the presence of a soft template formed by organic surfactants in oleylamine. The formation of platinum nanoparticles was investigated using in situ small-angle X-ray scattering experiments. Time-resolved measurements revealed that different particle shapes appeared during the reaction. After the nuclei were generated, they grew into anisotropic rod-shaped nanoparticles. The shape, size, number density, reaction yield, and specific surface area of the nanoparticles were successfully determined using small-angle X-ray scattering profiles. Anisotropic platinum nanoparticles appeared at a low reaction temperature (∼100 °C) after a short reaction time (∼30 min). The aspect ratio of these platinum nanoparticles was correlated with the local packing motifs of the surfactant molecules and their stability. Our findings suggest that the interfacial structure between the surfactant and platinum nuclei can be important as a controlling factor for tailoring the aspect ratio of platinum nanoparticles and further optimizing the fuel cell performance.
Shape-controlled platinum nanoparticles exhibit extremely high oxygen reduction activity. Platinum nanoparticles were synthesized by the reduction of a platinum complex in the presence of a soft template formed by organic surfactants in oleylamine. The formation of platinum nanoparticles was investigated using in situ small-angle X-ray scattering experiments. Time-resolved measurements revealed that different particle shapes appeared during the reaction. After the nuclei were generated, they grew into anisotropic rod-shaped nanoparticles. The shape, size, number density, reaction yield, and specific surface area of the nanoparticles were successfully determined using small-angle X-ray scattering profiles. Anisotropic platinum nanoparticles appeared at a low reaction temperature (∼100 °C) after a short reaction time (∼30 min). The aspect ratio of these platinum nanoparticles was correlated with the local packing motifs of the surfactant molecules and their stability. Our findings suggest that the interfacial structure between the surfactant and platinum nuclei can be important as a controlling factor for tailoring the aspect ratio of platinum nanoparticles and further optimizing the fuel cell performance.
Metal nanoparticles
(NPs) have attracted attention because of their
unique physicochemical properties such as local surface plasmon phenomena,[1,2] spin polarization,[3,4] and catalytic activity,[5,6] which differ from their bulk properties. Shape control is effective
in the design of these physicochemical properties.[7] Recently, shape-controlled platinum and platinum-based
NPs have been studied for their mass activity in the oxygen reduction
reaction.[8−15] Anisotropic shapes have excellent electron conductivity, an electrochemically
active surface area (ECSA), and specific activity. It is worth noting
that Arenz et al. presented a breakthrough concept for a self-supported
Pt–CoO catalyst capable of combining high specific activity
with an unprecedentedly high ECSA.[16] However,
it is still essential to control the shape of platinum NPs for fuel
cell applications.The growth mechanism of anisotropic gold
NPs has been rigorously
investigated for electronics and biomedical applications[17,18] because anisotropic gold NPs have two types of localized surface
plasmon absorption bands corresponding to the short and long axes
of elliptical NPs. These absorption bands vary along short and long
axis lengths. In the above-mentioned fields, precise control of the
aspect ratio has a critical effect on these properties. Therefore,
various synthesis methods have been proposed to design the shape of
gold NPs: electrochemical methods,[19] photochemical
reaction methods,[20] and seed-mediated colloid
growth methods.[21] In the seed-mediated
colloid growth method, anisotropic gold NPs are grown using a surfactant
as a soft template. The surfactant selectively adsorbed onto the metal
surface promoted the anisotropic growth of the nucleus.As Quinson
and Jensen summarized in their review article,[22] a variety of approaches have been reported to
obtain platinum NPs. Similarly, a review focused on their shape control
was summarized by Cheong et al.[23] For fuel
cell applications, the seed-mediated colloid growth method has often
been applied to the synthesis of anisotropic platinum NPs. Note that
research is being conducted on surfactant-free synthesis[23] or the surfactant removal process[24] since the process of removing surfactants is
necessary.[25] An extreme heating treatment
(>100 °C) for several hours was found to be an effective synthetic
protocol for the seed-mediated colloid growth method of platinum NPs.[14,15,26,27] Their reaction conditions are different from those of gold NP synthesis
(typically a milli-second-scale reaction at around room temperature).
This is likely due to their ionization properties. The nuclei of metal
NPs must be reduced from a metal cation M(X) to a metal M(0) in the
liquid phase, where the metal salt is dissolved. The most reducible
Au(III) ion enables the growth of gold NPs under mild reaction conditions
in a few seconds.[17,21] Polte et al. investigated the
differences and similarities between the formation processes of gold
and silver NPs.[28] They claimed that the
growth mechanism of gold NPs consists of only one process of coalescence
that proceeds within a few seconds after mixing the reactants, while
the growth of silver NPs proceeds via two distinct coalescence processes.
For this reason, it is difficult to find studies on the formation
mechanism of gold NPs under high-temperature conditions. However,
in situ studies on the formation process of platinum NPs under high-temperature
reactions have been reported elsewhere.[29−37] The reaction temperature and pressure strongly influence the structure,
size, and shape of the NPs.[36,37] However, to the best
of our knowledge, the effect of synthetic protocols on the seed-mediated
colloid growth method of platinum NPs, such as heating temperature,
time, and rate, on the shape, size, number density, reaction yield,
and specific surface area (SSA) of platinum NPs has not yet been investigated
for fuel cell applications.Real-time transmission electron
microscopy (TEM) observation[38] during the
synthesis of metal NPs provides direct
evidence of the formation process of metal NPs, but this cutting-edge
technology is not suitable for platinum NPs because it requires a
high-temperature reaction. In such cases, it is useful to perform
X-ray absorption fine structure (XAFS) and small-angle X-ray scattering
(SAXS) measurements.[39] From the results
of in situ quick XAFS measurements, the stages of the reduction–nucleation,
aggregative particle growth, and Ostwald ripening of metal atoms to
produce metal NPs were discriminated in course of reduction time.[39−42] Additionally, SAXS measurements allow for the quantitative analysis
of growth progress using parameters such as shape, size, and number
density of metal NPs.[39] Since the mid-2000s,
in situ time-resolved SAXS measurements have been established to study
the formation process of gold NPs, leading to a deeper understanding
of the growth mechanism.[43] Currently, this
technique is widely applied to monitor the nucleation and formation
processes of metal NPs.[28,34,35,44−60]In this study, we investigated the formation process of anisotropic
platinum NPs by in situ SAXS experiments to gain insight into the
optimization of the process parameters. Real-time measurements monitor
continuous changes in the shape of the platinum NPs during the reactions.
The randomly distributed rod model (Figure a) was applied to elucidate the shape, size,
number density, reaction yield, and SSA of the platinum NPs. Monitoring
during three different heating sequences (see Figure a) enabled us to discuss the growth mechanism
of anisotropic platinum NPs and propose process parameters aimed at
shape control for fuel cell applications.
Figure 1
(a) Illustration of a
rod with radius R [Å]
and length L [Å] oriented in the direction of
angle α [rad] for the referential axis. (b) 2D SAXS patterns
of platinum NPs synthesized by heating at 160 °C for 100 min.
(c) Circular averaged 1D SAXS profiles.
Figure 2
(a) Heating
sequences for the in situ time-resolved SAXS study. TR and tR represent
reaction temperature and reaction time, respectively. In sequences 1 and 3, the heating rate was fixed at 5 °C/min.
In sequence 2, the heating rate was fixed at 100 °C/min. TR was held at 160 °C in sequences 1 and 2. In sequence 3, TR was held at 100 °C for 60 min and finally
increased to 160 °C. (b–d) In situ SAXS profiles as a
function of reaction time tR in sequences 1–3.
(a) Illustration of a
rod with radius R [Å]
and length L [Å] oriented in the direction of
angle α [rad] for the referential axis. (b) 2D SAXS patterns
of platinum NPs synthesized by heating at 160 °C for 100 min.
(c) Circular averaged 1D SAXS profiles.(a) Heating
sequences for the in situ time-resolved SAXS study. TR and tR represent
reaction temperature and reaction time, respectively. In sequences 1 and 3, the heating rate was fixed at 5 °C/min.
In sequence 2, the heating rate was fixed at 100 °C/min. TR was held at 160 °C in sequences 1 and 2. In sequence 3, TR was held at 100 °C for 60 min and finally
increased to 160 °C. (b–d) In situ SAXS profiles as a
function of reaction time tR in sequences 1–3.
Results and Discussion
Figure S1 shows the TEM images of platinum
NPs synthesized by heating at sequence 3 (TR = 100 °C, tR = 75 min).
In this study, small amounts of nickel acetylacetonate and molybdenum
hexacarbonyl were added to inhibit particle enlargement and prevent
particle aggregation[14] (see the Experimental Section). Energy-dispersive X-ray spectroscopy
analysis confirmed that the particles were formed from pure platinum
(>98%) (Figure S1). The 2D SAXS pattern
of platinum NPs synthesized by heating at sequence 1 (TR = 160 °C, tR = 100 min) shows an isotropic pattern (Figure b), indicating the absence of orientated
platinum NPs dispersed in oleylamine. If the particle shape is unclear,
then distance distribution function (DDF) analysis would be a powerful
tool because neither approximation nor assumption is employed in the
analysis.Hatakeyama et al.[59] and
Morita et al.[60] successfully discussed
the growth progress of
gold nanorods based on DDF analysis. In the present study, rod-like
particles were observed in the TEM images sampled under different
reaction conditions (Figure S2). Therefore,
the randomly distributed rod model (Figure a) was applied to elucidate the shape, size,
number density, reaction yield, and SSA of the platinum NPs. Although
particles after reactions (Figure S3) can
be fitted with both sphere and rod models, we employed the rod model
overall reactions to systematically investigate time-sliced parameter
changes among sequences. Additionally, we noted that the isotropic
2D SAXS patterns (Figure b) support the assumption of a randomly distributed rod model.
The circular-averaged absolute scattering intensities were plotted
as a function of the q-scale (Figure c). These profiles have a crossover q–1-dependence to q–4-dependence at q ∼ 0.1 Å–1. The q–1-dependence
is a typical feature of the rod shape, and the crossover point corresponds
to the rod radius. Moreover, the scattering intensities point upward
at q < 0.2 Å–1, which can
be well explained by the model of randomly distributed rods (shown
as a solid line). Detailed analytical results are discussed later.Figure a shows
three heating sequences for the synthesis of platinum NPs in time-resolved
SAXS experiments. The scattering data after each heating sequence
is shown in Figure S4. These profiles have
the typical features of randomly distributed rods, as mentioned above.
It is worth noting that the Debye–Scherrer ring (indicated
by the black arrow) was observed after sequence 3 (Figure S4c), suggesting the presence of a self-assembled
structure of platinum NPs. The self-assembled structure during the
reaction has attracted significant interest because it is believed
to be related to particle growth.[44,55]Figure b–d shows waterfall
plots of time-resolved SAXS profiles obtained using each heating protocol
(sequences 1–3). A plateau was observed in the
first scan, indicating the absence of platinum NPs before the heating
treatment. The most characteristic change is a monotonic increase
in the scattering intensity at q < 0.2 Å–1. This increase in the scattering intensity supports
the nucleation and growth of platinum NPs with an increase in the
reaction temperature TR. A continuous
upturn in intensity (Figure b) was observed as TR increased
at a constant heating rate, whereas a stepwise TR increase in sequence 3 induced a discontinuous
upturn (Figure d).
When TR increased abruptly (Figure c), platinum NPs formed in
a matter of minutes. Sharp peaks originating from the self-assembled
structure, as previously discussed, appear and disappear at 0.1 Å–1 < q < 0.2 Å–1 during reactions. Similar results have been found in the growth
process of gold NPs.[44,55,56] However, a discussion of the self-assembled structure is beyond
the scope of this work focused on the shape of the platinum NPs.Figure shows the
results of plotting the time-resolved SAXS profiles for each heating
sequence against reaction time tR. All
fitting curves were in good agreement with the time-resolved SAXS
profiles (Figure S5). Immediately after
the start of the reaction, the obtained fitting parameters are scattered.
This is because the background at high q regions
affects the fitting parameters in the case of weak signals at low q regions. When small particles (rod radius and length <
10 Å) are born immediately after the start of measurement, the
spectrum is not beyond the background level. Therefore, information
about the small particles is lost in Figure . The heating protocol had a pronounced effect
on the formation of platinum NPs (Figure a,b). The results of sequences 1 and 2 illustrate that the rod radius R [Å] becomes larger as the heating rate decreases (Figure a).
Figure 3
Structural evolution
as a function of reaction time tR for
anisotropic platinum NPs: (a) rod radius R [Å],
(b) rod length L [Å],
(c) aspect ratio [—] equal to L/2R, and (d) number density of particles N [particles
cm–3]. Immediately after the start of the reaction,
the obtained fitting parameters were scattered because the weak signals
shown in Figure were
not properly fitted by the rod model.
Structural evolution
as a function of reaction time tR for
anisotropic platinum NPs: (a) rod radius R [Å],
(b) rod length L [Å],
(c) aspect ratio [—] equal to L/2R, and (d) number density of particles N [particles
cm–3]. Immediately after the start of the reaction,
the obtained fitting parameters were scattered because the weak signals
shown in Figure were
not properly fitted by the rod model.In the present study, the rod length L [Å]
was not affected by the heating rate (Figure b). In sequence 3, the rods
become thicker and shorter as the TR increases
from 100 to 160 °C (Figure a,b). The reduction of rod length and aspect ratio
in sequence 3 is due to the fragmentation of long rod-shaped
particles (see Figure S6). The aspect ratio
(=L/2R) plotted in Figure c demonstrates that anisotropic
platinum NPs can be synthesized at a lower reaction temperature and
a shorter reaction time. In the present study, all heating sequences
ended at TR = 160 °C, resulting in
platinum NPs with a low aspect ratio (∼1.3). The final shape
of the platinum NPs estimated from the analysis was matched with the
TEM images (see Figure S3). Figure d shows the number density
of the platinum NPs. In sequences 1 and 2, the number density increased after the start of the reaction and
then remained almost constant. Meanwhile, in sequence 3, the number density increases as TR increases
from 100 to 160 °C. The rise in N may be due
to two processes: (i) the additional nucleation from platinum precursors
and (ii) the fragmentation of long rod-shaped particles. The yield
of platinum reduction Y [%] (Y =
100 × ϕPt(0)/ϕPt(II)0, where ϕPt(0) and ϕPt(II)0 are the volume
fractions of the reduced and platinum precursors, respectively) was
calculated from ϕPt(0), which was obtained by multiplying
the particle volume V [cm3] (calculated
from the data shown in Figure a,b) by the number density of particles N (particles cm–3) (Figure d). The value of ϕPt(II)0 was 0.004167 based on the
sample composition. At the end of each sequence, Y was 20–30% (Figure a). These values were roughly consistent with those estimated
from the particle weights gathered by centrifuging, washing, and drying
in the laboratory. As seen in Figure a, a comparison of sequences 1 and 2 supports the fact that the sudden increase in TR results in a decrease in Y. This is
probably because nuclear growth cannot keep up with reductant consumption.
In sequence 3, Y drastically increased
at TR ranging from 100 to 160 °C,
which was attributed to an increase in the volume (Figure a,b) and the number density
of particles (Figure d), that is, nuclear growth and nucleation. The simultaneous processes
had an impact on particle size distribution (Figure S3c).
Figure 4
(a) Yield of platinum reduction Y [%]
and (b)
SSA [mPt2 gPt–1] of platinum NPs as a plot of reaction time tR [min]. These values were calculated from the obtained fitting
parameter displayed in Figure .
(a) Yield of platinum reduction Y [%]
and (b)
SSA [mPt2 gPt–1] of platinum NPs as a plot of reaction time tR [min]. These values were calculated from the obtained fitting
parameter displayed in Figure .We now discuss the optimization
of the reaction conditions from
in situ time-resolved SAXS experiments. What is the optimal reaction
temperature? When should the reaction end? A reasonable answer can
be proposed from an electrochemical perspective. Figure b displays the dependence of tR on the SSA, defined as Sm/(VmDPt), where Sm [m2], Vm [m3], and DPt [g m–3] are the surface area and volume
of platinum NPs and the density of platinum (2.145 × 107 g m–3), respectively. The Paul Scherrer Institute
research group[61] investigated the analogy
between ECSA [mPt2 gPt–1] and SSA estimated from anomalous SAXS studies. They reported that
the SSA of the catalyst layer consisting of platinum-supported carbon
catalysts (TEC10V30E) and the ionomer (Nafion 117 dispersion) with
an ECSA of 65 was 107 mPt2 gPt–1. An ECSA value lower than that of the SSA was explained
by the aggregation of catalyst NPs.[61] Therefore,
although a high SSA does not necessarily indicate a high ECSA, SSA
is an indicator of a desirable particle shape for fuel cell applications.
In the present study, the largest SSA (>120 mPt2 gPt–1) was observed in sequence 3 (Figure b). Holding at TR = 100 °C and a
shorter reaction time (∼30 min) is suitable for acquiring anisotropic
platinum NPs with a higher SSA. However, Y decreased
from 30 to 10% when the reaction was stopped at a shorter reaction
time (Figure a). This
problem persists in fuel cell applications.Let us now discuss
the growth mechanism and its parameters for
shape control. Complex formation is promoted by the action of the
polar head of cetyltrimethylammonium chloride (CTAC), which adsorbs
onto the platinum surface and is stabilized by the hydrocarbon chain
of CTAC located on the oleylamine side.[26] Previous reports have demonstrated that the amounts of CTAC, metal
acetylacetonate, and metal carbonyl all affect the particle aspect
ratio.[14] In the absence or insufficiency
of these agents, spherical NPs and their aggregates are formed. In
this work, we discuss the growth mechanism with a focus on the surfactant
geometry and TR. The growth mechanism
inferred from the in situ time-resolved SAXS experiments is illustrated
in Figure . The affinity
between the platinum surface and the hydrophilic head of the surfactant
depends on the curvature of the platinum surface. Surfactants are
likely to be adsorbed on the longitudinal site rather than the end-cap
site;[62−64] it is only possible to validate this interfacial
structure by contrast-variation small-angle neutron scattering.[65−69] Therefore, the precursor is reduced on the end-cap side (there is
no “attack” on the longitudinal site). The possibility
of the growth originating from the connection of small particles has
been eliminated from the result of high-resolution TEM observations
(see Figure S6). This is consistent with
those of previous studies.[14] The frequency
of nuclear growth increases on the bare end-cap site at a moderate
reaction temperature, TR1 (illustrated
in Figure ). However, Figure b shows an obvious
drop in the rod length and aspect ratio in the first 40 min in sequence 3 (see also Figure S2). This trend
suggests that even under moderate reaction conditions, nuclear growth
on the longitudinal site cannot be ignored when the reaction time
is increased.
Figure 5
Possible growth mechanism for anisotropic platinum NPs.
CTAC forms
cylindrical micelles. After spherical particles are generated at nucleation,
they form anisotropic NPs via nuclear growth. Arrangement of CTAC
on the longitudinal site of the Pt nucleus assists anisotropic growth
as more platinum precursors Pt[acac]2 (yellow dots) are
introduced to the nucleus as platinum atoms (gray dots) at moderate
reaction temperature TR1. At high reaction
temperature TR2, platinum precursors easily
attack the longitudinal site resulting in isotropic nuclear growth.
Possible growth mechanism for anisotropic platinum NPs.
CTAC forms
cylindrical micelles. After spherical particles are generated at nucleation,
they form anisotropic NPs via nuclear growth. Arrangement of CTAC
on the longitudinal site of the Pt nucleus assists anisotropic growth
as more platinum precursors Pt[acac]2 (yellow dots) are
introduced to the nucleus as platinum atoms (gray dots) at moderate
reaction temperature TR1. At high reaction
temperature TR2, platinum precursors easily
attack the longitudinal site resulting in isotropic nuclear growth.It is well known that CTAC forms cylindrical micelles
above its
critical micelle concentration.[17] In this
work, CTAC was added well above the critical micelle concentration
(see the Experimental Section). The micelle
structure of surfactants is directly related to the particle shape
in the seed-mediated colloid growth method.[63] The persistence length of micelles depends strongly on the scission
energy: the surface charge and end-cap energy of the micelles.[70] Kusano et al.[71] found
that the end-cap energy was strongly related to the surfactant geometry.
More intuitively, the ease of end capping can be explained using the
surfactant packing parameter proposed by Israelachvili et al.[72] The unitless packing parameter p is defined as p = v/Al, where v [cm3] is the effective volume
of the hydrocarbon chain, A [cm2] is the
effective area of the polar headgroup, and l [cm]
is the length of the hydrocarbon chain. Because the polar head of
the surfactant is adsorbed onto the platinum surface in this system,
a surfactant with p > 1 that forms an inverted
micelle
structure easily adsorbs onto the end cap and suppresses nuclear growth
at this site. However, a surfactant with p < 1
destabilizes the adsorption state at the end-cap site, which leads
to the growth of anisotropic NPs. The packing parameter of CTAC was
lower than 1, indicating that CTAC stabilized the exposed end-cap
state. A surfactant with a longer hydrophobic chain instead of CTAC,
for example, octadecyltrimethylammonium chloride, would be preferable
for enhancing the aspect ratio of platinum NPs. Huang et al. reported
the synthesis of platinum-based shape-control catalysts using the
surfactant geometry.[73] However, a systematic
study focusing on the packing parameter has not yet been performed.
For the synthesis of shape-controlled gold NPs in an aqueous medium,
the packing parameter was strategically coordinated by the hydrocarbon
length of surfactants,[63] pH,[74,75] and electrostatic shielding.[76] Shape-controlled
platinum NPs can be designed by controlling the surfactant geometry;
however, pH adjustment and salt addition are not effective in lipophilic
oleylamine.In the following, we discuss the influence of the
heating rate
and TR on the aspect ratio of platinum
NPs. Surfactants do not have a fixed structure; their micelle structure
is constantly formed and disrupted in dynamic equilibrium; therefore,
rapid heating is not recommended. Although the number density of particles
was almost constant in sequences 1 and 3, the number density of particles decreased within 40 min in sequence 2 (Figure d). The reduction could be explained by the presence of a coalescence
process due to the inability of the protection provided by surfactants
to keep up with rapid heating. The Gibbs energy (ΔG = ΔH – TΔS) determines whether the surfactant promotes the formation
of micelles. In general, the entropy term TΔS is dominant in micelle formation, so the “soft
template” is likely to collapse at a high reaction temperature TR2 (illustrated in Figure ). Platinum precursors easily attack the
longitudinal site at TR2, resulting in
isotropic nuclear growth. This hypothesis was supported by a study
by Gou and Murphy.[77] Their paper reported
that additional input of ascorbic acid as a reductant preferentially
deposits more metal at the end-cap site, and heat treatment induces
deposition on the entire particle surface. In the case of platinum,
previous studies proposed the use of glucose as a reductant, but this
requires a high reaction temperature (>100 °C).[14]
Conclusions
We investigated the
formation process of anisotropic platinum NPs
synthesized by the reduction of a platinum complex in the presence
of a soft template formed by CTAC in oleylamine using in situ SAXS.
Time-resolved measurements displayed scattering data that supported
the nucleation and growth of platinum NPs during the reactions. Furthermore,
time-resolved scans captured diverse shapes every 60 s during the
reaction. We successfully established a fitting model to elucidate
the shape, size, number density, reaction yield, and SSA of the platinum
NPs in each scan. The growth mechanism of platinum NPs is reasonably
explained by the distinct local packing motifs of the surfactants
and their stability. It was found that platinum NPs with high aspect
ratios appeared at lower reaction temperatures (∼100 °C)
and shorter reaction times (∼30 min); however, the reaction
yield decreased from 30 to 10% when the reaction was stopped under
these conditions. A novel synthesis protocol at lower reaction temperatures
would lead to the development of favorable platinum catalysts for
fuel cell applications.
Experimental Section
Sample Preparation for
In Situ Time-Resolved SAXS Measurements
Platinum acetylacetonate
Pt(acac)2 (10 mg) and CTAC
(32 mg) were dissolved in oleylamine (5 mL). In this sample specification,
the CTAC concentration was well above its critical micelle concentration.
In addition, nickel acetylacetonate Ni(acac)2 (6.4 mg)
and molybdenum hexacarbonyl Mo(CO)6 (3 mg) were added to
inhibit particle enlargement and prevent particle aggregation, respectively.[14] The mixture was ultrasonicated for 1 h and then
heated using three different heating sequences, 1–3, as shown in Figure a.
In Situ Time-Resolved SAXS Measurements and Data Conversion
In situ time-resolved SAXS experiments were performed at BL8S3
at the Aichi Synchrotron Radiation Center (Aichi-SR). The ultrasonicated
mixture was placed into three Kapton tubes with a diameter of 2 mm.
The tubes were annealed during each heating sequence (sequences 1–3) on a hot stage (LK-600PM, Linkam Scientific Instruments
Ltd.). The SAXS data were recorded with an X-ray wavelength of 0.92
Å using a 2D pixel detector (PILATUS 100 K, DECTRIS Ltd.). The
exposure time for each data set was set to 58 s because the total
interval of each measurement was 60 s. The sample-to-detector distance
was fixed at 1.16 m. This setup covers momentum transfers (q ≡ 4π sin θ/λ, where 2θ
[rad] and λ [Å] are the scattering angle and the wavelength
of the X-ray, respectively) ranging from 0.04 to 0.4 Å–1. Scattering from empty cells was subtracted from all SAXS data.
After circular averaging, 1D scattering data were converted from relative
to absolute intensity using a pre-calibrated glassy carbon reference
provided by the National Institute of Standards and Technology.[78]
Fitting Model and Data Analysis for SAXS
Data
In this
system, the absolute scattering intensity Iabs(q) [cm–1] can be expressed aswhere ρPt [cm–2] and ρOAm [cm–2] are the scattering
length densities of platinum and oleylamine, respectively. N [particles cm–3] and V [cm3] are the number density and volume of the platinum
NPs, respectively. The unitless P(q) and S(q) are the form and structure
factors of platinum NPs, respectively, and Ibkg(q) [cm–1] is the background
scattering intensity mainly derived from oleylamine. In this work, P(q) was modeled using monodisperse rods,
and S(q) was approximated as 1. For a rod with radius R [Å]
and length L [Å] oriented in the direction of
angle α [rad] for the referential axis, the scattering amplitude Arod(q) is given bywhere J1(x) is the Bessel function of the order 1. The form
factor
of a rod is expressed asGiven that rods are randomly distributed
in oleylamine, the above form factor should be corrected for orientational
averaging as follows